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Convective heat transfer in a rotary kiln Tscheng, Shong Hsiung 1978

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CONVECTIVE HEAT TRANSFER IN A ROTARY KILN  by  SHONG HSIUNG TSCHENG  B.E., M.S.,  N a t i o n a l Taiwan U n i v e r s i t y , Taiwan, 19 6 8 West V i r g i n i a U n i v e r s i t y , U.S.A., 1972  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 to the required  THE  standard  UNIVERSITY OF BRITISH COLUMBIA September, 1978  ©  Shong-Hsiung Tscheng, 1978  In p r e s e n t i n g t h i s  thesis  in p a r t i a l  fulfilment of  an advanced degree at the U n i v e r s i t y of B r i t i s h the L i b r a r y I  further  for  this  freely  available  for  agree t h a t permission f o r e x t e n s i v e  scholarly  by h i s of  s h a l l make i t  the  Columbia,  I agree  reference and copying o f  this  representatives. thesis for  It  i s understood that  copying or  Department of  £VL^<y? -e^r> \PJ  The U n i v e r s i t y o f B r i t i s h  Columbia  2075 Wesbrook Place Vancouver, Canada V6T 1W5  Skjde.r*t*r  ^9j  /97#  that  thesis or  publication  f i n a n c i a l g a i n s h a l l not be allowed without my  (^$C*n<  for  study.  purposes may be granted by the Head of my Department  written permission.  Date  requirements  ABSTRACT Convective heat t r a n s f e r i n a r o t a r y k i l n was as a f u n c t i o n of o p e r a t i n g parameters.  studied  The experiments were  c a r r i e d out i n a s t e e l k i l n of 0.19 m i n diameter and 2.44 m. in length.  The o p e r a t i n g parameters covered i n c l u d e d gas flow  r a t e , s o l i d throughput, r o t a t i o n a l speed, degree of s o l i d up, i n c l i n a t i o n angle, p a r t i c l e s i z e and temperature.  hold-  To m i n i -  mize r a d i a t i o n e f f e c t s , a i r was used as the h e a t i n g medium and maximum i n l e t a i r tempera'tures were l i m i t e d to 650 K.  Ottawa  sand was used i n a l l the runs except i n the study o f the e f f e c t of p a r t i c l e s i z e where limestone was employed.  The experiments  v/ere conducted under c o n d i t i o n s where the bed h e i g h t along the k i l n was maintained constant and the bed was i n the r o l l i n g mode. Both • the heat t r a n s f e r c o e f f i c i e n t s from the gas to the s o l i d s bed and the gas t o the r o t a t i n g w a l l were found to be significantly  i n f l u e n c e d by gas flow r a t e .  Increasing  rotation  a l speed i n c r e a s e s the gas t o bed heat t r a n s f e r , but decreases the gas t o w a l l heat t r a n s f e r . small.  The former e f f e c t i s r e l a t i v e l y  The e f f e c t o f degree of f i l l was s l i g h t l y n e g a t i v e i n  the gas to s o l i d s bed heat t r a n s f e r , and i n s i g n i f i c a n t i n the heat t r a n s f e r from the gas to w a l l .  The e f f e c t s of i n c l i n a t i o n  angle , s o l i d - t h r o u g h p u t , p a r t i c l e s i z e and- temperature were  found n e g l i g i b l e over the range t e s t e d .  One o f the major  f i n d i n g s i n t h i s study i s t h a t c o n t r a r y t o suggestions i n the l i t e r a t u r e , the c o e f f i c i e n t s f o r gas t o bed heat t r a n s f e r a r e about an order o f magnitude h i g h e r than those f o r gas to w a l l . The higher c o e f f i c i e n t s f o r gas t o s o l i d s bed a r e a t t r i b u t e d to two f a c t o r s , the underestimation o f the t r u e area by basing c o e f f i c i e n t s on the plane chord area and the e f f e c t on the gas f i l m r e s i s t a n c e o f the r a p i d p a r t i c l e v e l o c i t y on the bed s u r face. The experimental data were c o r r e l a t e d i n a form f o r design purposes,  suitable  and the r e s u l t s compared with meager  data  a v a i l a b l e i n the l i t e r a t u r e . A mathematical  model was developed  f o r c o n v e c t i v e heat  t r a n s f e r from the gas to a r o l l i n g s o l i d s bed.  The mode] r e -  q u i r e s the knowledge of the gas to p a r t i c l e heat t r a n s f e r coe f f i c i e n t and the r o l l i n g v e l o c i t y o f the a e r a t e d p a r t i c l e s . The model g i v e s a reasonable p r e d i c t i o n o f the gas to bed c o e f f i c i e n t i n a r o t a r y k i l n u s i n g v a l u e s o f the gas to p a r t i c l e c o e f f i c i e n t taken from the l i t e r a t u r e .  The' r e q u i r e d data  on the s u r f a c e v e l o c i t y of p a r t i c l e s was o b t a i n e d i n a l u c i t e k i l n o f the same s i z e .  Residence  time d i s t r i b u t i o n o f p a r t i c l e s  was a l s o s t u d i e d b r i e f l y to v e r i f y t h a t s o l i d s were n e a r l y i n a x i a l plug flow. A simple mathematical changer i s presented. temperatures  model o f a r o t a r y k i l n -'heat ex-  T h i s model p r e d i c t s gas, s o l i d s and wall-  i n a k i l n as a f u n c t i o n of the k i l n design and  operating  parameters  developed  in this  using  work.  the  ho.at t r a n s f e r  correlations  TABLE OF CONTENTS  ABSTRACT  ,  i i  ACKNOWLEDGEMENTS  x  L 1ST "OF TABLES" ""  INTRODUCTION  2.  LITERATURE REVIEW  i  i x  LIST OF .FIGURES 1.  v  x  i  1 ,  8  2.1  Mechanism o f Charge Movement  8  2.2  R e t e n t i o n Time and Holdup  15  2.3  Residence Time D i s t r i b u t i o n  21'  2.4  Surface Time  28  2.5  Heat T r a n s f e r  31.  a.  Conduction  32  b.  Convection  40  c.  Radiation  . . . I  »  44  3.  SCOPE OF PRESENT WORK  47  4.  APPARATUS AND MATERIALS  49  4.1  Apparatus  49  a.  Kilns  49  b.  Feeding System  54  vi.  4.2 5.  c.  R e c e i v i n g System  d.  A i r Heating  e.  Thermocouples  . . . . .  ^4  System  56 56  Materials  6  EXPERIMENTAL PROCEDURE  0  6 4  5.1  Retention  Time and S o l i d Throughput  5.2  Residence Time D i s t r i b u t i o n  65  5.3  Surface Time  6 7  5.4  Heat T r a n s f e r  6 9  a.  Experimental  b.  P r e l i m i n a r y Test  c.  Operating  . . .  ^4  Procedure 7 0 71  6.  RESULTS AND  Conditions  . , ,  DISCUSSION  7  3  3  6.1  Types o f Bed Movement  7  6.2  L a t e r a l and R a d i a l V e l o c i t y  7 3  6.3  Surface Time  7 8  6.4  S o l i d Throughput and R e t e n t i o n Time  6.5  Residence Time D i s t r i b u t i o n  6.6 6.7  Gas and Bed Temperatures A x i a l Temperature D i s t r i b u t i o n  6.8  C a l c u l a t i o n Method Coefficients  . . .  85  , .  9 3  in?  6.9  f o r Heat T r a n s f e r  J  ,  Bed t o Wall Heat t r a n s f e r  6.in Heat T r a n s f e r a.  1  1  2  2  0  Coefficients  L o c a l Heat T r a n s f e r C o e f f i c i e n t s  . . .  "1 o o  i 1  vii.  b.  E f f e c t of A i r Temperature  c.  F f f e c t o f Gas Flow  d.  E f f e c t of R o t a t i o n a l Speed  e.  E f f e c t of degree o f F i l l  f.  E f f e c t o f S o l i d Throughput and I n c l i n a t i o n Angle  g.  E f f e c t of P a r t i c l e Size  h.  Comparison w i t h Previous Work  6:11 Correlation  2  7  130 ,  135 137 1  4  0  144 .  151  6.12 Scaleup  153  A MODEL FOR GAS TO BED HEAT TRANSFER  161  7.1  True Surface Area  161  7.2  Individual  165  7.3  Gas to Bed Heat T r a n s f e r C o e f f i c i e n t  7.4  Gas t o P a r t i c l e Heat T r a n s f e r  7.5  P a r t i c l e Heat T r a n s f e r . . .  168  Coefficient  171  Comparison w i t h Experimental Data  174  3.  MODELLING OF ROTARY KILN HEAT EXCHANGER  9.  CONCLUSIONS  10.  1  o f Heat T r a n s f e r C o e f f i c i e n t s  1  7.  127  RECOMMENDATION  . . . .  182 200  FOR FUTURE WORK  202  NOMENCLATURE  204  REFERENCES  2 09  APPENDIX A  Calibration  o f Equipment  B  Surface Area and Surface V e l o c i t y  C  Sample C a l c u l a t i o n s  215 223 . •  233  viii  D  Computer  E  Data  Programs  244 257  - J'  ix  LIST OF TABLES Table 2-1  E f f e c t of K i l n Length on D and Pe  . . . .  29  2-2  Radiant Heat T r a n s f e r C o e f f i c i e n t  . . . .  46  4-1  Key to F i g u r e  4- 2  P h y s i c a l P r o p e r t i e s of Ottawa Sand  51  4-1  63  and Limestone  72  5- 1  K i l n Operating  6- 1  R e l a t i o n s h i p of V,/V  6-2  Operating C o n d i t i o n s and C a l c u l a t i o n R e s u l t s of RTD Experiments . L o c a l Heat Flows and Heat T r a n s f e r Coefficients  6-3  Conditions  84  vs N 94 124  6-4  E f f e c t of Degree of F i l l on Heat T r a n s f e r -Rate and Bed Surface . . .  138  6-5  Gas to S o l i d s Heat T r a n s f e r C o e f f i c i e n t Limestone  143  6-6  Comparison of A i r - W a l l Heat T r a n s f e r C o e f f i c i e n t i n Empty K i l n s  148  6-7  R e s u l t of Regression  6- 8  g to R e s u l t of Regression A n a l y s i s f o r Nu„„ gw Input Data f o r Equation 7-14 3  7- 1  154  A n a l y s i s f o r Nu 1  7-2  C a l c u l a t i o n f o r G a s - P a r t i c l e Heat Transfer C o e f f i c i e n t  7-3  C a l c u l a t i o n o f h „ from Equation gs  156 176 177  7-14  . .  180  X  8-1  Coefficients  f o r Equations 8-5 and 8-6  8-2  Parameters i n F i g u r e 8-2  . . . .  186 1  9  0  Appendix A-l  C a l i b r a t i o n of Thermocouples  A-2  Thermocouple Data  C-l  T a b u l a t i o n of C a l c u l a t i o n  . . .  219 220  f o r RTD run (R2)  .  .  2 3 4  TABLE OF FIGURES  Figure 1-1  B a s i c Components of Rotary K i l n  2  1- 2  Heat T r a n s f e r Modes i n Rotary K i l n  5  2- 1  Types o f P a r t i c l e Movement i n Rotary K i l n  2-2  Mechanism of Slumping Charge i n a Rotary K i l n  11  Path of a P a r t i c l e Rotary K i l n  11  2-3 2-4  2-5 2-6 2-7 2-8  10  i n an I d e a l  R e l a t i o n s h i p of A x i a l Coefficient  . .  Dispersion  and R o t a t i o n a l Speed  ' Bed-Wall; Keat T r a n s f e r by Conduction  27 . . . .  P e n e t r a t i o n Model f o r Bed-Wall Heat T r a n s f e r Proposed by Wachters and Kramers Two-region P e n e t r a t i o n Model f o r B a l l - W a l l Heat T r a n s f e r Proposed by Lehmberg e t a l . . Convective Heat T r a n s f e r C o e f f i c i e n t Bed to A i r , Data of Wes e t a l  .33 33 39  from 43  4-1  Schematic Diagram of Apparatus  50  4-2  End Box and S e a l System  53  4-3  C o n i c a l Receiver  55  4-4  Schematic Diagram of Thermocouple Arrangement  57  4-5  Diagram of S u c t i o n Thermocouple  59  4-6  T y p i c a l Response of S u c t i o n Thermocouple  4-7  Commutator Copper Rings  . .  59 61  xii  6-1  Photographs  6-2  Trace of I n d i v i d u a l  6-3  Particle Velocity  6-4  R e t e n t i o n Time and Surface Time v s . R o t a t i o n a l speed  6-5  6-7 6-8 6-9 6-10  6-11  -74  Particle in Kiln  7 5  i n a Rotary K i l n  77 80  R a t i o of Surface Time to R e t e n t i o n Time vs.  6-6  o f Bed Motions  N/N  Surface V e l o c i t y  81 v s . R o t a t i o n a l Speed  . . . .  82  E f f e c t of R o t a t i o n a l Speed on S o l i d Throughput i n a Uniform Bed Depth Rotary Kiln . E f f e c t of K i l n I n c l i n a t i o n on S o l i d Throughput i n a Uniform Bed Depth Rotary K i l n . . . .  86 87  R e l a t i o n s h i p of S o l i d Throughput and Degree of F i l l i n a Uniform Bed Depth Rotary K i l n . .  88  E f f e c t of R o t a t i o n a l Speed and I n c l i n a t i o n Angle on R e t e n t i o n Time i n a Uniform Bed Depth Rotary K i l n  91  E f f e c t of Degree of F i l l in  on R e t e n t i o n Time  a Uniform Bed Depth Rotary K i l n  9 2  6-12  Cumulative Response Curve i n a Rotary K i l n  . .  95  6-13  Residence Time D i s t r i b u t i o n  (Pe=404)  9 7  6-14  Residence Time D i s t r i b u t i o n  (Pe=371)  9 8  6-15  Residence Time D i s t r i b u t i o n  (Pe=567)  9 9  6-16  Residence Time D i s t r i b u t i o n  (Pe=382)  l°  6-17  R e l a t i o n s h i p of D and N/N  6-18  R a d i a l S o l i d Temperatures  6-19  R a d i a l Gas Temperature  n  101  c  i n Rotary K i l n Bed  Profile  .  103 105  xdii  6-20  T y p i c a l A x i a l Temperature P r o f i l e s along a Rotary K i l n  6-21  R e p r o d u c i b i l i t y of A x i a l Temperature along Rotary K i l n  6-22  E f f e c t o f A i r Flow Rate on A x i a l P r o f i l e s along K i l n  6-23  6-24  Profiles  Temperature  E f f e c t of S o l i d Throughput and R o t a t i o n a l Speed on A x i a l Temperature P r o f i l e s along Rotary K i l n  D i f f e r e n t i a l S e c t i o n of Rotary K i l n  6-26  C o r r e l a t i o n of Solids  Bed to Wall Heat  Transfer C o e f f i c i e n t  . . . .  6-27  L o c a l Heat T r a n s f e r C o e f f i c i e n t  6-28  E f f e c t of Gas Temperature on Heat Transfer C o e f f i c i e n t E f f e c t o f Gas Flow Rate on Heat T r a n s f e r Coefficient E f f e c t of R o t a t i o n a l Speed on Heat Transfer C o e f f i c i e n t  6-31 6-32 6-33  6-34 6-35  I l l  113  6-25  6-30  110  E f f e c t o f A i r I n l e t Temperature on A x i a l Temperature P r o f i l e  6-29  107  E f f e c t o f N on h i n Both Slumping and R o l l i n g Beds . ? . . . . .  H5  121 1 2  6  128 129 131 1 3  3  E f f e c t of Degree of F i l l on Heat T r a n s f e r Coefficient  136  E f f e c t s of S o l i d Throughput and I n c l i n a t i o n Angle on G a s - S o l i d s Bed Heat T r a n s f e r Coefficient  139  E f f e c t s of S o l i d s Throughput and I n c l i n a t i o n Angle on Gas-Wall Heat T r a n s f e r C o e f f i c i e n t .  141  Comparison of Experimental Data w i t h Literature  145  xiv  6-36 6-37  6-38 6-39 6- 40  G a s - t o - W a l l Heat T r a n s f e r C o e f f i c i e n t i n an Empty K i l n V a r i a t i o n o f L o c a l N u s s e l t Number i n T h e r m a l E n t r y R e g i o n o f a Tube w i t h C o n s t a n t H e a t Rate per U n i t o f Length Comparison o f E x p e r i m e n t a l Data w i t h P r e d i c t e d V a l u e s f o r Nu gs Comparison o f E x p e r i m e n t a l Data w i t h P r e d i c t e d V a l u e s f o r Nu gw • P r e d i c t e d Heat T r a n s f e r C o e f f i c i e n t for  1  4  7  1  5  0  155 157  Scaleup  7- 1  Heat T r a n s f e r  7-2  Arrays of Surface P a r t i c l e s  -*-^  7-3  R e p o r t e d R e s u l t s f o r G a s - P a r t i c l e Heat T r a n s f e r i n F i x e d Bed and R o t a r y D r y e r . . . Comparison o f T h e o r e t i c a l Curve w i t h  112  7-4  f r o m Gas  t o S o l i d s Bed  . . . .  1  6  2  4  17 5  7-5  E x p e r i m e n t a l Data E f f e c t o f R o t a t i o n a l Speed on T h e o r e t i c a l B a s - S o l i d s Bed H e a t T r a n s f e r C o e f f i c i e n t ,  8-1  F l o w C h a r t o f Computer P r o g r a m f o r Temperature P r o f i l e s  8-2  E f f e c t o f Heat T r a n s f e r C o e f f i c i e n t on M o d e l l i n g o f R o t a r y K i l n Heat Exchanger.  8-3  Effect  o f Gas F l o w R a t e on M o d e l l i n g  178  . .  of TOT  Rotary K i l n 8-4  Heat E x c h a n g e r  •  E f f e c t o f R e f r a c t o r y I n s u l a t i o n on M o d e l l i n g o f R o t a r y K i l n Heat Exchanger  8-5  E f f e c t o f K i l n L e n g t h on M o d e l l i n g o f R o t a r y K i l n Heat Exchanger  8-6  Effect  of K i l n  D i a m e t e r on M o d e l l i n g  L J J  . .  of  1 Q7 Rotary K i l n  Heat Exchanger  XV  8-7  E f f e c t of L/D on M o d e l l i n g of Rotary K i l n Keat Exchanger  19 8  Appendix A A-l  Calibration  of Thermocouple i n Metal Baths . .  216  A-2  Calibration  Curve of Thermocouples  217  A-3  A i r Flow Rate versus Reading on Rotameter Scale  221  S u c t i o n Rate versus Reading on Rotameter Scale  222  A-4  Appendix B B-l  P a r t i c l e C o n f i g u r a t i o n i n Surface Layers . . .  224  B-2  Emerging Ra-teof Pa-rtiieles from Bed Region to Surface Region  228  B-3  Particle Velocity  P r o f i l e i n Surface Region  .  231  ACKNOWLEDGEMENTS  The guidance  author wishes  t o thank  and a d v i c e t h r o u g h o u t  author would l i k e t o thank Engineering ing  Financial  of  the course o f t h i s  the faculty  D e p a r t m e n t and t h e s t a f f  Workshop f o r t h e i r  Research  Dr. Paul Watkinson  useful  The  i sreally  author  L t d . i n t h e form  o f the Chemical  Engineer-  from  theNational  the Standard  O i l Company  of fellowship,  f o r which  grateful.  i s also  h e r p a t i e n c e and c o n t i n u a l  The  s u g g e s t i o n s and h e l p .  C o u n c i l o f Canada, a n d from  the author  study.  members o f C h e m i c a l  a s s i s t a n c e was r e c e i v e d  B r i t i s h Columbia  for his  indebted to h i s wife, J i n j y , f o r support throughout  this  work.  1  CHAPTER 1 INTRODUCTION The r o t a r y k i l n i s one o f the most w i d e l y used i n d u s t r i a l r e a c t o r s f o r h i g h temperature processes i n v o l v i n g solids.  I t c o n s i s t s o f a metal c y l i n d e r , l i n e d w i t h b r i c k ,  r o t a t e d about i t s i n c l i n e d a x i s as shown i n F i g u r e 1-1. solid  The  feed i s i n t r o d u c e d i n t o the upper end o f the k i l n by  v a r i o u s methods, i n c l u d i n g i n c l i n e d chutes, overhung conveyors and s l u r r y p i p e s .  screw  The charge then t r a v e l s down  along the k i l n by a x i a l and c i r c u m f e r e n t i a l movements, due t o the  k i l n ' s i n c l i n a t i o n and r o t a t i o n . K i l n i n c l i n a t i o n depends on the process w i t h a t y p i c a l  range o f v a l u e s from 0.02-0.063 m/m.  