UBC Theses and Dissertations

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UBC Theses and Dissertations

Psychrometric studies Henry, Herbert Clarke 1969

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PSYCHROMHTRIC STUDIES by HERBERT CLARKE HENRY B.Sc., Queen's U n i v e r s i t y , 1965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of CHEMICAL ENGINEERING We accept t h i s t h e s i s as conforming t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA February, 1969 , In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h C olumbia, I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and Study. I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f Chemical Engineering The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date March lU, 1969 ABSTRACT The l o c a l and macroscopic wet-bulb temperature depressions have been measured f o r naphthalene, p-dichlorobenzene and d-camphor p a r t i c l e s s u b l i m a t i n g i n t o an a i r or helium gas stream. The o r g a n i c chemicals were moulded i n t o c y l i n d r i c a l , s p h e r i c a l and f l a t p l a t e 'wet-bulbs'. A simple model based on the analogy between heat and mass t r a n s p o r t p o s t u l a t e s the dependence of the macroscopic psychro-m e t r i c r a t i o of a c y l i n d e r i n c r o s s f l o w , a sphere or a f l a t p l a t e , and the l o c a l p s y c h r o m e t r i c r a t i o of a p l a t e , on the Lewis number of the system. A second model i s developed which enables the c a l c u l a t i o n , by means of a B i o t number c o r r e c t i o n , of the l o c a l p s y c h r o m e t r i r a t i o of a c y l i n d e r or a sphere when heat i s conducted i n t e r n -a l l y through the body. T h i s l o c a l p s ychrometric r a t i o can a l s o be r e l a t e d t o the system Lewis number. Two models are a l s o developed t o p r e d i c t the ' l i m i t i n g ' wet-bulb temperature d e p r e s s i o n f o r a c y l i n d e r , sphere or f l a t p l a t e under c o n d i t i o n s of pure molecular d i f f u s i o n of heat and mass. The measured l o c a l and macroscopic psychrometric r a t i o s f o r a l l wet-bulb shapes s t u d i e d were found to be independent of the gas temperature l e v e l , gas v e l o c i t y , f r e e stream t u r b u l e n c e i n t e n s i t y and i n t e g r a l s c a l e of t u r b u l e n c e , i n accordance with the models. For spheres and c y l i n d e r s , the p a r t i c l e diameter d i d not a f f e c t the measured l o c a l and macroscopic psychrometric I l l r a t i o s . The e x p e r i m e n t a l wet-bulb temperature d e p r e s s i o n s were found to vary l i n e a r l y with the measuring thermocouple wire diameter t o the t h r e e - h a l v e s power. The macroscopic p s y c h r o m e t r i c r a t i o , , of spheres and c y l i n d e r s has been c o r r e l a t e d with the f i l m Lewis No., Lef , f o r e i g h t e e n gas-vapor systems by. ^3^ = Le^ ° - 5 7 > -p n e author's data have extended the upper l i m i t of Lewis number f o r c o r r e l a -t i o n of. macroscopic p s y c h r o m e t r i c r a t i o from 3 . 7 to 7 . 2 . The author's measurements i n helium i n d i c a t e t hat the s e m i e m p i r i c a l c o r r e l a t i o n of B e d i n g f i e l d and Drew i s the best p r e v i o u s r e l a -t i o n s h i p f o r p r e d i c t i n g the macroscopic p s y c h r o m e t r i c r a t i o f o r a c y l i n d e r . Under c o n d i t i o n s of f o r c e d c o n v e c t i o n , the l o c a l psychro-m e t r i c r at i o , /3/S , at the f r o n t s t a g n a t i o n p o i n t of spheres and c y l i n d e r s can be c o r r e l a t e d by fij3 = L e f ^ - ^ ^ T h i s r e s u l t v e r i f i e s the C h i l t o n - Colburn analogy f o r a t t a c h e d laminar boundary l a y e r flow. The l o c a l p s y c h r o m e t r i c r a t i o at the r e a r s t a g n a t i o n p o i n t of spheres and c y l i n d e r s can be p r e d i c t e d by n 0 -0.46 p p = Le^ when a wake e x i s t s behind the p a r t i c l e . T h i s r e s u l t i s ' s u g g e s t i v e that a t r a n s p o r t mechanism such as that proposed by Danckwerts may be c o n t r o l l i n g the t r a n s p o r t pro-cesses i n the wake. The l o c a l p s y c h r o m e t r i c r a t i o s on a f l a t p l a t e under c o n d i t i o n s of laminar boundary l a y e r flow are i n c l o s e agree-ment with the C h i l t o n - Colburn analogy. The i n t e n s i t y and l o n g i t u d i n a l s c a l e of t u r b u l e n c e down stream of screens i n a f o u r - i n c h square wind t u n n e l are presented. i v ACKNOWLEDGEMENTS The author wishes to express h i s thanks t o the f a c u l t y and s t a f f of the Chemical E n g i n e e r i n g Department, The U n i v e r s i t y c f B r i t i s h Columbia., S p e c i a l thanks are extended to Dr« N. E p s t e i n , under whose guidance t h i s work was undertaken. The author i s indebted t o the Chemical E n g i n e e r i n g Work-shop p e r s o n n e l f o r t h e i r a s s i s t a n c e i n assembling the e x p e r i -mental equipment. There are many other people who cannot be acknowledged p e r s o n a l l y , but the debt i s n o n e t h e l e s s heavy. F i n a n c i a l support f o r t h i s r e s e a r c h was most g r a t e f u l l y r e c e i v e d from the N a t i o n a l Research C o u n c i l of Canada and from S h e l l Canada L i m i t e d . V TABLE OF CONTENTS Page CHAPTER ONE - INTRODUCTION CHAPTER TWO - REVIEW OF PERTINENT PRIOR WORK 6 I. P s ychrometric s t u d i e s 6 1. Macroscopic p s y c h r o m e t r i c r a t i o f o r f o r c e d c o n v e c t i o n 6 a. E x p e r i m e n t a l data 6 b. T h e o r e t i c a l models 10 c. S e m i e m p i r i c a l models 18 2. Psychrometric s t u d i e s i n a r a r e f i e d atmosphere. 19 I I . Methods of measuring s u r f a c e temperatures 21 I I I . G e n e r a l c o n s i d e r a t i o n s of mass, heat and momentum t r a n s f e r from p a r t i c l e s 22 1. Spheres 22 2. C y l i n d e r s 24 3. F l a t p l a t e s 26 4. Tu r b u l e n t boundary l a y e r s 27 IV. Turbulence phenomena 29 1. Measurement of i n t e n s i t y and s c a l e of t u r b u l e n c e 29 2. Decay of t u r b u l e n c e behind g r i d s 38 CHAPTER THREE - THEORY AND INITIAL DECISIONS 42 I. Theory 42 v i Page 1. B a s i c equations and a n a l y t i c a l approach 42 2. Macroscopic p s y c h r o m e t r i c r a t i o dependence on Lewis number 4-\ 3. L o c a l p s y c h r o m e t r i c r a t i o dependence on the Lewis and B i o t numbers 52 a. Sphere 52 b„ C y l i n d e r 58 c. F l a t p l a t e 60 4. G e n e r a l i z e d r e l a t i o n s h i p f o r the p s y c h r o m e t r i c r a t i o 60 5. L i m i t i n g wet--bulb temperature d e p r e s s i o n i n a quiescent atmosphere 62 Method one 62 a. Sphere 62 b„ C y l i n d e r 65 c. F l a t p l a t e 67 Method two ' 67 II. F a c t o r s to be s t u d i e d 68 III. F a c t o r s t o be o m i t t e d 69 CHAPTER FOUR - APPARATUS AND EXPERIMENTAL PROCEDURE 70 I. Equipment d e s c r i p t i o n 70 1. Wind t u n n e l ' 70 a. Main duct 70 b. Sample s e c t i o n 72 2. Gas r e c i r c u l a t i n g apparatus 75 a. Main tank and duct 75 b. Sample s e c t i o n 77 v i i Page 3. Thermocouple i n s t a l l a t i o n 77 4 Hot wire anemometer and a u x i l i a r y components , 77 II„ E x p e r i m e n t a l o p e r a t i n g procedures 81 1. Psychrometric measurements i n the wind t u n n e l 81 a. Run p r e p a r a t i o n 81 b 0 Run e x e c u t i o n 81. 2. Psychrometric measurements i n the , gas r e c i r c u l a t i n g apparatus 83 a. Run p r e p a r a t i o n 83 b. Run e x e c u t i o n 84 3. Psychrometric measurements i n a quiescent atmosphere 85 4. Psychrometric measurements f o r the a i r - water system 86 CHAPTER FIVE - PRESENTATION AND ANALYSIS OF RESULTS 87 I. V e l o c i t y , t u r b u l e n c e i n t e n s i t y and s c a l e of t u r b u l e n c e measurements 87 1. Both ducts without t u r b u l e n c e promoters 87 2. Downstream of screens i n the wind t u n n e l 100 3. Downstream and upstream.of a s i n g l e c y l i n d e r i n the wind t u n n e l 107 I I . P s y c h r o m e t r i c measurements i n the ducts with no t u r b u l e n c e promoters 115 v i i i ix Page I I I . P s y c h r o m e t r i c measurements downstream of screens i n the wind t u n n e l 160 IV. Psychrometric measurements i n a quiescent atmosphere 168 V. Measurement e r r o r s 171 CHAPTER SIX - CONCLUSIONS AND RECOMMENDATIONS 174 I. C o n c l u s i o n s 174 II. Recommendations f o r f u r t h e r work 177 NOMENCLATURE 178 LITERATURE CITED 187 APPENDIX ONE - SELECTION AND PROPERTIES OF SAMPLE MATERIALS AND TEST FLUIDS 1-1 I. S e l e c t i o n of m a t e r i a l s and f l u i d s 1-1 II. P r o p e r t i e s of t e s t f l u i d s 1-3 A i r 1-3 1. Molecular weight 1-3 2. V i s c o s i t y - temperature r e l a t i o n s h i p 1-3 3. Heat c a p a c i t y - temperature r e l a t i o n s h i p 1-3 4. D e n s i t y - temperature r e l a t i o n s h i p 1-3 5. Thermal c o n d u c t i v i t y - temperature r e l a t i o n s h i p 1-4 6. Force constant and c o l l i s i o n diameter 1-4 Helium 1-4 1. Molecular weight 1-5 2. V i s c o s i t y - temperature r e l a t i o n s h i p 1-5 3. Heat c a p a c i t y 4. D e n s i t y - temperature r e l a t i o n s h i p 5. Thermal c o n d u c t i v i t y - temperature r e l a t i o n s h i p 6. Force constant and c o l l i s i o n diameter I I I . P r o p e r t i e s of sample m a t e r i a l s 1. S u p p l i e r s ' i n f o r m a t i o n 2. Vapor p r e s s u r e - temperature r e l a t i o n s h i p 3. Latent heat - temperature r e l a t i o n s h i p : 4. Heat c a p a c i t y - temperature r e l a t i o n s h i p of the vapor 5. Thermal c o n d u c t i v i t y of naphthalene and p-dichlorobenzene 6. C o l l i s i o n diameters of sample m a t e r i a l s 7. E m i s s i v i t y IV. Combined p r o p e r t i e s of the sample m a t e r i a l s and t e s t f l u i d s 1. D i f f u s i o n c o e f f i c i e n t s 2. Force c o n s t a n t s APPENDIX TWO - EQUIPMENT SPECIFICATIONS I. Wind t u n n e l 1. Measurement of bulk a i r v e l o c i t y 2. Heat source 3. Wind t u n n e l p r e s s u r e c o n t r o l 4. P r e s s u r e measurement 5. Humidity measurement Page I I . Gas r e c i r c u l a t i n g apparatus 11-13 1. F a b r i c a t i o n 11-13 2. Heat source 11-14 3. Vacuum equipment 11-15 4. Gas v e l o c i t y r e g u l a t i o n 11-15 5. Gas blower and blower support 11-15 6. E l e c t r i c a l input to blower motor 11-16 7. P r e s s u r e measurement 11-18 I I I . Turbulence measurements 11-19 1. Turbulence promoters 11-19 a. Screens 11-19 b. C y l i n d e r s 11-21 2. Hot - wire anemometer s p e c i f i c a t i o n s 11-23 3. O s c i l l o s c o p e 11-25 4. Recorder 11-26 5. S c a l e measurement c i r c u i t r y 11-27 a. O p e r a t i o n a l m a n i f o l d and hardware k i t 11-27 b. R e s i s t o r s and c a p a c i t o r s -s p e c i f i c a t i o n s 11-28 c. A m p l i f i e r s , squarer, power supply 11-29 d. E l e c t r i c a l analogue c i r c u i t response 11-32 e. T e s t i n g c i r c u i t 11-53 IV. Sample moulding 11-55 1. Moulds 11-55 2. Moulding technique 11-62 V. Temperature measurement 11-64 Page \. Free stream temperatures 11-64 2. Wet-bulb temperatures 11-68 .3. Wall temperatures 11-68 a. Wind t u n n e l 11-68 b„ Gas r e c i r c u l a t i n g apparatus 11-72 4. Potentiometer 11-73 APPENDIX THREE - CALIBRATIONS I I I - l I. Thermocouple c a l i b r a t i o n s I I I - l I I . Anemometer hot - wire c a l i b r a t i o n s 111-12 1. Hot - wire c h a r a c t e r i s t i c s 111-12 2. C a l i b r a t i o n i n a i r 111-19 3 0 C a l i b r a t i o n i n helium 111-24 4. Comparison of hot - wire c a l i b r a t i o n i n a i r and helium 111-27 APPENDIX FOUR - ISOTHERMS AND ADIABATICS INSIDE A CYLINDER IV-1 I. Boundary c o n d i t i o n s IV-1 I I , Numerical s o l u t i o n of L a p l a c e ' s e q u a t i o n IV-2 I I I . Numerical s o l u t i o n of Cauchy - Riemann equations IV-6 IV. C o n t o u r i n g of temperature and heat flow f i e l d s IV-10 V. Data and r e s u l t s IV-11 APPENDIX FIVE - CALCULATIONS V - l x i i I. C a l c u l a t i o n of the p a r t i a l p r e s s u r e of subli m a t e i n the gas r e c i r c u l a t i n g apparatus ater a time T V - l I I . C a l c u l a t i o n of the l o c a l p s y c h r o m e t r i c r a t i o at the f r o n t of a naphthalene sphere i n the wind t u n n e l V—3 I I I . C a l c u l a t i o n of the l o c a l p s y c h r o m e t r i c r a t i o at the f r o n t s t a g n a t i o n p o i n t of a naphthalene sphere s u b l i m a t i n g i n t o helium i n the gas r e c i r c u l a t i n g apparatus V-12 IV. C a l c u l a t i o n of average v a l u e s of the psy c h r o m e t r i c r a t i o and Lewis number exponents V-17 * APPENDIX SIX - TABLES OF DATA AND CALCULATED RESULTS VI-1 x i i i LIST OF TABLES Ta b l e Page 1. P a r t i c l e f low parameters 22 2. Average psychrometric r a t i o s and Lewis number exponents measured i n the wind tunnel. 138 3. Psychrometric r a t i o s and Lewis number exponents measured i n the gas r e c i r c u l a t i n g apparatus 140 4. C o r r e l a t i o n of psychrometric data 142 1-1. V i s c o s i t y of helium 1-5 1-2. Thermal c o n d u c t i v i t y of helium 1-6 1-3. Sample m a t e r i a l s 1-7 1-4. Vapor p r e s s u r e s of sample m a t e r i a l s 1-7 1-5. Heat c a p a c i t y of naphthalene and p-dichlorobenzene vapors 1-10 1-6. Thermal c o n d u c t i v i t y of p-dichlorobenzene 1-11 1-7. C o l l i s i o n diameters of sample m a t e r i a l s 1-12 1-8. Force c o n s t a n t s f o r naphthalene, p-dichlorobenzene and d-camphor 1-17 I I - l . C h a r a c t e r i s t i c dimensions of o r i f i c e II-4 .11-2. A i r heater i n wind t u n n e l II-6 II—3-.. Gas r e c i r c u l a t i n g apparatus blower s p e c i f i c a t i o n s 11-16 II-4. Screen s p e c i f i c a t i o n s 11-20 II-5. S p e c i f i c a t i o n s f o r anemometer 11-23 II-6. Noise le.vel with type 55A22 hot - wire 11-24 II-7. S p e c i f i c a t i o n s f o r hot - wire probe 11-24 XIV T a b l e Page .1.1-8. E l e c t r i c a l c h a r a c t e r i s t i c s of o s c i l l o s c o p e 11-25 I I - 9 . S p e c i f i c a t i o n s of r e c o r d e r input module 11-26 11-10. C h a r a c t e r i s t i c s of PS5AU a m p l i f i e r 11-29 11-11. C h a r a c t e r i s t i c s of P35AU a m p l i f i e r 11-29 11-12. C h a r a c t e r i s t i c s of P45A a m p l i f i e r 11-30 11-13. C h a r a c t e r i s t i c s of P656 a m p l i f i e r 11-30 11-14. C h a r a c t e r i s t i c s of PSQ-P trans c o n d u c t o r 11-31 11-15. Maximum power consumption and supply 11-31 11-16. Wet-bulb moulds 11-62 11-17. Wall temperatures - a i r flow 0.039 l b . / s e c . 11-70 11-18. Wall temperatures - a i r flow 0.073 l b . / s e c . 11-70 11-19. Wall temperatures - a i r flow 0.122 l b . / s e c . 11-71 11-20. P r e d i c t i o n of wind t u n n e l w a l l temperatures 11-72 I I - 21. Potentiometer s p e c i f i c a t i o n s 11-73 I I I - l . Thermocouples I I I - 3 I I I - 2 . C a l i b r a t i o n of thermocouples 7 , 8 , 9 I I I - 6 I I 1 - 3 . C a l i b r a t i o n of thermocouples 1 to 5 (24 gauge) and 6 I I I - 7 I I I - 4 . C a l i b r a t i o n of thermocouples 1 to 5 (30 gauge) and 6 I I 1 - 8 I I J . - 5 . C a l i b r a t i o n of thermocouples 1 t o 5 (40 gauge) and 6 I I I - 9 I I I - 6 . Thermocouple curve f i t paramaters 111-10 I I I - 7 . R.M.S. t o t a l and s t a t i s t i c a l e r r o r s f o r the thermocouple curve f i t parameters I I I - 1 1 I I I - 8 . C a l i b r a t i o n of r e f e r e n c e hot - wire i n a i r 111-21 XV Table Page I I I - 9 . Constants i n c a l i b r a t i o n of hot-wires no. . . 12 to 15 111-22 111-10. C a l i b r a t i o n of hot-wires no. 12 to 15 111-23 I I I - l l . Hot-wire curve f i t parameters 111-24 111-12. C a l i b r a t i o n of hot-wire no. 14 i n helium 111-26 111-13. Grashof number f o r hot-wire 111-27 IV-1. Temperature measurements i n a c y l i n d e r IV-11 IV-2. Temperature f i e l d f o r a c y l i n d e r IV-15 IV-3. Heat flow f i e l d f o r a c y l i n d e r IV-15 VI-1. Wet-bulb temperature d e p r e s s i o n s i n a quiescent atmosphere VI-2 VI-2. Temperature measurements i n the wind t u n n e l VI-3 VI-3. Psychrometric data i n wind t u n n e l VI-14 VI-4. Wet-bulb temperature d e p r e s s i o n s measured i n the wind t u n n e l e x t r a p o l a t e d to zero thermocouple wire diameter VI-18 VI-5. C a l c u l a t i o n of l o c a l and macroscopic p s y c h r o m e t r i c r a t i o s , Lewis number and B i o t number e f f e c t s from measurements i n the v/ind t u n n e l VI-20 VI-6. C a l c u l a t i o n of best f i t p s y c h r o m e t r i c r a t i o s and Lewis number exponents. VI-30 VI-7. Temperature measurements i n the gas r e c i r c u -l a t i n g apparatus VI-33 VI-8. Wet-bulb temperature d e p r e s s i o n s measured i n the gas r e c i r c u l a t i n g apparatus e x t r a p o l a t e d to zero thermocouple wire diameter VI-35 x v i T a b l e Page . VI-9. C a l c u l a t i o n of l o c a l and macroscopic psychro-m e t r i c r a t i o s , Lewis number and Bi o t number e f f e c t s f o r measurements i'n the gas r e c i r c u -l a t i n g apparatus VI-37 VI-10. Measurement of a i r v e l o c i t y , turbulence i n t e n s i t y and s c a l e of t u r b u l e n c e VT-41 VI-11. Measurement of i n t e n s i t y and s c a l e of t u r b u l e n c e i n helium VI - 4 4 x v i i LIST OF FIGURES F i g u r e Page 1. \ Comparison of p r e v i o u s c o r r e l a t i o n s with p r e v i o u s e x p e r i m e n t al data f o r macroscopic psychrometric r a t i o s of c y l i n d e r s 12 2. Sh/Nu versus Le 7 f o r a sphere 50 3. Temperature g r a d i e n t i n a s p h e r i c a l wet-bulb 52 4. Conduction e f f e c t a c r o s s a sphere 53 5... Temperature g r a d i e n t i n a c y l i n d r i c a l wet-bulb 58 6. Conduction e f f e c t s a c r o s s a c y l i n d e r 59 7. . Wind t u n n e l 71 8. Sample s e c t i o n i n wind t u n n e l 73 9. Sample s e c t i o n l i d and sample support i n the wind t u n n e l 74 10. Gas r e c i r c u l a t i n g apparatus 76 11. Sample s e c t i o n of the gas r e c i r c u l a t i n g apparatus 78 12. Sample s e c t i o n l i d f o r the gas r e c i r c u l a t i n g apparatus . 79 13. V e r t i c a l v e l o c i t y p r o f i l e s through c e n t e r of wind t u n n e l 88 14. V e r t i c a l p r o f i l e s of i n t e n s i t y and s c a l e of t u r b u l e n c e through the center of the wind t u n n e l , with no t u r b u l e n c e promoters 89 15. V e r t i c a l p r o f i l e s of v e l o c i t y and i n t e n s i t y of t u r b u l e n c e i n the wind t u n n e l , with no t u r b u l e n c e promoters 90 XVI11 F i g u r e Page 16. E f f e c t of a i r temperature on the l o c a l v e l o c i t y , i n t e n s i t y and s c a l e of t u r b u l e n c e at the center of the wind t u n n e l 92 17. V e l o c i t y p r o f i l e s f o r a i r and helium i n the gas r e c i r c u l a t i n g apparatus 93 18. Turbulence i n t e n s i t y p r o f i l e s f o r a i r and helium i n the gas r e c i r c u l a t i o n apparatus 95 19. . E f f e c t of a i r temperature on the c a p a c i t y of the blower i n the gas r e c i r c u l a t i o n apparatus 96 20. Comparison of p r e v i o u s f r e e stream t u r b u l e n c e i n t e n s i t y data with e x p e r i m e n t a l measurements 97 21. Comparison of p r e v i o u s f r e e stream s c a l e of t u r b u l e n c e data with e x p e r i m e n t a l measurements 99 22. . C e n t r a l v e r t i c a l p r o f i l e s of v e l o c i t y , i n t e n s i t y and s c a l e of t u r b u l e n c e behind a s c r e e n i n the wind t u n n e l 101 23. E f f e c t of v e l o c i t y on change of t u r b u l e n c e i n t e n s i t y and s c a l e behind a 0.5 i n c h mesh sc r e e n i n the wind t u n n e l 103 24. Decay of t u r b u l e n c e behind s c r e e n s i n the wind t u n n e l 104 25. S c a l e of t u r b u l e n c e behind screens i n the wind t u n n e l 106 26. Comparison of p r e v i o u s data on decay of t u r b u l e n c e behind s c r e e n s with e x p e r i m e n t a l measurements 108 27. Turbulence i n t e n s i t y upstream of a c y l i n d e r i n the center of the wind t u n n e l 109 X I X F i g u r e Page 28. Turbulence i n t e n s i t y downstream of a c y l i n d e r i n the center of the wind t u n n e l 111 29. Turbulence i n t e n s i t y upstream of a c y l i n d e r i n the center of the wind t u n n e l f o r c o n d i t i o n s of high f r e e stream i n t e n s i t y 112 30. Turbulence i n t e n s i t y downstream of a c y l i n d e r i n the cen t e r of the wind t u n n e l f o r c o n d i t i o n s of high f r e e stream i n t e n s i t y 113 31. T r a n s i e n t wet-bulb temperature d e p r e s s i o n curves (measured i n the wind t u n n e l ) 116 32. E f f e c t of thermocouple diameter on the l o c a l wet-bulb temperature d e p r e s s i o n at the f r o n t s t a g n a t i o n p o i n t of a naphthalene c y l i n d e r (measured i n the wind t u n n e l ) 117 33. Comparison of p r e v i o u s macroscopic wet-bulb temperature d e p r e s s i o n data f o r naphthalene c y l i n d e r s with e x p e r i m e n t a l wind t u n n e l measure-ments f o r c y l i n d e r s , and the e f f e c t of thermocouple diameter on t h i s measurement 119 34. E f f e c t of thermocouple diameter on the l o c a l wet-bulb temperature d e p r e s s i o n at the r e a r s t a g n a t i o n p o i n t of a naphthalene c y l i n d e r (measured i n the wind t u n n e l ) .121 35. E f f e c t of thermocouple diameter on the l o c a l wet-bulb temperature d e p r e s s i o n at the f r o n t s t a g n a t i o n p o i n t of a naphthalene sphere (measured i n the wind t u n n e l ) 122 X X F i g u r e Page 36. E f f e c t of thermocouple diameter on the macroscopic wet-bulb temperature d e p r e s s i o n of a naphthalene sphere (measured i n the wind t u n n e l ) 123 37. E f f e c t of thermocouple diameter on the l o c a l wet-bulb temperature d e p r e s s i o n at the r e a r s t a g n a t i o n p o i n t of a naphthalene sphere (measured i n the wind t u n n e l ) 124. 38. Comparison of p r e v i o u s macroscopic wet-bulb temperature data f o r p-dichlorobenzene c y l i n d e r s with e x p e r i m e n t a l wind t u n n e l measurements f o r c y l i n d e r s , and the e f f e c t of thermocouple diameter on t h i s measurement 126 39. V a r i a t i o n of wet-bulb temperature d e p r e s s i o n s •around naphthalene c y l i n d e r s and spheres as measured by d i f f e r e n t thermocouple s i z e s 128 40. C o r r e c t i o n of f r o n t s t a g n a t i o n p o i n t wet-bulb temperature d e p r e s s i o n s of naphthalene spheres and c y l i n d e r s t o zero thermocouple t h i c k n e s s 129 41. C o r r e c t i o n of macroscopic wet-bulb temperature d e p r e s s i o n s of naphthalene spheres and c y l i n d e r s t o zero thermocouple t h i c k n e s s 130 42. C o r r e c t i o n of r e a r s t a g n a t i o n p o i n t wet-bulb temperature d e p r e s s i o n s of naphthalene spheres and c y l i n d e r s t o zero thermocouple t h i c k n e s s 131 43. E f f e c t of s o l i d wet-bulb thermal c o n d u c t i v i t y on c a l c u l a t e d v a l u e of Lewis number exponent (measured i n the wind tunnel) 134 x x i F i g u r e Page 44. Best f i t c o r r e l a t i o n of e x t r a p o l a t e d wet-bulb temperature d e p r e s s i o n s f o r naphthalene spheres (measured i n the wind t u n n e l ) 136 45. C o r r e l a t i o n of l o c a l and macroscopic psychrometric r a t i o s f o r c y l i n d e r s and spheres at high Reynolds numbers 146 46. High Reynolds number valu e s of the Lewis number exponent 148 47. C o r r e l a t i o n of l o c a l p s y c h r o m e t r i c r a t i o s at the f r o n t and r e a r s t a g n a t i o n p o i n t s of c y l i n d e r s and spheres 149 • 48. Comparison of p r e v i o u s c o r r e l a t i o n s with e x p e r i m e n t a l macroscopic p s y c h r o m e t r i c r a t i o s f o r c y l i n d e r s and spheres 150 49. L o c a l wet-bulb temperature d e p r e s s i o n measurements f o r water e v a p o r a t i n g from a.0.5-inch diameter c y l i n d r i c a l wick i n the wind t u n n e l 152 50. L o c a l wet-bulb temperature d e p r e s s i o n s on a naphthalene p l a t e (measured i n the wind t u n n e l , a i r f l ow 0.122 l b . / s e c . ) 153 51. L o c a l wet-bulb temperature d e p r e s s i o n s on a naphthalene p l a t e (measured i n the wind- t u n n e l , a i r f l ow 0.078 l b . / s e c . ) 155 52. L o c a l wet-bulb temperature d e p r e s s i o n s on a p - d i c h l o r o b e n z e n e p l a t e (measured i n the wind t u n n e l ) 156 53. Comparison of p r e v i o u s t h e o r e t i c a l c o r r e l a t i o n s X X I I F i g u r e Page with e x p e r i m e n t a l l o c a l psychrometric r a t i o s f o r f l a t p l a t e s 158 54. , E f f e c t of t u r b u l e n c e on the macroscopic and l o c a l wet-bulb temperature d e p r e s s i o n s of a naphthalene c y l i n d e r (measured i n the wind t u n n e l ) 161 55. E f f e c t of t u r b u l e n c e on the macroscopic and l o c a l wet-bulb temperature d e p r e s s i o n s of p-dichlorobenzene c y l i n d e r s and spheres (measured i n the wind t u n n e l , 24 gauge thermocouples) 163 56. E f f e c t of t u r b u l e n c e on the macroscopic and l o c a l wet-bulb temperature d e p r e s s i o n s of p-dichlorobenzene c y l i n d e r s and spheres (measured i n the wind t u n n e l , 30 gauge thermocouples) 164 57. E f f e c t of t r a n s v e r s e l o c a t i o n of sample i n wind t u n n e l on t u r b u l e n t wet-bulb temperature d e p r e s s i o n s 166 58. E f f e c t of t u r b u l e n c e on the l o c a l wet-bulb temperature d e p r e s s i o n s on naphthalene and p-dichlorobenzene p l a t e s (measured i n the wind t u n n e l ) - 167 59. Comparison of t h e o r e t i c a l and measured wet-bulb temperature d e p r e s s i o n s f o r naphthalene and p-dichlorobenzene spheres and c y l i n d e r s i n quiescent a i r 169 x x i i i F i g u r e Page I I - l . Flov/ c o e f f i c i e n t of o r i f i c e as a f u n c t i o n of Reynolds number II-3 II-2. Heater c i r c u i t i n wind t u n n e l II-7 II- 3 . Wind t u n n e l p r e s s u r e c o n t r o l II-8 II-4. P r e s s u r e measurement II-9 II-5. Humidity measurement 11-12 II-6. Blower support i n gas r e c i r c u l a t i o n apparatus 11-17 II-7 . Turbulence promoters 11-19 II-7a. Wire scr e e n dimensions 11-21 II-8. Brass c y l i n d e r and support 11-22 II-9. Anemometer output s i g n a l 11-34 11-10. F l u c t u a t i n g segment of anemometer output s i g n a l 11-34 11-11. P r a c t i c a l d i f f e r e n t i a t o r 11-35 11-12. P r a c t i c a l d i f f e r e n t i a t o r g a i n 11-37 11-13. A m p l i f i e r 11-37 11-14. R-C c i r c u i t 11-39 11-15. Cascaded R-C c i r c u i t 11-41 11-16. M o d i f i e d cascaded R-C c i r c u i t 11-41 11-17. Complete R-C cascaded c i r c u i t 11-42 11-18. Square* 11-43 11-19. I n t e g r a t i o n c i r c u i t 11-45 11-20. Analogue c i r c u i t with s i g n a l f i l t e r 1*1-48 11-21. M o d i f i e d c i r c u i t 11-49 11-22. Analogue c i r c u i t without f i l t e r 11-50 11-23. T e s t i n g c i r c u i t 11-53 11-24. Sample mould number 1 11-56 F i g u r e 11-25. Sample mould number 2 11-26. Sample mould number 3 11-27. - Sample mould number 4 11-28. Sample mould number 5 11-29. Sample mould number 6 11-30. Thermocouple probes f o r measuring gas temperature 11-31. Temperature p r o f i l e i n wind t u n n e l as measured with a s t r a i g h t probe 11-32. Temperature p r o f i l e i n wind t u n n e l as measured with a bent probe I I - 33. L o c a t i o n of w a l l temperature measurements i n wind t u n n e l I I I - l . Thermocouple w i r i n g diagram I I I - 2 . T y p i c a l hot-wire c a l i b r a t i o n curve I I I - 3 . The hot-wire anemometer II1-4. Hot-wire c a l i b r a t i o n i n a i r I I I - 5 . Hot-wire c a l i b r a t i o n curves i n a i r and helium IV-1. C y l i n d e r c o - o r d i n a t e s IV-2. G r i d f o r s o l u t i o n of L a p l a c e ' s e q u a t i o n IV-3. G r i d f o r s o l u t i o n of Cauchy - Riemann equations IV-4. Temperature measurement p o i n t s i n a c y l i n d e r IV-5. Temperature p r o f i l e around a s u b l i m a t i n g naphthalene c y l i n d e r IV-6. Isotherms and a d i a b a t i c s i n a s u b l i m a t i n g naphthalene c y l i n d e r x x i v Page 11-57 11-58 11-59 11-60 11-61 11-65 11-66 11-67 I I - 69 I I I - 4 111-13 111-13 111-20 111-29 IV-1 IV-3 IV-7 r v - i i IV- 12 IV-16 CHAPTER ONE INTRODUCTION The use of the wet-bulb hygrometer f o r the measurement of a i r humidity was one of the e a r l i e s t p s ychrometric a p p l i c a t i o n s . The o p e r a t i o n of a hygrometer i s based on the f a c t t h at a t h e r -mometer, the bulb of which i s covered by a porous wick and kept wet, w i l l i n d i c a t e a lower temperature than w i l l a dry thermo-meter i n the same a i r , and that the humidity of the a i r i s r e l a t e d t o the barometric p r e s s u r e and t o the d i f f e r e n c e i n the dry and wet thermometer r e a d i n g s , or the 'wet-bulb temperature d e p r e s s i o n ' . The d i s c o v e r y of the e x i s t e n c e of such a pheno-menon i s g e n e r a l l y a t t r i b u t e d t o Dr. James Hutton of Edinburgh who used wet-bulb thermometers about 1792, some 180 years a f t e r G a l i l e o had i n v e n t e d the l i q u i d - i n - g l a s s thermometer (112). The f i r s t development of a theory r e l a t i n g the v a r i a b l e s a s s o c i a t e d with wet-bulb temperature d e p r e s s i o n measurements was a t t r i b u t e d by Maxwell t o Apjohn i n 1834, but appears essen-t i a l l y i n the same form by Ivory (58) i n 1822. The theory, sometimes known as 'convection t h e o r y ' , i s based on the i d e a that a i r coming i n con t a c t with the wet-bulb i s c o o l e d t o the wet-bulb temperature and leaves s a t u r a t e d with water vapor. It i s assumed that the heat g i v e n up by t h i s a i r i n c o o l i n g from the d r y - b u l b a i r temperature t o the temperature of the wet wick i s s u f f i c i e n t t o p r o v i d e the l a t e n t heat of v a p o r i z a t i o n needed to s a t u r a t e the same q u a n t i t y of a i r . T h i s heat balance i s wr i t t e n C S ( tDB -*W } = X H 2 0 ( HW- HQ > CD Many years l a t e r i t was shown that Eq. ( l ) does not d e s c r i b e the a c t u a l wet-bulb p r o c e s s , but r a t h e r the a d i a b a t i c s a t u r a -t i o n p r o c e s s . About 1877 James Maxwell (87) p r e s e n t e d what may be termed the ' d i f f u s i o n t h e ory'. C o n c e i v i n g the wet s u r f a c e to be surrounded by a f i l m of stagnant a i r through which heat and water vapor must d i f f u s e , Maxwell equated the r a t e of d i f f u s i o n of heat t o the wet-bulb to the r a t e of heat output, the l a t t e r b e i n g expressed as the product of the l a t e n t heat of vaporiza - r t i o n and the r a t e of d i f f u s i o n of water vapor from the wet s u r f a c e t o the ambient a i r . T h i s concept i s expressed by the e q u a t i o n k A i t t V - ° V P ( P W " P D B y M W A X H 2 6 — u D B -tyy-; (2) x' R g T f P B M x ' The l e f t - h a n d s i d e expresses the r a t e of heat input by the F o u r i e r c o n d u c t i o n e q u a t i o n ; the r i g h t - h a n d s i d e employs the S t e f a n e x p r e s s i o n f o r d i f f u s i o n of one gas or vapor through another. But when flow c o n d i t i o n s adjacent to the wet- s u r f a c e are complex, the simple concept of a stagnant f i l m i s a gross o v e r - s i m p l i f i c a t i o n . One of the best known simultaneous measurements of wet-bulb and dew-point temperatures of humid a i r can be a t t r i b u t e d t o 3 P r o f e s s o r F e r r e l (30). In 1908 W i l l i a m Grosvenor (40) pub-l i s h e d the o r i g i n a l v e r s i o n of the humidity or psychrometric ch a r t now found i n a l l e n g i n e e r i n g handbooks. In 1911 C a r r i e r (17) noted the e x c e l l e n t agreement between the observed wet-bulb measurements r e p o r t e d by P r o f e s s o r F e r r e l and the c a l c u l a t e d v a l u e s of what C a r r i e r termed the 'tempera-t u r e of a d i a b a t i c s a t u r a t i o n ' . He p i c t u r e d an i n f i n i t e l y long a d i a b a t i c duct with wet inner s u r f a c e s , i n t o which a i r at some constant temperature and humidity was blown. In p a s s i n g through the duct the a i r would c o o l and p i c k up moisture u n t i l i t be-came s a t u r a t e d . The f i n a l temperature may be c a l c u l a t e d by the heat balance i n c o r p o r a t e d i n Eq. (1), where t and Hyy re p r e s e n t the f i n a l a i r temperature and humidity. Reviewing the s i t u a t i o n i n 1922, W. K. Lewis.(76) rewrote Eq. (2) as h (t QQ - t w ) = k ' X H 2 ( ) ( H w - H a ) (3) where h r e p r e s e n t s the c o e f f i c i e n t of heat t r a n s f e r , a i r to wet s u r f a c e , and k' i s a c o e f f i c i e n t of water vapor t r a n s f e r . Lewis a l s o r e d e r i v e d C a r r i e r ' s e x p r e s s i o n f o r a d i a b a t i c wet ducts. c s ( t D B - t e ) = X H 2 0 ( H e - H Q ) (4) S i n c e f o r air- w a t e r the c a l c u l a t e d a d i a b a t i c s a t u r a t i o n temperature was equal t o the experimental v/et-bulb temperature, by comparing Eq. (3) with Eq. (4) Lewis concluded that 4 ( i ) h/k' • = C s ( i i ) . t w = t e ( i i i ) H w = H e He a l s o concluded that the same r e l a t i o n s h i p s apply to any l i q u i d and any gas with which i t s vapor i s mixed. But by 1933 f u r t h e r experiments u s i n g o r g a n i c l i q u i d s i n s t e a d of water showed that the o r i g i n a l deductions of Lewis were unsound. Lewis then p u b l i s h e d a note c o r r e c t i n g h i s e a r l i e r paper. The f a c t t h at h/k' = Cg f o r the a i r - w a t e r system i s a convenient happen-chance r e l a t i o n s h i p that has allowed Eq. ( l ) to be used e x t e n s i v e l y i n the design of water c o o l i n g towers and a i r c o n d i t i o n i n g , but i s i n a p p l i c a b l e t o any other gas-vapor systems. For the design of c o o l i n g towers, d r i e r s , h u m i d i f i e r s , d e h u m i d i f i e r s , d i f f u s i o n a l e v a p o r a t o r s (eg. s o l a r e v a p o r a t o r s ) , s u b l i m a t o r s , e t c . , where the working f l u i d s are not a i r - w a t e r , i t i s necessary t o have r e l i a b l e methods of p r e d i c t i n g both l o c a l and macroscopic ( o v e r a l l average) s u r f a c e temperatures. The wet- and d r y - b u l b phenomenon i s a part of a l l v a p o r i z a t i o n and s u b l i m a t i o n p r o c e s s e s . A p a s s i n g remark by T r e y b a l (123) and an exchange between E p s t e i n and Wilke (129) i n d i c a t e the p o s s i b l e importance of the shape of the e v a p o r a t i n g wet-bulb on wet- and dry-bulb psychrometry. Many p u b l i c a t i o n s i n the 5 past have made the assumption that i f one determined the wet-bulb temperature with a thermometer, i t would be the same temperature as one would get on a wetted w a l l column or on an e v a p o r a t i n g sphere. The d i f f e r e n c e s c o u l d be very important i n c a l c u l a t i n g t r a n s f e r c o e f f i c i e n t s . Thus, a study has been i n i t i a t e d to examine the e f f e c t of shape of a wetted s u r f a c e , and the a s s o c i a t e d f l u i d dynamics and t r a n s f e r p r o p e r t i e s , on l o c a l and macroscopic wet-bulb temperatures. 6 CHAPTER TWO REVIEW OF PERTINENT PRIOR WORK I. PSYCHROMETRIC STUDIES 1. Macroscopic p s y c h r o m e t r i c r a t i o f o r f o r c e d c o n v e c t i o n a. E x p e r i m e n t a l data P s y c h r o m e t r i c measurements were made by Mark (85) em-p l o y i n g water, chlorobenzene, benzene, carbon t e t r a c h l o r i d e , t e t r a c h l o r o e t h y l e n e , e t h y l a c e t a t e and toluene to wet the wick of a wet-bulb. B e d i n g f i e l d and Drew (8) i n d i c a t e that 12 of Mark's 64 runs were ' o b v i o u s l y ' i n e r r o r and these data have been i g n o r e d i n t h e i r a n a l y s i s . In the comparisons made by the author these data have been s i m i l a r l y i gnored. A r n o l d (3) conducted psychrometric measurements with t o l u e n e , chlorobenzene and m-xylene on a wet wick 4.3 cm. long i n a wind t u n n e l 4 inches square. A r n o l d ' s r e s u l t s i n d i c a t e a v a r i a t i o n of k^ /h with R e p to the 0.07 power. C a l c u l a t i o n s p r e s e n t e d by B e d i n g f i e l d and Drew (8) of the heat conducted by the thermometer stem i n d i c a t e a p o s s i b l e e r r o r which v a r i e s i n v e r s e l y with- v e l o c i t y from 8 to 14 percent, and when allowed f o r , tends to reduce f u r t h e r the i n d i c a t e d s m a l l v a r i a t i o n of kc /h with Rep . Using water and an a d i a b a t i c chamber, Dropkin (24) i n v e s -tigated-' the d e v i a t i o n of the wet-bulb temperature from the* temperature of a d i a b a t i c s a t u r a t i o n . He d i d not r e p o r t the humidity of the a i r p a s s i n g the wet-bulb, but i t i s p o s s i b l e t o c a l c u l a t e i t from the a d i a b a t i c s a t u r a t i o n temperatures he r e p o r t e d . H i s wet-bulb thermometers were covered with wicks 8 inches i n l e n g t h to make n e g l i g i b l e the e r r o r due to heat c o n d u c t i o n along the thermometer stem. B e d i n g f i e l d and Drew (8) r e c a l c u l a t e d Dropkin's r e s u l t s and found that no v a r i a t i o n of k^ /h with e i t h e r temperature or Reynolds number i s i n d i -c a t e d f o r the s i x v e l o c i t i e s at which Dropkin made h i s runs. P o w e l l has conducted e x t e n s i v e e x p e r i m e n t a t i o n on the e v a p o r a t i o n of water from s a t u r a t e d s u r f a c e s (100, 101, 102). H i s r e s u l t s are i n e x c e l l e n t agreement with the psyc h r o m e t r i c data f o r water of Mark and Dropkin f o r Reynolds numbers up to 5 10 (8). Beyond t h i s Powell's r e s u l t s are h i g h e r . Downing (23) measured the wet-bulb temperature d e p r e s s i o n s of acetone, benzene, hexane and water drops supported on a thermocouple t i p . He found that the wet-bulb temperatures measured v a r i e d l i n e a r l y with the .diameter of the thermocouple wire. H i s wet-bulb temperatures are e x t r a p o l a t e d t o the hypo-t h e t i c a l case of zero thermocouple wire diameter t o account f o r heat c o n d u c t i o n along the wires i n t o the drop. The i n t e r -p r e t a t i o n of h i s data i s c o m p l i c a t e d by the f a c t t h at the wet-bulb temperatures of pendant drops are higher than that meas-ured f o r climbed drops. Since the drop wet-bulb temperatures are a s t r o n g f u n c t i o n of the p h y s i c a l e x p e r i m e n t a l c o n d i t i o n s , the data p r e s e n t e d are not c o n s i d e r e d i n the a n a l y s i s of the present author's r e s u l t s . J a r v i s (59, 60, 61) has examined the e f f e c t of o r g a n i c mononiolecular f i l m s on s u r f a c e temperatures at a i r - w a t e r i n t e r f a c e s . He has found that c e r t a i n mononiolecular f i l m s which r e t a r d the e v a p o r a t i o n of water, a l s o i n c r e a s e the tem-o p e r a t u r e o.p the water s u r f a c e by 5 or 6 C. The use of s o l i d wet-bulbs e l i m i n a t e any such e f f e c t s i n p s y c h r o m e t r i c measure-ments. C a r r i e r and L i n d s a y (17) and Dropkin (24) have examined the e f f e c t of r a d i a t i o n at low a i r v e l o c i t i e s on the wet-bulb thermometer. The e f f e c t i v e n e s s of t h e i r a n a l y s i s i s l i m i t e d , -s i n c e the wet-bulb thermometer has s e v e r a l other s i g n i f i c a n t s ources of e r r o r when i t i s used to measure the wet-bulb tem-p e r a t u r e at low a i r v e l o c i t i e s . W i l l i a m s (130, 131) has prepared p s y c h r o m e t r i c c h a r t s f o r t h r e e systems of a i r / w a t e r - s o l u b l e s a l t s * He p o s t u l a t e s two models f o r p r e d i c t i o n of the s a l t s o l u t i o n wet-bulb tempera-t u r e s that depend on a knowledge of the a i r / w a t e r p s y c h r o m e t r i c c h a r t . Such measurements are of i n t e r e s t i n i n d u s t r i a l a p p l i -c a t i o n f o r c o n t r o l l i n g the moisture content i n b u i l d i n g s . McKeough and co-workers (90) have pr e s e n t e d a p s y c h r o m e t r i c c h a r t f o r the a i r / w a t e r vapor/sulphur d i o x i d e system. The a n a l -y s i s of such a multicomponent system i s complex, and the d i s -c r e p a n c i e s between the e x p e r i m e n t a l and the c a l c u l a t e d v a l u e s of the wet-bulb temperature are mainly a t t r i b u t e d t o l a c k of an a c c u r a t e knowledge of the system p r o p e r t i e s . Brown, Sato and Sage (14) have pr e s e n t e d the e f f e c t of gas stream t u r b u l e n c e on the macroscopic m a t e r i a l t r a n s p o r t from spheres. A part of the e x p e r i m e n t a l work i n v o l v e d measurement of the average s u r f a c e temperature of a porous 0 . 5 inch sphere from which n-heptane i s e v a p o r a t i n g i n t o an a i r j e t . F i g u r e s 4, 5 and 6 of t h e i r paper are inisleadingo They give the im-p r e s s i o n t h a t the wet-bulb temperature i s a f u n c t i o n of bulk v e l o c i t y and t u r b u l e n c e l e v e l . But these r e s u l t s r e f e r t o t h e i r own p a r t i c u l a r n o n - a d i a b a t i c s u r f a c e temperatures. The main reason f o r the s u r f a c e being noi>-adiabatic i s the c o n t i n -uous i n t r o d u c t i o n of n-heptane i n t o the wet-bulb v i a a connec-t o r at the f r e e stream temperature. Venezian, Crespo and Sage (125) l a t e r p r e s e n t e d s i m i l a r measurements f o r n-octane taken from the same apparatus f o r a 1 i n c h porous sphere. But i n t h i s case the c o n n e c t i o n c o n d u c t i o n e f f e c t s were a much s m a l l e r p r o p o r t i o n of the t o t a l heat t r a n s f e r than they were f o r the data of Brown and co-workers. They found that the v a r i a t i o n of the average s u r f a c e temperature with t u r b u l e n c e l e v e l and f r e e stream v e l o c i t y v/as not s i g n i f i c a n t . Most ps y c h r o m e t r i c r e s u l t s are o b t a i n e d i n an e n c l o s e d duct, w h i l e those of Brown, Venezian and co-workers were ob-t a i n e d i n a f r e e j e t . The r e s u l t of t h i s type of g e o m e t r i c a l d i f f e r e n c e w i l l l i k e l y be more s i g n i f i c a n t f o r the macroscopic r a t e of m a t e r i a l t r a n s p o r t than f o r the psychrometric r a t i o (13). The l o c a l s u r f a c e temperature v a r i a t i o n around a sphere as measured by Brown and co-workers (15) s h o u l d be r e p r e s e n t -a t i v e of the form of the t r u e wet-bulb temperature v a r i a t i o n , s i n c e each s u r f a c e temperature w i l l have approximately the same c o r r e c t i o n f a c t o r i n c o n v e r t i n g i t to a t r u e wet-bulb temperature. They found that the s u r f a c e temperature f o r the highest- Reynolds' number- runs at the f r o n t s t a g n a t i o n r e g i o n 1 0 of a sphere has a higher value than that o b t a i n e d i n the wake r e g i o n . Since a l l l o c a l s urface.temperatures were i n t e g r a t e d i n t o an average s u r f a c e temperature f o r a n a l y s i s purposes, no attempt was made to i n t e r p r e t t h i s v a r i a t i o n . However, lower Reynolds number runs showed an o p p o s i t e v a r i a t i o n of s u r f a c e temperature with p o s i t i o n . P r e v i o u s i d e n t i c a l measurements made by Hsu and Sage (52, 53) a l s o i n d i c a t e an o p p o s i t e v a r i a t i o n of s u r f a c e tempera-t u r e with angle around a sphere. As would be expected, the v e l o c i t i e s s t u d i e d by Hsu and Sage correspond to those used by Brown and co-workers f o r t h e i r lower Reynolds number e x p e r i -ments. b. T h e o r e t i c a l models Sherwood and Comings (113) p r e s e n t e d wet-bulb thermometer data f o r seven o r g a n i c l i q u i d s and water. They found that the a d i a b a t i c s a t u r a t i o n theory was an inadequate wet-bulb temper-atu r e p r e d i c t i o n method f o r the o r g a n i c l i q u i d s . Attempts to c o r r e l a t e the data by the d i f f u s i o n theory met with only moder-ate s u c c e s s . Sherwood and Coming's work was reviewed by Colburn (113), who suggested that the psychrometric data might be s u c c e s s f u l l y c o r r e l a t e d by use of the C h i l t o n - C o l b u r n analogy between mass and heat t r a n s f e r i n t u r b u l e n t flows (18). By assuming that (5) 11 then f30 = (Sc/Pr) -0,67 (6) -0.67 (7) = Le The t h e o r y p r e d i c t s that the macroscopic psychrometric r a t i o v a r i e s with the Lewis number to the -0.67 power. T h i s model a l s o p r e d i c t s t h at a system with a Lewis number equal to u n i t y w i l l e x h i b i t a p s y c h r o m e t r i c r a t i o of u n i t y . Eq. (7) i n d i -c a t e s that the p a r t i c l e Reynolds number a f f e c t s the heat and mass t r a n s f e r p r o c e s s e s a n a l o g o u s l y , and thus, that the f r e e stream v e l o c i t y and p a r t i c l e diameter w i l l have no e f f e c t on the p s y c h r o m e t r i c r a t i o . S i m i l a r r e a s o n i n g may be a p p l i e d to p r e d i c t the e f f e c t of the gas f r e e stream t u r b u l e n c e on the p s y c h r o m e t r i c r a t i o . In g e n e r a l the theory suggested by C o l b u r n gives lower p r e d i c t i o n s of the wet-bulb temperature d e p r e s s i o n than the v a l u e s measured by Sherwood and Comings. A comparison of the C h i l t o n - C o l b u r n analogy with accurate macroscopic p s y c h r o m e t r i c measurements from the l i t e r a t u r e i s shown i n F i g u r e 1. It can be seen that t h i s analogy p r e d i c t s the macroscopic p s y c h r o m e t r i c r a t i o t o be lower than the exper-i m e n t a l v a l u e s when the Lewis number i s g r e a t e r than u n i t y , and higher when the Lewis number i s l e s s than u n i t y . Lynch and Wilke (80) suggested that the C h i l t o n - C o l b u r n analogy s h o u l d be the most adequate way of c o r r e l a t i n g t h e i r wet-bulb thermometer data f o r the helium-water, a i r - w a t e r and freon-12-water systems. But they found that t h e i r psychro-12 1 1 1 — i — i — r i 1 i — i — r © - ARNOLD ( 3 ) e - BEDINGFIELD, DREW (8 A - D R O P K I N ( 2 4 ) V _ L Y N C H , W I L K E ( 8 0 ) x - MARK (8 5) 4.0-3.0 2 .0-1.0-0 .8 -0 .6-0 . 5 -0 .4 -0 . 3 -L Y N C H - W I L K E T H E O R Y ( j H = I.I j D ) CHILTON - C O L B U R N A N A L O G Y ( j h = j d ) B E D I N G F I E L D - D R E W ( E M P I R I C A L ) W I L K E - W A S A N T H E O R Y ( Re = I0 8 ) 0 .2 i i i i i i J 1 1 L 0. 0 .2 0.3 0.4 0.6 0.8 1.0 Le 2.0 3.0 4.0 6.0 8.0 FIGURE 1. COMPARISON OF PREVIOUS CORRELATIONS WITH PREVIOUS EXPERIMENTAL DATA FOR MACROSCOPIC PSYCHROMETRIC RATIOS OF CYLINDERS 13 m e t r i c r a t i o data v a r i e d with the Lewis number t o the -0.5 power r a t h e r than to the -0.67 power that i s p r e d i c t e d by the C h i l t o n - C o l b u r n analogy. Thus, they suggest t h a t t h e i r data p l u s the data of A r n o l d (3), B e d i r g f i e l d and Drew ( 8 ) , Mark (85) and Dropkin (24) best s a t i s f i e s a m o d i f i e d j-number analogy. S i n c e a l l of the data c o n s i d e r e d above except that f o r freon-12-water i s c l u s t e r e d i n a narrow span of the Lewis num-ber, t h i s r e s u l t depends g r e a t l y on the v a l i d i t y of the meas-urement f o r the freon-12-water system (see F i g u r e 1). T h i s model does p r e d i c t a s m a l l e r dependence of the psychr ometr i c r a t i o on the Lev/is number as was suggested by p r e v i o u s experimentators, but i t has the l i m i t a t i o n that the p s y c h r o m e t r i c r a t i o i s p r e d i c t e d to be 0.91 when the Lewis num-ber i s u n i t y . The many experiments with the a i r - w a t e r system seem to i n d i c a t e t h a t the psychrometric r a t i o i s c l o s e to u n i t y when the Lewis number i s u n i t y . Three years l a t e r Lynch and Wilke (81) proposed a second theory f o r p r e d i c t i n g the macroscopic psychrometric r a t i o . L i n , Moulton and Putman (77) had d e r i v e d an equation f o r mass t r a n s f e r from the s o l i d w a l l of a pipe under t u r b u l e n t flow, J H 1 • 1 J n (8) which i s e q u i v a l e n t to (9) 14 that i s k Q = f c t n ( v e l o c i t y , f r i c t i o n f a c t o r ) •.. <£> (Sc) (10) where 0 (Sc) i s a c o m p l i c a t e d f u n c t i o n of the Schmidt number. Lynch and Wilke s t a t e that i t i s not p o s s i b l e to make a d i r e c t a p p l i c a t i o n of t h i s e q u a t i o n to mass t r a n s f e r from c y l i n d e r s , but i t i s c o n c e i v a b l e that i t may be q u i t e c o r r e c t i n d e t e r -mining the form of the Schmidt number;dependence. Using the r e s u l t s of t h e i r p r e v i o u s paper (80), they propose that the macroscopic psychrometric r a t i o f o r c y l i n d e r s i s p r e d i c t e d by 1 + 0. 56 (h (Pr) /3 0 = 0.91 — (11) 1 + 0 . 5 6 Cp (Sc) T h i s more s o p h i s t i c a t e d but more e m p i r i c a l method has the l i m i t a t i o n of t h e i r p r e v i o u s model p l u s that of p r e d i c t i n g f o r gases the same v a r i a t i o n of the p s y c h r o m e t r i c r a t i o with Lewis number as does the C h i l t o n - C o l b u r n analogy. In the same year White and C h u r c h i l l (127) r e s u s c i t a t e d the d i f f u s i o n model, on the b a s i s of which they proposed an a l t e r n a t e approach to the mathematical a n a l y s i s of wet-bulb temperatures. They suggested an a n a l y s i s based on p o t e n t i a l -g r a d i e n t i n s t e a d of p o t e n t i a l - d i f f e r e n c e . The model ig n o r e s a l l f l u i d flow around the wet-bulb and assumes t h a t the t h e r -mal and d i f f u s i o n a l r e s i s t a n c e i s p r o v i d e d by a l a y e r of stagna.nt f l u i d over a plane s u r f a c e , which i s a c t i n g as the wet-bulb. They conclude that the wet-bulb temperature depres-15 s i o n can be expressed by (12) D.. C. a t , p - p w White and C h u r c h i l l s t a t e that the new model c o r r e l a t e s the a v a i l a b l e wet-bulb temperature data as r e a d i l y as p r e v i o u s p r e d i c t i o n methods. They suggest f u r t h e r experiments to t e s t the e f f e c t of the heat c a p a c i t y of the v a p o r i z e d l i q u i d on the wet-bulb temperature o C a l c u l a t i o n s by the present author, however, show that the model g i v e s h i g h l y i n a c c u r a t e p r e d i c t i o n s of e x p e r i m e n t a l p s y c h r o m e t r i c data o b t a i n e d f o r c o n d i t i o n s of f o r c e d c o n v e c t i o n . P o s s i b l y the theory may be an e f f e c t i v e method f o r wet-bulb temperature p r e d i c t i o n when f o r c e d c o n v e c t i o n and r a d i a t i o n e f f e c t s are n e g l i g i b l e and n a t u r a l c o n v e c t i o n e f f e c t s are s m a l l . Wilke and Wasan (129) have developed a theory f o r p r e -d i c t i n g the macroscopic psychrometric r a t i o of c y l i n d e r s by adopting an approach s i m i l a r t o that vised by Lynch and Wilke (81). Wasan and Wilke (126) proposed an analogy treatment f o r t u r b u l e n t pipe flow i n which the Stanton numbers f o r heat and mass t r a n s f e r are r e l a t e d t o a g e n e r a l i z e d f u n c t i o n of the P r a n d t l or Schmidt numbers r e s p e c t i v e l y . T h e i r major assump-t i o n i s that the same P r a n d t l or Schmidt number f u n c t i o n as f o r f low i n p i p e s i s a p p l i c a b l e t o the case of flow around a 16 wet-bulb element. But u n f o r t u n a t e l y t h i s a n a l y s i s p r e d i c t s t hat the p s y c h r o m e t r i c r a t i o v a r i e s not only with the system Schmidt and P r a n d t l numbers, but a l s o with the p a r t i c l e -Reynolds number. Wilke and Wasan found that the curve f o r «\ 5 Reynolds number of 10 gave the best f i t of the psychrometric data of A r n o l d , B e d i n g f i e l d and Drew, Dropkin, Lynch and Wilke, and Mark (see F i g u r e 1). They conclude that the analogy treatment i s i n agreement with data o n l y at very high gas v e l o c i t i e s . An e m p i r i c a l e q u a t i o n i s d e r i v e d from the theo-r e t i c a l r e l a t i o n s h i p s which p r e d i c t s the macroscopic psychro-m e t r i c r a t i o of c y l i n d e r s t o be a f u n c t i o n of the P r a n d t l and Schmidt numbers s e p a r a t e l y , but not of the Lewis number per se: 1 + 0 . 7 ( P r ° ° 7 7 - 1 ) -V I T 0 . 7 ( S c 0 ' 7 7 - 1 ) . U 3 ) Thus, a l l of the t h e o r e t i c a l attempts t o p r e d i c t the macroscopic p s y c h r o m e t r i c r a t i o of c y l i n d e r s have met with o n l y l i m i t e d success. Very l i t t l e new understanding and i n -s i g h t i n t o the p s y c h r o m e t r i c phenomenon has been pr e s e n t e d s i n c e the s u g g e s t i o n of Colburn (113) to r e p r e s e n t the com-bi n e d heat and mass t r a n s f e r p r o c e s s e s that are a part of a l l wet-bulb temperature measurements by the C h i l t o n - C o l b u r n analogy. U n t i l the p u b l i c a t i o n of Kauh, Peck and Wasan (62) no attempts had been made to t h e o r e t i c a l l y p r e d i c t v a l u e s of the p s y c h r o m e t r i c r a t i o f o r any other p a r t i c l e shape but c y l i n d e r s , These authors present a t h e o r e t i c a l c o r r e l a t i o n f o r the 17 ps y c h r o m e t r i c r a t i o of a f l a t p l a t e . T h e i r a n a l y t i c a l ap-proach i s s i m i l a r t o that used by Lynch and Wilke (81) and W.ilke and Wasan (129). S p a l d i n g (116, 117) has n u m e r i c a l l y s o l v e d the problem of heat t r a n s p o r t i n a t u r b u l e n t boundary l a y e r near the s u r -face of a f l a v p l a t e f o r cases when the P r a n d t l number i s near u n i t y . Gardner and K e s t i n (32) and o t h e r s have extended S p a l d i n g ' s work and produced a s o l u t i o n t o the problem f o r a wide range of P r a n d t l numbers. The l o c a l Stanton number on a f l a t p l a t e i s a complex f u n c t i o n of the l o c a l l e n g t h Reynolds number along the p l a t e and the P r a n d t l number. By a p p l y i n g the heat and mass t r a n s f e r analogy t o the c a l c u l a t i o n of mass t r a n s f e r c o e f f i c i e n t s , the l o c a l p s y c h r o m e t r i c r a t i o along f l a t p l a t e s may be c a l c u l a t e d from the r a t i o of the Stanton number f o r mass t r a n s f e r t o the Stanton number f o r heat t r a n s -f e r . The theory p r e d i c t s that the l o c a l p s y c h r o m e t r i c r a t i o i s a s t r o n g f u n c t i o n of the Schmidt and P r a n d t l numbers and the l o c a l l e n g t h Reynolds number. Kauh and co-workers have d e f i n e d a macroscopic p s y c h r o m e t r i c r a t i o f o r a f l a t p l a t e which v a r i e s with the Schmidt and P r a n d t l numbers of the system and the t o t a l l e n g t h Reynolds number. Since t h e r e were no e x p e r i -mental wet-bulb temperature data f o r f l a t p l a t e s i n the l i t e r -ature, i t was d i f f i c u l t t o e v a l u a t e the e f f e c t i v e n e s s of t h e i r t heory. The t h e o r e t i c a l macroscopic p s y c h r o m e t r i c r a t i o curves f o r f l a t p l a t e s at e i t h e r l o c a l or t o t a l Reynolds 4 5 numbers of 10 and 10 are shown to bracket p r e v i o u s data o b t a i n e d from c y l i n d e r s . They conclude that s i n c e a n a l o g i e s seem t o e x i s t between pipe flow and flow over a c y l i n d e r , 18 s i m i l a r a n a l o g i e s e x i s t between f l a t p l a t e s and c y l i n d e r s and thus, that t h e i r theory i s adequate to p r e d i c t the macro-s c o p i c p s y c h r o m e t r i c r a t i o of a f l a t p l a t e at high gas v e l o c -i t i e s . Kauh et a l . seem to ignore the f a c t that the theory of S p a l d i n g a p p l i e s o n l y to a t u r b u l e n t boundary l a y e r . In the l e n g t h Reynolds number range 10^ to 10^ on a f l a t p l a t e the boundary l a y e r i s laminar. Thus, e x p e r i m e n t a t i o n i n t u r b u l e n t 5 boundary l a y e r s (Re„ > 3.2 x 10 ) i s necessary t o v e r i f y the I range of Reynolds numbers over which the t h e o r y of Kauh and co-workers may apply. c. S e m i e m p i r i c a l models The most r e l i a b l e and a c c u r a t e p s y c h r o m e t r i c measurements i n the l i t e r a t u r e are those of, B e d i n g f i e l d and Drew (8). They measured the macroscopic wet-bulb d e p r e s s i o n s in a i r of c y l i n -ders c a s t from naphthalene, p-dichlorobenzene, p-dibromobenzene and d-camphor. The use of s u b l i m i n g wet-bulb elements e l i m i -nates many of the e r r o r s t o which the u s u a l v a r i a t i o n s of the wet wick method are s u s c e p t i b l e . B e d i n g f i e l d and Drew found that the macroscopic psychro-m e t r i c r a t i o of a c y l i n d e r i s not a f f e c t e d by the f r e e stream temperature, by the p a r t i c l e Reynolds number f o r s e v e r a l d i f -f e r e n t c y l i n d e r diameters and a i r v e l o c i t i e s , and by the c y l i n d e r l e n g t h f o r l e n g t h t o diameter r a t i o s exceeding 9.3. A p r e l i m i n a r y t h e o r e t i c a l study showed that the psychro-m e t r i c r a t i o i s r e l a t e d t o the system Lewis number by a c o n s t a n t exponent. The best e m p i r i c a l f i t of t h e i r data i n 19 a model of t h i s form was L e - ° ' 5 6 (14) A comparison of B e d i n g f i e l d and Drew's equation v/ith other e x i s t i n g t h e o r i e s i s shown i n F i g u r e 1. Ingebo (55) has p r e s e n t e d a method of p r e d i c t i n g wet-bulb temperatures from b o i l i n g - p o i n t data on the g i v e n l i q u i d and wet-bulb data f o r water. He evaporated e i g h t d i f f e r e n t organ-i c l i q u i d s and water from a 0.688 cm. diameter cork sphere. No mention i s made of the l o c a t i o n of h i s s u r f a c e thermocouples r e l a t i v e t o the a i r stream flow d i r e c t i o n . S ince some of the o wet-bulb temperature d e p r e s s i o n s were as high as 260 C, heat c o n d u c t i o n along the thermocouple wires and r a d i a t i o n may have had a l a r g e i n f l u e n c e on the r e s u l t s . Although Ingebo's em-p i r i c a l e q u ations appear t o f i t h i s data q u i t e w e l l , no a t -tempt was made t o check h i s method with other p s y c h r o m e t r i c data. Because of the p o s s i b l e e r r o r s i n h i s r e s u l t s and s i n c e h i s proposed method does not c o n t r i b u t e toward a more b a s i c u n d e r s t a n d i n g of psychrometry, Ingebo's work i s not c o n s i d e r e d f u r t h e r . 2. P s ychrometric s t u d i e s i n a r a r e f i e d atmosphere Madden (83) and Madden and H a l f e n (84) have examined wet-bulb temperature d e p r e s s i o n s f o r s u b l i m a t i n g naphthalene spheres at low p r e s s u r e s . They found that t h e i r e x p e r i m e n t a l temperature d e p r e s s i o n measurements i n the micron p r e s s u r e range agree w e l l with p r e d i c t i o n s based on heat and mass 20 t r a n s f e r c o n s i d e r a t ions„ The system geometry was shown to markedly a f f e c t the temperature d e p r e s s i o n and hence the evap-o r a t i o n r a t e . The r e s u l t s of Madden's a n a l y s i s should as the pressure i n c r e a s e s , e x t r a p o l a t e i n t o the curve p r e d i c t i n g wet-bulb tem-p e r a t u r e s i n a quiescent atmosphere, although no i n f o r m a t i o n i s a v a i l a b l e c o n c e r n i n g the exact p r e s s u r e range over which each t r a n s f e r mechanism predominates. 21 I I . METHODS OF MEASURING SURFACE TEMPERATURES S e v e r a l a l t e r n a t e methods of measuring s o l i d or l i q u i d s u r f a c e temperatures have been suggested i n the l i t e r a t u r e . The f o l l o w i n g l i s t t a b u l a t e s some common techniques. i interfermometer techniques (27, 28, 107) i i use of the t h e r m i s t o r which i s s l o w l y r a i s e d across a l i q u i d - g a s i n t e r f a c e (60) i i i use of thermocouples i n wicks or near the o u t s i d e of s u r f a c e s (most common method) i v i n f r a r e d t echniques (120) v use of a wet-bulb thermometer t o r e p r e s e n t any geometry (93) v i thermocouples moulded i n s i d e s o l i d wet-bulbs (8) The t e c h n i q u e s i n v o l v i n g measurements by l i g h t d i f f r a c t i o n have on l y l i m i t e d a p p l i c a t i o n s when the o b j e c t being c o n s i d e r e d i s more than two-dimensional. 2 2 I I I . GENERAL CONSIDERATIONS OF MOMENTUM, HEAT AND MASS TRANSFER FROM PARTICLES TABLE 1 PARTICLE FLOW PARAMETERS Sphere C y l i n d e r P l a t e Rep t o i n i t i a t e > 1 > 1 s e p a r a t i o n ( 7 8 ) ( 6 8 ) Maximum angle of wake separ at i o n from p a r t i c l e f r o n t 8 3 ° ( 7 8 ) 8 1 ° ( 1 1 1 ) Reynolds number to i n i t i a t e a t u r b u l e n t boundary l a y e r i n low t u r b u l e n c e i n t e n s i t y flow R e p 5 3 x 10 ( 1 1 0 ) R e p 5 x 1 0 5 ( n o ) R e v 3 . 2 x 1 0 5 ( 1 1 0 ) 1. Spheres Momentum, heat and mass t r a n s f e r from spheres has been e x t e n s i v e l y examined i n the l i t e r a t u r e (see Tab l e 1 ) . Rowe, C l a x t o n and Lewis ( 1 0 8 ) present a d e t a i l e d review of heat and mass t r a n s f e r from a s i n g l e sphere i n an e x t e n s i v e f l o w i n g f l u i d . They conclude from t h e i r own c a r e f u l measure-ments t h a t i n a low t u r b u l e n c e i n t e n s i t y a i r stream 23 Nu* ( o r Sh* ) = 2 + 0.69 Re P r i / J ( or Sc ) (15) C o n s i d e r a b l e a t t e n t i o n has been devoted to the l i m i t i n g v a lue of the N u s s e l t and Sherwood numbers when n a t u r a l and f o r c e d c o n v e c t i o n e f f e c t s are n e g l i g i b l e . T h e o r e t i c a l l y the l i m i t i n g v a l u e can be shown to be equal to 2 f o r a sphere. Thus, t r a n s f e r r e s u l t s can be r e p r e s e n t e d as a sum of the d i f -f u s i o n a l t r a n s f e r p l u s f o r c e d c o n v e c t i o n t r a n s f e r assuming that n a t u r a l c o n v e c t i o n e f f e c t s are n e g l i g i b l e . Garner and Hoffmann (33) and Gauvin and Narasimham (92) have d i s c u s s e d i n d e t a i l the t r a n s i t i o n from f r e e t o f o r c e d heat c o n v e c t i o n f o r spheres. Complete reviews of the e f f e c t of t u r b u l e n c e on heat and mass t r a n s f e r from spheres have been pre s e n t e d by Clamen and . Gauvin (19), Galloway and Sage (37, 38) and R a i t h b y and E c k e r t (103). Galloway and Sage f i n d t h at both mass and heat t r a n s f e r from spheres e x h i b i t a maximum r a t e at a f i x e d Reynolds num-ber and t u r b u l e n c e i n t e n s i t y when the s c a l e parameter /dp equals a value of 1.6. S i m i l a r r e s u l t s were o b t a i n e d f o r c y l i n d e r s by Van Der Hegge Z i j n e n (134). A l l authors agree that mass and heat t r a n s f e r r a t e s are i n c r e a s e d by an i n c r e a s e i n the f r e e stream t u r b u l e n c e i n t e n s i t y , but much disagreement e x i s t s as to the c o r r e c t r e l a t i o n s h i p of the N u s s e l t and Sherwood numbers with the Reynolds number, t u r b u -lence i n t e n s i t y and s c a l e of t u r b u l e n c e . Clamen and Gauvin (19) show that the drag c o e f f i c i e n t on spheres are changed by the presence of e i t h e r mass t r a n s f e r or f r e e stream turbulence,, At a t u r b u l e n c e i n t e n s i t y of 30 p e r c e n t , the t r a n s i t i o n from a laminar t o t u r b u l e n t boundary l a y e r on a sphere i s shown to occur at a p a r t i c l e Reynolds number of approximately 2000. Thus, the t r a n s i t i o n Reynolds number of a sphere s h a r p l y decreases as the t u r b u l e n c e i n t e n -s i t y increases., Hughmark (54) has r e p l o t t e d data from the l i t e r a t u r e f o r mass and heat t r a n s f e r from r i g i d spheres to f i n d the e f f e c t of the system P r a n d t l and Scmidt numbers. In the range 0.5< Pr (Sc)< 10, f o r p a r t i c l e Reynolds numbers of 10, 100 and 1000, the Nu (Sh) i s shown to vary with Pr (Sc) t o the 0.31, 0.34 and 0.34 powers r e s p e c t i v e l y . The data p r e s e n t e d i n the 3 5 range 10 <Pr (Sc)< 10 apply t o l i q u i d systems and show c o n s i s t e n t l y higher powers. Hughmark concludes that the exponent f o r the Schmidt and P r a n d t l numbers i n c r e a s e s with the Reynolds number. T h i s i n c r e a s e may be caused by the 3 r a p i d l y growing wake i n the range 10 £ R e p < 10 . The Schmidt and P r a n d t l number exponent f o r moderate Reynolds number flow i s p r e d i c t e d by F r o s s l i n g (31) to be 0.33 and i s i n agreement with the f i n d i n g s of Hughmark. 2. C y l i n d e r s C o n s i d e r a b l e a t t e n t i o n has been given t o momentum, heat and mass t r a n s f e r from c y l i n d e r s . The heat or mass t r a n s f e r from a c y l i n d e r i n a t u r b u l e n t f l u i d of low i n t e n s i t y may be 25 p r e d i c t e d by an equation proposed by Ulsaraer (124) from measurements over the range 50<Rep < 10,000: Nu* (Sh*) = 0.6 R e p 0 - 5 P r 0 ' 3 1 ( S c 0 * 3 1 ) (16) There i s disagreement i n the l i t e r a t u r e c o n c e r n i n g the l i m i t i n g v alue of the N u s s e l t or Sherwood numbers f o r c y l i n d e r s . McAdams (88) and Richa r d s o n (106) suggest v a l u e s of 0.42 P r U t and 0.37 r e s p e c t i v e l y . Many c o r r e l a t i o n s f o r f o r c e d c o n v e c t i o n t r a n s p o r t ignore the e f f e c t of the d i f f u s i o n a l t r a n s p o r t completely. Van Der Hegge Z i j n e n (133) prese n t s an a n a l y s i s f o r combined n a t u r a l and f o r c e d heat c o n v e c t i o n from c y l i n d e r s . A thorough e xperimental a n a l y s i s and review of l o c a l and macroscopic heat t r a n s f e r from c y l i n d e r s i n a t u r b u l e n t a i r stream i s p r e s e n t e d by Galloway and Sage (35). They f i n d that the angle of s e p a r a t i o n on a c y l i n d e r i s not a f u n c t i o n of t u r b u l e n c e i n t e n s i t y at a p a r t i c l e Reynolds number of 2667 but becomes a s t r o n g f u n c t i o n of the t u r b u l e n c e i n t e n s i t y at a Reynolds number of 33000. These c o n c l u s i o n s are i n agreement with the r e s u l t s of Clamen and Gauvin (19) from spheres. As i n the case of spheres, the N u s s e l t number of a c y l i n d e r i s shown t o i n c r e a s e with i n c r e a s i n g f r e e stream t u r b u l e n c e i n t e n s i t y . As a l r e a d y noted, Van Der Hegge- Z i j n e n (134) has shown that the N u s s e l t number of a c y l i n d e r has a maximum value when /dp = 1.6. 26 3. F l a t p l a t e s The t h e o r e t i c a l a n a l y s i s of momentum, heat and mass t r a n s f e r from a f l a t p l a t e i s c o n s i d e r a b l y s i m p l i f i e d by the two-dimensional nature of the o b j e c t . The l o c a l heat and mass t r a n s f e r data f o r a p l a t e i n a low t u r b u l e n c e i n t e n s i t y f l u i d have been adequately c o r r e l a t e d (67) by the t h e o r e t i c a l e q u a t i o n N u v ( S h v ) = 0.332 R e v 1 / 2 p r 1 / 3 ( S c 1 / 3 ) (17) f o r laminar boundary l a y e r flow. The o v e r a l l t r a n s p o r t i s p r e d i c t e d by Nu* (Sh*) = 0.664 R e L 1 / 2 P r 1 / 3 ( S c 1 / 3 ) • (18) Free stream t u r b u l e n c e has been shown by s e v e r a l authors to have no e f f e c t oh the r a t e of heat t r a n s f e r a c r o s s a laminar or t u r b u l e n t boundary l a y e r with a f a v o r a b l e pressure g r a d i e n t . Changes of f r e e stream t u r b u l e n c e cause l a r g e v a r i a t i o n s i n the N u s s e l t number over f l a t p l a t e s when there i s a p r e s s u r e g r a d i e n t opposing the flow. I n c r e a s i n g the f r e e stream t u r b u l e n c e i n t e n s i t y promotes boundary l a y e r t r a n s i t i o n at a lower Reynolds number (64). 27 4 „ T u r b u l e n t boundary l a y e r s Very l i t t l e i n f o r m a t i o n i s a v a i l a b l e i n the l i t e r a t u r e c o n c e r n i n g the dependence of the Shorwood and N u s s e l t numbers on the Schmidt and P r a n d t l numbers r e s p e c t i v e l y i n a high i n t e n s i t y t u r b u l e n t flow f i e l d . In Danckwert's model (21), s u r f a c e elements are r e p l a c e d by f r e s h f l u i d a f t e r some random time which i s determined by a s u r f a c e renewal r a t e . T h i s device p r e d i c t s that heat and mass t r a n s f e r c o e f f i c i e n t s w i l l depend on the d i f f u s i v i t y and thermal c o n d u c t i v i t y r e s p e c t i v e l y to the one-half power. But t h i s model does not p r o v i d e any b a s i s f o r r e l a t i n g the t r a n s f e r to the t u r b u l e n c e l e v e l . One of the key and l i m i t i n g assumptions i n t h i s model i s that s p e c i f y i n g the absence of a v e l o c i t y g r a d i e n t at the t r a n s f e r i n t e r f a c e . If the system i s i n a very t u r b u l e n t regime, the t r a n s f e r may be p o s t u l a t e d as being c o n t r o l l e d by an exchange between the source and the e d d i e s , so that any v e l o c i t y g r a d i e n t i n the f l u i d has l i t t l e i n f l u e n c e on the d i f f u s i v e p r o c e s s . It s h o u l d be emphasized t h a t an independent e v a l u a t i o n of the average time exposure of a s u r f a c e element i s not p o s s i b l e i n exchange events between eddi e s and a s i n k or source, and evidence f o r support of the o r i g i n a l p e n e t r a t i o n theory or the Danckwerts m o d i f i c a t i o n t h e r e o f r e s t s upon f i n d i n g a 0.5 power dependence of the t r a n s -f e r r a t e upon the Schmidt or P r a n d t l numbers. Leont'ev (74) s t a t e s that the accepted v a l u e s of the exponent on the P r a n d t l number f o r heat t r a n s f e r i n q u a s i -28 i s o t h e r m a l t u r b u l e n t boundary l a y e r flow i s equal t o 0.25 while that f o r the constant heat f l u x case w i l l be 0.40. The q u a s i - i s o t h e r m a l r e s u l t i s supported by the a n a l y s i s of H a r r i o t (44) and L e v i c h (75) who found that f o r mass t r a n s -f e r i n t u r b u l e n t boundary l a y e r flow, Sh CC S c 1 / 4 (19) In c o n t r a s t , the c o r r e s p o n d i n g exponent on Sc (or Pr) f o r laminar boundary l a y e r s i s 1/3 (110). 29 IV. TURBULENCE PHENOMENA 1„ Measurement of i n t e n s i t y and s c a l e of t u r b u l e n c e The phenomenon of t u r b u l e n c e p l a y s a r a t h e r important r o l e i n f l u i d mechanics. It appears that a l l flow c o n f i g u r a t i o n s con t a i n i n g s o l i d boundaries become t u r b u l e n t above a f i n i t e c r i t i -c a l Reynolds number. T h e o r e t i c a l c o n s i d e r a t i o n s a l s o i n d i c a t e that the behavior d e s c r i b e d by the n o n l i n e a r i t y of the governing hydrodynamic equations i s i n s t r u m e n t a l i n c a u s i n g t u r b u l e n c e ( 6 6 ) In the past the d i f f e r e n t t h e o r e t i c a l approaches to the problem of t u r b u l e n c e always have c o n t a i n e d a few h e u r i s t i c elements, so the r o l e of e x p e r i m e n t a t i o n has been q u i t e impor-tant i n e x p l o r i n g f o r i n s p i r a t i o n . The p r i n c i p a l measuring technique now i n use to discover, both the g e n e r a l p r o p e r t i e s and the d e t a i l e d dynamic s t r u c t u r e of t u r b u l e n t flows i s undoubtedly the hot-wire anemometer. Other methods have been d i s c u s s e d i n d e t a i l by Kovasznay (66) and Brodkey (12), but so f a r none of them present a s e r i o u s c h a l l a n g e t o the hot-wire technique. The hot-wire anemometer was f i r s t used i n 1914 by L. V. King (65) t o measure mean v e l o c i t i e s . Then i n 1928, with the i n v e n t i o n of e l e c t r o n i c thermal l a g compensation by Dryden and Kuethe, the instrument was used to measure r a p i d t u r b u l e n t f l u c t u a t i o n s . To measure the mean flow v e l o c i t y , a r e l i a b l e instrument such as a p i t o t tube or b a r c e l l p r e s s u r e sensor must be used 30 as a r e f e r e n c e f o r c a l i b r a t i o n . The anemometer bridge DC v o l t a g e s h o u l d be p l o t t e d a g a i n s t flow v e l o c i t y , v a r y i n g the v e l o c i t y . through the range of i n t e r e s t . T h i s c a l i b r a t i o n curve w i l l o n l y h o l d f o r a s p e c i f i c probe operated at a s p e c i f i c over-h e a t i n g r a t i o i n a s p e c i f i c medium (unless the c a l i b r a t i o n i s expressed i n a dime n s i o n l e s s form). Turbulence measurements are based upon the sl o p e A' i n v o l t s / f t . / s e c . of the c a l i b r a -t i o n curve, taken at the mean v e l o c i t y i n q u e s t i o n . The percentage of t u r b u l e n c e i s d e f i n e d as the r a t i o of the RMS v e l o c i t y d i v i d e d by the mean v e l o c i t y : % t u r b u l e n c e = { V u^ /U } x 100 (20) The anemometer r e c o r d s the RMS v o l t a g e from the t u r b u l e n c e s i g n a l . Thus, V R o x 100 % t u r b u l e n c e = - ^ - ^ (21) A' U where V R M S = / V ' 2 ( 2 2 ) and v' i s the f l u c t u a t i n g v o l t a g e s i g n a l . It i s p o s s i b l e t o c a l c u l a t e the percentage t u r b u l e n c e i f one assumes the e x i s t e n c e of a l i n e a r r e l a t i o n s h i p between e l e c t r i c a l power input t o the transducer and the square root of the flow v e l o c i t y , without knowing the value of A'. 31 One form of 'King's Law'states that V 2 = V 2 + Const, x < v/u (23) where V i s the bridge v o l t a g e and i s the b r i d g e v o l t a g e at zero flow v e l o c i t y . By d e f i n i t i o n , dV A ' = (24) dU Const. (25) 4 V Thus, Const, x /U A' U = ^ — (26) 4 V But V 2 -V^2 A} = , (27) V Const o T h e r e f o r e 32 V 2 -Vj? 4 V A ' X U = — (28) S u b s t i t u t i n g Eq. (28) i n t o Eq. (21), one obtains the r e s u l t that 4 V % turbulence = —g ^ x V R M S x 100 (29) v -v 0 The bridge voltage at zero flow v e l o c i t y may be e a s i l y measured by o p e r a t i n g the transducer without removing i t s pro-t e c t i v e cover. Thus measurements of turbulence i n t e n s i t y do not a c t u a l l y r e q u i r e p l o t t i n g the bridge voltage versus flow v e l o c -i t y c a l i b r a t i o n curve. The E u l e r i a n l o n g i t u d i n a l macro or i n t e g r a l s c a l e of t u r -bulence i s defined as (46) /•CO L x = J o f ( x ) dx (30) where < U , ) A ( u . > B f ( x ) = = — (31) uf and where f ( x ) i s c a l l e d the c o r r e l a t i o n c o e f f i c i e n t i n the 1 or l o n g i t u d i n a l d i r e c t i o n ; S i m i l a r l y the E u l e r i a n l a t e r a l macro or i n t e g r a l s c a l e of turbulence i s d e f i n e d as L v = / g(y) dy (32) y 0^ The E u l e r i a n l o n g i t u d i n a l i n t e g r a l s c a l e of turbu l e n c e can be o b t a i n e d by i n t e g r a t i o n of the f ( x ) curve. D i f f i c u l t i e s may a r i s e when the c o r r e l a t i o n o s c i l l a t e s p e r s i s t e n t l y about the 0- a x i s at great v a l u e s of d i s t a n c e . Randomly i n t e r r u p t i n g the curve at a great d i s t a n c e i s an a r b i t r a r y process and i s not c o r r e c t (47). If the t u r b u l e n t f l u i d f i e l d i s homogeneous (that i s , the t u r b u l e n c e has q u a n t i t a t i v e l y the same s t r u c t u r e i n a l l p a r t s of the flow f i e l d and thus i s i n v a r i a n t with r e s p e c t to p a r a l -l e l t r a n s f o r m a t i o n s of the c o - o r d i n a t e system) and has a con-st a n t mean v e l o c i t y i n the l o n g i t u d i n a l d i r e c t i o n , then a r e l a -t i o n known as T a y l o r ' s h y p o t h e s i s (119) a p p l i e s : 6 = - u l , • • (33) d t * d x The E u l e r i a n time c o r r e l a t i o n i s d e f i n e d by T a y l o r (118) as u. ( r ) u , ( T - t * ) R ( t * ) = - — (34) where the f l u c t u a t i n g v e l o c i t y u, i s c o n s i d e r e d at a f i x e d p o i n t but at d i f f e r e n t times. In a steady flow f i e l d , 34 a v e r a g i n g the time c o r r e l a t i o n with r e s p e c t to time produces the E u l e r i a n i n t e g r a l time s c a l e of t u r b u l e n c e L = f R ( t * ) d t * (35) 1 • -b t , For the s p e c i a l case of i s o t r o p i c t u r b u l e n c e (that i s , the s t a t i s t i c a l f e a t u r e s of the flow have no p r e f e r e n c e f o r any d i r e c t i o n so that p e r f e c t d i s o r d e r r e i g n s ) i t can be shown that L x = 2 L y (36) It i s assumed that T a y l o r ' s h y p o t h e s i s i s v a l i d , a n d i f the t u r b u l e n t motion has a uniform mean motion such that U >> u ( , then s i n c e x = U t * (37) i t f o l l o w s t h a t L x = U L t (38) Townsend (121) has proposed a very elegant method of meas-u r i n g the E u l e r i a n i n t e g r a l time s c a l e of t u r b u l e n c e by u s i n g the energy-spectrum f u n c t i o n E |.(n'). From the r e l a t i o n s h i p 35 1 ,03 R E 't*> = — J dn' E,(n') cos 27Tn't* (39) i t f o l l o w s that CO f R E ( t * ) ( t * ) dt* 0 1 r 0 0 r 0 0 , =|f J o E,(n') d n ' J </>(t*) cos 2 7Tn't*dt* (40) where <f> ( t * ) i s an a r b i t r a r y f u n c t i o n which must s a t i s f y the c o n d i t i o n s that ,00 , .CO 1. j R £ ( t * ) <£(t*)dt* = J R E ; ( t * ) d t * = L t (41) •'o A 00 i 2. / <p(t*) cos 2 7T n ' t * d t * converges, •'o 3. the i n t e g r a t i o n procedure with the f u n c t i o n cp ( t * ) i s f e a s i b l e by means of e l e c t r o n i c c i r c u i t s , , These c o n d i t i o n s can be s a t i s f i e d i f the f u n c t i o n <jf>(t*) i s such t h a t the d e v i a t i o n from u n i t y i s s m a l l f o r the value s of time where R^ ( t * ) s t i l l has a n o t i c e a b l e v a l u e , but decreases to zero when t * i s l a r g e so that the second i n t e g r a l w i l l converge. Such a t r a n s f o r m a t i o n which s a t i s f i e s a l l t h r e e c o n d i t i o n s 36 i s , f o r i n s t a n c e , <f> ( t * ) = | 1 + | ** 1 e ~ W t 0 > (42) 0 S u b s t i t u t i o n i n t o Eq„ (41) y i e l d s 1 .00 L x = -==• / E . (n 1 ) dn 1 f 2 ^0 f°°/l + — \ e" ( t* / t ;0 > cos 27Tn't*dt* (43) Jo\ t 0 J I n t e g r a t i o n by p a r t s y i e l d s •CO c * * 1 - ( t * / t ) e 0 cos 2 7Tn't*dt* 2 t Q (1 + 4w2 n''2 t ^ ) 2 Thus, from Eq. (44) and Eq. (43), CO 2 t, (44) L t = ~ / ^ E , ( n ' ) " U ° dn' (45) u f 0 (1 + 4 7 T 2 n ' 2 t§ ) 2 The value of tQ must be chosen so that c o n d i t i o n 1 i s sat-i s f i e d . T h i s i s accomplished i f tQ i s l a r g e with r e s p e c t t o 37 L * . If the r a t i o L ^ / t ^ i s not s m a l l , Eq 0 (45) y i e l d s too low a value f o r L A „ A refinement of Townsend's equation t o meet the case that L j / t Q i s not s m a l l y i e l d s the approximation (135) ( L . / t 0 ) L x = U L t 1 + ! : Y (46) 0 J 1 + — ! = yI ( 1 + 2 L t / t 0 )J The energy spectrum f u n c t i o n s a t i s f i e s the c o n d i t i o n that .CO uf = J E,(n') dn' (47) 0 when the f l u i d i s s t a t i s t i c a l l y homogeneous with r e s p e c t to t ime. If a f l u c t u a t i n g v e l o c i t y s i g n a l u, i s m u l t i p l i e d by a response s i g n a l t o produce u-| = u, x • (48) 1 + 47T < in' £tg and uJ i s squared and averaged t o give Cu' f = u,2 x , , (49) * ' (1 + 4 7T 2 n ' 2 t 2 )2 then i t can be shown (121) that 38 -00 dn' / E,(n') x ' 0 " (1 + 4 7 r 2 n ' 2 t 2 ; 2 uf x ~ (50) (1 + 4 i r d n l d t J )'-A more r i g o r o u s proof f o r Eq. (50) may be d e r i v e d by con-s i d e r i n g each frequency n' s e p a r a t e l y and d e v e l o p i n g the expres-s i o n as an i n f i n i t e s e r i e s , with each term r e p r e s e n t i n g a s i n g l e frequency. Thus, comparing Eq. (50) and Eq. (45), i t i s obvious that L = x 2 t n x { u ? x \ (51) * • uf ° I ' (1 + 4 7 r 2 n ' 2 t 2 )2 J To be d i m e n s i o n a l l y c o n s i s t e n t i t i s noted that t ^ must have the u n i t s of time. The e l e c t r o n i c c i r c u i t s developed to measure the s c a l e of t u r b u l e n c e are p r e s e n t e d i n Appendix Two-5-d. 2. Decay of t u r b u l e n c e behind g r i d s A common method used to c r e a t e t u r b u l e n c e i s to p l a c e a g r i d or s c r e e n at r i g h t angles to the mean f l u i d flow i n a duct The s c r e e n has a c h a r a c t e r i s t i c mesh length M', wire diameter d and s o - c a l l e d s o l i d i t y r a t i o /3. 39 Baines and Pe t e r s o n (7) show that the i n t e n s i t y of t u r b u -lence d i r e c t l y behind the s o l i d p o r t i o n of a l l g r i d s and l a t -t i c e s i n v e s t i g a t e d a t t a i n s a maximum at about X = 2 to 4 M' f o r any gi v e n value of M'/d. For any given X the i n t e n s i t i e s appear t o maximize at about M'/d = 1.5. They a l s o show that a d i s t a n c e of 5 to 10 mesh le n g t h s downstream of any sc r e e n i s necessary to i n s u r e that r e a s o n a b l y r e p r o d u c i b l e flow i s e s t a b -l i s h e d . T h i s requirement i s not i d e n t i c a l with that f o r f u l l y developed i s o t r o p y . The q u a n t i t y R^ i s the Reynolds number f o r the mesh U M' R M = (52) Dryden and co-workers (26) show that i n the range 2400 < R|y| < 17500 the i n t e n s i t y of t u r b u l e n c e does not depend on U or R^ . H a l l (41) f i n d s t h at "u7/U i n c r e a s e s s l i g h t l y with i n c r e a s i n g R^ while Van Der Hegge Z i j n e n (135) f i n d s that TT7/U decreases s l i g h t l y with i n c r e a s i n g R^ f o r a l l v a l u e s of X i n v e s t i g a t e d . Dryden (25) shows that the decay of t u r b u l e n c e behind a sc r e e n i s a l s o a f u n c t i o n of the f r e e stream t u r b u l e n c e up-stream of the scr e e n . Turbulence c l o s e r t o a g r i d than a c e r t a i n minimum d i s t a n c e w i l l not be i s o t r o p i c . T h i s minimum d i s t a n c e i s a com p l i c a t e d f u n c t i o n of many parameters but Van Der Hegge Z i j n e n suggests that i t may have a value c l o s e t o 20 M'. T a y l o r (118) d e r i v e d an e x p r e s s i o n f o r the decay of 4 0 t u r b u l e n c e behind a screen. He p r e d i c t e d that U/u"7 i s a l i n e a r f u n c t i o n of X/M'. Work by Dryden (25) showed that the d i f f e r e n c e between-) the r e s u l t s f o r woven screens and b i p l a n e screens it' unimportant , and that i f the r e s u l t s are p l o t t e d i n terms of X/d r a t h e r than X/M', the e f f e c t of d/M' i s s m a l l f o r v a l u e s of d/Iv!' near 0.2. A s i m i l a r c o r r e l a t i o n i s j u s t i f i e d by B a t c h e l o r and Townsend ( 6 ) from the viewpoint of drag over the s c r e e n elements. Van Der Hegge Z i j n e n proposes that t u r b u l e n c e i n t e n s i t y obeys a common law of decay ^ r x " x o i p p - 0 C \ - ( 5 3 ) U I d J where X ^ and PP are c o n s t a n t s that vary from s c r e e n to screen. X Q i s v i s u a l i z e d as l o c a t e d on an apparent o r i g i n of t u r b u -lence i n t e n s i t y downstream of the g r i d s . It i s determined by p e x t r a p o l a t i n g the l i n e a r p o r t i o n of the (U/u, ) versus X curve to (U/u| ) = 0. Few c o n c l u s i o n s can be drawn from the l i t e r a t u r e concern-i n g the dependence of L x on p o s s i b l e parameters. Dryden ( 2 5 ) and B a t c h e l o r and Townsend ( 6 ) suggest that s c a l e of t u r b u l e n c e data may be best c o r r e l a t e d by a p l o t of / d versus X/d„ The apparent o r i g i n of as found from p l o t t e d e x p e r i m e n t a l data i s q u i t e d i f f e r e n t from that of TT7/U f o r the same experiments. 2 P l o t s of versus X , L y, versus X/M', L^/M' versus X/M', L x versus ( X -X'Q ) and L ^ / d versus ( X -X' Q )/d f o r d i f f e r e n t s c r e e n s show l i t t l e agreement or c o r r e l a t i o n . F u r t h e r s t u d i e s of t u r b u l e n c e behind p e r f o r a t e d p l a t e s and woven wire screens have been presented by Raithby and E c k e r t (103) f o r measurements i n a 30.5 cm. by 61 cm. r e c t a n -g u l a r wind t u n n e l . They f i n d that the t u r b u l e n c e i n t e n s i t y i s a s t r o n g f u n c t i o n of the s o l i d i t y r a t i o and geometry of the g r i d . T h e i r i n t e n s i t y and s c a l e measurements behind the per-f o r a t e d p l a t e s show7 no dependence on the f r e e upstream v e l o c i t But s c a l e s measured behind the woven screen show a d e f i n i t e v e l o c i t y f u n c t i o n . The comparison of the data of Raithby and E c k e r t with p r e v i o u s data by a p l o t of L^/M' versus X/M' v e r i -f i e s t h a t no g e n e r a l c o r r e l a t i o n p r e s e n t l y e x i s t s f o r p r e d i c t -i n g the s c a l e of t u r b u l e n c e behind a g r i d . Thus, i t i s obvious that measurements of t u r b u l e n c e i n t e n s i t y and s c a l e are s t r o n g f u n c t i o n s of the apparatus i n which the measurements are conducted. Any e m p i r i c a l p r e d i c t i o n s of t u r b u l e n c e i n t e n s i t y and i n t e g r a l s c a l e behind a g r i d i n a win t u n n e l w i l l be of d o u b t f u l nature and i n order t o ensure an a c c u r a t e knowledge of these parameters, they must be measured d i r e c t l y . 42 CHAPTER THREE THEORY AND INITIAL DECISIONS I. THEORY 1. B a s i c equations and a n a l y t i c a l approach In order t o a n a l y t i c a l l y examine psychrometry, i t i s necessary t o s o l v e the equations governing combined heat and mass t r a n s f e r . The t r a n s f e r of s c a l a r q u a n t i t i e s and F j ^ to or from a s o l i d body i n a moving f l u i d depends on the v e l o c i t y f i e l d of the f l u i d around the s o l i d body and on the t r a n s f e r p r o p e r t i e s of the f l u i d with r e s p e c t t o or . The most simple case of the t r a n s f e r of or i n a steady s t a t e , non-turbulent flow of an i n c o m p r e s s i b l e f l u i d of constant p h y s i c a l p r o p e r t i e s i s d e s c r i b e d by the four, c o n s e r v a t i o n e q u a t i o n s . - e q u a t i o n of c o n s e r v a t i o n of momentum of the f l u i d (-Navier-.Stokes equation) which d e s c r i b e s the v e l o c i t y f i e l d dp d 2u. ( i th component) d x : d xi d x; (54) - equations of c o n s e r v a t i o n of the s c a l a r q u a n t i t i e s T and Fjy] , r e s p e c t i v e l y 43 dlh dTJ, ij — 1 = k l i - + S h (55) d x j dx j d XJ . U J =• D V S M (56) dx. dxj dx| - e q u a t i o n of c o n s e r v a t i o n of f l u i d mass ( c o n t i n u i t y equation) duj = 0 (57) dx. - boundary c o n d i t i o n s No g e n e r a l s o l u t i o n i s a v a i l a b l e f o r t h i s system of second order d i f f e r e n t i a l e q uations. Approximations may be based on s u p e r p o s i t i o n of s o l u t i o n s t o the l i n e a r i z e d e quations, but they apply t o a very l i m i t e d number of cases o n l y . Furthermore any d e v i a t i o n from the s i m p l i f y i n g assumptions made i n the d e r i v a t i o n of these equations r e s u l t s i n a d d i t i o n a l terms, so that experiments are o f t e n the onl y f e a s i b l e way to i n v e s t i g a t e heat and mass t r a n s f e r problems. A n u m e r i c a l s o l u t i o n of the governing equations i s p r o h i b i t i v e because of the l a r g e amounts of computer time that would be r e q u i r e d . 4 4 2. Macroscopic p s y c h r o m e t r i c r a t i o dependence on Lewis number Consider a homogeneous sphere or c y l i n d e r h e l d s t a t i o n a r y i n a moving f l u i d . I f the m a t e r i a l i s e v a p o r a t i n g or s u b l i m a t -in g from the s u r f a c e of the p a r t i c l e , then the geometric center of the sphere or c y l i n d e r at steady s t a t e w i l l e x h i b i t the 'surface average' temperature commonly r e f e r r e d t o as the ' o v e r a l l ' wet-bulb temperature and i n t h i s study as the 'macro-s c o p i c 'wet-bulb temperature 0 Consider a p a r t i c l e s u b l i m a t i n g and assume that t h e r e are no heat sources w i t h i n the p a r t i c l e 0 It i s assumed t h a t the f l u i d does not s l i p along the s u r f a c e of the p a r t i c l e , t h a t the temperature and f l u i d compositions are r e l a t i v e l y constant i n the main stream and that there i s no condensation i n the vapor phase. The s e n s i b l e heat t r a n s f e r r e d t o sublimate W pounds of m a t e r i a l at the wet-bulb temperature Is g i v e n by The heat t r a n s f e r r e d may a l s o be expressed i n terms of the temperature d r i v i n g f o r c e s where t w here r e f e r s t o the macroscopic wet-bulb temperature and the * s u p e r s c r i p t denotes a s u r f a c e averaged q u a n t i t y . If the r a t i o of the t o t a l r a d i a t i v e heat t r a n s f e r t o the t o t a l c o n v e c t i v e heat t r a n s f e r i s d e f i n e d as t (58) (59) 45 a*=H ( t W A -*W > ( 6 0 ) '1 ( ; D B - * W > ' and a t o t a l heat t r a n s f e r c o e f f i c i e n t i s d e f i n e d as h* - h* (1 +a *) (61) t c then combination of Eq. (60) and Eq. (61) leads to q f = h* f A ( t D B - t w ) (62) If the body i s s m a l l compared t o the surroundings, the r e l a t i v e heat t r a n s f e r c o e f f i c i e n t f o r grey-body r a d i a t i o n a c c o r d i n g t o McAdams (85) can be gi v e n by { ( T W A A 0 0 ) 4 - (T /100) 4} h* = 0.173 6 — — . ^ : J (63) r t - t " where T and are Rankine temperatures and C i s the e m i s s i v i t y of the wet-bulb. , The c o n v e c t i v e heat t r a n s f e r c o e f f i c i e n t h* i s an e f f e c -t i v e heat t r a n s f e r c o e f f i c i e n t which i n c l u d e s the heat t r a n s f e r due t o mass t r a n s f e r . If a heat t r a n s f e r c o e f f i c i e n t h** c i s d e f i n e d i n the absence of mass t r a n s f e r then h* h** •= - C (64) c y * 46 where y * accounts f o r the simultaneous e f f e c t o f mass t r a n s -port on c o n v e c t i v e heat t r a n s p o r t . y * i s u s u a l l y r e f e r r e d t o as an Ackermann c o r r e c t i o n (1, 10)„ It can be shown that (129) • XW f C P V f ( t D B _ t w M y * = Ln < 1 + >• (65) C P V f ^ DB _ tW ' X W For s m a l l v a l u e s of the group C pyf (t D B - t w ) y * can be expressed as ^ = i _ C p v f ( t D B - t w ) ^ 2 X w Since the f l u i d o u t s i d e the p a r t i c l e i s u n s a t u r a t e d with r e s p e c t t o the s u r f a c e m a t e r i a l , the m a t e r i a l sublimates from the bulb at a r a t e g i v e n by the r e l a t i o n s h i p W - k* MW WA <p w - P [ ) B ) (67) Combining Eq.'s (58), (59), (62), (64) and (67), an e x p r e s s i o n f o r the wet-bulb temperature can be obtained. 47 X W k G M WW (PW" PDB } t D B - t w = (68) y* (1 + « * ) h** ' c The macroscopic p s y c h r o m e t r i c r a t i o i s d e f i n e d as P0= -3—— (69) S t * h** c (70) S i n c e k*Y = k * G P B M M W B f <7 1> i t can be shown from Eq. (68) that R - ( t p B ~ t w } ( 1 + a * ) ^ * M W B f P B M C P f ( ? 2 ) ° MWW X w ( P W - P D B ) As was i n d i c a t e d i n the p r e v i o u s c h a p t e r , many e f f o r t s have been made t o r e p r e s e n t the 'macroscopic' or 'surface average' s u b c r i t i c a l f o r c e d c o n v e c t i o n heat and mass t r a n s p o r t from s i n g l e p a r t i c l e s by the f o l l o w i n g e m p i r i c a l e x p r e s s i o n s . Nu* = A , + B , Rep f PrJ*° (73) 48 Sh* = A j + B,.Rep f S c ^ 0 (74) The s u b s c r i p t f denotes a ' f i l m p r o p e r t y ' . In computing the Reynolds number the f l u i d v i s c o s i t y and d e n s i t y are taken at a temperature midway between t ^ and t p g . The v e l o c i t y i s t h a t at the duct center where the p a r t i c l e i s l o c a t e d . In computing the P r a n d t l and Schmidt numbers a l l p r o p e r t i e s are again taken, at the temperature midway between t ^ and t • The molecular weight MW^ ^ i s analogously taken f o r a p a r t i a l p r e s s u r e midway between p and p^ p , . W DB Although t h e r e i s c o n s i d e r a b l e d i s p u t e i n the l i t e r a t u r e as t o the exact value of the Reynolds number exponent n, and l i t t l e a t t e n t i o n has been g i v e n t o e x p e r i m e n t a l l y determine M Q , i t i s assumed i n t h i s a n a l y s i s that a simple analogy between mass and heat t r a n s f e r a p p l i e s to the combined mass and heat t r a n s f e r process. In low t u r b u l e n c e i n t e n s i t y f l u i d flow, when the p a r t i c l e Reynolds number i s s u f f i c i e n t l y , high, then Sh* r S c l M 0 Nu* L P r JF (75) When MQ equals o n e - t h i r d , Eq. (75) r e p r e s e n t s the analogy between t r a n s f e r of mass and heat i n t u r b u l e n t flows that was f i r s t emphasized by C h i l t o n and Colburn (18). B e d i n g f i e l d and and Drew ( 8 ) show by v e c t o r i a l a n a l y s i s of the c o n s e r v a t i o n equations that Eq. ( 7 5 ) may be used f o r any wet-bulb geometry t o c o r r e l a t e the psy c h r o m e t r i c r a t i o . The e r r o r t hat i s i n t r o d u c e d by n e g l e c t i n g the constant A, of Eq. ( 7 3 ) and Eq. ( 7 4 ) can be examined by c o n s i d e r i n g a c t u a l values of A , , B | , n and MQ that are determined from heat and mass t r a n s f e r experiments. I f the Rowe, C l a x t o n and Lewis e q u a t i o n ( 1 0 8 ) f o r mass or heat t r a n s f e r from spheres i n t o a i r i s c o n s i d e r e d as an example, i t can be seen from F i g u r e 2 that f o r the case of a s o l i d s u b l i m i n g i n t o a gas with Prf ~ 0 . 7 , the e r r o r i n t r o d u c e d by c o n s i d e r i n g the parameter A|;, to be n e g l i g i b l e becomes l a r g e r with i n c r e a s i n g Schmidt number and d e c r e a s i n g Reynolds number. At Reynolds numbers of 1 0 0 0 and 1 0 , 0 0 0 f o r a naphthalene sphere i n a i r , the e r r o r s i n t r o -duced by a p p l y i n g Eq. ( 7 5 ) are approximately 3 . 5 and 0 . 0 8 percent r e s p e c t i v e l y . For a c y l i n d e r the parameter A ( has an approximate t y p i c a l value of 0 . 3 5 , and thus Eq. ( 7 5 ) w i l l apply to a much lower p a r t i c l e Reynolds number range. Since k* L Sh* = ( 7 6 ) D V f Nu* = h** L c ( 7 7 ) 50 51 k* k* = (78) 6 ^ 9 T f then k* _ 1 D V f Sh* h** R n T f k, Nu* c g i f T h e r e f o r e Eq. (68) becomes (l + a*) y* kf Rg T , (79) 1 D..f f S c l M 0 M — \ <80> R g T f k f I Pr J f _ = „ W "W ^ w ^ D B ' "Vf. ( 8 1 ) The d i m e n s i o n l e s s r a t i o of the Schmidt number d i v i d e d by the P r a n d t l number i s known as the Lewis number. Eq. (81) may be w r i t t e n r<t D B - t w ) (1 +a*) y* k f Rg T f -s Log < — \ M 0 - 1 ^ <PW ' " O B > DV. i ( 8 2 ) Log ( L e f ) Thus i t i s p o s s i b l e to c a l c u l a t e the macroscopic psychro-m e t r i c r a t i o dependence on the Lewis number from a s i n g l e experiment at high p a r t i c l e Reynolds numbers. 5 2 The value of M Q determined from t h i s unique method can be f u r t h e r used i n macroscopic mass and heat t r a n s f e r c o r r e l a t i o n s t o p r e d i c t the dependence of the Nu s s e l t and Sherwood numbers on the P r a n d t l and Schmidt numbers r e s p e c t i v e l y f o r f o r c e d c o n v e c t i o n . 3. L o c a l p s y c h r o m e t r i c r a t i o dependence on the Lewis and If l o c a l v a r i a t i o n s of s u r f a c e temperature e x i s t on a . sphere, t h e r e w i l l be heat t r a n s f e r r e d through the p a r t i c l e due t o the i n t e r n a l temperature g r a d i e n t s . Consider a sphere sub-l i m i n g i n a duct and having i n t e r n a l and e x t e r n a l temperature g r a d i e n t s as shown i n F i g u r e 3. B i o t numbers a. Sphere FREE STREAM \ TEMPERATURE CONSTANT TEMPERATURE GAS FLOW 0 DISTANCE FROM DUCT CENTER FIGURE 3. TEMPERATURE GRADIENT IN A SPHERICAL WET-BULB Consider a h a l f - s p h e r e with a c y l i n d r i c a l annular element 53 about the x - a x i s as shown i n F i g u r e 4. Z do X GAS FLOW FIGURE 4. CONDUCTION EFFECT ACROSS A SPHERE In order t o o b t a i n a u s e f u l s o l u t i o n to the problem of con-d u c t i o n heat t r a n s f e r through the sphere the f o l l o w i n g assump-t i o n s w i l l be made: (1) The temperature i n the z-plane of the p a r t i c l e i s constant at x - 0. • (2) . No temperature g r a d i e n t e x i s t s i n the f r e e stream f l u i d approaching the p a r t i c l e . (3) A constant l o c a l heat and mass t r a n s f e r c o e f f i c i e n t may be assumed to e x i s t over the e n t i r e symmetrical s u r f a c e e l e -ment on the sphere. (4) A uniform temperature g r a d i e n t i n the x - d i r e c t i o n e x i s t s i n the s o l i d p a r t i c l e . (5) The i n t e r n a l heat flow i n the p a r t i c l e i s only i n the x - d i r e c t i o n . A c t u a l e x p e r i m e n t al measurements show assumptions (1), (2), and (3) to be q u i t e a c c u r a t e . To show the v a l i d i t y of assump-54 t i o n s (4) and (5), the ' a d i a b a t i c s ' and 'isotherms' i n a s i n g l e c y l i n d e r have been c a l c u l a t e d from e x p e r imental s u r f a c e temperatures by the simultaneous n u m e r i c a l s o l u t i o n of the L a p l a c e and the Cauchy-Riemann equ a t i o n s . These r e s u l t s are p r e s e n t e d i n Appendix Four. From the knowledge of the a d i a b a t i c s i n a c y l i n d e r , the sphere i s expected to have 'heat f l o w tubes' or 'tubular a d i a b a t i c s ' c o n c e n t r i c with the x - a x i s and mainly p a r a l l e l t o t h i s a x i s . The sphere i s assumed to be e x p e r i e n c i n g f o r c e d c o n v e c t i o n and r a d i a t i v e heat t r a n s f e r . On the annular s u r f a c e element, t C t 161 dQ' - k . (27Tz dz) — (83) b x where dQ' i s the r a t e of heat flow through the c y l i n d r i c a l element of s o l i d sphere and t w now r e f e r s to the l o c a l wet-bulb temperature. A heat balance over the c y l i n d r i c a l s u r f a c e element on the sphere i s as f o l l o w s : h*** ( 1 +a)y 2 7Tz ( t 0 B - t w ) dS XW M WW k6 2 W Z (PW " PDB } d S + d Q ' ( 8 4 ) where h C c r (85) 55 The element of s u r f a c e area a v a i l a b l e f o r heat t r a n s f e r to the gas may be r e l a t e d t o dz as f o l l o w s : dz dS = — — — (86) cos cp d p — ~ dz (87) 2x where dp i s the diameter of the s p h e r i c a l p a r t i c l e , If a B i o t number i s d e f i n e d as h f r h*** (1 +a ) y r B i = X- = ~± (88) k s k s where dp r n - (89) u 2 then Eq„ (84) s i m p l i f i e s t o 1 ( f f . . X W M W W k G (PW-PPB' — u n R - t r ; + B i U b 0 h*** (1 + 0! ) / t D B - t w = " 1 ° 1 + — B i 56 It can be seen that i f B i — » 0 then Thus, i f the p a r t i c l e has an i n f i n i t e thermal c o n d u c t i v i t y i t w i l l e xperience the same temperature over the whole s u r f a c e . T h i s i s s i m i l a r t o the type of behavior found f o r drops with i n t e r n a l c i r c u l a t i o n . I f B i —«> CO then t - t — X w M W w K G ( % - P D B > ( 9 2 ) DB w h*** ( i + a ) y T h i s r e s u l t i s s i m i l a r to Eq. (81) which c o n s i d e r s the macroscopic wet-bulb temperature d e p r e s s i o n f o r which conduction e f f e c t s are not a f a c t o r . Eq. (90) may be r e w r i t t e n as He - * w + - <*c - * w ' h „ * ( 1 + a ^ < 9 3 ) 57 Thus the l o c a l s u r f a c e value of the psychrometric r a t i o d e f i n e d i n an analogous manner to Eq. (70), i s g i v e n by *DB - V + ~ ~ ( t C > } ( 1 + Q > / M W B f P B M C P f /5/5 = (94) M W W X W ( p W - p D B } A s i m i l a r a n a l y s i s t o that p r e s e n t e d f o r the macroscopic wet-bulb temperatures can be a p p l i e d t o l o c a l wet-bulb tempera-t u r e s . The o n l y d i f f e r e n c e i s that the l o c a l N u s s e l t and Sherwood numbers on the sphere are c o n s i d e r e d r a t h e r than the macroscopic v a l u e s . When n a t u r a l c o n v e c t i o n e f f e c t s are n e g l i g i b l e and at high p a r t i c l e Reynolds numbers, then the l o c a l t r a n s p o r t e quations analogous to Eq. (79) and Eq. (80) may be w r i t t e n : k G 1 D V f S h (95) D V f f S c MM (96) Rg T f k f L P r J f Combining Eq. (93) and Eq. (96), t DB -*W + ~ ( t C " tw >f ( 1 + Q , ) / k f , RQ T f ' Log M W W X W ( p W ~ p DB } D V f ( 9 ? ) Log ( L e ^ ) 5S Thus the l o c a l p s y c h r o m e t r i c r a t i o f o r a sphere can be r e l a t e d t o both the Lewis and B i o t numbers of the system. The val u e of MM can be used to p r e d i c t the dependence of the l o c a l N u s s e l t and Sherwood numbers on the P r a n d t l and Schmidt numbers r e s p e c t i v e l y f o r l o c a l heat and mass t r a n s f e r c o r r e l a t i o n s . b o C y l i n d e r Consider a c y l i n d e r i n c r o s s f l o w e x p e r i e n c i n g the same c o n d i t i o n s as d e s c r i b e d i n part (a) f o r a sphere. F i g u r e s 5 and 6 present a schematic r e p r e s e n t a t i o n of the c y l i n d e r i n the duct.> FREE STREAM \ ^ GAS FLOW CONSTANT TEMPERATURE 0 DISTANCE FROM DUCT CENTER TEMPERATURE FIGURE 5. TEMPERATURE GRADIENT IN A CYLINDRICAL WET-BULB 59 GAS FLOW FIGURE 6. CONDUCTION EFFECTS ACROSS A CYLINDER The assumptions that are pres e n t e d f o r the s p h e r i c a l case apply e q u a l l y t o a c y l i n d e r . A d i s c u s s i o n of e x i s t i n g isotherms and a d i a b a t i c s i n s i d e a c y l i n d e r i s presented i n Appendix Four. From a heat balance f o r the s u r f a c e element of a c y l i n d e r Y f e e t long. t - t dQ' = k (Ydz) ? S x (98) h * * * d + a ) y ( t - t ) Y dS C / L)fc5 W XwMWiit k Y (p -p ) dS +• dQ' W W G W DB (99) dS = dz 2x (100) where dp i s the diameter of the c y l i n d e r . D e f i n i n g a B i o t number for. a c y l i n d e r s i m i l a r t o that f o r a sphere, then the equations can be s i m p l i f i e d t o give f o r a 60 c y l i n d e r the same r e s u l t s as d e r i v e d f o r a sphere. Of course the r e l a t i o n s h i p s w i l l not be expected t o be v a l i d near the ends of the c y l i n d e r , nor even at the middle of a s h o r t c y l i n d e r . c F l a t p l a t e The e f f e c t of the p l a t e B i o t number on the l o c a l psychro-m e t r i c r a t i o s cannot be c o n s i d e r e d i n a manner s i m i l a r t o the a n a l y s i s p resented f o r spheres and c y l i n d e r s . I f the temperature g r a d i e n t along the s u b l i m a t i n g p l a t e i s l i n e a r , then each p o i n t along the f l a t s u r f a c e s h o u l d be r e c e i v -i n g and l o s i n g the same amount of heat by a x i a l c o n d u c t i o n through the sample. Thus, the measured wet-bulb temperature s h o u l d have no dependence on the p l a t e thermal c o n d u c t i v i t y and Eq. (72) and Eq. (82) f o r the macroscopic wet-bulb temperature measurements w i l l apply at each l o c a l p o i n t on the p l a t e . B i o t number c o r r e c t i o n s w i l l be important very near the l e a d i n g edge and at the r e a r of the p l a t e . 4. G e n e r a l i z e d r e l a t i o n s h i p f o r the ps y c h r o m e t r i c r a t i o From the p r e v i o u s a n a l y s i s , i t i s p o s s i b l e t o develop a d i r e c t r e l a t i o n s h i p between the psychrometric r a t i o and Lewis number i n f o r c e d c o n v e c t i o n . The macroscopic p s y c h r o m e t r i c : r a t i o can be w r i t t e n as k* P, MW C c (101) From Eq. (80) i t i s known that 61 k* D h** R„ T« k g A f K f ^ (Le ) M 0 f (102) T h e r e f o r e P B M M W B f C P f D V f .Mn  : (Le ) u Rg T f k f f (103) But P. = P B M M W B f R g T t (104) Thus /So " L e , 0 M„-l (105) S i m i l a r l y f o r the l o c a l p s ychrometric r a t i o PJ3 = Le 1-1 f (106) It can be seen from Eq. (105) and Eq. (106) that when the Lewis number equals u n i t y , the l o c a l and macroscopic p s y c h r o m e t r i c r a t i o s both equal u n i t y r e g a r d l e s s of the va l u e s of the exponents M and MM. Thus a p r i o r i i t can be p r e d i c t e d 62 that t h e r e i s no l o c a l v a r i a t i o n of s u r f a c e temperature on a s u b l i m i n g or e v a p o r a t i n g p a r t i c l e when the Lewis number of the system i s equal t o u n i t y . 