Different  rotational  speeds are used depending on the process and k i l n  s i z e from  very low, i . e . , a p e r i p h e r i a l speed o f 0.015 m/s, f o r a TiO^ pigment k i l n , t o 0.227 m/s f o r a cement k i l n , t o 0.633 m/s f o r a u n i t c a l c i n i n g phosphate m a t e r i a l .  The s i z e s o f i n d u s t r i a l  k i l n s range from 1.7 m.I.D. x 11.8 m long f o r f i r i n g  light  weight aggregate, t o 5.9 m x 12 5 m f o r i r o n ore d i r e c t  reduction.  Rotary k i l n s are v e r s a t i l e r e a c t o r s i n t h a t p a r t i c l e s i z e and s o l i d d e n s i t y are not r e s t r i c t e d as i n the case o f f l u i d i z e d or  spouted beds, d i r e c t f i r i n g o r i n d i r e c t h e a t i n g may be used,  and the k i l n can operate i n e i t h e r c o c u r r e n t o r c o u n t e r - c u r r e n t  2  INCLINED WITH HORIZONTAL  F i g u r e 1-1  B a s i c Components o f Rotary K i l n  3  flow.  The  l a t t e r feature  s o l i d conversion  i s required.  dry s t a t e , or as a wet The  i s important where high extent of S o l i d s may  paste.  main uses of r o t a r y k i l n s are i n the processes of  calcining, fusing, nodulizing, reducing  be f e d e i t h e r i n the  of s o l i d m a t e r i a l s .  r o a s t i n g , i n c i n e r a t i n g , and Lime, magnesia and  alumina  are  c a l c i n e d to r e l e a s e carbon d i o x i d e  and water, at temperatures  i n the ranges of 1260-1500 K.  n o d u l i z i n g process i s a p p l i e d  to phosphate rock and to 1600  K.  1600  to o x i d i z e and  K,  various  The  c e r t a i n i r o n ores with temperatures,  Roasting occurs at temperatures between 800  ores,  d r i v e o f f s u l f u r and  including gold,  arsenic  s i l v e r , iron, etc.  (1).  The  process are i n the range of 570-970 K. t y p i c a l of reducing The  The  rotary  r e a c t i o n temperatures are around 1300  temperatures i n t h i s  i n rotary K.  670-770 K,  of a c t i v a t e d carbon and  of z i n c from other metals duction  of p l a s t e r of p a r i s A considerable  to dry s o l i d s and t y p i c a l wet length  kilns.  of expanded  ( i n two  stages,  a c t i v a t i o n , 1170-1270 K), (1200  K, Waelz p r o c e s s ) ,  (382  t o 404  recovery  and  pro-  K).  p o r t i o n of the k i l n l e n g t h may  be  used  b r i n g them up to r e a c t i o n temperature.  process cement k i l n ,  60%  of the 137  i s r e q u i r e d to dry the s l u r r y and  whereas the c a l c i n i n g zone and  is  Other major  a p p l i c a t i o n s of r o t a r y k i l n s i n c l u d e p r o d u c t i o n  carbonizing  for  Iron ore r e d u c t i o n  processes c a r r i e d out  aggregate, p r o d u c t i o n  and  from  k i l n i s s u c c e s s f u l l y used as a pre-combustion r e a c t o r i n c i n e r a t i o n of p l a s t i c s wastes  K  1500  In a  meter k i l n  heat s o l i d s to 1100  burning zones occupy 22%  and  K,  18% o f the l e n g t h , r e s p e c t i v e l y .  S t e l c o r e p o r t e d (2) p e r f o r -  mance data f o r i t s f i r s t commercial i r o n ore d i r e c t r e d u c t i o n k i l n i n the SL/RN p r o c e s s .  About 70% o f the 125 meter k i l n  l e n g t h i s used t o preheat the s o l i d s up t o 1120 K, l e a v i n g only 30% f o r r e d u c t i o n .  The thermal design o f a r o t a r y  kiln  i s thus o b v i o u s l y important. To d e s i g n a k i l n one should c a l c u l a t e the l e n g t h o f each i n d i v i d u a l zone f o r d r y i n g , h e a t i n g , and chemical r e a c t i o n based on heat t r a n s f e r and k i n e t i c data. are  Unfortunately there  few d e t a i l e d d a t a - 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 c a l -  c u l a t i o n o f heat flow. The heat t r a n s f e r p r o c e s s i s complex, p a r t i c u l a r l y i n a f i r e d k i l n i n which r a d i a t i o n , c o n v e c t i o n and conduction a l l p r o v i d e c o n t r i b u t i o n s t o the t r a n s f e r o f heat from and t o the gas, the w a l l and the s o l i d s .  The modes o f heat t r a n s f e r i n  a f i r e d k i l n are shown i n F i g u r e 1-2.  The gas, a heat source,  p r o v i d e s heat t o t h e s o l i d s , a heat s i n k , and t h e w a l l , a regenerator.  The w a l l , a f t e r r e c e i v i n g heat from the gas,  t r a n s m i t s i t by d i r e c t r a d i a t i o n t o the s o l i d s bed s u r f a c e , and by conduction when i t r o t a t e s t o the underside o f the bed. A p o r t i o n o f the heat the w a l l r e c e i v e s passes t o the s u r roundings through i t s o u t e r s h e l l as a heat l o s s .  In a d i r e c t  f i r e d k i l n o f l a r g e diameter the major amount o f heat t h a t reaches the s o l i d bed i s t r a n s f e r r e d by r a d i a t i o n from the hot gas.  R a d i a t i o n from the exposed w a l l t o the charge  ranks next i n importance.  usually  Convection from the gas and con-  d u c t i o n from t h e underside w a l l p r o v i d e s l e s s than one q u a r t e r of  the t o t a l heat r e c e i v e d by the s o l i d charge.  However, i n  5  Hot Gases  —  Conduction  F i g u r e 1-2  Heat T r a n s f e r Modes i n Rotary" K i l n .  6  k i l n s used f o r b i c a r b o n a t e c a l c i n a t i o n t u r e s are around  (3) where the tempera-  450-470 K, and i n the d r y i n g and p a r t s of  the h e a t i n g s e c t i o n s of f i r e d k i l n s , c o n v e c t i o n and conduction c o n t r i b u t i o n s are expected t o outweigh A l s o , Brimacombe and Watkinson  t h a t of r a d i a t i o n .  (4) have shown t h a t i n d i r e c t  f i r e d k i l n s of s m a l l diameter o p e r a t i n g at s o l i d up t o 1100  temperatures  K c o n v e c t i o n from the gas i s the primary mode of  heat t r a n s f e r t o the s o l i d s .  However, t h e r e i s no i n f o r m a t i o n  a v a i l a b l e t o determine under what c o n d i t i o n s c o n v e c t i o n can be ignored i n a f i r e d Recent  kiln.  i n v e s t i g a t o r s have attempted  model the performances  of alumina k i l n s  t o s i m u l a t e and  (5,6), cement k i l n s  (7,8), i r o n ore r e d u c t i o n k i l n s  (9,10), aggregate k i l n s  and simple heat exchanger  (12-17, 54).  kilns  (11)  In these s t u d i e s  a number of d i f f e r e n t i a l equations were formulated t o p r e d i c t gas and s o l i d temperature important parameters  p r o f i l e s along the k i l n .  of the models i n c l u d e d heat  The  transfer  c o e f f i c i e n t s f o r gas t o s o l i d s , w a l l t o s o l i d s , and gas t o wall.  U n f o r t u n a t e l y t h e r e are no d e t a i l e d data on heat t r a n s f e r  c o e f f i c i e n t s t o i n c o r p o r a t e i n t o the models.  The v a l u e s of  the c o e f f i c i e n t s were e i t h e r c a l c u l a t e d by u s i n g equations the r e l i a b i l i t y of which i s t o be v e r i f i e d , or v a l u e s of the c o e f f i c i e n t s were assumed without f u r t h e r j u s t i f i c a t i o n . p a u c i t y of data f o r r o t a r y k i l n s was  a l s o r e c o g n i z e d by a  working p a r t y r e p o r t of the I n s t i t u t e of Chemical i n 1971  (18).  Engineers  The r e p o r t c a l l e d f o r a comprehensive  heat t r a n s f e r processes over wide temperature s o l i d s bed, gas and w a l l i n r o t a r y  The  kilns.  study of  ranges between  7  The p u r p o s e mental  to  the  investigation of  reaction-free was  of  cover  on h e a t  system the  transfer  velocity  of  present  c o n v e c t i o n heat  effects  of  coefficients.  speed,  a i m was  determine which  kilns, design  heat  and t o  s o l i d bed  transfer report  purposes.  the  These  holdup, of  these  from the results  gas  make  experi-  the  The  operating  parameters  an  in  kiln.  s o l i d throughput,  rotational  governing  a v a r i e t y of  to  transfer  a non-fired rotary  and t e m p e r a t u r e ,  to  w o r k was  study  parameters  included  inclination  angle,  and p a r t i c l e  size.  factors  important  to  the  i n a manner  were  solids  in  suitable  gas  The in  rotary for  8  CHAPTER 2 LITERATURE REVIEW To gas  investigate  t o the  the heat t r a n s f e r mechanisms from  s o l i d s bed,  behavior and  how  i t i s e s s e n t i a l t o understand  and  charge m a t e r i a l  due  the  in a rotating  r a d i a l motion of  t o the k i l n ' s r o t a t i o n  the a x i a l motion of p a r t i c l e s along the k i l n mainly  to i n c l i n a t i o n . the  material  v e l o c i t y components appear:  p a r t i c l e s of the  bed  i t i s a f f e c t e d by k i l n o p e r a t i n g parameters.  During the movement of f r e e f l o w i n g k i l n , two  the  The  due  l a t t e r type of p a r t i c l e motion determines  r e s i d e n c e time of s o l i d m a t e r i a l  i n the  k i l n , whereas  the  former type of p a r t i c l e motion p r o v i d e s s o l i d mixing. 2.1  Mechanism of Charge Movement An  the  excellent  s o l i d bed  d e s c r i p t i o n of c i r c u m f e r e n t i a l  i n a r o t a r y drum was  g i v e n by Rutgers  motion of (19).  a r o t a t i n g c y l i n d e r a s o l i d p a r t i c l e i s taken up the w a l l  In to  a p a r t i c u l a r h e i g h t , depending on w a l l f r i c t i o n , s p e c i f i c g r a v i t y and  shape.  on account of the  A mass of g r a n u l e s may  The  higher  i n t e r a c t i o n between the p a r t i c l e s and  r e s t r i c t e d r e l a t i v e movements of the the mass.  be taken up  i n d i v i d u a l grains  c e n t e r of g r a v i t y of the whole mass of  p a r t i c l e s i s displaced  to a p o s i t i o n e c c e n t r i c  to the  the within the  axis  of  9  the  cylinder.  loading  The e c c e n t r i c i t y  decreases with  and i t becomes somewhat g r e a t e r w i t h  increasing  higher  speeds o f  rotation. For  e a c h drum r a d i u s t h e r e  is a critical  o f r o t a t i o n where c e n t r i f u g i n g s t a r t s along  with  t h e moving w a l l .  =  /g /R  types Figure  o f movement 2-1 g i v e s  r a d i a l motion. to  0.6 N  particles cylinder  i s taken  by  = 42.3//!)  (2-1)  rpm,  i n t e n s i t y may be  several discerned.  a c r o s s - s e c t i o n a l p i c t u r e o f these In c a t a r a c t i n g , which takes  occurs.  typical  linear  somewhat on p a r t i c l e  place  types of  about  0.55  s h a p e , some o f t h e  particles The  a relatively  surface  A t l o w e r s p e e d s o f 0 . 1 < N / N < 0.6 c  Here t h e c r o s s - s e c t i o n a l f r e e s u r f a c e has  lunar or kidney  considerably  described  i s given  Below N , t h e c r i t i c a l  and f a l l downwards.  b e l o w 0.1 N , the  and a p a r t i c l e  speed  a r e showered t h r o u g h t h e u p p e r s e c t i o n o f t h e  cascading the  c  of decreasing  depending  c  or N  :  where R, D i n m e t e r .  This  angular  shape o f F i g u r e 2 - l a . A t s p e e d s thin  layer of p a r t i c l e s  as shown i n F i g u r e  2-lb.  l o w e r a s l u m p i n g m o t i o n may  no l o n g e r  roll  s l u m p i n g phenomena, as d e p i c t e d by Z a b l o t n y  (20) and P e a r c e  motion o f the c y l i n d e r the s u r f a c e  down  I f t h e speeds a r e  occur  down t h e s u r f a c e  rolls  where t h e  continuously. i n Figure  (16). During  of the.charge  2-2, was rotary  gradually  (a)  (b)  Nc (rpm) =  1.  42.3  D(m)  CENTRIFUGING N > Nc  2. CATARACTING Nc > N > 0 . 6 Nc 3  CASCADING 0.6 N c > N > 0.1 Nc  4  ROLLING 0.1 Nc > N  gure 2-1  Types of P a r t i c l e Movement i n Rotary K i l n (19).  F i g u r e 2-2  Mechanism of Slumping of Charge i n a Rotary K i l n (20) .  F i g u r e 2-3  Path of a P a r t i c l e Rotary K i l n (20) •  i n an I d e a l  moves from p o s i t i o n C-C i n t o the p o s i t i o n marked by the s t r a i g h t l i n e A-A, forming the angle, A, with the h o r i z o n t a l , which was d e f i n e d as the angle of repose by S u l l i v a n (21) , o r s t a t i c angle o f s l i d e by Zablotny.  In t h i s t h e s i s the term  s l i d i n g w i l l be r e s t r i c t e d t o motion r e l a t e d t o s l i p p a g e a t the w a l l o f the k i l n and Zablotny's c a l l e d the angle o f repose.  angle of s l i d e w i l l be  A t the moment when the s u r f a c e  of the charge a t t a i n s p o s i t i o n A-A the s u r f a c e l a y e r o f the charge i s detached i n the upper p a r t o f the segment and then slumping o f the m a t e r i a l begins. m a t e r i a l i s shown s c h e m a t i c a l l y which simultaneously angle.  The q u a n t i t y o f slumping i n F i g u r e 2-2 by the A-O-B,  forms the angle (J> , c a l l e d the shearing  A f t e r r a p i d slumping o f t h a t p a r t o f the m a t e r i a l , the  s u r f a c e o f the charge i s i n dynamic e q u i l i b r i u m , as i t i s s i t u a t e d under an angle d e f i n e d as t h e dynamic angle o f repose. A new s u r f a c e B-O-B i s then moved up t o A-O-A, which r e s u l t s i n a second slumping. experimentally.  The shearing angle must be determined  I t depends on the p h y s i c a l p r o p e r t i e s o f the  charge m a t e r i a l as w e l l as the r o t a t i o n a l speed. angle diminishes  t o zero as the r o t a t i o n a l speed  The shearing increases  u n t i l a continuous r a t h e r than p e r i o d i c slumping o c c u r s .  This  a c t i o n i s r e f e r r e d t o as r o l l i n g . Henein, Brimacombe and Watkinson  (22) r e p o r t e d  experi-  mental r e s u l t s on slumping and r o l l i n g beds i n a 0.4 meter diameter r o t a r y c y l i n d e r and k i l n .  They i n d i c a t e d t h a t the  t r a n s i t i o n between slumping t o r o l l i n g not only depends on r o t a t i o n a l speed, but a l s o on the l o c a l holdup r a t i o o f m a t e r i a l  i n the k i l n , and on the s i z e and shape of p a r t i c l e s .  They  have suggested t h a t the mode of the bed behaviour may  strongly  i n f l u e n c e the t r a n s f e r o f heat i n the k i l n .  The c r i t e r i a f o r  t r a n s i t i o n from slumping to r o l l i n g have not y e t been w e l l defined. I n d u s t r i a l r o t a r y k i l n s are r o t a t e d a t speeds r a n g i n g from 0.4  t o 3 rpm depending on processes and s i z e s .  diameters o f t y p i c a l i n d u s t r i a l k i l n s are 1.8 i n t u r n , have apparent c r i t i c a l  speeds N  c  The  t o 5.9 m which,  o f 32 t o 17  rpm.  Most i n d u s t r i a l k i l n s are thus operated at speeds o f 0.1 > N  /N  >. 0.01,  c  where the s u r f a c e of the bed i s expected t o be  i n r o l l i n g motion. kiln  For i n s t a n c e the 5.9  m  diameter S t e l c o  (2) operates at a r o t a t i o n a l speed of 0.44  rpm or N/N  c  =  0.0257. Themelis, e t a l (23) s t a t e d t h a t r o t a t i o n a l speed the of  major f a c t o r o f dynamic s i m i l a r i t y f o r s c a l e - u p .  speed i n s t e a d o f the r o t a t i o n a l speed may to  In view  the types o f motion of p a r t i c l e s i n a k i l n d e s c r i b e d  i t would be a p p r o p r i a t e t o say the f r a c t i o n o f the  was  above,  critical  be a b e t t e r  factor  use, so t h a t s i m i l a r i t y o f bed motion be p r e s e r v e d i n  scale-up.  A c c o r d i n g t o the l a t t e r c r i t e r i o n , t o s c a l e - u p a  l a b o r a t o r y k i l n o f diameter 0.19  m w i t h a r o t a t i o n a l speed o f  3 rpm t o an i n d u s t r i a l s c a l e k i l n o f 3.0 m diameter, the r o t a t i o n a l speed has t o be reduced t o 0.75'r.pm, a c c o r d i n g t o  N = N /ITyD" 1  (2-2)  T h i s should m a i n t a i n the same p a t t e r n of bed motion.  Details  of bed behaviour, s o l i d s motion, e f f e c t of p a r t i c l e s i z e d i s t r i b u t i o n and  shape i n k i l n s e c t i o n s of v a r i o u s  diameters  are under study by Henein, Brimacombe and Watkinson  (22).  K i l n s used i n i n d u s t r i a l processes have i n c l i n a t i o n o angles of about 1-4  , that i s , considerably  l e s s than  the  dynamic angle of repose, which i s about 30-40  f o r most  materials.  slide  Thus the mass of m a t e r i a l does not  During r o t a t i o n of the k i l n ,  solid  axially.  i n d i v i d u a l p a r t i c l e s of f r e e -  flowing m a t e r i a l are r e p o r t e d l y  (20)  s h i f t e d along  the  axis  of the k i l n i n f l a t t e n e d h e l i c a l motion, the components of which are the path of a p a r t i c l e i n the depth of the bed the plane o f r o t a t i o n and as shown i n F i g u r e  2-3.  a path on the s u r f a c e of the charge A p a r t i c l e of m a t e r i a l l o c a t e d i n the  bottom l a y e r of the charge a t p o i n t 1, d u r i n g together  in  w i t h the charge along  r o t a t i o n , moves  the path arc 1-1'.  Then by  the  e f f e c t of the f o r c e of g r a v i t y , t h a t p a r t i c l e r o l l s a short a x i a l distance  from p o i n t 1' along  the s l a n t i n g s u r f a c e  p o i n t 2, from which i t again t r a v e l s together along  the path 2-2',  etc.  The  and  progressive  bed.  2',  a x i a l t r a n s p o r t of the e n t i r e charge  surface  of the r o l l s of i n d i v i d u a l  ( i . e . , 1-1'  and  2-2')  along  However, t h i s p i c t u r e i s probably v a l i d o n l y f o r an rolling  charge  emerges on the s u r f a c e at p o i n t  r e s u l t s , t h e r e f o r e , from the sum p a r t i c l e s over the  w i t h the  to  the  ideally  kiln  2.2  R e t e n t i o n Time and Holdup One o f the most important f a c t o r s i n d e s i g n of r o t a r y  k i l n s i s the r e t e n t i o n time or r e s i d e n c e time o f the charge f o r h e a t i n g or chemical r e a c t i o n .  As e a r l y as 1927,  Sullivan,  Maier and R a l s t o n (21) p i o n e e r e d an e x t e n s i v e experimental study of the e f f e c t s of o p e r a t i n g parameters on r e t e n t i o n time in rotary k i l n s .  The experiments were conducted i n 2.13  meter  long k i l n s w i t h v a r y i n g diameters of 0.076, 0.152, 0.292 and 0.5 meters.  The parameters covered i n c l i n a t i o n angle,  r o t a t i o n a l speed, angle o f repose, s o l i d feed r a t e , diameter, temperature, and d i s c h a r g e c o n s t r i c t i o n s . range of m a t e r i a l s was  kiln A wide  employed i n t h e i r study, i n c l u d i n g  Ottawa sand, c o a l , sawdust, and copper s l a g .  They found t h a t  the r e t e n t i o n time i s p r o p o r t i o n a l t o the square r o o t of the s t a t i c repose angle o f the s o l i d , and i n v e r s e l y  proportional  to k i l n diameter, r o t a t i o n a l speed, and i n c l i n a t i o n angle o f kiln.  As expected the time of passage i s independent of  temperature a t l e a s t up t o 1170  K.  At f i x e d r o t a t i o n a l  speed  and i n c l i n a t i o n angle the r e t e n t i o n time f o r a g i v e n m a t e r i a l and k i l n s i z e i s independent of the s o l i d feed r a t e over a c o n s i d e r a b l e range.  Under these c o n d i t i o n s i n c r e a s i n g  r a t e r e s u l t s i n i n c r e a s i n g hold-up o f s o l i d s . e m p i r i c a l r e l a t i o n s h i p was  The  feed  following  presented f o r a k i l n w i t h no d i s -  charge c o n s t r i c t i o n s ,  t =  1.77  L a  Q  /§Z n D  (2-3)  For a k i l n w i t h an end c o n s t r i c t i o n , a lengthy c o e f f i c i e n t was m u l t i p l i e d t o the above equation. Bayard  (24) l a t e r proposed a formula based on h i s own  data and t h a t of S u l l i v a n e t a l . ,  t -  °- a n ^D 31  (  4 + e )  (2-4)'  L  v  This equation d i f f e r s from equation 2-3 dependence on the repose angle of the  i n the form of the  solid.  A n a l y t i c a l e x p r e s s i o n s f o r the r e l a t i o n s h i p of r e t e n t i o n time and other parameters Saeman (25) f o r l i g h t l o a d i n g  L  s  i  n  were developed i n 1951  by  kilns,  (2-5)  9  IF D n  (a+ty cos0)  K  D >  and by P i c k e r i n g et a l . (2 6)  •LsinG' IT D n sma  (2-6)  where 0 and 0' are s t a t i c and dynamic angle of repose, respectively.  i s angle between bed s u r f a c e and k i l n  Varentsov and Yufa  axis.  (27) a p p l i e d dimensional a n a l y s i s  to i n v e s t i g a t e r o l e o f v a r i o u s  f a c t o r s a f f e c t i n g the moving  rate of s o l i d s i n a rotary k i l n .  A s e r i e s o f experiments  conducted i n k i l n s 6 m long w i t h i n s i d e diameters o f 0.3 0.55  m.  chips,  Solid material  used i n these t e s t s i n c l u d e d  sand, coke and p y r i t e .  investigated:  JU L  where m*  0. 01  Four p a r t i c l e s i z e ranges were  proposed:  -0.33  ,6.0.66 , 4 ^ , 0.08  /*D.0.93  (2-7)  x 10~ ; 3  D = 2.0 m.  The  c o r r e l a t e d by u t i l i z i n g the data o f S u l l i v a n  et a l . f o r v a r i o u s  diameters.  0.75  x 10~  3  For D= 0.5 m,  f o r D = 1.0 m;  the v a l u e of m*  0.25  x 10~  3  for  Gas v e l o c i t y , i n e q u a t i o n 2-7, has l i t t l e e f f e c t  on r e t e n t i o n time exercise  marble  i s a c o e f f i c i e n t depending on the k i l n diameter.  value o f m* was  i s 1.7  and  0.35-0.56, 1.51-1.70, 3.81-4.40 and 7.07-7.28 mm  The f o l l o w i n g e q u a t i o n was  r  was  (t  a  R e ^ * ^ ) , and p a r t i c l e s i z e doesn't  a s i g n i f i c a n t i n f l u e n c e as seen i n the e q u a t i o n s i n c e  the  sum o f the powers o f p a r t i c l e s i z e , d , appearing i n Ga 1? (-d • ) , 4d /TT D Y| and d /D, i s 0.1. I t was a l s o concluded t h a t p p ' P 3  2  2  gas temperature doesn't a f f e c t the s o l i d throughput i n the k i l n The holdup, n , although appearing i n 4d /^D "n, 2  2  does not have  a s i g n i f i c a n t e f f e c t on r e t e n t i o n time e i t h e r . Zablotny  (20) a l s o employed d i m e n s i o n a l a n a l y s i s  c a r r i e d out experiments i n a k i l n of 3.55 diameter.  m long  The f o l l o w i n g e q u a t i o n was p r e s e n t e d ,  and  and 0.352 m  The r e t e n t i o n time, obtained from the r a t i o of bed weight/discharge  r a t e , g i v e s the average  time of s o l i d s r e -  s i d i n g i n the k i l n by assuming uniform bed depth and constant a x i a l v o l u m e t r i c r a t e o f s o l i d s along the k i l n .  These  assumptions are not always v a l i d i n i n d u s t r i a l k i l n s where the bed depths along the k i l n are not uniform o r the p a r t i c l e s change i n p h y s i c a l p r o p e r t i e s due t o r e a c t i o n o r d r y i n g . Vahl and Kingma  (2 8) showed t h a t d i f f e r e n t i a l s i n bed  h e i g h t e x i s t along a h o r i z o n t a l r o t a t i n g c y l i n d e r and thus s o l i d s can be t r a n s p o r t e d c o n t i n u o u s l y through  it.  This  c o n t r a d i c t s the e m p i r i c a l equation of S u l l i v a n e t a l . , a c c o r d i n g to which the t r a n s p o r t would be n i l i n h o r i z o n t a l r o t a r y k i l n s . Vahl and Kingma d e r i v e d a d i f f e r e n t i a l equation which r e l a t e d the s o l i d throughput  t o the bed h e i g h t T w i t h d i s t a n c e x  the feed f o r a h o r i z o n t a l c y l i n d e r . Kramers and Croockewit  Based on t h i s  from  equation  (2 9) i n t r o d u c e d the i n c l i n a t i o n  angle  and gave the f o l l o w i n g equation f o r r o t a r y k i l n s :  F  4 3  * t a n a _ dr sinB dx (  By approximation of  x _ j | V* R R  ( 2  _  9 )  -,. . and i n t r o d u c i n g the dimensionless group, ®k ~ L tana '  a n c  ^ ^ t  i e  =  n  boundary c o n d i t i o n , x = x  L  FsinG -)R  3  a n a  and  f o r x = L,  equation 2-9 becomes  - 0.193  + 0.193 RN<J>  RN(j>  X _ _ RN^ 0  1  9  L-x LN  3  (2-11)  k  T h i s equation shows, i n dimensionless form, the r e l a t i o n s h i p of bed h e i g h t =- (or holdup K o p e r a t i n g parameters.  n) and d i s t a n c e —, and other Li  When ^  = 0.19 3, a constant h e i g h t  i s o b t a i n e d over the whole l e n g t h o f the k i l n .  After re-  arrangement t h i s equation can be r e w r i t t e n as  F = 1.295 x  x  L  T  L  n D  2  tana/ s i n 9  (2-12)  i s the bed depth, which i s r e l a t e d t o holdup by the  expressions  n =  and  ^  (3 - s i n 3)  = i - cos %  (2-13)  where 3 i s the c e n t r a l angle o f the s e c t o r occupied by the s o l i d s i n the c r o s s - s e c t i o n o f the k i l n .  The r e t e n t i o n time can be d e r i v e d from the r a t i o o f bed w e i g h t / s o l i d throughput,  IL 4" D Ln 2  (2-14)  S u b s t i t u t i o n o f equations 2-12 and 2-13 i n t o equation 2-14 and approximation  of tan a - a y i e l d s  -  LsinG  =  n  D  a  1-cos  f  The r e t e n t i o n time f o r a uniform bed depth i s thus not only a f u n c t i o n o f the group, LsinO/nDa, but a l s o depends on holdup n. Saeman (25) o b t a i n e d a s i m i l a r a n a l y t i c a l e x p r e s s i o n f o r an i n c l i n e d k i l n w i t h v a r i o u s degrees  F = 4- n D s i n b 3  3  of loading,  £ (i^cosG + a) / sinQ 2  For uniform bed depth,  (2-16)  cos6 = o, and s u b s t i t u t i o n  of equation 2-13 i n t o equation 2-11 g i v e s  -  =  LsinG nDa  _ n _ ^ 3 | s i n  ( 2  _  1 7 )  The r e t e n t i o n time i n t h i s equation has a d i f f e r e n t dependence of holdup term from equation 2-12.  (Note t h a t 3  i s f u n c t i o n of n). From equation 2-9  one w i l l note t h a t t h e r e are f o u r  o p e r a t i n g parameters, which are i n t e r r e l a t e d i n a r o t a r y k i l n operated a t uniform bed depth:  solid  throughput,  holdup, r o t a t i o n a l speed and i n c l i n a t i o n angle.  For example,  at constant holdup and i n c l i n a t i o n angle, r o t a t i o n a l  speed  can not be i n c r e a s e d without s o l i d throughput being i n c r e a s e d . Thus, t h r e e of the four o p e r a t i n g v a r i a b l e s i n a uniform bed depth k i l n are 2.3  independent.  Residence Time D i s t r i b u t i o n The c o n v e r s i o n of s o l i d s i n a r o t a r y k i l n  depends not o n l y on chemical parameters  reactor  and the mean r e s i d e n c e  time of p a r t i c l e s i n the r e a c t o r but a l s o , i n g e n e r a l , on the spread i n r e s i d e n c e times and the way brought about.  the spread i s  I t i s t h e r e f o r e important t o know what  spread i n r e s i d e n c e time d i s t r i b u t i o n i s caused by the flow p a t t e r n of the s o l i d s i n the k i l n .  As i n d i c a t e d above, the  p a r t i c l e s i n a r o t a r y k i l n have v e l o c i t y components i n both the l o n g i t u d i n a l direction.  Due  ( a x i a l ) d i r e c t i o n and the t r a n s v e r s e ( r a d i a l ) t o t h e i r more or l e s s random behaviour, the  movements are o f t e n d e s c r i b e d mathematically by a type of d i f f u s i o n or mixing c o e f f i c i e n t , i n the a x i a l and directions.  radial  The a x i a l v e l o c i t y p r o f i l e as w e l l as the a x i a l  mixing c o e f f i c i e n t w i l l c o n t r i b u t e t o a spread i n r e s i d e n c e  time.  Conversely,  the r a d i a l mixing  coefficient  will  d i m i n i s h the e f f e c t of the a x i a l v e l o c i t y p r o f i l e thereby  reduce the spread  k i l n the r a d i a l mixing  i n r e s i d e n c e time.  and  In a r o t a r y  c o e f f i c i e n t causes a more or  less  uniform d i s t r i b u t i o n of element p a r t i c l e s over the c r o s s s e c t i o n of the k i l n , which tends to make the r a d i a l g r a d i e n t of s o l i d c o n c e n t r a t i o n i n a r e a c t i n g system zero. A survey of the mixing  of g r a n u l a r m a t e r i a l s i n  r o t a r y c y l i n d e r s has been given by Rutgers w i t h some experimental 0.50  together  data on a x i a l d i s p e r s i o n .  meter r o t a r y c y l i n d e r was  s i o n s and  (19)  A 0.16  x  equipped w i t h v a r y i n g dimen-  shapes of the i n l e t and o u t l e t s e c t i o n s , which  r e s u l t e d i n v a r i o u s holdups of the s o l i d s .  His  results  showed t h a t a x i a l d i s p e r s i o n c o e f f i c i e n t i s d i r e c t l y p o r t i o n a l to the square r o o t of r o t a t i o n a l speed at r e s i d e n c e time i n a h o r i z o n t a l c y l i n d e r , and  proconstant  approximately  i n v e r s e l y p r o p o r t i o n a l t o the square r o o t of holdup at constant r o t a t i o n a l speed.  The P e c l e t number i n h i s work  i s i n the order, of magnitude of two  to t h r e e .  T r a c e r methods are u s u a l l y used to study r e s i d e n c e time distribution.  In r o t a r y k i l n t e s t s t r a c e r p a r t i c l e s  to the feed except food dyes.  f o r c o l o r are r e a d i l y prepared  identical  by use  of  I f c , the i n i t i a l c o n c e n t r a t i o n of t r a c e r par-  t i c l e s , r e p r e s e n t s the number of t r a c e r p a r t i c l e s  injected  d i v i d e d by the t o t a l weight of p a r t i c l e s i n the holdup volume, t <; = — ( t , t average r e s i d e n c e t i m e ) , then the a x i a l d i s p e r s i o n model f o r and c  x (C,z) i s the c o n c e n t r a t i o n at z = — and L  the t r a c e r i n d i m e n s i o n l e s s form i s (30, 31, 32):  3C(g,z)  3C(g, z) 9?  3'C  where  and  (2-15)  9 z  C(e.,z) = c ( e , z ) / c  Pe = uL/n  1 8 C(g,z) Pe 2 2  =  Q  P e c l e t number  For an impulse input o f t r a c e r s i n j e c t e d i n t o the i n l e t of the r o t a r y c y l i n d e r , which i n i t i a l l y contained  no  t r a c e r , Abouzeid e t a l . (30) p r e s e n t e d the f o l l o w i n g s e t o f i n i t i a l and boundary  conditions  C(o,z) = o  (2-16a) (2-16b)  'ac(ci)  (2-16c)  =  9z  where  Moriyama and Suga  6 (?) = 1  £ = o  = o  5 > o  (32) r e p l a c e d  the second boundary  condition,  equation  16c, with  (2-16d)  C(C,°°) = f i n i t e  and  s o l v e d equation  2-15.  T h i s c o n d i t i o n , they argued,  corresponds t o the f a c t t h a t the mixing r e g i o n of the part i c l e s i s limited  t o the s u r f a c e r e g i o n o f the bed i n the  k i l n and t h a t t h i s r e g i o n i s almost u n a f f e c t e d by the dam near the discharge end. The  s o l u t i o n s o f equation  boundary c o n d i t i o n s  (equations  2-15 with  i n i t i a l and  2-16a, b o r c) were  lengthy  and given i n the p u b l i c a t i o n by Abouzeid e t a l . (30). The P e c l e t numbers are u s u a l l y d e r i v e d from the v a r i a n c e the r e l a t i v e v a r i a n c e  OQ o f the experimental  o^ or 2  residence  time  distribution,  (2-17)  0  i n s t e a d o f from the s o l u t i o n o f equation ship of r e l a t i v e variance  2-15.  The r e l a t i o n -  and P e c l e t number i s obtained  (19,  33) f o r a c l o s e d - c l o s e d system i n the a x i a l d i s p e r s i o n model:  (2-18)  The v a l u e s of Pe, i n r o t a r y k i l n s , are l a r g e enough t h a t the f o l l o w i n g approximation i s v a l i d .  Pe - — -  (2-19)  0-  Moriyama and Suga (32) a p p l i e d dimensional a n a l y s i s to o b t a i n the r e l a t i o n s h i p o f Pe and o t h e r o p e r a t i n g  variable  Based on t h e i r data on a p l a s t i c h o r i z o n t a l c y l i n d e r  (0.20 x  2.0 meter) and t h a t of Matsui  ( 3 4 ) , the f o l l o w i n g  equation  was presented,  i  Pe = 1.06 x 1 0  4  ,w^3^0.516  (F/D n)  JJ  -  U  , _  0.524 ,„ ^ 5.55-0.604f  ( L / D ) ' - ^ (&./D) T  u  (2-20)  where f i s f r i c t i o n c o e f f i c i e n t (= t a n O ) . 1  The P e c l e t number  i n t h e i r s t u d i e s a r e i n the range o f 250-5000. persion  c o e f f i c i e n t s were found t o be d i r e c t l y  Axial disproportional  to r o t a t i o n a l speed. The e f f e c t s of o p e r a t i n g r o t a t i o n a l speed on r e s i d e n c e  parameters i n a d d i t i o n t o  time d i s t r i b u t i o n were  reported  by Abouzeid, e t a l . ( 3 0 ) . The experiments were conducted i n a small s c a l e c y l i n d e r of 0.08 x 0.24 m. the a x i a l d i s p e r s i o n c o e f f i c i e n t i n c r e a s e s  I t was found t h a t with increasing  i n c l i n a t i o n angle, r o t a t i o n a l speed and s o l i d feed r a t e , but  26 i s independent o f p a r t i c l e s i z e .  Lu, e t a l . (35) a p p l i e d a  m u l t i - s t a g e combined model t o d e s c r i b e the mixing c o n d i t i o n of p a r t i c l e s i n a r o t a t i n g c y l i n d e r w i t h c r o s s a i r flow. The model c o n s i s t e d o f a s e r i e s o f stages, each stage comp r i s i n g a p l u g - f l o w r e a c t o r , a complete-mixing back flow and a dead volume. to f i t t h e i r experimental  Although  reactor with  the model was claimed  data w e l l , the r e s u l t a n t  equation  i s probably too complicated t o be p r a c t i c a l and r e q u i r e s too many parameters t o be s p e c i f i e d . A study o f the e f f e c t o f p a r t i c l e s e g r e g a t i o n on p a r t i c l e motions was presented by Sugimota and co-workers (36-38).  The e f f e c t of c r o s s a i r flow was shown by Lu, e t  a l . (35). The t r a n s p o r t o f s o l i d s i n r o t a r y c y l i n d e r d e v i c e s i s w e l l represented by the a x i a l d i s p e r s i o n model a c c o r d i n g t o several investigators,  (30-32).  U n f o r t u n a t e l y t h e r e are no  d e t a i l e d data t o p r e d i c t the v a l u e s o f D except the c o r r e l a t i o n equation o f Moriyama and Suga (equation 2-2 0) .  This  equation was e s t a b l i s h e d from the data o b t a i n e d from l a b o r a t o r y s c a l e h o r i z o n t a l c y l i n d e r s of L/D - 10. The r e s u l t s o f s e v e r a l i n v e s t i g a t i o n s on the r e l a t i o n s h i p o f a x i a l d i s p e r s i o n c o e f f i c i e n t and r o t a t i o n a l speed are compared i n F i g u r e 2-4. still  As shown i n the f i g u r e there i s  no agreement on how the a x i a l d i s p e r s i o n c o e f f i c i e n t i s  r e l a t e d t o r o t a t i o n a l speed, i . e . whether types.  