5. L i m i t i n g wet-bulb temperature d e p r e s s i o n i n a quiescent atmosphere In the absence of f o r c e d and n a t u r a l c o n v e c t i o n , a wet-bulb w i l l e x h i b i t a temperature d e p r e s s i o n due to d i f f u s i o n a l mass and heat t r a n s f e r . T h i s d e p r e s s i o n can be c o n s i d e r e d t o be a ! l i m i t i n g ' , but not n e c e s s a r i l y a minimum, v a l u e . It i s p o s s i b l e to c a l c u l a t e t h i s ' l i m i t i n g wet-bulb temperature d e p r e s s i o n ' f o r thr e e geometries -- a sphere, a c y l i n d e r and a f l a t p l a t e -- by two d i f f e r e n t methods. Method one: a. Sphere Consider a sphere s u b l i m a t i n g i n t o a quiescent atmosphere. The s e n s i b l e heat t o c o o l the surrounding gas i s equal t o the heat c o n d u c t i n g t o the sphere: a t By c o n t i n u i t y , a t ar (107) ^ f v r = G 0 <r0 / r ) (108) 63 The boundary c o n d i t i o n s are d e f i n e d at r = r 0 w G 0 XW r=r, S o l v i n g Eq. (107), a p p l y i n g the a p p r o p r i a t e boundary c o n d i t i o n s , Ln 4 1 + ' P V f  X W ( t _ , U - !oSy£pJ , _ ^ (109) k f For d i f f u s i o n a l mass t r a n s f e r of one component through another (62), N, - D v f / 0 f d ( x A ) 1 - dr (110) But N A G 0 ( r 0 / r ) ' (111) Thus P dr r f — 0 0 r 2 - D V f Pi "clCx A) 1 - x (112) When r = r 0' X A XAW But 64 x A = p/P (113) S o l v i n g Eq. (112), one o b t a i n s the r e s u l t t h at G o r o * 1 - D V f pi Ln P - p p - P. W (114) Combining Eq. (114) and Eq. (109), > D V C p ^ t - t w PVf p - p P - p (115) The l i m i t i n g wet-bulb temperature d e p r e s s i o n i s ob t a i n e d by s e t t i n g p = p D B when t = t , t h a t i s "PV X tDB ~' *W W PVf k P - p D3l P - R - 1 W (116) The group yOD^ Cpy /k i s a 'vapor Lewis number'. The u s u a l Lev/is number i s d e f i n e d u s i n g the heat c a p a c i t y of the surround-i n g gas but i n t h i s case, the a n a l y s i s p r e d i c t s that the heat 65 c a p a c i t y of the s u b l i m a t i n g vapor should be important. b„ C y l i n d e r Consider a c y l i n d e r s u b l i m i n g i n t o a quiescent atmosphere. E x p r e s s i n g the energy balance mathematically one o b t a i n s p.c f "PVf 'r d x at i a | at f r a r l dr (117) and by c o n t i n u i t y , Pf v r = G 0 ( r 0 / r ) (118) When r = r , 0 t = t, w ' lSj,-r0" ° ° X W S o l v i n g these equations as b e f o r e , Ln < 1 + ^ (t - t w ) j - G ° ^° ° ™ L n l w f (119) C o n s i d e r i n g the mass t r a n s f e r from the c y l i n d e r , 66 D V f Pi d ^ A > . N = (120) M 1 - x A dr N A = G 0 - 7 ( 1 2 1 ) x A = p/P (122) S o l v i n g the above t h r e e equations, and knowing that p = p W when r = r^ , one o b t a i n s G o r o L n 7 = DvfPi Mp-Hr^ (123) Combining Eq. (123) and Eq. (119), the l i m i t i n g wet-bulb temperature d e p r e s s i o n f o r a c y l i n d e r i s giv e n by fi°Dv C P V 1 k i f C, P - P. P V f L V. ^ w (116) It i s not s u r p r i s i n g t h a t t h i s r e s u l t i s i d e n t i c a l t o that o b t a i n e d f o r a sphere. It i s important t o note that f o r the case of a sphere Eq 0 (109) has a f i n i t e value of t when r -»CO But i n Eq. (119) there i s no f i n i t e value of t when r CO T h i s i m p l i e s t h a t the bulk value of t i s some value f a r removed from the s u r f a c e . T h i s d i f f i c u l t y i s removed by combining Eq„ (119) and Eq. (123), thus e l i m i n a t i n g the d i s t a n c e parameter 67 from the r e s u l t i n g Eq. (116). c. F l a t p l a t e The combined d i f f u s i o n a l heat and mass t r a n s f e r a n a l y s i s f o r a f l a t p l a t e i s pr e s e n t e d by White and C h u r c h i l l (127). The r e s u l t i s i d e n t i c a l t o that o b t a i n e d f o r a sphere and a c y l i n d e r . But they i n c o r r e c t l y present the theory as a com-p e t i t i v e model t o the f o r c e d c o n v e c t i o n a n a l y s i s (Eq. (68)). Method Two. A second type of approach may be a p p l i e d to the p r e d i c t i o n of l i m i t i n g wet-bulb temperature d e p r e s s i o n s i n a quiescent atmosphere. It can be shown that the N u s s e l t and Sherwood numbers of a sphere are both equal t o 2.0 i n the absence of f r e e and f o r c e d c o n v e c t i o n . I f i t i s assumed that the l i m i t i n g , v a lue of the N u s s e l t number equals that of the Sherwood number f o r each of spheres, c y l i n d e r s and f l a t p l a t e s , r e s p e c t i v e l y , then i t can be shown that the l i m i t i n g macroscopic psychrometric r a t i o f o r each of these shapes i s g i v e n by B. = Le *"1 (124) OL f Thus i t i s of i n t e r e s t t o determine whether Eq. (124) or Eq. (116) g i v e an a c c u r a t e p r e d i c t i o n of the wet-bulb tempera-t u r e d e p r e s s i o n i n the absence of force d , a n d near absence of f r e e , c o n v e c t i o n . 68 I.I. FACTORS TO BE STUDIED It i s proposed t o e x p e r i m e n t a l l y examine how the wet-bulb temperature d e p r e s s i o n i s a f f e c t e d by (1) wet-bulb s i z e and shape (2) p o s i t i o n on the wet-bulb (3) gas v e l o c i t y (4) f r e e stream t u r b u l e n c e i n t e n s i t y and s c a l e (5) system Lewis number In order t o p r e d i c t the i n t e n s i t y and s c a l e of tu r b u l e n c e behind screens i n a wind t u n n e l i t i s necessary t o experimen-t a l l y examine the (1) decay of t u r b u l e n c e downstream of v a r i o u s screens at d i f f e r e n t v e l o c i t y l e v e l s (2) s c a l e of t u r b u l e n c e downstream of v a r i o u s screens at d i f f e r e n t v e l o c i t y l e v e l s In a d d i t i o n t o a knowledge of the f r e e stream t u r b u l e n c e parameters, i t i s proposed to e x p e r i m e n t a l l y examine how these parameters are a f f e c t e d by the presence of a wet-bulb. L i m i t i n g wet-bulb temperature depressions may be experimen t a l l y determined i n a quiescent atmosphere and compared with Eq. (116) and Eq. (124). 69 I I I . FACTORS TO BE OMITTED If the wind t u n n e l blockage i s s m a l l , i t w i l l have no sy s t e m a t i c e f f e c t on the psyc h r o m e t r i c measurements. Thus t h i s e f f e c t w i l l not be examined. P o s s i b l y i t might be of i n t e r e s t to examine the dependence of the wake wet-bulb temperature d e p r e s s i o n on the t r a n s p o r t behavior i n the forward r e g i o n of a sample. U n f o r t u n a t e l y , i s o l a t i n g the wake area of a sample leads t o l a r g e heat conduc-t i o n e f f e c t s which are d i f f i c u l t t o e l i m i n a t e e x p e r i m e n t a l l y or a n a l y t i c a l l y . It i s thought that the wake area combined heat and mass t r a n s f e r p r o c e s s e s w i l l not depend a p p r e c i a b l y on the heat and mass t r a n s f e r c h a r a c t e r i s t i c s at the f r o n t of the sample. The presence of a f i n i t e , i n t e r f a c i a l v e l o c i t y normal to a s u r f a c e where simultaneous heat, mass and momentum t r a n s f e r are t a k i n g p l a c e a l t e r s the magnitude of the t r a n s f e r c o e f f i c i e n t s and a f f e c t s the s t a b i l i t y of the flow due to the d i s t o r t i o n of the temperature, c o n c e n t r a t i o n and v e l o c i t y p r o f i l e s . In g e n e r a l , mass t r a n s f e r from the s u r f a c e t o the mainstream de-c r e a s e s the t r a n s f e r c o e f f i c i e n t s and d e s t a b i l i z e s the flow (28a).. The o r g a n i c chemicals used i n t h i s study were chosen such that they would e x h i b i t very low vapor p r e s s u r e s i n the temperature range of i n t e r e s t . Thus the mass t r a n s f e r r a t e s are s u f f i c i e n t l y s m a l l t o ensure that the 'blowing v e l o c i t y ' w i l l have l i t t l e or no e f f e c t on the wet-bulb heat and mass t r a n s f e r c o e f f i c i e n t s . 70 CHAPTER FOUR APPARATUS AND EXPERIMENTAL PROCEDURE I. EQUIPMENT DESCRIPTION 1. Wind t u n n e l D e t a i l s of the wind t u n n e l components are p r e s e n t e d i n Appendix Two. a. Main duct A schematic of the wind t u n n e l i s shown i n F i g u r e 7. The four i n c h square duct i s f a b r i c a t e d from number f o u r t e e n gauge g a l v a n i z e d i r o n and i s i n s u l a t e d w i t h a s i n g l e l a y e r of one i n c h f i b e r g l a s s i n s u l a t i o n . The duct s e c t i o n s are s e a l e d t o -gether with rubber gaskets to e l i m i n a t e n o i s e and v i b r a t i o n s . The. g r a d u a l l y c o n v e r g i n g s e c t i o n from the heater to the wind t u n n e l , and the s i x f e e t of t u n n e l before the sample s e c t i o n , are c o n s i d e r e d to be adequate to e l i m i n a t e momentum and thermal e n t r y e f f e c t s . It i s assumed that the v e l o c i t y and thermal pro-f i l e s are at l e a s t symmetrical, i f not f u l l y developed, at the sample s e c t i o n . If the c h a r a c t e r i s t i c diameter of the duct i s chosen to be four times the h y d r a u l i c r a d i u s , then D e c ) = 4.0 inches FIGURE 7. WIND TUNNEL 72 'entrance ^ 18 D eq L, e x i t = 12 D eq b. Sample s e c t i o n The sample s e c t i o n i s four inches square to c o i n c i d e with the duct, and s i x inches long. The sample s e c t i o n i s f a b r i c a -t e d from one-half inch t h i c k brass as shown i n F i g u r e 8. Three-e i g h t h s i n c h h o l e s i n the sample s e c t i o n top and s i d e can be used f o r i n s e r t i o n of temperature or t u r b u l e n c e s e n s i n g probes. Under o r d i n a r y o p e r a t i n g c o n d i t i o n s these h o l e s are plugged. As i n d i c a t e d i n F i g u r e 8, an a d d i t i o n a l hole i s p r o v i d e d f o r i n -s t a l l a t i o n of the thermocouple to measure the f r e e stream tem-p e r a t u r e . The top of the sample s e c t i o n can be completely removed f o r i n s t a l l a t i o n of t u r b u l e n c e promoters, and the sample can be i n s t a l l e d i n t o the sample s e c t i o n top by means of the four inch c i r c u l a r t r a n s p a r e n t l i d . The l i d i s t r a n s p a r e n t to enable the sample to be seen d u r i n g the course of a run. Samples are h e l d by a one-eighth inch aluminum pi p e , which i n t u r n i s supported by a t h r e e - e i g h t h inch swagelok f i t t i n g i n the l i d center as shown i n F i g u r e 9. During the course of a run, and when b r i n g i n g the appara-tus to steady s t a t e , the sample s e c t i o n Is covered by a s i n g l e l a y e r of one i n c h f i b e r g l a s s i n s u l a t i o n . FIGURE 8. SAMPLE SECTION IN WIND TUNNEL 74 THERMOCOUPLES '/8", ALUMINUM PIPE 3/", SWAGELOK FITTING r - r SAMPLE SECTION LID (Plastic) SCALE- I"= 2" SAMPLE GAS FLOW FIGURE 9. SAMPLE SECTION LID AND SAMPLE SUPPORT IN THE WIND TUNNEL 75 2. Gas r e c i r c u l a t i n g apparatus D e t a i l s of the gas r e c i r c u l a t i n g apparatus f a b r i c a t i o n and components are p r e s e n t e d i n Appendix Two. a. Main tank and duct The s t e e l tank and duct are presented i n F i g u r e 10. The two f l a n g e s on the blower end of the tank p r o v i d e a means of s e r v i c i n g the blower motor. These f l a n g e r s are t i g h t l y gas-ket e d with one-quarter inch t h i c k rubber. The main four i n c h type K copper duct has an i n t e r n a l d i -ameter of 3.86 inches. Both the tank and d u c t i n g are covered with one i n c h f i b e r g l a s s i n s u l a t i o n . Under the i n s u l a t i o n , a one-half inch copper tube i s wrapped t i g h t l y around the main tank at s i x inch s p a c i n g s . T h i s tube serves as a stream j a c k e t to heat the gas i n the tank i n a d d i t i o n to the i n t e r n a l steam • c o i l . To c a l c u l a t e the e n t r y and e x i t length p i p i n g requirements, the sample s e c t i o n can be c o n s i d e r e d as a flow n o z z l e having a diameter r a t i o of 1.0. A c c o r d i n g to the A. S. M. E. Power Test Codes (5) f o r the p i p i n g combination under c o n s i d e r a t i o n , the e n t r y and e x i t l e n g t h s r e q u i r e d are 18 and 4 pipe diameters r e s p e c t i v e l y . The apparatus has the dimensions ^entrance = 17 D L e x i t - 6 D 1 P R E S S U R E S A M P L E SECTION | " i 2 0 N P T ^ (Thermo, no. 6 ) 12' - 2 4 ' W A T E R - * * _ n / S T E A M W ^ J ^ T O S T E A M N \ T R A P POWER TO B L O W E R 8 4 " f D U C T - TYPE K COPPER PIPE ( 3 . 8 6 " ID ) M A T E R I A L S | T A N K . S T E E L ( 2 4 " ID ) FIGURE 10. GAS RECIRCULATING APPARATUS CD 77 Thus, the v e l o c i t y p r o f i l e s h ould be f u l l y developed at the sample s e c t i o n . b.. Sample s e c t i o n F i g u r e s 11 and 12 show the d e t a i l s of the sample s e c t i o n . The two t h r e e - e i g h t h inch threaded ho'i*?s i n the sample s e c t i o n l i d serve to support a p i t o t tube or hot-wire anemometer sen-s i n g element or samples i n a manner s i m i l a r t o that d i s c u s s e d f o r the wind t u n n e l sample s e c t i o n . An e x c e l l e n t s e a l between the sample s e c t i o n and the sam-p l e s e c t i o n l i d i s o b t a i n e d by u s i n g a gasket f a b r i c a t e d from two l a y e r s of d e n t a l rubber covered with Dow s i l i c o n e high vac-uum grease. 3. Thermocouple i n s t a l l a t i o n The thermocouples that are used to measure the wet-bulb temperatures are c a r e f u l l y l o c a t e d i n the mould before c a s t i n g the wet-bulb. (See Appendix One - Sample Moulding) Thermo-couples that are to be used to measure the l o c a l wet-bulb tem-p e r a t u r e s are p l a c e d l e s s than o n e - s i x t e e n t h of an inch from the sample s u r f a c e . The thermocouple that measures the macroscopic wet-bulb temperature i n a c y l i n d e r or a sphere i s l o c a t e d at the sample geometric c e n t e r . 4. Hot-wire anemometer and a u x i l i a r y components L o c a l v e l o c i t i e s and t u r b u l e n t i n t e n s i t i e s were measured i n the f l u i d s by a DISA model 55A01 constant temperature hot-wire anemometer with a type 55A22 probe. FIGURE 11. SAMPLE SECTION OF THE GAS RECIRCULATING APPARATUS FIGURE 12. SAMPLE SECTION LID FOR THE GAS RECIRCULATING APPARATUS 80 A d d i t i o n a l e l e c t r o n i c components manufactured by the P h i l b r i c k Company were used i n c o n j u n c t i o n with the hot-wire anemometer to measure the E u l e r i a n i n t e g r a l time s c a l e of. t u r -bulence. The e l e c t r o n i c output was r e c o r d e d on a Hewlett Packard model 7100 B r e c o r d e r and the c i r c u i t r y was checked with a type 502 A T e k t r o n i x o s c i l l o s c o p e . F u l l d e t a i l s of the of the above mentioned equipment can be found i n Appendix Two (Turbulence Measurements) and i n Appendix Three (Anemometer Hot-Wire C a l i b r a t i o n s ) . 81 I I . EXPERIMENTAL OPERATING PROCEDURES 1. Psychrometric measurement's i n the wind t u n n e l a. Run p r e p a r a t i o n (1) Adjust the a i r i n l e t v a l v e u n t i l the d e s i r e d pressure drop i s r e c o r d e d a c r o s s the o r i f i c e . (2) Adjust the duct e x i t area u n t i l the p r e s s u r e i n the sample s e c t i o n i s approximately one atmosphere-(3) Switch on the Dewcel and heater , a d j u s t i n g the heater to the d e s i r e d load. (4) A l l o w the equipment t o operate u n t i l steady s t a t e i s ' o b -t a i n e d . (5) While the equipment i s r e a c h i n g steady s t a t e , mould a wet-bulb a c c o r d i n g t o the technique d e s c r i b e d i n Appendix Two. b. Run e x e c u t i o n At the i n i t i a t i o n and t e r m i n a t i o n of each experimental run the f o l l o w i n g parameters are noted: - a i r i n l e t p r e s s u r e (to o r i f i c e ) - a i r i n l e t temperature (to o r i f i c e ) - o r i f i c e p r e ssure drop - a i r i n l e t dew point - room temperature - room pr e s s u r e - sample s e c t i o n pressure 82 - Dewcel flow r a t e - Dewcel p r e s s u r e - sample m a t e r i a l and dimensions - sample l o c a t i o n and d e t a i l s - thermocouple l o c a t i o n s - thermocouple gauge i n sample - step s w i t c h no. 1 s e t t i n g - step switch no. 2 s e t t i n g - t r ansformer no. 1 s e t t i n g - t r ansformer no. 2 s e t t i n g D u r i n g the course of an experiment the f o l l o w i n g parame-t e r s are noted at 5 minute i n t e r v a l s : - duct a i r temperature - wet-bulb temperature d e p r e s s i o n s A run i s t e r m i n a t e d when the s u r f a c e thermocouples become exposed. T h i s c o n d i t i o n can be n o t i c e d v i s u a l l y or can be r e -c o g n i z e d when the wet-bulb temperature that i s b eing r e c o r d e d has a sudden i n c r e a s e and s t a r t s to approach the dry-bulb tem-p e r a t u r e . In the course of 'moving' from the sample i n t e r i o r t o the f r e e stream, the thermocouple t i p must c r o s s the sample s u r f a c e Thus, from a p l o t of wet-bulb temperature d e p r e s s i o n versus time, the t r u e ' s u r f a c e ' or l o c a l wet-bulb temperature depres-s i o n can be i n t e r p o l a t e d f o r a set thermocouple s i z e , as i s shown i n F i g u r e 31. Heat c o n d u c t i o n along each thermocouple i n the sample w i l l 83 i n f l u e n c e the temperature r e a d i n g s . Since the temperature g r a d i e n t along the wire i s unknown, i t i s i m p o s s i b l e to accu-r a t e l y c a l c u l a t e the extent of t h i s e f f e c t . To e l i m i n a t e t h i s e r r o r , s i m i l a r experiments were conducted with three d i f f e r e n t thermocouple wire s i z e s used i n the samples. The wet-bulb tem-pe r a t u r e d e p r e s s i o n o b t a i n e d f o r each thermocouple s i z e and f o r any f i x e d e x p e r i m e n t a l c o n d i t i o n can then be e x t r a p o l a t e d to zero thermocouple t h i c k n e s s . By t h i s technique i t i s p o s s i b l e to o b t a i n a c c u r a t e e s t i m a t e s of the s u r f a c e temperature of a wet-bulb. At the end of a run the heater must be allowed to c o o l be-f o r e the a i r supply i s terminated. 2. Psychrometric measurements i n the gas r e c i r c u l a t i n g apparatus a. Run p r e p a r a t i o n (1) P l a c e the d e s i r e d flow c o n s t r i c t o r i n the duct and clamp the sample s e c t i o n l i d t i g h t l y i n p l a c e . (2) Evacuate the tank to a p r e s s u r e l e v e l of one mm. of mer-cury a b s o l u t e . (3) F i l l the tank with the working f l u i d t o atmospheric p r e s -sure. (4) Re-evacuate the tank. (5) R e f i l l the tank with working f l u i d t o a pressure of p l u s one cm. of mercury gauge. (6) Turn on the steam and gas blower and a l l o w to operate un-t i l steady s t a t e i s o b t a i n e d . 84 (7) While the apparatus i s r e a c h i n g steady s t a t e , mould a sam-p l e a c c o r d i n g to the procedure d e s c r i b e d i n Appendix Two. b. Run e x e c u t i o n At the i n i t i a t i o n and t e r m i n a t i o n of each experiment the f o l l o w i n g parameters are noted: - room a i r humidity - room temperature - room p r e s s u r e - gas p r e s s u r e i n duct - sample m a t e r i a l and dimensions - thermocouple l o c a t i o n s i n sample - thermocouple s i z e i n sample Durdng the course of an experiment the f o l l o w i n g parame-t e r s are noted at 5 minute i n t e r v a l s : - sample s e c t i o n o u t s i d e w a l l temperature - duct gas temperature - wet-bulb temperature d e p r e s s i o n s A run i s t e r m i n a t e d a f t e r a maximum of t h i r t y minutes s i n c e the r e c i r c u l a t i n g gas approaches s a t u r a t i o n with sublimate as time passes. T h i r t y minutes i s more than s u f f i c i e n t time t o e l i m i n a t e heat source or s i n k e f f e c t s from w i t h i n the s o l i d p a r t i c l e . S i nce the c o n c e n t r a t i o n of sublimate i n the f r e e stream i n c r e a s e s with time, the wet-bulb temperature d e p r e s s i o n w i l l decrease with time. Thus e x t r a p o l a t i o n of wet-bulb data t o 85 zero thermocouple t h i c k n e s s must be performed on•measurements taken a f t e r equal time i n t e r v a l s from the b e g i n n i n g of the r e s p e c t i v e experiments, and on the samples h a v i n g i d e n t i c a l dimensions. From the knowledge of the t o t a l time a sample has been s u b l i m a t i n g , i t i s p o s s i b l e t o c a l c u l a t e the gas f r e e stream c o n c e n t r a t i o n of the sublimate at the time of measurement, and make a p p r o p r i a t e c o r r e c t i o n s i n the ps y c h r o m e t r i c a n a l y s i s (See Appendix F i v e - Sample C a l c u l a t i o n s ) . When a run t e r m i n a t e s , the sample i s removed from the ap-para t u s and the ev a c u a t i o n procedure i s i n i t i a t e d t o prepare f o r the next experiment. 3. Psychrometric measurements i n a quiescent atmosphere The a i r i n a l a b o r a t o r y oven having i n t e r n a l dimensions of 36 x 48 x 28 inches i s allowed t o heat and r e c i r c u l a t e u n t i l a d e s i r e d temperature l e v e l i s reached. The heater i s switched o f f and the warm a i r i s allowed to r e c i r c u l a t e f o r one hour t o b r i n g the i n s i d e temperature of the i n s u l a t e d w a l l s as c l o s e as p o s s i b l e t o the a i r temperature. While the oven i s coming t o steady s t a t e , a sample i s moulded with a c e n t r a l l y l o c a t e d 30 gauge thermocouple. Before i n i t i a t i n g the experiment the oven blower i s sw i t c h e d o f f * The sample i s hung by means of the thermocouple at a cen-t r a l l o c a t i o n i n the oven. The thermocouple l e a d s out of the oven under a gasket i n the oven door to the potentiometer. Instead of u s i n g an i c e bath as a r e f e r e n c e temperature f o r the thermocouple e.m.f. measurement, the r e f e r e n c e thermocouple i s 86 p l a c e d i n the oven a few inches from the sample. Thus, the potentiometer i s measuring the wet-bulb temperature d e p r e s s i o n d i r e c t l y . The bulk a i r temperature i n the oven i s noted from . a 0-212°F. Cenco thermometer hanging i n the oven. The sample i s l e f t i n the oven u n t i l the wet-bulb tempera-t u r e d e p r e s s i o n reaches a steady valut,. Then the sample i s r e -moved and the oven a e r a t e d f o r f u r t h e r experiments. 4. Psychrometric measurements f o r the a i r - w a t e r system A one-half i n c h diameter c y l i n d e r of porous paper, was f a b r i c a t e d around a one-eighth i n c h diameter aluminum pipe. Three 40 gauge thermocouple ends are bent up from the c y l i n d e r bottom so that the t i p s are h e l d at v a r i o u s angular p o s i t i o n s on the c y l i n d e r s u r f a c e . The paper c y l i n d e r and thermocouple are t i g h t l y wrapped with a c l o t h . The o u t s i d e diameter of the c y l i n d e r i s approx-i m a t e l y 0.5 i n c h e s . The c y l i n d e r i s soaked i n d i s t i l l e d water f o r s e v e r a l hours to ensure s a t u r a t i o n . Then the l o c a l wet-bulb tempera-t u r e s f o r a i r - w a t e r are measured i n a manner s i m i l a r to that d e s c r i b e d f o r s o l i d wet-bulbs i n the wind t u n n e l . The use of f i n e thermocouples w i l l e l i m i n a t e most of the heat c o n d u c t i o n along the thermocouples. 87 CHAPTER FIVE PRESENTATION AND ANALYSIS OF RESULTS L VELOCITY, TURBULENCE INTENSITY AND SCALE OF TURBULENCE 1 MEASUREMENTS 1. Both ducts without t u r b u l e n c e promoters V e l o c i t y p r o f i l e s f o r t h r e e a i r mass flow r a t e s i n the wind t u n n e l are shown i n F i g u r e 13, In the c e n t r a l r e g i o n of the duct, where psyc h r o m e t r i c measurements are conducted, the p r o f i l e s are e s s e n t i a l l y f l a t . Thus one can j u s t i f y the use of the ce n t e r t u n n e l v e l o c i t y i n the c a l c u l a t i o n of p a r t i c l e Reynolds numbers. The t u r b u l e n c e i n t e n s i t y and s c a l e p r o f i l e s i n the wind t u n n e l c o r r e s p o n d i n g t o the v e l o c i t y l e v e l s shown i n F i g u r e 13 are p r e s e n t e d i n F i g u r e 14. It can be seen t h a t the t u r b u l e n c e i n t e n s i t y i s a minimum at the duct center f o r each v e l o c i t y l e v e l . The t u r b u l e n c e i n t e n s i t y f o r each p r o f i l e appears t o decrease s l i g h t l y with i n c r e a s i n g a i r v e l o c i t y . The p r o f i l e of the l o n g i t u d i n a l s c a l e of t u r b u l e n c e i s shown t o be very u n d u l a t i n g , but symmetric about the duct a x i s . As the f r e e stream v e l o c i t y i n c r e a s e s , the s c a l e of t u r b u l e n c e s i m i l a r l y i n c r e a s e s . F i g u r e 15 p r e s e n t s v e r t i c a l p r o f i l e s of v e l o c i t y and t u r b u -lence i n t e n s i t y i n the wind t u n n e l when no t u r b u l e n c e promoters are p r e s e n t . It can be seen that the t u r b u l e n c e i n t e n s i t y l e v e l DISTANCE FROM TOP OF WIND TUNNEL (Inch) CO - . — • • •- — ' . _ oo FIGURE 13. VERTICAL VELOCITY PROFILES THROUGH CENTER OF WIND TUNNEL -89 18 - X 1.4 16 ~ 1.3 14 V 1,2 12 - I.I 10-t 8 oo z LU 5 6h (D 2 A A .-'JB e A i.o 0.9 u c - 0.8 LU < o CO 0.7 I U M (ft/sec) INTENSITY S C A L E 6.3 CD A 11.8 e V 17.4 O X - 0.6 -0.5 I 2 3 DISTANCE FROM T O P O F WIND T U N N E L (Inch) FIGURE 14. VERTICAL PROFILES OF INTENSITY AND SCALE OF TURBULENCE THROUGH THE CENTER OF THE WIND TUNNEL, WITH NO TURBULENCE PROMOTERS \ \ \ n - — n- - - -« ' '•! / V \ / / N \ v / / \ V / / \ CD CD / \ \ / ' \ \ • / e <D^ © \ \ ' \ • / . DISTANCE FROM DUCT SIDE (Inch) V E L O C I T Y INTENSITY 1 O 0 2 X © ! I 1 _ J I i 7 5 U> z UJ 0 I 2 3 4 DISTANCE F R O M T O P OF DUCT (Inch) FIGURE 15. VERTICAL PROFILES OF VELOCITY AND INTENSITY OF TURBULENCE IN THE WIND TUNNEL, WITH NO TURBULENCE PROMOTERS i n the square duct i s symmetric about the center s i n c e the v a l u e s measured one and t h r e e inches from the duct top and two inches from the s i d e w a l l s are both s i m i l a r t o the value measured two inches from the duct top and one inch from the s i d e w a l l . The v e r t i c a l v e l o c i t y p r o f i l e measured one i n c h l'rom the duct w a l l i s v i r t u a l l y unchanged from the v e r t i c a l v e l o c i t y p r o f i l e measured through the wind t u n n e l c e n t e r , It was of i n t e r e s t t o know how the f r e e stream parameters changed with i n c r e a s e d temperature f o r a constant mass flow r a t e through the wind t u n n e l . The r e s u l t s p l o t t e d i n F i g u r e 16 show t h a t the c e n t e r v e l o c i t y i n c r e a s e s i n a manner t h a t i s p r e d i c t e d by the i d e a l gas law. Some e r r o r may be i n c o r p o r a t e d i n t o the h i g h temperature measurements s i n c e the d i m e n s i o n l e s s form of the c a l i b r a t i o n curve f o r the hot-wire was determined at room temperature. At high a i r temperatures the r e l a t i v e amount of heat l o s t t o the hot-wire supports may have changed from the room temperature v a l u e . The t u r b u l e n c e i n t e n s i t y at the duct c e n t e r i n c r e a s e s s l i g h t l y as the f r e e stream temperature i n -c r e a s e s . The s c a l e of t u r b u l e n c e i n c r e a s e s with i n c r e a s e d temperature. Thermal c o n v e c t i o n e f f e c t s i n c r e a s e i n s i d e the duct as the a i r temperature i n c r e a s e s . It would be expected t h a t the s c a l e of t u r b u l e n c e would be more a f f e c t e d by thermal c o n v e c t i o n than the i n t e n s i t y of t u r b u l e n c e . T h i s c o n c l u s i o n seems t o be v e r i f i e d i n F i g u r e 16. F i g u r e 17 p r e s e n t s the v e l o c i t y p r o f i l e s measured i n the gas r e c i r c u l a t i n g apparatus c i r c u l a r duct. P r o f i l e s are p r e -s e n t e d f o r both helium and a i r flow. S i n c e the v i s c o s i t y of 54^ 48 42 36 U ft, 30 /sec 24 18 12 o e NON C O N S T R I C T E D D U C T o o A O AIR ( P I T O T T U B E ) © HELIUM (PITOT TUBE) A AIR ( A N E M O M E T E R ) A AIR ( A N E M O M E T E R - OUT OF C A L I B R A T I O N R A N G E OF HOT WIRE) 0 6 CONSTRICTOR * G CONSTRICTOR # 2 0 _L 0.259 0.518 0.770 FIGURE 1 7 . VELOCITY PROFILES FOR AIR AND HELIUM IN THE GAS RECIRCULATING APPARATUS 94 helium i s almost equal to that f o r a i r , the blower c a p a c i t y i s almost the same f o r both gases. At low v e l o c i t i e s the helium v e l o c i t y p r o f i l e s are more p a r a b o l i c i n shape than the p r o f i l e s f o r a i r . T h i s behavior i s expected s i n c e f o r the same v e l o c i t y , the Reynolds number of helium i s o n l y 14 percent that f o r a i r . E x c e l l e n t agreement was o b t a i n e d between the v e l o c i t y measurements of the a i r with the p i t o t tube and with the hot-wire anemometer where the hot-wire was w i t h i n i t s range of c a l i b r a t i o n . The t u r b u l e n c e i n t e n s i t y p r o f i l e s i n the gas r e c i r c u l a t i n g apparatus duct are shown i n F i g u r e 18. As i s expected, they again show a minimum at the duct c e n t e r . The c e n t e r i n t e n s i t y i n c r e a s e s as the f r e e stream v e l o c i t y decreases, and f o r " t h e same f r e e stream v e l o c i t y , the helium e x h i b i t s a higher t u r b u -lence i n t e n s i t y than a i r . These r e s u l t s can be i n t e r p r e t e d as a Reynolds number e f f e c t ; t h a t i s , the f r e e stream t u r b u l e n c e i n t e n s i t y i s i n c r e a s i n g as the Reynolds number decreases. The temperature of the gas i n the gas r e c i r c u l a t i n g appa-r a t u s i s shown to have no e f f e c t on the duct c e n t e r v e l o c i t y i n F i g u r e 19. Thus, the v e l o c i t y p r o f i l e s , p r e s e n t e d i n F i g u r e 17 can be expected to be r e p r e s e n t a t i v e of the v e l o c i t y p r o f i l e s found i n the duct f o r any temperature l e v e l of helium or a i r . The center l i n e t u r b u l e n c e i n t e n s i t y measurements made i n both of the ducts with no t u r b u l e n c e promoters are compared t o p r e v i o u s measurements i n F i g u r e 20. Data from the present study compare f a v o u r a b l y with p r e v i o u s measurements. The 95 10 8 oo z UJ I-z r 9 + e V 0.259 0 e O 8 , HELIUM CD - ~ 21 , HELIUM 0 - ~ 51 , HELIUM A - ~ 7.5, AIR + - ~ 21 , AIR V - ~ 54, AIR I 0.518 'R* 0.770 FIGURE 18, TURBULENCE INTENSITY PROFILES FOR AIR AND HELIUM IN THE GAS RECIRCULATION APPARATUS ( AIR - NO CONSTRICTION ) 56 55 M M f kec 54 53 52 1 1 1 1 1 1. 1 1 _o o o o _ 1 1 1 1 1 1 1 1 70 80 90 100 110 120 TEMPERATURE °F 130 140 150 160 FIGURE 19. EFFECT OF AIR TEMPERATURE ON THE CAPACITY OF THE BLOWER IN THE GAS RECIRCULATION APPARATUS 97 —I 1 1 1 I MM ' 1 1 1—I—I.I Ml— - -i —I T—i—i i i i SYMBOLS CD - TOWNSEND ( 1 2 2 ) O, - LAUFER ( 7 1 ) , 1 0 " PiPE S - SOO, IHRIG, KOUH (115 ) , 3" SQUARE DUCT O ' - LAVENDER, PEI ( 7 2 ) , 4" SQUARE DUCT — - SANDBORN CORRELATION (109) , 4" PIPE A - AUTHOR , 4" SQUARE DUCT 1 fAIR V - AUTHOR , 4 " PIPE J X - A U T H O R , 4 " PIPE} HELIUM Q NOTE I F O R T H E AUTHOR& D A T A , Re d IS BASED ON U M 0.10-FIGURE 20. COMPARISON OF PREVIOUS FREE STREAM TURBULENCE INTENSITY DATA WITH EXPERIMENTAL MEASUREMENTS 98 measurements of Lavender and P e i (72) e x h i b i t a much stronger dependence on the duct Reynolds number than do the other d a t a 0 The measurements f o r helium flow agree with both the author's and p r e v i o u s data f o r a i r flow through ducts. In g e n e r a l i t can be concluded from F i g u r e 20 t h a t the f r e e stream c e n t e r l i n e t u r b u l e n c e i n t e n s i t y i n a pipe or duct decreases with i n c r e a s i n g Reynolds number. At low v a l u e s of the Reynolds number, when the gas flow through the duct i s laminar, the t u r b u l e n c e i n t e n s i t y would be expected to be zero. Thus a t u r b u l e n c e i n t e n s i t y versus Reynolds number c o r r e l a t i o n i s expected to go through a maximum at some c r i t i c a l Reynolds number a f t e r t u r b u l e n t flow i s i n i t i a t e d . B u t t h i s c r i t i c a l Reynolds number f o r gas flow i s s e n s i t i v e t o flow c o n d i t i o n s and the duct geometry. Thus no g e n e r a l c o r r e l a t i o n can be d e r i v e d from F i g u r e 20, s i n c e s e v e r a l duct shapes and e x p e r i -mental c o n d i t i o n s are being r e p r e s e n t e d . The i n t e g r a l s c a l e of t u r b u l e n c e as measured by the author when t h e r e are no t u r b u l e n c e promoters i n the ducts i s compared to p r e v i o u s data i n F i g u r e 21. The f r e e stream l o n g i t u d i n a l s c a l e s of t u r b u l e n c e r e p o r t e d by Soo and co-workers (115) and Lavender and P e i (72) have been o b t a i n e d from the i n t e g r a l of the measured c o r r e l a t i o n c o e f f i c i e n t s . (Eq. (30)) The data of the author have been o b t a i n e d by the s i n g l e hot-wire method proposed by Townsend (121). Soo and co-workers conclude from t h e i r data that the f r e e stream s c a l e of t u r b u l e n c e i n c r e a s e s as the bulk v e l o c i t y i n c r e a s e s . But F i g u r e 21 does not show any d e f i n i t e c o r r e l a t i o n 99 SYMBOLS 0 .20 -0.15 O - SOO, IHRIG, KOUH (115 ) , 3" SQUARE DUCT 0 - LAVENDER , PEI (72) , 4" SQUARE DUCT A V X X - AUTHOR , 4 " PIPE - A U T H O R , 4 " S Q U A R E DUCT - AUTHOR, 4 " PIPE} HELIUM } ui 0.10 _i < o CO 0.05 6 S e e e o o o o G . 8 e < P 20 4 0 60 80 100 B U L K V E L O C I T Y ( f t / s e c ) FIGURE 21. COMPARISON OF PREVIOUS FREE STREAM SCALE OF TURBULENCE DATA WITH EXPERIMENTAL MEASUREMENTS 100 between the s c a l e of t u r b u l e n c e and the bulk v e l o c i t y . There i s no p r e c i s e reason known to e x p l a i n the l a c k of c o r r e l a t i o n except tuat the i n t e g r a l s c a l e of t u r b u l e n c e may be a f u n c t i o n of the apparatus i n which i t i s measured. The s c a l e of t u r b u l e n c e can be i n t e r p r e t e d as being p r o p o r t i o n a l to the eddy mixing l e n g t h . In homogeneous flow, the eddy mixing l e n g t h approaches the duct diameter as the v e l o c i t y decreases toward laminar flow c o n d i t i o n s . Thus the measurements at low Reynolds numbers would be expected t o e x h i b i t l a r g e r s c a l e s of t u r b u l e n c e than the measurements at higher Reynolds numbers. However, F i g u r e 21 seems to g i v e o n l y a rough i n d i c a t i o n of such a t r e n d . The l a r g e s t s c a l e s are measured f o r the helium system, which has a Reynolds number only 14 percent of that f o r the a i r system at the same v e l o c i t y . 2. Downstream of screens i n the wind t u n n e l F i g u r e 22 shows, t y p i c a l v e r t i c a l p r o f i l e s of the a i r v e l o c i t y , t u r b u l e n c e i n t e n s i t y and s c a l e of t u r b u l e n c e down-stream of a one-half i n c h mesh s c r e e n i n the wind t u n n e l . It can be seen that the v e l o c i t y and t u r b u l e n c e i n t e n s i t y p r o f i l e s are f l a t t e r than the c o r r e s p o n d i n g p r o f i l e s measured i n the empty duct. The s c a l e of t u r b u l e n c e does not vary from the ce n t e r l i n e value i n t h i s case as much as i t d i d f o r the empty duct measurements. As i s expected, the s c a l e of t u r b u l e n c e has a value which i s c h a r a c t e r i s t i c of the s c r e e n mesh s i z e . The t u r b u l e n c e i n the c e n t r a l r e g i o n of the duct* s h o u l d be i s o t r o p i c , s i n c e the measurements were conducted at a d i s t a n c e e „ - - - -o- - — o -X - e ~ @_-^-^ e x X X= 10" ^'=0.5" O - VELOCITY 0 - INTENSITY X - SCALE I I I . 2 3 DISTANCE FROM TOP OF DUCT (Inch) - 0.9 5 4 si >-CO ~71 -2 I - 0 - 4 4 0.8 0.7 "§ LU _ J O.S o CO 0.5 URE 22. CENTRAL VERTICAL PROFILES OF VELOCITY, INTENSITY AND SCALE OF TURBULENCE BEHIND A SCREEN IN THE WIND TUNNEL 102 20 M' downstream of the screen (135). It s h o u l d a l s o be noted that the t u r b u l e n c e i n t e n s i t y has almost decayed to the value that would be measured i f no t u r b u l e n c e promoter were i n the duct „ F i g u r e 23 examines the e f f e c t of v e l o c i t y on the change of t u r b u l e n c e i n t e n s i t y and s c a l e behird. a. one-half inch mesh screen i n the wind t u n n e l . As i s suggested by T a y l o r (118), the r e s u l t s have been c o r r e l a t e d by the parameter X/M'. As f o r the f i n d i n g s of Dryden (26) and Raithby and E c k e r t (103), the t u r b u l e n c e i n t e n s i t y downstream of the s c r e e n i n the wind t u n n e l does not show any dependence on the f r e e stream v e l o c i t y . R a i t h b y and E c k e r t (103) f i n d t h a t the scales of t u r b u l e n c e measured behind woven wire screens show a v e l o c i t y dependence, while measurements behind p e r f o r a t e d p l a t e s are independent of v e l o c i t y . C l e a r l y , from F i g u r e 23, the s c a l e of t u r b u l e n c e i s a f u n c t i o n of the f r e e stream v e l o c i t y and d i s t a n c e down-stream of the woven wire s c r e e n used by the present author. The s c a l e of t u r b u l e n c e appears to i n c r e a s e l i n e a r l y with the parameter X/M' f o r each of the three a i r v e l o c i t i e s examined. In F i g u r e 16 the s c a l e of t u r b u l e n c e i n the empty duct i s shown to i n c r e a s e with i n c r e a s i n g v e l o c i t y . A s i m i l a r t r e n d i s noted i n F i g u r e 23. The decay of t u r b u l e n c e behind d i f f e r e n t screens i n the wind t u n n e l at a f i x e d v e l o c i t y i s c o r r e l a t e d i n F i g u r e 24 with the parameter X/d as i s suggested by Dryden (25) and B a t c h e l o r and Townsend (6). The r e s u l t s show a s l i g h t i n c r e a s e of t u r b u l e n c e i n t e n s i t y f o r a f i x e d X/d r a t i o as the mesh s i z e of 103 16 k I4L-U M ( f t /sec) I N T E N S I T Y S C A L E \ 5.8 A V 1 A 11.4 O O i 17.4 X 0 / \ / \ / I2f- » ? I'Or- * \ i >-co 9 ' / V UJ H Z 8 6^ x , / / tf / 6 h m ee \ / e / X 1.6 - M 1.2 11.0 2 u ! 0.8 40.6 UJ _j < o CO 0.4 0.2 10 20 30 40 50 60 70 FIGURE 23. EFFECT OF VELOCITY ON CHANGE OF TURBULENCE INTENSITY AND SCALE BEHIND A 0.5 INCH MESH SCREEN IN THE WIND TUNNEL A ,6 O M ' ( lnch) d(lnch) 14 U 0 0 _ 0 .029 0.018 12 10 <£ 8 O - 0.125 0 . 0 7 2 A - 0 - 2 5 0.120 X X - 0 . 5 0 0 .177 (D - 0 . 6 2 5 0.192 AIR F L O W 0.122 lb/sec CD t D B ~ 7 5 ° F X 0 A * X J I I L I i 0 2 0 4 0 6 0 8 0 100 120 140 1 6 0 1 8 0 ' ' 5 5 5 - / / §L x FIGURE 24. DECAY OF TURBULENCE.BEHIND SCREENS IN THE WIND TUNNEL 105 the s c r e e n i n c r e a s e s . A s i m i l a r r e s u l t was o b t a i n e d by Van Der Hegge Z i j n e n (135). A s c r e e n i n a duct can f u n c t i o n e i t h e r as a t u r b u l e n c e promoter or as a 'flow calmer'. Measurements at X/d = 555 behind a f i n e 0.029 inch mesh scree n i n d i c a t e a t u r b u l e n c e i n t e n s i t y of 2.07 percent at the wind t u n n e l c e n t e r . T h i s value i s approximately 50 percent of that measured i n the empty duct. The s c a l e of t u r b u l e n c e downstream of screens i n the wind t u n n e l i s c o r r e l a t e d with the parameter X/d, as i s suggested by Dryden (25) and B a t c h e l o r and Townsend (6), i n F i g u r e 25. The r a t i o L x /d i n c r e a s e s i n a l i n e a r f a s h i o n f o r any one s c r e e n as the group X/d i n c r e a s e s . The s l o p e of the L x / d versus X/d curve decreases as the mesh s i z e of the screens i n c r e a s e s . A s i m i l a r t r e n d i s shown i n the data of Van Der Hegge Z i j n e n (135). Thus, when the s c r e e n mesh s i z e a p p r o x i -mates the empty duct s c a l e of t u r b u l e n c e , the s c a l e of t u r b u -lence w i l l change on l y s l i g h t l y downstream of the s c r e e n . But when the s c r e e n mesh s i z e i s much s m a l l e r than the empty duct s c a l e of t u r b u l e n c e , the s c a l e w i l l change r a p i d l y downstream of the s c r e e n t o r e e s t a b l i s h i t s e l f t o a new f r e e stream v a l u e . Most measurements of t u r b u l e n c e i n t e n s i t y and s c a l e behind screens or p e r f o r a t e d p l a t e s are conducted i n very l a r g e ducts, as compared to the 4 inch square duct and 4 inch pipe s t u d i e d here. Only Simmons' t u r b u l e n c e decay data as p r e s e n t e d i n a paper by T a y l o r (118) are f o r a 4 i n c h p i p e . Thus a comparison of the decay of t u r b u l e n c e i n t e n s i t y behind a 106 d 18 - M'(lnch) d(lnch) e - 0.029 0.018 16 o - 0.125 0.072 - 0.25 0.120 14 X - 0.50 0.177 CD - 0.625 0.192 12 A R FLOW 0.122 lb/sec V ~ 7 5 ° F . 8-O' "0|- A" ^ , x • p' e ' x ^ / A ' 0 i L i x 20 40 60 80 100 120 !40 160 180 200 */d: FIGURE 25. SCALE OF TURBULENCE BEHIND SCREENS IN THE WIND TUNNEL 107 s c r e e n i s made between the present data and the measurements of Simmons i n F i g u r e 26. The parameter U/u ( i s shown to be a l i n e a r f u n c t i o n of X/d. For vhe same v e l o c i t y l e v e l , the sl o p e of the U/u", versus X/d curve i s g r e a t e r f o r the data of Simmons than f o r the present data f o r a 0.5 inch s c r e e n . The s o l i d a r i t y r a t i o of the present author's s c r e e n i s higher than t h a t of the screen used by Simmons. The r e s u l t s from a 0.25 inch mesh screen having n e a r l y the same s o l i d a r i t y r a t i o as that used by Simmons produced a s l o p e s i m i l a r t o that o b t a i n e d by Simmons. The va l u e s of U/u, o b t a i n e d f o r the 0.25 i n c h mesh scr e e n are higher than the r e s u l t s of Simmons because of the d i f f e r e n t f r e e stream v e l o c i t i e s b e i n g c o n s i d e r e d . The same o b s e r v a t i o n i s made from F i g u r e 24. Thus from F i g u r e 24 and F i g u r e 26 the t u r b u l e n c e i n t e n s i t y behind a g r i d i s a f u n c t i o n of the s o l i d a r i t y r a t i o of the g r i d . A s i m i l a r r e s u l t has been found by s e v e r a l authors (103, 25, 135). 3. Downstream and upstream of a s i n g l e c y l i n d e r i n the wind t u n n e l The presence of a s i n g l e c y l i n d e r i n the wind t u n n e l w i l l a l t e r the t u r b u l e n c e i n t e n s i t y and a i r v e l o c i t y i n the v i c i n i t y of the c y l i n d e r . The a i r v e l o c i t y and t u r b u l e n c e i n t e n s i t y at the wind t u n n e l center l i n e upstream of a c y l i n d e r are p r e s e n t e d i n F i g u r e 27. There are no scre e n s i n the duct upstream of the c y l i n d e r . The t u r b u l e n c e i n t e n s i t y near the i i i i 1 1 U b ( f t / s e c ) l M'(in) 1 M'/ d • i % OPEN 13' o - SIMMONS (118 ) , 4" PIPE 5 0.41 2 .00 4 4 . 5 2.25 A - AUTHOR 4" SQUARE DUCT 1 7 0.625 3.25 58.5 1.71 e - AUTHOR, 4" SQUARE DUCT 5 0.50 2.83 54.5 1.84 X - AUTHOR, 4" SQUARE DUCT 17 0.25 2.08 45.7 Z. 19 2 0 -16 -12 8 -12 16 24 30 36 42 48 5 4 FIGURE 26. COMPARISON OF PREVIOUS DATA ON DECAY OF TURBULENCE BEHIND SCREENS WITH EXPERIMENTAL MEASUREMENTS o oo AIR FLOW O HOT WIRE COPPER CYLINDER DIAM. 0.5 " LENGTH 2" f r o n t s t a g n a t i o n p o i n t of the c y l i n d e r i s i n c r e a s e d by approximately 50 percent above the f r e e stream v a l u e . Tne d i s t u r b a n c e caused by the 0.5 inch diameter c y l i n d e r i s ma n i f e s t e d up to 2 inches upstream of the c y l i n d e r . Thus the t u r b u l e n c e i n t e n s i t y t h a t the c y l i n d e r s u r f a c e e x p e r i e n c e s i s not equal t o the f r e e stream value. P o s s i b l y the i n c r e a s e i n the value of \T /U i s due to the decrease of U as one approaches the f r o n t s t a g n a t i o n p o i n t of the c y l i n d e r . The a i r v e l o c i t y and t u r b u l e n c e i n t e n s i t y at the wind t u n n e l center l i n e downstream of a c y l i n d e r are pre s e n t e d i n F i g u r e 28. The c y l i n d e r Reynolds number i s about 4500 and thus the c y l i n d e r wake can be c o n s i d e r e d as being f u l l y developed. The t u r b u l e n c e i n t e n s i t y one i n c h downstream of the c y l i n d e r i s 64 per c e n t . Thus the c y l i n d e r has c r e a t e d a high l e v e l o f t u r b u l e n c e i n the a i r stream. The v e l o c i t y d i s t u r -bance p e r s i s t s f o r at l e a s t t h r e e inches from the r e a r stagna-t i o n p o i n t . The t u r b u l e n c e i n t e n s i t y has not r e t u r n e d t o the empty duct value at a d i s t a n c e of f i v e inches from the r e a r s t a g n a t i o n p o i n t . The experiments p r e s e n t e d i n F i g u r e 27 and F i g u r e 28 are d u p l i c a t e d i n F i g u r e 29 and F i g u r e 30 r e s p e c t i v e l y , except that t h e r e i s a s c r e e n i n the wind t u n n e l upstream of the c y l i n d e r i n both cases. In F i g u r e 29, the c y l i n d e r has no e f f e c t on the a i r t u r b u l e n c e i n t e n s i t y and v e l o c i t y u n t i l the d i s t a n c e from the f r o n t s t a g n a t i o n p o i n t i s 1.5 and 0.5 inches r e s p e c t i v e l y . Near the f r o n t s t a g n a t i o n p o i n t , t u r b u -lence i n t e n s i t i e s up to 46 percent are measured. Thus the I N T E N S I T Y (%) I T T 6 0 -10-0" FIGURE JL 0.5 _ L 1.0 -4 0.5" i AIR FLOW L S C R E E N HOT WIRE C O P P E R CYLINDER DIAM. 0.5" L E N G T H 2" VALUE FOR NO CYLINDER o — IN DUCT NO CYLINDER _ o 18 16 ~ o 14 v. 12 ^ 10 8 6 4 o o _l LU > 1.5 3.0 3.5 4 .0 4.5 2.0 2.5 L (Inch) 29. TURBULENCE INTENSITY UPSTREAM OF A CYLINDER IN THE CENTER OF THE WIND TUNNEL FOR CONDITIONS OF HIGH FREE STREAM INTENSITY to 7 0 60 50 -j - 40 CO z Ul I-z - 30 20 10 FLOW SCREEN COPPER CYLINDER DIAM. 0.5 " L E N G T H 2" HOT WIRE VALUE FOR NO CYLINDER IN DUCT J_ _L JL NO CYLINDER _ L 18 16 14 S 10 12 -10 ^ H8 o o _i U J -4 - 2 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 L ( Inch ) FIGURE 30. TURBULENCE INTENSITY DOWNSTREAM OF A CYLINDER IN THE CENTER OF THE WIND TUNNEL FOR CONDITIONS OF HIGH FREE STREAM INTENSITY i— 1 00 114 l e v e l of the f r e e stream t u r b u l e n c e i n t e n s i t y seems to have an e f f e c t on the t u r b u l e n c e i n t e n s i t y near the f r o n t stagna-t i o n p o i n t of a c y l i n d e r . At high l e v e l s of f r e e stream . t u r b u l e n c e i n t e n s i t y the v e l o c i t y d i s t u r b a n c e due to the c y l i n d e r i s not n o t i c e a b l e as f a r upstream of the c y l i n d e r as i t i s f o r the low t u r b u l e n c e i n t e n s i t y c a s e " ( F i g u r e 27). From F i g u r e 30 and F i g u r e 28 i t can be seen that the t u r b u l e n c e i n t e n s i t y i n the wake near the r e a r s t a g n a t i o n p o i n t i n c r e a s e s with i n c r e a s e d upstream t u r b u l e n c e i n t e n s i t y . The l e n g t h s of the v e l o c i t y d i s t u r b a n c e downstream of the c y l i n d e r are equal f o r the c o n d i t i o n of high upstream t u r b u -lence i n t e n s i t y t o that f o r the low upstream t u r b u l e n c e i n t e n s i t y measurements. T h i s i m p l i e s that the length of a wake behind a c y l i n d e r i s not a l t e r e d by i n c r e a s i n g the f r e e stream t u r b u l e n c e i n t e n s i t y . 115 II„ PSYCHROMETRIC MEASUREMENTS IN THE DUCTS WITH NO TURBULENCE PROMOTERS Wet-lulb temperature d e p r e s s i o n s at the f r o n t and r e a r s t a g n a t i o n p o i n t s (+90° and -90° r e s p e c t i v e l y ) and at the center of a s u b l i m a t i n g naphthalene sphere are r e c o r d e d as a f u n c t i o n of time i n F i g u r e 31. A f t e r 15 minutes the sample has reached a steady s t a t e c o n d i t i o n with the s u r r o u n d i n g a i r . Then, a f t e r 35 minutes, the wet-bulb temperature d e p r e s s i o n at the f r o n t -s t a g n a t i o n p o i n t of the sphere suddenly decreases, thus i n d i c a -t i n g t h at the thermocouple measuring the temperature at the f r o n t s t a g n a t i o n p o i n t has become exposed t o the a i r stream. At t h i s p o i n t the run i s terminated. The v a l u e s of the wet-bulb temperature d e p r e s s i o n s measured under steady s t a t e c o n d i t i o n s are averaged t o y i e l d a mean value of the wet-bulb temperature d e p r e s s i o n t o be used i n subsequent c a l c u l a t i o n s . Data f o r a l l experiments conducted i n the wind t u n n e l are pre s e n t e d i n T a b l e VI - 2. The average steady s t a t e wet-bulb temperature d e p r e s s i o n s f o r each run are p r e s e n t e d i n Table VI -3. Wet-bulb temperature measurements o b t a i n e d i n the gas r e -c i r c u l a t i n g apparatus are pre s e n t e d i n Tab l e VI - 7. The e f f e c t of the measuring thermocouple wire diameter on the wet-bulb temperature d e p r e s s i o n at the f r o n t s t a g n a t i o n p o i n t of a s u b l i m i n g naphthalene c y l i n d e r i s p r e s e n t e d i n F i g u r e 32. The c y l i n d e r diameter has no e f f e c t on the measured wet-bulb temperatures. At high a i r temperatures, the wet-bulb temperature d e p r e s s i o n i n c r e a s e s as the s i z e of the thermocouple 116 10 8 u. 7 o ~ 6 < o RUN # 6 6 A I R - N A P H T H A L E N E S P H E R E , D p = 1.0" A I R F L O W R A T E 0.122 \b/s*c t D B = 144 « F 4 0 G A U G E T H E R M O C O U P L E S e o (D 9 0 ° - C E N T E R — + 9 0 ° S T E A D Y S T A T E V A L U E 0 O - 0 - -e-O (D -CD- -<r> -e-•o--<D -e- H •o 10 15 20 TIME (Minutes) 25 30 35 FIGURE 31. TRANSIENT WET-BULB TEMPERATURE DEPRESSION CURVES (MEASURED IN THE WIND TUNNEL) 117 170 160 150-140 - ° 130 120 110 1 0 0 -o / / O .0' ' /CD o 0// ///CD o / / o / / © /Si i e A I R - N A P H T H A L E N E CYLINDER, L = 2" POSITION + 9 0 ° AIR FLOW R A T E 0.122 lb /sec D p (Inch) / e / / P R e p THERMOCOUPLE GAUGE 0.375 0.519 100 ° F 3140 4 3 5 0 I 7 0 ° F 2 9 0 0 4 0 0 0 2 4 0 o 30 e 40 CD 0 2 4 6 8 10 12 At. (°F) FIGURE 32. EFFECT OF THERMOCOUPLE DIAMETER ON THE LOCAL WET-BULB TEMPERATURE DEPRESSION AT THE FRONT STAGNATION POINT OF A NAPHTHALENE CYLINDER (MEASURED IN THE WIND TUNNEL) 118 wire decreases. T h i s can be e x p l a i n e d by the f.act that the amount of heat being t r a n s f e r r e d i n t o the wet-bulb through the thermocouple w i l l decrease as the c r o s s s e c t i o n a l area of the thermocouple wire decreases. I f the temperature g r a d i e n t along the wire i s known, the amount of heat being t r a n s f e r r e d i n t o the c y l i n d e r c o u l d be c a l c u l a t e d from F o u r i e r ' s Law. But sine-7* t h i s g r a d i e n t i s not known, i t i s necessary t o devise another method to c o r r e c t f o r the thermocouple wire heat conduction. T h i s aspect of the a n a l y s i s w i l l be d e a l t with l a t e r i n the d i s c u s s i o n . The dashed l i n e s i n F i g u r e 32 i n d i c a t e the best 'freehand' l i n e s c o r r e l a t i n g the a i r temperature with the wet-bulb temperature d e p r e s s i o n f o r d i f f e r e n t thermocouple wire s i z e s . The mass flow r a t e through the wind t u n n e l was f i x e d f o r each set of experiments. The data were c u r v e - f i t t e d 'by eye' so that any i n t e r p o l a t e d r e s u l t s would not be p r e j u d i c e d by the form of a c u r v e - f i t e q u a t i o n . The macroscopic wet-bulb temperature d e p r e s s i o n e x h i b i t e d at the g e o m e t r i c a l center of a naphthalene c y l i n d e r i s presented i n F i g u r e 33. These r e s u l t s are compared with the measurements of B e d i n g f i e l d and Drew (8). The measurements of the author were taken i n a lower Reynolds number range than those of B e d i n g f i e l d and Drew, but i f the c o n c l u s i o n of B e d i n g f i e l d and Drew that the Reynolds number has no e f f e c t on the wet-bulb temperature f o r p u r e l y f o r c e d c o n v e c t i o n heat and mass t r a n s f e r i s v a l i d , then the r e s u l t s s h o u l d be comparable. The measuring thermocouple wire s i z e i s not s t a t e d f o r the data of B e d i n g f i e l d and Drew but t h e i r r e s u l t s compare w e l l w i t h the data of the 1 1 9 1 7 0 1 6 0 1 5 0 1 4 0 1 3 0 1 2 0 1 1 0 1 0 0 ,o 'X ' o' 0 sx / y x 0/ X r BEDINGFIELD, DREW ( 8 ) AIR-NAPHTHALENE CYLINDER; Dp=0.375", 0.72 " i L = 3.5"14.5"6.75" Re p = 4360 - 12220 THERMOCOUPLE SIZE UNKNOWN / / x © O / / ,(D / / 0 AIR-NAPHTHALENE CYLINDER, L = 2.0" POSITION CENTER AIR FLOW RATE 0. 122 lb/sec e / / 9 9 THERMOCOUPLE GAUGE — I D P (Inch ) 0.375 0519 10 0 ° F 3140 4 350 170-F 2900 4 0 0 0 24 0 o 30 e 40 e CD-1 0 1 2 A t , ( ° F ) FIGURE 33. COMPARISON OF PREVIOUS MACROSCOPIC WET-BULB TEMPERA-TURE DEPRESSION DATA FOR NAPHTHALENE CYLINDERS WITH EXPERIMENTAL WIND TUNNEL MEASUREMENTS FOR CYLINDERS, AND THE EFFECT OF THERMOCOUPLE DIAMETER ON THIS MEASUREMENT 120 author. V a r i a t i o n s between the two s e t s of data c o u l d be a r e s u l t of i n c r e a s e d r a d i a t i o n heat t r a n s f e r at lower Reynolds numbers. The r e s u l t s show that the wet-bulb temperature d e p r e s s i o n i s not a f u n c t i o n of the c y l i n d e r diameter. The same c o n c l u s i o n was found f o r a l l subsequent wet-bulbs. F i g u r e 34 shows the wet-bulb temperature depressions measured at the r e a r s t a g n a t i o n p o i n t of a naphthalene c y l i n d e r . The wet-bulb temperature d e p r e s s i o n again depends on the s i z e of measuring thermocouple wire. Since the m e l t i n g p o i n t of naphthalene i s 176° F., no experiments were conducted where the f r e e stream a i r temperature was above 175° F.. At high f r e e stream temperatures the mass t r a n s f e r from the wet-bulb was high enough to deform the sample s l i g h t l y before the t e r m i n a t i o n of a run. But s i n c e the wet-bulb temperature i s not a f u n c t i o n of the wet-bulb diameter, t h i s s l i g h t change of shape was not con-s i d e r e d t o e f f e c t the measurements. P a r t i a l l y s u b l i m a t e d c y l i n d r i c a l wet-bulbs e x h i b i t s e p a r a t i o n l i n e s which approximate the l i n e s where the a t t a c h e d boundary l a y e r flow becomes wake flow. T h i s s e p a r a t i o n l i n e u s u a l l y o c c u r r e d approximately 90 degrees from the f r o n t s t a g n a t i o n p o i n t when no t u r b u l e n c e promoters were i n the duct upstream of the sample. Wet-bulb temperature d e p r e s s i o n s measured at the f r o n t and r e a r s t a g n a t i o n p o i n t s and at the center of s u b l i m a t i n g naphtha-lene spheres are p r e s e n t e d i n F i g u r e 35, F i g u r e 37 and F i g u r e 36 r e s p e c t i v e l y . The sphere diameter again does not appear to have any e f f e c t on the wet-bulb temperature d e p r e s s i o n . For each p o s i t i o n i n the sphere, the measured wet-bulb temperature de-p r e s s i o n i s a f u n c t i o n of the thermocouple wire diameter, as 121 170 160 150 140 !30 1 2 0 110 100 -P 0/ p . 4 ' 'CD / / V 0',' 1 // /// • AIR-NAPHTHALENE CYLINDER, L= 2" POSITION - 9 0 ° / e / . o' / O 6 AIR FLOW RATE 0.122 lb/sec (Inch) 0.375 0.519 100° F 3140 4350 Re D P I 7 0 ° F 2900 4000 24 0 O THERMOCOUPLE 30 0 GAUGE 1 40 9 1 <D 6 8 10 12 At, ( °F) FIGURE 34. EFFECT OF THERMOCOUPLE DIAMETER ON THE LOCAL WET-BULB TEMPERATURE DEPRESSION AT "THE REAR STAGNATION POINT OF A NAPHTHALENE CYLINDER (MEASURED IN THE WIND TUNNEL) 122 170 160 150 140 130 120 110 100 9' CD' e 0 / / / / / / / / 4 . 11 II 11 ir 00 AIR-NAPHTHALENE SPHERE POSITION + 9 0 ° AIRFLOW RATE 0.122 lb/sec Dp(lnch) Re p THERMOCOUPLE GAUGE o 0.75 1.0 IOO°F 6300 8 4 0 0 I 7 0 ° F 5800 7 7 3 0 24 o 30 St e 40 0 8 12 0 2 4 6 A t , ( 0 F ) FIGURE 35. EFFECT OF THERMOCOUPLE DIAMETER ON THE LOCAL WET-BULB TEMPERATURE DEPRESSION AT THE FRONT STAGNATION POINT OF A NAPHTHALENE SPHERE (MEASURED IN THE WIND TUNNEL) 123 I70h O leok s y 1501-140}- Q/ 0 u. o 130)- // AIR-NAPHTHALENE ' SPHERE POSITION CENTER / AIRFLOW RATE 0.122 lb/sec I20h / d) Dp (Inch) / / HOh- % Re p i THERMOCOUPLE IOOU CD / GAUGE 0.75 1.0 IOO°F 6300 8 4 0 0 170° F 5800 7 7 3 0 24 0 O 3 0 e 4 0 CD At, ( ° F FIGURE 36. EFFECT OF THERMOCOUPLE DIAMETER ON THE MACROSCOPIC WET-BULB TEMPERATURE DEPRESSION OF A NAPHTHALENE SPHERE (MEASURED IN THE WIND TUNNEL) 124 170 160 -150-140 • s o S i ' 130-~°I20-110-100-i/ /y i e AIR-NAPHTHALENE SPHERE POSITION - 9 0 ° AIR FLOW RATE 0. 122 lb /sec THERMOCOUPLE GAUGE DP (Inch) 0.75 1.0 IOO°F 6300 8400 170 °F 5800 7730 24 0 0 30 e 40 CD 4 6 At, C F ) 10 12 FIGURE 37. EFFECT OF THERMOCOUPLE DIAMETER ON THE LOCAL WET-BULB TEMPERATURE DEPRESSION AT THE REAR STAGNATION POINT OF A NAPHTHALENE SPHERE (MEASURED IN THE WIND TUNNEL) 125 was found f o r c y l i n d e r s . At the sphere f r o n t s t a g n a t i o n p o i n t i t i s d i f f i c u l t t o d i s c e r n between the r e s u l t s o b t a i n e d with 30 and 40 gauge thermocouples. Thus only one l i n e f o r both s e t s of r e s u l t s i s shown i n F i g u r e 35. P a r t i a l l y s u b l i m a t e d s p h e r i c a l wet-bulbs e x h i b i t s e p a r a t i o n r i n g s which i n d i c a t e the l o c a t i o n of minimum mass t r a n s f e r on the s p h e r i c a l s u r f a c e , and approximate the t r a n s i t i o n c i r c l e from an a t t a c h e d laminar boundary l a y e r flow t o wake flow. T h i s r i n g o c c u r r e d v i s u a l l y at approximately 90 degrees from the • forward s t a g n a t i o n p o i n t f o r the Reynolds numbers concerned i n F i g u r e s 35, 36 and 37. A comparison of p r e v i o u s macroscopic wet-bulb temperature d e p r e s s i o n data f o r p-dichlorobenzene c y l i n d e r s with experimen-t a l wind t u n n e l measurements f o r c y l i n d e r s i s p r e s e n t e d i n F i g u r e 38, The author's measurements taken with 24 and 30 gauge thermocouples i n the wet-bulbs are seen to bracket the data of B e d i n g f i e l d and Drew (8). For the a i r p-dichlorobenzene system the wet-bulb temperature i s again shown to be a f u n c t i o n of measuring thermocouple wire diameter, as was found f o r measurements on the a i r - n a p h t h a l e n e system. The 40 gauge thermocouples have a wire diameter of 0.003 inc h e s . These f i n e thermocouples tended t o break e a s i l y when new samples were moulded i f they were not handled with extreme care. Thus i t was d e s i r e d t o e s t a b l i s h a g e n e r a l i z e d r e l a t i o n -s h i p between the wet-bulb temperature d e p r e s s i o n s measured with t h r e e d i f f e r e n t thermocouple wire s i z e s , so t h a t a c curate e x t r a -p o l a t i o n s c o u l d be made from measurements taken with j u s t two 126 130 120-110 100 90 80-70 60 / / / / / / A / BEDINGFIELD,DREW ( 8 ) AIR- P-DICHLOROBENZENE CYLINDER j Dp =0.375", 0.72" L = 3.5",4.5" Re. 5370 - 16300 THERMOCOUPLE SIZE UNKNOWN // // // AIR -P-DICHLOROBENZENE CYLINDER , L - 2 " POSITION CENTER AIR FLOW RATE 0.122 lb /sec Dp = 0.519 (Inch) 7 0 ° F 4530 120 °F 4230 THERMOCOUPLE 24 O GAUGE 30 0 _L 0 2 4 6 8 10 At, CF) 12 FIGURE 38. COMPARISON OF PREVIOUS MACROSCOPIC WET-BULB TEMPERATURE DATA FOR P-DICHLOROBENZENE CYLINDERS WITH EXPERIMENTAL WIND TUNNEL MEASUREMENTS FOR CYLINDERS, AND THE EFFECT OF THERMOCOUPLE DIAMETER ON THIS MEASUREMENT 127 thermocouple s i z e s . Then i t would not be necessary to do any f u r t h e r e x p e r i m e n t a t i o n with the troublesome 40 gauge thermo-c o u p l e s . It was proposed to e x t r a p o l a t e the measured wet-bulb tem-pe r a t u r e d e p r e s s i o n s to the h y p o t h e t i c a l case of a thermo-couple which has a wire diameter of zero i n c h e s , and thus c o r r e c t f o r heat conduction e f f e c t s i n t o the wet-bulbs. Downing (23) has found that the wet-bulb temperature of drops suspended on thermocouple t i p s i s a l i n e a r f u n c t i o n of the diameter of the measuring thermocouple wire. By a t r i a l and e r r o r method, the wet-bulb temperature data o b t a i n e d by the author was found to be a l i n e a r f u n c t i o n of the measuring thermo-couple wire diameter r a i s e d to the t h r e e - h a l v e s power. Such a r e l a t i o n s h i p e x i s t s f o r both l o c a l and macroscopic wet-bulb temperature measurements, as i s shown i n F i g u r e s 39, 40, 41 and 42. The data f o r these p l o t s are taken from the best curves drawn to the data i n F i g u r e s 32, 33, 34, 35, 36 and 37. A s i m i l a r form of r e l a t i o n s h i p e x i s t s between the wet-bulb tempera-t u r e and thermocouple wire diameter at the forward and r e a r s t a g n a t i o n p o i n t s and at the center of c y l i n d e r s and spheres. It i s evident from the p l o t s that the wet-bulb temperature de-p r e s s i o n measured at the s u r f a c e o f, or i n s i d e , a sphere i s i d e n t i c a l with that measured at the e q u i v a l e n t p o i n t of a c y l i n d e r . F u r t h e r , from F i g u r e 39, i t can be seen that the wet-bulb temperature which i s measured at the f r o n t s t a g n a t i o n p o i n t of a s p h e r i c a l or c y l i n d r i c a l wet-bulb i s c o n s i d e r a b l y lower than that measured at the r e a r s t a g n a t i o n point of the u. ^10.0 4 0 9 5 or a. UJ a 9.0 UJ a: I-< 8 5 tc UJ CL £ 8.0 CO -j QQ 7.5 UJ 7.0 e o G 6 — ^ 40 GAUGE 30 GAUGE H F 1 1 r — -AIR - NAPHTHALENE (WIND TUNNEL) AIR FLOW RATE 0.122 lb/sec AIR TEMP. 160 °F e - CYLINDER ; D p = 0.519", 0.375" •, L =2" O - SPHERE ; D p = 1.0", 0.75" 90' CENTER ^8 - - - _ 490' 24 GAUGE] _L _L _L _L JL 0.0003 0.0006 0.0009 0.0012 0.0015 0.0018 0.0021 0.0024 0.002 7 0.003 3 /2 * 2 (THERMOCOUPLE DIAMETER)" (Inch) FIGURE. 39. VARIATION OF WET-BULB TEMPERATURE DEPRESSIONS AROUND NAPHTHALENE CYLINDERS AND SPHERES AS MEASURED BY DIFFERENT THERMOCOUPLE SIZES T | | | i ; i : • i : 1 r ll.o 10.0 9.0 8.0 tn UJ or 7.0 a. ui a (E < ui 6.0 Q. s Ixl I-0D _l m I- 5.0 4.0 3 .0 AIR - NAPHTHALENE (WIND TUNNEL) AIR FLOW R A T E 0.122 l b / s e c 9 - C Y L I N D E R ; Dp = 0.519 ", 0 . 3 7 5 " •, L = 2 ' O - S P H E R E ; Dp =1 .0 " , 0 . 7 5 " O ' D B 170 F -8 DB t n B "• 160 F t D B = 150 F -0 "O - - - e- °l I 4 0 ° F _ 40 GAUGE 30 GAUGE 8 24 GAUGE _L 0 0.0006 0.0012 0.0018 (THERMOCOUPLE DIAMETER ) 3 / 2 (Inch) 3' 2 0.0024 0.003 FIGURE .40. CORRECTION OF FRONT STAGNATION POINT WET-BULB TEMPERATURE DEPRESSIONS OF NAPHTHALENE SPHERES AND CYLINDERS TO ZERO THERMOCOUPLE THICKNESS 130 O 11^- e -10 9 -cn ir ° a. hi o tr t-2 7 UJ a ffi 6 AIR - N A PH T H A L EN E (WIND TUNNEL) AIR FLOW R A T E 0.122 lb/sec 0 - CYLINDER; Dp • 0.519",0.375" f L= 2 " O - SPHERE; Dp = l.0",0.75 " e - ~ -t D B - 170 F t D B - 160 F •9 -t D B • 150' F g _ t „ - 140° F 40QAUGE 30 GAUGE 24 GAUGE 0.0006 0.0012 0.0016 0,0024 (THERMOCOUPLE D IAMETER)* 8 (Ineh)** 0.003 FIGURE 41. CORRECTION OF MACROSCOPIC WET-BULB TEMPERATURE DEPRESSIONS OF NAPHTHALENE SPHERES AND' CYLINDERS TO ZERO THERMOCOUPLE THICKNESS 12 10 z o 8 in in Ul CC a. ui o a: 7 < Ul 0. s 03 6 - I o I Ul e 1 1 1 1 —\ r AIR - NAPHTHALENE (WIND TUNNEL) AIR FLOW RATE 0.122 lb/sec 9 - CYLINDERi Dp = 0.519 ",0.375"«, L = 2 O " SPHERE ; Dp= 1.0 ",0.75" t D 8 ° 1 7 0 " F o e t 0 B = 160 ° F - 8 - _ t „ - 150° F t D B » 140' F 40 GAUGE 30 GAUGE 24 GAUGE _ L _l_ 0 0.0006 0.0012 0.0018 0.00 2 4 0.003 (THERMOCOUPLE DIAMETER) 8* ( Inch) 8 * FIGURE 42. CORRECTION OF REAR STAGNATION POINT WET-BULB TEMPERATURE DEPRESSIONS OF NAPHTHALENE SPHERES AND CYLINDERS TO ZERO THERMOCOUPLE THICKNESS'-132 sample. I f the sample f r o n t s t a g n a t i o n p o i n t wet-bulb tempera-t u r e ir. assumed to be c h a r a c t e r i s t i c of a t t a c h e d laminar boun-dary l a y e r f low and i f the r e a r s t a g n a t i o n p o i n t wet-bulb temperature i s assumed t o be s i m i l a r l y c h a r a c t e r i s t i c of s e p a r a t e d wake flow, then, knowing that approximately h a l f of the sphere or c y l i n d e r i s e x p e r i e n c i n g laminar boundary l a y e r flow, and the other h a l f wake flow, i t would be expected that the macroscopic wet-bulb temperature w i l l be the average of the l o c a l wet-bulb temperatures at the f r o n t and r e a r s t a g n a t i o n p o i n t s . Such a r e s u l t i s i n d i c a t e d i n F i g u r e 39. Since there i s a temperature g r a d i e n t a c r o s s the s u b l i m a t i n g c y l i n d r i c a l or s p h e r i c a l wet-bulbs, heat w i l l be conducted from the f r o n t of the p a r t i c l e s t o the r e a r . A d e t a i l e d a n a l y s i s of the heat flow i n a c y l i n d e r i s p r e s e n t e d i n Appendix Four. The a d i a b a t i c s are found t o be e s s e n t i a l l y p a r a l l e l t o the d i r e c t i o n of a i r flow past the c y l i n d e r . The macroscopic wet-bulb temperature measured at the center of a c y l i n d e r i s found t o be equal t o th a t measured on the c y l i n d e r s u r f a c e 90 degrees from the f r o n t s t a g n a t i o n p o i n t . The s l o p e of the curves of wet-bulb temperature d e p r e s s i o n versus thermocouple wire diameter r a i s e d t o the t h r e e - h a l v e s power i n c r e a s e with i n c r e a s i n g f r e e stream temperature. Thus, the e f f e c t of heat c o n d u c t i o n i n t o the samples becomes i n -c r e a s i n g l y important as the f r e e stream temperature i n c r e a s e s . A l l subsequent experiments with s p h e r i c a l and c y l i n d r i c a l wet-bulbs are performed with only the 30 and 24 gauge thermo-cou p l e s . The r e s u l t s are e x t r a p o l a t e d l i n e a r l y to zero thermo-I 3 3 couple wire diameter as i n F i g u r e s 39 to 42. The wet-bulb temperature measurements i n the wind t u n n e l and i n the gas r e -c i r c u l a t i n g apparatus are presented i n T a b l e s VI - 2, VI - 3 . and VI - 7. The e x t r a p o l a t e d values of the wet-bulb tempera-t u r e s measured i n the wind t u n n e l are pre s e n t e d i n Table VI -4, and those measured i n the gas r e c i r c u l a t i n g apparatus — i n Tabl e VI - 9. When measurements are a v a i l a b l e f o r only two thermocouple wire s i z e s , a s t r a i g h t l i n e i s used t o determine the e x t r a p o l a t e d wet-bulb temperature. But when three thermo-couple wire s i z e s have been c o n s i d e r e d , a q u a d r a t i c f i t of the data i s used t o give maximum accuracy, and i n each case the . value of the c o e f f i c i e n t m u l t i p l y i n g the q u a d r a t i c term i s found t o be s m a l l compared to the other c o e f f i c i e n t s . A value of the psychrometric r a t i o and Lewis number ex-ponent may be c a l c u l a t e d from each e x t r a p o l a t e d wet-bulb temperature d e p r e s s i o n . Table VI- 5 and Tab l e VI - 9 l i s t the system p r o p e r t i e s that are used t o c a l c u l a t e these dimension-l e s s parameters. F i g u r e 43 i n d i c a t e s the v a r i a t i o n of the c a l c u l a t e d Lewis number exponent with the f r e e stream a i r temperature at the r e a r s t a g n a t i o n p o i n t of a naphthalene sphere. For spheres and c y l i n d e r s the l o c a l p s ychrometric r a t i o c o r r e c t e d f o r thermal con d u c t i o n a c r o s s the wet-bulb i s c a l c u l a t e d a c c o r d i n g t o Eq. (94) and the l o c a l Lewis number exponent s i m i l a r l y c o r r e c t e d i s c a l c u l a t e d a c c o r d i n g to Eq. (97). The v a l u e s of the l o c a l p s ychrometric r a t i o and Lewis number exponent f o r spheres and c y l i n d e r s u n c o r r e c t e d f o r 0.7 0.6 0.5 0.4 0.3 0.2 0.1 }-0 100 FIGURE 43. o e no O e 120 1 1 1 AIR - N A P H T H A L E N E S P H E R E , Dp = 1.0" POSITION ON S A M P L E - 9 0 ° AIR FLOW R A T E 0.122 l b / s e c o -o-H3" -©-G - MM ( C O R R E C T E D FOR T H E R M A L CONDUCTIVITY OF SOLID W E T B U L B ) - M ( U N C O R R E C T E D FOR T H E R M A L CONDUCTIVITY OF SOLID WET BULB) - B E S T F IT O F MM - BEST FIT OF M 130 f DB 140 ( ° F ) 150 160 170 160 EFFECT OF SOLID WET-BULB THERMAL CONDUCTIVITY ON CALCULATED VALUE OF LEWIS NUMBER EXPONENT (MEASURED IN THE WIND TUNNEL) CO 1.35 thermal c o n d u c t i o n a c r o s s the wet-bulb, and the macroscopic p s y c h r o m e t r i c r a t i o and Lewis number exponent, may be c a l c u -l a t e d from Eq„ (72) and Eq. (82) r e s p e c t i v e l y 0 The Lewis number exponent i s much more s e n s i t i v e t o data v a r i a t i o n s than i s the ps y c h r o m e t r i c r a t i o . When the wet-bulb temperature d e p r e s s i o n i s l a r g e enough to make temperature measurement e r r o r s n e g l i g i b l e , the Lewis number exponent i s shown i n F i g u r e 43 to be i n v a r i a n t as the f r e e stream tempera-t u r e i n c r e a s e s . The psyc h r o m e t r i c r a t i o i s a l s o found t o be' i n v a r i a n t with f r e e stream temperature l e v e l above a c e r t a i n minimum wet-bulb temperature d e p r e s s i o n l e v e l f o r a l l runs. Since k i n e t i c theory leads one t o expect the Lewis number t o vary l i t t l e with temperature, such a c o n c l u s i o n i s t h e o r e t i c a l -l y c o n s i s t e n t with Eq. (105) and Eq. (106). The psychrometric r a t i o s and Lewis number exponents measured f o r a f i x e d mass flow r a t e i n the wind t u n n e l are averaged a c c o r d i n g t o Eq. (V - 7) and Eq. (V - 8)„ F i g u r e 43 a l s o i n d i c a t e s the e f f e c t of heat c o n d u c t i o n from the f r o n t t o the r e a r of the sphere. F i g u r e 44 compares the e x t r a p o l a t e d wet-bulb temperature data f o r a naphthalene sphere with the best f i t curves p r e -d i c t e d from Eq. (94) and Eq. (97). Above a wet-bulb tempera-t u r e d e p r e s s i o n of 3 0 F t h e r e i s an e x c e l l e n t agreement between the f i t t e d and experimental data. For 1 low v a l u e s of the wet-bulb temperature d e p r e s s i o n the r e l a t i v e temperature measure-ment e r r o r s and r a d i a t i o n e r r o r s are l a r g e s t and t h e r e f o r e these data are d i s c a r d e d i n the a n a l y s i s of r e s u l t s . The d e v i a t i o n of f i t t e d p s ychrometric data from the experimental v a l u e s i s p r e s e n t e d i n Table VI - 6. 0 136 FIGURE 44. BEST FIT CORRELATION OF EXTRAPOLATED WET-BULB TEMPERATURE DEPRESSIONS FOR NAPHTHALENE SPHERES (MEASURED IN THE WIND TUNNEL) 137 Average v a l u e s of the psychrometric r a t i o s and Lewis number exponents measured i n the wind t u n n e l are presented i n Table 2. Values of the psychrometric r a t i o s and Lewis number exponents c a l c u l a t e d from measurements i n the gas r e c i r c u l a t i n g apparatus are presented i n Table 3. The l o c a l and macroscopic psychrometric r a t i o s are curve-f i t t e d a c c o r d i n g to Eq. (106) and Eq. (105) r e s p e c t i v e l y . The best f i t parameters f o r each curve, the a p p r o p r i a t e standard d e v i a t i o n s and 95 percent c o n f i d e n c e l i m i t s are presented i n T a b l e 4. It can be seen that the r e s u l t o b t a i n e d f o r the f r o n t s t a g n a t i o n p o i n t of spheres or c y l i n d e r s agrees c l o s e l y with the C h i l t o n - C o l b u r n analogy f o r a t t a c h e d laminar boundary l a y e r flow. The 95 percent c o n f i d e n c e l i m i t s f o r both the present author's data i n c l u d e the l i n e p r e d i c t e d by the C h i l t o n - Colburn analogy, that i s , (B(3 = L e - f - 0 - 6 7 . I f the heat conducted a c r o s s the wet-bulb i s not c o n s i d e r e d , the Lev/is number exponent i s s l i g h t l y higher than f o r the case where i t i s c o n s i d e r e d . The l o c a l p s y c h r o m e t r i c r a t i o at the r e a r s t a g n a t i o n point i n the wake of spheres or c y l i n d e r s v a r i e s with the f i l m Lewis number to the -0.46 power. The c o r r e l a t i o n of the high Reynolds number r e s u l t s above i n d i c a t e a s l i g h t l y d i f f e r e n t value of -0.43. The measurements at the r e a r s t a g n a t i o n p o i n t of a c y l i n d e r or sphere i n d i c a t e that a t r a n s p o r t mechanism such as that suggested by Danckwerts (21) l e a d i n g to a Lev/is number exponent of-0.5, may be c o n t r o l l i n g the heat and mass TABLE 2 AVERAGE PSYCHROMETRIC RATIOS AND LEWIS NUMBER EXPONENTS MEASURED IN THE WIND TUNNEL Gas Sample Shape P o s i -t i o n W S M, M Q MM PP A i r Naphthalene Sphere +90° 0. 122 0. 352 0. 325 0.448 0. 433 A i r Naphthalene C y l i n d e r +90° 0. 122 0. 367 0. 341 0.457 0. 442 A i r p-Dichlorobenzene C y l i n d e r + 90° 0. 122 0. 348 0. 333 0.480 0.472 A i r Naphthalene Sphere Center 0. 122 0.440 0.500 A i r Naphthalene C y l i n d e r Center 0. 122 0.422 0.488 A i r p-Dichlorobenzene C y l i n d e r Center 0.122 0.422 0.523 A i r Naphthalene Sphere o -90 0. 122 0.556 0. 587 0.579 0.601 A i r Naphthalene C y l i n d e r o -90 0.122 0. 549 0. 605 0. 573 0.614 A i r p-Dichlorobenzene C y l i n d e r -90° 0. 122 0.455 0. 461 0. 543 0. 547 A i r Naphthalene C y l i n d e r o +90 0.078 0. 175 0. 040 0. 359 0. 302 A i r p-Dichlorobenzene C y l i n d e r +90° 0.078 0.297 0. 266 0.455 0.439 A i r Naphthalene C y l i n d e r Center 0.078 0. 384 0.466 A i r p-Dichlorobenzene C y l i n d e r Center 0.078 0.431 0. 530 A i r Naphthalene C y l i n d e r -90° 0.078 0.405 0. 434 0.475 0.495 • TABLE 2 (CONTINUED) AVERAGE PSYCHROMETRIC RATIOS AND LEWIS NUMBER EXPONENTS MEASURED IN THE WIND TUNNEL Gas Sample Shape P o s i -t i o n W g . M, M 0 MM P,P0 . PP A i r p-Dichlorobenzene C y l i n d e r - 9 0 ° 0 . 0 7 8 0 . 4 3 1 0 . 4 3 8 6 . 5 2 9 0 . 5 3 3 A i r Naphthalene C y l i n d e r + 9 0 ° 0 . 0 3 9 0 . 2 5 1 0 . 0 7 2 0 . 3 9 6 0 . 3 1 6 A i r p-Dichlorobenzene C y l i n d e r + 9 0 ° 0 . 0 3 9 0 . 3 6 6 0 . 3 5 2 0 . 4 9 0 0 . 4 8 4 A i r Naphthalene C y l i n d e r Center 0 . 0 3 9 0 . 4 9 4 0 . 5 3 5 A i r p-Dichlorobenzene C y l i n d e r Center 0 . 0 3 9 0 . 4 0 1 0 . 5 0 9 A i r Naphthalene C y l i n d e r - 9 0 ° 0 . 0 3 9 0 . 5 5 6 0 . 5 9 3 0 . 5 7 8 0 . 6 0 6 A i r p-Dichlorobenzene C y l i n d e r - 9 0 ° 0 . 0 3 9 0 . 4 5 6 0 . 4 8 4 0 . 5 4 8 0 . 5 6 0 A i r Naphthalene P l a t e X,=l" 0 . 1 2 2 0 . 2 2 0 . 38 A i r Naphthalene P l a t e X,=2" 0. 1 2 2 . 0 . 2 4 0 . 3 9 A i r Naphthalene P l a t e V =oit A j o 0 . 1 2 2 0 . 2 6 0 . 4 0 A i r p-Dichlorobenzene P l a t e X , = 2 " 0 . 1 2 2 0 . 2 9 0 . 4 6 TABLE 3 PSYCHROMETRIC RATIOS AND LEWIS NUMBER EXPONENTS MEASURED IN THE GAS RECIRCULATING APPARATUS Gas Sample Shape P o s i -t i o n R e p R e y M, M Q MM A / 3 0 0/3 A i r d-Camphor Sphere +90* 24100 0. 163 0. 346 A i r d-Camphor Sphere Center 24100 0. 387 0.462 A i r d-Camphor Sphere -90° 24100 0. 579 0.592 Helium d-Camphor Sphere +90° 1225 0.244 0. 258 Helium d-Camphor Sphere Center 1225 0.431 0. 372 Helium d-Camphor Sphere • o -90 1225 0.585 , 0.503 Helium d-Camphor Sphere +90° 450 0. 373 0. 332 Helium d-Camphor Sphere Center 450 0.411 0. 357 Helium d-Camphor Sphere -90° 450 0. 531 0.452 Helium Naphthalene Sphere + 90° 1225 0. 300 0 .289 0.299 0. 292 Helium Naphthalene Sphere + 90° 1225 0. 307 0 . 298 0. 303 0.297 Helium Naphthalene Sphere +90° 1225 0. 324 0 . 320 0. 313 0. 312 Helium Naphthalene Sphere Center 1225 0. 395 0. 356 Helium Naphthalene Sphere Center 1225 0.404 0. 363 TABLE 3 (CONTINUED) PSYCHROMETRIC RATIOS AND LEWIS NUMBER EXPONENTS MEASURED IN THE GAS RECIRCULATING'APPARAT Gas Sample Shape P o s i -t i o n R e p  R e X , M, M 0 MM A A, Helium Naphthalene Sphere Center 1225 0.407 • 0. 365 -Helium Naphthalene Sphere o -90 1225 0.472 0. 487 0.411 0.427 Helium Naphthalene Sphere. • o -90 1225 0.471 0. 479 0.411 0.420 Helium Naphthalene Sphere o -90 1225 0.479 0. 486 0.417 0.425 Helium Naphthalene P l a t e X, =1" 450 0. 349 0. 32 Helium Naphthalene P l a t e X, =2" 2480 0. 380 0. 34 Helium Naphthalene P l a t e X, =2" 900 0.299 0.29 Helium Naphthalene P l a t e X, =2" 900 0. 308 0. 30 Helium Naphthalene P l a t e X. =3" 3720 0. 314 0. 30 Helium Naphthalene P l a t e X, =3" 3720 0. 313 0. 30 Helium Naphthalene P l a t e X, =3" 1350 0.282 0.28 He 1 i'um Naphthalene P l a t e X (=3" 1350 0.231 0.26 TABLE 4 CORRELATION OF PSYCHROMETRIC DATA Note: To c o r r e l a t e N data p o i n t s by the equ a t i o n fi = L e f M o - 1 N I L o g 1 0 / 5 0 x L o g 1 0 L e f Standard D e v i a t i o n I ( L o g 1 0 L e f ) 2 1 N ? ( ^0 " ^0 CALC > N - 1 Standard D e v i a t i o n 95% Confidence L i m i t s = (M. 0-l) ± - i r — V l , 0 , 0 5 g > vLog 1 0Le f) i S i m i l a r forms are used to c a l c u l a t e M-l and MM-1 from data f o r fiand fifi r e s p e c t i v e l y . The author's macroscopic data are c o r r e l a t e d with the p r e v i o u s macroscopic data of B e d i n g f i e l d and Drew, Mark, Lynch and Wilke, Dropkin and A r n o l d . The p r e v i o u s data are t a b u l a t e d by Lynch and Wilke (SO). The c o r r e l a t i o n r e p r e s e n t s data f o r 18 d i f f e r e n t systems. ^ CO TABLE 4 (CONTINUED) CORRELATION OF PSYCHROMETRIC DATA Shape P o s i t i o n i Refer To N C o r r e i a t i o n M 0 - l M - 1 MM- 1 Std. Dev. 95% Confidence L i m i t s C y l i n d e r or Sphere Front St agnat i o n P o i n t F i g u r e 45 F i g u r e 45 3 3 (3 =Le f M - 1 f3{3 = L e f ™ - l - 0 . 6 3 2 - 0 . 6 5 6 0 . 0 0 6 1 0 . 0 0 4 5 - 0 . 6 0 4 : - 0 . 6 6 0 - 0 . 6 3 5 : - 0 . 6 7 7 C y l i n d e r or Sphere Front St agnat i o n Po i n t T a b l e s 2&3 F i g u r e 47 13 10 /3=Le f M-l {3{3 = L e f ™ - l - 0 . 6 5 6 - 0 . 6 9 2 0 .0407 0 . 0 5 6 5 - 0 . 6 i 9 : - 0 . 6 9 3 - 0 . 6 2 8 : - 0 . 7 5 6 . C y l i n d e r or Sphere Rear St agnat i o n Po i n t F i g u r e 45 F i g u r e 45 3 3 /5=Le f M-l / S / ^ L e / ^ 1 - 0 . 4 6 5 - 0 . 4 3 4 0 .0371 0 .0527 - 0 . 2 9 1 : - 0 . 6 3 9 - 0 . 1 8 7 : - 0 . 6 8 1 C y l i n d e r or Sphere Rear St agnat i o n Po i n t T a b l e s 2&3 F i g u r e 47 13 10 , £ = L e f M - l /3/3-Le f M M-l - 0 . 4 5 2 -0o464 0 .0501 0 .0436 - 0 . 4 0 7 : - 0 . 4 9 7 - 0 . 4 1 5 : - 0 . 5 1 3 C y l i n d e r or Sphere Center F i g u r e 45 F i g u r e 48 A l l D a t a 1 3 13 34 / ? 0 = L e f M o - l . / ? 0 = L e f M o - l A>=LefM°-l - 0 . 5 6 1 - 0 . 5 4 3 - 0 . 5 6 7 0 .0065 0 . 0 2 2 2 0 .0690 - 0 . 5 3 0 : - 0 . 5 9 2 - 0 . 5 2 3 : - 0 . 5 6 3 - 0 . 5 2 0 : - 0 . 6 1 4 P l a t e L o c a l F i g u r e 53 12 /5=LefM-' - 0 . 6 6 1 0 .0316 - 0 . 6 3 4 : - 0 . 6 8 9 r—' CO t r a n s f e r p r o c e s s e s i n the wake. T h i s o b s e r v a t i o n i s f u r t h e r supported by the hot-wire anemometer measurements which i n d i c a t e that very high t u r b u l e n c e i n t e n s i t i e s e x i s t i n the wake r e g i o n of a c y l i n d e r . Thus the c o n t r o l l i n g t r a n s f e r may be between ;':he wet-bulb s u r f a c e and the eddies i n the wake, while the t r a n s f e r due to the molecular d i f f u s i o n process may be r e l a t i v e l y n e g l i g i b l e . The macroscopic psychrometric data f o r c y l i n d e r s and spheres agree c l o s e l y with the c o r r e l a t i o n of B e d i n g f i e l d and Drew (8) and the measurements of other authors. The exponents on the Lewis numbers f o r the best c o r r e l a t i o n of the present author's high Reynolds number data and f o r a l l of the author's macroscopic data are -0.56 and -0.54 r e s p e c t i v e l y . The. macroscopic p s y c h r o m e t r i c data of the author, f o r c y l i n d e r s and spheres, together with the macroscopic data o b t a i n e d by p r e v i o u s i n v e s t i g a t o r s f o r c y l i n d e r s , are best c o r r e l a t e d by P = L e f - ° - 5 7 (125) 0 Eq, (125) r e p r e s e n t s data from 18 d i f f e r e n t systems and i n some cases, s e v e r a l d u p l i c a t i o n s of each measurement by d i f f e r e n t authors. It can be seen that t h e r e i s e x c e l l e n t agreement between Eq. (125) and the best f i t of the author's macroscopic data alone. As would be expected, the 95 percent c o n f i d e n c e l i m i t s f o r the c o r r e l a t i o n of the author's data are c l o s e r together 145 than f o r Eq. (125). L o c a l psychrometric r a t i o s measured along a f l a t p l a t e (see T a b l e s 2-4) show e x c e l l e n t agreement with the C h i l t o i . -Colburn analogy. The p l a t e Reynolds number f o r a l l runs was l e s s than that r e q u i r e d f o r a t u r b u l e n t boundary l a y e r . T h e r e f o r e i t i s assumed that a laminar boundary l a y e r e x i s t e d over the p l a t e f o r a l l runs. Thus the r e s u l t s f o r the f r o n t s t a g n a t i o n p o i n t of a c y l i n d e r or sphere and a f l a t p l a t e are i n agreement with the p r e d i c t i o n s of laminar boundary l a y e r theory. It i s of i n t e r e s t t o note that t h e r e are no o v e r l a p p i n g of the 95 percent c o n f i d e n c e areas f o r the c o r r e l a t i o n of the p s y c h r o m e t r i c r a t i o at the f r o n t s t a g n a t i o n p o i n t , center and r e a r s t a g n a t i o n p o i n t of spheres or c y l i n d e r s . Thus i t i s concluded t h a t two d i f f e r e n t and separate phenomena are o c c u r i n g on the s u r f a c e of c y l i n d e r s and spheres i n f o r c e d c o n v e c t i o n . At the f r o n t s t a g n a t i o n p o i n t , the boundary l a y e r flow i s laminar and thus the combined heat and mass t r a n s f e r process depends on the P r a n d t l and Schmidt numbers approximately to the o n e - t h i r d power. At the r e a r s t a g n a t i o n p o i n t where a wake e x i s t s , the P r a n d t l and Schmidt number exponent i s i n c r e a s e d to a value of 0.54. The macroscopic or ce n t e r p s y c h r o m e t r i c r a t i o i s an average of the s u r f a c e v a l u e s . The h i g h e s t Reynolds number psychrometric data o b t a i n e d by the author f o r c y l i n d e r s and spheres i n the wind t u n n e l i s shown i n F i g u r e 45. At a high Reynolds number the d i f f u s i o n a l heat and mass t r a n s f e r i s n e g l i g i b l e compared to the f o r c e d c o n v e c t i o n v a l u e s . The b e s t - f i t l i n e f o r each p o s i t i o n on I 2 3 4 5 6 7 8 9 1 2 _3 4_ 5 6 7 8 9 FIGURE 45. CORRELATION OF LQCAL AND MACROSCOPIC PSYCHROMETRIC RATIOS FOR CYLINDERS AND SPHERES AT HIGH REYNOLDS NUMBERS * • 147 the sample i s i n d i c a t e d . The average v a l u e s of the Lev/is number exponents measured on spheres and c y l i n d e r s and c a l c u l a t e d a c c o r d i n g to Eq, (V-8) are p r e s e n t e d i n F i g u r e 46. The value of MM at the f r o n t s t a g n a t i o n p o i n t agrees c l o s e l y with laminar boundary l a y e r theory and does not appear to depend on the p a r t i c l e Reynolds number. The macroscopic Lewis number exponent has a value of +0.44 and that at the r e a r s t a g n a t i o n p o i n t a value of approximately +0.55, The measured value f o r a i r - p - d i c h l o r o b e n z e n e c y l i n d e r s at the r e a r s t a g n a t i o n p o i n t i s lower than that f o r the a i r - n a p h t h a l e n e spheres and c y l i n d e r s . The author has no ready e x p l a n a t i o n f o r t h i s r e s u l t . The l o c a l p s ychrometric r a t i o s measured at the f r o n t and r e a r s t a g n a t i o n p o i n t s of spheres and c y l i n d e r s i s p r e s e n t e d i n F i g u r e 47. The s c a t t e r i n the data appears to be mainly caused by experimental e r r o r r a t h e r than by any dependence on the p a r t i c l e Reynolds number. The l o c a l data from d-camphor wet-bulbs i s not i n c l u d e d i n the b e s t - f i t c o r r e l a t i o n s i n c e the r e s u l t s are not c o r r e c t e d f o r i n t e r n a l heat t r a n s f e r a c r o s s the wet-bulb, the value of k g f o r d-camphor not being a v a i l a b l e . The l o c a l c o r r e l a t i o n s r e p r e s e n t a p a r t i c l e Reynolds number range of 1225 to 8400. A comparison of p r e v i o u s c o r r e l a t i o n s with the experimental macroscopic psychrometric r a t i o s f o r c y l i n d e r s and spheres i s p r e s e n t e d i n F i g u r e 48. P r e v i o u s macroscopic psychrometric measurements f o r c y l i n d e r s have been conducted i n the range 0.335 < Le <3.76. The measurements of the author i n the helium 148 FLOW M0___ lb/sec M MM AIR-NAPHTHALENE SPHERE 0.122 O © AIR-NAPHTHALENE CYLINDER 0.122 ® X AlR-P-DICHLOROBENZENE CYLINDER 0.122 A V 0.6 X - 9 0 ° (D O 0.5L-0.4 h (D A CENTER O - 0 . 4 4 0 + 9 0 ° O — - 0 . 3 3 e 0.31 1 1 _L 5 6 R e _ ( x I 0 3 ) 8 FIGURE 46. HIGH REYNOLDS NUMBER VALUES OF THE LEWIS NUMBER EXPONENT € WIND TUNNEL M E A S U R E M E N T ( R e p = 1470 - 8 4 0 0 ) NOTE | tr GAS RECIRCULATING A P P A R A T U S M E A S U R E M E N T O- A IR-NAPHTHALENE, S P H E R E , AIR FLOW RATE 0.122 lb/sec e 0 - A IR-NAPHTHALENE, CYLINDER,AIR FLOW RATE 0.122 lb/sec e>V © - AIR-P-DICHLOROBENZENE,CYLINDER, AIR FLOW R A T E 0. 122 lb/sec e>ty 19.- A I R - N A P H T H A L E N E , CYLINDER, AIR FLOW RATE 0.078 lb/sec 0- AIR-NAPHTHALENE , CYLINDER,AIR FLOW RATE 0.039 lb/sec V - AIR-P-DICHLOROBENZENE, CYLINDER, AIR FLOW RATE 0.078 lb/sec '• 'r ' A - AIR-P-DICHLOROBENZENE, CYLINDER.AIR FLOW RATE 0.039 lb/see «'V X - A I R - C A M P H O R , SPWFBF R» = 9 a m r > a> ^ HERE, ep= 24100 © - HELIUM - CAMPHOR, SPHERE, Rep=l225 9 - HELIUM - CAMPHOR, SPHERE, Rep = 450 • - HELIUM-NAPHTHALENE, SPHERE, Rep=l225 6 7 8 9 FIGURE 47. CORRELATION OF LOCAL PSYCHROMETRIC RATIOS AT THE FRONT AND REAR STAGNATION POINTS OF CYLINDERS AND SPHERES 150 .4.0 3.0 2.0 A, 1.0 0.8 0.6 0.5 0.4 0.3 0.2 NOTE « WIND TUNNEL MEASUREMENT (Rep= 1470-8400) cr RECIRCULATING GAS APPARATUS MEASUREMENT AIR-NAPHTHALENE, SPHERE, O e 0 V A X o AIR FLOW RATE 0.122 lb /Sec « AIR-NAPHTHALENE, CYLINDER, AIR FLOW RATE 0.122 lb/sec AIR-P-DICHLOROBENZENE,CYLINDER, AIR FLOW RATE 0.122 lb/sece AIR-NAPHTHALENE, CYLINDER,AIR FLOW RATE 0.078 lb/sec 6 AIR-NAPHTHALENE, CYLINDER, AIR FLOW RATE 0.039 lb/sec « AIR-P-DICHLOROBENZENE, CYLINDER,AIR FLOW RATE 0.078 lb/sec' AiR-P-DICHLOROBENZENE,CYLlNDER,AlR FLOW RATE 0.039 lb/sec * AIR-CAMPHOR , HELIUM - CAMPHOR , HELIUM " CAMPHOR, SPHERE, Re P 24100 SPHERE, Rep = l225 SPHERE, Re„»450 - HELIUM- NAPHTHALENE, SPHERE, Rep = 1225 T — r — i — r ~ r 1 l I i l I r LYNCH "WILKE THEORY ( jH= I.I j„) CHILTON-COLBURN ANALOGY ( Jh = J d ) BEDINGFIELD- DREW (EMPIRICAL) WILKE - WASAN THEORY (Re = I05 ) J L_J_ 0.2 0.3 0.4 0.6 0.8 1.0 Le 2.0 3.0 4.0 6.0 8.0 FIGURE 48. COMPARISON OF PREVIOUS CORRELATIONS WITH EXPERIMENTAL 'MACROSCOPIC PSYCHROMETRIC RATIOS FOR CYLINDERS AND SPHERES 151 system have extended the upper l i m i t t o a Lewis number of 7.2. A l l p r e v i o u s p s y c h r o m e t r i c data, except that f o r freon-12-water (Le^O.335), applj' to systems which have a Lewis number i n the range 0.86< Le< 3.76. Over t h i s narrow range the competing models i n F i g u r e 48 show good agreement. But o u t s i d e of t h i s range the models d i v e r g e . Data o b t a i n e d i n the present helium experiments seem to i n d i c a t e t hat the B e d i n g f i e l d and Drew (8) s e m i e m p i r i c a l model best r e p r e s e n t s the p s y c h r o m e t r i c p r o c e s s . The Wilke and Wasan p r e d i c t i o n l i e s below the helium data w h i l e the Lynch and Wilke theory g i v e s a higher p r e d i c t i o n of the macroscopic psychrometric r a t i o . The r e s u l t s of the author show no c o n s i s t e n t dependence of the macroscopic p s y c h r o m e t r i c r a t i o on the p a r t i c l e Reynolds number f o r the range 450< Re p<24,100. Eq.. (106) p r e d i c t s t h a t t h e r e w i l l be no l o c a l v a r i a t i o n s of the wet-bulb temperature around a c y l i n d r i c a l or s p h e r i c a l wet-bulb when the system Lewis number i s u n i t y . Measurements around a 0.5 inch diameter c y l i n d r i c a l wick from which water i s e v a p o r a t i n g i n t o a i r i n d i c a t e t hat the wet-bulb temperature d e p r e s s i o n at the f r o n t and r e a r s t a g n a t i o n p o i n t s are eq u a l . The measurements are p r e s e n t e d i n F i g u r e 49. L o c a l v a r i a t i o n s of the wet-bulb temperature d e p r e s s i o n on a s u b l i m a t i n g naphthalene p l a t e i n the wind t u n n e l are p r e s e n t e d i n F i g u r e 50. The s u r f a c e temperature measurement on a f l a t p l a t e does not depend on the wire diameter of the measuring thermocouple, presumably because an adequate l e n g t h of wire i s moulded w i t h i n the p l a t e . The wet-bulb temperature d e p r e s s i o n i n c r e a s e s s l i g h t l y with d i s t a n c e from the p l a t e 23 * 2 2 OB a 21 5 1 I i e 3 o o O - t D B =78.6°F,HUMIDITY=l9% 1 © - t D B =78.2°F, HUMIDITY = 21% L e = 0 . 8 6 R e D « 3 0 0 0 0 A N G L E FROM FRONT STAGNATION POINT (Radians) FIGURE 49. LOCAL WET-BULB TEMPERATURE DEPRESSION MEASUREMENTS FOR WATER EVAPORATING FROM A 0.5-INCH DIAMETER CYLINDRICAL WICK IN THE WIND TUNNEL 153 170 160 150 . 140 £130 m a 120 no 100 / / / / / ' />'/ / / / / / / pea) / / / /// / / / / AIR-NAPHTHALENE LENGTH 4" PLATE {wiDTH 2" / / / A/V / / ' / / / / / /: / ' 11 i i 1 i 1 THICKNESS 0.375" AIR FLOW RATE 0.122 lb/sec X, (Inch) 1 2 3 100 °F 8418 16840 2SZ70 Re „ 1 I70°F 7805 15620 25440 THERMOCOUPLE 24 o e <D GAUGE 30 A V X 0 10 12 At, CF] FIGURE 50. LOCAL WET-BULB TEMPERATURE DEPRESSIONS ON'A NAPHTHALENE PLATE (MEASURED IN THE WIND TUNNEL, AIR FLOW 0.122 l b . / s e c . ) l e a d i n g edge at a constant a i r v e l o c i t y . The i n c r e a s e i n the l o c a l wet-bulb temperature d e p r e s s i o n between curves shown i n F i g u r e 50 r e p r e s e n t s a change i n the l o c a l p sychrometric r a t i o of 2.5 p e r c e n t . The l o c a l p s y c h r o m e t r i c r a t i o s measured on the p l a t e are independent of the s u r r o u n d i n g f r e e stream temperature when the r a d i a t i o n part of the t o t a l heat t r a n s f e r t o the wet-bulb i s l e s s than 25 p e r c e n t . F u r t h e r f l a t p l a t e experiments were conducted i n the wind t u n n e l at lower a i r v e l o c i t i e s . The r a d i a t i o n component of the heat t r a n s f e r was g r e a t e r than the f o r c e d c o n v e c t i o n component and thus the r e s u l t s are not analyzed i n any f u r t h e r d e t a i l . ' The measured l o c a l wet-bulb temperature d e p r e s s i o n i s shown i n F i g u r e 51 to not depend on the diameter of the thermocouple wire. The wet-bulb temperature d e p r e s s i o n on the p l a t e s u r f a c e i n c r e a s e s with d i s t a n c e from the p l a t e l e a d i n g edge. The temperature g r a d i e n t along the p l a t e s u r f a c e appears to be l i n e a r at both f r e e stream v e l o c i t y l e v e l s , but the g r a d i e n t appears to i n c r e a s e with . deer e a s i n g a i r v e l o c i t y . T h i s o b s e r v a t i o n may be due to the g r e a t e r r a d i a t i o n e f f e c t s at the low a i r v e l o c i t i e s . Measurements of the l o c a l wet-bulb temperature depressions on a p-dichlorobenzene p l a t e i n the wind t u n n e l are p r e s e n t e d i n F i g u r e 52. The thermocouple wire diameter again does not appear to i n f l u e n c e the measurements, The p-dichlorobenzene p l a t e does not e x h i b i t s i m i l a r l o c a l v a r i a t i o n s of the wet-bulb temperature d e p r e s s i o n to what was observed on naphthalene p l a t e s . At high f r e e stream temperatures, the d e v i a t i o n of the measurement taken t h r e e inches from the p l a t e l e a d i n g 155 170 160 150 140 130 a a 120 110 1 0 0 -0 y y / / / / ' ' y / . y y / A /O /e,XD / / / / / / a v / / / / x / / / / /' ' / / / ' / / I / / / / / Q ft® ! 1 ' I I. J ! 1 1 J J J AIR-NAPHTHALENE LENGTH 4" PLATE {wiDTH 2" THICKNESS 0.375" AIR FLOW RATE 0.078 lb/sec X , (Inch) 4> ' / / / ' J ' ' A y x 100° F 5677 11360 17060 Re„ 170 ° F 5265 10540 15820 THERMOCOUPLE 24 o e Q GAUGE 30 A V X A t , ( ° F ) 10 12 FIGURE 51. LOCAL WET-BULB TEMPERATURE DEPRESSIONS ON A NAPHTHALENE PLATE (MEASURED IN THE WIND TUNNEL, AIR FLOW 0.078 l b ./sec.) 156 • — i 1 1 1 1 I20h X / f i / / / / y HOI— / / • X ^ AIR-P-DICHLOROBENZENE / / LENGTH 4" *|OOr- / P L A T E { w i D T H 2" / THICKNESS 0.375" / AIR FLOW RATE 0.122 tt)/sec / X, (Inch) 90 K / I 2 3 / / 8 0 ° F 17360 / R e x / i 120 °F 16650 _ THERMOCOUPLE 24 O © <D •80f- / GAUGE 30 A V X / / J I I : I : : 1 L 0 2 4 6 8 10 12 A t ( ° F ) FIGURE 52. LOCAL WET-BULB TEMPERATURE DEPRESSIONS ON A P-DICHLOROBENZENE PLATE (MEASURED IN THE WIND TUNNEL) edge, from the measurements taken one and two inches from.the l e a d i n g edge, i s probably due to thermal c o n d u c t i o n e f f e c t s along the p l a t e support. The dat'hed curve i s c o n s i d e r e d to be r e p r e s e n t a t i v e of the l o c a l wet-bulb temperature depression at the middle of the p-dichlorobenzene p l a t e ( i e . , two inches from the l e a d i n g edge.) The l o c a l p s y c h r o m e t r i c r a t i o s measured on p l a t e s are p r e s e n t e d i n F i g u r e 53 as a f u n c t i o n of the system f i l m Lewis numbers. As mentioned p r e v i o u s l y , the best f i t of the data shows a c l o s e agreement with the C h i l t o n - Colburn analogy. The theory of Kauh, Peck and Wasan approaches the p r e d i c t i o n of the C h i l t o n - Colburn analogy as the l o c a l p l a t e Reynolds number decreases. The e x p e r i m e n t a l r e s u l t s do not i n d i c a t e that the l o c a l p s y c h r o m e t r i c r a t i o on. a p l a t e i s a s t r o n g f u n c t i o n of the l o c a l p l a t e Reynolds number. The t h e o r e t i c a l p r e d i c t i o n s of Kauh, Peck and Wasan f o r the case of Re.. = 10 do not r e p r e s e n t the measured psy c h r o m e t r i c r a t i o s on a f l a t p l a t e as i s supposed 3 i n t h e i r p u b l i c a t i o n . The curve f o r R e y = 10 much more c l o s e l y approximates the present experimental data. But the d e r i v a t i o n of Kauh, Peck and Yfasan i s based on t u r b u l e n t boundary l a y e r theory, and a t u r b u l e n t boundary l a y e r w i l l 3 d e f i n i t e l y not e x i s t on a f l a t p l a t e when Re = 10 . It i s x, i n t e r e s t i n g t o note that a very l a r g e v a r i a t i o n i n the l o c a l p s y c h r o m e t r i c r a t i o on a f l a t p l a t e with l o c a l Reynolds number i s p r e d i c t e d when R e x > 10 • and Le > 5. Such a phenomenon might be of importance i n p r e d i c t i n g the d r y i n g schedules and s u r f a c e temperatures of o r g a n i c polymer f i l m s on p l a s t i c sheets. 158 FLAT P L A T E X,(lnch) R e X ( 0- AIR-P-DICHLOROBENZENE °" 2 - 1 7 0 0 0 O - AIR-NAPHTHALENE °" 1 - 8 0 0 0 e - AIR-NAPHTHALENE 0 " 2 ~ 16000 (D - AIR- NAPHTHALENE °" 3 ~ 2 4 0 0 0 A - HELIUM- NAPHTHALENE € 2 ~ 2500 v - HELIUM-NAPHTHALENE € 3 - 3700 x - HELIUM - N A P H T H A L E N E 6 1 ~ 450 Q - HELIUM-NAPHTHALENE € 2 ~ 900 e - HELIUM-NAPHTHALENE € 3 ~ 1350 0.21 I l- i : I I I I L I 2 3 4 5 6 7 8 9 f L e f FIGURE 53. COMPARISON OF PREVIOUS THEORETICAL CORRELATIONS WITH EXPERIMENTAL LOCAL PSYCHROMETRIC RATIOS FOR FLAT PLATES 159 5 For the case of Re, > 3.2 x 10 t h e r e w i l l be a t u r b u l e n t V boundary l a y e r on the p l a t e and the theory of Kauh, Peck and Wasan may p o s s i b l y o f f e r r e l i a b l e p r e d i c t i o n s of the l o c a , p s y c h r o m e t r i c r a t i o s . The author was unable to e x p e r i m e n t a l l y examine the l o c a l p s y c h r o m e t r i c r a t i o of a p l a t e under c o n d i t i o n s of a t u r b u l e n t boundary l a y e r because of gas veloci'-y l i m i t a t i o n s i n both p i e c e s of apparatus used. Both the C h i l t o n - Colburn analogy and the theory of Kauh et a l . p r e d i c t that the l o c a l and macroscopic psychrometric r a t i o s on a f l a t p l a t e w i l l be u n i t y and have no Reynolds number dependence when the system Lewis number i s u n i t y . 160 I I I . PSYCHROMETRIC MEASUREMENTS DOWNSTREAM OF SCREENS IN THE WIND TUNNEL It i s un c l e a r from the work of p r e v i o u s i n v e s t i g a t o r s i f the l o c a l and macroscopic wet-bulb temperature d e p r e s s i o n s of a p a r t i c l e are dependent on the f r e e stream t u r b u l e n c e i n -t e n s i t y and s c a l e . The mass and heat t r a n s f e r from p a r t i c l e s has been shown t o i n c r e a s e as the f r e e stream t u r b u l e n c e i n t e n s i t y i n c r e a s e s . The macroscale of t u r b u l e n c e has been shown to have a maximum e f f e c t on the heat and mass t r a n s f e r from c y l i n d e r s and spheres when L^/dp =1.6. If the f r e e stream t u r b u l e n c e i n t e n s i t y and s c a l e a f f e c t the combined t r a n s p o r t r a t e s s i m i l a r l y , then the p a r t i c l e p s ychrometric r a t i o would not be expected to be a f u n c t i o n of these p a r a -meters. Such i n t u i t i v e r e a s o n i n g i s an e x t e n s i o n of Reynolds analogy. The l o c a l and macroscopic wet-bulb temperature d e p r e s s i o n s f o r a naphthalene c y l i n d e r are examined f o r c o n d i t i o n s of a constant f r e e stream t u r b u l e n c e i n t e n s i t y l e v e l of 8 percent and v a r y i n g s c a l e of t u r b u l e n c e , i n F i g u r e 54. For the con-d i t i o n s of L^/dp < 1.6, L^/dp ~ 1.6 and L ^ / d p > 1.6, the measured l o c a l and macroscopic t u r b u l e n t wet-bulb temperature d e p r e s s i o n shows no c o n s i s t e n t v a r i a t i o n with L^/dp and no s i g n i f i c a n t d e v i a t i o n from the wet-bulb temperature d e p r e s s i o n measured at low t u r b u l e n c e i n t e n s i t i e s i n the empty wind t u n n e l . The s i z e of the measuring thermocouple does not a l t e r the r e s u l t s . A l l v a r i a t i o n s shown i n F i g u r e 54 are w i t h i n the 16 0.1 -0.0 -o.i-\ 0.1 0.0 -0.1 -< x L o.i h < o.oi--0.1 - 0 . 2 -1 1 1 1 H ~T A t R - N A P H T H A L E N E AIR FLOW R A T E 0.122 l b / s e c CYLINDER j Dp = 0519", L • 2" THERMOCOUPLES M'(lnch) 0 .500 0.250 0.125 0. 500 DB 132 132 132 165 + 9 0 ' 24GAUGE 30 GAUGE o e A -ev-0 V CENTER - 9 0 ° A 0 07 © 0 V x 1.0 2 .0 3.0 DISTANCE DOWNSTREAM OF S C R E E N (Inch) 8 \ CD O O J 4 .0 FIGURE 54. EFFECT OF TURBULENCE ON THE MACROSCOPIC AND LOCAL WET-BULB TEMPERATURE DEPRESSIONS OF A NAPHTHALENE CYLINDER (MEASURED IN THE WIND TUNNEL) 162 accuracy of the experimental measurements. Measurements of the l o c a l and macroscopic t u r b u l e n t wet-bulb temperature d e p r e s s i o n s f o r p-dichlorobenzene spheres and c y l i n d e r s at v a r y i n g d i s t a n c e s downstream of screens i n the wind t u n n e l are pre s e n t e d i n F i g u r e s 55 and 56. There i s no s i g n i f i c a n t v a r i a t i o n of the wet-bulb temperature depression with e i t h e r the t u r b u l e n c e i n t e n s i t y l e v e l or the s c a l e of t u r b u l e n c e . For runs where the wet-bulbs are c l o s e to the sc r e e n s , t u r b u l e n t boundary l a y e r s may have been prematurely induced on the p a r t i c l e s because of the high l e v e l of t u r b u -lence, i n t e n s i t y . Experiments 40 inches downstream of the 0.029 inch mesh screen experience a f r e e stream t u r b u l e n c e l e v e l of 2 percent. T h i s l e v e l i s approximately one-half of the t u r b u l e n c e i n t e n -s i t y i n the empty wind t u n n e l at the same v e l o c i t y . In t h i s case the scree n i s f u n c t i o n i n g as a 'flow calmer' r a t h e r than a t u r b u l e n c e promoter. No d e v i a t i o n of the f r o n t and rear s t a g n a t i o n p o i n t and macroscopic wet-bulb temperature de-p r e s s i o n s i s noted at t h i s low l e v e l of t u r b u l e n c e i n t e n s i t y from the c o r r e s p o n d i n g v a l u e s o b t a i n e d when no t u r b u l e n c e promoters are i n the wind t u n n e l . Thus, the psychrometric data measured i n the wind t u n n e l with no t u r b u l e n c e promoters, and i n the gas r e c i r c u l a t i n g apparatus, can be c o n s i d e r e d to be r e p r e s e n t a t i v e of any f r e e stream t u r b u l e n c e i n t e n s i t y and s c a l e . P o s s i b l e e r r o r s might be i n t r o d u c e d i n t o the measurement of wet-bulb temperature d e p r e s s i o n s i f the wet-bulb i s not l o c a t e d e x a c t l y i n the duct c e n t e r . Wet-bulb temperatures 0.0 0.1 0.0 - 0 . O.I oo o O CD AIR - P - D I C H L O R O B E N Z E N E M ' ( l n c h ) AIR F L O W R A T E 0.122 lb/sec o - 0.250 C Y L I N D E R ; D p - 0.519", L * 2" ~ , 9 2 ° F e - 0.500 CYLINDER ; Dp.- 0.519", L = 2 " 24 G A U G E T H E R M O C O U P L E S CD - 0 . 125 CYLINDER ; Dp = 0 .519", L = 2 " a - 0 . 029 CYLINDER; D p = 0.519", L = 2 " v - 0 .125 SPHERE, Dp = 1.0" X - 0.125 SPHERE. Dp = 0.7 5" -e-e v o (D © + 9 0 " o o o A. X V - 9 0 * o ~ i — " — r © v o V o e 9 o V 4 S 6 7 8 DISTANCE DOWNSTREAM OF S C R E E N (Inch) FIGURE 55. EFFECT OF TURBULENCE ON THE MACROSCOPIC AND LOCAL WET-BULB TEMPERATURE DEPRESSIONS OF P-DICHLOROBENZENE CYLINDERS AND SPHERES (MEASURED IN THE WIND TUNNEL, 24 GAUGE THERMOCOUPLES) —I 1 1 — : — AIR - P-DICHLOROBENZENE AIR FLOW R A T E . 0.122 lb / sec t D B ~ 9 2 " F 30 GAUGE THERMOCOUPLES -ii—v M 1 (Inch) o - 0.2S0 CYLINDER; D p » 0.519", L - 2" e - 0.500 CYLINDER;D p =0 .5 l9" , L « 2" CD - 0.125 CYLINDER; D p = 0 5 1 9 " , L " 2" A - 0.029 CYLINDER; Dp =0519" , L " 2" V 0.125 S P H E R E , D p » 1.0" X 0.125 SPHERE, D p • 0.75" cb <s 3 x o V o e + 9 0 » o V CD CD 9 -o.i -0 . 2 i < i e e 9 ° v o e g CD CD -o.i 0.2 r e o OJO -CD CD A -8 * e e o e v JD_ CD e -v-4. 5 6 7 8 DISTANCE DOWNSTREAM OF SCREEN (Inch) FIGURE 56. EFFECT OF TURBULENCE ON THE MACROSCOPIC AND LOCAL WET-BULB TEMPERATURE DEPRESSIONS OF P-DICHLOROBENZENE CYLINDERS AND SPHERES (MEASURED IN THE WIND TUNNEL, 30 GAUGE THERMOCOUPLES) 165 for a naphthalene c y l i n d e r were measured for d i f f e r e n t t r a n s -verse l o c a t i o n s of the c y l i n d e r i n the wind t u n n e l . Even very near the wind t u n n e l w a l l there i s no v a r i a t i o n of the measure-ment from the value measured at the duct cen te r . Thus i t can be concluded that s l i g h t e r r o r s i n wet -bu lb l o c a t i o n i n the ducts has no e f f ec t on the r e s u l t s . The data are presented i n F i g u r e 57. F i g u r e 58 i n d i c a t e s tha t the l o c a l wet -bulb temperatures on a f l a t p l a t e too do not depend s i g n i f i c a n t l y on the f ree stream tu rbu lence i n t e n s i t y and s c a l e . 166 AIR-NAPHTHALENE CYLINDER-, D p=0.5l9", L = 2" 30GAUGE THERMOCOUPLES A I R FLOW RATE 0.122 l b / s e c M' = 0 .25" W 1 3 8 2 ° F + 0.2 Lu 1, +0 . I -O.I POSITION ON DISTANCE CYLINDER FROM S C R E E N CYLINDER 1.25" 2 . 0 " + 9 0 ° o e C E N T E R 0 - 9 0 ° A V 0 0 O I V e _L 0 0.4 0.8 1.2 1.6 DISTANCE FROM CYLINDER AXIS TO DUCT C E N T E R L INE (Inch) FIGURE 57. EFFECT OF TRANSVERSE LOCATION OF SAMPLE IN WIND TUNNEL ON TURBULENT' WET-BULB TEMPERATURE DEPRESSIONS 167 o.i 0.0 -0.1 1 i i LENGTH = 4' i 1 i FLAT PLATE j WIDTH = 2" THICKNESS = 0.3 75" AIR FLOW RATE 0.122 lb/sec M' = 0.50" THERMOCOUPLES 24 GAUGE 30 GAUGE A I R - NAPHTHALENE ~I63 o e AIR - P-DICHLOROBENZENE ~ 9 3 A V •" '•' 1 1  e V e V X, = i " e - d o o 0.1 0.0 © e e > o A X, = 2" o O A A < I -0.1 0.1 -0.0 -0.1 4 X , = 3" o 1 o 1 1 1 0 1.0 2.0 3.0 4.0 5.0 6.0 DISTANCE BETWEEN PLATE LEADING EDGE AND SCREEN (Inch) FIGURE 58. EFFECT OF TURBULENCE ON THE LOCAL WET-BULB TEMPERA-TURE DEPRESSIONS ON NAPHTHALENE AND P-DICHLOROBENZENE PLATES (MEASURED- IN THE WIND TUNNEL) 168 IV. PSYCHROMETRIC,MEASUREMENTS IN A QUIESCENT ATMOSPHERE The wet-bulb temperature d e p r e s s i o n e x h i b i t e d by a sphere or c y l i n d e r i n a quiescent atmosphere can be p r e d i c t e d t h e o r e t i c a l l y from e i t h e r Eq. (116) or Eq. (124). Measure-ments of the macroscopic wet-bulb temperature depressions i n quiescent a i r of naphthalene and p-dichlorobenzene c y l i n d e r s and spheres are pre s e n t e d i n F i g u r e 59. The measurements are c o n s i s t e n t l y higher than the p r e d i c t i o n s of Eq. (116) but much sm a l l e r than the wet-bulb temperatures measured f o r c o n d i t i o n s of f o r c e d c o n v e c t i o n . Eq. (124), on the other hand, p r e d i c t s u n c o r r e c t e d v a l u e s of the psychrometric r a t i o higher than the measured v a l u e s . The oven w a l l temperature was not measured duri n g the course of experiments. When the oven a i r temperature i s not too d i f f e r e n t from the ambient temperature, i t i s expected t h a t the oven w a l l temperature i s approximately equal to the oven d r y - b u l b temperature. Thus the r e s u l t a n t r a d i a t i o n heat t r a n s f e r w i l l tend t o reduce the t r u e wet-bulb temperature de-p r e s s i o n s f o r the p - d i c h l o r o b e n z e n e - a i r system. C o r r e c t i n g the wet-bulb temperature depressions f o r r a d i a t i o n and f r e e con-v e c t i o n heat t r a n s p o r t w i l l tend to s h i f t the data t o the r i g h t i n F i g u r e 59 and show a b e t t e r agreement with Eq. (124). The a i r - n a p h t h a l e n e experiments were performed at a higher temperature range than those f o r the a i r - p - d i c h l o r o b e n -zene system. For these c o n d i t i o n s the term ^V\/A - tW ^ (t -tin ) i s r e l a t i v e l y s m a l l , thus r e d u c i n g the r a d i a t i o n 169 150 140 130 CD a 120 110 100 T AIR - NAPHTHALENE SAMPLE CENTER O - CYLINDER; Dp=0.5l9"L=2" © - SPHERE •, Dp - 1.0" EQ. (116) E Q . 0 2 4 ) ' EQ. ( I4 ) ' J L AU°F) 120 110 ~ 100 at a 90 80 70 AIR - P-DICHLOROBENZENE SAMPLE CENTER O - CYLINDER! D p = 0.5l9",L= 2" © - SPHERE , Dp-1.0" EQ. (116) 1 EQ.(I24)' E Q . 0 4 ) 1 O - o / XJ I | - Not / Note corrected for radiation or nat'l. conv. J : I I L 0 1 2 3 4 A M ° F ) FIGURE 59. COMPARISON OF THEORETICAL AND' MEASURED WET-BULB TEMPERATURE DEPRESSIONS FOR NAPHTHALENE AND P-DICHLOROBENZENE SPHERES AND CYLINDERS IN QUIESCENT AIR ] 7 0 component of heat t r a n s f e r between t h e sample s u r f a c e and oven w a l l . As can be n o t e d i n F i g u r e 59, t h e u n c o r r e c t e d p r e d i c t e d v a l u e s from E q . (124) of the w e t - b u l b t e m p e r a t u r e d e p r e s s i o n show ap p r o x i m a t e agreement w i t h t h e a c t u a l measurements f o r t h e a i r - n a p h t h a l e n e system. I f the,oven w a l l t e m p e r a t u r e i s lower t h a n t h e sample s u r f a c e t e m p e r a t u r e , t h e n r a d i a t i o n and f r e e c o n v e c t i o n w i l l have m u t u a l l y compensating e f f e c t s . 