D  N or D <* / N or other  As w e l l , the d i s p e r s i o n c o e f f i c i e n t s d i f f e r by an  order o f magnitude depending on the p h y s i c a l p r o p e r t i e s o f the  —i—i—i  • CM  E  60  A  i n n  1  1—i—i  it  i n  Matsui ,0.2m Dx 1.86 m. L , dp = 11.2 mm. Sugimoto,et a l , 0.255 x 0 . 6 m , dp =13mm. Rutgers, 0.16 x 0.50m, dp = 1.9 mm. Moriyama a Suga, 0.20 x 2.0m., dp =2.87 mm. Abouzeid , et a l , 0.08 x 0.24 m., dp =.35 mm.  40 x o  30  /  20  •  V  U J  o  UJ  10  8  8.0 •z. 6.0 o  2 U J  a-  CO  o  4.0 3.0 20  X  <  1.0 0.8 0.6 J__J  3  L  5  10  ROTATIONAL  F i g u r e 2-4  20  30  50  SPEED, rpm.  Relationship of.Axial Dispersion C o e f f i c i e n t and R o t a t i o n a l Speed.  MM.  100  particulate  material  (particle size, internal  shape), k i l n dimensions, degree o f f i l l , put.  and s o l i d through-  There are very few data p o i n t s i n the r o t a t i o n a l  r e g i o n t y p i c a l o f the r o t a r y k i l n . 2-20  friction,  speed  As i n d i c a t e d i n e q u a t i o n  the r a t i o o f L/D has a s i g n i f i c a n t e f f e c t on P e c l e t  number.  In t y p i c a l i n d u s t r i a l k i l n s  (39) the r a t i o of  L/D  ranges from 14 f o r petroleum coke k i l n s t o 30 f o r long lime kilns.  However the experimental k i l n s used f o r the  experiments have a s m a l l e r L/D  RTD  r a t i o , about 3 f o r c y l i n d e r s  of Rutgers, Abouzeid et a l . and Sigumoto et a l . , and about 10 f o r Matsui and Moriyama and Suga. d i d not study the i n f l u e n c e of Wes  e t a l . (31) used an i n d u s t r i a l s c a l e drum, 0.6  samples were taken at 3.65  end of the r o t a t i n g L/D  46.9  In t h e i r  rpm,  experiments  r e p r e s e n t two  different  of t h e i r experiments are g i v e n i n  Pe i n c r e a s e s from 55 t o 204 a t N=6  to 145 at N=2  when L/D  rpm,  and from  i n c r e a s e s from 6.09  t o 15.  T h i s suggests t h a t the P e c l e t number i n i n d u s t r i a l k i l n s be even h i g h e r . the 2.4  m  m from the entrance and a t the  drum, which may  r a t i o s . The r e s u l t s  Table 2-1.  investigators  L/D.  I.D. x 9.0 m long t o study the RTD. the  These  may  T h i s h i g h P e c l e t number then c h a r a c t e r i z e s  s o l i d flow i n a r o t a r y k i l n as e s s e n t i a l l y  p l u g flow (33).  Surface Time The s u r f a c e time i s the time the i n d i v i d u a l  particle  spends on the a e r a t e d s u r f a c e l a y e r b e f o r e i t r e t u r n s t o the bed.  After residing  i n the bed and moving along w i t h the w a l l ,  29  TABLE 2-1 E f f e c t of  L  L/D  N  n  t  (m)  (-)  (rpm)  (%)  (s)  3. 65*  9  K i l n Length on D and Pe (Wes, et. a l . )  6.08  15  p  D  (m /s)  e  (-)  2  6  20.1  2.33xl0  6  20.0  2.26  2  35.4  3.97  7.15  6  19. 8  5. 63  7.05  204  6  19. 8  5.65  7.59  189  2  31.4  8.94  6.24  145  3  10.4xl0~  5  12.3  *The midway d i s t a n c e where samples were taken.  55.1 47.9 46.9  i t r e t u r n s t o the s u r f a c e l a y e r .  The time t h i s  r e s i d e s i n the bed i s r e f e r r e d as bed time.  particle  The sum of  s u r f a c e time and bed time i s c a l l e d the c y c l e time.  Cycle  time, s u r f a c e time and bed time are f u n c t i o n s of r o t a t i o n a l speed, holdup, k i l n diameter, p a r t i c l e p h y s i c a l p r o p e r t i e s and r a d i a l p o s i t i o n i n the k i l n .  Since the p a r t i c l e t r a v e l s  along the k i l n i n a h e l i c a l motion, c y c l e time, s u r f a c e  time  and bed time are d e f i n e d as averages taken over a c e r t a i n l e n g t h o f the k i l n . Surface  time i s expected t o be important i n heat  t r a n s f e r processes  where p a r t i c l e s i n the s u r f a c e l a y e r s are  exposed t o hot gases.  Heat t r a n s f e r r e d from the gas phase  to the s u r f a c e l a y e r o f the s o l i d s i s d i s t r i b u t e d t o the bulk m a t e r i a l by s o l i d mixing t a k i n g p l a c e i n the c i r c u l a t o r y In a d i r e c t f i r e d k i l n i t has been estimated face temperature w i l l r i s e by 8 0 K i n 0.1  (18) t h a t  bed.  sur-  seconds, and by  270 K i n one second, i n which l a t t e r p e r i o d the s u r f a c e i s renewed. supply may  At a depth of 1 mm  below the s u r f a c e l a y e r the heat  account to only one percent  the s u r f a c e .  Surface  time i s a l s o b e l i e v e d to p l a y an im-  p o r t a n t r o l e i n the c o n v e c t i v e experimental  of t h a t r a d i a t e d t o  r e s u l t s of Wes  heat t r a n s f e r process.  e t a l . (31) showed t h a t some s o r t  of p e n e t r a t i o n mechanism might e x i s t f o r c o n v e c t i o n gas t o the downflowing p e n e t r a t i o n theory,  The  particles.  Thus, a c c o r d i n g  from the to  a short s u r f a c e time g i v e s a higher  average heat t r a n s f e r c o e f f i c i e n t .  In a d d i t i o n a s h o r t time  y i e l d s more p a r t i c l e s f l o w i n g down the s u r f a c e t h a t  certainly  i n c r e a s e s the heat  flux.  Although heat t r a n s m i s s i o n by r a d i a t i o n and t o the aerated little  s u r f a c e l a y e r i s important,  convection  there i s very  i n f o r m a t i o n i n the l i t e r a t u r e about s u r f a c e time  except from the work of Hogg, S h o j i and A u s t i n  (40).  They  r e p o r t e d t h a t i n t h e i r r o t a r y c y l i n d e r , 0.095 m i n diameter and  0.248 m long the f r a c t i o n of s u r f a c e time to c y c l e time  i s 0.49  at a r o t a t i n g speed of 90 rpm  or N/N  c  =0.64.  a r o t a r y k i l n where r o t a t i n g speeds are operated  In  below 6  rpm,  the f r a c t i o n of s u r f a c e time t o c y c l e time i s f a r below There i s a l s o l a c k of i n f o r m a t i o n i n the about the t h i c k n e s s of the s u r f a c e l a y e r .  literature  I t i s believed that  the t h i c k n e s s depends on r o t a t i o n a l speed, i n t e r n a l friction,  i n c l i n a t i o n angle, holdup, e t c .  calciners  (3) the t h i c k n e s s of the l a y e r was  particle  In r o t a r y soda stated theoreti-  c a l l y equal to the diameter of the p a r t i c l e s at 4 rpm the r o l l i n g p a t t e r n s t a r t s .  No  0.49.  where  s i z e s of the c a l c i n e r s and  the p a r t i c l e s were g i v e n . In the present work some experiments are c a r r i e d to study  out  the i n f l u e n c e of o p e r a t i n g v a r i a b l e s on s u r f a c e time,  and a f i l m study on the t h i c k n e s s of the s u r f a c e l a y e r i s reported. 2.5  Heat T r a n s f e r Bowers and Reed  (41) c o r r e l a t e d heat t r a n s f e r data  from f o u r i n d u s t r i a l k i l n s : burning,  dolomite  limestone  c a l c i n a t i o n and  c a l c i n a t i o n , dry cement  shale expansion.  From the  former two kilns-they concluded t h a t the o v e r a l l gas-bed heat t r a n s f e r c o e f f i c i e n t has the f o l l o w i n g r e l a t i o n s h i p with k i l n  diameter,  U  where U  q  :  q  = 18.6 D  (2-21)  o v e r a l l g a s - s o l i d heat coefficient  D  :  transfer  (W/m K) 3  k i l n diameter  (m)  Equation 2-21 i s o b v i o u s l y u n s a t i s f a c t o r y f o r design and can o n l y show the order o f magnitude o f heat  purposes  transfer  c o e f f i c i e n t s , because the c o r r e l a t i o n was based on a l i m i t e d number  (6) o f s c a t t e r e d data.  I t a l s o excludes the e f f e c t s  of r o t a t i o n a l speed, s o l i d and gas throughput,  inclination  angle, p a r t i c l e s i z e and does not r e f l e c t the complexity o f the a c t u a l process t h a t occurs i n the k i l n . 2.5a  Conduction Heat t r a n s m i s s i o n by conduction occurs a t the under-  s i d e o f the bed which i s i n c o n t a c t with the r o t a t i n g w a l l . At the moment when the p a r t i c l e s r e t u r n from the s u r f a c e l a y e r t o the bed, i n which they become a t r e s t r e l a t i v e t o the w a l l and t o t h e i r neighbours,  the p a r t i c l e s adjacent t o  the w a l l r e c e i v e heat from the w a l l  (Point A i n F i g u r e 2-5),  Tw  i  AREA  0,  =AREA  I  . AREA  0  2  Ts  N I  y=0  Figure  2-6  y=d  P e n e t r a t i o n Model f o r Bed-to-Wall Heat T r a n s f e r Proposed by Wachters and Kramers (3).  0  2  u n t i l they move up t o the p o i n t on t h e s u r f a c e again.  (B i n F i g u r e 2-5) and r o l l  T h e r e f o r e , Wachters and Kramers (3),  Wes e t a l . (42), Lehmberg e t a l . (43) and N i k i t e n k o (44) proposed an unsteady s t a t e p e n e t r a t i o n model f o r heat duction.  con-  The f o l l o w i n g assumptions were made:  a) The temperature o f the bulk m a t e r i a l f a r from the w a l l i s constant d u r i n g the c o n t a c t time t c . b) The r e g i o n a t the w a l l i n which heat  conduction  takes p l a c e i s t h i n compared w i t h the r a d i u s o f the c y l i n d e r , so t h a t the c u r v a t u r e may be n e g l e c t e d . c) T a n g e n t i a l heat conduction  can be n e g l e c t e d .  d) A t t - o the contents o f the w a l l l a y e r a r e mixed with the bulk m a t e r i a l . A heat balance  f o r a c i r c u m f e r e n t i a l element c o n s i s t i n g  of p a r t i c l e s adjacent t o the w a l l y i e l d s  9 T 2  —  = a  (2-22)  at  where a i s the heat d i f f u s i v i t y initial  o f p a r t i c l e s , m /s. 2  The  and boundary c o n d i t i o n s used by Wes e t a l . were  T(o,y) = T  s  T(t,o) = T w T(t,°°) = T ' s  (2-23)  Experimental measurements were made by Wes i n d u s t r i a l s c a l e drum of 0.6  x 9.0  m.  et a l . i n an  Potato s t a r c h and  yellow d e x t r i n e s o l i d s w i t h p a r t i c l e s i z e s of 15~100 were used i n the h e a t i n g process to determine coefficients, h  ws  heat  from the w a l l t o the s o l i d s .  ym,  transfer  The e x p e r i -  mental r e s u l t s were claimed t o be i n agreement w i t h the f o l l o w i n g equation, which i s d e r i v e d from the  simple  p e n e t r a t i o n model with equation 2-2 3.  2 k h ws =  Nikitenko  /uat  -  or  2 k b  c  /~"n~ v  a3  (44) used the f o l l o w i n g s e t of  (2-24)  initial  and boundary c o n d i t i o n s .  T  (0,y) =  T  (t,0) = T  dT  T  s  (2-25)  w  (t,°°) = T dy  (0,y)  and obtained the f o l l o w i n g r e l a t i o n s h i p .  (2-26)  No e x p l a n a t i o n was made o f the use o f the l a s t  boundary  c o n d i t i o n , and no experimental r e s u l t s were d i s p l a y e d i n his  paper. In  a study by Wachters  and Kramers ( 3 ), experiments  were conducted i n a 0.152 x 0.475 m copper c y l i n d e r and values of h i , were r e p o r t e d t o be 1/3 t o 1/2 o f those ws ' c  p r e d i c t e d from equation 2-24. the  They assumed t h a t whereas  bulk o f the g r a n u l a r bed has a uniform temperature t h e r e  i s a t h i n l a y e r a t the w a l l always c o n s i s t i n g o f the same p a r t i c l e s arid t h a t when these r o l l back, they o n l y mix among themselves.  Based on these assumptions, the w a l l  l a y e r d' i n t h i c k n e s s , was proposed t h a t was i n i t i a l l y a t a temperature T^ f o r o<y<d" as g i v e n i n F i g u r e 2-6.  The  average temperature o f the l a y e r was assumed t o not change d u r i n g the time o f c o n t a c t , e t c .  Thus the f o l l o w i n g  boundary  c o n d i t i o n s were used,  T (o, o<y<d) = T (o, y>d)  = T  s  T (t,o)  = T  w  T (t,°°)  = T„  T h e i r experimental r e s u l t s i n d i c a t e d t h a t a t h i g h e r speed (or  lower t ) where d'> 4/at , the w a l l l a y e r reduces the  heat t r a n s f e r c o e f f i c i e n t s by a f a c t o r of 3 w i t h r e s p e c t to t h a t obtained from a simple p e n e t r a t i o n model,  h  2 k. ws  (2-28)  10 rpm < N < 40  3 /irat.  At r e l a t i v e l y low speed  (high c o n t a c t time, t ) , h>-^ c  g r a d u a l l y changed a c c o r d i n g t o  h  /iTat  -1 c  2 k.  ws  2  d'  k.  N < 10  (2-29)  The^wall l a y e r t h i c k n e s s , d', was o b t a i n e d by e x t r a p o l a t i n g the experimental data from the above equation,  d' = 1.12 x 10~  The values of d' were 1.8 mm  3  /3  and 1.5 mm w i t h 6=2.53 and  1.83 r a d i a n s , r e s p e c t i v e l y i n t h e i r experiments. the dependence of d  1  (2-30)  However  i n equation 2-30 on 3, the c e n t r a l  angle  of the s o l i d s bed,  can not be p h y s i c a l l y  explained.  Recently Lehmberg et a l . (43) i n t r o d u c e d the of the presence of a gas f i l m between the w a l l and s o l i d s i n t o the p e n e t r a t i o n model. gas  f i l m was  a l s o recognized by E p s t e i n and Mathur  In order to f i t t h e i r own  et a l . proposed two The  the  The presence of a  f o r w a l l to bed heat t r a n s f e r i n the annulus of a bed.  concept  experimental  (45) spouted  data Lehmberg  heat t r a n s f e r r e g i o n s near the w a l l .  simple p e n e t r a t i o n model as given i n equation  a p p l i e d i n the r e g i o n between the w a l l and  2-24  was  6 , the t h i c k n e s s  at the c o n t a c t p o i n t between w a l l and p a r t i c l e . of the model i s i l l u s t r a t e d i n F i g u r e 2-7.  The  basis  In the second  r e g i o n , bounded by 6^ and the p a r t i c l e r a d i u s , the gas was  added to the model.  In a d d i t i o n to the f i r s t  6 , they i n t r o d u c e d a second parameter h , 1  film  parameter  (termed the  rela-  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 s the r a t i o of the gas f i l m heat t r a n s f e r c o e f f i c i e n t h_' to the e f f e c t i v e g thermal c o n d u c t i v i t y of s o l i d s , k . The o v e r a l l wall-bed s J  heat t r a n s f e r c o e f f i c i e n t s across these two  regions  was  given i n lengthy form as f o l l o w s :  h  1  +  ws c  c  2 2 exp (h at ) erfc (h' at ) 1  h' /at  T  1  h where h  1  =  k  g s  (2-31)  39  I  9 ^ — i  F i g u r e 2-7  Two-region P e n e t r a t i o n Model f o r Wall-Bed Heat T r a n s f e r Proposed by Lehmberg e t a l . ( 43)  By a d j u s t i n g the values of h was  and .6  1  equation  r e p o r t e d i n good agreement with t h e i r own  data.  6^ was  found  s i z e s of 157,  323,  the gas f i l m  (Vh )  sizes;  equal to 9ym, 794  and  1038  experimental  compared to the  um.  2-31  particle  The mean t h i c k n e s s of  i n c r e a s e s with i n c r e a s i n g p a r t i c l e  1  The parameters, h  1  and 6.  were determined  e x p e r i m e n t a l l y , t h e r e f o r e equation  2-31  f o r w a l l to  bed  heat t r a n s f e r c o e f f i c i e n t i s not r e a d i l y used f o r design purpose.  For long c o n t a c t time,  be a f u n c t i o n of time. f i t the data of Wes  <$ was  a l s o r e p o r t e d to  u  In a d d i t i o n equation  r e p r e s e n t a l l the p u b l i s h e d experimental  not  satisfactorily data, an  attempt  made i n t h i s work to c o r r e l a t e a l l the a v a i l a b l e data  w i t h i n the frame of the p e n e t r a t i o n model. i s d i s c u s s e d i n Chapter 2.5b  can  e t a l . unless h' -> °° (or Vh'-*- 0).  Since no model yet proposed c o u l d  was  2-31  This c o r r e l a t i o n  6.  Convection The  following empirical relationship  h  where G  gw  = 0.0981 G ° ' g  (2-32)  6 7  = gas mass f l u x kg/hr m  i s recommended by P o r t e r e t a l . (46)  2  (cross s e c t i o n k i l n )  f o r the c o n v e c t i v e  t r a n s f e r c o e f f i c i e n t from gas to w a l l i n a r o t a r y k i l n , i s a l s o used to p r e d i c t the gas to bed c o e f f i c i e n t .  heat and  In an  e a r l i e r p u b l i c a t i o n (47) the same authors used an equation with a s m a l l e r exponent on gas mass f l u x , and which i n c l u d e d the e f f e c t o f k i l n  diameter:  h  = 0.0608 G °' /D gw g '  (2-33)  46  A t h i r d e x p r e s s i o n used f o r c o n v e c t i v e heat  transfer  c o e f f i c i e n t i n k i l n s i s a m o d i f i e d N u s s e l t type equation f o r heat t r a n s f e r i n tubes,  h  Gygi  gw  =5.2x10"  2  k D '  V  Du P <_iL-a u g  uC n7Rfi ^L_£g_) -786 k g  .  0  (48) used t h i s e x p r e s s i o n t o c a l c u l a t e c o n v e c t i v e  /->o/i\ (2-34)  heat  t r a n s f e r c o e f f i c i e n t f o r cement k i l n i n the p r e h e a t i n g zone. However, no e x p r e s s i o n has been r e p o r t e d t o e v a l u a t e heat t r a n s f e r c o e f f i c i e n t from the gas t o the s o l i d bed. S e v e r a l i n v e s t i g a t o r s (5, 12) have used equation 2-32 f o r gas to w a l l c o n v e c t i o n t o c a l c u l a t e heat flow from gas t o charge. The area i s taken t o be the chord l e n g t h times the k i l n  length  T h i s c o n v e c t i v e c o e f f i c i e n t i s a p p a r e n t l y independent o f the speed o f r o t a t i o n , p a r t i c l e s i z e , and i n c l i n a t i o n o f the k i l n The equations h = h = 0.023 ^ gs gw D  R  0  e  -  8  P °' r  4  were a l s o used  f o r m o d e l l i n g i r o n ore r e d u c t i o n (9) and h = h = c ( k D)^* gs gw g  0 8 (U /C ) g pg  f o r an alumina k i l n  (6).  