171 V, MEASUREMENT ERRORS The thermocouple m i l l i v o l t measurements were i n d i c a t e d oh a m i l l i v o l t m e t e r with a maximum r e a d a b i l i t y of ^  0.001 inv. T h i s corresponds t o a temperature range of approximately 0.05 °F at room temperature. The wet-bulb temperature depression i s the d i f f e r e n c e between two temperatures and thus i t i s ex-pec t e d t o have b e t t e r than - 0.1° F accuracy. The e s t i m a t i o n of r a d i a t i o n heat t r a n s f e r from the wet-bulb t o the duct w a l l i s p o s s i b l y the l a r g e s t source of e r r o r i n the c a l c u l a t i o n of the psychrometric r a t i o . The e m i s s i v i t y of the wet-bulb s u r f a c e s i s known only approximately. In most cases, experiments having v a l u e s of the term Ct greater than 0.20 are n e g l e c t e d i n the a n a l y s i s of r e s u l t s . F o r t u n a t e l y , f o r most runs, r a d i a t i o n c o n t r i b u t i o n s are shown to i n c r e a s e when the wet-bulb temperature decreases, due t o simultaneous i n c r e a s e i n the value of ~^\jy ^ ^ D B ~^ W^ 0 Thus the measurements - with the highest r e l a t i v e r a d i a t i o n and tempera-t u r e e r r o r s are r e j e c t e d t o improve the accuracy of r e s u l t s . For a few experiments at low gas v e l o c i t i e s i t was necessary to i n c l u d e r e s u l t s where 01 was gr e a t e r than 20 percent. The average n e i g h b o u r i n g duct w a l l temperature i s known only w i t h i n i" 0.5° F due to l o c a l v a r i a t i o n s w i t h i n the duct. For each experiment the sample s e c t i o n l i d i s at room tempera-t u r e when the run i s i n i t i a t e d . The sample i s at steady s t a t e b efore the l i d comes t o a f u l l y steady s t a t e . Thus the wet-bulb surroundings are not at a constant temperature. T h i s 172 e f f e c t i s not c o n s i d e r e d t o be too s e r i o u s s i n c e - t h e sample s e c t i o n l i d d c c u p i e s l e s s than 5 percent of the wet-bulb su r r o u n d i n g s . It if thought that the r a d i a t i o n component of the heat t r a n s f e r i s known w i t h i n ± 10 percent of the t r u e value. Thus i f the maximum v a l u e s - o f CL c o n s i d e r e d are 0.2, then the maximum e r r o r i n t r o d u c e d i n the c a l c u l a t i o n of the psychro-m e t r i c r a t i o by an i n a c c u r a t e knowledge of the r a d i a t i o n heat t r a n s f e r i s ± 2. percent. E s t i m a t i o n s of the heat t r a n s f e r c o e f f i c i e n t f o r the c a l -c u l a t i o n of d f o r spheres and c y l i n d e r s are made from equa-t i o n s f o r the macroscopic heat t r a n s f e r c o e f f i c i e n t . Thus the heat t r a n s f e r c o e f f i c i e n t s at the f r o n t and r e a r s t a g n a t i o n p o i n t s of spheres and c y l i n d e r s w i l l be s l i g h t l y g r e a t e r than the p r e d i c t e d v a l u e s . The e r r o r i n t r o d u c e d by t h i s f a c t o r i s s m a l l compared t o the r a d i a t i o n e r r o r s . E r r o r s i n the measurement of f r e e stream v e l o c i t y , t u r b u -lence i n t e n s i t y and s c a l e w i l l not a f f e c t the c a l c u l a t i o n of the p s y c h r o m e t r i c r a t i o . The accuracy of each of these measure-ments depends on the v e l o c i t y l e v e l because of the n o n l i n e a r r e l a t i o n s h i p between the hot-wire anemometer v o l t a g e and f r e e -stream v e l o c i t y . The hot-wire anemometer v o l t a g e can be r e a d w i t h i n ± 0.05 v o l t s between 5 and 10 v o l t s . T h i s corresponds t o a v e l o c i t y accuracy of "i 0.12 f t / s e c when the v e l o c i t y l e v e l i s 24.7 f t / sec. If the br i d g e D.C„ v o l t a g e i s known e x a c t l y , the anemo-meter R.M„S. v o l t a g e i s known w i t h i n 0.1 mv. Thus at low t u r b u l e n c e i n t e n s i t i e s the e r r o r i n the t u r b u l e n c e i n t e n s i t y 173 w i l l be l e s s than 1 per c e n t . The measurement of the s c a l e of t u r b u l e n c e i n v o l v e s the use of s i x r e s i s t o r s , the combined r e s i s t a n c e of which i s known w i t h i n 1 percent. The a b s c i s s a and o r d i n a t e of the r e c o r d e r can each be r e a d w i t h i n 1 percent. Thus i t i s expected that the t u r b u l e n c e time s c a l e measurements are a c c u r a t e w i t h i n an 8 percent range. The accuracy of each of the system p r o p e r t i e s i s d i s c u s s e d i n Appendix One, where the a c t u a l v a l u e s of the p r o p e r t i e s are presented. The l a r g e s t e x p e r i m e n t a l e r r o r s i n the c a l c u l a t i o n of R The. s m a l l e s t wet-bulb temperature d e p r e s s i o n s c o n s i d e r e d were above 2 F. The l a r g e s t v a l u e s of (2 and Le^ c o n s i d e r e d were 0.2 and 7.2 r e s p e c t i v e l y . The l o c a l p s y c h r o m e t r i c r a t i o at the f r o n t s t a g n a t i o n p o i n t of a sphere or c y l i n d e r or on a f l a t p l a t e has a value of 0.27 when the system Lewis number i s 7.2. I f the system p r o p e r t i e s are assumed to be exact, then an estimate of the maximum p o s s i b l e e r r o r i n J3Q or fijS w i l l be - 7 pe r c e n t . The co r r e s p o n d i n g maximum probable e r r o r w i t h i n 95 percent c o n f i d e n c e l i m i t s w i l l be approximately - 3 perc e n t . If the e r r o r s a s s o c i a t e d with each of the system p r o p e r t i e s are ro u g h l y e s t i m a t e d and i n c l u d e d with the other e r r o r s , then the maximum c o n c e i v a b l e e r r o r f o r t h i s extreme s i t u a t i o n w i l l be ^ 11 p e r c e n t . The co r r e s p o n d i n g maximum probable e r r o r w i t h i n 95 percent c o n f i d e n c e l i m i t s w i l l be approximately - 4 pe r c e n t . or /3/3 occur when A t , i s s m a l l , Q i s l a r g e and Le f i s l a r g e . 174 CHAPTER SIX CONCLUSIONS AND RECOMMENDATIONS CONCLUSIONS The f o l l o w i n g c o n c l u s i o n s were c o r r o b o r a t e d from the t u r -bulence measurements i n the absence of mass t r a n s f e r : i The i n t e n s i t y of t u r b u l e n c e i n the f r e e stream decreases with i n c r e a s i n g duct Reynolds number f o r both the a i r and helium systems, i i The decay of t u r b u l e n c e downstream of a woven wire Y s c r e e n i s not a f u n c t i o n of f r e e stream v e l o c i t y . i i The l o n g i t u d i n a l i n t e g r a l s c a l e of t u r b u l e n c e down-stream of a screen i n c r e a s e s v/ith i n c r e a s i n g f r e e stream v e l o c i t y and i n c r e a s i n g X/M'. i v . As the mesh s i z e of a scree n i s i n c r e a s e d , the i n t e n s i t y of t u r b u l e n c e i s shown t o i n c r e a s e s l i g h t l y f o r a f i x e d X/d r a t i o . v The s l o p e of the p l o t s of L ^ /d versus X/d are shown to decrease as the s o l i d a r i t y r a t i o of the screen i n c r e a s e s . v i The presence of a c y l i n d e r g r e a t l y a f f e c t s the f r e e stream t u r b u l e n c e i n t e n s i t y l e v e l both upstream and downstream of the o b j e c t . Under c o n d i t i o n s of f o r c e d c o n v e c t i o n , the l o c a l psychro-m e t r i c r a t i o at the f r o n t s t a g n a t i o n p o i n t of c y l i n d e r s 175 and spheres can be p r e d i c t e d by /9 j9 = Le -0. 69 f (126) T h i s r e s u l t i s i n c l o s e agreement with the C h i l t o n -Colburn analogy f o r a t t a c h e d laminar boundary layer flow. Under c o n d i t i o n s of f o r c e d c o n v e c t i o n , the l o c a l psychro-m e t r i c r a t i o at the r e a r s t a g n a t i o n p o i n t of c y l i n d e r s and spheres can be p r e d i c t e d by T h i s r e s u l t suggests that a t r a n s p o r t mechanism such as that proposed by Danckwerts (21) may be c o n t r o l l i n g the t r a n s p o r t process i n the wake. For f o r c e d c o n v e c t i o n , experimental measurements of the macroscopic psychrometric r a t i o of spheres and c y l i n d e r s over the range 0.355 < L e f < 7.2 i n d i c a t e t hat the data i s best c o r r e l a t e d by -0. 46 (127) O (125) 176 The measurements of the author i n helium i n d i c a t e that the c o r r e l a t i o n of B e d i n g f i e l d and Drew (8) i s the best p r e v i o u s model f o r p r e d i c t i n g the macroscopic psychro-metr i c r a t i o of spheres and c y l i n d e r s . In f o r c e d c o n v e c t i o n , the l o c a l p s ychrometric r a t i o on a f l a t p l a t e can be p r e d i c t e d from /3 = L e f - ° ' 6 6 (128) when the boundary l a y e r over the p l a t e i s laminar. T h i s r e s u l t i s again i n c l o s e agreement with the C h i l t o n -Colburn analogy as w e l l as with boundary l a y e r theory. The l o c a l and macroscopic p s y c h r o m e t r i c r a t i o s of c y l i n d e r s spheres or f l a t p l a t e s are not a f u n c t i o n of the f r e e stream v e l o c i t y , temperature l e v e l , t u r b u l e n c e i n t e n s i t y and i n t e g r a l s c a l e . The l o c a l and macroscopic p s y c h r o m e t r i c r a t i o f o r a c y l i n d e r or sphere does not depend on the p a r t i c l e diameter An e s t i m a t e of the l i m i t i n g macroscopic psychrometric r a t i o f o r a c y l i n d e r , sphere or f l a t p l a t e can be made from the t h e o r e t i c a l r e l a t i o n s h i p = L e j " 1 (124) c o n v e c t i o n t r a n s f e r , and thermal are n e g l i g i b l e . i f f r e e and f o r c e d r a d i a t i o n e f f e c t s , 177 I I . RECOMMENDATIONS FOR FURTHER WORK The p s y c h r o m e t r i c r a t i o under c o n d i t i o n s of t u r b u l e n t boundary l a y e r flow has not been measured d i r e c t l y i n t h i s i n v e s t i g a t i o n because of gas v e l o c i t y l i m i t a t i o n s . As was mentioned p r e v i o u s l y , the high l e v e l of f r e e stream turbulence and mass t r a n s f e r encountered f o r a few runs may have promoted premature t u r b u l e n t momentum boundary l a y e r s on the wet-bulbs. But t h e r e i s no d i r e c t evidence of t h i s happening. It i s of i n t e r e s t t o know i f the psychrometric r a t i o measured f o r c o n d i t i o n s of a t u r b u l e n t boundary l a y e r flow i s s i m i l a r to that measured i n a wake. Such i n f o r m a t i o n w i l l p r o v i d e v a l u a b l e i n s i g h t i n p r e d i c t i n g the dependence of the N u s s e l t and Sherwood numbers on the P r a n d t l and Schmidt numbers r e s p e c t i v e l y f o r c o n d i t i o n s of a t u r b u l e n t boundary l a y e r . The theory of Kauh and co-workers (62) f o r the psychro-m e t r i c r a t i o on a f l a t p l a t e a p p l i e s i f a t u r b u l e n t boundary l a y e r e x i s t s over the p l a t e . High Reynolds number data (Re > 3.2 x 10^) are needed to v e r i f y or d i s p r o v e t h i s theory. F u r t h e r s t u d i e s might be conducted with f l a t p l a t e wet-bulbs t o determine i f the l o c a l v a r i a t i o n s of the psychrometric r a t i o with R e v depend on the f r e e stream v e l o c i t y or d i s t a n c e along the p l a t e or both. Psychrometric data from a v a r i e t y of long p l a t e wet-bulbs, taken over a wide range of Reynolds numbers, w i l l r e s o l v e . t h e s e q u e s t i o n s . 173 NOMENCLATURE o A area, f t . A-± c o e f f i c i e n t (Eq. (73)) A3 a m p l i f i e r g a i n A' s l o p e of anemometer c a l i b r a t i o n curve, v o l t s / f t . / s e c , a r a d i a l g r i d l e n g t h , f t . a' c o e f f i c i e n t - (Eq. (.111-4)) B c o e f f i c i e n t (Eq. (1-13)) B i B i o t number B-^ c o e f f i c i e n t (Eq c (73)) b angular g r i d l e n g t h , r a d i a n s b' c o e f f i c i e n t (Eq. ( I I I - 4 ) ) C * c a p a c i t a n c e i n cascaded R - C c i r c u i t , f a r a d s C c o e f f i c i e n t (Eq. ( 1 - 8 ) ) , watt/cm.°C Cp heat c a p a c i t y of f l u i d , Btu./lb.°F Cp' heat c a p a c i t y dry a i r , Btu./lb.°F C p V heat c a p a c i t y of sublimate vapor, Btu./lb.°F C g heat c a p a c i t y per pound dry a i r p l u s water vapor a s s o c i a t e d with i t , Btu./lb.°F C 0 o r i f i c e d i s c h a r g e c o e f f i c i e n t Cj2 S u t h e r l a n d constant (Eq. (1-17)) D diameter duct, f t . D1..3 parameters f o r p r e d i c t i o n of tyy f t D y molecular d i f f u s i v i t y , f t . /hr. d scre e n wire diameter, f t . d diameter of p a r t i c l e , f t . 179 d w diameter of hot-wire f t . ^ l * * n v o l t a g e , v o l t s E i (n') energy spectrum f u n c t i o n e vapor p r e s s u r e of water vapor at dew p o i n t , mm. Hg e i - - n v o l t a g e , v o l t s F - L body f o r c e f frequency; cps. f ( x ) c o r r e l a t i o n c o e f f i c i e n t G mass f l u x at a d i s t a n c e r from the center of a p a r t i c l e , l b . / h r . f t . ^ Gr Grashof number G G mass f l u x at a p a r t i c l e s u r f a c e , l b . / h r . ft-. ^  g c g r a v i t a t i o n a l c onstant, f t . 2 / h r . H heat generated, Btu./hr. H a a b s o l u t e humidity of a i r , lb„ water v a p o r / l b . dry a i r H e a b s o l u t e humidity of a i r s a t u r a t e d at the a d i a b a t i c s a t u r a t i o n temperature, l b . water v a p o r / l b . dry a i r H w a b s o l u t e humidity of a i r s a t u r a t e d at the wet-bulb temperature, l b . water v a p o r / l b . dry a i r o h heat t r a n s f e r c o e f f i c i e n t , Btu./hr. f t . ° F h G c o n v e c t i v e heat t r a n s f e r c o e f f i c i e n t i n the presence of mass t r a n s f e r , Btu./hr. ft.^° F h c * macroscopic c o n v e c t i v e heat t r a n s f e r c o e f f i c i e n t i n the' presence of mass t r a n s f e r , Btu./hr. f t . ^ ° F h c * * macroscopic c o n v e c t i v e heat t r a n s f e r c o e f f i c i e n t i n the absence of mass t r a n s f e r , Btu./hr. ft.^° F 180 c o n v e c t i v e heat t r a n s f e r c o e f f i c i e n t i n the absence of mass t r a n s f e r , Btu./hr. f t . 2 o F r a d i a t i v e heat t r a n s f e r c o e f f i c i e n t , Btu./hr. f t . 2 ° F t o t a l heat t r a n s f e r c o e f f i c i e n t , Btu./hr, f t . 2 ° F imaginary operator j - f a c t o r f o r mass t r a n s f e r ( S t M Sc2/3) m o d i f i e d j - f a c t o r f o r mass t r a n s f e r ( S t ^ Sc-^/2) j - f a c t o r f o r heat t r a n s f e r ( S t ^ Pr^/3) 1/2 m o d i f i e d j - f a c t o r f o r heat t r a n s f e r ( S t ^ Pr ' ) c u r r e n t , amps. c u r r e n t through an a m p l i f i e r , amps. Boltzmann constant o r i f i c e f low c o e f f i c i e n t p r o p o r t i o n a l i t y constant thermal c o n d u c t i v i t y , Btu./hr. f t . 2 o F / f t . c o e f f i c i e n t of water vapor t r a n s f e r , l b . water vapor/ o hr. f t . l b . dry a i r / l b . water vapor mass t r a n s f e r c o e f f i c i e n t , l b . moles/hr. f t . l b . 3 m o l e s / f t . 2 mass t r a n s f e r c o e f f i c i e n t , l b . moles/hr. f t . / atm. thermal c o n d u c t i v i t y of wet-bulb, Btu./hr. f t . °F/ft. mass t r a n s f e r c o e f f i c i e n t , . lb./hr„ f t . mass-f r a c t i o n l e n g t h , f t . E u l e r i a n time s c a l e of t u r b u l e n c e , hr. i n t e g r a l l o n g i t u d i n a l s c a l e of t u r b u l e n c e , f t . Lewis number 181 Ln n a t u r a l l o g a r i t h m Log l o g a r i t h m to the base 10 M - l (or M) l o c a l Lewis number exponent u n c o r r e c t e d f o r thermal c o n d u c t i v i t y of s o l i d wet-bulb MM-1 (or MM) l o c a l Lewis number exponent c o r r e c t e d f o r thermal c o n d u c t i v i t y of s o l i d wet-bulb M' screen mesh s i z e , i n . -M Q-1 (or M q) macroscopic Lewis number exponent M W (or MWJJ^Q) molecular weight of water MW' molecular weight of f l u i d I D MWW molecular weight of the sublimate or vapor mass f l u x of vapor, l b . / h r . f t . Nu N u s s e l t number n Reynolds number exponent n' frequency, cps. nn number of data p o i n t s P barometric p r e s s u r e , atm. P B M p a r t i a l p r e s s u r e gas i n f i l m , atm. Pr P r a n d t l number P Q power generated i n hot-wire, watts p p a r t i a l p r e s s u r e , atm. PDB p a r t i a l p r e s s u r e of sublimate or evaporate i n f r e e stream, atm. p>H.20 p a r t i a l p r e s s u r e of water, atm. p w vapor p r e s s u r e of vapor or sublimate at the wet-bulb temperature, atm. Q' heat t r a n s f e r e d from the f r o n t of a p a r t i c l e t o the 182 back of the p a r t i c l e , Btu./hr. q t t o t a l heat t r a n s f e r from wet-bulb, Btu./hr. R r e s i s t a n c e i n cascaded R-C c i r c u i t , ohms R E ( t * ) E u l e r i a n time c o r r e l a t i o n , hr. Re Reynolds number based on Re P p a r t i c l e Reynolds number based on U M R e d duct Reynolds number based on Ujyj R e L t o t a l l e n g t h Reynolds number on a p l a t e R e Y l o c a l l e n g t h Reynolds number on a p l a t e 3 o gas lav/ constant = 0.73 atm. f t . / l b . mole R RHW c o l d hot-wire r e s i s t a n c e , ohms RM mesh Reynolds number R o duct r a d i u s , f t . ^oper o p e r a t i n g hot-wire r e s i s t a n c e , ohms R l - -n r e s i s t a n c e v a l u e s , ohms r r a d i u s , f t . V p a r t i c l e r a d i u s , f t . r 1 2 • ( r g i + rQ2)/2 = c o l l i s i o n diameter, angstroms S s u r f a c e area, f t . Sc Schmidt number Sh Sherwood number s h source (or s i n k ) of E h SM source (or s i n k ) of I"^  . st h Stanton number f o r heat t r a n s f e r st M Stanton number f o r mass t r a n s f e r T t e m p e r a t u r e , 0 R T c temperature,° K 183 Tg b o i l i n g temperature, ° K T f l u i d f l u i d temperature around hot-wire, ° F T G p e r o p e r a t i n g temperature of hot-wire, ° F T^ y temperature of wet-bulb s u r f a c e , 0 R "^WA temperature of v/et-bulb s u r r o u n d i n g w a l l s , 0 R t t e m p e r a t u r e , 0 F t temperature of center plane of p a r t i c l e at a r i g h t angle to the f l o w , 0 F tjjg d r y - b u l b temperature of gas,. ° F t e a d i a b a t i c s a t u r a t i o n temperature, °F t time constant (=RC), sec. o t wet-bulb temperature, l o c a l or macroscopic, °F *WA temperature of wet-bulb s u r r o u n d i n g w a l l s , 0 F t * time, hr. A 11 (tj-jg - t w ) wet-bulb temperature d e p r e s s i o n when no screens i n d u c t , 0 F ^ Toper " T f l u i d ) ' ° F At^. • wet-bulb temperature d e p r e s s i o n measured behind the s c r e e n , ° F U f l u i d v e l o c i t y , f t . / h r . u v e l o c i t y component i n f l u i d , ft„/hr. u-^  f l u c t u a t i n g t u r b u l e n t f l u i d v e l o c i t y , f t . / h r . u-j-' f l u c t u a t i n g t u r b u l e n t s i g n a l d e f i n e d by Eq. (48) Uj_ ensemble average square r o o t of the square of the f l u c t u a t i n g v e l o c i t y i n the i d i r e c t i o n , f t . / h r . V v o l t a g e , v o l t s V G . molecular volume, cc„/gm. mole 184 : v f l u c t u a t i n g anemometer v o l t a g e , v o l t s v r r a d i a l v e l o c i t y component, f t . / h r . W r a t e of s u b l i m a t i o n , l b , / h r . Wg r a t e of a i r flow, l b . / h r . ^£l) c o l l i s i o n i n t e g r a l X d i s t a n c e downstream from scr e e n , f t . X-^  d i s t a n c e along f l a t p l a t e , f t . X Q value of X at the h y p o t h e t i c a l o r i g i n of turbulence' i n t e n s i t y downstream of a g r i d , f t . X ' value of X at the h y p o t h e t i c a l o r i g i n of the s c a l e of t u r b u l e n c e downstream of a g r i d , f t . x l e n g t h component i n gas p a r a l l e l t o the gas flow, f t . x^ mole f r a c t i o n of component A i n f l u i d at a d i s t a n c e r XAW mole f r a c t i o n of component A i n f l u i d at the wet-bulb s u r f a c e x' t h i c k n e s s of stagnant a i r f i l m , f t . y v e r t i c a l c o - o r d i n a t e at r i g h t angles t o the f l u i d flow, f t . z h o r i z o n t a l c o - o r d i n a t e at r i g h t angles t o the f l u i d flow, f t . Z^., n impedance, ohms Greek L e t t e r s a h r ( t w - t W A ) / h c ( t w - t D B ) Q 1 c o e f f i c i e n t (Eq. ( 1-8))-, ° C" 1 0! l i n e a r r e s i s t i v i t y c o e f f i c i e n t , ° C _ 1 185 q u a d r a t i c r e s i s t i v i t y c o e f f i c i e n t , ° C " ^ l o c a l p s y c h r o m e t r i c r a t i o u n c o r r e c t e d f o r the thermal c o n d u c t i v i t y of s o l i d wet-bulb l o c a l p sychrometric r a t i o c o r r e c t e d f o r the thermal c o n d u c t i v i t y of the wet-bulb o r i f i c e diameter r a t i o macroscopic psychrometric r a t i o s o l i d i t y r a t i o of a g r i d , (Eq. (II - 8)) c o e f f i c i e n t of expansion, ° F - ^ s c a l a r q u a n t i t y f o r t r a n s f e r of heat and mass, r e s p e c t i v e l y Xh /h ***) l o c a l Ackermann c o r r e c t i o n f a c t o r (h */h **) macroscopic Ackermann c o r r e c t i o n f a c t o r c o r r e c t i o n f a c t o r e m i s s i v i t y of wet-bulb s u r f a c e ( ^ / i f | ) energy of molecular i n t e r a c t i o n , ergs angle, degrees l a t e n t heat of s u b l i m a t i o n at t , B t u . / l b . w l a t e n t heat of water e v a p o r a t i o n , B t u . / l b . dynamic v i s c o s i t y , l b . / h r . f t . 3.1416 3 d e n s i t y of gas, l b . / f t . t ime, hr . angle, degrees -angular frequency, s e c . 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In a d d i t i o n , s o l i d wet-bulbs are not as s u s c e p t i b l e t o s u r f a c t a n t e f f e c t s . S i n c e l o c a l wet-bulb d e p r e s s i o n s are of i n t e r e s t , i t i s advantageous to use homogeneous sa.mple m a t e r i a l s having low thermal c o n d u c t i v i t y , but no i n t e r n a l c i r c u l a t i o n such as i s found i n s i d e drops. The ch e m i c a l s naphthalene, p-dichlorobenzene and d-camphor were chosen as working m a t e r i a l s s i n c e they are e a s i l y moulded i n t o wet-bulbs and s i n c e i n a i r and helium they e x h i b i t both o v e r a l l a n d T l o c a l wet-bulb temperature d e p r e s s i o n s which can be meas-ured a c c u r a t e l y . Water i n a wick was used i n a few experiments t o i n v e s t i g a t e a system with a Lewis number approximately equal t o u n i t y . The working f l u i d s were chosen to be a i r and helium. A i r has the advantage of being cheaply and e a s i l y obtained,, Helium i s nonflammable and combined with naphthalene, p - d i c h l o r o b e n -zene, d-camphor or water produces a higher Lewis number than the c o r r e s p o n d i n g q u a n t i t i e s i n the a i r system. It would be v i r t u a l l y i m p o s s i b l e t o measure wet-bulb temperatures i n s o l i d -l i q u i d systems s i n c e such systems u s u a l l y e x h i b i t a wet-bulb 1-2 d e p r e s s i o n of the order of one-thousandth of a degree F a h r e n h e i t at normal temperatures. 1-3 II. PROPERTIES OF TEST FLUIDS A i r 1. M olecular weight - 28.97 2. V i s c o s i t y - t e m p e r a t u r e r e l a t i o n s h i p The v i s c o s i t y of a i r i s p r e d i c t e d from data to w i t h i n 2.3 percent by Zahn (132) as fJL = 0.0219 + 0.000288 (t + 2 0 0 ) 0 , 7 7 5 ( I - l ) over the temperature range -100 < t < 300 ° F . at ;P=1 atm. 3. Heat c a p a c i t y - t e m p e r a t u r e r e l a t i o n s h i p Zahn (132) p r e s e n t s a c o r r e l a t i o n f o r the heat c a p a c i t y of humid a i r . Over the temperature range - 1 0 < t < 300 ° F, the e x p r e s s i o n p r e d i c t s the heat c a p a c i t y w i t h i n 0.5 percent. C p ' = 0.24 + 2.49 (10~ 7) t + 2.99 (10~ 8) t 2 (I-2a) C p = C p ' + 0.44 (H a) (l-2b) where C p' r e f e r s t o dry a i r and C p t o humid a i r . 4. Density-temperature r e l a t i o n s h i p The d e n s i t y of moist a i r depends on the temperature, p r e s s u r e and humidity. It can be p r e d i c t e d (42) by the expres-s i o n r - 4 f50CP| fP (760) - 0.378 p = 0.0794 \ lh y (1-3) ^ T J [ 760 1 where P i s the barometric p r e s s u r e i n atmospheres and e i s the vapor p r e s s u r e of water vapor i n m i l l i m e t e r s of mercury at the dew po i n t of the moist a i r . 5. Thermal c o n d u c t i v i t y - t e m p e r a t u r e r e l a t i o n s h i p Data f o r the thermal c o n d u c t i v i t y of a i r were f i t t e d by Zahn (132) w i t h i n 0.4 percent over the temperature range -100< t < 300 ° F to the e x p r e s s i o n k = 0.00692 + 0.00.00738 (t + 2 0 0 ) ° ' 8 3 8 (1-4) 6. Force constant and c o l l i s i o n diameter Wilke and Lee (128) r e p o r t the f o r c e constant and c o l l i s i o n diameter f o r a i r to be 97.0 ° K arid 3.617 angstroms r e s p e c t i v e -l y . Helium The helium gas was s u p p l i e d by Canadian L i q u i d A i r Co. i n s i z e H (230 cu. f t . at S.T.P.) s t a n d a r d c y l i n d e r s . The helium has the f o l l o w i n g s p e c i f i c a t i o n s : P u r i t y 99.995 % min. H£ 20 p.p.m. Ne 50 p.p.m. 0 2 + N2 2 p.p.m. 1-5 1. Molecular weight - 4.0026 2. V i s c o s i t y - t e m p e r a t u r e r e l a t i o n s h i p TABLE I - l VISCOSITY OF HELIUM (43) o Temperature, C V i s c o s i t y , m i c r o p o i s e -191.6 87. 1 0 186.0 20 194. 1 100 228.1 200 267.2 250 285.3 282 299.2 3. Heat c a p a c i t y The heat c a p a c i t y as r e p o r t e d by K e l l y (63) i s f a i r l y c o n stant over the range 0 t o 200 °C. C p = 1.24 cal/gm. K 4. Density-temperature r e l a t i o n s h i p The d e n s i t y of helium can be e m p i r i c a l l y p r e d i c t e d from (69) 460 p = 0.012 <J V P (1-5) 1-6 over a moderate temperature and p r e s s u r e range. 5. Thermal c o n d u c t i v i t y - t e m p e r a t u r e r e l a t i o n s h i p TABLE 1-2 THERMAL CONDUCTIVITY OF HELIUM (43) Temperature, ° F Thermal C o n d u c t i v i t y _ c a l . / s e c . cm. C (xlO ) 0 324 20 333.5 40 343.42 60 352.10 80 360.36 100 368.63 120 376.07 200 401 (11) 6. Force constant and c o l l i s i o n diameter Wilke and Lee (128) r e p o r t the f o r c e constant and c o l l i s i o n diameter f o r helium t o be 6.03 ° K and 2.70 angstroms r e s p e c -t i v e l y . I I I . PROPERTIES OF SAMPLE MATERIALS 1. S u p p l i e r s ' i n f o r m a t i o n TABLE 1-3 SAMPLE MATERIALS Manufacturer Lot-No. Formula MW w Melt i n g Pt.° C Naphthalene ( C r y s t a l Reagent) A l l i e d Chemical Y-232 C 1 0 H 8 128.16 79-81 p-Dichlorobenzene J. T. Baker. Chemical Co. 8-824 C 6 H 4 C 1 2 147.0 53-54 d-Camphor J. T. Baker Chemical Co. 8-452 C 1 0 K 1 6 ° 152.2 177-179 The p-dichlorobenzene and d-camphor are of Baker grade p u r i t y , The naphthalene has a r e s i d u e a f t e r i g n i t i o n of l e s s than 0.002 per c e n t . 2. Vapor pressure-temperature r e l a t i o n s h i p TABLE 1-4 VAPOR PRESSURES OF SAMPLE MATERIALS (8) Naphthalene Temp. ° C P w MM.Hg. 50.0 0.764 55.0 1. 142 60.0 1. 692 66.0 2. 655 p-Dichlorobenzene Temp. ° C p w MM.Hg. 29.2 1.41 35. 2 2. 32 41.0 3. 66 45. 1 4.95 d-Camphor Temp. ° C P w MM.Hg. 40.0 1.230 55.0 1. 672 60.0 2.240 66.0 3.240 1-8 B e d i n g f i e l d and Drew (8) compared t h e i r vapor p r e s s u r e data with v a l u e s found i n the I n t e r n a t i o n a l C r i t i c a l T a b l e s (.56) „ The l a r g e s t d e v i a t i o n between t h e i r data and those found i n I.C.T. was f o r p-dichlorobenzene. They a t t r i b u t e d t h i s d e v i a t i o n to the presence of the ortho isomer. In each case they conclude that the m a t e r i a l s appeared t o behave l i k e a pure substance as f a r as psych r o m e t r i c experiments were con-cerned. Since the chemicals used i n the author's experiments are s i m i l a r i n p u r i t y t o those used by B e d i n g f i e l d and Drew, t h e i r measured vapor p r e s s u r e s were used i n a l l c a l c u l a t i o n s . 3. Latent heat-temperature r e l a t i o n s h i p The r e l a t i v e l a t e n t heats of s u b l i m a t i o n f o r each of the or g a n i c s o l i d s was found by u s i n g the C l a u s i u s - Clapeyron e q u a t i o n i n the p e r f e c t gas form to i n t e r p r e t the s l o p e of a p l o t of the Logarithms of the vapor p r e s s u r e s versus those f o r a r e f e r e n c e substance, i n t h i s case water. The C l a u s i u s - Clapeyron equation i s g i v e n by d p w \ w W - W ( 1-6) dT T ( V B - V A) For two substances at the same temperature, assuming << Vg and that V i s giv e n by the i d e a l gas law, X W M W w _ _ _ P H 2 0 d P W _ d ( L n pw> • X H 2 0 M W H 2 0 P w d f J H P 0 d < L n P H o 0 ) The r e l a t i v e l a t e n t heats of s u b l i m a t i o n f o r the chemicals are found to be Naphthalene 1.66 p-Dichlorobenzene 1.45 d-Camphor 1.29 There i s a p r i n t i n g e r r o r i n the p u b l i c a t i o n of B e d i n g f i e l d and Drew (8) with r e s p e c t to the above v a l u e s . The l a t e n t heat of v a p o r i z a t i o n of. water can be o b t a i n e d from a set of steam t a b l e s . 4. Heat c a p a c i t y - t e m p e r a t u r e r e l a t i o n s h i p of the vapor At o r d i n a r y temperatures and p r e s s u r e s the chemicals naphthalene, p-dichlorobenzene and d-camphor e x i s t as s o l i d s . Under these c o n d i t i o n s t h e r e are no experimental v a l u e s a v a i l a b l e f o r the heat c a p a c i t y of the vapor. The heat c a p a c i t i e s f o r naphthalene and p-dichlorobenzene vapor were c a l c u l a t e d by a method s i m i l a r t o that used by B u t l e r (16). The v i b r a t i o n a l s p e c t r a assignments f o r naphtha-lene were taken from L i p p i n c o t t and O'.Reilly (79), and the t o t a l moment of i n e r t i a from M i l l e r (91). The v i b r a t i o n a l s p e c t r a assignments and moments of i n e r t i a f o r p - d i c h l o r o b e n -zene were taken from Godnev and S v e r d l i n (39). The r e s u l t s are t a b u l a t e d i n T a b l e 1-5. and assume i d e a l gases at 1 atmosphere. i - i o TABLE 1-5 HEAT CAPACITY OF NAPHTHALENE AND.P-DICHLOROBENZENE VAPORS Naphthalene p-Dichlorobenzene Temp. °K CpvBtu/lb'. mole°F Temp. °K C p v Btu/lb.mole°F 278.16 29.757 273.16 25.361 280. 0 29.970 275.0 25.502 290. 0 31.128 280.0 25.882 298.16 32.069 285.0 26.261 300.0 32.281 290. 0 26.638 31.0.0 33.428 295. 0 27.014 320. 0 34.566 300. 0 27.387 330.0 35.695 305.0 27.758 340.0 36.811 310.0 28.126 350.0 37.915 315. 0 28.492 . 360.0 39.044 320.0 28.856 370. 0 40.078 325.0 29.217 The r e s u l t f o r naphthalene i s i d e n t i c a l at 300 K to that c a l c u l a t e d by M c C l e l l a n and Pimentel (89). A l s o the heat c a p a c i t i e s c a l c u l a t e d f o r p-dichlorobenzene agree with a value of 27.26 p r e s e n t e d by Godnev and S v e r d l i n at 298.2 °K. 5. Thermal c o n d u c t i v i t y of naphthalene and p - d i c h l o r o -benzene o Over the range -160 4- t ' C ^ 80, the thermal c o n d u c t i v i t y of naphthalene s o l i d i s given by (57): k s = c •[ i +a ' t' (io~ 4) j (1-8) where C --- 38 (10~ 4) watt/cm. ° C a' = -33 ° C" 1 R a v i c h and Burtsev (104) r e p o r t the thermal c o n d u c t i v i t y of p - d i c hlorobenzene s o l i d over the range -40 < t ' ° C < 30. TABLE 1-6 THERMAL CONDUCTIVITY OF P-DICHLOROBENZENE Temperature, ° C Thermal C o n d u c t i v i t y cal./gm.sec ° C ( x l O 5 ) - 30 34 - 20 33 - 10 32 o 31 10 30 20 29 30 28 6. C o l l i s i o n diameters of sample m a t e r i a l s An e x p r e s s i o n t o p r e d i c t the c o l l i s i o n diameter f o r a •vapor has been proposed by Wilke and Lee (128). 1-12 ' / 3 r o i = 1 ' 1 8 V o i (1-9) The m o l a l volume of the l i q u i d at i t s normal b o i l i n g point can be c a l c u l a t e d from data p r e s e n t e d by Le Bas (73). Table 1-7 t a b u l a t e s the v a l u e s of the l i q u i d m olal volumes and c o l l i s i o n diameters f o r the sample m a t e r i a l s under c o n s i d e r a -t i o n . TABLE 1-7 COLLISION DIAMETERS OF SAMPLE MATERIALS M o l a l Volume, C o l l i s i o n Diam. Sample M a t e r i a l cc/gm.mole angstroms Naphthalene 147.6 6.236 p-Dichlorobenzene 131.8 6.012 d-Camphor 188.1 6.773 7. E m i s s i y i t y There are no e x p e r i m e n t a l data a v a i l a b l e i n the l i t e r a t u r e f o r the e m i s s i v i t y of smooth naphthalene, p-dichlorobenzene or camphor s u r f a c e s . _ T y p i c a l v a l u e s of the e m i s s i v i t y f o r sub-s t a n c e s with s u r f a c e s s i m i l a r t o t h a t of the sample m a t e r i a l s — earthenware, i c e and white paper — are r e s p e c t i v e l y 86, 92 and 95 percent at 100 ° F (114). Mathers, Madden and P i r e t (86) have determined that a value of 0.85 f o r the e m i s s i v i t y of naphthalene w i l l g i v e a best f i t of t h e i r mass t r a n s f e r data. Thus the best estimate that can be made f o r the e m i s s i v i t y of the t h r e e sample m a t e r i a l s i s 0.85. Since the r a t i o of the r a d i a t i o n c o n t r i b u t i o n t o the t o t a l t r a n s f e r i s only a s m a l l percentage i n most cases, even a l a r g e e r r o r i n the value of the e m i s s i v i t y r e s u l t s i n a s m a l l e r r o r i n the c a l c u l a t i o n s . 1-14 IV. COMBINED PROPERTIES OF SAMPLE MATERIAL AND TEST FLUIDS 1. D i f f u s i o n c o e f f i c i e n t s When e x p e r i m e n t a l l y determined d i f f u s i v i t i e s are not a v a i l a b l e , s e v e r a l p r e d i c t i o n methods based on the k i n e t i c t h e o r y of gases are a v a i l a b l e t o p r o v i d e e s t i m a t e s . When acc u r a t e e s t i m a t e s are d e s i r e d , the Wilke and Lee m o d i f i c a t i o n of the H i r s c h f e l d e r , B i r d and Spotz equation i s recommended (50). H i r s c h f e l d e r , B i r d and Spotz (48, 49, 50) have c a r r i e d out c a l c u l a t i o n s f o r non-polar gases, which have an energy of a t t r a c t i o n v a r y i n g with the i n v e r s e s i x t h power of the d i s t a n c e between c e n t e r s of adjacent molecules, and a. r e p u l s i v e energy v a r y i n g with the i n v e r s e of the t w e l f t h pov/er. For p a i r s of non-polar gases, the f i r s t approximation f o r the d i f f u s i o n c o e f f i c i e n t s i s expressed as f o l l o w s : The term A i s a c o r r e c t i o n f a c t o r , a s m a l l q u a n t i t y u s u a l l y l e s s than 0.03 (128). D e t a i l e d equations f o r A are gi v e n (49, 50)„ For the purpose of simple c a l c u l a t i o n s , the val u e of A has been e s t i m a t e d and pr e s e n t e d g r a p h i c a l l y by Wilke and Lee as a f u n c t i o n of MW',/MWR and K T / w o c 12 For mixtures of two non-polar gases, D v (1-10) 1-15 r l + r 2 12 (1-11) and 6 1 2 =ye-€ 1 2 (1-12) The c o l l i s i o n i n t e g r a l wjjj has been c a l c u l a t e d by H i r s c h f e l d e r , B i r d and Spotz as a f u n c t i o n of K T c / £ -j^-R e p r e s e n t a t i v e v a l u e s are l i s t e d i n Tab l e 14-45 of the Chemical Engineers'Handbook (94). A c c o r d i n g t o theory, the nume r i c a l constant B i s equal t o 9.2916 x 10~ 4. Wilke and Lee (128) have found B t o be r e l a t e d t o the molecular p r o p e r t i e s by B MWW + MWR1l/2"-' 10.7 - 2.46 'B MWW MWB 10 -4 (1-13) Thus, a l l of the parameters necessary t o c a l c u l a t e D y are known except the f o r c e c o n s t a n t s f o r the s o l i d t e s t m a t e r i a l s . 2. Force Constants In the absence of v i s c o s i t y data H i r s c h f e l d e r , C u r t i s s and B i r d (51) recommend the f o l l o w i n g equations t o p r e d i c t the f o r c e constant of a vapor: € /K = 0 77 T fc|/jv u.// A C R I T (1-14) 1-16 <£ /K = 1.15 T BOIL (1-15) £,/K = 1.92 T MELT (1-16) where the temperatures are expressed i n K. The vapor f o r c e constant can be c a l c u l a t e d by an a l t e r n a t e method. I f a value of the d i f f u s i v i t y i s known,the f o r c e con-s t a n t may be b a c k - c a l c u l a t e d from Eq. (1-10) f o r p r e d i c t i n g d i f f u s i v i t i e s . These v a l u e s are pre s e n t e d i n Tabl e 1-8. Of the th r e e sample m a t e r i a l s , d i f f u s i v i t y measurements are a v a i l a b l e only f o r the system naphthalene i n a i r . Mack (82) Obtained a val u e of 0.0611 cm. /sec. at 25 ° C and 760 MM.Hg. Pe r r y (98) quotes a value of 0.0513 cm. '/sec. at 0 C and 760 MM.Hg. These two va l u e s show a dependence on the temperature to the 1.5 power as i s p r e d i c t e d by the A r n o l d equation. The s e m i - e m p i r i c a l method of A r n o l d (128) g i v e s a value of 0.0672 cm. 2/sec. f o r the a i r - n a p h t h a l e n e system at 25 ° C and 760 MM.Hg. Thus, the p r e d i c t e d v a l u e s of A r n o l d a l l l i e above the l i n e through the exp e r i m e n t a l p o i n t s . Rowe, C l a y t o n and Lewis (108) f i n d t h a t a d i f f u s i v i t y c o r r e l a t i o n f o r naphthalene based on the e x p e r i m e n t a l l y determined d i f f u s i v i t i e s g i v e s a best c o r r e l a t i o n of t h e i r heat and mass t r a n s f e r data. B e d i n g f i e l d and Drew (8) used the G i l l i l a n d e q uation t o c a l c u l a t e v a l u e s of the d i f f u s i v i t y f o r the a i r - p - d i c h l o r o b e n -zene and air-d-camphor systems. But Wilke and Lee (128) show f o r the 64 systems which they examine, that the average d e v i a -TABLE 1-8 FORCE CONSTANTS FOR NAPHTHALENE, P-DICHLOROBENZENE, D-CAMPHOR €,/K ° K Chemical T CRIT ° K T BOIL ° K TMELT ° K D v cm. /sec. Eq. (1-14) Eq. (1-15) Eq. (1-16) from . D v Naphthalene 748.4 (28) 490.9 (29) 352.2 (29) 0.0513* 0.0611** 576 565 678 959.2 p - D i c h l o r o -benzene 447.0 (30) 326.0 (30) 0.0595*** 514 625 635. 0 d-Camphor 482.0 (31) 451.5 (31) 0.0513*** 553 865 • 638.9 * E x p e r i m e n t a l value at 0 ° C, 1 atm. (98) ** E x p e r i m e n t a l value at 25 ° C, 1 atm. (82) *** C a l c u l a t e d v a l u e from A r n o l d e q u a t i o n (128) at O ° C, 1 atm. 1-18 t i o n of the d i f f u s i v i t y p r e d i c t i o n s from the e x p e r i m e n t a l data f o r the G i l l i l a n d equation i s 20 percent compared t o 8.4 per-cent f o r the A r n o l d equation. Thus the A r n o l d equation has been used to p r e d i c t d i f f u -s i v i t y v a l u e s f o r the a i r - p - d i c h l o r o b e n z e n e and air-d-camphor systems. The A r n o l d e q u a t i o n i s g i v e n by (128) 3/2 MWW + MWB") '/2 0.00837 T'^ L MW MWg D v - — 7 73 , „i73 '- ( I ~ 1 7 ) P(V 0 1 + V Q 2 ) ( 1 + C | 2 / T c ) where the S u t h e r l a n d constant may be c a l c u l a t e d from the ex-p r e s s i o n 1/3 1/3 3 2/Vo, V 0 2 " C 1 2 ~ \ v,/2 ^ ,/ 2 ^ / C I C 2 ( J - 1 8 ) V 0 I + V02 The c o n s t a n t s C| and are o b t a i n e d from the a b s o l u t e b o i l i n g temperatures (° K): C, = 1.47 T B 0 1 | _ (1-19) C 2 = 1 . 4 7 T B Q | L 2 (1-20) In the absence of e x p e r i m e n t a l data i s determined by u s i n g Kopp's Law of a d d i t i v e volumes. From these d i f f u s i v i t y 1-19 v a l u e s the f o r c e c o n s t a n t s are c a l c u l a t e d . From Table 1-8 i t can be seen that t h e r e i s a l a r g e v a r i a -t i o n i n the v a l u e s of the f o r c e constant between the four p r e -d i c t i o n methods used. Since the A r n o l d equation has been shown to, g i v e a r e a s o n a b l e p r e d i c t i o n of d i f f u s i v i t e s of vapor-gas systems, and s i n c e the d i f f u s i v i t y i s not a s t r o n g f u n c t i o n of the f o r c e c o n s t a n t , i t was decided to use the value of the f o r c e constant as b a c k - c a l c u l a t e d from the H i r s c h f e l d e r , B i r d and Spotz e q u a t i o n when the d i f f u s i v i t y i s c a l c u l a t e d by the A r n o l d method. These f o r c e c o n s t a n t s can now be used to c a l c u l a t e the a p p r o p r i a t e d i f f u s i v i t e s i n the a i r and helium systems by the H i r s c h f e l d e r , B i r d and Spotz method, Eq. (1-10). I I - l APPENDIX TWO EQUIPMENT SPECIFICATIONS I. WIND TUNNEL lo Measurement of mean a i r v e l o c i t y A i r i s s u p p l i e d t o the wind t u n n e l by a water c o o l e d Nash # 1251 compressor l o c a t e d i n the basement of the Chemical E n g i n e e r i n g b u i l d i n g . Since the compressor i s water c o o l e d , the compressed a i r i s f u l l y s a t u r a t e d with water vapor at the com-pr e s s o r e x i t p r e s s u r e of 50 p s i g . But a f t e r the a i r i s ex-panded to atmospheric p r e s s u r e i n the wind t u n n e l , i t i s only approximately 20 percent s a t u r a t e d . An o r i f i c e which was o r i g i n a l l y b u i l t by Galloway (35) was i n c o r p o r a t e d i n t o the 2 inch i n l e t copper p i p i n g as shown i n F i g u r e 7 t o measure the mean a i r f l o w i n t o the wind t u n n e l . The d e t a i l s of the o r i f i c e design are given i n Table I I - l . The o r i f i c e adequately covered the range of f l o w r a t e s encom-passed i n t h i s i n v e s t i g a t i o n . The manometer arrangement that was used to measure the i n l e t p r e ssure and the pressure drop acr o s s the o r i f i c e i s d e s c r i b e d i n a subsequent s e c t i o n of t h i s appendix. The design of the o r i f i c e arrangement was based on the "recommendations of the A.S.M.E. r e p o r t on f l u i d meters ( 4 ) . Thus, i t was unnecessary to c a l i b r a t e the o r i f i c e . Bulk a i r v e l o c i t i e s measured by means of the o r i f i c e were c o n s i s t e n t with 11-2 anemometer v e l o c i t y measurements. The s t a n d a r d discharge c o e f f i c i e n t s t h a t were used t o c a l c u l a t e mean a i r v e l o c i t i e s are shown i n F i g u r e I I - l , and were taken from the A.S.M.E. Power Test Codes (5). The flow c o e f f i c i e n t s were e m p i r i c a l l y c u r v e - f i t t e d f o r use i n a computer program. For a diameter r a t i o of 0.3935, the flow c o e f f i c i e n t i s g i v e n by K, = 0.00217 (Log R e ) 2 - 0.0245 (Log Re) + 0.678 ( I I - l ) over the range 2 x 10 4< Re < 10 6 and ,2 K, = 0.0271 (Log Re) - 0.236 (Log Re) + 1.128 (II-2) over the range 3 x 10 3 < Re < 2 x 1 0 4 and where <-0 K. = . — = = = — ( H - 3 ) i The Reynolds number i s based on the pipe diameter. The c h a r a c t e r i s t i c dimensions of the o r i f i c e and comparison with recommended, design v a l u e s are shown i n T a b l e I I - l . PIPE REYNOLDS NUMBER FIGURE I I - l . FLOW COEFFICIENT OF ORIFICE AS A FUNCTION OF REYNOLDS NUMBER 11-4 TABLE I I - l CHARACTERISTIC DIMENSIONS OF ORIFICE In s i d e diameter of pipe d^, i n . 1.985 O r i f i c e diameter d Q , i n . 0.793 /3, = d c / d t 0.3995 Length of hole i n p l a t e L Q , i n . 0.060 Recommended Max. L Q , 1/30 d^ - , i n . 0.066 1/8 d G, i n . 0.099 1/8 (d t - d D ) , i n . 0.149 Width of s l i t , d s , i n . 0.040 R a t i o d s/d^ 0.0202 Recommended r a t i o d s / d t 0.02 E x i t l e n g t h L^, i n . 86 E x i t l e n g t h r a t i o L^/d^ 43 Recommended Min. L^/d^ 3 Entrance length Lg, i n . 180 Entrance l e n g t h r a t i o , I-^/d^ - 90 Recommended Min. Lg/d^ 10 P l a t e t h i c k n e s s , Lp, i n . 0.125 Th i c k n e s s r a t i o , Lp/ d^ . 0.063 The weight r a t e of flow of a i r i s c a l c u l a t e d from the •formula (5) Wg = 359 C G F d c 2 F a Y / \ J ~ h (II-4) II-5 where Wg = weight r a t e of flow, lb/hr. = c o e f f i c i e n t of di s c h a r g e F a = thermal expansion f a c t o r Y = expansion f a c t o r h w = d i f f e r e n t i a l p r e s s u r e , i n . H 20 at 68 ° F p^ = s p e c i f i c weight of f l o w i n g f l u i d at the i n l e t s i d e 3 of the primary element, l b / f t . d Q = diameter of o r i f i c e t h r o a t , i n . F = v e l o c i t y of approach f a c t o r = l / N / l -The expansion f a c t o r f o r square edged c o n c e n t r i c o r i f i c e s used with f l a n g e taps, and having a r a t i o of gas s p e c i f i c heats, k' - C p / C y = 1.4, i s given by (5) 4 X' Y = 1 - (0.41 + 0.35/Q, ) - (II-5) where P, - P 2 x> = _L-—i ( n - 6 ) The area f a c t o r F c o r r e c t i n g f o r thermal expansion of a primary elements i s equal t o u n i t y i n the temperature range of i n t e r e s t . 2. Heat source A Chromalox type DHF f i n t u b e duct heater was used to heat II-6 the a i r e n t e r i n g the wind t u n n e l . Table II-2. o u t l i n e s the main heater design d e t a i l s . TABLE II-2 AIR HEATER IN WIND TUNNEL Power r a t i n g , kw. 10 Heat output r a t i n g , Btu/hr. 34120 Dimensions, width, i n . 12 h e i g h t , i n . 12 depth, i n . 6 1/2 V o l t a g e , v o l t s A.C 0 208 (3 phase) No. of elements 6 Catalogue No. DHF -12-12-10 The heater has i n c o r p o r a t e d i n i t a temperature s e n s i t i v e s a f e t y s w i t c h to prevent o v e r h e a t i n g of the elements i n case of sudden stoppage of the a i r flow. .It was necessary t o r e w i r e the power input to the heater t o p r o v i d e a method of c o n t r o l l i n g the a i r temperature i n the wind t u n n e l . The c i r c u i t i s shown i n F i g u r e I I - 2 . The 3 phase, 240 v o l t power f i r s t goes through a main s w i t c h and 50 amp c i r c u i t breaker to prevent p o s s i b l e damage due to power surges. For convenience a 0.5 watt l i g h t i n d i c a t e s when the c i r c u i t i s o p e r a t i v e . The top and bottom two elements of the heater are each connected to the main power source by 3 way switches, thus p r o v i d i n g 12 p o s s i b l e f i x e d l e v e l s of heat input i n t o the heater. Each of the two c e n t r a l elements are connected to the main - c / j o 7 — ^ V i O A S j i r -cy o ^ Q-MN T O T E M P S A F SW HTR PWR MN SW C K T BKR L T 2 4 0 V O L T 6 0 C Y C L E TRANSFORMER I 3 S T E P S W ! t t H E A T E R • v A A W V " / W V W V I 3 S T E P S W 2 M R U A A A A W -FIGURE II-2. HEATER CIRCUIT IN WIND TUNNEL II-8 power source by 240 v o l t , 9.4 amp. v a r i a b l e t r a n s f o r m e r s . To keep a check that both t r a n s f o r m e r s maintain the same duty, the Armaco ammeter. The step switches can be a d j u s t e d so that they supply approximately t w o - t h i r d s of the r e q u i r e d heat duty; then the power input i n t o the heater can be a c c u r a t e l y c o n t r o l l e d by ma n i p u l a t i o n of the t r a n s f o r m e r s which c o n t r o l the two center heater elements. 3. Wind t u n n e l p r e s s u r e c o n t r o l The p a r t i a l l y contaminated a i r l e a v i n g the wind t u n n e l i s removed by a s u c t i o n fume removal system. It was d e s i r e d t o mai n t a i n the sample s e c t i o n of the wind t u n n e l as c l o s e as p o s s i b l e t o atmospheric p r e s s u r e . Thus, i t was necessary t o devi s e a c o n n e c t i o n between the v e n t i n g system and the wind t u n n e l t h a t would a l l o w f o r removal of a l l of the contaminated a i r but would at the same time c o n t r o l the a i r p r e s s u r e i n the duct. These requirements were met by f a b r i c a t i n g on t o the end of the four i n c h square duct the apparatus shown i n F i g u r e II-3. c u r r e n t i n t o each i s measured by a 240 v o l t , 10 amp. maximum FUME ROOM AIR ADJUSTABLE SLIDES WIND TUNNEL FIGURE II - 3 . WIND TUNNEL PRESSURE CONTROL II-9 The p r e s s u r e at the sample s e c t i o n can be a c c u r a t e l y con-t r o l l e d by a d j u s t i n g the s l i d e s as shown i n F i g u r e II-3 u n t i l t h ere i s a balance between the p o s i t i v e upstream a i r p r e s s u r e and the s l i g h t vacuum i n the fume vent. 4 . P r e s s u r e measurement The value of the atmospheric p r e s s u r e was taken from a st a n d a r d V e r n i e r l a b o r a t o r y barometer. The sample sect ion,'Dewcel'and o r i f i c e i n l e t gauge p r e s s u r e s , and the o r i f i c e p r e s s u r e drop, were measured i n e i t h e r a water or mercury manometer depending on the magnitude of the pr e s s u r e being measured. The s w i t c h i n g c o n n e c t i o n s between the pre s s u r e measurement p o i n t s and the manometer are shown i n F i g u r e I I - 4 . PRESSURE MANIFOLD 1 - SAMPLE SECTION MERCURY WATER 2 - DEWCEL MANOMETER MANOMETER 3 - ORIFICE INLET 4 - ORIFICE OUTLET FIGURE I I - 4 . PRESSURE MEASUREMENT 11-10 The c o n n e c t i o n s between the pressure m a n i f o l d and measure-ment p o i n t and manometers were made with f l e x i b l e 1/8 inch copper t u b i n g and t h o r o u g h l y checked f o r p o s s i b l e l e a k s . 5 . Humidity measurement It i s of i n t e r e s t t o know the humidity of the a i r supply. The d e t e r m i n a t i o n of moisture content by measuring the dew p o i n t i s c o n s i d e r e d by E w e l l (29) as the most accurate absolute method. A Foxoboro 'Dewcel', which measures dew p o i n t auto-m a t i c a l l y t o the nearest 0.5 ° F was used i n t h i s i n v e s t i g a t i o n . M o i sture d e t e r m i n a t i o n by the 'Dewcel' i s based on t n e f a c t t h a t f o r every water vapor p r e s s u r e i n contact with a s a t u r a t e d s a l t s o l u t i o n t h e r e i s an e q u i l i b r i u m temperature at which t h i s s o l u t i o n n e i t h e r absorbs nor g i v e s up moisture t o the surround-i n g atmosphere. The 'Dewcel' i s a t h i n - w a l l e d metal socket c o v e r e d with a woven g l a s s tape inpregnated with l i t h i u m chloride, and wound with a p a i r of s i l v e r wires connected to a 25 v o l t a l t e r n a t i n g c u r r e n t power supply. The l i t h i u m chloride, b e i n g h y g r o s c o p i c , absorbs moisture and becomes a s o l u t i o n . The c o n d u c t i v i t y of the s a l t i s i n c r e a s e d , a l l o w i n g a l a r g e r c u r r e n t to flow through the s i l v e r wires with the r e s u l t that the temperature of the 'Dewcel' r i s e s , the s o l u t i o n d r i e s up and the amount of c u r r e n t p a s s i n g through the wires i s reduced. The 'Dewcel' then c o o l s , absorbs more moisture and the c y c l e i s r e p e a t e d u n t i l e q u i l i b r i u m i s a t t a i n e d . A l i q u i d expansion thermometer i n d i c a t e s the temperature of the 'Dewcel' and i s r e c o r d e d on a chart c a l i b r a t e d i n terms of dew-point temperature. A check on the 'Dewcel' accuracy was made u s i n g a wet-and dry-11-11 bulb thermometers. In t h i s case the 'Dewcel' i n d i c a t e d a s l i g h t l y lower humidity. Since i t i s probable that the measured wet-bulb temperature was too high due t o r a d i a t i o n , the humidity as i n t e r p r e t e d from a p s y c h r o m e t r i c chart would be higher than the a c t u a l humidity. Thus, i t was b e l i e v e d that the 'Dewcel' was r e a d i n g a c c u r a t e l y . D e t a i l s of and o p e r a t i n g procedure f o r the 'Dewcel' are p r e s e n t e d i n the Foxboro manual 2000 - 6/60. A s i d e stream of a i r was taken upstream of the main c o n t r o l v a l v e t o p r o v i d e an a i r supply f o r the 'Dewcel'. As mentioned p r e v i o u s l y t h e r e was very l i t t l e v a r i a t i o n i n the incoming a i r h u m i d i t i e s from run to run. The apparatus used f o r measurement of humidity i s shown i n F i g u r e II-5. The recommended a i r flow of 20 to 30 standard c u b i c f e e t per hour through the 'Dewcel' was e s t a b l i s h e d by a d j u s t i n g the c o n t r o l v a l v e s u n t i l the d e s i r e d flow r a t e was i n d i c a t e d on the wet testmeter. . The c o n t r o l v a l v e s a l s o act as p r e s s u r e r e d u c i n g v a l v e s so t h a t the p r e s s u r e i n the 'Dewcel' element does not exceed the maximum o p e r a t i n g pressure of 5 p s i g . 115 VOLT 60 CPS POWER UNIT I AIR 4 f SAMPLE IN TO MANOMETER WET TESTMETER TWO PEN FOXBORO TEMPERATURE RECORDER FIGURE I1-5. HUMIDITY MEASUREMENT i—i i DO 11-13 11 . GAS RECIRCULATING APPARATUS 1. F a b r i c a t i o n The o v e r a l l b a s i c design of the gas r e c i r c u l a t i n g apparatus i s shown i n F i g u r e 10. Very l a r g e q u a n t i t i e s of helium would be r e q u i r e d f o r e x p e r i m e n t a t i o n i n a n o n - r e c i r c u l a t i n g system. In the design of a gas r e c i r c u l a t i n g apparatus the major problem i s to d e v i s e a system where the a i r can be completely removed and helium put i n i t s p l a c e . Lynch and Wilke (80) found that e s s e n t i a l l y complete a i r removal c o u l d be e f f e c t e d from t h e i r apparatus by a s i n g l e steam purge. But they were c o n s i d e r i n g the e v a p o r a t i o n of water i n t o a i r , helium and f r e o n -12, and thus c o u l d t o l e r a t e the humidity i n the system s i n c e i t was measured as a matter of course. Since i n the present experiments i t was d e s i r e d to use pure helium gas, i t was d e c i d e d to remove the a i r from the apparatus by an e v a c u a t i o n t echnique. Thus a l l components were designed t o w i t h s t a n d an a b s o l u t e vacuum and m a i n t a i n 1 mm. Hg. a b s o l u t e p r e s s u r e . The c y l i n d r i c a l tank was c o l d - r o l l e d from 5/16 inch s t e e l and the welded end p l a t e was f a b r i c a t e d from 1 1/4 i n c h m i l d s t e e l p l a t e . The f l a n g e and removable end p l a t e were made from 1 inch and 1 1/4 inch m i l d s t e e l r e s p e c t i v e l y . S t e e l w e l d Company of Vancouver f a b r i c a t e d the components of the tank and welded them together as shown i n F i g u r e 10. S i x inch diameter h a l f c o u p l i n g s were c e n t r a l l y welded on t o the f i x e d end p l a t e and removable end p l a t e f o r c o n n e c t i o n of the tank to the d u c t i n g . Two 1/2 inch c o u p l i n g s were welded t o 11-14 the 1/2 i n c h h o l e s i n the f i x e d end p l a t e f o r i n s t a l l a t i o n of a c o i l f o r gas temperature c o n t r o l . Twelve 1/2 i n c h s t e e l b o l t s secure the removable end p l a t e t o the. f l a n g e . A rubber gasket 1/4 i n c h t h i c k and 4 inches wide i s used to make an a i r t i g h t s e a l between the f l a n g e and end p l a t e . The Chemical E n g i n e e r i n g Department workshop f a b r i c a t e d and welded t o the h a l f c o u p l i n g on the removable end p l a t e a second s t e e l f l a n g e . The main d u c t i n g i s type K copper tube. Both ends of the 4 inch duct (3.86 inches I.D.) connect to 6 i n c h type K copper t u b i n g through a r e d u c e r . The 6 i n c h , tube i s connected to the welded end p l a t e by a 6 inch type K copper connector and to the removable end p l a t e by a brass f l a n g e and rubber gasket. Tank and d u c t i n g supports were c o n s t r u c t e d i n the Chemical E n g i n e e r i n g workshop. 2. Heat source A 3/8 i n c h diameter, 20 f o o t long c o i l i n s i d e the tank can f u n c t i o n e i t h e r as a h e a t i n g or c o o l i n g c o i l . One end of the c o i l i s connected to both steam and water s e r v i c e s . The c o i l e n t e r s and e x i t s from the tank through the two 1/2-inch h a l f c o u p l i n g s on the welded end p l a t e . As an a d d i t i o n a l heat source a steam j a c k e t was added to the tank s e c t i o n . The j a c k e t i s f a b r i c a t e d from 1/2 inch copper t u b i n g at 6 i n c h spacings and i s covered with one inch f i b e r g l a s s i n s u l a t i o n . Steam or water from the i n t e r i o r h e a t i n g c o i l and steam from the e x t e r i o r heater flow through a steam t r a p to the d r a i n . 11-15 3. Vacuum equipment A."enco-Megavac vacuum pump, s t y l e 395, proved to be adequate t o mai n t a i n a p r e s s u r e of l e s s than 1 MM of Hg i n the apparatus. The pump was connected t o the tank through a one in c h diaphragm v a l v e as. shown i n F i g u r e 10. 4. Gas v e l o c i t y r e g u l a t i o n The gas v e l o c i t y i n the 4 i n c h pipe was c o n t r o l l e d at th r e e d i f f e r e n t l e v e l s . The hi g h e s t v e l o c i t y was that i n a n o n - c o n s t r i c t e d p i p e . The two other flow v e l o c i t i e s are ach i e v e d by i n s e r t i n g i n t o the pipe an o r i f i c e or flow con-s t r i c t o r c o n s t r u c t e d of 3/4 i n c h plywood. It i s p o s s i b l e t o pl a c e the flow c o n s t r i c t o r i n t o the pipe through the sample s e c t i o n and s l i d e i t downstream 3 pipe diameters from the sample s e c t i o n . The low and medium fl o w r a t e c o n s t r i c t o r s have r e s -p e c t i v e l y 1 1/4 and 2 in c h c e n t e r e d h o l e s . 5. Gas blower and blower support The gas i s r e c i r c u l a t e d by a T o r r i n g t o n g e n e r a l purpose blower, s i z e 2A. D e t a i l s of the blower are g i v e n i n Ta b l e I I -3. 11-16 TABLE I1-3 GAS RECIRCULATING APPARATUS BLOWER SPECIFICATIONS S e r i a l No. AA -610-325-2 Motor r a t i n g 1/6 H.P. Amps. 3. 9 R.P.M. 1725 V o l t a g e 115 Max. s t a t i c p r e s s u r e Max. a i r flow 475 CoF.M. (Zero s t a t i c p ress.) 1.0 i n . water The blower i s equipped with a s p e c i a l e x p l o s i o n - p r o o f Wagner-Leland motor as a p r o t e c t i o n against the vacuum and e x p l o s i v e c o n d i t i o n s that may e x i s t i n s i d e the tank. The blower i s supported i n s i d e the l a r g e c y l i n d r i c a l tank s e c t i o n by a support welded t o the removable end p l a t e . D e t a i l s of t h i s support are shown i n F i g u r e II-6. To the i n s i d e of the 6 in c h c e n t r a l hole i n the removable end p l a t e i s welded a 2 inch rim. A s e c t i o n of car inner tube and two clamps complete the co n n e c t i o n between the, blower e x i t and the r im. 6. E l e c t r i c a l input t o the blower motor It was necessary t o make an e l e c t r i c a l c o n n e c t i o n to the •blower motor and maintain a vacuum-tight s e a l where t h i s connec-t i o n e n t e r e d the tank. T h i s was accomplished by p l a c i n g a 3/8 inch p y r o t e n i x wire and- 3/8 inch T t o the MPT copper connector i n the removable end FIGURE II-6. BLOWER SUPPORT IN GAS RECIRCULATION APPARATUS 11-18 p l a t e , and c o n n e c t i n g the e l e c t r i c a l wires on the i n s i d e and o u t s i d e of the tank a c c o r d i n g l y . 7. P r e s s u r e measurement The p r e s s u r e i n the apparatus i s measured at the sample s e c t i o n by a mercury manometer connected t o the pipe through a 1/4 inch f l a r e angle v a l v e as shown i n F i g u r e 10. 11-19 i n . T U R B U L E N C E , M E A S U R E M E N T S lo Turbulence promoters . a. Screens Turbulence of a d e f i n i t e s c a l e and i n t e n s i t y can be prod-uced or c o n t r o l l e d i n a gas stream by a g r i d of r e g u l a r l y spaced bars. In the present experiments T y l e r woven medium brass wire screens were p l a c e d i n the a i r duct t o serve as t u r b u l e n c e promoters. The screens are cut and f o l d e d i n t o a shape as shown i n F i g u r e II-7 to f i t i n t o the wind t u n n e l . A 4 " <— 4" —> FIGURE.11-7. TURBULENCE PROMOTERS D e t a i l s of the screens used are shown i n T a b l e I I - 4 . 11-20 TABLE I1-4 SCREEN SPECIFICATIONS M' d % open M' /d i n c h inch area 0.75 0. 207 61.4 3. 62 1.63 0.625 0.192 58.5 3. 25 1.71 0. 50 0. 177 54. 5 2. 83 1.84 0.25 0. 120 45. 7 2. 08 2.19 0.125 0.072 40. 3 1. 74 2.48 0. 104 0.063 38.9 1. 65 2.57 (6 mesh) 0.051 0.032 37. 5 1. 59 2.70 (12 mesh) 0.0375 0.025 36.0 1. 50 2.81 (16 mesh) 0.0287 0.018 32.4 1. 59 3.08 (24 mesh) M' = mesh l e n g t h of scree n d = wire diameter i n g r i d p1 = s o l i d a r i t y or s o l i d i t y of scre e n = t o t a l g r i d a rea/area of i n t e r s p a c e s The s c r e e n dimensions are determined as shown i n F i g u r e I I - 7 a . 11-21 —* t ~~ d FIGURE II-7a. WIRE SCREEN DIMENSIONS The s o l i d i t y r a t i o and percentage open area are both f u n c t i o n s of the r a t i o n M'/d. % open area = 100/fi1 (II-7) £>' = 1 + 2 ( d/M' ) + ( d/M' ) 2 (II-8) b. C y l i n d e r s It i s of i n t e r e s t t o know the e f f e c t of a c y l i n d r i c a l body on the a i r f r e e stream v e l o c i t y , t u r b u l e n c e i n t e n s i t y and s c a l e . A 0„5 in c h b r a s s c y l i n d e r was c e n t r a l l y supported i n the wind t u n n e l as shown i n F i g u r e II-8. It i s p o s s i b l e t o r a i s e the c y l i n d e r t o any d e s i r e d e l e v a t i o n i n the wind t u n n e l by t u r n i n g the c y l i n d e r . The support can be s l i d along the wind t u n n e l bottom t o l o c a t e the c y l i n d e r a d e s i r e d d i s t a n c e upstream or downstream from a f i x e d hot-wire. II A I R F L O W 1 Yz 0 D B R A S S T U B E J f c " ' N . C T B R A S S N U T v v v v v ^  v ^ ^ r I I B A S E - F I B E R B O A R D ( 3 H W i d e ) FIGURE II - 8 . BRASS CYLINDER AND SUPPORT 11-23 2. Hot-wire anemometer s p e c i f i c a t i o n s A DISA model 55A01 constant temperature hot-wire anemome-t e r was s e l e c t e d as the best means of measuring instantaneous mass flow of helium and a i r . Analyses of the measurement of mean gas v e l o c i t y and t u r b u l e n c e i n t e n s i t y and s c a l e are p r e s -ented i n the s e c t i o n s c o n c e r n i n g anemometer c a l i b r a t i o n s and the l i t e r a r y review. Complete d e t a i l s of the anemometer c o n s t r u c t i o n and opera-t i o n and a u x i l i a r y component d e t a i l s are o u t l i n e d i n the DISA i n s t r u c t i o n manual (22). T e c h n i c a l data f o r the anemometer and probe are p r e s e n t e d i n Tab l e I I - 5 , Tab l e II-6 and Table II-7„ TABLE II-5 SPECIFICATIONS FOR ANEMOMETER Frequency response, 0-60 kc/s with 5 m. c a b l e Probe o p e r a t i n g r e s i s t a n c e range, 1-50 ohms Max. a v a i l a b l e probe c u r r e n t , 250 mA. A m p l i f i e r transconductance, A.C., 8 mA./mV. A m p l i f i e r transconductance, D.C., 300 mA./mV. at 125 mA. E q u i v a l e n t input d r i f t , - 2 5 ^ V at 125 mA. output C o l d r e s i s t a n c e measurement accuracy, 0.5 % D.C. voltmeter accuracy, 1 % R„M 0S„ i n d i c a t o r accuracy, 2 % Low-pass f i l t e r , R.C. f i l t e r (-3 d.b.) High-pass f i l t e r , (-3 d.b.) Dimensions, 305 mm. high, 410 mm. wide, 365 mm. deep Weight, 22 kilograms TABLE I I - 6 NOISE LEVEL WITH TYPE 55A22 HOT-WIRE F i l t e r s w i tch s e t t i n g s Noise l e v e l High-pass Low-pass Values kc/sec mV. Out Out 3.7 Out 50 2.3 Out 20 1.6 Out 5 0.7 Out 1 0.22 TABLE II-7 SPECIFICATIONS FOR HOT-WIRE PROBE ( TYPE 55A22 ) Wire type, p l a t i n u r a - p l a t e d tungsten Wire diameter, 0.005 mm. Wire l e n g t h , 0.12 cm. R e s i s t a n c e 20 °C, 3.5 * 8l5 o n m — ° —1 Temperature c o e f f i c i e n t of r e s i s t a n c e , 4 (10 °)°C Max. wire o p e r a t i n g temperature, 300 °C Max. ambient temperature, 150 °C Max. a i r - f l o w v e l o c i t y , 150m./s. Recommended o p e r a t i n g r e s i s t a n c e , 1.8 R ^ Recommended c u r r e n t f o r c o l d r e s i s t a n c e meas., 3.5 mA. D.C. Upper frequency l i m i t (-3 d.b.) at 15 kc./s. at 10 m./s. 20 °C 11-25 Normal o p e r a t i n g c o n d i t i o n s , 50 kc./s. at 100 m./s. T y p i c a l wire s e l f time c o n s t a n t , 1 ins. The hot-wire probe i s connected t o the anemometer through a 5 meter long c o a x i a l . probe c a b l e (DISA type 06A107) and probe support (DISA type 55A20). A DISA type 55A15 dummy probe i s s u b s t i t u t e d i n p l a c e of the hot-wire and probe support f o r approximate adjustment of the anemometer c o i l s . With a DISA type 55A24 s h o r t i n g probe connected'to the probe c a b l e and support, i t i s p o s s i b l e t o balance out the c a b l e r e s i s t a n c e and then measure the probe c o l d r e s i s t a n c e . 3. O s c i l l o s c o p e A T e k t r o n i x type 502A du a l beam o s c i l l o s c o p e i s used to check that the anemometer and e l e c t r o n i c c i r c u i t r y are func -t i o n i n g p r o p e r l y . Some of the more important e l e c t r i c a l c h a r a c t e r i s t i c s are l i s t e d i n Ta b l e II-8 f o l l o w i n g . TABLE I1-8 ELECTRICAL CHARACTERISTICS OF OSCILLOSCOPE Accur acy, S e n s i t i v i t y , 0.1 mV./cm. to 20 V./cm. 0.1 mV./cm., - 3 % 0.2 mV./cm. to 20 V./cm • > - 2 % Bandwidth (-3 d.b.) Upper l i m i t s , 5 mV./cm. to 20 V./cm., > 1 mHz. 0.1 mV./cm • > > 10 kHz. 11-26 Lower l i m i t s , D.C.-coupled, 0 Hz. A.C.-coupled, < 2 Hz. Noise, < 6 JJLV. R.M.S.' When the o s c i l l o s c o p e was used with a T e k t r o n i x type P6006 probe, a l l measurements made i n c o n n e c t i o n with the anemometer and a s s o c i a t e d e l e c t r o n i c s were w e l l w i t h i n the l i m -i t a t i o n s l i s t e d above. 4. Recorder The continuous v o l t a g e output from the c i r c u i t r y t h a t meas-ures the s c a l e of t u r b u l e n c e i s r e c o r d e d on a Hewlett Packard model 7100B one pen s t r i p c h a r t r e c o r d e r . The r e c o r d e r i s c o n t r o l l e d by a model 17501A input module which has the s p e c i f -i c a t i o n s shown i n Tabl e I I - 9 . TABLE I1-9 SPECIFICATIONS OF RECORDER INPUT MODULE Zero, s e t , c o n t i n u o u s l y a d j u s t a b l e -Input r e s i s t a n c e , 1 megohm at n u l l V o l t a g e span; 1,2, 5, 10, 20, 50, 100, 200, 500 mV. 1,2, 5, 10, 20, 50, 100 V. Accuracy, 0.2 % of f u l l s c a l e Dead band, 0.1 % of f u l l s c a l e L i n e a r i t y , 0.1 % of f u l l s c a l e 11-27 It i s p o s s i b l e to operate the 10 inch wide chart paper at any of 12 speeds: 1, 2 i n . / n r . , 0.1, 0.2, 0.5, 1, 2 in./min.; 0.1, 0.2, 0.5, 1, 2 i n . / s e c . Th^ r e c o r d i n g mechanism has a f u l l s c a l e response time of one-htIf second. 5. S c a l e measurement c i r c u i t r y It has been shown i n Chapter Two that the E u l e r i a n i n t e g r a l time s c a l e of t u r b u l e n c e can be determined from a s i n g l e hot-wire by the e q u a t i o n _ _ _ _ (51) (1 + 4 77" n' t D ) It i s necessary to devise an e l e c t r o n i c c i r c u i t that w i l l measure each of the terms i n the above equation. A f t e r e v a l u a t i o n of systems that are a v a i l a b l e f o r b u i l d -i n g e l e c t r o n i c analogue c i r c u i t s , i t was d e c i d e d to use compo-nents manufactured by P h i l b r i c k Company. The i n d i v i d u a l com-ponent and completed c i r c u i t r y s p e c i f i c a t i o n s are presented i n d e t a i l i n the f o l l o w i n g d i s c u s s i o n . a. O p e r a t i o n a l m a n i f o l d and hardware k i t P h i l b r i c k Researches Company manufacture commercially a s m a l l 5 i n t e r c h a n g e a b l e a m p l i f i e r analogue computer c i r c u i t board c a l l e d an O p e r a t i o n a l R„P. M a n i f o l d . T h i s m a n i f o l d has 5 r e c e p t a c l e s f o r p l u g - i n s o l i d s t a t e o p e r a t i o n a l a m p l i f i e r s of the P h i l b r i c k 'E.P.' type, an i n t e g r a l r e g u l a t e d D.C. power supply and a j a c k panel on which c i r c u i t r y can be assembled L t - - ~ ~ 2 to 11-28 c o n v e n i e n t l y and q u i c k l y . In a d d i t i o n , two other r e c e p t a c l e s accomodate a P h i l b r i c k o p e r a t i o n a l c i r c u i t p l u g - i n such as a q u a d r a t i c , l o g a r i t h m i c or s i n u s o i d a l .trans conductor or a c h o p p e r - s t a b i l i z e d h i g h - g a i n a m p l i f i e r . An e l e c t r i c a l ' f r e e -f l o a t i n g ' r e c e p t a c l e i n c l u d e d i n the panel a c c e p t s an a d d i t i o n -a l 10-pin p l u . j - i n . module such as a P or EP s i z e o p e r a t i o n a l a m p l i f i e r , a booster a m p l i f i e r or o p e r a t i o n a l c i r c u i t p l u g - i n , or any a r b i t r a r i l y s e l e c t e d set of c i r c u i t elements pre-assem-b l e d on an OP-O uncommitted p l u g - i n u n i t . To f a c i l i t a t e the immediate a p p l i c a t i o n of the model R.P. M a n i f o l d , a model MAK-2 co n n e c t i o n hardware k i t and the nec-e s s a r y computing grade r e s i s t o r s , c a p a c i t o r s and diodes are necessary. The most re a s o n a b l e compromise between accuracy and cost i s p r o v i d e d by components having an accuracy of ~ 1 %. b. R e s i s t o r s and c a p a c i t o r s - s p e c i f i c a t i o n s The value of a l l r e s i s t o r s used i n the c i r c u i t r y were pre -determined to an accuracy g r e a t e r than - 1 % by the manufactu-r e r . In the c i r c u i t s d e s c r i b e d i n the f o l l o w i n g s e c t i o n , i t i s n ecessary to know a c c u r a t e l y the v a l u e s of the c a p a c i t o r s used i n the cascaded R-C c i r c u i t . CDE p o l y s t y r e n e c a p a c i t o r s having a c a p a c i t a n c e of 1 J_L F and a t o l e r a n c e of - 10 percent were chosen t o be i n c o r p o r a t e d i n the cascaded R-C c i r c u i t . The quoted v a l u e s were checked on a General Radio Company imped-ance b r i d g e , type 1650-A, s e r i a l no. 6558 i n the E l e c t r i c a l E n g i n e e r i n g Department. Each were found to have a c a p a c i t a n c e of 0.95yU.F ± 0. 1 p e r c e n t . These measured v a l u e s were then used- i n subsequent c a l c u l a t i o n s . The v a l u e s of the other 11-29 c a p a c i t o r s used i n the main c i r c u i t s are not r e q u i r e d i n the c a l c u l a t i o n of the s c a l e of t u r b u l e n c e and, thus, commercial p o l y s t y r e n e c a p a c i t o r s having an accuracy of - 10 percent were adequate. c. A m p l i f i e r s , squarer and power supply The c h a r a c t e r i s t i c s of a m p l i f i e r s and the q u a d r a t i c t r a n s -conductor (squarer) are l i s t e d i n Table 11-10, 11-11, 11-12, 11-13, and 11-14. TABLE 11-10 CHARACTERISTICS OF P85AU AMPLIFIER + Supply v o l t a g e , - 15 V. D.C. Supply, c u r r e n t (max.), < - 4 mA... Output v o l t a g e range, - 11 V. Output c u r r e n t range, - 2 mA. Open-loop g a i n , D.C., > 50,000 (25 °C) Gain bandwidth, 2 mcps. o o Storage temperature, -62 C to 125 C o o O p e r a t i n g temperature, -25 C t o 85 C T A B L E ' I I - l l CHARACTERISTICS OF P35A AMPLIFIER + Supply v o l t a g e , - 15 V. D.C. Supply c u r r e n t (max.), < - 6 mA. Output v o l t a g e range, - 11 V. 11-30 Output c u r r e n t range, - 2 mA. Open--loop g a i n , D.C, > 100,000 (25 °C) Gain bandwidth, > 4 kcps. o o Storage temperature, -55 C to 85 C o o O p e r a t i n g temperature, -25 C to 85 C TABLE 11-12 CHARACTERISTICS OF P45A AMPLIFIER Supply v o l t a g e , - 15 V. D.C. -i-Supply c u r r e n t , 23 mA. Output v o l t a g e range, - 11 V. Output c u r r e n t range, - 20 mA. Open-loop g a i n , D.C 300,000 (25 °C) Gain bandwidth, > 15 mcps. Storage temperature, -55 °C t o 85 °C O p e r a t i n g temperature, -25 °C t o 85 °C TABLE 11-13 CHARACTERISTICS OF SP656 AMPLIFIER Supply v o l t a g e , - 15 V. D.C. Supply c u r r e n t (max.), - 28.2 mA. Output v o l t a g e range, - 10 V. + Output c u r r e n t range, - 20 mA. Open-loop g a i n , D.C, 50,000,000 Gain bandwidth, > 10 kcps. Photochopper e x c i t a t i o n , 50 - 80 eps. 11-31 6.3 v o l t s f o r demodulator and 115 v o l t s A.C. at 5 mA f o r photochopper Storage temperature, -55 °C to 75 °C Operating' temperature -25 °C to 65 °C TABLE 11-14 CHARACTERISTICS OF PSQ-P TRANSCONDUCTOR Input, 0 - 10 V. @ 1.2 mA. maximum Output, 0 - 0 . 5 mA. Power requirements, - 15 V. D.C. @ 2.6 mA. Optimum o p e r a t i n g temperature, 25 °C To p r o v i d e the necessary c u r r e n t t o operate the components shown i n F i g u r e 11-20, i t i s necessary t o wire a P h i l b r i c k PR-30 bench u n i t , r e g u l a t e d power supply i n p a r a l l e l with the model RP O p e r a t i o n a l M a n i f o l d power supply. The power d i s t r i b u -t i o n under maximum consumption c o n d i t i o n s i s shown i n Table 11-15. TABLE 11-15 MAXIMUM POWER CONSUMPTION AND SUPPLY Model RP O p e r a t i o n a l M a n i f o l d with model OSPR-30, dual r e g u l a t e d power supply £ 30 mA. at - 15 V. Model PR-30 bench u n i t r e g u l a t e d power supply ± 30 mA. at - 15 V. T o t a l c u r r e n t a v a i l a b l e , P35A a m p l i f i e r , P45A a m p l i f i e r , P85AU a m p l i f i e r , SP606 a m p l i f i e r , PSQ-P q u a d r a t i c t r a n s c o n d u c t o r , T o t a l c u r r e n t consumption, It i s h i g h l y improbable that a l l of the a m p l i f i e r s w i l l be at f u l l l o a d s i m u l t a n e o u s l y and, thus, the proposed power supply i s adequate. The SP656 a m p l i f i e r r e q u i r e s an a d d i t i o n a l 115 V. A.C. power supply at 5 mA. to operate the photochopper and demodula-t o r . For proper o p e r a t i o n of the SP656 a m p l i f i e r , t h i s 115 V. power supply must have the proper p o l a r i t y . S ince t h i s ampli-f i e r i s chopper s t a b a l i z e d and, thus, minimizes D.C. d r i f t and o f f s e t , i t i s used i n the i n t e g r a t i o n c i r c u i t . d. E l e c t r i c a l analogue c i r c u i t response A DISA type 55A01 constant temperature hot-wir,e anemometer i s used t o r e c o r d the f l u c t u a t i n g v e l o c i t i e s i n the t u r b u l e n t f l u i d . The anemometer r e c o r d s these v e l o c i t i e s i n the form of a f l u c t u a t i n g A.C. v o l t a g e which' may have a value as high as one v o l t depending on the i n t e n s i t y of the f l u i d t u r b u l e n c e . T h i s v o l t a g e s i g n a l i s a d i r e c t l y p r o p o r t i o n a l measurement of u-. , that i s 11-32 - 60 mA. at - 15 V. - 8 mA. at - 15 V. - 23 mA. at - 15 V. - 6 mA. at - 15 V. 28.2 mA. at - 15 V. - 2.6 mA. at - 15 V. - 67.8 mA. at - 15 V. 11-33 v = K* u± ( I I - 9 ) at any i n s t a n t (where v i s the i n s t a n t e n o u s value of the f l u c t u a t i n g v o l t a g e ) . For steady s t a t e t u r b u l e n t flow, "u7 = 0 (11-10) If the f l u c t u a t i n g A.C. v o l t a g e i s c o n s i d e r e d as c o n s i s t i n g of a p o s i t i v e and a n e g a t i v e part denoted by u^ and u^ r e s p e c t i v e l y , then s t a t i s t i c a l l y over a p e r i o d of time (U]_ + ) 2 = ( u x " ) 2 (11-11) and (u., ) 2 = 2 ( U 1 + ) 2 (11-12) E l e c t r o n i c c i r c u i t s may be used to e v a l u a t e the two un-2~ Vi,2 known terms i n Eq„ (51), that i s , u-^  and (1 + 47T2 n , 2 t 0 2 ) 2 U n f o r t u n a t e l y the t u r b u l e n c e b u t - s i g n a l of a DISA constant temperature hot-wire anemometer i s superimposed on a D.C. v o l -tage s i g n a l . It i s i m p o s s i b l e to e l e c t r o n i c a l l y manipulate the f l u c t u a t i n g s i g n a l without removing the D.C. p o r t i o n of the output. 11-34 The t u r b u l e n c e o u t - s i g n a l on the anemometer appears, as i n F i g u r e I1-9 V O L T S 0 ' O F F S E T T I M E FIGURE I1-9. ANEMOMETER OUTPUT SIGNAL It i s d e s i r e d t o convert t h i s s i g n a l i n t o the form shown i n F i g u r e II-10. V O L T S 0 TIME FIGURE 11-10. FLUCTUATING SEGMENT OF ANEMOMETER OUTPUT SIGNAL It i s proposed t o use a p r a c t i c a l d i f f e r e n t i a t o r t o e l i m i n a t e the unwanted D.C. v o l t a g e . The d i f f e r e n t i a t o r can be s i m u l t a n e o u s l y used as an a m p l i f i e r . Consider the c i r c u i t shown i n F i g u r e 11-11. eQ - e< Z 2 (H-13) 11-35 F I G U R E 11-11. P R A C T I C A L D I F F E R E N T I A T O R Z X = RlN + 30J C I N z 2 = Rf Z 2 < j Rf (J C I N Z X 1 + JU) C I N R I N (11-14) (11-15) (11-16) Cc* C I N Rf ^ / i + cu2 c IT (11-17) I N R I N If <<• R I N U I N then 1 1 - 3 6 Z 2 R f - = ( 1 1 - 1 8 ) Z l R I N ^IN ^ s chosen to be a 2 5 fj, F e l e c t r o l y t i c c a p a c i t o r . In order t o operate, t h i s c a p a c i t o r must experience a p r o p e r l y p o l a r i z e d D„C. v o l t a g e . T h i s r e s t r i c t i o n i s overcome by the nature of the s i g n a l . Thus, i t i s not recommended to b i a s the D.C. anemometer output v o l t a g e t o a low l e v e l f o r t h i s type of c a p a c i t o r , as i t would be necessary to do with a f i l m c a p a c i t o r t o stop c u r r e n t leakage. The r e s i s t a n c e R J N has a t y p i c a l value of 1 0 0 k . For t h i s s i t u a t i o n the ' c u t o f f frequency' i s g i v e n by W CUTOFF = ( I I ~ 1 9 )  K I N IN - 1 = 0 . 4 sec. f CUTOFF ^CUTOFF/ 2 7 7" = 0 . 0 6 4 ops. T y p i c a l l y , the frequency of the t u r b u l e n t s i g n a l that i s b e i n g measured i s much l a r g e r than 0 . 0 6 cps. Thus, the p r a c t i -c a l d i f f e r e n t i a t o r w i l l f u n c t i o n as a pure a m p l i f i e r with a t y p i c a l g a i n as shown i n F i g u r e 1 1 - 1 2 . 11-37 u-EVALUATION OF (1 + 4 7 T 2 n * 2 t 0 2 ) 2 The v o l t a g e l e v e l of an e l e c t r o n i c s i g n a l may be too l a r g e or s m a l l t o be c o n v e n i e n t l y manipulated i n other c i r c u i t s , The s i g n a l may be s c a l e d up or down by means of an a m p l i f i e r and two r e s i s t o r s connected as shown i n F i g u r e 11-13. FIGURE 11-13. AMPLIFIER The response of the above c i r c u i t i s given by IT-38 e 0 = - ( R 2 / R i ) e ± • (11-20) I f a s i g n a l i s o v e r - a m p l i f i e d , t h e r e may be a r e s u l t i n g e r r o r . Consider the c i r c u i t shown i n F i g u r e 11-13. Assume that the a m p l i f i e r has a g a i n A3 and that no c u r r e n t passes through the a m p l i f i e r . e^ - e e + A o e i = _ i = . — £ (11-21) R1 R 2 where e Q = - A 3 e Combine and s i m p l i f y : e o . , N / f 1 + A 3 R 2 = - ( R o / R j / 1 + > (11-22) e i / I A 3 A 3 R l -For an exact and i d e a l a m p l i f i e r , R 2 A3 > > • ; A3 >> 1.0 R l and thus 11-39 e i R l (11-20) The value of Ag f o r an a m p l i f i e r depends on s e v e r a l par 5 meters. T y p i c a l l y Ag has a value of 10 . I f a s i g n a l i s being a m p l i f i e d such that •- i o 3 then the r e a l g a i n w i l l be e o 3, e i 0.99 (10 ) 3 i n s t e a d of the c a l c u l a t e d g a i n of -10 . P r e c a u t i o n s were taken t o ensure that the s i g n a l s were 2 never a m p l i f i e d by more than a f a c t o r of 2 (10 ). Thus, a l l e r r o r s a r i s i n g from the f a c t that the a m p l i f i e r s have a f i n i t e g a i n are n e g l i g i b l e . Consider the c i r c u i t shown i n F i g u r e 11-14. R i A e e I ~ ° "2 x~ FIGURE 11-14. R-C CIRCUIT 11-40 The t o t a l , impedance of the c i r c u i t i s . given by 1 Z x = R - j (11-23) (DC I f the c u r r e n t i s denoted by i , z i _ (H-24) V R + l/or c The impedance of the c a p a c i t o r i s Z 9 = - j/CUG (11-25) Thus, 1 1 Z 2 | = y R 2 „2,„2 (H-26) c oj + i If two r e s i s t a n c e - c a p a c i t a n c e c i r c u i t s of the- type shown i n F i g u r e 11-15 are cascaded and s e p a r a t e d by a cathode f o l l o -wer with high impedance c h a r a c t e r i s t i c s t o prevent i n t e r a c t i o n of the two c i r c u i t s , the f o l l o w i n g a n a l y s i s i s ob t a i n e d . 11-41 FIGURE 11-15. CASCADED R-C CIRCUIT The cathode f o l l o w e r has a gain of minus u n i t y . The o r i g -i n a l c i r c u i t s used by Townsend omitted the cathode f o l l o w e r , and e x p e r i m e n t a l l y i t can be seen that the c i r c u i t output i s v i s u a l l y u n a l t e r e d by e x c l u d i n g the f o l l o w e r . T h e r e f o r e , the c i r c u i t appears as i n F i g u r e 11-16. FIGURE 11-16. MODIFIED CASCADED R-C CIRCUIT Thus, assuming that the cascaded r e s i s t a n c e - c a p a c i t a n c e c i r c u i t s are independent of each other, from Eq. (11-26) i t i s known that e 0 = e- 2 2 2 „ R cu C + 1 (11-27) S i m i l a r l y 11-42 2 2 9 e 3 = e2• / v R < a J C + 1 (i : - 2 8 ) T h e r e f o r e , e3 = e x / (R 2 a/2 C 2 + 1) (11-29) But i t can be r e a d i l y seen from Eq. (11-29) that f o r the c i r c u i t shown i n F i g u r e 11-16, the output v o l t a g e eg w i l l be very s m a l l f o r l a r g e frequency A.C. s i g n a l s . Thus, a m p l i f i e r s may be i n s t a l l e d before and a f t e r the c i r c u i t t o r a i s e the input s i g n a l v o l t a g e t o a maximum t o l e r a b l e l e v e l and to r a i s e the output s i g n a l v o l t a g e t o a r e a d i l y usable range. Such a c i r -c u i t i s shown i n F i g u r e 11-17. FIGURE 11-17. COMPLETE R-C CASCADED CIRCUIT From Eq. (11-18) and Eq. (11-29), i t can be shown f o r the c i r c u i t i n F i g u r e 11-17 that 11-43 R- R 3 J (R 2 CO ^  C 2 + 1) (11-30) where v i s the output of the hot-wire anemometer. Combining Eq-. (II-9) and Eq. (11-30) g i v e s R, u-e. = K 1 4 (11-31) R3J (R OJ c C + 1) The output from the r e s i s t a n c e - c a p a c i t a n c e cascade c i r -c u i t i s squared i n a commercially produced e l e c t r o n i c squar-i n g c i r c u i t . For t h i s a p p l i c a t i o n a P h i l b r i c k Researches Com-pany squarer c i r c u i t can be used, as shown i n - F i g u r e - 11-18. , FIGURE 11-18. SQUARER For the c i r c u i t shown i n F i g u r e 11-18, 11-44 e 5 = e 4 2 /10 (11-32) The PSQ-P q u a d r a t i c t r a n s c o n d u c t o r accepts only p o s i t i v e input s i g n a l s . Thus the squarer squares o n l y the p o s i t i v e p a r t of the A.C. s i g n a l r e c e i v e d as e 4 . But i t has been shown p r e v i o u s l y that + 2 2 ( u l ) " ( u l } / 2 (H-12) and s i m i l a r l y ( e 4 + ) 2 = ( e 4 2 ) / 2 (11-33) The a m p l i f i e r shown i n F i g u r e 11-18 produces a s i g n i n -v e r s i o n , and the output f l u c t u a t i n g v o l t a g e i s gi v e n by 10 L R - J lR3J |^  R CO C + 1 The output s i g n a l e^ may be averaged by means of an integ-r a t i o n c i r c u i t . The average s i g n a l from e^ i s d e f i n e d as i T> e 5 — J e 5 d t * (11-35) where ' T, i s . t h e time of i n t e g r a t i o n . I f the s i g n a l 11-45 i s r e c o r d e d , the time over which the i n t e g r a t i o n i s allowed to operate can be determined from the r e c o r d e r c h a r t . The i n t e g r a t i o n c i r c u i t shown i n F i g u r e 11-19 i n c o r p o r a t e s two t o g g l e s w i t c h e s ; which serve t o s i m u l t a n e o u s l y i s o l a t e the a m p l i f i e r and r e s e t the i n t e g r a t i o n c i r c u i t , or when switched the other way, connect the a m p l i f i e r and begin the i n t e g r a t i o n . OFF o o S W I T C I ^ ^ 6^ o o I N T E G R A T E C -6 D 1 » D 2 - PROTECTIVE DIODES FIGURE 11-19. INTEGRATION CIRCUIT For the c i r c u i t shown i n F i g u r e 11-19, 11-46 t * 0 R 5 C l 0 e c dt* (11-36) From Eq. (11-35) and Eq. (11-36), 0 R 5 C l T l e 5 0 (11-37) and 6 K* R2 0 10 R 5 C± IR± R4V R 3 j 1 (R 2 C 2 CO 2 + 1) (11-38) But s i n c e u- . u l 9 9 9 , 2 (.R C (*) + 1) 2 ( R 2 C 2 W 2 + l ) 2 (11-39) then K .2 T . [ R 2 20 R5C]! (jR^ 2 ' R 4 > 2 R-u-( R 2 C 2 CU 2 + l ) 2 u-constant X ( R 2 C 2 O J 2 +' l ) 2 (11-40) 11-47 But CO = 2 7T n (11-41) and thus u-= constant (.! + 4 7T 2 n ' 2 R 2 C 2) 2 (11-42) Compare Eq.. (11-42) and Eq. (51). It i s obvious that o RC (11-43) Thus, u 1 (1 + 4 7T 2 n ' 2 t Q 2 ) 2 20 R 5 C1 R-K' R, ^3 R. (11-44) The complete analogue c i r c u i t f o r computing the r i g h t s i d e of Eq. (11-44) i s shown i n F i g u r e 11-20, and the s p e c i f i c ampli-f i e r s used i n each c i r c u i t are l a b e l l e d a c c o r d i n g l y . EVALUATION OF u-Consider the c i r c u i t shown i n F i g u r e 11-20 begi n n i n g at D l > D 2 ~ PROTECTIVE DIODES INTEGRATE C> Q SWITCH I - PHILBRICK SOLID STATE P45A AMPLIFIER 2- » " « P 85 AU AMPLIFIER 3- u « II PSQ - P QUADRATIC T R A N S C O N D ' U C T O R 4" » " P3 5 A A M P L I F I E R 5- " " " SP656 AMPLIFIER W I T H PHOTOCHOPPER i—i FIGURE 11-20. ANALOGUE, CIRCUIT WITH SIGNAL FILTER co 11-49 p o i n t a, and v a r y i n g R3 and R 4 t o R33 and R44 . r e s p e c t i v e l y as shown i n F i g u r e 11-21. FIGURE 11-21. MODIFIED CIRCUIT From the f i r s t a m p l i f i e r the output i s -(R44/R33) K' U ] _ The output from the squarer i s K E l = — 10 ,2 R 4 4 l 2  R 3 3 J + . 2 (11-45) Using the i n t e g r a t o r with the same time constant as used i n the former c i r c u i t , the output of the t o t a l c i r c u i t as shown•in F i g u r e 11-22 i s K ,2 E6 '0 R 5 C r 10 l R 3 3 j 0 d t * (11-46) D l » D 2 ~ PROTECTIVE DIODES INTEGRATE I - PHSLBR5CK SOLID STATE P 4 5 A ' AMPLIFIER 3 - II n n . P S Q - P Q U A D R A T I C TRAMSCONOUCTOR 4 - « . M a i P 3 5 A A M P L I F I E R 5- • os M ii . S P 6 5 6 A M P L I F I E R WITH PHOTOCHOPPER FIGURE 11-22. ANALOGUE CIRCUIT WITHOUT FILTER n - 5 : But (u n ) f s 2 / _ ( u ^ ) 2 d t * '2 0 ( 1 1 - 4 7 ) and + 2 (u-j ) 9 n 2 ^ LI -j ( 1 1 - 1 2 ) S u b s t i t u t e Eq. ( 1 1 - 1 2 ) and Eq. ( 1 1 - 4 7 ) i n t o Eq. ( 1 1 - 4 6 ) "1 = E 6 T 2 R 5 C 1 2 0 0 R 33 T2 K'2 R 44 . ( 1 1 - 4 8 ) Combine Eq. ( 1 1 - 4 8 ) and Eq. ( 1 1 - 4 4 ) u l u-X ( 1 + 4 TT 2 n ' 2 t Q 2 ) . 2 ;6 0 T o R-R 2 R, % 3 Y R 4 4 J ( 1 1 - 4 9 ) Thus, comparing Eq. ( 1 1 - 4 9 ) and Eq. ( 5 1 ) , 11-52 :J (2 RG) 0 To 0 T, { R. R 4 4 . (11-50) The time of i n t e g r a t i o n Tt may be c a l c u l a t e d from the r e c o r d e d i n t e g r a t o r output. If the a b s c i s s a under the i n t e g r a -t i o n curve has a l e n g t h ABSC 1 inches long and the cha r t speed i s CHT SPD 1 inches/minute, then ABSC 1 CHT SPD 1 x 60 (11-51) S i m i l a r l y T2 = ABSC 2 CHT SPD 2 x 60 (11-52) For the c i r c u i t proposed, R and C are chosen t o be respec-t i v e l y R = 10 k X I C = 0.95^. F The v a l u e s of these components were checked w i t h i n 0.1 'percent on a General Radio Company impedance b r i d g e , type II-5 1650-A, s e r i a l 6552 i n the E l e c t r i c a l E n g i n e e r i n g Department at U.EvCV The valu e s of R5 and Cx were l e f t u n a l t e r e d f o r a l l runs at 1 m £L and O.l^xF r e s p e c t i v e l y . The c i r c u i t r y as shown i n F i g u r e 11-20 may be q u i c k l y c o n v e r t e d t o that i n F i g u r e 11-22 by the f o l l o w i n g procedure: (1) remove the second R-C cascade. (2) in t e r c h a n g e Rg and R^  by R^ g and R r e s p e c t i v e l y . (3) move the input s i g n a l from the P85AU a m p l i f i e r to the P35A a m p l i f i e r . d. T e s t i n g c i r c u i t s To t e s t the c i r c u i t r y i t i s convenient t o have a v a i l a b l e known v o l t a g e l e v e l D.C. s i g n a l . The model R.P. O p e r a t i o n a l + M a n i f o l d p r o v i d e s t h r e e a c c u r a t e - 15 v o l t sources. But the maximum input v o l t a g e of each a m p l i f i e r i s - 10 v o l t s . Thus, a d e s i r a b l e s i g n a l l e v e l was chosen t o be - 1 v o l t f o r f i n a l c h e c k i n g of complete c i r c u i t s . A p o t e n t i a l d i v i d e r was c o n s t r u c t e d t o p r o v i d e t h i s - 1 v o l t s i g n a l as shown i n F i g u r e 11-23. 9+I5V SWITCH 15 V * 14 k£l<> - A r IkQ, + IV FIGURE 11-23. TESTING CIRCUIT 11-54 When the k n i f e switch i s c l o s e d i n p o s i t i o n A, the v o l t a g e drop acr o s s the 1 k XI r e s i s t o r i s 1000 V A = x 15 = +1 v o l t 15000 The c u r r e n t drawn from the power supply i s I A = 1 mA„ • S i m i l a r l y with the s w i t c h i n p o s i t i o n B, V B = -1 v o l t Ij3 .= -1 mA„ Thus, the p o t e n t i a l d i v i d e r s e r v e s as an economical and handy power r e g u l a t o r . 11-55 IV. SAMPLE MOULDING 1. Moulds During the p e r i o d of an experiment a s m a l l amount of s o l i d c h e m i c a l i n a. wet-bulb sublimes i n t o the s urrounding f l o w i n g gas stream. Since the thermocouples that measure the s u r f a c e temperature become exposed near the t e r m i n a t i o n of each run, and thus i n v a l i d a t e the sample f o r f u r t h e r experiments, i t was necessary t o have an e f f i c i e n t method of f a b r i c a t i n g the s o l i d wet-bulbs with the e n c l o s e d thermocouples. Garner and Keey (34) s t a t e that m a t e r i a l s used i n the making of s o l i d spheres (such as benzoic a c i d ) are u s u a l l y c r y s t a l l i n e , and t h a t compression of the s o l i d i s p r e f e r a b l e t o c a s t i n g , as the l a t t e r p r ocess tends t o g i v e d i f f e r e n t i a l o r i e n t a t i o n t o the c r y s t a l s . But t h e r e are n o . a v a i l a b l e data t o v e r i f y t h a t the d i f f e r e n t i a l o r i e n t a t i o n , i f i t e x i s t s , has any e f f e c t on mass t r a n s f e r or p s y c h r o m e t r i c experiments. The author attempted t o f a b r i c a t e spheres by compressing c r y s t a l l i n e naphthalene at room temperature. The r e s u l t i n g spheres were u n s a t i s f a c t o r y s i n c e they tended t o have non-uniform s u r f a c e s and to f a l l apart e a s i l y . But a moulding technique was found to g i v e s t u r d y , uniform samples. The samples were moulded from the s i x moulds l i s t e d i n T a b l e 11-16. The d e t a i l s of these moulds can be found i n F i g u r e s 11-24 to 11-29. 11-56 FIGURE 11-24. SAMPLE MOULD NUMBER 1 11-57 LJ -1 1 1 1 I » t 1 *8 l£ . 20NCT (2 Req'd) 2/2 lA ROD GUIDE ( 2 Req'd) MATERIAL- BRASS FIGURE 11-25. SAMPLE MOULD NUMBER 2 v ^ 4V ^ i / 4 » « 1J4 / 8 ROD GUIDE (2 Req'd) k4" » 2 0 N C T (2 Req'd) MATERIAL - ALUMINUM FIGURE 11-26. SAMPLE MOULD NUMBER 3 1 1 - 5 9 l/4 , 2 0 NCT (2 Req'd) l/4"R0D GUIDE (2 Req'd) M A T E R I A L - BRASS FIGURE-11-27. SAMPLE MOULD NUMBER 4 11-60 FIGURE .11-28. SAMPLE MOULD NUMBER 5 11-61 o o T -?9 M l * - * 2 1/2° >| , , iTTW 2 >/2 l / 8 " , 2 0 N C T (4 Req'd) MATERIAL - BRASS 2 SIDES REQ'D 1/8 HOLE (4 Req'd) '/e HOLE ( 2 Req'd) SECTION A-A FIGURE 11-29. SAMPLE MOULD NUMBER 6 11-62 TABLE 11-16 WET-BULB MOULDS Mould No. Sample shape Dimensions, inch 1 C y l i n d e r d p = 0.519, L = 2 2 C y l i n d e r d p = 0.375, L = 2 3 Sphere dp = 1.0 4 Sphere : dp = 0.75 5 C y l i n d e r dp = 0. 5, L = 3 6 F l a t p l a t e L = 4, W = 2, T = 0.375 2. Moulding technique The moulds are thoroughly washed with acetone and allowed t o dry b e f o r e a sample i s c a s t . With one-half of the mould s e c u r e l y h e l d i n p l a c e , the thermocouples t h a t are t o be c a s t i n t o the sample are l o c a t e d and h e l d i n t h e i r d e s i r e d p o s i t i o n s i n the empty mould. Then the mould i s c l o s e d and the two h a l v e s t i g h l y screwed t o g e t h e r . Naphthalene and p-dichlorobenzene c r y s t a l s i n a beaker r e a d i l y melt when the beaker i s immersed i n a b o i l i n g water bath. D-camphor c r y s t a l s , which have a higher m e l t i n g p o i n t , must be p r e p a r e d f o r moulding i n an o i l bath. The molten chemical i s poured i n t o the mould d i r e c t l y from the melt beaker. Since the chemical tends to c o n t r a c t s l i g h t l y as i t c o o l s , i t i s necessary to make s l i g h t a d d i t i o n s t o the mould. A f t e r f i f t e e n minutes the sample can be removed from the mould. There i s an excess of sample around the area where 1 1 - 6 3 the c h e m i c a l i s poured i n t o the. mould. T h i s excess sample i s f i l e d away be f o r e u s i n g the sample i n an experiment. 11-64 V. TEMPERATURE MEASUREMENT 1. Free stream temperatures In the wind t u n n e l the temperature of the a i r f l o w i n g through the o r i f i c e i s measured by a s t a i n l e s s s t e e l sheathed 24 gauge thermocouple h e l d c e n t r a l l y i n the two i n c h i n l e t pipe by a swagelok f i t t i n g . S i nce the incoming a i r temperature i s approximately the same as the room temperature, t h e r e i s no need t o c o r r e c t f o r thermal c o n d u c t i o n e f f e c t s along the thermo-couple wires and s h e a t h i n g . The temperature of the a i r or helium that flows past the samples must be known a c c u r a t e l y . The gas o p e r a t i n g temperature can d i f f e r from the room temperature by as much as 100 ° F, thus c r e a t i n g temperature e r r o r s due to thermal c o n d u c t i o n along the temperature s e n s i n g probe. The temperature p r o f i l e a c r o s s a c e n t r a l l y l o c a t e d s e c t i o n of the i n s u l a t e d wind t u n n e l was measured with a s t r a i g h t , 24 gauge sheathed thermocouple probe as shown i n F i g u r e 11-30 (thermocouple No. 9). The r e s u l t i n g p r o f i l e as shown i n F i g u r e 11-31 becomes h i g h l y unsymmetric as the l e n g t h of the thermo-couple i n s i d e the duct i s decreased. T h i s measurement e r r o r i s the r e s u l t of c o n d u c t i o n along the probe, due t o the 80 ° F temperature g r a d i e n t between the duct f r e e stream and ambient temperature. An e f f o r t was made to e l i m i n a t e the c o n d u c t i o n e r r o r by m o d i f y i n g the probe as shown i n F i g u r e 11-30. The r e s u l t i n g p r o f i l e as shown i n F i g u r e 11-32 i s much more symmetric, thus 11-65 rrh Z Z Z Z 2 I Z Z Z Z Z S - S - S H E A T H E D T H E R M O C O U P L E PROBE GAS FLOW SAMPLE SECTION DUCT WALL Y/////////777r7r\ 1 BENT T H E R M O C O U P L E P R O B E GAS < FLOW < 1 ->| SAMPLE SECTION DUCT WALL FIGURE .11-30. THERMOCOUPLE PROBES FOR MEASURING GAS TEMPERATURE 11--66 2.70 2.68 2.5 8 2.56 _ _ _ - O - - - -o. p' rvO-.45°F \ RE d w 30,000, AIR TEMPERATURE » 15 0° F \ b f \ 0.5 1.0 1.5 2.0 2.5 3.0 3.5 DISTANCE F R O M S A M P L E S E C T I O N B O T T O M ( Incheo) 4.0 FIGURE • 11-31. TEMPERATURE PROFILE IN WIND TUNNEL AS MEASURED WITH A STRAIGHT PROBE 11-67 270 2.69 2.68 > - 2.67 u.' ui CL "D O o o £ ui x H 266 2.65 2.64 2.63 1 1 1 1 1 o 1 1 „ - - o - ~ S _ / / / s P \ K / H / \ / \ / V / \ - / / / \ \ ~ \ / \ i* \ 7 - y ™ 7 ) rv0.45°F _ 1 < REd « 30,000. AIR TEMPERATURE « |50°F — ......1 1 1 ,1 , I 0.5 1.0 1.5 2.0 2.5 -3.0 3.5 DISTANCE FROM SAMPLE SECTION BOTTOM (Inches) 4.0 FIGURE 11-3 2. TEMPERATURE PROFILE IN WIND TUNNEL AS MEASURED WITH A BENT PROBE 11-68 i n d i c a t i n g t h a t the bent thermocouple probe i s more l i k e l y t o be r e c o r d i n g the c o r r e c t gas temperature. It can be seen that the temperature p r o f i l e over the c e n t r a l two i n c h square area i s almost f l a t . The f r e e stream temperature f o r each run i s measured by a bent probe l o c a t e d one i n c h from the top and one inch from the s i d e of the wind t u n n e l i n the sample s e c t i o n . Thus l o c a t e d , the probe does not d i s t u r b the a i r flow i n f r o n t of the sample. In the gas r e c i r c u l a t i n g apparatus, the probe i s maintained one i n c h from the pipe w a l l i n the sample s e c t i o n . 2. Wet-bulb temperatures The wet-bulbs are c e n t r a l l y supported i n the sample s e c t i o n by a 1/8 inch aluminum p i p e . The pipe i s bent p a r a l l e l t o the d i r e c t i o n of gas flow f o r 4 inches to reduce conduction e f f e c t s along the thermocouples as e x p l a i n e d p r e v i o u s l y . The pipe reaches only t o the near s u r f a c e of the sample (see F i g u r e 9). The sample weight i s supported by the thermocouples themselves. The thermocouples i n s i d e the sample are p o s i t i o n e d before c a s t i n g . C e n t r a l l y l o c a t e d thermocouples measure the macro-s c o p i c wet-bulb temperatures. D e t a i l s of the technique asso-c i a t e d with measurement of exact s u r f a c e temperatures are p r e s e n t e d i n the e x p e r i m e n t a l procedure s e c t i o n . 3. Wall temperatures a. Wind t u n n e l To be able t o c a l c u l a t e the amount of r a d i a t i o n heat t r a n s -f e r between the sample and wind t u n n e l w a l l s , the temperature 1 1 - 6 9 of the wind t u n n e l must be known-. The w a l l temperature of the i n s u l a t e d wind t u n n e l i s a f u n c t i o n of the a i r v e l o c i t y and temperature and the ambient temperature. But the ambient temperatuie remains almost constant and, thus, the wind t u n n e l w a l l temperature may be expressed o n l y as a f u n c t i o n . o f the a i r f r e e stream temperature and mass v e l o c i t y . Wind t u n n e l w a l l temperatures were measured at four l o c a -t i o n s f o r t h r e e a i r v e l o c i t i e s and over a wide range of a i r temperatures. Since i t was d e s i r e d t o measure the temperature very c l o s e t o the w a l l s u r f a c e , the very t h i n 40 gauge thermo-co u p l e s were used. These thermocouples were h e l d t i g h t l y along the wind t u n n e l w a l l i n t e r i o r with a t h i n f i l m of p l a s t i c i n e . The four thermocouple l o c a t i o n s are shown i n F i g u r e 1 1-33. 1,2,3,4 REFER TO THERMOCOUPLE LOCATION FIGURE 1 1-33. LOCATION OF WALL TEMPERATURE MEASUREMENTS IN WIND TUNNEL For each a i r temperature the apparatus r e a c h e d a steady ate w a l l temperature a f t e r one hour. TABLE 11-17 WALL TEMPERATURES - AIR FLOW 0.039 l b . / s e c . A i r Temp. ° F o Wall Temperature F Thermocouple Locat ion 1 2 3 4 146.0 125.9 124.5 128. 5 126.2 147.0 127.2 125.8 129.0 127. 2 114.0 102. 5 102.3 104.8 103. 5 114.9 103.4 103.0 105. 5 104. 5 138.1 122. 5 121.7 124.1 122.8 TABLE 11-18 WALL TEMPERATURES - AIR FLOW 0.078 lb.-/sec, A i r Wall Temp. A i r W a l l Temp. Temp. Locat i o n Temp. L o c a t i o n o F 1 ° F 4 124.8 110. 7 123.4 111.6 140. 3 125. 1 140.3 123.8 164. 1 144. 1 155.8 138.4 142.5 125.1 183.5 157. 5 131. 5 116. 8 166.6 140.7 73. 3 71. 3 74.9 73.8 84.8 80. 1 97. 3 89.8 105.0 96.4 114.2 104.8 92. 4 86.8 103. 9 95. 5 107.4 96.6 117. 3 103.4 TABLE 11-19 WALL TEMPERATURES - AIR FLOW 0.122 l b . / s e c . A i r Wall Temp. Temp. Locat ion ° F 1 68. 6 67. 3 91.4 86. 3 102. 1 94. 9 109. 2 102.1 120.7 109.7 68.9 67. 3 91.3 86. 3 101.4 94.9 109. 5 102. 1 119.0 109.7 A i r Wall Temp. Temp. Locat i o n ° F 4 115. 8 109. 1 138. 3 128.3 155.7 142.4 169. 2 154.7 The wind t u n n e l w a l l temperature data were c u r v e - f i t t e d by le a s t ' squares t o an equation of the form t W A - D + D2 *DB + D3 *PB (11-53) 11-72 The r e s u l t s of the c u r v e - f i t s are l i s t e d i n Table 11-20, where t ^ i s the wind t u n n e l wt'-ll temperature i n ° F and t i s the f r e e stream a i r temperature i n ° F. TABLE 11-20 PREDICTION OF WIND TUNNEL WALL TEMPERATURES A i r Flow l b / s e c D l D2 D 3 x 10 3 R.M.S. E r r o r i n Parameters T o t a l S t a t i s t i c a l D 2 D3-103 D 2 D -103 3 0.039 25. 42 0. 606 0. 385 4.04 0.68 0.28 4. 10 0. 69 0.28 0.078 14. 54 0.776 0.018 5.20 0.86 0. 34 3.49 0. 57 0.23 0. 122 11. 12 0.793 0. 330 3.45 0. 60 0. 26 3.81 0. 67 0.28 . It w i l l be noted that the q u a d r a t i c term of the c u r v e - f i t i s almost n e g l i g i b l e , as expected. b. Gas r e c i r c u l a t i n g apparatus w a l l temperatures The w a l l temperature of the gas r e c i r c u l a t i n g duct was measured c o n t i n u a l l y f o r each run. Thermocouple number seven was g l u e d t o the o u t s i d e of the copper d u c t i n g under the i n s u l a -t i o n at a l o c a t i o n c o r r e s p o n d i n g t o the sample l o c a t e d i n s i d e 1 . . . . . the duct. Under steady s t a t e c o n d i t i o n s , the o u t s i d e duct w a l l temperature v a r i e d by l e s s than 0.4 0 F f o r s e v e r a l l o c a t i o n s along and around the sample s e c t i o n . The s i n g l e temperature r e a d i n g was assumed t o be s u f f i c i e n t t o c h a r a c t e r i z e the o u t s i d e duct w a l l temperature. It can be shown t h a t , f o r the range of Reynolds numbers and 11-73 gas temperatures-encountered- i n the experiments,'for both a i r and helium, the i n s i d e duct w a l l temperature minus the o u t s i d e duct w a l l temperature i s never g r e a t e r than 0.07 ° F. Since t h i s d i f f e r e n c e i s s m a l l compared t o l o c a l v a r i a t i o n s i n the duct w a l l temperature, the value f o r w a l l temperature used i n a l l c a l c u l a t i o n s was that measured, on the o u t s i d e of the copper duct. T r a n s i e n t v a r i a t i o n s i n w a l l temperature r e s u l t from s t a r t i n g a run u s i n g a sample s e c t i o n l i d which i s c o o l e r than the preheated duct. ' 4. Potentiometer A Leeds and Northrup m i l l i v o l t potentiometer was used t o determine the p o t e n t i a l of the thermocouples. A l l the thermo-couples were connected to a m u l t i p o i n t s w itch and the leads from the sw i t c h were taken t o the potentiometer. D e t a i l s of the potentiometer are gi v e n i n Table 11-21. . TABLE 11-21 POTENTIOMETER SPECIFICATIONS Leeds and Northrup, p o r t a b l e p r e c i s i o n p o t e n tiometer, No. 8662, Ch. E. 1648A Range 0 - 1 6 mV. 0 - 80 mV. Accuracy - 0.001 mV. The potentiometer balance was checked b e f o r e each r e a d i n g a g a i n s t a s t a n d a r d c e l l made by Eppley L a b o r a t o r i e s Inc., s e r i a l 11-74 No. 737516. The v o l t a g e of the s t a n d a r d c e l l was last, checked on December 27, 1960 and was found w i t h i n 0.01 percent t o be 1.01924 a b s o l u t e v o l t s at 22 ° C. I I I - l APPENDIX THREE CALIBRATIONS . . . I. THERMOCOUPLE CALIBRATIONS The s t a n d a r d used t o c a l i b r a t e the thermocouples numbers 1 to 6 was a Leeds and Northrup ' F i s h t a i l ' P l a t i n u m R e s i s t a n c e Thermometer, s e r i a l No. 678368. T h i s thermometer had been c a l i -b r a t e d by the N a t i o n a l Research C o u n c i l on October 6, 1959. It was found that between 0 °. and 100 ° C, agreement with the I n t e r n a t i o n a l Temperature S c a l e of 1948 w i t h i n t 0.002 ° C was o b t a i n e d by . R + = R (1 + A' t + B' t 2 ) ( I I I - l ) where R t = r e s i s t a n c e of pl a t i n u m r e s i s t o r at t ° C, ohms R o A' = r e s i s t a n c e of platinum r e s i s t o r at 0 ° C, ohms o - 1 = 0.0039817 ° C B' = -0.5842 x 1 0 - 6 ° C~ 2 R o - 25.558 ohms R e s i s t a n c e of the p l a t i n u m r e s i s t a n c e thermometer was measured by a Leeds and Northrup # 46712 Mueller Temperature Br i d g e . . The b r i d g e was found t o have a zero c o r r e c t i o n of + 0.0002 ohms. Measurements of R i n an i n s u l a t e d ice-water mixture . o gave c o n s i s t e n t v a l u e s of 25.5309 ohms. Thus, a value of R Q = 25.5609 was used f o r a l l c a l i b r a t i o n s . r The s t a n d a r d used to c a l i b r a t e the thermocouples numbers 7 t o 9 was a Leeds and Northrup Platinum R e s i s t a n c e Thermometer, s e r i a l No. 169314. The thermometer had been c a l i b r a t e d by the N a t i o n a l Research C o u n c i l on October 6, 1959. It was found t h a t between 0 ° and 100 ° C, agreement with the I n t e r n a t i o n a l Temperature S c a l e of 1948 w i t h i n - 0.002 ° C was o b t a i n e d by R = R (1 + A f l t + B ' H 2 ) ( I I I - 2 ) t o where r e s i s t a n c e of p l a t i n u m r e s i s t o r at t ° C, ohms r e s i s t a n c e of p l a t i n u m r e s i s t o r at 0 ° C, ohms 0.0039329 ° C -7 o -2 -5.8138 x 10 C 2^128 ohms -The r e s i s t a n c e of the p l a t i n u m r e s i s t a n c e thermometer was measured by a Leeds and Northrup # 8067 Mueller Temperature B r i d g e . The b r i d g e v/as found t o have a zero c o r r e c t i o n of -0.001 ohms and an R value of 2.5128 ohms. A t o t a l of 18 copper constantan thermocouples were c a l i -b r a t e d . These thermocouples were i d e n t i f i e d and used as out-l i n e d i n T a b l e I I I - l . R, R o A' 1 B 1 ' R o I I I - 3 TABLE I I I - l THERMOCOUPLES Thermocouple Number Measurement L o c a t i o n 1 24 gauge Insi d e t o 30 gauge Sample 5 40 gauge 6 ( s . s . sheathed) 7 (24 gauge) 8 ( s . s . sheathed) 9 ( s . s . sheathed) Sample s e c t i o n Duct w a l l Upstream of o r i f i c e Temp, p r o f i l e meas. These thermocouples were .wired i n t o the m u l t i p o i n t s w i t c h as shown i n F i g u r e I I I - l . It s h o u l d be noted t h a t the f i v e thermocouples which v/ere used f o r measuring the sample tempera-t u r e c o u l d be e a s i l y detached from the system by removing the. banana p l u g s . It was necessary t o i n c l u d e these banana plugs so t h a t the thermocouples c o u l d be c o n v e n i e n t l y moulded i n t o each sample. The p l a t i n u m r e s i s t a n c e thermometer and thermocouples were p l a c e d i n an i n s u l a t e d water c o n t a i n e r , the temperature of which was c o n t r o l l e d by an U l t r a Thermostat, type KLZ 42.65-4-88D C o l o r a constant temperature bath. The c o l d j u n c t i o n s of the thermocouples were p l a c e d i n a thermos f l a s k c o n t a i n i n g a mixture of water and crushed i c e . A mixture of tap water and i c e was found t o come to the same e q u i l i b r i u m temperature, as a mixture of d i s t i l l e d water and crushed i c e made from d i s t i l l e d III-4 P O T E N T I O M E T E R CONNECTION G H O T JUNCTION e COLO JUNCTION V BANANA PLUG —— C O P P E R — CONSTANTAN FIGURE I I I - l . THERMOCOUPLE WIRING DIAGRAM I I I - 5 water. The hot j u n c t i o n s were p l a c e d v e r t i c a l l y i n the water bath t o a depth of about 6 inches. A l l of the temperature measuring d e v i c e s were p l a c e d at' c l o s e together i n the bath as was p o s s i b l e . The r e s u l t s of the c a l i b r a t i o n of the thermocouples are t a b u l a t e d i n the f o l l o w i n g t a b l e s . Eq„ ( I I I - l ) and Eq. ( I I I -2) were used to c a l c u l a t e the temperature from the r e s i s t a n c e of the r e s p e c t i v e p l a t i n u m r e s i s t a n c e thermometers. The temperature of the thermocouple hot j u n c t i o n v a r i e s almost l i n e a r l y with the thermocouple E.M.F. For convenient use on the computer, the c a l i b r a t i o n curves were c u r v e - f i t t e d by l e a s t squares t o the f o l l o w i n g e q u a t i o n : t = Cj + C£ (E.M.F.) + CI (E.M.F.) 2 + C^ (E.M.F.) 3 (III-3) where t = temperature ° C E.M.F. = thermocouple v o l t a g e mV. C'^ ^ - constant f o r one thermocouple The v a l u e s of the c o n s t a n t s f o r Eq. ( I I I - 3 ) are given i n Tabl e I I I — 6 . For the c u r v e - f i t s l i s t e d , the d e v i a t i o n of the c a l c u l a t e d from the measured temperatures i s always l e s s than 0.1 ° F. The R.M.S. t o t a l and s t a t i s t i c a l e r r o r s f o r the parameters are l i s t e d i n Tab l e I I I - 7 . TABLE III-2 CALIBRATION OF THERMOCOUPLES 7,8,9 R t C a l c u l a t e d Temp. Thermocouple Rdg., mV V C a l c u l a t e d Temp. . Th.Rdg.mV Ohms ° C .# 7 # 8 Ohms ° C °.F # '9 2.5128 0.0 32.0 0.0 0.0 2.5128 0.0 32.0 0.0 2.7225 21.286 70.314 0.860 0.861 2.7313 22.182 71.927 0. 889 2.74S0 23.883 74.990 0.962 0.964 -2.7801 27.156 80.88.1 1. 091 2.8370 32.965 91.337 1. 340 1.340 2.8407 33.434 92.018 1. 349 2.9320 42.687 108.836 1.760 .1.761 2.9287 42.348 108.227 1.731 3.0297 52.714 126.885 2.200 2.211 3.0264 52.375 126.274 2. 169 2.1199 61.998 143.597 2.610 •2.610. 3.1237 62.390 144.302 2. 611 3.2078 71.071 159.928 3. 010 3.020 3.2197 72.281 162.105 3. 050 3.3133 81.993 179.588 3. 512 3. 512 3.3040 81.029 177.852 3.450 • 3.4168 92.744 198.939 4.014 4.019 3.3948 90.456 194.820 3.890 M 1—! I—( I o TABLE I I I - 3 CALIBRATION OF THERMOCOUPLES 1 TO 5 (24 GAUGE) AND 6 R t C a l c u l a t e d Temp. Thermocouple Reading, mV Ohms ° C o F # 1 # 2 # 3 # 4 # 5 # 6 25.5609 0.0 32.0 c 0. 0 0.0 0.0 0.0 0.0 0.0 28.1338 25,375 77.674 0. 994 0. 994 0.994 0.994 0. 994 0.986 28.8015 31.991 89,583 1. 257 1.257 1.257' 1.257 1.257 1. 257 29.8030 41.939 107.490 1 • 671 1.671 1.671 1.671 1.671 1.6.68 30.7924 51.796 125.233 2. 081 2. 081 2.081 2.081 2.081 2. 075 31.7430 61.294 142.328 2. 491 2.491 2.491 2.491 2.491 2.481 32.7100 70.983 159.769 2. 925 2. 925 2.925 2.925 2.920 2.896 33.7432 81.367 178.460 3. 380 3. 380 3. 380 3. 380 3. 380 3. 358 / TABLE II1-4 CALIBRATION OE THERMOCOUPLES 1 TO 5 (30 GAUGE) AND 6 R t C a l c u l a t e d Temp. Thermocouple Reading, mV Ohms ° C ° cF # 1 # 2 #' 3 # 4 # 5 # 6 25.5609 . 0.0 32. 0 0.0 0.0 0.0 0.0 0.0 0.0 2S.0543 24.579 ' 76.242 0.961 0.961 -0.961 0.961 0.961 0. 961 28.7851 31.828 89.291 1.252 1.252 1.252 1.252 1. 252 1.250 29.8343 42.250 108.051 1.687 1.687 1. 687 1.687 1.687 1.684 30.7899 51,771 125.18S 2.090 2.090 2.089 2 ?086 2.090 2.084 31.8386 62.250 144.050 2. 