In other m o d e l l i n g  s t u d i e s s p e c i f i c v a l u e s were used w i t h no r e p o r t e d j u s t i f i cation including h =22.8 W/m K, h =28.4 W/m K f o r wet ^ gs ' gw ' ' 2  process cement k i l n s ^  (7,8); h = h = 14.0 gs gw  l i g h t weight aggregate  kiln  and 4.9  W/m K f o r a 2  (11); and h =1.5 gs  a r o t a r y k i l n heat exchanger Wes  2  2  2  (15).  e t a l . (42) p u b l i s h e d experimental v a l u e s of 5.1  W/m K f o r w a l l t o a i r heat t r a n s f e r c o e f f i c i e n t i n 2  an empty drum equipped w i t h f l i g h t s , w i t h 550 m  W/m K f o r  a i r mass f l u x , r e s p e c t i v e l y .  and 336  kg/hr  They a l s o r e p o r t e d l o c a l  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 s from potato s t a r c h and y e l l o w d e x t r i n e t o c o o l a i r i n a h o r i z o n t a l r o t a t i n g drum. The r e s u l t s are given i n F i g u r e 2-8.  Wes e t a l . claimed  there might e x i s t a k i n d of p e n e t r a t i o n mechanism f o r the heat t r a n s f e r t o the down f l o w i n g s o l i d s on the s u r f a c e because of a l i n e a r r e l a t i o n s h i p of to  6.5 rpm.  One  n S  g .  between 3 rpm  a  can conclude from the work of Wes e t a l .  that the gas to s o l i d s c o n v e c t i o n c o e f f i c i e n t i s roughly 12 to 2 5 times the magnitude of the gas to w a l l c o n v e c t i o n c o e f f i c i e n t i n a r o t a r y k i l n w i t h low f l i g h t s . Marshall  (49) gave h  g  g  of 26.5  a i r mass r a t e , and of 20.4  and  W/m K a t G 2  38.2  g  Friedman  = 782  W/m K a t G 2  g  and  kg/hr m  2  = 15.60  kg/  hr m . 2  Brimacombe and Watkinson  (4) r e c e n t l y r e p o r t e d  experimental data of 120 t o 240 W/m K f o r gas t o s o l i d s 2  convection c o e f f i c i e n t s . a pilot  The experiments  were conducted  s c a l e f i r e d r o t a r y k i l n , which has 0.406 m I.D.  in and  43  Wes et al. LJ  Wg:  r r CM £  R  Li- \ L U  ^  O  -  Distance from Air Entrance:  150  o or LU u_ CO 2  Q  L U  or < co "~ Q  ^  d  L U  CO  X  s  100 90 80 70 60  g  50 40 30  1  15  2  3  4  1  5  6  ROTATIONAL SPEED N, rpm  Figure  2-8  Convective Feat T r a n s f e r C o e f f i c i e n t Bed to A i r , Data of Wes, e t a l (42)  from  8  5.5  m long.  The gas flow r a t e s ranged  with average throughput  temperature,  675  545  to 820 kg/hr  to 830 K, and the  were 70 to 135 kg/hr.  2  solid  T h e i r data show t h a t heat  t r a n s f e r c o e f f i c i e n t i n c r e a s e s w i t h i n c r e a s i n g gas ture and gas flow r a t e , and the e f f e c t o f s o l i d is  m  tempera-  throughput  insignificant. Chen e t a l . (50) s t u d i e d the e f f e c t of a i r c r o s s  flow on the gas t o p a r t i c l e heat t r a n s f e r i n a r o t a r y d r y e r . The d r y e r was  c o n s t r u c t e d w i t h two  The i n s i d e c y l i n d e r was  concentric cylinders.  o . l 5 m i n diameter  f o r a t e d p l a t e w i t h 1.5 mm  h o l e s , 10 mm  by a screen of 150 mesh.  Hot a i r was  and made of per-  square p i t c h ,  covered  allowed t o flow  the annualar space i n t o the i n s i d e c y l i n d e r .  The  through  heat  t r a n s f e r c o e f f i c i e n t s between gas and p a r t i c l e s were found . to be i n the same range of the data i n the f i x e d 2.5c  bed.  Radiation The  Stefan-Boltzmann  equation has been widely  used  f o r the thermal a n a l y s i s of a r o t a r y k i l n , due t o the l a c k of r e p o r t e d data.  The r a d i a t i v e heat t r a n s f e r  i s s t r o n g l y dependent on the form, Table 2-2  (1\ "*-T_. ) / (T\-Tj ) . k  l i s t s equations used f o r r a d i a n t heat t r a n s f e r by  s e v e r a l i n v e s t i g a t o r s who s i m i l a r t a b l e was temperature 3  were m o d e l l i n g r o t a r y k i l n s .  drawn up by Venkateswaren  dependence of Lyon e t a l . was  2(T^ + T j ) . 3  coefficient  (54).  A  The  s i m p l i f i e d to  These s e t s of equations have d i f f e r e n t  values  of f a c t o r s which are dependent on e m i s s i v i t i e s of gas,  solid  and w a l l .  K a i s e r and Lane (51) have recommended i n Saas  equations t h a t the term fe S  in h  should be r e p l a c e d by  W S / J*T  the e x p r e s s i o n o f E c k e r t and Drake  (52) g i v e n i n Table 2-2  which take's into-account re-radiat'ion •.frombed temperature,  solids.  Luethge  g  T , the s o l g  was used i n the equations shown i n Table  i n s t e a d o f t h e bed s u r f a c e temperature. l a r g e r than T  1  by a few hundred degrees  The l a t t e r may be as i n d i c a t e d by  (53). Since r a d i a t i o n takes p l a c e t o the aerated  charge s u r f a c e , the c a l c u l a t e d value o f h  r  based on the  equations i n Table 2-1 would appear t o overestimate the radiation  contribution.  TABLE 2-2  R a d i a n t Heat T r a n s f e r C o e f f i c i e n t  hgw,r  Investigators  gs,r  ws, r  Saas (12)  pe (T -T )/(T -T ) g g w " g w'  pe (T ^-T ")/(T -T ) 9 9 s 9 s'  Lyons et a l . (7)  2pe e (T +T ) g w s w  2pe e (T +T ) g s g s  h  v  3  Toyama et a l . (11) M** w s £  Manitius et a l . (6)  £  L  3  [  3  l+(l-e J (1-e J 3' g  3  2(>~-  A  p  A  g w T -T g w  L_1+(1-ew )(1-e A  4.96x10  Riffaud et a l . (5)  pe (T "-T ")/(T -T ) 9 9 w g w'  pe g  Wingfield e t a l . (9)  pe (T*-T ")/(T--T ) g s w • g w  Pe (T *-T V(T -T )  1  1  £  s f  e (T +T ) sw w s' 3  3  A T —T £ e„e (1-e )--M S Wv g'A T - T w w s 4  £ e e M sg  4.96xl0~ e f e T "-E (T" )T "1 w ^ g g g w wJ 8  s  z  g  I  (T ' ' - T " ) / ( T  g  g  s "  s  g g  M = 1 - (1-e ) (1-e )' 1 - (e + .e - e e ) w g , s g sg A  *  e. function of e and e 1 s w  < s s*' T  g  )T  -T )  s s  g  ( A i s recommended (47) by substitution of ^ - +  **  ,  e fe T s  s_ T -T 9 s  _9  w  s  3  4.96x10  P  E  ee s w  * ( T ; - T  S  - ) / (  W  pe (T - T ) / (T -T ) s w s ' w s' v  s  (— - 1) 1 ~  s  1  CHAPTER 3 SCOPE OF PRESENT WORK As has been shown above few experimental data on  heat  t r a n s f e r c o e f f i c i e n t s have been p u b l i s h e d f o r c o n v e c t i o n i n rotary k i l n s .  No  s y s t e m a t i c study of the e f f e c t s of  o p e r a t i n g parameters on c o n v e c t i v e heat t r a n s f e r c o u l d be found i n the l i t e r a t u r e . been proposed  Some equations  (46,4 7,48)  have  f o r the c o n v e c t i o n p r o c e s s , but none have had  experimental v e r i f i c a t i o n , and i n c l u d e d e f f e c t s of o p e r a t i n g parameters other than gas I t was  velocity.  the o b j e c t i v e of the present work, t h e r e f o r e ,  to make an experimental study of the i n f l u e n c e of k i l n o p e r a t i n g parameters on c o n v e c t i v e heat t r a n s f e r in a non-fired rotary k i l n . mize r a d i a t i v e e f f e c t s .  coefficients  C o n d i t i o n s were chosen to m i n i -  The parameters t o be s t u d i e d  i n c l u d e d k i l n r o t a t i o n a l speed, i n c l i n a t i o n angle, gas s o l i d charge  feed r a t e , d e g r e e of f i l l ,  veloci  p a r t i c l e s i z e and  tem  perature. In order t o understand  the heat t r a n s f e r p r o c e s s ,  knowledge of the p a r t i c l e motion i n the k i l n i s r e q u i r e d . The secondary  o b j e c t i v e , t h e r e f o r e , was  ship of s o l i d charge  feed r a t e , charge  t o study the load, k i l n  relation  rotational  speed and i n c l i n a t i o n angle, e s p e c i a l l y under c o n d i t i o n s of  uniform bed depth along the k i l n .  I t was a l s o intended t o  i n v e s t i g a t e the f a c t o r s i n f l u e n c i n g the time spend on the s u r f a c e of the bed.  particles  A b r i e f study of r e s i d e n c e  time d i s t r i b u t i o n i n the k i l n was a l s o i n c l u d e d i n t h i s work. With t h i s experimental i n f o r m a t i o n , a model of the c o n v e c t i o n process i n a r o t a r y k i l n was t o be formulated and design equations  presented.  49  CHAPTER 4 APPARATUS AND MATERIALS 4.1  Apparatus A schematic diagram o f the e x p e r i m e n t a l system used  f o r heat t r a n s f e r and p a r t i c l e motion experiments i s shown i n F i g u r e 4-1.  I t c o n s i s t s o f f i v e primary components:  the r o t a r y k i l n , the s o l i d f e e d i n g system, the r e c e i v i n g system, the a i r h e a t i n g system and the i n s t r u m e n t a t i o n and r e c o r d i n g system.  Two k i l n s o f the same s i z e were used.  A l u c i t e c y l i n d e r was p r i m a r i l y used i n the i n v e s t i g a t i o n of p a r t i c l e motion i n the k i l n , and a s t e e l c y l i n d e r was used f o r the heat t r a n s f e r experiments. 4.1a  Kilns The t r a n s p a r e n t l u c i t e r o t a r y c y l i n d e r was 2.44 m i n  l e n g t h , 0.1905 m I.D. and 6.35 mm i n w a l l t h i c k n e s s , and p r o v i d e d w i t h end f l a n g e s o f 0.2 54 m diameter.  The s o l i d s  i n l e t f l a n g e had an opening o f 0.076 m diameter, whereas three d i f f e r e n t f l a n g e s w i t h openings o f 0.133, 0.114 and 0.089 meters were used a t the s o l i d s o u t l e t end t o m a i n t a i n the d e s i r e d bed depths.  During the i n i t i a l experiments  slip  was found between the smooth k i l n w a l l and the s o l i d s bed.  F i g u r e 4-1  Schematic Diagram of Apparatus.  TABLE 4-1 to F i g u r e  4-1  Rotameter End box Temperature  controller  V a r i a b l e speed d r i v e S o l i d r e c e i v i n g cone Screw feeder Chain and sprocket Electric  furnace  Rotary k i l n Funnel and chute Dam S u c t i o n pump Temperature r e c o r d e r Slip  ring  A i r temperature probe S o l i d s bed temperature probe Wall temperature probe 2.54  cm s t e e l pipe  Suction  line  Potential transmitting  line  Eight  equally  surface The  spaced s t r i p s were then glued along the i n t e r i o r  of the  c y l i n d e r , p a r a l l e l to i t s l o n g i t u d i n a l  s t r i p s were 4.80  sat on  mm  s i x metal 0.067 m x 0.10  rubber 0 - r i n g s .  The  The  s t e e l frame which could  The  mm  high.  2.44  the  rotated  on the r o l l e r s  accessories  be  was  speed  supported by  a  a d j u s t e d to a d e s i r e d i n c l i n a t i o n  k i l n used f o r the heat t r a n s f e r experiments  same s i z e as the  The  mm  wall thickness. of the  The  o u t s i d e w a l l was  L/D  tube was  t h i c k l a y e r of r e f r a c t o r y cement, and s o l i d s bed  s t e e l pipe.  was It  l u c i t e c y l i n d e r , 0.1905 m I.D.  i n t e r i o r surface  prevent the  by  horizontal.  m long x 6.35  12.8.  cylinder  m long r o l l e r s , equipped w i t h  c o n s t r u c t e d of seamless, c o l d drawn m i l d was  The  by a h horsepower v a r i a b l e  k i l n w i t h the  angle t o the  3.2  c y l i n d e r was  a f r i c t i o n b e l t driven motor.  wide and  axis.  was  x  r a t i o was  coated w i t h 1  mm  roughened to  from s l i p p i n g d u r i n g r o t a t i o n .  i n s u l a t e d w i t h two  thus  l a y e r s of 3.2  mm  The thick  ceramic paper, then covered w i t h 0.2 08 m diameter, 0.076 m thick f i b e r g l a s s pipe i n s u l a t i o n . i n l e t end  p l a t e was  The  0.076 m diameter.  opening of the Three o u t l e t  with openings of 0.133, 0.114  and  holdups of 6.5%,  respectively.  11%  and  17%,  r o t a t i n g k i l n were sealed meter x 0.2 54 m long end boxes and rotated  on  steel  plates  0.089 m diameter allowed Both ends of  the  w i t h carbon r i n g s i n 0.254 m d i a boxes.  The  construction  carbon r i n g s i s shown i n F i g u r e 4-2. four metal r o l l e r s by  by a h horsepower v a r i a b l e  The  a sprocket and  speed motor.  The  of the kiln  chain  end was  driven  support f o r  the  CARBON  RING  ROTATING  END  F i g u r e 4-2  KILN  BOX  End  Box  and  Seal System  (JO  s t e e l k i l n was the same c o n s t r u c t i o n as t h a t f o r the l u c i t e cylinder. 4.1b  Feeding The  System  f e e d i n g system c o n s i s t e d o f a bulk m a t e r i a l  storage hopper, a screw feeder with a constant and a feed chute.  rate controller,  The f e e d i n g equipment was manufactured  by Mechanical Development C o r p o r a t i o n , Wisconsin, #400 SCR.  The hopper c a p a c i t y was 0.035 m , 3  feed r a t e was 0.142 m /hr. 3  Model  and the maximum  The feed r a t e was c o n t r o l l e d  manually by an a d j u s t a b l e c o n t r o l l e r capable  o f a c h i e v i n g an  accuracy  The c a l i b r a t i o n  o f 1 - 2% f o r most d r y m a t e r i a l s .  of t h i s equipment f o r Ottawa sand and p o l y s t y r e n e i s g i v e n i n the appendix.  The m a t e r i a l d e l i v e r e d by the feeder was  dropped e s s e n t i a l l y i n s t a n t a n e o u s l y  i n t o the r o t a r y k i l n  through a feed chute, which was made o f a f u n n e l and a 4 5 degree 0.013 m diameter copper tube, bent i n t o the end o f the  kiln.  4.1c  Receiving  System  For the heat t r a n s f e r experiments a cone o f about 0.04 m  3  volume was attached t o the d i s c h a r g e  c o n s t r u c t i o n i s shown i n F i g u r e 4-3.  end box.  The  The bottom s i d e of the  d i s c h a r g e box was welded w i t h a 0.102 m diameter s h o r t pipe with a f l a n g e a t the other end o f the p i p e .  The cone was  s e a l e d and clamped t o the d i s c h a r g e  Under t h e average  flange.  s o l i d throughput the cone became f u l l every t h i r t y minutes.  Then the cone was  r e p l a c e d w i t h another empty one.  The  interchange took only a few seconds so t h a t i t would not d i s t u r b the system.  For r e s i d e n c e time d i s t r i b u t i o n  studies,  the c o n i c a l r e c e i v e r s were not used. 4.Id  A i r Heating System An e l e c t r i c furnace was  entered the k i l n . diameter and 0.62  used t o heat a i r b e f o r e i t  The furnace was  c o n s t r u c t e d o f a 0.0635 m  m long s t a i n l e s s s t e e l tube, packed w i t h  0.0177 m ceramic B e r l s a d d l e s .  The tube was heated by  two  s e m i - c y l i n d e r h e a t i n g elements, each having 3.6 kW  capacity.  The system, then, was  i n s u l a t e d i n a 0.30  m x 0.76  long f i r e b r i c k box.  The f u r n a c e was  m x 0.30  c o n t r o l l e d by an o n - o f f  temperature c o n t r o l l e r which had a temperature d e v i a t i o n = 4.1e  m  2K.  Thermocouples Twenty thermocouples were used to measure the tempera-  t u r e s o f s o l i d s bed and a i r at f i v e a x i a l l o c a t i o n s along the k i l n - t h r e e f o r s o l i d s bed and one f o r a i r at each location.  The arrangement  of the thermocouples i s shown  s c h e m a t i c a l l y i n F i g u r e 4-4.  The o r i g i n a l purpose of the  i n s t a l l a t i o n of the three thermocouples f o r s o l i d s bed at one l o c a t i o n was  t o measure r a d i a l temperature d i s t r i b u t i o n  i n the bed. The thermocouples were c o n s t r u c t e d of 3 0 gauge i r o n constantan, and supported by a 0.012 7 m diameter, 2.54 long s t e e l tube.  m  The probes were s i t u a t e d a t the d i s t a n c e s ,  |«0.2I m * | - « — 0 . 5 1 m  » * f * - 0 . 5 3 m—s*|-«*-0.53 m  5 0 8  RECORDER  F i g u r e 4-4  m  m  7 6 . 2 m  m  * * f « — 0 . 5 3 m—*-|  Schematic Diagram of Thermocouples Arrangement  TO  RECORDER  0.21,  0.72,  1.25,  end of the k i l n . the  1.78  and 2.32  meters from the s o l i d  feed  A l l the probe w i r e s were extended through  s u p p o r t i n g tube out o f i t s two ends t o the r e c o r d e r .  The s u p p o r t i n g tube was passed through the c e n t e r of the rotary  kiln. The thermocouples were c a l i b r a t e d i n a white o i l  constant temperature bath up t o 400 K.  They were a l s o  b r a t e d i n f r e e z i n g t i n (504.8 K) and z i n c  cali-  (692.4 K) baths.  The c a l i b r a t i o n data given, i n the appendix showed a maximum d e v i a t i o n of 1.8 K a g a i n s t the ASTM standard t a b l e (55). The a i r temperature probe was  s h i e l d e d , and a i r was  through i t by a pump l o c a t e d o u t s i d e the k i l n . of  sucked  The  construction  the s h i e l d and s u c t i o n system i s shown i n F i g u r e  The d e s i g n of the s h i e l d s u c t i o n thermocouples was  4-5. modified  from the d e s i g n of H i l l s e t a l . (56).  In t h e i r study the  minimum s u c t i o n r a t e f o r the e f f i c i e n t  o p e r a t i o n o f a 1.5  mm  —6 pt  - pt/Rh thermocouple was  r a t e of about 1.5 x 10 for  15 x 10  m /s. 3  m /s 3  at an a i r flow  A s i m i l a r curve was o b t a i n e d  the i r o n - c o n s t a n t a n thermocouples used i n t h i s study. -6 q  The minimum necessary s u c t i o n r a t e was as shown i n F i g u r e 4-6.  