545 2.542 2. 541 2. 540 2. 540 2.538 32.8402 72.290 162.121 2.983 2.982 2.980 2. 980 2.981 2.971 33.7960 81.898 179.417 3.418 3.417 3.415 3. 414 3.416 3.405 TABLE I I I - 5 CALIBRATION OF THERMOCOUPLES 1 TO 5 (40 GAUGE) AND 6 R f C a l c u l a t e d Temp. Thermocouple Reading, mV Ohms ° C " o F # 1 # 2 # 3 # 4 # 5 # 6 25.5609 0.0 32.0 0.0 0.0 0.0 0.0 0.0 0.0 27.8244 22.313 72.164 0.871 0.871 0.871 0.871 0.871 0.870 28.8344 32.317 90.171 1.275 1.275 1.275 1.275 1.275 1.272 29.3074 41.983 107.569 1.678 1.678 1.678 1. 678 1. 678 1.671 30.8405 52.276 126.096 2. 115 2. 115 2. 115 2. 115 2. 115 2. 107 31.7899 61.763 143. 173 2. 521 2. 521 2. 521 2.521 2. 521 2.514 32.7607 71.492 160.685 2.951 2.951 2. 951 2. 951 2.951 2.945 33.7255 81.189 178.139 3. 389 2.951 2.951 2.951 . 2.951 3. 369 111-10 TABLE 111-6 THERMOCOUPLE CURVE- FIT PARAMETERS Thermo. No. Data C' r ' 2 °3 °4 No. Gauge P o i n t s x 10 2 x 10" 1 x 1 0 + 1 x 10 2 1 24 8 -1.238 2. 638 -8.070 3. 570 2 24 8 -1. 238 2.638 -8.070 3. 570 3 24 8 -1.238 2.638 -8.070 3.570 4 24 8 -1.238 2. 638 -8.070 3. 570 5 24 8 -0.753 2.631 -7.460 2.435 1 30 8 .0.054 2. 642 -8.941 5.209 2 30 8 0.288 2. 637 -8.456 4.274 3 30 8 0: 362 2.634 -8.257 3.986 4 30 8 0. 185 2. 632 -7.943 3. 276 5 30 8 0.455 2. 633 -8.144 3.700 1 40 8 0. 528 2.627 -7.927 3.268 2 40 8 0. 528 2. 627 -7.927 3. 268 3 40 8 0. 528 2. 627 -7.927 3.268 4 40 - 8 0. 528 2. 627 -7.927 3.268 5 40 8 0. 528 2. 627 -7.927 3. 268 6 24 24 0. 146 2. 638 - 8 . I l l 4.292 7 24 10 0.731 2. 543 -7.344 3.913 8 24 10 1.074 2.543 -7.732 4.783 9 24 10 7.297 2. 543 -5.434 0.0 I I I - l l TABLE II1-7 R.M.S. TOTAL AND STATISTICAL ERRORS FOR THE THERMOCOUPLE CURVE FIT PARAMETERS Thermo, No. Gauge R .M.S. E r r o r i n Parameters T o t a l St at i s t i c a l C' °2 °3 C'xlO 4 C 1 C 2 C 3 C'xlO 4 1 24 0. 11 0.27 0.2.0 0. 39 0. 99 2. 52 1.87 3. 67 2 24 0. 11 0. 27 0.20 0. 39 0. 99 2. 52 1.87 3.67 3 24 0. 11 0.27 0. 20 0. 39 0. 99 2. 52 1.87 3.67 4 24 0. 11 0.27 0.20 0.39 0. 99 2. 52 1.87 3.67 5 24 0.07 0. 18 0. 13 0. 26 0. 99 2. 52 1.87 3.67 1 30 0. 05 0. 13 0. 10 0. 19 0. 99 2.49 1.82 3. 55 2 30 0. 05 0. 12 0.09 0. 17 0. 99 2.49 1.82 3. 55 3 30 0.05 0. 13 0.09 0. 18 0. 99 2. 50 1.82 3. 56 4 30 0.05 0. 12 0.08 0. 16 0. 99 2. 50 1.83 3. 56 5 30 0.05 0. 13 0.09 0. 18 0.99 2.50 1.82 3. 55 1 40 0.04 0. 11 0.08 0, 16 0. 99 2. 53 1.85 3.61 2 40 0.04 0. 11 0.08 0. 16 0. 99 2. 53 1.85 3.61 3 40 0.04 0. 11 0.08 0. 16 0. 99 2. 53 1.85 3. 61 4 40 0. 04 0. 11 0.08 0. 16 0.99 2. 53 1.85 3. 61 5 40 0.04 0. 11 0. 08 0. 16 0.99 2. 53 1.85 3.61 6 24* 0. 09 0. 23 0. 17 0. 33 0. 57 1.46 1.08 2. 11 7 24 0. 09 0. 18 0. 11 0. 18 0. 9S 1. 97 1. 17 1. 92 8 24* 0. 14 0.28 0. 17 0. 28 0. 98 1.97 1. 16 1. 91 9 24* 0.08 0.08 0.20 0.89 0.99 0. 23 * S t a i n l e s s s t e e l sheathed 111-12 I I . ANEMOMETER HOT-WIRE CALIBRATIONS 1. Hot-wire c h a r a c t e r i s t i c s The s e n s i t i v i t y of the hot-wire anemometer t o v e l o c i t y f l u c t u a t i o n s and to a i r temperature f l u c t u a t i o n s depends on the p a r t i a l d e r i v a t i v e s of the heat l o s s f u n c t i o n with r e s p e c t to these flow v a r i a b l e s . The f i r s t s y s t e m a t i c study of the heat l o s s , both t h e o r e t i c a l l y and e x p e r i m e n t a l l y , was made by King (65). He found that the heat l o s s H i s approximately propor-t i o n a l t o the temperature d i f f e r e n c e between the f l u i d f r e e stream and the wire, and that i t i s a l i n e a r f u n c t i o n of the square r o o t of the mass flow. H = ('roper ~ T f i u i d ) ( a ' v / ? ? + b , ) ( I I I - 4 ) The heat l o s s may be c a l c u l a t e d from the product of r e s i s -tance of the hot-wire and the c u r r e n t t h a t i s f l o w i n g through i t . H. = I 2 R' o p e r x 3.413 (I I I - 5 ) F i g u r e I I I - 2 shows the t y p i c a l c a l i b r a t i o n curve of a hot-wire i n low v e l o c i t y flow. Free c o n v e c t i o n v a r i e s a c c o r d i n g t o the wire o r i e n t a t i o n ( h o r i z o n t a l or v e r t i c a l ) . For higher v e l o c i t i e s (Reynolds numbers), the heat l o s s i s s t i l l a l i n e a r f u n c t i o n of the square root of the v e l o c i t y , 111-13 FIGURE I I I - 2 . TYPICAL HOT-WIRE CALIBRATION CURVE although the c o n s t a n t s may change from Re,. = 10 t o Re = 40 P p co r r e s p o n d i n g t o known changes i n the flow p a t t e r n around c y l i n d e r s (66). FIGURE I I I - 3 . THE HOT-WIRE ANEMOMETER 111-14 The hot-wire anemometer i s b a s i c a l l y a simple Wheatstone b r i d g e with one arm being the hot-wire. The D.C. voltmeter r e a d i n g i s a measure of V J - J J. At a c o n d i t i o n of balance i n the Wheatstone b r i d g e , ^ 1 9 ^HW — = — (I I I - 6 ) R l l R 1 3 When = = 100 ^l, then can be measured by manipu-l a t i o n of Rg u n t i l the b r i d g e i s i n balance. Then R-^ g i s set at a predetermined value ( u s u a l l y at R-^ g = 1,8 R-^y) •> The brid g e unbalance appears as a v o l t a g e at VQ-JJJW T h i s v o l t a g e i s a p p r o p r i a t e l y a m p l i f i e d and f e d t o Vj-^. A f t e r a few seconds of. o p e r a t i o n the temperature of the hot-wire i s such that i t s r e s i s t a n c e has reached a value such as t o balance the b r i d g e . The anemometer c i r c u i t r y m a i n t a i n s the hot-wire at a constant temperature and thus e l i m i n a t e s thermal c a p a c i t y e f f e c t s . The measured f l u c t u a t i o n s i n V T > T are thus a measure of the change IN of heat t r a n s f e r t o the hot-wire and t h e r e f o r e a measure of the v e l o c i t y f l u c t u a t i o n s . Complete d e t a i l s of the o p e r a t i o n of a DISA hot-wire anemometer i s o u t l i n e d i n the I n s t r u c t i o n Manual (43). The Bridge D.C. voltmeter g i v e s a value which i s 4 percent too low due to i n c o r p o r a t e d cathode f o l l o w e r s i n the c i r c u i t . Thus V I N = VREAD x 1 - 0 4 ( I I I - 7 ) . 111-15 From. Ohm's c i r c u i t law, the c u r r e n t through Rpj W i s given by Bridge D.C. v o l t a g e x 1.04 I ( I I I - 8 ) 100 + c a b l e r e s i s t a n c e + R 0 p e r where R o p e r - R 1 3 = ^ 8 R HW ( I I I - 9 ) The c a b l e r e s i s t a n c e i s s p e c i f i e d as 0.12 ohm/m. Th e r e f o r e , for a 5 meter c a b l e , the r e s i s t a n c e i s 0.6 ohms. Thus, Bridge D.C. v o l t a g e x 1.04 I = (111-10) 100.6 + 1.8 R For a p u r e l y r e s i s t i v e l o a d the power generated i n the wire i s g i v e n by P D - I 2 x 1.8 R H W, watts ( I I I - l l ) 2 H = 3.413 x 1.8 x I • R R W, Btu./hr. (111-12) It i s assumed that no heat i s l o s t through conduction from the hot-wire t o the supports, then II = h A A T 2. (111-13) 111-16 H = 3.413 x 1.8 x I 2 R H W (111-14) In Eq. (III-13) j A Tg i s the temperature d r i v i n g f o r c e between the hot-wire s u r f a c e and the f l u i d f r e e stream, and A i s the area of the hot-wire. Thus the heat t r a n s f e r c o e f f i c i e n t i s g i v e n by h = 3.413 x 1.8 x I 2 R F F L V / A A T 2 (111-15) For a c y l i n d e r , A = 7T d-• L (111-16) w Then h dw Nu = (111-17) 2 3.413 x-1.8 x I R T ™ N u = _ (111-18) TT L k A T 2 It i s common to use a ' r e s i s t a n c e r a t i o ' ^oper r H W ~ • v - — = 0.8 (111-19) RHW as p r e v i o u s l y d e s c r i b e d . 111-17 If we assume that the hot-wire r e s i s t a n c e i s of the form R = RREF ( 1 + a i 4 Q 2 < t- tREF ) + "> " ( H I - 2 0 ) then some t y p i c a l v a l u e s of the r e s i s t i v i t y c o e f f i c i e n t s f o r a platinum-coated tungsten wire are Pla t i n u m 01 1 = 3.5 x 1 0 - 3 ( 0 C _ 1 ) ; a 2 =-5.5 x 10" 7 ( ° C _ 2 ) Tungsten a x = 5.2 x 10~ 3 (°C S ; a 2 = 7 - ° x 1 0 " 7 ( ° C - 2 ) It can be seen that under o r d i n a r y o p e r a t i n g temperatures the q u a d r a t i c term may be d i s r e g a r d e d because a. << a 2 A c c o r d i n g t o the DISA manual (pg. 87), the r e s i s t i v i t y c o e f f i c i e n t of plat i n u m - c o a t e d hot-wires i s o - l a, = o . 0 0 4 - c o If t i s taken as 0 C, then REF RREF ^ + C i l Toper) = 1 ' 8 RREF ( l + Q l T o } ( H I - 2 1 ) where T Q (° C) i s the temperature at which the c o l d r e s i s t a n c e of the hot-wire was measured.-III-18 0.8 T o o e r ( O = + 1.8 T (111-22) T n n o v (° C) = 200. + 1.8 T (111-23) Thus A T 9 (° F) =. (T - T_ T T T T_) 1.8 (II1-24) * oper FLUID It i s p o s s i b l e now to co r i - e l a t e the hot-wire data i n the t r a d i t i o n a l form 1/2 1/3 Nu = A1 •+ B1 Re Pr / 0 (73) T h i s c o r r e l a t i o n may be made by u s i n g any one of (1) bulk f l u i d p r o p e r t i e s (2) f i l m p r o p e r t i e s (3) f i l m p r o p e r t i e s , but d e f i n i n g a Reynolds number u s i n g a bulk d e n s i t y . It"was decided t o use the form (3) to be able t o compare the r e s u l t s with those p r e s e n t e d by McAdams (88) f o r heat trans-f e r from c y l i n d e r s i n c r o s s f l o w . The f i l m temperature i s d e f i n e d as 111-19 where f i n d i c a t e s a f i l m p r o p e r t y . The Reynolds number and P r a n d t l number are d e f i n e d r e s p e c t i v e l y as Re d U p w r pf Pi : p f fJ-f ( I H - 2 6 ) (111-27) McAdams (88) recommends f o r c y l i n d e r s i n c r o s s f l o w , 0.2 1/2 1/3 Nu f =0.42 P r f + 0.57 R e p f P r f (II1-28) f o r 0.01 < R e p f < 10,000 Hinze (45) p r e s e n t s a d i s c u s s i o n of e r r o r s i n t r o d u c e d due t o r a d i a t i o n and n a t u r a l c o n v e c t i o n from hot-wires and concludes that these e f f e c t s are n e g l i g i b l e i n most a p p l i c a t i o n s . 2. C a l i b r a t i o n i n a i r The anemometer was checked a c c o r d i n g t o the procedure out-l i n e d i n the DISA i n s t r u c t i o n manual (22). The frequency : response of the o v e r a l l anemometer system was such that 3 d e c i b e l a t t e n u a t i o n o c c u r r e d at 6,650 c y c l e s / s e c . at an a i r v e l o c i t y of approximately 17 f t . / s e c . i n the wind t u n n e l . T h i s was measured with a square wave generator b u i l t i n t o the 111-20 anemometer c i r c u i t . The anemometer was equipped with both a h i g h - and a low-pass f i l t e r t o e l i m i n a t e unwanted s i g n a l s . In p r a c t i c e only the low-pass f i l t e r was used t o e l i m i n a t e ' e l e c -t r o n i c n o i s e above 10,000 c y c l e s / s e c . The r e f e r e n c e hot-wire was c a l i b r a t e d i n a i r u s i n g a c a l i b r a t i o n apparatus l o c a t e d i n the Department of Oceanography at U.B.C. T h i s apparatus i s shown i n F i g u r e I I I - 4 . DUCT 4" x 4" EXHAUST FAN HOT-WIRE FIGURE II1-4. HOT-WIRE CALIBRATION IN AIR The pr e s s u r e ' d r o p between the hot-wire and scree n was measured by a b a r o c e l l p r e s s u r e sensor. The v e l o c i t y of the a i r i s p r e d i c t e d by UAIR = 0 ' 3 0 2 1 t D B + 460^ 1/4 AIR ( A P C ) 1/4 (111-29) where 111-21 tDB = ambient temperature, ° F PAIR — atmospheric p r e s s u r e , i n . Hg. A P c • = p r e s s u r e drop, jj, bars UAIR - a i r v e l o c i t y , m„/sec. The c a l i b r a t i o n of the r e f e r e n c e hot-wire i s o u t l i n e d i n Tabl e I I I - 8 . TABLE II1-8 CALIBRATION OF REFERENCE HOT-WIRE IN AIR Hot-wire c o l d r e s i s t a n c e O p e r a t i n g r e s i s t a n c e Hot-wire v o l t a g e at R e p = 0 A i r temperature A i r p r e s s u r e UAIR V mm. Hg. f t . / s e c . v o l t s Nu R e p f E r f 0.0018 1.96 6.06 0.742 0. 136 0.68 0.001.4 5.47 6. 61 0.883 0.435 0. 68 0.0268 7. 56 6.83 0.943 0. 613 0.68 0.0450 9.80 7.00 0. 990 0.776 0. 68 0. 140 17.29 7.48 1. 130 1. 371 0. 68 0.216 21. 47 7.66 1. 185 1. 650 0. 68 0. 285 24. 66 7. 80 1. 229 1. 889 0.68 3.33 ohms 5.99 ohms 5.56 v o l t s 24.4 ° C 29.65 i n . Hg. II1-22 The data i n Table III--8 was c u r v e - f i t t e d by l e a s t squares to the form of King's Law pres e n t e d i n Eq. ( I I I - 4 ) . The r e s u l t a n t e quation i s 27.84 -!• 6.70 y t l AIR (111-30) with a standar d d e v i a t i o n of 0.36. Eq. (III--30) can be con-v e r t e d i n t o the form of Eq. (73) . It then becomes 1/2 1/3 Nu f = 0.563 + 0.551 R e p f Pr (111-31) Four other hot-wires were c a l i b r a t e d i n the wind t u n n e l u s i n g the r e f e r e n c e hot-wire as a c a l i b r a t i o n standard. The c a l i b r a t i o n of hot-wire numbers 12 to 15 are presented, i n Table I I I - 9 and Tabl e 111-10. TABLE II I - 9 CONSTANTS IN CALIBRATION OF HOT-WIRES NO. 12 TO 15 Hot wire number Reference 12 13 14 15 Hot-wire c o l d r e s i s t a n c e , ohms 3. 34 3. 57 3.43 3.41 3. 56 Op e r a t i n g r e s i s t a n c e , ohms 6. 01 6.43 6. 17 6. 14 6.41 Vo l t a g e at R e p f = 0, v o l t s 5.49 . 5..2.8 5. 37 5.40 5. 28 A i r temperature 23 ° C A i r p r e s s u r e 1 atm. P r f 0.681 TABLE I11-10 CALIBRATION OF HOT WIRES NO. 12 TO 15 VREF V o l t s . Nu f Ref UATR f t / s e c Re _ pf Hot-wire 12 Hot-wire 13 Hot-wire 14 Hot-wire 15 V v o l t s Nu f V v o l t s Nu f V v o l t s Nu^ X V v o l t s Nu f 6. 52 0.867 4. 99 0. 393 6. 31 0.861 6.42 0.860 6.46 0.867 6. 32 0.862 6.79 0.940 7. 69 0. 605 6. 59 0.936 6.70 0.937 6.73 0.941 6. 5S 0.934 6. 95 0. 985 9. 63 0.758 6.75 0.983 6.85 0. 980 6.90 0.989 6.75 0.983 7. 08 1.018 11. 40 0.897 6.86 1.021 6.96 1.011 7.02 1.023 6.86 1.015 7. 18 1.048 12.89 1.014 6.96 1.051 7.07 1.044 7.12 1.053 6.95 1.042 7.25 1.069 14. 00 1.102 7.03 1.073 7. 14 1.064 7. 19 1.074 7. 03 1.066 7. 33 1. 096 15. 34 1. 207 7. 12 1. 097 7. 21 1. 085 7.27 1.098 7. 12 1.094 7.40 1.121 16. 58 1. 304 7.20 1. 119 7. 30 1.113 7.35 1.122 7.19 1. 115 7.48 1. 146 18.06 1.421 7.28 1. 144 7.38 1. 137 7.42 1. 143 7. 27 ' 1.140. 7. 58 1. 178 20.03 1. 576 7. 38 1. 176 7.47 1. 165 7. 52 1 1. 174 7. 37 1. 172 111-24 The c a l i b r a t i o n data were c u r v e - f i t t e d by l e a s t squares to the equation 1/2 1/3 Nu f + B 1 R e p f P r f (73) The f i t t e d curve parameters are l i s t e d i n Tab l e I I I - l l . TABLE I I I - l l HOT-WIRE CURVE FIT PARAMETERS Hot-wire No. data p o i n t s [ A l B l R e ference 7 0.563 0. 551 12 10 0. 546 0. 570 13 10 0. 558 0. 550 14 10 0. 560 0.557 15 10 0. 551 0.561 0.393 ^ Re , < 1.576 PJ-For each curve s t d . dev. < 0.001 3. C a l i b r a t i o n i n helium T h e o r e t i c a l l y i t may be supposed that the dime n s i o n l e s s form of a hot-wire c a l i b r a t i o n s h o u l d apply t o any f l u i d system. But the hot-wires c a l i b r a t e d i n a i r were found t o gi v e very poor II1-25 e s t i m a t e s of the v e l o c i t y i n f l u i d s other than a i r . The f i r s t s tep taken to understand t h i s anomaly was to c a l i b r a t e hot-wire number 14 i n the r e c i r c u l a t i n g gas duct u s i n g helium as the working f l u i d . The l o c a l v e l o c i t y i n the helium gas was measured with a C e n t r a l S c i e n t i f i c Company ca t a l o g u e number 20830 s t a t i c p i t o t tube. The working equation f o r a p i t o t tube i s u s u a l l y w r i t t e n where the value of C ranges between 0.98 and 1.0 (99). The value of C was chosen t o be u n i t y f o r t h i s a p p l i c a t i o n . The impact p r e s s u r e was measured by a Flow C o r p o r a t i o n model MM3 micromanometer. C P . b u t y l a l c o h o l having a S.G. of 0.8166 was o b t a i n e d f o r use i n the micromanometer. With t h i s manometer f l u i d , the u n i t can measure pr e s s u r e d i f f e r e n c e s as high as 0.06 t 0. 000006 p. s . i . , The data f o r c a l i b r a t i o n of hot-wire number 14 i n helium i s p r e s e n t e d i n T a b l e 111-12. The best f i t l i n e to the data i n Table 111-12 was ob t a i n e d by a l e a s t square a n a l y s i s t o be P/pRe (111-32) Nu^ = 0.356 + 0.361 Re , f P-L 1/2 Pr 1/3 (111-33) f f o r 0.0288 < Re pf £ 0.517 I 11-26 TABLE II1-12 CALIBRATION OF HOT-WIRE NO. 14 IN HELIUM Hot-wire c o l d r e s i s t a n c e O p e r a t i n g r e s i s t a n c e Hot-wire v o l t a g e at R e p f = 0 Helium temperature Helium p r e s s u r e P r f p Urr He V i n . B.A. f t / s e c Re „ Pf V o l t s Nu„ i 0.0003 2.82 0.0288 10. 39 0. 421 0..0006 3.96 0". 0404 10. 55 0.434 0.0015 6. 30 0.0642 10.60 0.438 0.00185 7.07 0.0712 10. 63 0.441 0.0099 16.2 0. 165 10. 99 0.472 0.0147 19.7 0. 201 11. 13 0. 484 0.0171 21.2 0.216 11.22 0.491 0.0179 21. 8 0.222 11. 26 0.495 0.0701 42.9 0.437 12. 09 0.570 0.0859 47.7 0.486 12.25 0. 585 0.0923 49. 2 0.501 12..30 0. 590 0.0976 50.7 0. 517 12. 32 0. 593 3.41 ohms 6.14 ohms 9.70 v o l t s 23 ° C 1 atm. 0. 695 111-27 4. Comparison of hot-wire c a l i b r a t i o n i n a i r and helium Hot-wire number 14 was c a l i b r a t e d i n both the a i r and helium systems. The two c o r r e l a t i o n s are compared with McAdams' p r e d i c t i o n f o r heat t r a n s f e r from c y l i n d e r s Eq. (111-28) i n F i g u r e I I I - 5 . The data f o r the a i r system l i e s c o n s i s t e n t l y above that f o r the helium system, but the two c a l i b r a t i o n curves show approximately the same dependence on the Reynolds number. It i s p o s s i b l e t o examine n a t u r a l c o n v e c t i o n e f f e c t s by c a l c u l a t i n g the Grashof number of the hot-wire f o r both systems. T a b l e 111-13 o u t l i n e s the v a r i a b l e s used i n c a l c u l a t i n g the Grashof number. TABLE II1-13 GRASHOF NUMBER FOR HOT-WIRE G r f = p f g p " A T 2 y rf Temperature hot-wire Temperature f r e e stream 20 F i l m temperature p , l b / f t ' P ' ' ° F~ A T 2 , w f t fi. , l b / f t . sec, AIR 0. 055 1.36 x 10" 396 1.64 x 10 1.60 x 10 -5 -5 220 C o 275 HELIUM 0.008 1.40 x 10' 396 1.64 x 10 1.55 x 10 -5 -5 (111-34) 111-28 g, f t / s e c . 2 32.2 32.2 G r f 9.7 x 10~ 7 2.05 x 10~ 8 G r f 1 / 3 0.99 x 10~ 2 2.72 x 10~ 3 .1/: Free c o n v e c t i o n has been shown to be important when Re „< pf Gr"""' ~ ( l l ) s . The lowest Reynolds numbers encountered during c a l i b r a t i o n i n the a i r and helium systems were 0.136 and 0.0288 r e s p e c t i v e l y . Thus n a t u r a l c o n v e c t i o n w i l l be having very l i t t l e e f f e c t on the c a l i b r a t i o n curves. . But the d i s c r e p a n c y that i s shown between the two c a l i b r a -t i o n curves i n F i g u r e I I I - 5 may be r a t i o n a l i z e d i f the heat l o s s from the hot-wire to the supports i s c o n s i d e r e d . In both systems the hot-wire temperature i s the same and thus the heat l o s s t o the supports w i l l be n e a r l y equal. The r a t i o of the heat t r a n s f e r c o e f f i c i e n t s on the hot-wire s u r f a c e at a f i x e d R e p f 1 / / 2 P r f 1 / / 3 i s e s t i m a t e d by He JAIR k He 5.5 (111-35) k AIR If the heat l o s s t o the supports i s d e f i n e d as qg^pp, and the heat l o s s from the hot-wire to the a i r and helium as q. T r > and q-r_je r e s p e c t i v e l y , then Nu AIR (q ; IR + q c TJPP ) d /A A To k A. w AIR N u H e (5.5 q A I R + q s u p p ) d w / A A T 2 k J I e (111-36) H O T W I R E • 14 C A L I B R A T I O N I N A I R { CALIBRATION IN HELIUM DATA CURVE FIT DATA CURVE FIT 0.0 M c A D A M ' S CORRELATION FIGURE I I I - 5 . HOT-WIRE CALIBRATION CURVES IN AIR AND HELIUM i — i 1—! I C D 111-30 I f q = 0, then SUPP •^uHe ~ N u A I R ( I U - 3 7 ) as would be expected, For the c a l i b r a t i o n curve shown i n F i g u r e I I I - 5 , when 1/2 1/3 R e p f Pr^. =0.6, N u A I R ~ 1.5 (IT.I-38) N u H e 1/2 1/3 T h i s suggests from Eq. (111-36) that when R e p £ P r f = 0.6, qgTjop - — — ~ 0.66 (111-39) qAIR and t h a t i n the a i r system approximately 40 percent of the heat that i s generated i n the hot-wire i s l o s t through the supports. In the helium system approximately 10 percent of the generated heat i s being l o s t t o the supports. In the c a l c u l a t i o n of the N u s s e l t number, the s u r f a c e area of the hot-wire was used. But the e f f e c t i v e s u r f a c e area f o r heat t r a n s f e r i s l a r g e r than the wire s u r f a c e area i n each case. Thus, c a l c u l a t e d N u s s e l t numbers w i l l be g r e a t e r than the a c t u a l N u s s e l t numbers. T h i s e f f e c t w i l l be g r e a t e r i n the a i r system . than i n the helium system because of the p r e v i o u s l y noted l a r g e d i f f e r e n c e i n gas c o n d u c t i v i t i e s . These t r e n d s are c l e a r l y I l l shown i n F i g u r e I I I - 5 where .'.he a i r system c a l i b r a t i o n curve l i e s above the helium system c a l i b r a t i o n curve and the c o r r e l a t i o n of McAdams, which i s r e s t r i c t e d to a i r . IV-1 APPENDIX FOUR ISOTHERMS AND ADIABATICS INSIDE A CYLINDER I. BOUNDARY CONDITIONS Consider a c y l i n d r i c a l sample with the c y l i n d r i c a l co-o r d i n a t e s d e f i n e d as i n F i g u r e IV-1. 6=0 FLOW _ > -I FIGURE IV-1. CYLINDER CO-ORDINATES o There i s a temperature symmetry along the a x i s Q = - 3J-2 fo r a l l v a l u e s of the r a d i u s . The temperature i s known f o r s e v e r a l v a l u e s of Q on the outer s u r f a c e of the c y l i n d e r and at the c y l i n d e r c e n t e r . • IV-2 I I . NUMERICAL SOLUTION OF LAPLACE'S EQUATION L a p l a c e ' s equation i s gi v e n i n c y l i n d r i c a l c o - o r d i n a t e s by d f • dT' 1 l <32T* 1 r « V f = 0 (IV-1) dr ' J r ' 5 6/ z which s i m p l i f i e s to d 2 T ' i d T ' 1 ^ 2 t + — + = 0 (IV-2) <5r'2 r ' d r ' r ' 2 <} # Subst i t ute T' = T + CONST (IV-3) r ' = R M A X R (IV-4) i n t o Eq. (IV-2) . Then d 2 T 1 d T 1 d 2 T • • — ; o + + ~ T — T o = 0 (IV-5) d R 2 R c)R R c) 0 Thus the temperature on the c y l i n d e r a x i s can be a r b i t r a r i l y set as zero and a l l other temperatures c o r r e c t e d a c c o r d i n g to Eq. (IV-3).. A l s o the r a d i u s parameter may be normalized a c c o r d i n g t o Eq. (IV-4) t o s i m p l i f y the s o l u t i o n of the equa-t i o n s . IV-3 The e x p r e s s i o n s f o r the f i r s t and second d e r i v a t i v e s of a f u n c t i o n i n f i n i t e d i f f e r e n c e form are d e r i v e d from a T a y l o r expansion, which i s v a l i d f o r any or t h o g o n a l s e t . Thus i t i s p o s s i b l e vo use these f i n i t e d i f f e r e n c e approximations i n the (R,8 ) plane. A g r i d can be e s t a b l i s h e d as shown i n F i g u r e IV~2. 6= - 7772 FIGURE IV-2. GRID FOR SOLUTION OF LAPLACE'S EQUATION R(J) i s the dime n s i o n l e s s d i s t a n c e from the c e n t e r of the c y l i n d e r t o the p o i n t T ( J , I ) and a = R /JM (IV-6) . MAX b = 7T/IM (IV-7) where JM and IM are the number of g r i d s i n the R and Q d i r e c -t i o n s r e s p e c t i v e l y . The f i n i t e d i f f e r e n c e approximations of the temperature • d e r i v a t i v e s are as f o l l o w s ( 2 ) : I V~4 dT T ( J + 1,1) - T ( J - 1,1) d.R 2a ( I V - 8 ) dT T ( J , I + 1) - T ( J , I - 1) dQ 2b ( I V - 9 ) dAT T ( J + 1 , I ) + T ( J - 1 , I ) - 2 T ( J , I ) dR 2 a ( I V - 1 0 ) 5 2 T T ( J , I + 1 ) + T ( J , I - 1 ) -2T ( J , I ) 2 ( I V - 1 1 ) S u b s t i t u t e the f i n i t e d i f f e r e n c e approximations i n t o Eq. ( I V - 5 ) and s o l v e f o r T ( J , I ) : T ( J , I ) T ( J + I , I ) + T ( j - i ; , i ) a + 2 a R ( J ) T ( J + 1 , I ) - T ( J - 1 , I ) + b 2 R ( J ) 2 T ( J , I + 1 ) + T ( J , I - 1 ) + a 2 b 2 R ( J ) 2 ( I V - 1 2 ) IV-Knowing the boundary c o n d i t i o n s around a h a l f c y l i n d e r i t i s p o s s i b l e t o i t e r a t e Eq. (IV-12) and s o l v e f o r the temperatur f i e l d w i t h i n the cylinder,, IV-6 I I I . NUMERICAL SOLUTION OF THE CAUCHY - RIEMANN EQUATIONS In a s o l i d shape there e x i s t s a set of l i n e s r u n ning at r i g h t angles to the isotherms and a l s o n o n i n t e r s e c t i n g . These are c a l l e d the 'flow l i n e s ' or ' a d i a b a t i c s ' and two adjacent flow l i n e s form a 'flow tube' through which passes some in c r e m e n t a l amount of heat. The flow l i n e s and isotherms form an 'orthogonal net' with the f o l l o w i n g p r o p e r t i e s : (1) The isotherms and a d i a b a t i c s are o r t h o g o n a l . (2) Isotherms and a d i a b a t i c s do not i n t e r s e c t t h e i r own k i n d w i t h i n the s o l i d . The f a m i l y of curves which are o r t h o g o n a l to the isotherms r e s u l t i n g from a s o l u t i o n of L a p l a c e ' s equation are governed by the Cauchy -Riemann equa t i o n s . The Cauchy - Riemann equations i n c y l i n d r i c a l c o - o r d i n a t e s are (70) a T 1 (IV-13) a R R d6 and a T a # (IV-14) R d Q a R where i s the value of the a d i a b a t i c at a p o i n t i n the f i e l d . IV-7 Consider the g r i d shown i n F i g u r e IV~3„ e--o 0=-7T/2 T ( J + I , I ) T.(J,I+I) FLOW T ( J - U ) I 6 = 7T/2 FIGURE IV-3. GRID FOR SOLUTION OF C AUCHY - R IE MANN EQUATIONS where a = RMAX / M (IV-15) b = TT / IM (IV-16) and JM and IM are the number of g r i d s i n the R and Q d i r e c t i o n s r e s p e c t i v e l y 0 The f i n i t e d i f f e r e n c e approximations of the a d i a b a t i c d e r i v a t i v e s are as f o l l o w s : d\\f i|/(J, i + i ) - uV ( J , i - i ) d R (IV-17) 2a a u/ l|/(J+l, I) - yv ( J - 1 , I) (IV-18) 2b IV-8 S i m i l a r l y f o r the g r i d i n F i g u r e IV-3 dT T ( J , 1+1) - T ( J S I - l ) _ = _ (IV-19) d R 2a dT . T.(J+1, I) - T ( J - 1 , I) — (IV-20) dQ 2b and R(I) i s the dim e n s i o n l e s s d i s t a n c e from the center of the c y l i n d e r t o the p o i n t T ( J , I). Thus 11/(J, 1+1) - 11/(J, I - l ) 1 X 2a R(I) T(J+1, I) - T ( J - 1 , I) (IV-21) 2b W/CJ+1, I) - \Lf ( J - l , I) — — R ( I ) X 2b T ( J , 1+1) - T ( J , I - l ) 2a (IV-22) For the i t e r a t i v e s o l u t i o n of Eq„ ( I V - 2 1 ) } knowing a l l v a l u e s of T ( J , I) i n t h e - f i e l d , i t i s a l s o necessary t o know tha t IV-9 uV (1 77/2, R) = 0 (IV-23) and Vj/(1 TT/o. ± b, R) = ^ ( t 77/2 - b, R) (IV-24) The above boundary c o n d i t i o n s f a c i l i t a t e the c a l c u l a t i o n of the f u n c t i o n \|/ ( 8, R) over the range 0 < R < (loO - a) - (7T/2) < 8 < (7T/2) From Eq, (IV-22) i t i s p o s s i b l e t o c a l c u l a t e the s u r f a c e v a l u e s of the f u n c t i o n \]/( 8 , i) over the range - (7T/2) < # < (7T/2) The v a l u e s of the temperature and heat f i e l d may be n o r m a l i z e d by T N (Q , R) = T ( 8, R) / T(7T/2, 1) (IV-25) > N ( # , R) = ty(8 , R) / \|/(0, 1.0) (IV-26) IV-10 IV. CONTOURING OF TEMPERATURE AND HEAT FLOW FIELDS The'grids' of p o i n t s c o n t a i n i n g v a l u e s of the temperature and heat f l o w f u n c t i o n are contoured n u m e r i c a l l y by the D.B.C, computing center program U 0B 0Co TOUR 1. The program p l o t s oh a f o u r " i n c h r a d i u s h a l f - c y l i n d e r , ten di m e n s i o n l e s s isotherms and t en dime n s i o n l e s s adiabatics„ IV-11 V. DATA AND RESULTS Ex p e r i m e n t a l s u r f a c e temperature data f o r a c y l i n d e r are shown i n F i g u r e IV-5. The data were taken at p o i n t s as shown i n F i g u r e IV-4 and are pr e s e n t e d i n Table IV-1 AIR FLOW FIGURE 'IV-4. TEMPERATURE MEASUREMENT POINTS IN A CYLINDER TABLE IV-1 • TEMPERATURE MEASUREMENTS.IN A CYLINDER . System, a i r - n a p h t h a l e n e Thermocouples, 24 gauge R e p ~ 4150 C y l i n d e r diameter, 0.519" C y l i n d e r l e n g t h , 2.0" A i r temperature, 141.9 ° F Data Source Locat i o n ( F i g . IV-4) t ° F Lw' r A t l 5 o F t r - t «- w °F F i g u r e 32 2 137.SO 4. 10 -0. 35 F i g u r e 33 1 137.45 4.45 0.0 F i g u r e 34 6 137.15 4.75 -1-0. 30 IV-13 3 137.76 4.14 -0. 31 Run 77 4 137.45 4.45 0.0 5 137.20 4.70 +0.25 The temperature along the c y l i n d e r a x i s at Q = 0 i s almost constant as i s e x p e r i m e n t a l l y shown an Table IV-1 at l o c a t i o n s 1 and 4. The v a l i d i t y of the assumption of a constant c e n t e r -plane temperature depends on the degree of wake development behind the c y l i n d e r . The assumption can be expected to be approximately v a l i d f o r 1 0 3 < R e n < 1 0 5 i n low t u r b u l e n c e i n t e n s i t y f l u i d flow, s i n c e the wake i s almost f u l l y developed at R e p ~ 1000 and the t u r b u l e n t boundary l a y e r does not develop u n t i l R e p > 10^. For a h a l f c y l i n d e r having a dim e n s i o n l e s s r a d i u s one un i t long, the angle was d i v i d e d i n t o 36 increments and the r a d i u s was d i v i d e d i n t o 40 increments. A f t e r 1500 i t e r a t i o n s , Eq. (IV-12) was found t o produce a f u l l y converged temperature f i e l d . No r e l a x a t i o n f a c t o r was used t o improve the c a l c u l a t i o n e f f i c i e n c y , s i n c e the temperature f i e l d i n onl y one h a l f -c y l i n d e r was of i n t e r e s t . Knowing the temperature f i e l d and a p p l y i n g Eq. (IV-21) and Eq. (IV-22) with the a p p r o p r i a t e boundary c o n d i t i o n s , the value of the a d i a b i a t i c at each g r i d p o i n t can be c a l c u l a t e d . The num e r i c a l v a l u e s of the tempera-t u r e f i e l d f o r every other g r i d p o i n t i n the h a l f - c y l i n d e r are shown i n Table IV-2. S i m i l a r l y the values of the a d i a b a t i c s IV-14 at every other g r i d p o i n t are p r e s e n t e d i n Table IV-3. The dimensionless isotherms and a d i a b a t i c s f o r the h a l f -c y l i n d e r are shown i n F i g u r e IV-6. It can be seen that the heat flow between the f r o n t and back s t a g n a t i o n p o i n t s of the c y l i n d e r i s almost one-dimensional, as i s assumed f o r the development of Eq„ (94) and Eq, (97). TABLE IV-2 IV-15 TEMPERATURE FIELD IN CYLINDER ( t c - t w , . ° F) t9( Radians) -1.571-1. 396-1.?<>2-l . 047-0.073-0.698-0.524-0.349-0. 175 0.000 0. 175 0.349 0.524 0.698 0.873 1.047 1.22 1.396 1.571 "HR ; ' ; : "~~ o . o o o o .ooo o .ooo o .ooo o . o o o o .ooo o .ooo o.ooo o . o o o o . o o o o . o o o o . o o o o . o o o o .oop o .ooo o .ooo o .ooo b .ooo o .ooo o.'ooo 0.050 0.08 0.08 0.07 0.006 6.004 0.002-0.001-0.04-0.007-0.OiO-O.013-0.016-0.019-0.022-0.024-0.026-0.027-0.028-0.023 0.100 0.023 0.e2  0.021 0.018 0.015 0.010 0.005-0.001-0.007-0.013-0.019-0.025-0,031-0.036-0.041-0.44-0.047-0.04B-0.049 0.150 0.039 0.038 0.036 0.032 0.027 0.020 0.012 0.004-0.005-0.015-0.024-0.033-0.042-0.050-0.056-0.062-0.065-0.68-0.069 0.200 0.05  0.054 0.051 0.046 0.039 0.031 0.020 0.9-0.003-0.016-0.029-0.D41-0.52-0.063-0,071-0.079-0.084-0. 087-0.089 0.250 0.072 0.071 0.067 0.061 0.052 0.041 0.029 0.014-0,01-0.017-0.03 3-0.048-0.063-0.076-0.086-0.095-0.102-0.105-0.10 7 0.300 0.08  0.087 0.083 0.075 0.065 0.052 0.037 0.020 0.002-0.18-0.037-0.056-0.073-0.068-0. 101-0. 112-0.119-0.124-0. 125 0.350 0.105 0.103 0.098 0.090 0.078.0.064 0.046 0.026 0.005-0.018-0.041-0.06 3-0.084-0.101-0.116-0.128-6.137-0.142-0.143 0.400 0.121 0.119 0.14 0.105 0.09;! 0.075 0.056 0.03  0.008-0.019-0.U45-U.0 11-0.094-U.114-U.1i1-U.144-U.154-U.159-U.161 0.450 0.137 0.135 0.129 0.19 0.105 0.087 0.065 0^040 0.011-0.019-0.049-0.07B-0.105-0.128-0.146-0.161-0.171-0. 17-0.179 0.500 0.153 0. 151 0. 145 0. 134 0. 19 0.09  0.075 0.047 0.015-0 . 019-0 . 054-0. 086-0 .1 I 6-0. 1 41-0,161-0. 1 7-0 . 188-0. 194-0 . 196 ~0,5Q - 0.169 0.167 0,160 0.149 0.131 0.112 p,085 0.05T"0. 01 9-0 . 019-0Trf58-0. 09 5-0, 1 2 7 - 07T5"5 - u . 1 7-0,193-0.204-0.21-0.213' 0,60  0.1 85 0. IB? 0. 1 75 0. 164 0. 147 0.124 0.096 P.16? 0, li 2 3-0 . p 19-0 . Oo 3-0 . 103-0. 1 39-0. 1 69-0. 192-0. 2 09-0. 2? 1 -0. ? 28-0. 230 0.650 0.20  0. 198 0. 191 0. 178 0. 161 0. 137 0.1U7 0.(171 u,028-0.019-0.067-0.112-0,151-0.183-0,21) 7-0,225-0.237-0.244-0.246 0,7g0 0,2V5 q72l3-BV205 0 . 193 0, 175-0,150 0. 19 0 , n0n~0, 03 3-0. 019-0 .0 72^p, 1 2 2-0 .1 64-0, 198-0. 2  3-0 .241-0 , 2 !i3 = 0. 26q-a . 262 0,75.0 9,239 Q-227 0 .?2Q g,2g7 0,109. g,)ft4 0.131 11,009 n.03-ifi.oie=g,877=0.i3?-q.i'7-p,2i3-a,23?rfl,25^0i?ft8T0, 0,600 0 ,34* 9 ,24? 0.334 g,?P2 0,203 0,179 0 . 1 M l-OII 9.045=0, 017-0, 00 '=0, 143=0, 191-0, 220=0,J54-0, ?72-0,89<t-9, 2dfi=-n, p-ia -gyafj-g - ' ~ g , 25g- g,?<>b~ 0', i'si' O.yiCWfiTFtTWTT. 15ft "Q, fi i» n.TWKntflTK'i,WOt 1"fv?'7'fi-fr.Tf|n;;B7?'J'i--0, iflTTt', Jiif 9,000 Q, ? 73 0,270 0,?63 0,360 0,33? 0,20ft 9 . ( 6 * 1,(3? '1,959-9. 01 2-0. 996-9. (ft7-0, .V i-0. 2n9-0.? (6-0, 3O3-0,3 1 4-0, 3P0-0. 32  0,950 ft,296 9,876 0 . 2 M O.Wt 9.220 Oil'i. 0,134 0,pft<!=(!,968-", 194-0 . (a11=0,J t(j-Q,27ft-.1, i O ? - o , 31 a-fi,32B-0, 3ft ' V 7 O T 0 - '0;Tgg--gY207- 0,?9,'; n . n !••»,')'!,!> B V i l § ~ 9 r i 9 l TJ, !4§ "9.-971 g,'Bg0=BVlH=B-.lT6"=8;253=9,T9X= ftTSTJ^."PO •„. . „ -J-ABLE—Ly_?3 . ... - ._. HEAT FLOW FIELD IN 6YINDER 0) @ (Radians)  - ( , 5 7 1 = 1 ,39ft-( . ? 2 2 - t , 0*7=9,il7T = 0~,7>9fl = 0 ,524=0 ,349-g , 175 9,000 0 , 175 0,349 0 . M 4 9,6OT 9.873 1.047 l,a JJj» l.'IMt I . M I R o . o o o o . o o o o . o o o o . o o o o . o o o 0,000 0,000 o .ooo 0.000 o . o o o o . o o o 0.909 0,008 0,000 9,990 0,919 0,099 B.OOP 0.990 0,099 0 .P50 P.POO Q.Q92 0.005 Q,on7 0,001 11.0(0 0,911 P.QI2 0.012 t i . p l l 0,110 0, UQI'0.917 Q.Q04 0.001 - 0^002-0,006-p.01 0 6. n OJ) 0. 190 0,000 0.015 Q.OII 9,01ft 0,030 0.934 0,02/ 0-0211 0.029 0.029 0 .020 0,025 0,032 9.010 0,01," 0.006-0.000-0.>J07 O.OOO 0 . | » 0 O.OOO II. n [J 0 0,.(1l7 O.IV'p O.O-tl 0,047 0,042 0.945 0 .94? 0.047 0 ."r>'i 1 0,042 0,0*7 0.031 9,0,13 0, 01 5.0,00!>'B. ilQ'i 9.000 0.200 0.000 0.011 0.P23 0.033 0.043 0.051 0.057 P.Q62 Q.Q65 0,065 0.063 0.059 Q.053 0.044 0,Q35 Q.Q23 P ,QU=g .Q02 0.000 0.250 0,009 0.014 0,028 9,042 0 .054-0 -064 0.073 0.079 0.OP2 0.083 0,981 0,07ft O-PftB 0.058 0,046 0.032 0,017 0 .00 ! O.OOP 0.309 O.OPO 0 .017 0.934 9.060 0,0ft§ 0,977 P.Otlfl 0,00ft 0, 100 0. 101 0.099 0.003 0,003 0.O71 0.057 0,040 0,9*2 0.00.) U.UUP O.lffft (i . e w d . o a o 9 . j u n 1..0.*H_5.V!L8»O'»i o . j u r o . m u . i t o . o . |J0 0 . \ } 1 J . \ \ 0 OtMl^.oji^OJbM. U.MH H.U/B o.onr. " . m m 9,409 0.009 U , 9 ? l 9,046 0.066 n,UU6 0.194 0,119 9.139 0.137 0 .130 0. 136 0- 137 9,115 0,091) 6.0711 0.086 S . Q " 8.91  O.OOP 0.950 0.090 O.OfS 0.060 0,07'. 0.096 0 . U 7 0 .(39 0.14? 0.155 0.(56 0 . 15ft 0 . C 5 u.t. lf i 0,(11 O.O'ID u.ur-'. 0,1110 0.011 9.DOS 0 .5QQ 0,000 0,028 0.Q55 0.001.9,106 0.(29 Q.I49 Q.164 0,174 0.17B 0 . (74 0.163 0,146 0,124 0,099 Q.Q7! Q.Q42 0 .0 )3 P.OUO 0,559 9,000 9.910 O.OftO O.OHO 0,11ft 0,142 fl.lftd 0.182 0,191 0, 197 0 , ( 9 3 9.(01 9.IM 0.137 o . inf j 0,078 0,0*7 0.P15 9.009 9.609 0 .009 0.OS? 0,064 9, 0-76 0. 126 0 . (54 0. 1 79 0 . 199 0.813 0.810 9 .2 (3 0, 199 9. 1/7 0 . 149 0. 111) 0,005 0.091 0.0( 7 0.000 0.650 0 ,000 0,034 0.060 0. I ng 0.115 O.lftS 0.193 9.317 0 , ?1? 0,880 Q,j.ji< .g.8J_I_0. . 'J?__0i l6 )_0 i _tJ 1_ 9.fl 'J. J 0 .C53 0,019 0. OOP 9.799 0,009 0.036 0.071 0,100 0 , (44 0.177 O.200 0,234 0 .812 0.860 0,855 0.83ft 9.206 0 .(73 0,136 9.090 0.059 0.981 0.990 9.759 0.090 0.038 9.076 O . l l ' t 9 . 153 0,100 0.82.2 0,851 0.873 0,86? 0,277 9,855 0,883 9. 185 0 . 1 H 0-103 O-Oftl 9.928 9,909 j h M O 0.000 .0,040 0.089 0 . 120 Q.lftQ 9.(99 0.3.16 0-,3ft9 0.294 0, 306 9.299 0,274 0.236 0,197 0-1S2 0.(09 Q._Shb_ 9 .084^0.090 0.850 0.000 y .O^g 0.904. 9.121 0.I67 0,310 0,290 0.297 0.315 9 .310 0 ,323 0.894 0.254 0,200 0 . (60 0 . 1 1 * 0.069 0.025 0.000 9.900 0.000 0.943 0.087 0 , (30 0 . (71 0 .229 0,264 9,39'- 9.338 0-357 9.349 0 , 3 ( 6 9,879 9.819 9,(67 9,(19 9 , 9 7 8 . 9 . 0 8 7 9,005 0.95Q . 9 .000 0.045 0.099 9,135 0.1BI 0,231 0.278 0.323 Q.3ft4 Q.3QB 0.379 0.336 0.287 p.231 0.176 0,125 0.077 0.030 9.009 1.009 9.990 0.946 0.091,0,(39 0.(07 0.240 0.290 0.339 0.380 0.415 0.407 0.395 0.J02 9.241 O.lfll 0.129 0.079 0.031 0.000 IV-16 V-1 APPENDIX FIVE CALCULATIONS I. CALCULATION OF THE PARTIAL PRESSURE OF SUBLIMATE IN THE CAS RECIRCULATING APPARATUS AFTER A TIME T Consider that a p a r t i c l e with a mass t r a n s f e r c o e f f i c i e n t * o 2 kQ l b - mole/hr. f t . atm. and area A f t . i s s u b l i m a t i n g i n t o the r e c i r c u l a t i n g f l u i d stream. Consider that the apparatus has a volume A f t . 3 and i s o p e r a t i n g at a pr e s s u r e P atm. and a temperature T ° R. If the r e c i r c u l a t i n g f l u i d i s f u l l y mixed i n the main tank, at any time T i t i s known that If at time T =0, the f r e e stream p a r t i a l p r e s s u r e i s ' zero, then (V-1) Thus p O f T=0 DB (V-2) R A g T T (V-3) V-2 S i m p l i f y Eq. (V-3) to give k*~ A R T T G g (V-4) For s m a l l v a l u e s of the group "*G A R g T T ' A the f r e e stream p a r t i a l p r e s s u r e i s g i v e n by f k * Q A Rg T T 1 *DB = %( A ~ " i There i s a s l i g h t e r r o r i n t r o d u c e d i n t o Eq. (V - 4 ) due to the s u r f a c e area of the p a r t i c l e d e c r e a s i n g with time as i t s u b l i m a t e s . But i n the course of an experiment the s i z e of a wet-bulb i s reduced only s l i g h t l y . k* A R T T G g A + (V-5) V-3 I I . CALCULATION OF THE LOCAL PSYCHROMETRIC RATIO AT THE FRONT STAGNATION POINT OF A NAPHTHALENE SPHERE IN THE WIND TUNNEL The technique f o r measuring the wet-bulb temperature d e p r e s s i o n of a p a r t i c l e i s d e s c r i b e d i n d e t a i l i n Chapter Five. The e x t r a p o l a t i o n technique which c o r r e c t s the wet-bulb tempera-t u r e d e p r e s s i o n t o a h y p o t h e t i c a l v alue c o r r e s p o n d i n g to the case when no heat is t r a n s f e r r e d i n t o the p a r t i c l e through the support, i s a l s o p r e v i o u s l y d i s c u s s e d i n d e t a i l . From F i g u r e 39 or Table VI-4, the e x t r a p o l a t e d value of the wet-bulb temperature d e p r e s s i o n at the f r o n t s t a g n a t i o n p o i n t of a one inch diameter naphthalene sphere i s 7.9. °F when the a i r flow r a t e i n the wind t u n n e l i s 0.122 f t . 3 / s e c . and the a i r temperature i s 1G0 °F. For. l a t e r c a l c u l a t i o n s , i t i s noted that the e x t r a p o l a t e d wet-bulb temperature d e p r e s s i o n at the center of the sphere i s 8.39 °F f o r the same c o n d i t i o n s . From Eq. (11-53) the w a l l temperature of the duct f o r an a i r flow of 0.122 l b . / s e c . i s 146.5 °F. The f i l m temperature f o r system p r o p e r t y determi-n a t i o n s i s gi v e n by (V-6) = 156.04 °F For the experiment, the sample s e c t i o n p r e s s u r e was ' V-4 determined to be 0.995 atm. and the humidity 0.004 l b . water/lb. dry a i r . The system p r o p e r t i e s were determined t o be AIR P r o p e r t y Value Temperature Reference V i s c o s i t y D e n s i t y Heat c a p a c i t y Conduct i v i t y 2.04 x 10" p o i s e 1.02.x 10"^ gm./cin.° 2.42 x 10™ 1cal./gm°C 7.05 x 10"" 5cal./cm. sec,°C 156. 04 °F Eq;;, (I -1) 156. 04 °F Eq. (I -3) 156. 04 °F Eq. (I -2b) 156. 04 Op Eq. (I -4) NAPHTHALENE Latent heat 130.4 cal./gm. 152. 1 °F Eq. (I -7) Conduct i v i t y 7.09 x 10~ 4cal./cm.sec.°C 152. o 1 F Eq. (I -8) Vapor heat c a p a c i t y 36.9 cal./gm. mole C 156. 04 °F Table I -5 E m i s s i v i t y 0.85 (86) Vapor p r e s s u r e 2.83 mm, Hg. 152. 1 °F Table I -4 From F i g u r e 13 or Table VI-10, the v e l o c i t y at the wind t u n n e l center (where the sphere i s l o c a t e d ) i s 17.43 f t . / s e c . o o at 25 C. The center v e l o c i t y at 160 F i s •UM = 17.43 (620/537) 2.54 x 12 616 cm./sec. Thus the Reynolds number f o r the sphere i s R e p f = ( UM Pf V . / ^ f V-5 616 cm./sec. x 1.02 x 10 2 gm./cm.3 x 2.54 cu. Rep-f =  2.04 x 10~ 4 gm./cm.sec. = 7830 The computer program output g i v e s Rep^ = 7837 f o r t h i s case (Table VI-5). The P r a n d t l number: i s giv e n by C p f H-t Pr. ' -1 *t 2.4 x 10 1 cal./gm.° C x 2.04 x 10 4 gm./cm.sec, 7.05 x 10~ 5 cal/cm.sec. ° C 0.70 To c a l c u l a t e the d i f f u s i v i t y c o e f f i c i e n t , the molecular weight of the gas f i l m around the sample must be known. The f i l m i s assumed t o have a c o n c e n t r a t i o n of naphthalene vapor midway between p and Ppg* The vapor p r e s s u r e of naphthalene i n the f i l m i s given by p f = pw / 2 = 1.41 mm. Hg. V-6 Thus . P ~ P f "1 I p f l 'Bf B V T , J ' " " V P W P i . 4 i | f 1.4: 28.97 < 1 - y + 128. 16 760 x 0.995 760 x 0.995 = 29.34 gm./gm.mole o For naphthalene the f o r c e constant G / K = 959.2 K (Table 1-8). For a i r ^^/K = 97 ° K (Appendix One). The c o l l i -s i o n diameters of naphthalene and a i r are 6.236 and 3.617 angstroms r e s p e c t i v e l y . (Table 1-7 and Appendix One). From Eq. (1-12), € /K = 3.05 x 10 2 ° K. Since K T f / € = 1.13, from Eq. (94) the c o l l i s i o n i n t e g r a l f o r d i f f u s i o n i s equal t o 0.68. The f a c t o r (49,50) i s equal t o u n i t y . From Eq. (1-11), r 1 2 = (6.236 + 3.617)/2 = 4.926 angstroms 2 2 r 1 2 = 24.2 angstroms MW1IF + MWN, 128.16 + 29.34 MW x MWTJ-C 128.16 x 29.34 W til = 4. 19 x 10 2 V-7 From Eq. (1-13) , = { 10.7 - 2.46 (4.19 x J 0 ~ 2 ) 1 / 2 } x 10~4 B - 10.19 Thus the d i f f u s i v i t y i s gi v e n by Eq. (1-10) as 10.19 x (341.9) 3 / 2 x (4.19 x 1 0 _ 2 ) 1 / 2 D v f 0.995 x 24.2 x 0.68 = 0.0804 cm. 2/sec. The computer program estimate i s 0.081 cm.^/sec. (Table VI-5) The Schmidt number i s c a l c u l a t e d to be S c f p f D y f 2.04 x 10~4 gm./cm.sec. 1.02 x 10~2 gm./cm.3 x 0.81 cm. 2/sec, = 2.47 The Lewis number has a value of V-8 2.47 L e f = 0.70 = 3.53 Since the sample s u r f a c e temperature and the w a l l temperature are known, the r a d i a t i v e heat t r a n s f e r c o e f f i c i e n t can be c a l -c u l a t e d from Eq, (63) : (6.065 4 - 6.121 4 ) h r = 0.173 x 0.85 -606.5 - 612.1 1.33 Btu./hr. f t . 2 ° F From Eq. (15) the c o n v e c t i v e heat t r a n s f e r c o e f f i c i e n t i n the absence of mass t r a n s f e r i s e s t i m a t e d from Nu| = 2 + 0.69 R e p f 1 / 2 P r f 1 / < = 2 + 0.69 ( 7 8 3 0 ) 1 / 2 ( 0 . 7 0 ) 1 / / 3 56.2 The c o n v e c t i v e heat t r a n s f e r c o e f f i c i e n t i s gi v e n by Nuf k, c V-9 56.2 x 7.05 x 10~ 5 cal./cm.sec. ° C h = x 1.0 i n . x 1/12 f t . / i n . Btu./hr.ft.° F 2.4175 x 1.0^  c a l o/cm.sec.° C h * * * •= 11.5 Btu./hr. ft.° F The c o r r e c t i o n f a c t o r f o r r a d i a t i v e heat t r a n s f e r i s , from Eq. (60), 1.33 (-5.6) a = x 11.5 (7.91) 0. 082 The computer program i n d i c a t e s a value of - 0.08 f o r CJ (Table VI-5). The Ackermann c o r r e c t i o n f a c t o r i s p r e d i c t e d by Eq. (66) 36.9 cal./gm.mole ° C x (7.91/1.8) ° C 128.16 gm./gm.mole x 2 x 130.4 cal./gm. = 0. 99 V-10 The E i o t number f o r the sphere i s , a c c o r d i n g t o Eq. (88), Btu 11.5 (1-0.082) x 0.99 x ( 1/24) f t . h r . f t . 2 ° F B i = . _ _ . c a l . B t u / h r . f t . 2 ° F 7 . 0 9 x l 0 - 4 : x 2.4175xl0 2  gm.sec. 0 C cal./gm.sec. ° C 2. 54 In the f r e e stream the c o n c e n t r a t i o n of naphthalene i s zero. Thus PDB = 0 Now a l l of the v a r i a b l e s are known to c a l c u l a t e the psy c h r o m e t r i c r a t i o from Eq. (94): n n (('tDB - t w ) + ( l / B i ) ( t c - t w ) ) (1+ a ) y MW P C f P P =• r — (94) M Ww A w (Pw-PDB > -(-0.48>{ -}• (l-0.082)x0. 5.54 J 9 7,9.1+ r(- \  } (1-0. 082)x0. 99x29. 34x0. 995x0. 242 2, 128.16 x 130.4 x (2.83/760.0) 0.443 It i s i n t e r e s t i n g to note that i f the thermal c o n d u c t i v i t y of the naphthalene wet-bulb were assumed t o be zero, as has y - n always been done i n the past, the value of the psychrometric r a t i o would have been 0.454. The value of the Lewis number exponent i s c a l c u l a t e d a c c o r d i n g t o E q 0 (97). f^DB-tw + ( l / B i ) ( t c - t v , ) ) (1+a ) y k f R T F * Log MWW X w ( p w - P D B ) D v f Log ( L e f ) • 1 " 1 5 7.91 - (-0.48)^—(1-0.082) 0.99x7.05 2.54 J 9 Log <; • : • X 128.16 x 130.4 x (2.83/760) x 0.082 1 0 - 5 x 82.06 x 341.9^ / Log (3.53) Log (1.54) / Log (3.53) 0.342 If the thermal c o n d u c t i v i t y of the v/et-bulb had not been accounted f o r ( B i = 00 ), the value of the Lewis number exponent would have been 0.361. V-12 I I I . CALCULATION OF THE LOCAL PSYCHROMETRIC RATIO AT THE FRONT STAGNATION POINT OF A NAPHTHALENE SPHERE SUBLIMATING INTO HELIUM IN THE GAS RECIRCULATING APPARATUS. The wet-bulb temperature depressions are measured i n the gas r e c i r c u l a t i n g apparatus by a s i m i l a r technique t o that used i n the wind t u n n e l . The a n a l y s i s of r e s u l t s i s c o m p l i c a t e d by the g r a d u a l b u i l d u p of sublimate i n the f r e e stream with time. Wet-bulb temperature d e p r e s s i o n s measured f o r one thermocouple gauge must be e x t r a p o l a t e d with the e q u i v a l e n t measurements from other thermocouple s i z e s taken at the same time from the i n i t i a t i o n of the runs. Consider the data from runs 610b and 611a. C a l c u l a t i o n procedures w i l l be i n d i c a t e d when the measurements were taken 25 minutes a f t e r the i n i t i a t i o n of the run. From Ta b l e VI-7 i t can be seen that f o r a one inch diameter naphthalene sphere s u b l i m a t i n g i n t o a helium stream, the f o l l o w i n g measurements apply at the sample f r o n t s t a g n a t i o n p o i n t : Thermocouple gauge t D B ° F A t-^ ° F ' tw^ ° F 24 155.7 4.80 136.3 30 157.6 5.31 138.2 In order t o e x t r a p o l a t e these data t o the e q u i v a l e n t zero thermocouple t h i c k n e s s wet-bulb temperature d e p r e s s i o n , they must be c o r r e c t e d to a common helium f r e e stream temperature. It i s p o s s i b l e t o p r e d i c t the approximate v a r i a t i o n of the wet-V-13 bulb temper at ui"e d e p r e s s i o n with f r e e stream temperature knowing that/3p ~ Le^ 0.^>9 j r o m t j i e w j _ n t j t u n n e l experiments,, The r e s u l t s are c o r r e c t e d to a common f r e e stream tempera-t u r e of 156 ° F and e x t r a p o l a t e d l i n e a r l y w i t h the thermocouple diameter t o the t h r e e - h a l v e s power. Since the i n s i d e of the wet-bulb cannot 'see' the surroundings, the same r e l a t i o n s h i p between the wet-bulb temperature d e p r e s s i o n and thermocouple diameter i s expected to be v a l i d f o r helium as was v a l i d i n a i r . For a helium f r e e stream temperature of 156 ° F, the e x t r a p o l a t e d wet-bulb temperature d e p r e s s i o n i s 5.40 ° F and the w a l l temperature i s taken as 137.2 ° F (Table VI-8). The percentage s a t u r a t i o n of the helium f r e e stream with naphthalene can be c a l c u l a t e d from - k £ A R T T A PDB = Pw < 1 - e r (IV"4> T h e . i n t e r n a l volume of the gas r e c i r c u l a t i n g apparatus i s 3 5 3 24 f t . (6.82 x 10 cm. ). The mass t r a n s f e r c o e f f i c i e n t can be e s t i m a t e d from Eq. (15) f o r a sphere: * 1/2 1 /°> Shu = 2 + 0.69 Re . S c / (15) f p i f By methods shown p r e v i o u s l y , Re , = 1225 pf ] TABLE VI-9 Scf = 4.55 V-14 Thus S h f =42.1 and k - S h f x d P 0.33 42.1 x 2. 54 = 5.47 cm./sec , kr = k* / R • (78) G c g f gm.mole 1.97 x 10" 4  2 . secern, atm. The area f o r mass t r a n s f e r i s the s p h e r i c a l s u r f a c e area minus the support c r o s s s e c t i o n a l area. -jf I 3 x 2.54 1 2 A = 4 77(1.27) • 16 = 20.12 cm. 3 Re. = 82.06 (atm. cm. J/gm. mole ° K) V-15 T = 341.9 ° K T = 1500 sec, p,„ = 2.61 'mm. Hg. (Table 1-4) w Thus k G A R T T _ . = 0.24 A and 5J; L A Rff T T (J s A 1 - e f = 0.21 The value of p^g at = 25 minutes i s g i v e n by PDB = ° ' 2 1 P w • = 0.548 mm. Hg. T h i s v a l u e . o f the f r e e stream p a r t i a l p r e s s u r e of naphtha-lene may be used f u r t h e r i n Eq. (94) and Eq. (97) to c a l c u l a t e the p s y c h r o m e t r i c r a t i o and Lewis number exponent i n a manner s i m i l a r to that shown f o r measurements i n the wind t u n n e l . From Table VI-9 i t can be seen that Bj = 5 . 5 3 PP = 0.312 MM = 0.320 V-17 IV. CALCULATION OF AVERAGE VALUE FOR THE PSYCHROMETRIC RATIO AND LEWIS NUMBER EXPONENT Average v a l u e s of the psychrometric r a t i o and the Lewis number exponent were determined over a wide range of f r e e stream temperature l e v e l s . The macroscopic psychrometric r a t i o i s d e f i n e d as For measurements conducted at nn temperature l e v e l s , the average p s y c h r o m e t r i c r a t i o i s d e f i n e d by nn ( t D B - - t w ) ( l + q * ) / * MWBf P B M c p f MWW X w ( p w - p D B ) (72) 1 nn (V-7) The macroscopic Lewis number exponent i s d e f i n e d by M, (82) o Log ( L e f ) For measurements conducted at nn f r e e stream temperature l e v e l s , the average Lewis number exponent i s d e f i n e d by V-18 Log f ( tDB - V ^ 1 + a * ) y * k f V T f 1 MWW \ w ( p w - p D B ) D v f nn Log nn I ^ 1 nn (V-8) S i m i l a r procedures are used t o c a l c u l a t e the l o c a l average v a l u e s by c o n s i d e r i n g Eq. (94) and Eq. (97) i n s t e a d of Eq. (72) and Eq. (82) r e s p e c t i v e l y . VI-1 APPENDIX SIX TABLES OF DATA AND CALCULATED RESULTS TABLE VI-1. WET-BULB TEMPERATURE DEPRESSIONS IN A QUIESCENT ATMOSPHERE Sample A i r Room Wet-Bulb Chemical Shape Diameter Length Temp. Temp. Pre s s u r e Temp. Dep. i n . i n . o F ° F i n . Hg. ° F Naphthalene C y l i n d e r 0. 519 2.0 72.7 72.7 29.87 0. 55 Naphthalene C y l i n d e r 0. 519 2.0 104. 5 71.0 29. 57 0. 54 Naphthalene C y l i n d e r 0. 519 2.0 138. 0 73.0 29. 30 1. 80 Naphthalene C y l i n d e r 0. 519 2.0 111.0 76.0 29. 30 0. 67 Naphthalene C y l i n d e r 0.519 2.0 125.0 76.0 29. 30 0.75 Naphthalene Sphere • 1.0 104. 5 71.0 29. 57 0. 54 Naphthalene Sphere 1.0 138.0 73.0 29. 30 1.80 Naphthalene Sphere 1.0 111.0 76.0 29.30 0.76 P-dichlorobenzene C y l i n d e r 0. 519 2.0 72.0 72.0 29. 57 0.66 P-dichlorobenzene C y l i n d e r 0. 519 2.0 85. 0 71. 0 29. 57 0.85 P-dichlorobenzene C y l i n d e r 0. 519 2.0 125. 0 76.0 29. 30 3.80 P-dichlorobenzene Sphere .1.0 72.0 72. 0 29.82 0. 62 P-dichlorobenzene Sphere 1.0 104. 5 71.0 29. 57 2. 12 P-dichlorobenzene Sphere 1.0 138. 0 73.0 29. 30 7. 55 P-dichlorobenzene Sphere 1.0 111. 0 76.0 29. 30 2. 30 VI-3 TABLE VI-2 TEMPERATURE MEASUREMENTS IN THE WIND TUNNEL Word, d e f i n i t i o n s : ORIFICE AIR Incoming a i r temperature, ° F BULK GAS Bulk a i r temperature at sample, ° F TEMP Wet-bulb temperature, ° F TWB Wet-bulb temperature d e p r e s s i o n , G F Note - the temperatures f o r each run were r e c o r d e d at 5 minute i n t e r v a l s . 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UBD*(I>-TF6I-TF6I) GO TO ID VI-4 24 GAUGE THERMOCOUPLES IN SAMPLE —THERMS' NO « TSHmnn THERMO HITS ORIFICE AIR BULK GAS SAMPLE FRONT P.V TEMP MV TDB NT TEMP THB 571*0 TOTJ* iTsTs* loi.za iTio 9079* io71i~ 0.86C TO.16 1.311 101.1* 1.310 100.SB 0.4a o.*ai TO. ii l.no 101.so i.sn ioo.*j o,*7 INOTE-ALL TEMP. IH PEG. TBIiHO WtPl SAMPLE CENTER < TEMP TUB l.ll* loo.I* THERHQ HO 2 SAMPLE BACK I.Hit «T7lt 13.42 1.0) 10.36 1.8 1.301 100.50 1.00 1.51* 1D01T* 2* GAUGE THERMOCOUPLES IN SAMPLE THERMO NO t THEHMO NO * THERMO NO 5 . ORIFICE AIR BULK CAS UHPLE FRONT THERHO NO 1 SAMPLE CENTER THERMO NO I SAMPLE BACK 0.11} 0.181 T1.2* Tl.IB 1.401 .91  17 UT IS 91 1.8*0 1.87] 11S.T1 116.2* 2.14 l.*T 1.861 1.86B 16.41 116.02 2.40 1.91 1.*4 114.(7 11.1 2.48 2.DB o.ll 0.1*3 0.881 0.883 0.IB3 Ti.Ii 71.2* T1.2* 71.2* TI.  l.«U 1.920 1.42* 1.912 1.921 lit 10 I I I 0* 38+0 )* LIT! I.B81 l.lll 1.83 11*.J  11*.AO 16.90 11*.T  116.4 l.Tl 1.72 1.61 1.67 l.BTO l.T* 1.881 1.880 .IT  16.1  118.1* 16.SB 116.33 11*.s 1.4* 1.4* 2.00 l.BT 1.41 B*1.8T3 1.872 1.IT1 11.98 116.26 16.12 116.19 16.1  1.6* 2.D8 2.6 2.1 2.1 RUNNO. II (KOTE-ALl TEMP26 GAUGE THERMOCOUPLES IN SAMPLE ""THWWNO'4 " BULK CAS "Tl.41 iTaTJ 114.9* IDT i T1.91 2.120 131.29 Z.10 111.40 Tl.91 2.118 131.IT Z.260 111.82 -THERMOUO-I SAMPLE CENTER —r.TSS-T62TW JI75T 2.Z3 11.01 4.20 2.Z1T 131.*+ 1.1 THElkb Nd"! SAMPLE BACK U TEMP TUB iT5ii~roiT66— D:«— t.ZZO 110.93 4.3Z 1.210 1).31 3.82 1.89B Tl.91 IFIVMlI.EO.O.OI CO TQ il TC5II* AID . BI51*VH1|IJ f Ct51*VHSUH TFSI I l-TCSI I 1*19.0/1.01 O2.0  CO TO ISO.II.5213.141.NT? 10 0  10 I-1.H VHFRI>*VMlliI TFRI l-TFKIl TUBF1)• WBD1 I I I .110 CONTIUE  GO TO 10  VHFRI1)*VH3(1] TFKIl-TFlI 1 TMBFR1I-NB03II I JON 11 U! CD"TO 150  II K «*l 1 tl 1134 CONTINUE GO TO 111.1 5 0  1151.1, VMCEI[l"VMI TCEIl-TFl i 0  15* I'l.N vHCEii-vKjm TCEUI-IF2I1 ) TWBCEI1-HB021I GO TO 1530 T DO 11T 1*1iH VHCEIII-VN3U1 i-iTini TUBCEII)>UBD3II 1 ] TQ I 1 0  138 Kl.MVMCE(U'VN4I TCEII I-TF* C t TUBCFII ITSBO. B CONTINUE GO TO 1530 0 0  1*0 I-l.H i I-l.M Ul l-VMl I) TBAin-iFi TUBAM l-KBDHI 1 1 CONTIUE CO TO 1610 I DO 1*1 I-l," " i-VM2in T»I l-TFJI 1 I TUBAM 1-MB2I1) CNTIUE GO TO 1610 „y"B*j.n *v"i 1 IBM I I»IF31 I I THBBAII)*UBD3II> 1 CONTINUE GO TO 1*10 ..*3 TMBBAII)*UB04III CONTINUE GO TO 1610 m '-t.M VH8AII-VM3II  TBA(1 I*TF11 I) ' TUBBA(I-HBDII) 1*5 CONTIUE 60 TIE 'Rl.TfelAtli ' 2 FORMAT IX.7HRUN NO..111,a L TEMP, IN DEG. F.I,/I 81 F0RHATIU.3ZH24 GAUGE THERMOCOUPLES IN SAMPLE,l\ HftlTE<*.SZ> WF.NC.NB BZ F0RMATI1.+9H THEKMO HO 8 THERMO NO * THERtg NO . , 12H THERQ NO .11 .21H THERMO NO ,1./) URITEI6>I4I 14 F0RHAK11.4TH ORIFICE AIR 1 SAMPLE CENTER URITEI6.21) 21 FDRMATIU.101H MV TEMP IB My TEMP TUB OO 14 I*1,M H*ITEI*,1>> VM lh Jtti I) ID.THBFRI II.VMCEIII.TCEIU,-15 FORH*T(U.F*.3,FT.2, P9.1, 19 CONTINUE HR|TE<6.161  16 FORMAT!IX,//> GO TO 49 1000 STOP• ' SAMPLE FRONT 1.313 1)3.BB 132.41 3.4T 1.212 1)2.7 3.61 RUN NO. 14 (NOTE-AL  TEMP. IN 24 GAUGE THERMOCOUPLES IN SAMPLE THERMO NO * THERMO NO * THEAMD NO S ORIFCE AIR SAPLE FRT I ' TEMP . Tt SAMPLE CENitl ( TEMP TUB TltERMD tO 2 —i»spL(~Bicir~ 1.889 T1.52 2.115 1*3.21 3.13 2.504 RUN NO. 53 IHOTE-AL  TEMP. IN OfC, 24 GAUGE THERMOCOUPLES IN SAMPLE THC tWO NO » THfRMO NO 6 ' OPIFCE A IB BULK GAS MV TEMP MV TDB SAMPLE FRONT ~THE*MS~N6"T~ SAMPLE BACK 163,09 2.BIO 155.4 1*3^13 Z.fl* 115.59.. 