m /s,  At a t y p i c a l k i l n o p e r a t i o n i n t h i s  study the s u c t i o n r a t e was through the k i l n .  about 25 x 10  about 0.6%  of the a i r flow r a t e  The w a l l temperatures were measured by  four i r o n - c o n s t a n t a n thermocouples which were i n s t a l l e d on the  k i l n w a l l a t p o s i t i o n s , 0.31 m,  from the s o l i d charge end.  0.91 m,  1.52  m and 2.13  Since t h e . k i l n r o t a t e d i t was  necessary t o c o n s t r u c t commutator r i n g s t o t r a n s m i t the thermocouple p o t e n t i a l s t o a s u i t a b l e measuring d e v i c e .  The  m  f*-*|  6.4 mm  TJM  GAS  SUCTION  THERMOCOUPLE  r-¥-i SUCTION  12.7 m m  BED  g u r e 4-5  Diagram o f S u c t i o n  THERMOCOUPLE  Thermocouple  500i  Q.  JO-  •o-  UJ  QC Z>  <  450  or UJ a. UJ  400 200 SUCTION  gure 4-6  RATE  slO®  m /s 3  T y p i c a l Response of S u c t i o n Thermocouple  c o n s t r u c t i o n of commutator r i n g s i s shown i n F i g u r e 4-7. E i g h t s u i t a b l e r i n g s , 0.254 m O.D.,  made of 6.35 mm  diameter  copper wire, were c o n s t r u c t e d and mounted i n e l e c t r i c a l and t h e r m a l l y i n s u l a t i n g p l a s t i c r i n g s a t t a c h e d t o the k i l n  wall.  Copper s t r i p s were then used t o connect the commutator r i n g and i r o n - c o n s t a n t a n wires t o a m u l t i p o i n t r e c o r d e r .  Cali-  b r a t i o n o f t h i s d e v i c e i n d i c a t e d i t s e r r o r w i t h i n -2 K. The v a r i a t i o n which was noted was b e l i e v e d t o be caused by thermal and e l e c t r i c a l e f f e c t s i n the commutator assembly. Four a d d i t i o n a l thermocouples were i n s t a l l e d i n the i n s u l a t i o n l a y e r a t the same a x i a l l o c a t i o n s as t h e w a l l thermocouples. The thermocouples were l o c a t e d a t 6.35 mm wall.  from the o u t s i d e  The temperature measurements by these thermocouples  permit a c a l c u l a t i o n o f t h e w a l l heat l o s s . 4.2  Materials In the r e s i d e n c e time d i s t r i b u t i o n  (RTD) experiments  t r a n s p a r e n t STYRON p o l y s t y r e n e p a r t i c l e s s u p p l i e d by Dow Chemical of Canada L t d were used.  These p a r t i c l e s are of  e l l i p t i c c y l i n d e r shape w i t h dimensions of 1.9 x 3.1 x 3.6 and apparent d e n s i t y o f 653 kg/m . 3  c o l o r e d by a r e d food dye and thus  mm  T r a c e r p a r t i c l e s were were  not  different in  p h y s i c a l p r o p e r t i e s from the bulk m a t e r i a l . Alumina was used i n a f i l m study of p a r t i c l e and r a d i a l v e l o c i t y .  lateral  To o b t a i n the p a r t i c l e v e l o c i t y an  i n d i v i d u a l p a r t i c l e was i d e n t i f i e d a t a l o c a t i o n i n the k i l n ' s c r o s s s e c t i o n and was t r a c e d f o r a c e r t a i n time.  Thus l a r g e  Figure  4-7  Commutator Copper  Rings  62  particles In  o f opaque a l u m i n a  used.  (average diameter Ottawa sand  The  0.73  i n Table  mm).  10-20  was  since  used  s i z e s were 1.26,  gas  radiation.  radiation  sieved  0.51  mm,  of  and  are  into  given i n Table  p r e h e a t e d a i r was  three  The  motion  study,  throughput i n  negligible.  where c o n v e c t i o n i s used  rather  than  of i t s transparent property to  carbon dioxide,  gas  neglected.  to wall  and  amount o f  gas  to  0.07  Measurement o f m o i s t u r e i n t h e p r e s s u r e of water  W/m K, a f a c t o r 2  than the convective c o e f f i c i e n t s  and  thermodynamic p r o p e r t i e s  58,  59) .  water  solids  o f 0.004  o f the p r e s e n t study, g a s / w a l l  c o e f f i c i e n t s were a b o u t  average  4-1.  the p a r t i c l e t o be  particle  respectively.  Since a i r c o n t a i n s o n l y minimal  the temperatures  less  and  f l o w on  gases because  c a n be  of  used d u r i n g the p a r t i c l e  i n c o m i n g a i r showed a p a r t i a l At  (46, 57)  28-35 mesh.  the heat t r a n s f e r experiments  combustion  and  was  r e p o r t e d (21, 27)  primary i n t e r e s t  vapor  0.73  are a l s o  f l o w was  a r o t a r y k i l n was  of  20-30 mesh  to study the e f f e c t Limestone  t h e e f f e c t o f gas  In  s i z e was  inert  physical properties  mesh, 20-28 mesh and  Physical properties No  The  study  used.  4-2.  s i z e on h e a t t r a n s f e r .  particle  particle  have b e e n r e p o r t e d by o t h e r s  Limestone  sizes,  m i n d i a m e t e r were  the major p a r t o f the h e a t t r a n s f e r  Ottawa s a n d was  listed  o f 6.35  radiation  o f 35 t o 70  measured.  atm.  times  A i r transport  are g i v e n i n the l i t e r a t u r e  (46,  TABLE 4-2 P h y s i c a l P r o p e r t i e s o f Ottawa Sand and Limestone  Ottawa sand  Thermal Bulk  (49, 59)  conductivity  density  Particle  density  S p e c i f i c heat  0.268  W/m K  1650  kg/m  2627  kg/m  0.775  kJ/kg K  at  3 73 K  0. 821  kJ/kg K  at  44 8 K  0.692  W/m K  1680  kg/m  0.914  kJ/kg K  at  373 K  0.966  at  423 K  1.018  at  473 K  3  3  Limestone  Thermal Bulk  c o n d u c t i v i t y (58)  density*  S p e c i f i c heat*  *Measured  3  CHAPTER 5 EXPERIMENTAL PROCEDURE 5.1  R e t e n t i o n Time and  Solid  Throughput  P o l y s t y r e n e p a r t i c l e s were u s e d in  the l u c i t e  cylinder.  cylinder,  In t h e ? l a t t e r  thermocouples Before inclination  were  w h i l e Ottawa sand was  linder  speed.  t h e c y l i n d e r was  The  interval  The  leaving  (1~5 m i n u t e s  continued u n t i l  tube f o r  set at a predetermined  c y l i n d e r was  s o l i d m a t e r i a l was feeder u n t i l  Mass t h r o u g h p u t was  ing the m a t e r i a l  the long  steel  Then t h e end p l a t e s were a t t a c h e d a t t h e  t h r o u g h the screw  reached.  i n the  runs  removed.  b o t h ends o f t h e c y l i n d e r . rotational  throughput  used  r u n s t h e end b o x e s and  starting,  angle.  for solid  rotated  then f e d i n t o  t h e d i s c h a r g e end  a steady state  on  c o n d i t i o n was  cy-  was  and  weigh-  in a definite  flow r a t e ) .  fixed  the  the d e s i r e d holdup  m e a s u r e d by c o l l e c t i n g  depending  at a  time  R o t a t i o n was <  attained.  This  was  a c h i e v e d when t h e c o n s t a n t d i s c h a r g e r a t e became e q u a l t o  the  feed rate  required  from the screw  to reach steady state  To e n s u r e t h a t d e p t h had der.  feeder.  t o be  I f t h e bed  About  30~60 m i n u t e s  i n most c a s e s .  a u n i f o r m bed  d e p t h was  o b t a i n e d the  c o n s t a n t l y m o n i t o r e d a t b o t h ends o f t h e d e p t h was  were  bed  cylin-  n o t u n i f o r m , a d j u s t m e n t s were made  to the feed r a t e .  When the uniform bed depth a t steady s t a t e  c o n d i t i o n was o b t a i n e d , the feeder was terial holdup.  i n the c y l i n d e r was  5.2  ma-  removed, and weighed to determine the  The r e t e n t i o n time was  bed weight by the s o l i d  switched o f f and the  then c a l c u l a t e d by d i v i d i n g the  throughput.  Residence Time D i s t r i b u t i o n P r i o r to i n t r o d u c t i o n of t r a c e r m a t e r i a l steady s t a t e  flow c o n d i t i o n s f o r the uniform bed depth were assured as desc r i b e d i n the p r e v i o u s s e c t i o n . cer p a r t i c l e s was  A known number o f c o l o r e d  i n j e c t e d i n t o the feed chute a t an  arbitrary  zero time and samples were taken as soon as the f i r s t a r r i v e d at the end o f the c y l i n d e r . t r a c e r was  I t was  tracer  assumed t h a t the  i n j e c t e d over a s u f f i c i e n t l y small time  that the i d e a l i z e d impulse s t i m u l u s was  tra-  realized.  interval Separate  samples were taken over t h i r t y seconds i n t e r v a l s u n t i l a l l the t r a c e r m a t e r i a l had d i s c h a r g e d from the k i l n . then stopped and the m a t e r i a l holdup was  The r o t a t i o n  was  determined.  T r a c e r c o n c e n t r a t i o n i n each o f the d i s c h a r g e samples  was  e v a l u a t e d by d i r e c t counting o f the c o l o r e d p a r t i c l e s and weighi n g of the t o t a l sample.  T h i s gave i n f o r m a t i o n on the c o n c e n t r a -  t i o n c ( t ^ ) , at a number of d i s c r e t e times, tj_, i = 1,2, where M denotes the l a s t sampling i n t e r v a l i n which  . . . .M,  tracer  appeared i n the d i s c h a r g e . The r e l a t i o n s h i p s are given below of the mean, t , and 2  v a r i a n c e , a^, of the r e s i d e n c e time d i s t r i b u t i o n f o r the t r a c e r as f u n c t i o n s o f the e x i t age d i s t r i b u t i o n f u n c t i o n E.  Thus,  t  j'  =  tE(t)dt  Q  (5-1)  and .' 2  a  t  =  f"  (t - t) E ( t ) d t  (5-2)  The above e q u a t i o n s c a n be a p p r o x i m a t e d  (30)  f o r the  discrete  system  M t  = I i=l  t.E(t )At  (5-3)  i  and  M  2 a  t  X i=l  ~  (  t  i  2 -  t  )  (5-4)  E(ti)At  where  E(t±)  =  C  (  t  i  }  "S  (5-5)  E c(t )At i=l i  About  1.0  g tracer  was  u s e d i n a 0.08  A b o u z e i d e t a l (30) a t a s o l i d rotational 13.7  g.  i  s p e e d o f 42 rpm.  m x 0.24  m  drum^of  t h r o u g h p u t o f 8.64  kg/hr  In t h i s study the t r a c e r  O n l y one o f t h e r u n s u s e d  115  g of tracer  and  weight  material.  was  The culated  r e l a t i v e v a r i a n c e and P e c l e t  as o u t l i n e d  number were then  cal-  i n Chapter 2:  a"*  2  t _ z. t  (2-17)  and  Pe  T  (2-19)  a,  The dispersion  second equation allowed the c a l c u l a t i o n o f a x i a l c o e f f i c i e n t , n , a c c o r d i n g to  _ uL D ~  Pe  where u i s the average a x i a l v e l o c i t y , u = ^ t 5.3  Surface Time Steady s t a t e  S e c t i o n 5.1.  flow was f i r s t achieved as d e s c r i b e d i n  A l i m i t e d number of c o l o r e d p a r t i c l e s were dropped  i n t o the c y l i n d e r  through the feed chute.  A l e n g t h o f 0.2 m i n  the middle of.the lucite cylinder was chosen as the test- section. c o l o r e d p a r t i c l e reached the t e s t s e c t i o n , started  and the number o f the c y c l e s  When the  the time count was  which t h i s c o l o r e d p a r t i c l e  reappeared on the surface was noted u n t i l i t passed the o t h e r end of the t e s t s e c t i o n .  The above procedure was repeated a t  l e a s t f i v e times and the average value was taken. The average a x i a l d i s t a n c e surface  the p a r t i c l e advanced  on the  f o r each c y c l e was  (5-6)  where  "t "  the  length  the  t o t a l number of c y c l e s i n the s e c t i o n  and the c y c l e time, t  f c  of test  section  , i . e . the time the p a r t i c l e spent f o r  each c y c l e was c a l c u l a t e d by d i v i d i n g the t o t a l time i n the t e s t s e c t i o n by n^_.  To o b t a i n  the s u r f a c e  time t , the time the s  p a r t i c l e r e s i d i n g i n the bed,t^,' must be known and t h i s was ob>  t a i n e d w i t h the f o l l o w i n g equation  t  b  = 3/2Trn  (5-7)  where 6 i s the c e n t r a l angle the s o l i d s bed o c c u p i e d . surface  time, t h e r e f o r e ,  t  s  was o b t a i n e d by  = t  t  - t  b  The p a r t i c l e a x i a l speed on the s u r f a c e was as:  The  (5-8)  calculated  v  a  = d /t a s  (5-9)  T h i s value r e p r e s e n t s the a c t u a l a x i a l speed of the i n d i v i d u a l p a r t i c l e on the s u r f a c e . to  The l a t e r a l speed was  t h a t of the bed width d i v i d e d by t .  Vn  5.4  Heat  5.4a  1 = l .s/ t s  Transfer  Experimental Procedure The k i l n was  first  a d j u s t e d to the d e s i r e d  angle and the c o n i c a l s o l i d r e c e i v e r was charge end.  The a i r system was  switched on and the temperature  d e s i r e d temperature.  a t t a c h e d a t the d i s - •  The k i l n was  The e l e c t r i c furnace  c o n t r o l l e r was  gure 6-9.  The feed r a t e was  s e t at a  allowed to heat up f o r about  3 to 4 hours before r o t a t i o n of the k i l n was f e e d i n g began.  inclination  then turned on and the a i r flow  was measured by a c a l i b r a t e d rotameter. was  equal  s t a r t e d and the  determined a c c o r d i n g to F i -  The temperatures o f the a i r , the bed and the w a l l  were c o n t i n u o u s l y recorded. The c o n i c a l r e c e i v e r was at  50~18  full,  kg/hr s o l i d throughput.  i t was  minutes  J u s t b e f o r e the r e c e i v e r  removed and r e p l a c e d by another empty one.  exchange of the cones was was  f i l l e d up every 15~45  was  The  done w i t h i n a few seconds and there  no f l u c t u a t i o n o f a i r temperature observed i n the measure-  ments.  About one hour was  r e q u i r e d f o r the s o l i d flow to reach  the steady s t a t e c o n d i t i o n .  Then the m a t e r i a l i n the c o n i c a l  r e c e i v e r was emptied and weighed, and the s o l i d d i s c h a r g e r a t e calculated.  The s o l i d flow was assumed to be a t steady s t a t e  i f both the feed r a t e and the d i s c h a r g e r a t e were e q u a l . The r e c o r d i n g s o f the temperature u n t i l the steady c o n d i t i o n s p r e v a i l e d .  r e a d i n g s were continued Then the s u c t i o n pump  was switched on and the r e a d i n g s o f a i r temperature  taken once  the temperatures l e v e l l e d o f f . A complete run u s u a l l y took 5 to 8 hours. 5.4b  Preliminary Tests In e a r l y heat t r a n s f e r t e s t s , the k i l n was i n s u l a t e d w i t h  6.35 mm ceramic i n s u l a t i o n paper, and covered w i t h 3.2 mm  asbes-  tos c l o t h and 25.4 mm t h i c k f i b e r g l a s s i n s u l a t i o n m a t e r i a l . Heat balances on these t e s t s i n d i c a t e d that as much as 50% o f the heat g i v e n up by the a i r was l o s t through the k i l n w a l l . reduce these l a r g e heat l o s s e s from the k i l n ,  To  f i b e r g l a s s was  r e p l a c e d w i t h 0.203 m f i b r e d asbestos p i p e i n s u l a t i o n , 51 mm thick.  The k i l n end boxes and d i s c h a r g e system were a l s o  insu-  lated.  By t h i s procedure the heat l o s s under most o p e r a t i n g  c o n d i t i o n s was reduced t o l e s s than 20% o f the t o t a l heat g i v e n up by the a i r i n p a s s i n g through the k i l n . was i n d i c a t e d by Friedman  A similar  and M a r s h a l l (49) f o r heat  experiments i n a r o t a r y c y l i n d e r .  problem transfer  In a d d i t i o n the heat l o s s was  found to be non-uniform along the k i l n making i n t e r p r e t a t i o n o f the data s u b j e c t t o some e r r o r .  T h i s was due to the presence  of the s p r o c k e t , r o l l e r s and s l i p r i n g s which could not be i n -  sulated.  The commutator was l o c a t e d  from t h e charge end.  The c e n t r a l  between 1.0 2 a n d 1.22 m e t e r  s e c t i o n o f the k i l n  1.25 m a n d 1.78 m was c h o s e n a s t h e t e s t s e c t i o n since the  this section  kiln  ticle  5.4c  of the k i l n  was f a r enough away f r o m t h e two ends o f  t o m i n i m i z e t h e end e f f e c t s o n h e a t t r a n s f e r  motion,  because  between  and d i d n o t s u f f e r  and p a r -  from non-uniform heat  o f the presence o f sprocket,  roller  or s l i p  loss  ring.  O p e r a t i n g Range Table  5-1 shows t h e r a n g e o f o p e r a t i n g  in  t h i s study.  On  an empty k i l n  which i s about  variables  covered  A i r t h r o u g h p u t r a n g e d f r o m 18.6 t o 95 k g / h r . basis  t h e a i r f l u x was f r o m 650 t o 3300 kg/hr-m  i n t h e range o f i n d u s t r i a l k i l n s .  t e m p e r a t u r e was v a r i e d  f r o m 373 K t o 650 K.  The i n l e t a i r  The s o l i d  feed  rate  2  was of  i n t h e r a n g e o f 11~66 k g / h r o r 400~1750 kg/hr-m air/sblid  feed  rate  ranges  Rotational  r a n g e o f 0.9 t o 6.0 rpm.  b e d was a l w a y s  The k i l n  mode a t t h e s e r o t a t i o n a l s p e e d s .  slope of  fill  speeds  was v a r i e d  from  covered a  in. t h e r o l l i n g  One r u n was c a r r i e d o u t a t  w h i c h t h e b e d was i n t h e s l u m p i n g  o f the k i l n  The r a t i o  f r o m 0.5 t o 5 w h i c h compares w i t h  1~2 t y p i c a l f o r i n d u s t r i a l k i l n s .  0.4 rpm d u r i n g  .  state.  The  1.36° t o 4.1° a n d t h e d e g r e e  was s e t i n t h e r a n g e o f 6.5 t o 17% .  Table 5-1  K i l n Operating C o n d i t i o n s  A i r throughput  18.6 - 95 kg/hr  A i r mass v e l o c i t y *  650 - 3300 kg/m hr  Air inlet  373 -  Solids  temperature  used  particle  sizes  s o l i d s throughput s o l i d s mass v e l o c i t y *  2  650 K  wa - sand and limestone 0.51 11  -  - 1.26 mm 50 kg/hr  400 - 1750 kg/hr  R o t a t i o n a l speed  0.9-  Kiln  1.36°-4.1°  slope  percent  fill  2  6 rpm  6.5 - 17%  S u p e r f i c i a l - based on c r o s s - s e c t i o n a l empty k i l n  m  area o f  73  CHAPTER 6 RESULTS AND Particle 6.1  Motion  Type o f Bed Movement Figure  6.1  gives a series  t y p e s o f b e d movement The at  DISCUSSIONS  i n the cross  p h o t o g r a p h s were made u s i n g various rotational  o f photographs  speeds.  section  0.1..  speeds  Showering  above N/N  c  different cylinder.  particles  As shown i n t h e f i g u r e  of particles  = 0.6.  of rotating  a bed o f p o l y s t y r e n e  t y p e o f movement i s s e e n a t a r o t a t i o n a l than  showing  the r o l l i n g  s p e e d o f N/N  less  i s observed a t r o t a t i o n a l  The r e s u l t s  a r e i n agreement  observation  and d e s c r i p t i o n  by R u t g e r s  photographs  f o r the r o l l i n g  t y p e o f p a r t i c l e movement g i v e a  m e a s u r e d v a l u e o f t h e dynamic  (19).  The f i r s t  with the three  a n g l e o f r e p o s e o f 27° f o r p o l y -  styrene .  6.2  Lateral  A film  and R a d i a l  Velocity  s t u d y o f p a r t i c l e movement i n t h e c r o s s  was made.  Alumina  rotational  s p e e d was s e t a t 4.78  at  s p h e r e s o f 6.35  t h e h o l d u p r a t i o o f 26%.  tions  o f two i n d i v i d u a l  was t a k e n on t h e a e r a t e d  mm  d i a m e t e r were u s e d .  rpm, w h i c h  Figure  6-2  gave  The  a r o l l i n g bed  shows t r a c e s o f t h e p o s i -  p a r t i c l e s with time. s u r f a c e about  section  0.06  The f i r s t  particle  m f r o m P o i n t A as  N/N =0.031 c  0.056  0.091  Rolling  N/N =0.135 c  0.387  0.526  Cascading  N/N =0.684 c  0.747 Cataracting  F i g u r e 6-1  Photographs o f Bed Motions  0.808  F i g u r e 6-2  Trace of  Individual Particles  in Kiln U1  shown i n the f i g u r e . of 0.11  I t took 0.4 6 seconds to r o l l a d i s t a n c e  m down the s u r f a c e  r e t u r n e d to the bed.  (at a speed of 0.24  Once i n the bed,  r o t a t e d at the same angular  before  before i t  a d j o i n i n g the w a l l i t  speed as d i d the k i l n .  almost 5 seconds to t r a v e l a d i s t a n c e of 0.23 0.046 m/s)  m/s)  i t returned to the bed  m  It  spent  (at a speed of  surface.  I t stayed  on the top of the s u r f a c e l a y e r s f o r a w h i l e , then entered  a  second l a y e r , i n which i t t r a v e l l e d a t a lower v e l o c i t y than i t did at  i n the f i r s t  layer.  However i t d i d not r e t u r n to the  the same l o c a t i o n as the f i r s t  of p a r t i c l e s decreased 0.107  m/s  from 0.24  i n the second l a y e r .  time. m/s  The  lateral  bed  velocity  i n the f i r s t l a y e r to  Thus i t i s i n t e r e s t i n g to  see  the p a r t i c l e v e l o c i t y p r o f i l e across the s u r f a c e l a y e r s . second p a r t i c l e was  t r a c e d which t r a v e l l e d i n the s u r f a c e l a y e r  near the boundary between the s u r f a c e l a y e r s and seen i n F i g u r e 6-2.  The  v e l o c i t y was  p l o t s both r a d i a l and  f i l e s against k i l n radius p o s i t i o n . r a d i u s along the c e n t e r l i n e , OB, ure 6-3.  There are two  F i g u r e 6-3,  the bed  as  I t took more time to t r a v e l even a s h o r t e r  d i s t a n c e than the f i r s t one. F i g u r e 6-3  A  0.042  m/s.  lateral velocity  pro-  o r d i n a t e i s the  kiln  The  o f the bed as shown i n F i g -  r e g i o n s , e v i d e n t i n F i g u r e 6-2  and i n  the s u r f a c e r e g i o n i n which p a r t i c l e s r o l l down  the i n c l i n e d bed,  and  the bed  r e g i o n where p a r t i c l e s move as  a r i g i d body with the k i l n r o t a t i o n .  The  boundary between  them i s d e f i n e d as the d i v i d i n g l i n e , beyond which the c l e s on both s i d e s move i n o p p o s i t e d i r e c t i o n s . i s shown i n F i g u r e 6-2  and  F i g u r e 6-3,  and  The  parti-  boundary  i s approximated  by  T  RADIAL POSITION , (m )  F i g u r e 6-3  P a r t i c l e V e l o c i t y i n a Rotary  Kiln.  2.5 p a r t i c l e diameters below the s u r f a c e .  The p a r t i c l e  velocities  i n the s u r f a c e r e g i o n and the bed r e g i o n are r e f e r r e d as l a t e r a l v e l o c i t y and r a d i a l v e l o c i t y , r e s p e c t i v e l y .  In the r e g i o n of  s u r f a c e l a y e r s the v e l o c i t y drops s i g n i f i c a n t l y from the aerated s u r f a c e to the boundary.  This i s attributed to "the. internal, f r i c t i o n of  surface layer particles. The f r i c t i o n a l  f o r c e exerted  on the p a r t i c l e  increases  s u b s t a n t i a l l y with the d i s t a n c e down from the aerated  surface.  I n s i d e the bed the p a r t i c l e s move together  bouring  p a r t i c l e s a t the angular  speeds are represented  V  speed.  Their l i n e a r  with  neigh-  radial  by  r  = 2ir-nr  (6-1)  which agrees with the measured speed as given i n F i g u r e 6-3. 6.3  Surface  Time  I t has been p o s t u l a t e d above, t h a t the s u r f a c e time or p a r t i c l e v e l o c i t y on the s u r f a c e p l a y s an important r o l e on heat t r a n s f e r and- chemical  reaction.  Inasmuch as the r e l a t i o n -  s h i p o f r e t e n t i o n time with the o p e r a t i n g parameters i s w e l l e s t a b l i s h e d , i t i s worthwhile to o b t a i n a r e l a t i o n s h i p o f r e t e n t i o n time and s u r f a c e time. A s e t o f experiments using c o l o r e d p o l y s t y r e n e  as t r a c e r s  i n a bed o f the same m a t e r i a l was c a r r i e d out by v i s u a l observ a t i o n using a stopwatch.  The r o t a t i o n a l speed was v a r i e d and  the s o l i d flow r a t e a l s o v a r i e d i n such a way t h a t the holdup r a t i o was maintained constant.  Retention  time and s u r f a c e  time  79  were c a l c u l a t e d  by t h e p r o c e d u r e s d e s c r i b e d  results  i n Figure  plotted  t i m e and s u r f a c e expected v a r i e s rotational It  6-4  show t h e r e l a t i o n s h i p  time t o r o t a t i o n a l -  s p e e d t o t h e power of interest  shows t h e r e p l o t  of  Retention  time  t o know t h e e f f e c t o f time t o r e t e n t i o n  of Figure  6-4  and i n c l u d e s  time.  Figure  the data of  time t o r e t e n t i o n  f o r the r a t i o o f surface  racting The  speed,  t y p e o f bed i n t h e i r  data o f the present  cascading  types o f beds.  rotational  speed r e s u l t s  vidual  particles  surface ure ysis  tional  average v a l u e .  Lateral  of this  The s l o p e s  velocity,  f o r heat t r a n s f e r  and  i s important  by  Fig-  f o r anal-  transfer.  on t h e a e r a t e d  surface  i n Figure  and a x i a l  versus  6-6  rota-  r e p r e s e n t s an  f o r both of l a t e r a l v e l o c i t y  speed i n the l o g - l o g  plot  and a x i a l  a r e about  shows much h i g h e r v a l u e s t h a n a x i a l  However, t h e r a t i o o f V /V  and •  t i m e and  as a t t e s t e d  of l a t e r a l velocity  The l a t e r a l v e l o c i t y  vs. rotation  i n both r o l l i n g  reduces r e t e n t i o n  result  and h e a t  gives a plot  o f the p a r t i c l e s  speed.  velocity  6-6  cyM-ncLer.  f r a c t i o n o f time the i n d i -  length o f the k i l n  of chemical reaction  velocity  V .  i n a higher  The i m p l i c a t i o n  Figure  i n a cata-  As s e e n i n F i g u r e .6,-5 an i n c r e a s e o f  However, i t a l s o  time i n a g i v e n  6-4.  0.09 5 x 0.248 m r o t a r y  s t u d y were o b t a i n e d  a value  time a t a  90 rpm, w h i c h r e s u l t e d  a r e exposed,.to t h e f l u i d  chemical reaction.  to  rotational  of  rotational  retention,  i s proportional  Hogg e t a l c a l c u l a t e d  much h i g h e r  The  t i m e , as  Hogg e t a l (40) f o r c o m p a r i s o n . 0.49  5.  -0.5.  s p e e d on t h e r a t i o o f s u r f a c e 6-5  speed.  as N-*-, w h e r e a s s u r f a c e  i s also  i n Chapter  is little  affected  by  0.5. velocity,  rotational  — i — i  1  1  r  Kiln = 0.19m x 2.44 m Material = Elliptic Polystyrene Degree of Fill = 17.1% Test Section Length = 0.52 m Inclination Angle = 1.58°  400  -  300  \  w  O.  2001  100  \  70 50  •  30| 20  1  5  7  10  ROTATIONAL  F i g u r e 6-4  20  30  SPEED, rpm.  R e t e n t i o n Time and Surface Time versus R o t a t i o n a l Speed.  40  60 50  A  40 '-30  UJ  20 o  UJ  •\— UJ  or \  O  This Experiment  A  Hogg et al (38) ,  UJ  , Nc = 96.9 (rpm) Nc =137 (rpm)  UJ  8 DC ZD CO  .03  .05  .07  J_  0.1  0.2  0.3  0.4  0.5  1.0  N/Nc F i g u r e 6-5  The R a t i o of Surface Time to Rotation Time versus  N/N 00  0.31  " I — I — ' I ' M  0  0.2 0.15 0.1 0.08  E >H O O _J UJ >  0.06  Kiln = 0.19m x 2.44m Material = Elliptic Polystyrene Degree of Fill 17.1 % Inclination Angle = L58° =  0.041  002  o 0.01 G  0.006  i _  5  I  I  7  -L-J.  10  ROTATIONAL  F i g u r e 6-6  20  30  SPEED, rpm.  Surface V e l o c i t y versus R o t a t i o n a l Speed.  50  speed as given i n Table 6- 1. analytical  T h i s i s i n agreement w i t h the  r e s u l t (25),  sine V  a  a-+  (6-2)  iJ;cos(  where 0 i s the dynamic angle of repose, a the angle o f  incli-  n a t i o n and i> the angle between the s u r f a c e of the p a r t i c l e and the c y l i n d e r  axis.  For the present experiments the dynamic angle of repose is  2 7° and a i s 1.5 8°.  16,5 i s o b t a i n e d . given i n Table  By assuming ^ = 0, a value of V /V , J. a  T h i s value i s a l i t t l e higher than the values  6-1.  Equation 6-2 g i v e s the e f f e c t of i n c l i n a t i o n angle, a, on the r a t i o o f j _ / v ' V  a  The i n c l i n a t i o n angle, the angle o f the  k i l n a x i s to the h o r i z o n t a l i s o b v i o u s l y a major f a c t o r f o r a x i a l t r a n s p o r t of p a r t i c l e s , V^. expected  to be  insignificant.  The e f f e c t of a on  is  Table 6-1  R e l a t i o n s h i p of V./V  N (rpm)  V./V 1 a ( - )  5  16.3  6.9  16.0  10  15.1  14  14.5  15.4  13.8  vs. N  85  6.4  Solid  T h r o u g h p u t and  Although a n g l e on  solid  the  Retention  Time  e f f e c t s of r o t a t i o n a l  throughput  speed  and  inclination  were s t u d i e d t h e o r e t i c a l l y  and  experi-  mentally 'in .the' literature,- none-of these studies reported the' effects'.on- s o l i d throughput  i n a s y s t e m i n w h i c h t h e bed  is  uniform  along the k i l n .  be  one  since  o f major i t relates  industrial end  up  to  processes of  fill  kiln 31%  In  influencing  to the was  the  order  be m a i n t a i n e d  t o have 5% The  t o be  to eliminate t h i s  as u n i f o r m  were c a r r i e d  height along  the k i l n  s u r f a c e and  r a d i a n s or about The  0.1  i n F i g u r e s 6-7,  effect  of r o t a t i o n a l  e x t r a p o l a t i o n of the  angle  effect  t h e bed  the  degree  height  and  to determine rotational  c a r e f u l l y monitoring  In a l l e x p e r i m e n t s  the k i l n  picted  of  by  charge  transfer  as p o s s i b l e a l o n g the k i l n .  by  degree.  experimental  throughput  heat  affected  One  a t the  the  The  a x i s was  Ottawa sand  results 8,  and  no  9.  larger was  under these F i g u r e 6-7  than  solids.  to a r o t a t i o n a l The  linear  at  the  \\>, between 0.0014  used.  conditions are illustrates  s p e e d w i t h varying i n c l i n a t i o n line  ex-  bed  depth  the angle,  attempt  throughput  speed.  bed  should  An  out under c o n d i t i o n s o f u n i f o r m  ends o f t h e k i l n .  t h e bed  local  to  processes  transfer.  fill  fill  kiln.  made i n a s e r i e s o f e x p e r i m e n t s  periments  no  (2)  i s thought  transfer  f o r heat  d i s c h a r g e end.  with varying i n c l i n a t i o n  two  the heat  surface area  reported  a t the  degree of f i l l  are t h e r e f o r e expected  along r  was  factors  The  h e i g h t or degree of  speed  of  relationship  angle. zero of the  de-  the The gives through-  1  1  1  1 —  Kiln = 0.19 m x 2.44m Material = Ottawa sand 2 0 - 3 0 mesh Degree of Fill 11% \\f < 0.0014  KILN ROTATIONAL SPEED, rpm. F i g u r e 6-7  E f f e c t of R o t a t i o n a l Speed on S o l i d Throughput i n a Uniform Bed Depth Rotary K i l n .  Kiln = 0.19 x 2.44 m Ottawa sand 2 0 - 3 0 mesh  KILN INCLINATION, degree.  F i g u r e 6-8  E f f e c t of I n c l i n a t i o n Angle on S o l i d Throughput i n a Uniform Bed Depth Rotary K i l n .  SOLID FEED RATE, kg/hr  F i g u r e 6-9  R e l a t i o n s h i p of S o l i d Throughput and Degree o f F i l l i n a "Uniform Bed Depth Rotary K i l n .  put and r o t a t i o n a l  speed i s i n agreement with p r e v i o u s work  (19-21, 24-29, 40, 60-62). creasing rotational p a r t i c l e appearing particulate  I t has been shown above t h a t i n -  speed i n c r e a s e s the frequency.of on the bed s u r f a c e .  the s o l i d  Since a x i a l movement o f  m a t e r i a l takes p l a c e o n l y on the bed s u r f a c e , the  i n c r e a s i n g frequency  o f appearance o f p a r t i c l e on the bed s u r -  face i n c r e a s e s a x i a l movement i n a given time, which i n c r e a s e s axial velocity. velocity  Since the s o l i d throughput i s equal  multiplied  along the k i l n ,  to a x i a l  by the c r o s s s e c t i o n area which i s uniform  the s o l i d throughput c o r r e s p o n d i n g l y  increases  i n a way t h a t i t i s l i n e a r l y p r o p o r t i o n a l t o r o t a t i o n a l The  s o l i d l i n e s i n F i g u r e s 6-7 and 6-8 r e p r e s e n t the  f o l l o w i n g equation  (25)  3 Q = t nD pasin^B  W S  The  speed.  experimental  / sine  (2-16)  6  data are found i n good agreement with the  theory. The  e f f e c t o f i n c l i n a t i o n angle on the s o l i d throughput  i s given i n F i g u r e 6-8.  The l i n e a r i t y o f the r e l a t i o n s h i p  be e x p l a i n e d as f o l l o w s . the a x i a l displacement  I n c r e a s i n g i n c l i n a t i o n angle  increases  o f the p a r t i c l e while i t i s on the s u r f a c e .  I t a l s o means t h a t a x i a l v e l o c i t y Degree o f f i l l  can  increases i n proportion.  i s p l o t t e d a g a i n s t s o l i d throughput i n  F i g u r e 6-9 f o r a uniform  bed-depth k i l n a t v a r i o u s  speeds and i n c l i n a t i o n angles.  In order to operate  rotational a t a higher  degree the  of f i l l ,  the s o l i d  u n i f o r m bed In  p r e v i o u s work was  rotational  speed  fill  other.  might The  determined the  (19-21, 24-29, 40,  determined and  setting  inclination  degree  by r e m o v i n g  done  increased  of f i l l  was  60-62) t h e  end o f t h e k i l n  throughput,  fore  i f one  out of the k i l n volume.  and  Although a  bed w e i g h t of  time  by s o l i d  of f i l l  u n i f o r m bed  kiln  the  an  same h e i g h t .  bed w e i g h t  speed  t i m e was  throughput.  i s inversely  requires  speed,  theoretical of f i l l  was  has  and  feed  of f i l l ,  and  inclina-  The  results  throughput  bed  f o r t h e same  As e x p e c t e d  t o the r o t a t i o n  impact  increase of feed rate As a r e s u l t ,  there i s only  s i m p l y o b t a i n e d by d i v i d i n g  proportional little  rate,  There-  give a c e r t a i n uniform  on  as shown i n F i g u r e 6-11.  to s o l i d  depth i n  operating variables,  degree  a r e g i v e n i n F i g u r e 6-10.  ever degree  fill  independent  angle that w i l l  retention  experiments  tion  dividing  t o t h r e e t h r o u g h e q u a t i o n 2-16.  sets r o t a t i o n a l  inclination The  four  rotational  angle, are reduced  depth.  to the  usually experimentally  the e q u a t i o n f o r the degree  study,  tion  one  degree  complex.  heat t r a n s f e r  solid  solid  I n d o i n g so t h e  By o p e r a t i o n u n d e r c o n d i t i o n s f o r u n i f o r m bed the  to maintain  operating variables,  f r o m one  the k i l n  (29),  two  angle.  the holdup  volume o f h o l d u p by  l e n g t h y and  by  vary s i g n i f i c a n t l y  average  a n a l y s i s was  r a t e must be  depth.  throughput  of  feed  time  Increasing  retenHow-  for a  degree  t i m e , as a r a t i o  constant.  series  speed.  t o m a i n t a i n t h e bed  retention remains  retention  the  the  at of  of  91  o  Iz:  P IxJ  LL!  0.75 h  0.25 h  0  0.4 l/N  F i g u r e 6-10  0.6 .rpm-  1  E f f e c t of R o t a t i o n a l Speed and I n c l i n a t i o n Angle on R e t e n t i o n Time i n a Uniform Bed Depth Rotary K i l n .  O  N =1.5 (rpm)  , a = 1.36°  A  N = 3 0 (rpm)  ,  a = 1.36°  •  N =3.0 (rpm)  ,  a = 2.62°  9.2 •O  14.2 O—  Parameter  = Ws (kg/hr)  18.0  25.2 A  -A-  34.3  19.8  8  12 DEGREE  i g u r e 6-11  51-3  16 OF FILL, (%)  E f f e c t o f Degree of F i l l on R e t e n t i o n Time i n a Uniform Bed Depth Rotary K i l n .  