2.850 11T.0* 2.BO  114.95 8.14 ll.OT t'.Qt Z.B1B 131.68 INOTE-ALL TEMP. 2* GAUGE THERMOCOUPLES IN SAMPLE THERNO NO B TNEKMO NO * THERMO ND 1 ORIFICE AIR BULK GAS SAMPLE FRONT SAMPLE C THERMS ND Z SAMPLE BACK TEMP 7Z.*3 1.36T 1TB.25 TEMP 121.38 HV TEMF 1.790 12.68 bi.il 3.16T 1TB.Z5 RUN NO. IT INOTE-AL  TEMP. IN DEC, F.I 24 GAUGE THERMOCOUPLES FN SAMPLE THERMO NO 8 THERMO NO 6 THERMO NO 1 THERMO NO | ORIFCE AIR SAPLE CENTER I TEMP TUB SAMPLE BACK TEMP T 0.9)0 T1.30 0.930 73.0 0.930 T1.30 "i.t*f l!f.o3 2.R31 11*.4* 2.811 151.42 2.69 130.51 " *8a 432TR 130.02 ?.682 130. II-2.681 130.7 2.8TO *9*2 2.812 156.50 2.730 132.97 Z.6BT 110.12 INOTE-AL  TEMP, IN DEG. IN SAMPLE  THERMO NO 8 THERHQ HO ORIFCE AIR BULK GAS MV TEMP MV TOB THERM ND 5 SAMPLE FRONT THERMO NO I SAMPLE CENTER i TEMP TUB THERM3 NO 2 SAMPLE BACK TEMP 1 0.92T 73.IT 2.484 0.42T T1.T 2.474 oT42T n r n 27479" 2.36T 17.91 2.180 1)7.*2 RUN HO. 14 INOTE-ALL 7EMP. IN DEG. P IL GAU6I TMERWOCOTJFTR lw SAMPLE THERMO NO * ORIFICE AIR —HV WIT— 0.43Z 73.34 2.019 122.34 0.9)2 TJ.39 2.009 122.11 0.922 73.14 2.C10 122.16 THERMO NO 1 SIMPLE FRONT 2.360 17.61 THERMO NO 1 SAMPLE CENTER 2.174 1)7.) 1.172 I3T.14 THERMO NO Z SAMPLE BACK l.BD 1.*) >•»> 1.9T1 120,5B 1.9* 1.974 120.14 2.00 1.970 120.17 l.Tl 1.4*1 1ZD.ZB 1.B3 J.471 10.41 l.Tl 120.33 1.81 VI - 5 THERM NO B OK I ftLt MH THERMO NO 6 BUKC*S THERMD HO 5 SAMPLE FRONT THERMO NO 1 SAMPLE CENTER THE It MO NO 2 SIMPLE BACK RUN (£0. 69 (NOTE-AL TEMP. IN OEG. F 24 GAUGE THERMOCOUPLES IH SAMPLE THERMO NO • ORIFICE AIR MV TEMP' 0.912 7i.it 0*932 • 73.39 THERM HO A BULK GAS "TTTTJ 12.10 THERMO NO ) SAMPLE FRONT I TEMP Tt isl vTTTi Ti; I*T nnlti i! l.iii 1.712 THERMO HO 1 SAMPLE CENTER TEMP THB 1.T4 THERMO NO 2 SAMPLE BACK TEMP T I.2lT I'TIO 89. *9 2.3! 10S.R1 3.03 no. 10 l.ii RUM HO. TI IMOTE—AIL TEMP. IN DEC. F.I 14 GAUGE THERMOCOUPLES IH SAMPLE THERMO HO I • THERMO MO > THERMO NO 1 ORIFICE AIR BULK GAS SAMPLE FRONT MV TEMP MV TDB MV TEMP Tk LSAMPLE CENTER I TEMP . TUB THERMO NO 2 24 GAUGE THERMOCOUPLES IN SAMPLE THERMO HO B THE*MO NO A ORIFICE AIR BULK CAS  MV TEMP MV TDB 0.4*1 74.08 2.101 IS*.* 0.9* *OA 2.10 1*.81 0.94B 74.08 1.102 U*.9Q THERMONO 1 SAMPLE FRONT 2.21 131.' 1.258 12.ST THERMO NO 1 SAMPLE CENTER MV TEMP TUB 1.171 101.12 11.1 lino. .no." i*9i I.til 130.4V 171* 2*2*8 112.10 i'.u .TS2*212 TEMP THB 111.0* 21.16 TSoTia 2*0 13*1*5 0.980 75.4T a',no it'.M 2.948 161.29 2.95 161*9* m'so -i:Tfi"i!ti.T« 2.785 ISA.40 2*10  IH.02 RUM NO. 7* IM01E-AL TEMP." Jt 2» GAUGE THERMOCOUPLES IH SAMPLE THERMO NO B ORIFICE AIR THERMO MO * BULK GAS THERMO NO 1 SAMPLE FRONT I TEHP T> TTtTi—i*2.<i*"  2.74 151.8 2.TBS 154.13 THERMO HO 1 SAMPLE CENTER I TEHP T« 2.769 151.68 THERMO NO * SAMPLE BACK TEMP 1 RUN HO. 71 I NOTE-AIL TEMP. IN OEG. 24 GAUGE THERMOCOUPLES IN SAMPLE THERMO HO B THERMO NO 6 ORIFICE AIR BULK GAS MV 1EHP MV 'TDB THERMONO 1 SAMPLE FRONT TEHP TH THERMO NO 1 SAMPLE CENTER THERKO NO 2 SAMPLE BACK TEMP 1 I.S16 101.7* 1.11 10.61 0.969 74.B2 2.140 16.1 2.190 • 129.TI 2 7.1 0.961 74.B2 I.ISO 17.24 2.61 14B.91 (.21 0.96S 74.BI 2.142 16.91 2.692 10.59 6.12 0.961 74.B2 2.140 156.83 TO 10.92 1.90 I0.969_74.BI 2.147 17.1 2.701 10.96 6.18 2.141 157.0? t.721 11.78 RUN NO. 72 ' I NOTE-*AL TEMP. IN OEG. F.) 24 GAUGE THERMOCOUPLES IH SAMPLE THERMO NO I THERM NO 4 THERM a ft MV TEMP SAMPLE.FRONT I TEMP Tt 2.6BS 10.36 2.691 10.16 -2.681 liO.il-2.616 10.21 2.690 10.4 THERMO NO 1 SAMPLE CENTER I TEMP TUB 81 16.6 40.16 2.191 146.91 10.TI 2.60 149.21 TO2.672 149.70 7.12 2.679 149.9? 7.12 -I;-671-TIW:K—m 2.671 149.B2 6.SB 2.680 10.01 7.0 THERMO NO 2 "SAMPLE itK 24 GAUGE THERMOCOUPLES IN SAMPLE THERMO NO g THERMO NO 6 0.941 71.TB 0.941 Tl.TB 0.941 Tl.TB 0.941 71.78 0.941 71.71 1.891 17.17 1.8*6 17.29 1.B91 1)7.21 1.197 17.14 1.8*1 17.18 1.86 16.01 .81 16.7* 1.814 UT.21 1.896 17.29 SAMPLE FRONT I TEHP Tt US.29 11.47 11.1 SAMPLE CENTER "l.Boi-m;ii— 1.8*0 14.81 1.846 USOB1*7 11.1 1.128 1J4.1I THERMO NO 1 SAMPLE BACK 1.810 14.40 1.012 **81.829 14.19 nTRi TJo* 1.29 1 T<.,72 i.oTo 1*1.se io.T* 3To*4 164.86 11. 1.970 79.04 1.0 617 3.069 165.9* -2.17 3.043 164.82 -1.45 1.010 161.89 RUN NO. 81 [NOTE-AL TEHP. IN DEC. F.I I* GAUGE THERMOCOUPLES IN IAMPLE THERMO NO 8 THERMO NO 6 THERMO NO 1 THEftH NO4 SAMPLE CENTER THERMD NO 1 SAMPLE BACK ' RUN NO. 71 2* GAUGE THE I NOTE-AL TEMP. IN DEG. I S IN SAMPLE  THERMO NO B ORIFICE AIR MV TEMP THERMO HO 1 SAMPLE FRONT THERMO NO 1 SAMPLE CENTER THERMO NO 2 SAMPLE BACK 1.89 71.96 1.83B 15.67 1.818 11.91 60 9 B20~T7Bi6 1S.TS ITiJl—14.D! 1.89 1614 1.816 14.68 1.870 16.18 I.BT2 16.2 81 11.98 1.81 13.75 -1TBI5~HJTT~ 124 14.14 13.97 2.21 RUN NO. 74(NOTE-ALL TEMP. IN DEG. P.I 2* GAUGE THERMOCOUPLES IN SAMPLE THERMO NO 8 THERMO NO 6 THERMO NO 9 THERMO NO 1 THERMD NO 2 ORIFICE AIR BULK CAS SAMPLE FRONT MV TOB MV TEMP TI '»*_.143.9a_„, 2.051. 123.93 20. SAMPLE CENTER MV TEHP TMB ,1.610 105.79 18.1 SAMPLE BACK MV TEMP TUB 1.761 12.38 1.60 2.41 140.2 2*40 140.18 .,—l*°tl*-, 1.01 9.07 2.420 19.28 1.48 RUN NO. 79 INOTE-AL TEMP. IN DEC. F 24 GAUGE THERMOCOUPLE! IN SAMPLE THERMO NO B • THERMO NO6 THERMO KD 1 ORIFICE AIR BULK OAS SAMPLE FRONT NO  SAMPLE CENTER THERMO NO 2 SAMPLE BACK 1.414 72.61 2.910 161.13 2.71f 191,26 |.C 1.74 192.8* 8.47 2.718 12.41 6.42 ITTTI isi.il iris irm 1 RUN NO. T* ' iNofe-AilIN MeV'M" 24 GAUGE THERMOCOUPLES IN SAMPLE THERMO HO 8 THERMO NO 6 THERM! THERMO NO 1 ORIFICE AIR ' ;::H 1.910 1.681 I* 11,19 18,41 1.41 18.40 1.421- 18.91 LOI.04 -KltHtt*-1.80 16.16 61.B  16.81 84 9,1.  16.71 - SAMPLE CENTER •V TEMP TUI 1.514 10.76 16.18 SAMPLE BACK TEMP T 1:11 l:Ht m:ii i:U 1:11! IIS:ii i:ti .4 1.61 1.19 1.19 1.8)1 16.61 1.84 16.70 1.19 Ul.TI Ut.61 1.0t_ RUN NO. 7 <NOTI>AL TIMP. IN 0(0. 14 QAUfl IHIHMOCDUPlI IN 1AMPLB 1.31 19.71 11.7 0.95a 74.92 0.958 74.92 50.4SB 74.12 2.11 2.11 .15 in.as 2.1*0 136.09 2.141 16.13 136.09 .163 18.91 7.18 I.180 129.21 3 32(NOTE-AL TEMP. IN OEG. F 2.245 11.98 1.2*0 131.7 '1*' GAUGE tHERMflCOUlLEt IN SAMPLETHERMO NO 8 THERMD HO 6 THERMO NO 1 ORIFICE AIR BULK GAS SAMPLE FRONT SAMPLE CENTER THE*"3 NO 1 SAMPLE BACK 0.962 7*.69 4,69 2.798 193.49 2.981 1*1.9 2.*40 2*171 1*1 TEMP TUB ».19 14.15 RUN NO. 81 I NOTE-AL TEMP. IN OEG. 24 GAUGE THERMOCOUPLES IN SAMPLE  THERMO NO 8 ORIFICE AIR MV TEMP THERMO NO 6 BULK GAS THERMO NO 1 IAMPLE FRONT SAMPLE CENTER TEMP TUB THERMO NO 1 SAMPLE BACK o.9»' n:H I7BT5—ITiiT-0.939 73.92 1.0T1 146.17 0.419 71,12 1.0T2 16.31 BSD 16.17 ,810 9:t* 16.1T *.B9 81"571 J-1.821 19.80 10.2 29 171 - " ,837 16.46 9.81 ~r.U1- lJiTo! 10.11 22 196.09 10.18 I.10 16.IT 10.4 RUN NO. 14 I NOTE-AL TEMP. IN 24 CAUOE THERMOCOUPLE! IN SAMPLE THERMO NO 8 THERMO NO 6 SAMPLE FRONT SAMPLE CENTER SAMPLE BACK 0.978 8.4TI 071 libit 75.18 1.428 10.TO 2.01 146.01 11.19 1*1. » 161.15 16.91 14.6' 1.15 1.1L 1.410 081T.I8 160.6! 161.02 1.1* 14.41 1.61 2.11 14.0*6 121.07 92.1 Uo.*» 26.U 164.9* 19.76 0.471 T80.4B a.ATI TI.II ' 1.A4I 11.19 3 19 181.7* 1 0 18TI.I4 1.4» 110.91 04!91.0*6 16.42 I6T.I1 142Iti'.TI 14.48 l*.10 -fHJ-1.087 111.046 i.iae 16,60 162.1* 9l6T.l  14.7* 14*1 11.14 1.10 i. in 110V.4 1*7.12 1*,26 I6T.9T 4.141.1* 102 RUN NO.10* I NOTE-ALL TIMP. IN DEO. F, I -»'CAUci TBimeeounii-iwiAMHi THERMO NO I THIIMO NO * THIRNO NO'I OIIPICI AIR IULR OAS 1AMFLI FRONT ItMPLI CENTER THERMO NO SAMPLE IAC VI-6 0.41D 71.10 I . M I 149.1* 1.430 134.TO 9.4* 1.41* 119.14' 0.423 71.00. 2.0*8 114.62 2.018112.46 2.16 0.421 T1.00 2.0TO 124.71 2.023 112.66 2.0S ' 0.421 71.00 2.072 124.14 2.023 122.T4 2.0* 0.421 T3.00 2.072 124.TI 2.023 II1.T*. 2.01 2.012 121.1 2.31 2.OPT 121.44 2.3* "2.011 iii.il  .001 121.4 2.001 111.  -irm -1755 i.oir*tH.l!— 1.020 122.49 2.1 2.013 122.8 1.41 2.022 121.36 2.11 2.01T 122.16 2.43 . 2.011 111.62 2.1T 2.01* U2.41 2.18 1WQTE-*It TIM, IH DEB, P. I 1* 6MICE THERMOCOUPLES IH SAMPLE THERMD MO * THERMO NO 6 1AMPLE CENTER THE A19) NO 2 1AMHE BACK RUN.O.IT I NOTE—AL TEMP. IN 0 24 CAUSE THERMOCOUPLES IN SAMPLE THERMO NO 0 ORIFCE AIR MV TEMP THERMO NO 6 BULK CAS lf*40 140.2T THERMO NO 9 SAMPLE FRONT 2.34B 136.14 1.B9 136.IB 1.19 2* GAUCG THERMOCOUPLES IN SAMPLE THERMO NO B THERMO NO 6 THERMO NO 1 ORIFCE AIR BULK GAS SAMPLE FRONT 0.942 T1.B2 0.942 73*82 2.B32 116.32 9.11 "ItoTo^  164.19 2.833 lst.37 7.82 1*015 163*9  2.831 16*43 7.14 RUN NO.104 (NOTE-AL  TEMP. It 2* GAUGE THERMOCOUPLES IN SAMPLE THERMO NO B THERMO NO 6 THERMO HO I SAMPLE CENTER » TEHP TUl THERMD NO 2 SAMPLE BACK TEMP t 2.141 2*343 116.08 4.13 2.119 19.1 THERHO NO 1 SAMPLE CENTER .820 119.76 2*816 199.68 . 7HERK0 NO 2 SAMPLE BACK TEMP 1 t21 114.11 2* 0.440 73,74 1.099 167.2* 0.4*0 71.74 1.090 167.04 0.940 T1.74 1.091 167.1? ~0.4O 7374 lTBil 167.24 0.440 71.74 1.046 167.28 0.940. 71.74 . 1.,00 167,41 0.440 73.74 1.00 167.43 164.74 22.10 197.06 9.98 -- — ,9.3 2870 ISTBT Z.B70 1ST.8T 2.B79 198.08 2.80 198.18 4,ir 4.61 9.7 9.17 RUM NO. 126 I MOTE—AL -TEMP. IN DEC. 24 GAUGE THERMOCOUPLES IN SAMPLE THERMO HO 8 THERMO HO 6 - T ' MV TEMP 0.92O 72.87 0.9i5 72,B"f~ 0.920 72.87 0.920 72.87 0.92O 71.87 0.920 72.87 0.920 72.67 " 6.920 72.07'" 67193 0.891 0.447 SAMPLE FRONT MV TEHP Tt 0.866 71.02 ~6.896 0.860 0.861 0.861 0.B60 ii.il 71.73 71.B4 71.B8 71.73 71.01 RUN NO.127 IMOTB-AL  TEMP. IH OEG. F.l ~~34 GAUGT tHERNOCl&PliS IH SAMPLE THIRNO NO B THERHO NO 6 THERHO NO 9 ORIFCE AIR BULK CAS SAMPLE FRONT 0.871 70.74 0.871 70.74 0.871 70.74 84.79 W119 B4.29 84.81 liOO B1.91 84.79 1.102 62.60 64.61 1.098 81.42 2.190 118.04 29.21 , 2.840 194.16'- 10.46 1.B30 196.44 10.13 117.81 29.42 ' 191.76 11.16 196.11 10.49 186  11T.W" «7»S S.6H 196.9+—iO.T|— 2.861 197.41 9.83 2.8*0 196.IB 2.869 197.60 *.B9 2.690 156.99 2.880 118.11 9.24 2.890 196.99 SAMPLE CENTER ' TEMP TUB 0.880 72.68 Q.t -6.641 0.831 0.140 >17ST~ ri.99 71,78 71.82 72.00 72.00 THERM  NO1 SAMPLE CENTER —MV fBT 86.18 -un • 82.98 1.29 61.96 2.1 81.1 2.92 THERMO NO 2 SAMPLE BACK MV TEMP 1 0.883 72.81 ( 0.852 71.42 i 0.B90 71.33 I 0.897 TI,** I 0.896 71.60 I 0.860 ,. 71.78 I 0.161 • 71.82 1 THERMD NO 2 SAMPLE SACK .1.161 81.11 -0.15 0.92L 72.91 0.421 72.41 0.921 72.41 SAMPLE FR0N7 143.14 2.081 123.20 17.49 143*19 2*02 18*60 4.99 2.440 142.16 2.390 138.10 2.191 118.12 SAMPLE CENTER MV TEMP TUB Ll1 17.05 26.1* [."39  118.2* 4.94 1*110 I3T*62 4.T* SAMPLE BACK MV TEMP TUB -i 6H _rn;ii I I . T J -2.376 137.*9 9.3 2.187 17.91 3.28 2.380 117.62 *.4 .1T3 17.41 4.9* ~I7lTT~rjT7W—m& 1.871 70.74 J.BT1 70.74 1.871 70.74 1.52 84.87 1*19 83.01 1.099 1*101 12.47 62.96 RUN HQ.120 IMOTE-AL TEMP. IN DEC. F.l 24 GAUGE THERMOCOUPLES IN SAMPLE 2.41 2.49 THERMO NO * ORIFCE AIR MV TEMP THER NO HO 4 BULK GAS TM£MMO NO 9 SAMPLE FRONT * TEMP 7H 1.095 82.11 2.16 1.097 82.40 2.61 THERMO MO I SAMPLE CENTER V TEMP TUB 1.090 .092 82.09 82.IB 24 GAUGE THERMOCOUPLES IN SAMPLE THERMO NO B THERMO NO 6 ORIFCE AIR BULK GAS  THERMO NO 1 SAMPLE FRONT THERMD NO 1 SAMPLE CENTER THERHO NO I SAMPLE BACK 1.14 91.JT 4.35 1.12 42.80 0.920 72.87 ' 2.32 132.39 2.198 130.5 2.34 2.180 129.23 3.15 0.420 72.BV 2~7l"*0 131.89 2.184 129.46 2.43 2.16912B.TB S7TS RUN NO.Il INDTE-AL  7EHP. IN OEG. 24 GAUGE THERMOCOUPLES IN SAMPLE THERHO HO 8 ORIFCE AIR THERMO NO 1 SAMPLE FRONT SAMPLE CENTER MV TDB MV TEMP TUB MV TEHP 1MB —1.460 U6.01 iTSsi~us:rs STM rmo—iMTn-ranr-2.183 129.46 THERMO NO 2 SAMPLE BACK RJN~W.119 (55Ti=Ul 7*MP7'IN 6E6. F7» 24 GAUGE THERMOCOUPLES IN SAMPLE THERMO NO 8 THERMO MO 6 THERMO NO 3 l.BBl 71.18 1.609 104.41 1.463 98.42 THERMO NO 1 SAMPLE CENTER THERMO NO 2 SIMPLE BACK 1.499 48.IB . 1.4*1 48.43 6.49 - 1.454 98.21 1.940 119.09 2.6* 1.932 118.25 T7~l RUN : No.130 24 GAUGE THt (NOTE-AL  TEHP. IN OEG. F.l :pU,FLES IN SAMPLE  ' THERMO NO 8 .THERHO NO ORIFCE AIR SULK GAS MV TEMP MV TPB THERMO NO 3 SAMPLE FRONT THERMO HO 1 SAMPLE CENTER I TEMP THE THERMO HO 2 SAMPLE BACK - IEHE 3 RUN NO.112 (NOTE-AL  TEMP. I* 24 GAUCE THERMOCOUPLES IN SAMPLE THERMO HO 8 THERMO NO 6 ORIFCE AIR SULK GAS MV TEMP MV TOB 0.925 73.09 2.1B5 133.TB 1.913 73.09 J.423 71.09 SAMPLE FRONT I TEMP Tt ill 1(3.78 20. RUM HO.Il (NOTE-AL  TEMP. IN DEC. F.l 2* GAUGE THERMOCOUPLES IN SAMPLE THERMO NO B THERMO NO 6 THERHO NO 1 ORIFCE AIR BULK GAS SAMPLE FRONT SAMPLE CENTER 1.640 108.18 29 F* THERM  NO 1 SAMPLE CENTER TEMP 1 THERHO NO 2 3.B90 71.97 064 50.84  .5  1.8*9 115.11 1,849 115.11 I.849 115.11 1.532 101.94 1.641 106.16 1.699 106.BB 1.830 114.7 iTSil 106.BB 1.811 114.08 1.644 106.2 1.810 114.04 1.650 106.7 1.820 114.04 1.690 106.7 RUN NO.112 I NOTE-AL TEMP. IN OEG. F.) 2* GAUGE THERMOCOUPLES IN SAMPLE THERMO MO B THERMO NO 6 THERMO NO 1 ORIFCE AIR MV TEMP • 0.840 71.97 0.890 fl.1T " 0.990 71.97 0.690 71.7 0.890 71.7 0.190 71.97 0.896 71.57 71.6 71.33 71.29 11.9 SAMPLE FRONT ( TEMP Tt >00 T1.93 -" 161 TT779— 163 71.88 162 71.8* 1.99 1.90 1.* 1.90 1.470 98.6* 16.27 1.61* L09.6 9.13 1.691 106.70 8.41 1.691 106.70 8.20 1.696 "166V6S TTil 1.6*1 106.27 7.81 1.641 106.27 T.T 1.6*1 106.27 7.7 0,86* 0.861 0.160 0.B39 v. 11,31 y .v iu IS. kr 6.1« Tl.St BTsTI 7718" 0.859 TiTo" 1.16 71.96 i7*i 71.82 1.56 71.78 1.60 71.71 1.60 71.78 1.51 71.6* 1.91 ~ r r m — i 7 ! r .622 109.** 9.6T .642 106.1  B.80 1.6*9 106.** 8.46 THERHO NO 2 SAMPLE BACK t.804 195.19 RUN NO.I14 2.6671*9.75.99 2*678 150*. 02 9,99 . fEMP. IN OEG. F ! THERMOCOUPLES IN SAMPLE ORIFCE AIR 0.91O 73.10 7HRM0 NO 9 SAMPLE FRONT a.410 17ST 0.410 71.10 O.910 71.10 0.910 1 .30 0.410 71.10 0.910 71.10 2.1*1 1.996 144.89 1.996 144.89 1.990 1*4.61 2.951 149.04 2.101 113.96 -2.,4li-i4'.t4 l.*21 119.*7 2.421 119.47 2.411 111.47 2.411 119.14 61*11 H T l M 2.6*1 1*8.51 1.631 1*8.16 2.631' 1*8.4 2*60 149*21 7HERM0 NO 1 SAMPLE CENTER I TEMP 1 2.613 1*7.16 7.21 1.611 1*8.16 1.44 1.613 148.18 7.11 2.643 148.59 7.41 SAMPLE BACK TEMP TUB 1.900 1.411 119.24 1.414 119.45 1.419 119.49 1.196 UI.641.391 116.37 2.400 118.43 2.402 Ut.34 2.410 118.87 1.41B 119.08 RUN NO.14 INOTE-ALL TEHP. IN DEG. F.) •~2T~lEJ!"! TWI«.HMOUPLI.J IK~«KPTE ORIFC  AIR 0.840 T1.74 0.940 71,T4 0.940 71.74 THERMO NO 6 BULK GAS 1.612 109.06 THERMO NO 5 SAMPLE PROMT 1.45B 48.11 9.79 RUN NO.Il INOTE-AL  TEMP. JH 14 GAUGE THERMOCOUPLE! IN SAMPLE THERMO NO B THERMO NO 6 SAMPLE CENTER i f~Sf Tii •TO 98.64 9.1 •91 98.01 6.1 1.660 9*1*0 .431 98.18 1.461 WT*? 6TJJ lTWB «K*TJ C71T 1.46! 98.62 ' 6,11 .460 98.40 6.97 1.470 98.84 6.11 1 469 98,42 6.91 1.470 11,64 4.12 1.464 IB.98 6.4B VI-7 ORIFICE AIR SAMPLE FRONT I TEMP Tt SAMPLE CENTER SAMPLE BACK TENP 1 0.428 73.11 I.S5B 0.911 71.21 1.155 .0.421 71.22 1.312 0.428 71.12 91.67 1.11 1.242 89. TO iCTSi 17764" 176 « 11. 11 11.75 89.40 A.* 1.210 89,18 A.86 89.14 4. IT 1.7" 89.12 4.14 1.112 91.71 1.112 41.71 89.70 3.97 1.214 14.18 2.12) 13.8 111.14 1.14 11.81 3.37 RUN NO.TJl (NOTE-AL  TEMP. IN OEC. F.l 24 GAUGE THERMOCOUPLES IN SAMPLE THERMO ND 8 THERMO NO 6 THERMO NO 1 SAMPLE FRONT THERMO NO 1 SAMPLE1 BACK (NOTE-AL  TEMP. IN PEG. F.I 24 GAUGE THERMOCOUPLS IN SAML IHERND NO 8 THERMO NO 8 ORIFCE AIR BULK OAS  THERMO NO 9 SAMPIE FRONT THERMO ND 1 SAMPLE CENTER THERMO NO 2 SAMPLE BACR 0.910 72.43 107.21 4.00 1.572 101.IB . RUN NO.140 (NOTE-AL  TEMP. If 24 GAUGE THERMOCOUPLES IN SAMPLE THERMO ND I ORIFCE AIR THERMO NO 6 BULK GAS —THERMO NO i'" SAMPLE FRONT I TEMP TH "THERMS NO 'l SAMPLE CENTER t TEMP 1W< "' THERMS' MO 1 SAMPLE BACK 1.830 69.B3 1.244 B8.40 14,13 1.013 81.8* 23.37 OfilO 848 1.601 104,67 o'.BlO 69183 1*41 104^24 1.459 _l1B_ 1.454 98.14 1*5  98*18 1.448 97.88 6.79 1*444 47*42' 6*32 INOTE-AL, TEMP. IN PEG. 24 GAUGE THERMOCOUPLES IN SANPl THERMO NO 8 THERMO NO 6 THERMO NO 3 THERMO NO I ORIFCE AIR MV TEMP 1PLE CETER TEMP • Tlfl THERMO NO 2 SAKPTETACK 0.762 6T.31 0.T59 6T.21 0.740 *8.*3 1.7*2 67. Jl RUN NO.143 . INOTE-AL  TEMP. IN OEG. 24 GAUGE THERMOCOUPLES IH SAMPLE  THERMO NO * ORIFICE AIR THERMO NO 4 BULK GAS THERMO NO 3 SAMPLE FRONT ' TEMP Tt THERMO NO 1 SAMPLE CENTER THERMO ND 2 SAMPLE BACK TEMP I 1.244 91.8 8T.6* 3.TO 1.295 41.20 1.220 IT.84 1.211 8T.55 1.61 RUN ND. 146 iNOtVAL  tEMP".- IN DEG. *Ti 24 GAUGE THERMOCOUPLES IH SAMPLE THERMO NO 8 THERNO ND 6 THERMO N dRIFICf AlR Bui* CAS' ilNPLE F«DST I TEMP Tt ~siHPtrcENTer~-THERMO MO 2 -5AKFLE lCK" O.Bti B8.12- 1.424 96.81 5.67 1.67 1.38 1.710 104.14 1.05 1.TD5 104.01 RUN NO.240 I NOTE-AL TEMP. IK 24 GAUGE THERMOCOUPLES IN SAMPLE THERMO NO I THERMO NO * THERMO WO I THERMO NO 3 ORIFCE AIR MV TEMP 0.930 71.30 1.T18 110.08 SAPLE FRONT t TEMP 112 91.42 li S.410 T1.10 • 1.720 109.T3 1.4B9 108.34 SAMPLE CENTER MV TEMP TM 1.228 88.11 11.BT SAPLE BACR MV TEMP TM> 1.113 41.40 17.68 1.661 L07.30 2.43 RUN NO.2*3 (NOTE-AL  TEMP. IH OEG. F.t 14 GAUGE THERMOCOUPLES IN SAMPLE  THERMO NO 8 ORIFCE AIR MV TEMP THERMO NO * BULK GAS THERMO NO 1 SAMPLE FRONT I TEMP Tl THERMO NO * SAMPLE CENTER I TEMP THE THERMO NO 1 SAMPLE BACK TEMP I 3.4*1 73.93 2.0*8 123.TT 2.OOP 111.** 1.487 111.09 2.6 1.471 110.41 1.1* (MOTE-AL  TEMP. IM PES. 24 GAUGE THERMOCOUPLES IN AP THERMO NO 8 THERMO NO 8 PRIFCE AIR BJM-S*! THERMO NO 1 SAMPLE FRONT THERMO NO 4 SAMPLE CENTER THERMO NO 3 SAMPLE BACK ,412 T2.ll 2.711 131.** 1.ST2 2.4*0 1*0.1 2.540 144.2* 2.434 1+0.7 JN NO.234 (NOTE-AL  TEMP. I* t GAUGE THERMOCOUPLES IN SAMPLE THERMO NO 8 ORIFCE AIR THE**! NO l SAMPLE FRONT HV TEMP Tt TH'ER'Ud NO A SAMPLE CENTER -THE* HO MO i ' SAMPLE BACK TEMP T 0.81164.00 0.811 64.00 0.811 64.00 •2.70 l.OtB R2.T0 1.012 12.T4 1.0*8 1.071 tl.42 1 . 2 7 1 . 0 1 2 1.045 80.08 2.*1 1.051 1.011 40.13 2.39 1.031 80.35 2.31 1,011 80.13 2.6* RUN NO.25* (NOTE-AL  TENP. IN OEC. 1* GAUGE THERMOCOUPLES IN SAMPLE THERMO N ORIFCE . THERHd k3 I SAMPLE FRONT THERMO MO A SAMPLE CENTER -THIRHO NO i " SAMPLE BACK TENP 1 2.940 1*2.4 2.T4S 1)2.92 2* GAUGE THERMOCOUPLES IN SAMPLE THERMO NO 8 THERMO NO « ORIFCE AIR BULK GAS THERMO NO 3 SAMPLE FRONT THERMO NO 1 SAMPLE CENTER SAMPLE BACK RUN NO.261 (NOTE-AL  TEMP. IN DEG. 24 GAUGE THERMOCOUPLES IN SAMPLE  THERMO NO B ORIFCE AIR THERMO NO BULK GAS THERMO NO 1 SAMPLE FRONT I TEMP TV THERMO NO • SAMPLE CENTER THERMO NO 1 SAMPLE BACK 1.801 67.64 1.707 101.7 1.348102.1* 1.511 161.80 -onia" ii.it—i.m 141.3-1—inn—m.M - 1.794 13*.TP 8.BD l.TBB 13*.3T I.TIT i54.il—im r.m m.» RUN NO.130 2* CAUCi THERMO NO 8 N SAMPLE THERMO NO B THERMO NO 5 SAMPLE FRONT I.T13 104.6 11.3 IPLE BACK TEMP T RUN NO.261 (NOTE-ALL TEMP. 24 GAUGE THERMOCOUPLES IN SAMPLE THERMO NO a THERMO NO * ORIFICE AIR BULK GAS Hv TEMP" H7 Toi THERMO NO 1 SAMPLE FRONT r~—trs* n -l~lit 19.16 -THERMO NO * SAMPLE CENTER 1.14* 11.41 THERMO NO 1 SAMPLE BACK 1.763 111.34 4.12 1.734 111.3 4.31 RUN NO.134 (NOTE-AL  TENP. IN 0 14 GAUGE THERMOCOUPLES IN SAMPLE THERMD NO 8 THERMO NO 6 ORIFCE AIR flUL* GAS- THERMO NO 1 SAMPLE FRONT I • TEMP Tt THERMO NO * SAMPLE CEHTER I TEMP TUB THERMO ND 3 SAMPLE BACK TEMP 1 RUN HO.201 (NOTE-AL  TEMP. \ 2* GAUGE THERMOCOUPLES IN SAMPLE THERMO NO B THERNO NO 6 ORIFCE AIR BULK GAS  THERMO ND 3 SAMPLE FRONT THERMO NO 1 SAMPLE CENTER 2.161 111.4 116.18 LOT 1.091 I11.it 8.87 2.1T4 129.00 2.1T1 111.IT KIT*" 111.01 2.181 119,29 VI - 8 • UN HO.201 (NOTE-ALL TEMP. IN OEG. f.l 2.4 GAUGE THERMOCOUPLES IN 1IWH • THE UNO NO > ORIFICE RID HV TEMP THERHO NO I SAMPLE FRONT SAMPLE CENTER t TEMP THE - THERMO NO 2 SAMPLE BACK TEHP T 0.410 72.41 2.14 112.41 2.LR0 129.21 2.ITT 121.12 0.910 72-43 2.41 111.07 1.202 130.22 2.142 129.71 1.31 (MQTE-AL TEMP. IM PES. F.I 24 GAUGE THERMOCOUPLES IN SAMLE THERMD NO I THERMO NO A ORIFCE AIR BULK GAS THERMO NO 3 SAMPLE FRONT THERMO NO I SAMPLE CENTEI SAMPLE BACK 2.14 130.79 MV TEHP 2.060 124.22 116.29 11.51 TEMP I14.BT 0.910 72.41 2.13 0.910 72.41 2.13 0.910 72.41 2.14 O.910 T2.41 2.13 0.79 2.147 17.90 0.79 2.147 127.90 0.79 2.14B 127.99 0.71 2.J47 127.90 127.46 127.46 12T.52 127.46 RUN NO.207 24 GAUGE THERMO NO B . TEMP. IH OEG. THERMO MO 5 THERMO NO 2 SAMPLE FRONT 140.59 24.26 SAMPLE CENTER I TEMP TUl SAMPLE BACK 156,24 B.6B 2.819 159.56 194.74 10.16 0.669 71.92 1.11 41.00 0.669 71.2 1.14 92.04 0.B69 71.92 1.14 92.04 1.239 66.51 3.49 1.211 IB.41 1.6 1.21! 1.215 1666,31 66.51 as. 9  210 IB.10 ' 1.64 U4BOT 1.J1J .t.Mtf l.tJJ ••. 3 L o.ia9 TTTJi rms ~jzs6 urn ii.ir E-AL  TEMP. IN OEG. F.l ., ..... 3.96 1.230 .... 1.234 88.4B 1.56 1.211- 88.14 3.69 1.24 B8.4  1.96 1.211 88.14 1.69 1.2  68.41 3.6 .210 66.10 3.69 -T7S11 1741 J7H l.UO IS.-30—KM~ 2* GAUGE THERMOCOUPLES IN SAMPLE ~~ — THERMO NO 8 THERMO NO 6 THERMO NO 9 ORIFCE AIR BULK GAS SAMPLE FRONT THERM  NO 1 SAMPLE CENTER 3.867 71.44 ~«:"ilT""TlV«'" 1.316 1.17 1.111 ai.96 as. IT 8B.73 9.26 1.11 61.02 3.84 1.211 86.52 3.49 1.217 86.1 " 1.36 B8.3T 1.21 83.47 1.231 88.34 1.233 BB.41 -iTiviii. t» i.w mn—HTST-I GAUGE THERMOCOUPLES IH SAMPLE SAMPLE FRONT I TEMP T> 0.863 TO.48 2.48 114.11 0.869 70.48 1.296 91.29 0.863 - 70.48 1.93 41.0 0.661 70.46 1.245 41.20 0.B65 70.4B 1.246 41.5 SAMPLE CEHIER TUEI MO" WO ~1 SAMPLE BACK TEMP T 88.15 1.1 —iS74"Sf" 48:1— B7.42 1.83 8T.1 1.48 87.64 1.6 87.6B 87.90 8T.9 f.90 S756T-1.36 (NOTE-AL  TEMP. IN DEG. F.l 10 GAUGE THERMOCOUPLES 1 "THERMO NO B'~ 0R1FICE AIR TKIAKO NO 2 SAMPLE FRONT SAMPLE CEM1ER TEMP 1.70S 109.22 1.T10 109.10 1.711 104.11 1.710 109.10 1.481 106.02 1.669 106.19 1.669 106.19 1.490 49.62 9.60 1.679 107.80 1.41 1.681 107.69 1.31 1.669 106.* 1.2* 1.669 106.06 1.28 57437 71.61 iTtOB" 109.22 3.917 71.61 1.708 109.22 3.917 71.61 1.708 109.22 1.668 idiTTs I.689 108.19 1.686 108.15 ~T7**i'" 107.97 1.4 1.684 LOB.02 1.20 1.664 106.02 1.20 1.489 99.16 .675 107.60 .678 107.3 1.660 IQ7.SZ 1.661 107.16 1.660 107.82 l*»9 -"loT.T RUM N0.21  . TEMP. TN PEG. 24 GAUGE THERMOCOUPLS IN SAML THERMO NO B THERMO NO 6 ORIFCE AIR SULK CAS  THERMO NO 1 SAMPLE FRONT THERMD NO 1 SAMPLE CENTER THERMO NO 2 SAMPLE BACK 41.23 LOIS 91.20 1.11 91.20 1.220 TB.61 12.62 6T.53 1.67 3.16 0.84* 64.57 0.8*4 69.57 D.B** 69.57 1.299 1.295 1.296 67.60 3.*0 1.216 67.3 l.*3 1.219 B7.B0 3.40 1.011 76.54 12.68 1.210 67.42 3.74 1.217 87.1 3.52 3.6 3.56 82.11 BT.19 67.55 87.30 3.70 1.211 87.35 87.66 3.56 1.213 67.55 13.70 •UN NO. 86 (NOTE-ALL TEHPT-INTTEC. f.l 10 GAUGE THERMOCOUPLES IH SAMPLE THERMO NO 8 THERMO NO 6 THERMO NO 2 SAHPLE FRONT i TEMP TUS 10  104.13 59.83 0.932 T3.19 0.932 73.19 0.912 71.9 0.412 71.9 ~2"7034 12371. 2.015 123.22 2.017 123.10 2.018 123.11 1.035 123.22 2.034 123.16 SAMPLE CEHIER i TEMP TUB •10 104.62 94.16 1.964 119.4 2.91 THERMO NO 3 SAMPLE BACK'" 121.4 2.11 1.480 120.67 1.482 120.75 1.484 120.84 1.963 120.88 1.462 273~1.9T~S~  1.976 1.476 110,46 RUN NO.215 (HOTE-AL 2* GAUGE THERMOCOUPLES I THERMO NO 8 ORIFCE AIR THERMO NO 6 SAMPLE FRONT THESHO~N"D~I SAMPLE CENTER THERMO 'KO~I SAMPLE BACK 1.325 1.33 1.313 1.240 66.73 1.251 69.21 1.250 69,17 1.235 88.52 1.2*8 89.10 1.2*8 89.10 1.2*5 68.96 RUN NO.21/ (NOTE—AL  TEMP. : 2* GAUGE THERMOCOUPLES IN SAMPLE JJj E «M0„ HO J THE RMO_NO. .6 NO. 6 THE.AM0_MO_5„ 1  SAMPLE FRONT TDB MV TEHP Tu8 91.00 1.12 61.05 8.95 THERMO MO,1 SAMPLE CEMTfl SAMPLE BAC TEMP 0.653 69.6 .2T 1.235 im*—^T7BT~ ,.31* 92.0* 1.23* 86.*6 1.61_ RUM NO. 87 (NOTE-AL  TEMP. IN 10 GAUGE THERMOCOUPLES IM SAMPLE THERHO NO 8 ORIFCE AIR THERMO N BULK GAS THERMO HO 1 SAMPLE FRONT THERMO MO * SAMPLE CENTER I TEHP TUB THERMO NO 3 SAMPLE BACK 0.912 73.19 1.339 116.89 1.950 1)9.33 17.36 I.782 112.3 0.932 73.4 2.164 137.10 2.6* 132.3* 4.96 2.99 112.*2 0.932 71.9 2.370 117.33 2.89 131.38 1.76 2.81 131.3* 0.632 71.9 2.370 117.39 2.89 13.58 1.76 2.10 131^10 O.V32 73.9 1.72 117.*3 2.191 131.64 3.77 2.162 111.38 , .739 110.33 2.3  132.08 2.7  132.63 2.7  112.41 .73 1.040.432 73.4 2.367 137.22 2.170 132.61 IM NO. 86 I NOTE-AL TEN 1 GAUGE THERMOCOUPLES IN SAN rHERHO NO B ' THERMO NO 6 , IN DEC. F.l 1.7*0 71.7* 2.T28 191-21 2.725 132.09 0.940 73.7* 2.725 132.09 0.94  3.74 -2.719 151.65 * SAHPLE FRONT 118.73 29.49 I.5T9 1*5.*! 6.7 SAMPLE CENTER •V TEHP 'MB ,131 131.41 14. T3. SAHPLE BACK 3.9*0 73.7* 1.623 1*7.*0 3.3 . TEMP. IN OEG. 2* GAUGE THERMOCOUPLS IN SAMPL IHfRMO ND 8 THERMO HO 6 THERMO ND 1 ORIFCE AIR BULK GAS SAMPLE FRONT THERMO NO 1 SAMPLE CENTER iHLRMD NO 2 SAMPLE BACK 1.223 8B-06 1.090 82.09 10.13 1.10 1.211 87.*6 3.02 1.211 1.2*3 88.8 3.63 1.2*0 RUN NO.21 I NOTE-AL TEMP. IN OEG. F.l 2* GAUGE THERMOCOUPLES IN SAMPLE -_miBB4.Ng.|. THERHo_Ho.» TfljBajfl.i -HJJgflS.flfl.l- -fiSfiisja-i'-Hv iw HV m Mm II: Jl t M - MM mm HV m m umt HEX W iW IBS M1H i i H i.-ii 30 GAUCE THERMOCOUPLES IN SA THERHO NO 6 THERHO ND ORIFCE AIR BULK GAS THERMO M 2 SAMPLE FRONT SAMPLE CENTER THERMO MO 3 SAMPLE BACK 0.940 73.74 J.171 170.13 1.*2 127.43 42.90 0.940 73.74 3.1B1 170.12 2.904 18.B7 11.93 0.940 71.74 1.80 L70.69 2.910 199.2 10.77 0.940 71.74 3.161 170.73 1.9*1 160.37 10.37_ 1.492 121.16 49.13 2.892 158.49 12.32 .918 159.33 11.4 1.926 139.67 10_.B6_ 2.930 160.* 11.1 2.911 160.16 11.31 2.943 160.64 10.98 MV TEMP 2.012 121.98 2.671 157.59 2.B99 158.73 _2D6_ 159.10 2.412 159.26 2.919 159.14 2.425 139.79 RUN NO. 90 INOTE-AL  TEMP. tN DEC. F.[ 10 GAUGE THERMOCOUPLES IM SAMPLE THERMO MO 8 THERMO NO 6 THERMO MO 2 - imanm— -IttM-tttW utnt BMrf — nm m m iii;fi ftM ip-ii M \<m HUH MI buy imtt MI VI-9 0.420 72. BT 0.920 72.BT . 0.420 T.IT 1.2*0 112.12 1.*4 110.72 I.AO 1*TS6 Ul'o* 1*0 112.66 1.716 I LI.06 1.60 1.732 110.44 17T2-3.94 1.72 1.747 110.64 [7*  l"Io69 IT?T~ 'RUN MO. 41  NOTE-AL TENT*. IN DEC. t SO GAUGE THERMOCOUPLE! IM SAMPL-THERNO NO # THERMO NO 6 ORIPtCE AIR BULK CAS THERMO NO 2 SAMPLE FRONT THERMO NO 6 SAMPLE CENTER T~~1G» IM THERMO NO 3 SAMPLE BACR RUN NO. 94 INOTE-AL  TEMP. IN OEG. F.i 30 GAUGE THERMOCOUPLE£_I M SAMPLE THERMO NO B THERMO NO 4 THERMO NO 2 ORIFCE AIR BULK GAS SAMPLE FRONT THERM  NO 4 SAMPLE CENTER THERMO NO 1 SAMPLE BACK 0.472 TO.TB 2.B7B I3B.3B 0.BT2 T.T  2.441 13S.31 0.BT2 TO.TB 2.BB0 13B.4T 0.BT2 T.T  2.712.Til ,2.721 1.BT2 TO.TB 2.190 131.88 2.T40 132.14 2.693 130.46 2.647 150.34 2.644 " ' i;toi 130.49 ""TTBT" }.4*0 rsTjJT B T T T 0.924 71.04 0.924 71.04 0.924 71.04 0.924 T1.04 2.403 138.II 2.315 114.6T 2.310 14.31 2.303 134*34 RUN NO. 92 30 GAUGE THERMO NO THERNO NO 2 SAMPLE FRT * TEMP Tk SAMPLE BAC TEMP 1.460 I0T.I4 1.640 106.0 1.6*5 T06.3  1^*24 105.62 1.52 , IN OEG. F.I 30 GAUGE THERMOCOUPLES I  SAMPLE THERMO MO 1 THERMO NO 6 THERMO NO 2 ORIFCE AIM BULK CAS SAMPLE FRONT THERMO NO 4 SAMPLE, CENT THERNO NO 3 SAMPLE BACK 0.196 Tl.B) 2.073 124.13 "1789 2T65J-121759 J715-2.030 122.Tl 2.16 2.019 122.32 2.35 122.07 2.B1 RUN MO. 94 INOTE-AL  TENP. IN OEC. F.I 30 GAUGE THERMOCOUPLES IN SAMPLE  THERMO NO B ORIFCE AIR MV TEMP THERMO NO 6 THERMO NO 2 SAMPLE FRONT I TEMP U SAMPLE CENTER I TEMP THE THERMO NO 3 SAMPLE BACR TENP 1 ).403 72.11 2.342 115. T< INOTE-AL  TEMP. |H PEG. 10 GAUGE THERMOCOUPLES IN SAML THERMO NO S THERM NO 6 THERMO NO 2 8RIF1CE.R|R BULK GAS SAMPLE FRONT THERM  HO 4 SAMPLE CENTER THERMO NO 1 SANPLE BACK MV TEMP 0.410 T2.43 • 2.773 154.15 2.440 1*1.97 2.7*2 152.T4 2.402 144.3 2.3S4 146.1  k3.A 7.*4 0.910 72_.4|_ I.T41 152.75 2.603 14*.t _*!.»T6_143,3t. THERMO NO I INOTE-AL  TEMP. IN OEG. F.) IN SANPLE THERNO NO 6 THERNO MO 3 OIFCE AIR MV TEMP SAMPLE FRONT t TEMP TUB SAMPLE CENTER 1.921 T3.09 2.0' 2.001 121.52 2.69 17T»5~120781 1 D*l RUN NO.102 INOTE-AL  TENP. IN PEG. 30 GAUGE THERMOCOUPLES IN SAMPLE  THERMO NO B THERMO NO B THERNO NO 3 SAMPLE FRONT I TENP TH THERMO NO 2 SAMPLE CENTER THERMO NO 4 SANPLE BACK TEMP T 2.405 13B.1 123.59 15.22 1.B10 15.08 23.73 2.115 135.0 RUN NO.103 INOTE-AL  TENP. IN OEG. F.I 30 GAUGE THERMOCOUPLES IN SAMPLE THERMO NO 1 THERMO NO 6 THERMO NO 3 ORIFCE AIR MV TEMP SAMPLE FRONT SAMPLE CENTER SAMPLE BAC TEMP 0.901 T2.13 2.740154.772.618148.07 6.70 RUM NO.104 I NOTE-AL TEMP. IN OEG. 30 GAUGE THERMOCOUPLEl IN SAMPLE THERMO NO 8 ORIFCE AIR THERNO NO 6 BULK GAS THERNO NO 3 SAMPLE FRONT THERMO NO 2 SAMPLE CENTER THERMO NO 4 SAMPLE BACK "MV TEMP 1.400 T2.00 .3.516 184.23 MV TIMP TUS 2.800 14.TO 24.11 MV TEMP 2.310 144.0 NV TENP 2.480 149.83 3.443 113.14 "07966—TJToo 37STO—IiTti-3.1*3 164.8 11.42 3.125 1*7.4 15.*0 1.20 1*7.0 15.69 -rra.-ie i:n— 3.1*6 Ut.lt IS.l'o" "j7i3a~i6a.io_-n7w~ I NOTE-AL TEMP. IN OEG. F.I 10 GAUGE THERMCUPES IN SAMPLE THERMO NO 1 THERNO NO • ' ORIFCE AIR BULK GAS THERMO NO 3 SAMPLE FRONT THERMO NO 2 SANPLE CENTER SANPLE BACK RUN HO. 9* INOTE-AL  TEMP. IN DEG. F.I 30 GAUC1 THERMOCOUPLEl IN SAMPLE  THERMO NO 8 ORIFCE AIR THERMO NO 6 BULK CAS THERMO HO 2 SAMPLE FRONT THERNO NO 4 SAMPLE CENTER THERMO NO 1 SAMPLE BACK TEMP TDS NV "tEMP-~Til TEMP "TEMP- "TUB-O.920 T2.BT 3.092 1*7.12 2.B62 13T.16 9.6 2.841 136.42 10.TO 2.110 135.93 11.9 mi 0.420 T2.T 1.0N 14T.04 2.470 137.44 4.35 1.B32 15*.IT 10.IT 2.*J6_136.17 JO.87 0.920 T2.BT 17 040 I6T.04 2.120 15T.49 9.53 2.055 l3*74l~l0.QS 271*0 156.3) T07TI 0.420 T2.1T 1.090 167.04 2.870 19T.44 4.55 2.855 154.9 10.5 2.140 156.3) 10.71 0.420 T2.BT 1.015 166.84 2.163 137.11 9.73 Z.B30 134.74 10.5 2.835 15*.13 ID.71 0.920 72.87 3.090 167.04 2.172 I5T.57 9.47 2.833 156.99 10.5 2.840 156.33 10.T1 0.920 72.IT 1.040 167.04 2.873 1ST.69 9.33 2.835 116.14 10.5 2.8*0 156.33 10.Tl RUN NO. 9T INOTE-AL  TEMP. IN OEG. F.I 30 GAUGE THERMOCOUPLES IN SAMPLE THERNO NO 8 THECMO NO 6 THERNTTIHERHO'NO~4 THERflO~NO 3 ORIFCE AIR BULK GAS SAMPLE FRONT SANPLE CENTER SAMPLE BACK MV TEMP MV TDB MV TEMP TUB MV TENP TUB MV TEMP TUB •""b:i4i"'T6,;«"' "r.'tsi—no.**—ir*sd ~ifls7*s~"*TIV—i76iT~ioi7f B~~*7I*— utoj ~io*v5s *7or-0.862 70.33 I.741 110.64 t.TIO 109.09 1.55 1.702 108.T4 1.65 1.642 101.3) 2.31 0.162 70.35 1.741 110.6* 1.715 104.31 1.31 1.T01 109.03 1.34 t.TOO 101.68 1.4* 0.1*2 70.35 1.7*2 110.** 1.716 104.33 1.33 1.T09 104.09 1.59 1.701 101.72 1.46 0.62 70.33 1.7*1 110.** 1.T15 104.31 1.33 1.70* 104.03 1.34 1.701 10B.72 1.92 0.8*2 T0;15 1-740 110.60 1.714 109.2* U31 l^TOT 104.01 1.54 .1.700 101.68 1.92 0.862 70.13 1.742 IiO.*l 1.717 109.39 1.24 1.709 104704 1.59 1.701 108.7 RUN MO. 48 I NOTE- AL TEMP. IM PEG. F.I  30 GAUGE THERMO NO 4 ORIFCE AIR S N SAMPLE THERMO HO 6 THERMO NO 1 BULR CAS SAMPLE FRONT THERNO MO 4 SAMPLE CENT El TKERM3 NO 1 SAMPLE BACK 0.16* 70.32 2.101 0.8*6 70.32 _2.M 1_ 0.164 T0.3l 2.303 2.30 111.2 3.62 2.11 130.TO 1.S4 0.84* 70.52 2.312 1)4.2 2.39 131.49 0.1*6 70.52 2.322 1)3.4 2.44 131.91 0.1*6 70.52 2.311 I15.IT 2.43 131.  2.00 129.0 2.11 130*36 2.14 130*37 RUN MO.16 INOTE-AL  TENP. IN DEC. F.I 0 GAUGE THERMOCOUPLES IN SANPLE , THERMO NO 1 THERMO NO * THERMO NO 1 THERNO NO 2 ORIFCE AIR MV EMP SAMPLE P  NV TEMP SAMPLE CEHTEI I TEMP 1 SAMPLE BACK 0.932 71.39 3.0*1 163.13. E-AL  TENP. IN OEG. I 10* GAUGE THERMOCOUPLES IN SAMPLE-THERMO NO 1 THERMO HO 6 THERNO NO 1 ORIFCE AIR BULK CAS SAMPLE FRONT THERM  NO 2 SAMPLE CENTER THERMO NO 4 TEMP TUB 154.83 2.642 149^06 _ E.43P 14T.69 RUN NO.18 I NOTE-AL TEMP. IH OEG. F.I ORIFCE AIR MV TEMP SAMPLE FRONT I TEMP . TUB SAMPLE BACK i« m m mi im ma m w wmm m m VI-10 0.414 '71.10 l.llfl 144.02' 1.410 LM.4* 9.9* 0.410 79.10 1.5IT 143.40 1.411 IM.TO 9.10 0.410 71.10 l.»0 144.01 1.414 1M.41 t.ll 0.4 JO Tl.» 2.515 144.11 1.4*1 114.1* 9.01 0.410 11.10 1.511 144.11 1.410 114.44 4.14 0.4)6 Wllft 1.990 .44.01 1.4)0 1,4.49 ATM-I NOTE-ALL •«»>. IH O H . P.) 2.14* 11T.T0 2.1*4 117.7* i . m IIT.1T 1.1*1 111.11 3.401 • 111.14 1.416 "IFlTil 4.11 4. IS 4.19 4.11 1.170 I1T.M 4.41 i.iis in.14 ».*4 1.911 11T.I9 4.4T 1.114 11T.1* 4.14 1.141 111.00 4.19 K I M 111.11 s . n so CAUBI TMtu iMot lHc i IU U U H « ' T K I I M HQ 1 THERM M 4 TWRJW «o I -UNFll MONT i—jm 7B TMJCKM HO 1 SAMPLI CENTER i row—rn TH1KH0 MO 4 UMHl •*.» TIHf ". M U W I TMtRJROC0Vn.lt IN UMPLt THIRMO NO • . TttltMO NO 4 0R1FIC1 lift . lUtK flit „.HV. . ..TW. . KV . TM U M H S PROA* i .. TEMP TI THERMO NO 1 UMPLI CENTC! HV T1HP TM . _ TINP I T B T -O.tl*. 71.44 . O.tJ* 71.** O.tl* . 71.4* 0.*1* TJ.** 0.«l* 71.4* q.*i* Tl.4* 1.5T5 101.44 1.1TB 101.5* 1.17* 101.44 1.IT1 101.17 I.ITO 101.14 • l t I T * 101.90 i . 4 » ; 1.414 . 1.411 1.491 1.411 . T.41 4.11, 4T.0T 4 .M 47.1* 4.41 tT.OT 4 .M •7.01 4.14 47.01 4.11 4T.1* 4.14 1.175 44.51 4.0«: 1.171 *4.71 !::« a:K t:K 1:31 8:« 1.42B **.!• 4.4* 1.414 1.419 44.74 4.4* 1.410 1.411 V4.T4 4.41 1.411 1.425 *4.T4 4.41 1.410 1.410 94.44 4.91 1.414 **.*» 4,4* 44.41 4.T4 •4.17 4.47 *4.14 4.74 0.940. 71.74 1.111 124.41 ' 71,74 1.100 110.10 79.74 2.100 110.20 71.T4 1.1** 118.14 1.100 1».» 1.41 1.122 114.41' 1.91 2.1M 11*. M 1.14 ' 1.10 I'.iH. nlT*—YAH (u'Sfi—liflSt—ITT*-0.140 TJ.ll 2.1*9 12*.** 1.111 124.14 1.11 0.440 71.74 2.1*4 110.04 1.110 114.44 1.01 0.440 71.74 2.1*1 110.12 2.131 117.00 1,12 1.0*0 115.14 2.150 UT.TT 1.110 124.0* ' 1.110 124.0* i . i t i i i i . i i 2.110 114.0* l.tl 1.110 114.0* J.45 2.111 114.11 1.44 1.010' 124.40 4.71 ' 1.042 111.46 4.10 2.100 119.74 4.44 •• 1.101 119.71 4.11 Utti Ul.lT i.U 2.100 119.74 .. 4.11 2.101 119.Tl 4.19. 2.102. 129.41 4.2* HUM NO. 120 I NOT (-ALL TBH». IH CIO. P.l\> 10 QAU4I TMIRHOCOUPLIS IN MMttE RUN P40.ll* IN0TI-4U TEH*. IN DEB. 10 BWflE TWlRITOCpVPLll IH 1AMHI THltHO NO 1 o i i r i c i * t i _ra T|H» TMIRHO HQ 4 BULK Oil W TOO THERMO HO I SAMfLI PROMT t TEHP THE MO HO 1 U M F L 1 CCNTM I TEMP TM1 THERM RO 4 UMPLI BACR TIMP T TH1HMO HO » THERNO MO 1 OtlPICI 111 HV Tf MP 0.409 * 71.11 , 0.109 71.11 0.409 Tl.11 0.409 •71.22 0.401 72.11 •UL* OA! NV TM 1.411 ' 120**4 i!m ill:ai 1.411 111.01 1.4*0 110.11 1.410 110.11 1.471 110.74 l.*T* 110.1* fJUUHl M0H1 I TIN* . Tl Hg.IT. 10.1 1AH1L1 CIHT1* I T I K I T H U N P I I IACR TEMP T 0.4*0 T1.T4 0.440 71.74 0.140 T1.T4 - 0.4*0 71.14 8:18 «:« 0.4*0 71.74 0.940 71.74 1.194 •!••* 1.1*0 11.12 1.115 V1.14 1.240 '11.44 1.199 41.14 1.194 I * . * * 41.1* l.2M< M.44 0.74 9.11 *.*• :iU ifctt t:Si 11.94 1.141 - * * . 5 I i.ut n.n 1.0*0 12.01 11.14 1.210 14.21 9.41 1.191 •*.!* 4.44 1.159 14.11 4.92 1.194 44.1T 4.47 l.IH—H.1T" I.29T BV.41 1.114 44.1* 1.114 1.110 1.191 1.111 1.191 •1.94 10.19 41.21 9.41 09.19 4.4* .04.15 4.4* 14.11 4.4* -TTWi H.ll 1.291 14.10 • 4.71 1.291 . 14.19 ,-. 4.TJ 1:81 118:i'i 'S:iS 6 . 4 H 7 f . l l 1 . I U I H . I I 1.419 111.41 l .*ll 111.9* 1.492 111.9* 1.424 111.44. 1.410 111.91 1.410 1 1 1 .II 1.17 1.1* 1.2* 1.11 2.11 1.411 11T.4T 1.414 11T.*7 1.414 UT.1T l . f l l 117.4T 1.41* 111.01 ~nw i n . 6 r i . U 1.04 2.41 1.91 1.42 1.12 ~r.ii l.*IO 117.4* 1.410 111.14 1.110 117.4* l . * l l 117.74 1.410 U 7 . 4 4 1.14 • 11T.T4 ITTT^ 1.11 1.11 1.1* 1.14 . 1.04 RUH HO.Ill iHatf-RiC:tlHt>. IH DfS.^.I io eiuei TNiiMoeoupiit IH SIMPLE THIRMO HO 1 TMfRM HO 4 . THERMO MO 1 I . I l l I.'Ill INOTI-ALL T1HP. IN OH. 1.1 H I H e ! i l l NV TIMP 0.411 • 71.41 • VM ill i.m 115. 19 o i l i e r THHMUOLHHII I U U H H I THIRMO HO I THMHO NO 4 , THIRMO NO.l 0RIPIC1 1 1 1 BULK 0*1 tANPH PROMT 8:111 H:!l lii: THIRMO NO ] tAMPLI CEMTIt THIRMO NO 4 1AMPLI l i H 0.411 71.41 .0.111 72.41 0.411 71.41 0.411' 72.41 0.419 11.41 ii.TT 111.79 1.144 U I . V 2 1.141 . 1 U . B 0 1.140 119.79 l .»* l 114.RO liRHI HOMT MV TIMP . 1MB 1.411 . 44.11 14.40 1:8? 18:18 TMUHO NO 1 U H H I C I M T I I 1.499 109.11 1.44* 104.11. 1.(41 104.14 1.441 104.14 UM m.ii 4. IT 9.41 4*44 4 . U I . U 1.149 41.IT 12.4* 1:811 li:8 1.429 109.41 10.11 1.411 109.74 10.14 1.410 109.49 10.19 1.411 109.4* 10.04 • • * « 109.49 10.1* U H I L I uu : MV TIN* TM 1.410 ; 44.11 14.41 1.401. 104.44 I I . * * 1.411 1 H.P " 1 Q.H 1.411 109.10 10.49 1.411 109.40 10.11 1.419 109.47 10.11 1.424 109.11 10.14 1.411 101.47 10.11 HV TIMP 0.411 T1.04 0.411 T1.0* 0.411 Tl^* 701 MV 79.40 1.011 79.11 0.144 4 H ^ - " 0.414 t!:S: 8:;ii «:« V.IH ;i:li I:! 0.119 T lTS» OT»3H5 74.49" 0.41) 71.09 0.410 T4.45 0.1*0 TI.01 l.BT . 0.429 T1.0* 0.410 74.49 0.1*0 TI.OB l.BT 1.411 Tl.O* 0.490 T4.41 0.1*0 71.01 1.1T I .Ill T1.04 0,414 T4.ll 0.114 TI.04 I.IT 1.041 10.T* 0.1*2 T1.IB 0.11* 71.09 1.04 fl.iiT—rirn—iroo— 0.11* 11.41 2.04 0.114 12.*1 1.04 0.011 71.** 1.00 0.114 T l . t l 1.00 1.041 74.41 -4.01 0.144 71.11 1.11 0.114 11.04- 1.01 "B.in TT7T7 I T - — 0.111 71.TT ' 2.14 0.111 T1.T2 1.21 0.111 T1.7T 1.1* 0.111 T1.77 1.14 •UN.MO.Ill (MOTt-ALL TERf. IN 014. t.l I S BiUOl TUIIUMXSUPLII IN-TATTPTI THERHO NO 1 ORIFICE All —w THERHO HO 4 BULR Bit im BS T B I — TMIRHO NO 1 1AMPLI PROMT ' TINP TB THIRMO NO 1 tiMPii conn 1 TIN! T W -tMOTE-*lt TIB*. t« Of«. f>.l 10 BAUOE THIHKOC0UPLE1 IH 1ANPL1 THIRMO NO 1 0.110 71.11 1*101 104.** 0.110' 11.11 1,419 109.14 0.110 71.11 1.4(1 109.41 ORIflCl A|R MV TIM* THIRMO No 4 " IULK Oil HV TO! THIRHfl Nd I IAHPLI nOMT I TIM* 1MB HV THlRNfl Mfl 1 1AMPLI CIMTII TIN* THB ThIIH MB * 1AHRLI IACK 11 HI 8:118 11:11 l:iii 18i:S l:i 1.499 1.4*2 1.44* TOT 0.110 71.11 1.415 109.41 0.110' 71.11 1.414 105.47 0.1BO 71.11 1.411 109**1 1*47* 1.47* 1.47* * * . l l n.u «*.!! 4.11 4.71 -fc»-».B1 * . l l 4.11 1.491 41.07 " """ ' "1.01 1.411 1.441' •m-1.470 1.411 1.4T1 ~w— 1.440 • S . l l 41.10 W . H •B.72 *1.77 *B.77 4.41 7,11 1.11 1.451 4.4* " -1,41 1.40 1,9* T . l * T771 tTtli II7I7 T 7 1 T 4.40 1.441 1 1 . 1 * T.IT 4.40 1.44* 40.4* 7.11 4.14 1.441 H . 4 4 L I S 6.Ill 0.911 0.411 0.111 0.411 -otUI "TTTTT 71.19 T1.1* 71.11 T l . l l l.lld—ITTTT 1.990 41.74 1.111 42,11 I.Ill 41.11 1.122 * l . l * \\\\\ !1:U i . H * — n r n — r r n — 1.241 t l . l l 9.IT 1.144 11.11 1.4* 1.11* 11.41 l.Tl 1.140 11.44 l.Tl "TTTTT—Hm—4TiT 1.240 •*.»» 4.04 I .lit 11.41 1.41 1.111 11.11 4.04 I.Ill tl.tl 4.0* ill! "TTHO—ItTTI—4 7 f l ~ - I.119 11.*9 4.10 1.211 BI.*! »,01 1.114 11.11 4.1* 1.210 H . l l 4.1* 1:111 11:81 RUN MO.1*1 (MOTt-ALL TINP. tt 10 SAual THIRMOCOUHII IH IAN PL! THIRMO HO 1 7H1RM0 MO * 0,1» [ii | || III J! ii: 11 i i ill i l l i III r 1 I- Itl! lilt 1!; 1 i  - i « : • i jiii • :l l::t : IH—Mi !l II: 1 I •!*" :fl • U « I t i K I H i l l - I l l H » . IH BHi M H tlUII IHIinUUILII III I 1 W U - T u t l l l l t l uTn*nW-H(-t-m m.m imtii-ui mi. m HI, F,I It HUM THIIWISUILII III IHPII THIUD u • nimo w i nipiu in IUII ui TIM* HV h mm lion -JITFTtn TIW P U T — tn THIRMO M I lrotrrmr' THIIHO MS I . IUILI 1IHTII' TMIIMO NO 4 'iwrirmii--TMUMrMU • I M H I H I ! TIHI THI Tti lT-liiiniiiii liiii ijiiii i i mi i-miSiii mm tii!!;!i !;n mm\ m mm [.•00 HM* l.TTO 111.11 l.UI 10f.lt Ll.ll l.tll 10T.IO 149 1IW7B,ILL T1W. IH BIB. E.I » IRUOS T n o m o u i i i i IN U D P L I IHIMO NO • T H H W tn • THIBMO NO I RAR1LI ttmf THflNO NO I •1HW.1 tlHTII T H H W NO * HUN ND.lBI INOTWLL TOO. IN O H i •a witti miHMgu*i.ii IN umt mm w i OMMCI 111 T H I I U W I BULK Oil TNIUB mi U H H I MONT NV TK1U0 H I •*HHI CINTIR TUP THI liNPiil OUR TINP 1 M M • Tl.TT—*TTT-S:!!! it*!' ?!:.! §:»: ?f:it t:» O . IU H . l * O .HI 11.11 0.1*0 T l . l l 1.41 fl.Vll Tl.ll U1.4B 0.401 8:12! !!:« 1:11 Mil 0*111 Tl.il l.Tl O.lll O.lft TUIt I.TT •nrn 71.10 RUN NO. 1*4 INOTI-All, H H P . IN 000* P.l to o*Mi TKiomeouPiii IN I A W L I TUIIHB IU I •MOTE-ILL T I E * . IH BIO. P . l THIIRB KB I OHIPIGI B I B NV TINP THIIHO HB i •UL1 Oil i ua i UNPll'PBONT I . TIHP Tl •^TTiTO-•UHI GINTIN I TINP TBI 14IIHB U i U U W U O U N VI-11 0.110' 67.11 0.790 67.11 0.T90 67.11 0.7*0 67.11 0.740 47.21 0.1*067.21 0.1*0 67.21 . 1.910 U7.*9 i.foa •IIT.BI. 1.121 I16.16 1.916 16.6 I . M I ; - - i i . o s " 1.613 108.01 9.76' l.TOl 106.71 9.66' 1.711 109.15 9.51 1.1*1 . il.TO 19.19 l.W .95.21 21.61-UI< 107.03 10.71 l.*6J • 107.20 10.61 1.690. 106.21 10.1. 1.65 106.06 10.10 1.696t 101.91' 10.0* 1.691 101.12 10.14 704 106.61 ».*!; 1.69* 108.49 10.10 ORIFICE lit HV TEHP ' TB* umi PROMT 1 TIW ' TI 1.9S9 119.11 1.10* 11.1  6.46 IHOTE-ALTIHP. IN BIB. F.l'. 0.919 . 71.0* 1 2.011 121.19 0.923-.71.09 . 1.01* 111.16 _0.929 _T1.09 _ ... 2-012 121-09 0.929. 71.09 - 1.017 121.10 0.9IS ' 71.0* 2.011 -111.05 q.*19 71.09 2..M4 » » , » 1.11- 1.1 1.91 -I If .44 . 1. Mfl'-:.120.61 1.9* 11.01 -)*». 9>.m ijiti; .04 l.H .2.4* 2.10 SMtl CENTER. HV > TEMP ' TW 1. 11 07.1* . 19.9* l.M* 116.92 6.14 • 1.91  119.SO 1.9* 1.070 110.I* ' 1.16 l.*7» 110.19 2.70 -|.*T7 120.4* 1.T4 SAW LI BACK HV TEHP .. TT227 iSToT 1.900 . 17.1 1.942 I 110.01 1.91  11*. 41 1.960 ' 11*.77 10 CAUSE TE*HOCOUPLS IN SAMPLETH.E8.Ma NO 1 -THERHO NO 6 TM l l . l T 6.04 .4.01 . ».*» 1281.21 1.11 ' THESRHQ NO I ; THIRftO HO 1 THERHO NO 9 ORIFICE 6[R BULK OAS 1AMPLI PROMT SAMPLE CENTER SAMPLE BACK RUN NO.244 IHOTE-AHTEHP. IH OtSi' ft} ', MV TEHP 0.910 72.41 HV TOO 1.110V 101.06 HV TEMP r TM 1.180 94.10 6.IT • MV TEMP THB 0.000 0.00- 0.00 MV TIMP TM 1.140 91.09 6.02 10 6AUS1 THERMOCOUPLES IH SAMPLE THE4U80 MO 0" TKERHO NO 6 ' THERHO" NO 1 ' TKERKQ HO 1 -THERMO HO 9 0791672.41 0.910 72.41 0.410 72.41 0.910 72.41 0.910 72.41 1.920IOt.0* 1.310 101.06 1.910 101.06 1.320 101.06 1.910 101.06 l .STo100.45 0.61 1.910 100.49' 0.61 1.911 100.4*. 0.57 . 1.911 100.4* 0.57 1.111 100.49 0.97 0.000 0.000 o.oo o.oo 0.0 . 0.0 0.0 1.504100.20 1,904 100.20 1.909 100.29 1.505 100.25 1.509 .100.19 (MOTJ—ALL,TEMP. IN DEO..P.). •0 GAUCE THERMOCOUPLES f HURMO NO' I SARPLt THERMO NO 6 ORIFICE AIR BULK MV TEMP HV SAMPLE FRONT' TO THEEHS ua i—— SAMPLS CENTER I TEMP THE :1 THESW HD s' SAMPLE BACK TEMP 1 0.910 72.41 0.410 71.41 0.910 72.41 0.910 72.4} 0.910 72.41 0.910 71.41 1.958 114.09 1.918 119.0* 1.919 119.11 1.911 118.79 1.909 117.65 1.410 117.84 1.070 119.90 . 1.909 117.19 1.910 117.60 1.902 117.26 1.691 116.T9 1.691 116.79 0.000 o.oo 0.000 0.000 o.o o7o5~" 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 11.9 16.93 17.2116.1' 16.13 RUN MO.232 INOTE—AL TEMP. IN DeO. IIB GAUCE THERMOCOUPLE! IN SAMPLE  THERMO NO 8 ORIFICE AIR U TEHP THERMO HO 6 BULK GAS THERMO MO I SAMPLE FRONT t UBt I  THERHO NO 1 SAMPLE CENTER ' "HP U(B_ THERMO MO 5 SAMPLE BACK USE 3 0.131 69.00 2.111 116.91 1.999 121.IT 0.811 69.00 1.116 126.69 Z.099 121.90 0.811 64.00 1.110 126.40 1.0*0 123.94 1.46 0.811 69.00 2.114 126.IT 2.0*2 124.02 0.811- 64.00 2.121 126*87 1.0T9 124.57 0.811 69.00 2.116 126.69 1.0T1 124.40 1.19 0.631 69.00 1.110 126.40 1.669 114.19 2.15 0.000 0.00 0.00 0.600 0.00 0.00 0.000 0.00 0.00 "oToe 0750" o.o 0.000 0.00 0.00 0.000 0.00 O.OD 0.060 O.OO 0.00 1.944 119.10 1.036 112.99 1.041 2.044 111.41 2.059 123.96 1.052 111.67 1.049 111.54 TIMP TVS -0.13 TI.15: 0.85 '71.15 0.689 71.13 0.65 - 71.15 0.19 i Tl.15 0.889 . T1.39 1.720 111.1* I.T25 192.09 1.T15) 111.0* 1.726 191.1* 1.710 ' 112.10 2.716 ' 192.21 1.41 96.16 5.71-1.161 14.9 7.1 " 146.59 • • 5.54 km-146.91 . 1.62 1.604 144.66 1.61 1.601 146.99 ... 1.67 • 12 91.1 60.0* •: .41- 129.10 1.79 l*».l T.T1 1.1 0 91.2* 60.60 1.469 140.61 11.IT 1.549 144.21 7.66 2.19* 144.6.»7l2-1.962 144.*! 7.37 1.5*0 144.BI T.ST RUN NO. 1*4 (NOTE-AL-T6NP. IN OIC.'F.I 10 GRIME THfRHOCOUPLEl IN SAMPLE THERHO HO 1 ' THERMO NO 6. THERHO NO 3 THERHO,HQ 5 ORIFICE AIR HV TEMP 0.941 T4.0S -BULK OAS ~ SAMPLE FRONT HV TEMP . .. TI - 1.11S SAMPLE CENTER t TEMP TNI SAMPLE BACK TEMP 1 -B.48 7*. Si t.iii ltl.it hits iot.lloTST 0.948 T4.08 1.51  101.15 1.915 101.12 0.71 0.941 74.08 . 1.31* 101.1* 1.916 101.14 0.71 1.121' 87.81 11.91 I:1B lgg:» !:!! 1.4*8 1.192 . 9B.94 10.1 »-** *f.*3 1,*1 9.9*I.7  ~MUN NO,247 (NOTf-AU-TEHP. IN OH. F.l 10 SAUCE THERN0COUPL1 IH SAMPLE THERHO HO 1 THIRHfl NO * THWHO NO 1 THERHO NO 1 -THERHO NO 9 ORIFICE AIR MV TEHP 0.926 Tl.ll 1.440 140.17 SAMPLE FRONT 1.111 BT.l  51.45 1*0.T7 1.1 Si lU.il f7K~ 0.42* 73.11 1.440 140.17 2.1*1'. 116.62 1.69 0.926 71. IS 1.446 140.(7 2.M1 116.71 ' 1.97 6.916 TS.I1 1.440 140.17 2.164 116.75 1.51 0.916 Tl.ll 1.440 140.17 1.164 116.79 1.52 UATPLf CENT!* ' MV TEHP TUB 1.11* 17.74 11.31 2.182 l3l.il S T I J -1.110 IS9.11 3.04 2.111 115.1* 4.91. 1.116 111.40 4.7* 1.11T 115.51- 4.75 TEMP TVS *1.1* 47.01 1.28911.49 1.11 14.42 1.6 1.11 IS4.V9 11.120 lS6.il 9.6 1.11 I14.93 9.1 RUN NO. 21) (NOTE-ALL TEMP. 1* 10 OAUCE THERMOCOUPLES IN SAMPLE THERHO NO 8 ORIFICE AIR MV TDB SAKPLI FRONT I TEMP TI 'THiRMd'NO'l SAMPLE CENTER i TEHP rtn SAMPLE BACK TEMP TNI 0.84* 0.84* 0.149 0.84* 0.14* 0,6*9 2.61714570 2.611 141.25 2.640 141.31 1.618 148.90 1.617 141.44 1.160111.14 2.478 141.17 1.911 141.14 1.311 141.18 E.91* 141.06 TSTSI—inure—5753-- - - -,oo 0.14* 69.78 1.616 146.00 2,310 , 142.64 5.31 69.78 l 7¥22147.141.508 1*2.609.21 0.00 0.00 0.06 1.6)0 111.fi" IS.11 2.403 118.14 9,19 1.500 142.11 6.1 2.905 141.91 3.92 2.301 141.50 5.96 1.300 141.16 3.41 J 7 S 4 -1.31 2.491 142.29 RUM NO.113 IMOTE-ALL TEMP. IM PEC. 10 GAUGE THERMOCOUPLES IM SAMPLE THERHO NO 1 THERMO NO 6 THERHO MO 1 ORIFICE AIR BULK .GAS SAMPLE FRONT THERMO NO 1 SAMPLE CENTER THERMO NO 3 SAMPLE BACK TEMP T08 0.90 72.0 0.90 72.0 0.90 72.0 2.14 135.21 2.249 -2.131 2.231 O.OO 0.00 0.00 2.23 131.36 2.239 11.31 2.239 131.53 RUM NO.216 I NOTE-AL TEMP. IN DEC. F.l 10 GAUGE THERMOCOUPLES IN SAMPLE THERMO HO 1 THERMO NO 6 THERHO NO 3 THERHO NO 1 THERHO NO 5 ORIFICE AIR BULK GAS SAMPLE FRONT MV TEMP MV TOB HV TEMP . TNB SAMPLE CENTER I . TEHP THB SAMPLE BACK TEMP I •UN M0.190 . I NOTE-Al -TEMP, INHO  F.l MOAUBETHERMOCOUPLES INSAHPI.THERMO NO 1 THERHO NO 4 fHlKHb NO 1 TH*KMO W I IMUWMO I ORIFICE AIR •U  SA! tAMPLE FRONT SAMPLE CENTER - tAMPLE IAU HV TEHP HV TOB HV TEHP , TNB HV TEHP TW NV . TIKI Tn 0.140 69.1* 0.6*0 6*.It 0.840 69.19 0.140 69,19 1.170 44.SO 1.170 94.10 '' 1.169 94.4* 1.168' 94.41 I.1T1. 16.67 4.44 1.271 90.01 4.41 1.270' 19.9* 4.4B 1.249 89.91 . 4.4B 1.161 l«.T4 1.269 89.94 1.168 6f.lt 1.267 69.85 T 7 7 * ~ 4.3* . 4.96 4.96 I.ITS 40.H 1.272 90.0* 1.17* 90.19 1.171 90.10 -V7TT 6.44 4.11 4.11 RUN NO.251 (MOTE-ALL TEMP. IN DES.F.l SO SAUCE THERMOCOUPLES IN SAMPLE THERMO MO 1 THERMO NO 4 THERMO NO 1 THERHO NO 1 TWER MO NO 1 ORIFICE AIR SULK OA! SAMPLE FRONT SAMPLE CENTER •AMPLE.BACK HV TEHP HV TOB HV TEMP TUB HV TEMP TW . HV TIMP TKS 0.820 61.92 1.438 104.19 1.474 90.99 7.10 1.4*9 t«.90 7.6* I.4T9 - 46.9* T.ll O.B20 68.92 0.620 61.92 0.120 61.92 1.639 106.J3 69 106.11 1.640 106.21 1.4TI I.Ii T.ST 1.474 '91.90 7.31 1.480 99.16 . T.ll - 1.411 1.10 4T6 98.•• 1.477 99.01 T.41 7.16 T.16 1.48] 99.19 1.41* 99.55 1.490 99.9* -*.W 6 61 6.61 RUM NO.292 (NOTE-ALL TIN!. IN 616. i.l 30 GAUGE THERMOCOUPLES IN SAMPLE THERHO NO 1 TKERHO NO » THERHO HO 1 THERMO NO 1 TKERHO HO 9 ORIFICE AIRBULK GAi HMPLE FRONT UMPII CENTER LLMHI IIEK-HV TEMP MV TO! NV TEMP . THB NV TEMP TW HV 'TEHP TNB 0.11 71.26 0.103 71.2* 1.441 119.22 1.44S 114.10 1.T03 100.69 10.11 1.709 106.69 10.41 1.619 101.60 11.12 1.700 101.64 10.6* 1.70* 109.0* 1,715 109;11 0.16 -*.** 0.863 71.26 1.941 119.1* 1.T03 101.89 10.17 0.181 71.26 1.942 119.16 l.TOl 101.71 10.54 0.881 71.26 1.94S 119.19 1.700 101.61 I0.T1 l.TOl 108.77 10.44 1.703 101.63 10.40 1.709 101.19 10.91 1.711 109.37 . 9.61 1.711 109.79 *.9I 1.723 109.T9 9.64 0.910 72.43 1.723 104,93 1.62 107.04 2.1 1.SB9 103.17 * 6* 1.613 164.41 S.61 RUN NO.253 1 NOTE-ALL TEMP. IN OEG. F.l 30 GAUGE THERMOCOUPLES IN SAHPLE D.910 71.43 1.723 109.86 1.704 108.89 1.01 1.70 108.64 1 12 1.692 108.31 .54 THERHO NO » THERHO NO 6 THERMO HQ 1 THERHO NO 1: THERHO NO 9 ORIFICE AIR RUN NO.118 I NOTE-ALL TEHP. IN 0E6. P.I 10 GAUGE THERMOCOUPLES IN SAMPLE  IAMPLI CENTER * TEHP TNI IAMPLI lACi 1-01* 82.19 THERMO MO 8 ORIFICE AIR MV TEHP THERMO HO 6 BULK GAS HV TOB THERMO MO I SAMPLE FRONT I TEMP TUB THERHO HO 1 SAMPLE CENTER I TEHP till THERHO NO 9 SAMPLE BACK TEHP 1 SAMPLE FRONT t TEMP TNI H'« 1:8 t:8ii «:» IH i:8« B:S ?:« T9.42 2.9* 79.10- 1.10. I.041 78.91 1,61 RUN NQ.139 tNOTE-Alt. TEHP. IH OEO. F.l 0.899 71.96 1.313 143.40 2.101 134.29 9.11 0.149 71.96 1.316 141.44 , 2.411 118.70 4.74 0.199 71.96 2.519 141.40 2.414 134.24 4.16 0.B99 71.9* 2.315 141.40 2.421 114.20 4.20 0.849 71.96 1.411 141.01 1,409 118.49 1.97 6.1*9 71.96 1.901 IT 0.B49 71.96 1.4*9 14 1.160 121.14 1.171 136.94 1.404 131.11 1.409 131.91 1.199 197.91 1.400—111714" 2.S99 111.10 1.140 111.97 1.311 137.49 2.391 118.13 1.401 118.21 2.112 117.44 10 OAUSE THERMOCOUPLES IN SAMPLETHERMO NO I THERHO HO 6 THERHO NO 2 ORIFICE AIR BULK 0*1 .SAMPLE FRONT THERMO NO I SAMPLE CENTER THERHO NO 1 IAMPLI BACK HV . TEHP (NOTE-AL TEMP. IN PlO. »T1 10 OAUCE THERMOCOUPLES IN SAMPLE THIRMO NO 1 TKERHO HO 6 8:18) Jiili 1.040 149.00 1.040 163.00 \:tt\ lli:H I.101 14.91 10.10 (.140 196.1 1.47 l:ffl 1:1! ITB 192.74 I.IT IIll' 19.41 l:lil Iii:!? 17*1 11.16 11.TI 10 11.10 9,10 THIRMO NO 1 IAMPLI FRONT THIRMO NO 1 IAMPLI CEHTIR THERMO NO 9 IAMPLI BACK HT _ 2.16 191.07 1.11 11.61 TEHP TNB TEHP TM 0.443 ' 73.99 • 1.719 109.69 0.941 71.93 1.720 109.73 ' 0.949 71.91 1.T10 109.T1 0.449' TJ.9S [Tffl lTo7T2~ 0.949 71.93 1.719 10.1 0.943 71.9 1.71 10.1 0.149 Tl.ll |.Til 10.1 1.111 91,73 16.94 1.6*5 107.17 1.S6 1.703 108.89 0.84 TT6" 109.11 1V6T" 1.7 1 09.19 0.91 1.7 1 09,19 1.0* 1.711 109.19 1.01 1.111 92.12 17.67 1.511 101.1* 1.17 1.679 107.IT l.|7 "Lite ioi.il—ror-1.6*6 10B.4T 1.69 1.691 10B.9I 1.69 1.699 101.60 1,61 1.119 IB.17 11.91 1.550 101.10 7.34 1.6B 107.1* 1.4 T . H D ' " I O T : I I — 1.617 101.1  1.01 1 101.1* 2.09 1,61 ,6 1.03 RUN NO.297 INOTE—ALL TEMP. IN 10 OAUBE THERMOCOUPLE! IN SAHPLE THERMO NO 1 THIRMO NO 6 . THERHO NO I Miftei ii* IULK sii HV TIMP NV TOB 0.929 71.09 1.090 167.04 lAPLI FRHTTIMP TNI 1,71 1U64 1.40 THERHO NO 1 UMFlE C I W T H THIRMO NO 1 IAMPLI BACK' 1 RUN NO.1*1 INOTE-AL TIMP, IN BIB. F.l 10 BAUSI THERH0C0UPLE1 IH SAKPLI -m\ Ml 1:88 lt!:H I:it8 iH:8 !:!! 1.40 IS*.10 1T.14 1:118 lti:I! \Ml 9 1*4.1 1.1 l:lii »!:» 18:11 VI-12 RUN NO.1*0 (NOTE-AL  TEMP. IN OEC. F.> 10 GAUGE THERMOCOUPLES IN SANPLE THERMO NO • THERMO MO ft THERHQ W THERMO NO 1 THERMO MO 1 ORIFCE 1 1 GAS SAMPLE FRONT I TEMP Tl SANPLE CEHTEI I TEN* 1 4PLE BACKTENP 1 RUH NO.2*2 INOTE-AL  TENP. IN OEC. F.I 30 GAUGE THERMOCOUPLES IN SANPLE THERNO NO B THERMO NO ft THERMO NO 1 ORIFCE AIR SAMPLE FRONT NV TEMP Tl 1.2*0 8B.66 4. 1.2)8 SB.57 T1.5T 1.12 92.*} 1.240 8*.66 71.57 1.31) 92.SB 1.241 BI.TO 71.5T 1.)1 92.BB 1.2*1 SB.T  4.17 4.17 SAMPLE CENT MV TEMP 1.23* BB.40 1.214 **.40 L236 ••!*  1.2)7 B1.33 THERMO MO 1 SAMPLE BACK TENP T !*0 »B.ft5 «. RUN NO.ICO I NOTE-AL TEMP. IN OEG. f 10 GAUGE THERMOCOUPLES I THERMO Ht ORIFCE 1 TEMP ERMO NO tBULK GAS MV TDB THERMO NO 1 SAMPLE FRONT I TEMP TUB THERNO HO 2 SAMPLE CENTER '• TEMP TUB THERMO NO 4 SANPLE SACK TENP THI 0.410 Tl.30 1 0.930 73.0 0.9)0 73.0 0.930 T1.30 T3.J0 1.910 1.10 t.261 2.*7 2.** 2.*2 2.51 4o.6l ' 133.0) I32.9B L12.I  L32.35 1)1.27 5.17 • r.ito loi.s•-i<;«~" 1.10 129.06 2.19* 129.*Z 2.19ft 119.73 2.1*9 129.44 2.1*7 124.35 . 1.*1 • •-1.4* "T7SI5 91,7(0 -4.T4 1.35 117.14 5.*9 2.145 129.45 3.3) 2.191 114.4 3.53 1.11 129.07 1.4 1.79 12B.9* T.sl I.41 1.590 103.4* -11.93" 2.115 121.0* 4.9T 2.11B 129.44 3.5* 1.*5 129.32 3.50 2.171 12B.I 3.54 1.74 121.* " ~1*79 17*1 29.1 3.51 INOTE-AL  TEMP. IM DEG. 30 GAUGE THERMOCOUPLES IH SANPLE THERHO NO 0 THERNO NO 6 THERHQ ND 3 ORIFCE AIR SAMPLE FRONT I TENP TV THERHO NO 1 s AN P Li-ITCNTI t THERMO ND 4 SAMPLE BACK TEMP I .2.255 131.52 140 , 129.*B ,3.0*. 175 128.40 3.*2 0.909 72.39 2.145 132.10 2.183 129.19 0.909 72.39 2.43 32.10 2.1B3 129.19 0.909 72.39 2.4ft 132.1* 2.184 129.23 0.909 72.39 2.4B 132.3 2.IBB 129.40 121.1 12B.01 12B.9* 2.1T0 128.69 3.41 2.T BT3 T2.1T1 12*.73 3.41 2.175 128.90 3.3 30 GAUGE (NOTE-AL  TENP. IN OEG. F.l IN SANPLE THERNO ND 8 THERHO HO t ORIFCE AIR BULK GAS HV TEMP NV TOB THERHO NO 3 SAMPLE FRONT I TEMP Tl THERHO NO 2 SAMPLE CENTER THERHO ND 4 SAMPLE BACK 2.211 2.1)1 12T.B4 2.82 .2A*9 127. T* 2.91 , ,2.1*8. 127.T2 2.TO 2.14* 12T.60 1.40 Itl'.ll 141 11T.47 3.20 RUN HO.20ft INOTE-AL  TEMP. IM PEG. F.l 30 GAUGE THERMCOUPES IH SAHPlTHERHO NO 6 THERMO NO ft . ORIFCE AIR BULK GAS THERHO NO 3 SAMPLE FRONT THERMO NO 2 SAMPLE CENTER THERMO NO 4 SAMPLE BACK ' HV TEMP TDB TEMP TUB 0.910 72.* i.046 1 Mi? 5 2.8 41 15ft. 37 B.7 2.825 . 155.46 9.59 RUN NO.216 INOTE-AL  TEMP. IH OEG. F.l  10 GAUGE THERMOCOUPLES IH SAMPLE THERHO NO I THERHO NO 6 THERMO NO 3 PRIPICE AIR BULK GAS SANPLE FRONT THtRM  NO 2 SAMPLE CENTER THERHO NO 4 SAMPLE BACK TEMP TOB TEMP 4.34 1.40 11.61 *.1B *.34 1.241 B8.T0 4.11 4.3* 1.242 Bl.T* 4.14 0.B3S 0.85) 0.B53 49.4 69.4669.6 1.11 42.00 1.313 41.00 1.13 42.00 1.11 1.209 H i : •1.45 B7.lB7.93 4.0* *.•• 4.04 1.071 1.00 1.220 81.1 • 6.14 •T.7« 10.12 3.10 4.22 1.013 1.9* 1.217 74.04 •6.73 BT.65 11.96 5.1T 4.3* 0.13) 0.13) 0.133 0.153 69.* 69.6 69.6 69.44 1.11 92.00 1.1) 41.00 1.11 91.95 1.11 41.4) 1.214 1.214 1.1* 1.2) •7.95 17.45 •7.95 •7.91 4.04 4.00 4.0* 1.10 1.220 1.219 1.219 87.TB •7.1 •7.3 IT.1 4.21 4.22 4.12 4.11 1.21* 1.1T 1.13 1.21* BT.61 BT.65 •7.56 • T.61 4.39 4.34 4.14 RUN NO.Il I NOTE-AL TEMP. I* 10 OAUCE THERMOCOUPLES IN SAMPLE THERMO NO • ORIFCE AIR NV TENP THERNO NO * BULK GAS HV 0.9*1 73.76 0.441 71.76 0.441 71.71 1.11* 91.21 L321 4l5 _0,,9*1 73.78,. 0.9*1 73.TB 1.12 92.34 THERMO NO 1 SAMPLE FRONT TEMP TUB TB 15741 4.24 .1)1 11.31 4.04 21  11.31 4.04 THERMO HO 2 SAMPLE CENTER I TEMP THI 111 SftTl  !74*— 111 *al3 4^22 TTTTT tin* THERMO NO 4 SAMPLE BACK TENP I -BITST—i •7^96 4 .18 88.1) .24 1.11* 87.46 L1S 88.01 . RUN NO.120 . TEMP. IN DEG. f.i 30 GAUGE THERMOCOUPLS IN SAMPL THERMO NO B THERNO NO 6 ORIFCE AIR BULK GAS THERMO NO 1 SAMPLE FRONT THERMO NO 2 SAMPLE CENTER THERMO NO 4 , SAMPLE BACK . RUN NO.23 (NOTE-AL 30 GAUGE THERMOCOUPLES 1 TNP. II SAMPLE THERMO NO 8 ORIFCE AIR HV TENP THERMO NO A BULK GAS THERNO NO 3 SANPLE FRONT I TEHP Tl THERMO HO 1 SAMPLE CENTER I TEHP TUB THERHO NO 4 SANPLE BACK . TEMP T ).I60 70.16 ).B60 70.2* 1.60 70.26 92.39 1.33 88.35 92.4* 1.233 88.44 92.4B 1.236 88.48 1.210 81.21 4.17 1.231 BB.16 4.17 1.211 BB.31 4.1T 30 GAUGE THERMOCOUPLES IN SAMPLE THERMO NO B THERMO NO 6 THERNO NO 2 THERH3 NO 4 SAMPLE FRONT I TENP TUB 191 73.13 61.45 BT.38 3.4ft TO.TB 1.291 91.29 'l.lll'' BT.38 70.7* 1.00 91.41 1.213 ST.47 TO.TB 1.29B 91.33 1.210 BT.33 SAMPLE CENTER ..205 MV 'ii'MPLrBicr -TENP T .894 73.4S ftl IT.1ft 3.9ft, 1.201 BTH 1.208 87.25 1.203 87.12 1.03 BT.03 1.201 Bft.94' .199 1.86 86.90 • 7.03 •6.95 86.86 •*.T3 30 NO.21  (NOTE-AL  TEMP. Ik GAUGE THERMOCOUPLES IN SANPLE THERNO NO 8 ORIFCE AIR HV TEMP THERMO HO ft SULK GAS HV 70S THERMO NO V SAMPLE FRONT I TEMP Tl Y^S6»firfiO~z SAMPLE CENTS' f TEMP I "THIUMO NO .4 SAMPLE BACK TENP I 0.1*4 69.37 0.1*4 69.57 0.8*4 69.5T 0.1*4 A9.5T 0.844 69.S7 .0.1*4 69.57 1.301 1.298 1.294 1.293 1.292 1.295 91.47 91.33 91.6 91.1 41.OT 41.20 0.84* 69.5T 1.29) 91.0 0.8*4 69.5T 1.295 91.0 0.144 69.57 1.296 91.5 1.04 1.203 1.08 11.SB-B6.81 87.OT BT.07 87.03 17.23 V2.01 86.7 1.209 B7.29 3.91 1.10 87.33 3.87 1.210 87.33 3.91 .204 87.OT .04 1.203 9 1286.73 •6.8 •6.B6 86.86 86.90 •6.95 RUN MO.214 I NOTE-AL TEMP. II 30 GAUGE THERMOCOUPLES IN SAMPLE THERHO NO 8 THERHO HO 6 BTJtiTCTs— THERMO HO 3 SAMPLE MONT THERHO HO 2 .SAMPLE 'CENTER' ~SAMPLE BACK NV TEMP HV TOO' MV TEHP TUB HV TEMP TUB HV TEMP TUB 0.864 TO. 44 1.114 91.4S 1.112 • 6.10 6.31 1.111 •4.71 7.73 1.*3 •3.3) 7.11 0.864 TO. 44 1.323 91.4* Will •7.31 5.OA 1.20S •7.12 3.12 1.201 86.93 1.44 0.864 70.44 1.311 41.39 1.1)7 BB.31 4.04 1.211 •a. ii 4.26 1.22* •T.96 0.8