20  6.5  Residence  Time D i s t r i b u t i o n  For m o d e l l i n g o f heat t r a n s f e r and/or chemical  reaction  i n a r o t a r y k i l n i t i s g e n e r a l l y assumed t h a t s o l i d moves i n p l u g flow i n the a x i a l d i r e c t i o n and i s completely mixed i n the radial direction.  The v a l i d i t y of the former assumption  examined by the use o f the a x i a l d i s p e r s i o n model. number was r e p o r t e d l y (30, 31, 38) h i g h enough  can be  The P e c l e t  (above 50) t h a t  the s o l i d flow i n a x i a l d i r e c t i o n can be c o n s i d e r e d as p l u g flow In t h i s study f o u r RTD runs were conducted cylinder.  The impulse  stimulus method was used.  i n the l u c i t e The  experiment  a l c o n d i t i o n s are l i s t e d i n Table 6-2 and the r e s u l t s are g i v e n i n F i g u r e 6-12, p l o t t e d as the F-curve versus time.  The t r a c e r  of 115 g was used i n Run R l whereas about 13.7 g was used i n other runs.  Based on the experimental r e s u l t s the standard  d e v i a t i o n , P e c l e t number and a x i a l d i s p e r s i o n c o e f f i c i e n t were c a l c u l a t e d and a l s o are given i n Table 6-2.  The r e s u l t s  indi-  cate the P e c l e t numbers are i n the range 371 t o 567 and i n c r e a s e w i t h d e c r e a s i n g r o t a t i o n a l speed.  However d e c r e a s i n g r o t a t i o n a l  speed decreases a x i a l d i s p e r s i o n c o e f f i c i e n t . Now  i t i s o f i n t e r e s t t o compare the experimental  data  with t h a t c a l c u l a t e d from the a x i a l d i s p e r s i o n model w i t h the o b t a i n e d P e c l e t numbers. The a x i a l d i s p e r s i o n model was represented by equation 2-15.  Moriyama and Suga (32) s o l v e d t h i s equation w i t h  initial  and boundary c o n d i t i o n s as given i n equations 2-16a, b and d. The l a s t boundary c o n d i t i o n d e s c r i b e s a r o t a r y k i l n  having  Table 6-2 Operating C o n d i t i o n s and C a l c u l a t i o n  Results  of RTD Experiments  Run No.  T r a c e r weight  Rl  R2  R3  R4  0.115  0.0137  0.0138  0.0136  (kg) Bed Weight  8.7  9.4  8.4  9.3  15.6  5.5  4.8  (kg) R o t a t i o n speed  6.87  (rpm) Solid  Throughput  28.7  61. 2  19.8  19. 8  kg/hr Inclination  angle  1.5  1.5  1.5  1.5  7.04  7. 34  5.94  7.24  (degree)  a x Q  Pe  10  + 2  (-)  (-)  D x 10  404 5  (m. /s). 2  ,.r:28  371 2.91  567 0.69  382 0.90  1001  TIME AFTER TRACER FED, min. 8 9 10 II 12  80 g  tt  I  ?  j—  z: O  60  o o  Lul >  &  40  3 O  20  16  17  18  19  20  22  24  26  28  30  J  32  TIME AFTER TRACER FED, min. F i g u r e 6-12  L  34  Cumulative Respon.se Curve i n a Rotary K i l n .  36  96 ^  c o n s t r i c t i o n a t the d i s c h a r g e end more reasonably than 2-16c and  proposed  by Abouzeid  Suga f o r l a r g e Pe  e t a l (30).  ( >50  C(£) =  V  1+5  s o l u t i o n of Moriyama  ) i s given i n equation  1 Peg  5_  The  -  Exp  (1-g) Pe z  6-3.  (6-3)  4£  T  equation  In t h i s equation Pe, the o n l y parameter i n the model, i s determined 6-2.  from the experimental data and  F i g u r e s 6-13,  and equation 6-3.  14, The  i s given i n Table  15 and 16 compare the experimental  data  f i g u r e s show a reasonable agreement, how-  ever the peak c o n c e n t r a t i o n i s underestimated  i n each case.  Since s o l i d t r a n s p o r t through a r o t a r y k i l n can be r e p r e sented by the a x i a l d i s p e r s i o n model, i t i s u s e f u l to i n v e s t i gate the e f f e c t s of k i l n o p e r a t i n g parameters on P e c l e t number D.  or the a x i a l d i s p e r s i o n c o e f f i c i e n t parameters,  e s p e c i a l l y r o t a t i o n a l speed, on  by many i n v e s t i g a t o r s between  D and N/N  i n F i g u r e 6-17, vestigators. N/N  c  The e f f e c t of o p e r a t i n g  c  (19,30-32, 34,  n has been s t u d i e d  36, 62).  The  based on the present experiments  relationship i s shown  along with the experimental r e s u l t s o f other i n -  D i s p l o t t e d a g a i n s t N/N  , i n s t e a d of N, because  i s able to i n d i c a t e the flow p a t t e r n o f p a r t i c l e s i n a  r o t a r y c y l i n d e r , as d e s c r i b e d i n S e c t i o n 2-1. S e c t i o n 2-3  and seen i n F i g u r e 2-4  ment on the r e l a t i o n s h i p between r e s u l t s of Abouzeid,  As d i s c u s s e d i n  there has been l i t t l e D and N.  e t a l (30), Rutgers  The  agree-  experimental  (19) and Sugimoto e t  F i g u r e 6-13  Residence Time D i s t r i b u t i o n  (Pe =  404) vO  0.7  0.8  0.9  1.0  1.1  1.2  1.3  DIMENSIONLESS TIME  F i g u r e 6-14  Residence Time D i s t r i b u t i o n  (Pe =  371)  9L  1.4  DIMEN5I0NLE55 TIME F i g u r e 6-15  Residence Time D i s t r i b u t i o n  (Pe = 567). -o  9L 8L  CX O  <!>  PECLET N0.= ^  7  382  EXPERIMENTAL DflTfl EQURTION  6- 3  0  6  CE  5 LU (_)  4  o  CJ CO CO  o  3 2  I—i  CO LLJ  1  i—i  a  0  0.7  0.8  0.9  1 .3  1.0  1 .4  DIMENSIONLESS TIME F i g u r e 6-16  -Residence Time D i s t r i b u t i o n  (Pe =  382) Cr O  © a x o A v  This work Sugimoto et al Rutgers Morigama 8t Suga Abouzeid, et al Matsui  <=> 3 0 l2  20  10 6 4  <  2  0.6 h 0.01  0.02  0.04  0.07 Ql  0.2  0.4  N/Nc  F i g u r e 6-17  R e l a t i o n s h i p of  D  and N/N  .  0.7  (36-38) i n d i c a t e d t h a t D was  al  p r o p o r t i o n a l to the square  o f r o t a t i o n speed, however those of Matsui and Suga (32) r e p o r t e d D was speed.  The  (34) and Moriyama  d i r e c t l y proportional to r o t a t i o n  r e s u l t of the present experiments agree w i t h  and Moriyama and Suga.  root  Matsui,  The d i s c r e p a n c y i n s l o p e s seems to be  r e l a t e d to d i f f e r e n c e s i n flow regimes of bed p a r t i c l e s .  Figure  6-17  c l e a r l y i n d i c a t e s t h a t D i s d i r e c t l y p r o p o r t i o n a l to N a t  N/N  < 0.1  c  where the r o l l i n g type of bed movement was  whereas f o r the cascading bed, N/N the square  c  > 0.1,  obtained,  D i s p r o p o r t i o n a l to  r o o t of N.  The h i g h P e c l e t numbers o b t a i n e d i n d i c a t e t h a t the  solid  flow can be c o n s i d e r e d as plug flow i n k i l n s of the s i z e used in this  study.  Heat T r a n s f e r 6.6 6.6a  S o l i d and Gas Solid  Temperature  Temperature  The bed temperature i n r a d i a l d i r e c t i o n i s u s u a l l y assumed uniform i n the m o d e l l i n g of a r o t a r y k i l n although s u r f a c e temperature i s l i k e l y to be h i g h e r . t i o n was  confirmed  r a d i a l l y spaced  The  the  former assump-  i n t h i s study by measurements w i t h  thermocouples i n s e r t e d i n t o the bed.  three The  radial  bed temperatures  along the k i l n i n two  s e t s of data are g i v e n  i n F i g u r e 6-18.  Temperatures a t d i f f e r e n t bed depths are w i t h i n  + 2 K, and the bed can be taken as radially isothermal-in the E f f e c t i v e r a d i a l mixing  bulk.  i s a major c o n t r i b u t i o n to u n i -  103  550  Distance A 4.6 O I 6.3 • 29.0  below Bed Surface mm mm mm  Bed Height = 4 3 mm 500  450  400  ©  350  ®  to  30Q 0.5  1.0  1.5  2.0  DISTANCE FROM CHARGE END, m  F i g u r e 6-18  R a d i a l S o l i d Temperature i n the Bed  2.5  104 f o r m i t y o f r a d i a l bed temperatures.  The r a d i a l s o l i d flows  are i n the r o l l i n g p a t t e r n under c o n d i t i o n s t e s t e d .  Heat i s  t r a n s f e r r e d from a i r t o the exposed s u r f a c e l a y e r which i s w e l l mixed when r o l l i n g down to the f o o t o f the bed s u r f a c e .  Immed-  i a t e l y a new f r e s h l a y e r repeats the same phenomena as the previous l a y e r .  With such f a s t turnover o f s o l i d m a t e r i a l and  s h o r t exposure time on the s u r f a c e , the m a t e r i a l appears t o be t h e r m a l l y mixed when i t emerges i n t o the bed.  Thus, a s i n g l e  bed temperature can adequately r e p r e s e n t the s o l i d a t a given a x i a l 6.6b Gas  temperature  position.  Temperature  The c a l c u l a t i o n s o f heat balance and heat t r a n s f e r r e q u i r e the average gas temperature a t a given a x i a l p o s i t i o n .  To de-  termine a t r u e bulk temperature both r a d i a l gas temperature and v e l o c i t y p r o f i l e s would be r e q u i r e d along the k i l n . F i g u r e 6-19 shows a r a d i a l gas temperature p r o f i l e taken a t 1.7 m from the gas entrance u s i n g a p o r t a b l e s h i e l d e d probe. In the absence o f gas v e l o c i t y data, the average gas temperature was c a l c u l a t e d assuming plug flow o f gas u s i n g the f o l l o w i n g equation: T (x) = "I T (x,r) A./EA. g . g. I I  (6-3a  For the p r e s e n t t e s t , the average gas temperature was 409.2 K, compared to the c e n t e r l i n e  gas temperature o f 412.5 K.  If a  v e l o c i t y d i s t r i b u t i o n t h a t accounted f o r the v e l o c i t y decrease near the w a l l were used t o c a l c u l a t e a bulk temperature, the value would be even c l o s e r to the c e n t e r l i n e temperature.  The w a l l and  s o l i d s temperatures are shown as 347K and 376K r e s p e c t i v e l y .  The  105  430 Wg = 5 0 kg/hr 420  -Tg =420.8 K J 3 4 kg/hr ^ Q  410 ^ 4 1 2 . 5  x  O \  K  G  Oil  UJ  or  o_  18.6 kg/hr 390  •o  -o-  LU I -  co <  386.8  —o-  <  1  400  tr LU  , |  Q  Q  \  K  Q  380  370 0  1  10  20  1  30 40 50 60 70 80  90  RADIAL POSITION , mm  F i g u r e 6-19  Average R a d i a l Temperature P r o f i l e  100  106 a p p r o p r i a t e d r i v i n g f o r c e s f o r heat t r a n s f e r are thus AT^ 409.2-347=66.2  K and AT  = 409.2-376=33.2  K.  w  =  Experimental  gs difficulties  p r e c l u d e d the r o u t i n e measurement o f both r a d i a l  arid a x i a l temperatures. the at  Instead the temperature 25.4 mm  from  c e n t e r l i n e was used t o approximate the average temperature a given a x i a l p o s i t i o n .  This w i l l  give a s l i g h t l y l a r g e r  cal-  c u l a t e d AT f o r both g a s / s o l i d s and g a s / w a l l c o e f f i c i e n t s . In the present case the AT -412.5-376=36.5 K, and AT = 412.5-367= gs gw c  65.5 K. ative.  Thus r e p o r t e d heat t r a n s f e r c o e f f i c i e n t s w i l l be conservThe e f f e c t of u s i n g the n e a r - c e n t e r l i n e temperature r a t h e r  than the bulk temperature w i l l be small s i n c e on average and AT  gw  =70 K.  s  s  However a 3K d e v i a t i o n i n T w i l l make c o e f f i c i e n t s g  about 10% low a t low percentage f i l l , where AT^  AT^ ~67K  are about 30-40 K.  and low s o l i d s throughputs  On average the r e p o r t e d  coefficients  w i l l be about 4% low. 6.7 A x i a l Temperature D i s t r i b u t i o n F i g u r e 6-20 i s a t y p i c a l curve o f the a x i a l d i s t r i b u t i o n s found along the k i l n .  temperature  A i r temperatures and sand  temperatures were taken a t f i v e l o c a t i o n s , whereas w a l l temperat u r e s were taken a t four l o c a t i o n s .  The smooth curves along  experimental curves were o b t a i n e d by the use of s p l i n e For  functions.  most runs the sand temperature i s h i g h e r than the w a l l  erature u n t i l  temp-  they approach each o t h e r near the d i s c h a r g e end.  T h i s r e f l e c t s the g r e a t e r r a t e o f heat t r a n s f e r t o the bed than to  the w a l l , and the r e l a t i v e l y h i g h heat l o s s through the w a l l .  In t h i s t y p i c a l run as shown i n F i g u r e 6-20 the temperature p r o f i l e s are not l i n e a r and the temperature d i f f e r e n c e between gas and s o l i d s temperature i s f a i r l y c o n s t a n t along the k i l n a t about 55 K.  The temperature d r i v i n g f o r c e w i l l be reduced t o  107  600 Run No. = A23 Air Flow Rate = 3 4 . 0 kg/hr Sand Feed Rate = 15.0 kg/hr Rotational Speed = I .5 rpm Inclination Angle = I .2 o Holdup = 17.0 %  550h  500  UJ  or  450h  ZD \<  Tg  tr  UJ  o_  400  UJ I -  Ts  A-  350 A^Tw  300h  0.0  0.5  1.0  DISTANCE  F i g u r e 6-20  .Typical  1.5  _L  2.0  FROM SOLID FEED END, m  Axial  P r o f i l e s along a Rotary  Kiln  2.5  108  53 K i f t h e a v e r a g e section fer of  i s used.  coefficient  readings o u t two  gas  temperature.  kiln  temperature  r u n s a t t h e same o p e r a t i n g The  temperature, The  1.5  K for wall  effect  i n Figure  r u n s was  increases T  - T g  6-22.  the heat  flow rate  about  The  temperature —  carried  and  2.5  K  1.0  K for  temperature  a i r entering  The  flowrate.  heat t r a n s f e r  Then an  increase  f r o m gas  t h e same.  The  the  Since Q  were  coefficient  o f gas  to s o l i d s  The  reason  f l o w r a t e as h <*  W^.  flowrate  accordingly i f  W C AT , t h u s AT , g pg g g  s  t h e gas  conditions  for high a i r flowrate  i s a f u n c t i o n o f gas  than u n i t y .  remains  instead  k e p t a t t h e same t e m p e r a t u r e .  as f o l l o w s .  to solids  where n i s l e s s  trans-  temperature  temperature  f o u n d t o be h i g h e r t h a n t h o s e f o r l o w e r  f r o m gas  of  o f a i r f l o w r a t e on  t e m p e r a t u r e s o f a i r , s a n d and w a l l  explained  i s used  d a t a were r e p r o d u c i b l e w i t h i n  i s depicted  f o r t h e s e two  c a n be  increase of heat  shows t h e r e p r o d u c i b i l i t y  days a p a r t .  solids  gas  i n 4%  i n the p r e v i o u s  temperature.  6-21  for  as d i s c u s s e d  only  i f the average  f o r two  distribution  temperature  This results  the c e n t e r l i n e Figure  gas  d r o p , becomes d e p e n d i n g  on gas  flowrate i n  (1 n) —  a form o f w  .  Therefore increasing  gas  flowrate  decrease  g t h e gas  temperature The  effect  the temperature  drop.  of r o t a t i o n a l  profiles  below.  sand  throughput  6-23.  The  for a higher rotational  l o w e r t h a n t h o s e f o r a low  are explained  and  i s given i n Figure  r a t u r e s o f a i r , s a n d and w a l l f o u n d t o be  speed  speed.  As n o t e d i n S e c t i o n  6.4,  These  on  tempespeed  were  effects  i n o r d e r t o main-  109  Run No. A21 Run No. A 23 550  500h  Air Flow Rate Sand Feed Rate Rotational Speed Inclination Angle Degree of Fill  34.0 15.0 1.5 1.2 17.0  kg/hr kg/hr rpm degree %  450 UJ  ce  ZD  400k UJ  a. UJ  350h  300r-  I  0.0  I  I  I  I  0.5  1.0  1.5  2.0  DISTANCE FROM SOLID FEED END, m  Figure  6-21  R e p r o d u c i b i l i t y o f A x i a l Temperature along Rotary K i l n  Profiles  I 2.5  110  1  Air Flow Rate 81 kg/hr  550  Air Flow Rate Sand Throughput Rotational Speed Inclination Angle Degree of Fill  500  *  1  3 4 kg/hr  = 36 = 3.0 =2.0 = 11.0  kg/hr rpm degree %  450  LxJ QC  or  UJ  400  a.  UJ h350  300  0.0  0.5  1.0  1.5  1  2.0  DISTANCE FROM CHARGE END, m  Figure  6-22  E f f e c t o f A i r F l o w R a t e on A x i a l P r o f i l e s along Rotary K i l n  Temperature  2.5  Ill  (  550  Sand Throughput Rotational Speed  15 k g / h r 1.5 rpm  Sand Throughput Rotational Speed  3 4 kg/hr 3.0 rpm  Air Flow Rate Inclination Angle Degree of Fill  500  = 3 4 kg/hr = 1.36 degree = 17 %  450  Ixl  or z>  $  400  DC  IxJ Q.  UJ  350  300  1  0.0  0.5  1.0  L5  DISTANCE FROM CHARGE END ,  Figure  6-23  2.0 m  E f f e c t o f Sand T h r o u g h p u t and R o t a t i o n a l Speed on T e m p e r a t u r e D i s t r i b u t i o n  2.5  t a i n a uniform bed depth along the k i l n , d o u b l i n g r o t a t i o n a l speed r e q u i r e s a double sand f e e d r a t e .  Meanwhile an i n c r e a s e  of r o t a t i o n a l speed i n c r e a s e s the gas to s o l i d s heat t r a n s f e r c o e f f i c i e n t as w i l l be demonstrated i n S e c t i o n 6.10, which r e s u l t s i n an i n c r e a s e i n heat flow from gas t o sands  accordingly.  Since Q « w AT , the gas temperature drop i s expected t o be g q h i g h e r f o r a h i g h e r r o t a t i o n a l speed a t a constant gas f l o w r a t e , W .  Thus the s o l i d temperature i s a l s o expected t o be lower f o r  a h i g h r o t a t i o n a l speed. i n l e t temperature.  F i g u r e 6-24 shows the e f f e c t of a i r  A i r temperature near the d i s c h a r g e end drops  much more q u i c k l y f o r the h i g h i n l e t temperature run than f o r the low temperature run. 6.8  C a l c u l a t i o n Method f o r Heat T r a n s f e r C o e f f i c i e n t The c a l c u l a t i o n o f heat t r a n s f e r c o e f f i c i e n t s was based  on a simple but r e a l i s t i c e q u a t i o n with the f o l l o w i n g 1.  The gas phase i s i n p l u g flow and a t uniform temperature at each a x i a l  2.  assumptions  position.  S i n c e the s o l i d bed temperature i s r a d i a l l y uniform, t h e r e f o r e , the s o l i d temperature i s a f u n c t i o n o f a x i a l distance only.  3.  S o l i d s move i n plug flow.  The w a l l temperature i s taken to be independent o f angle and time.  The e x p e r i m e n t a l r e s u l t s show i n s i g n i f i c a n t  f l u c t u a t i o n s o f w a l l temperature under c o n d i t i o n s used. 4.  The bed s u r f a c e i s assumed f l a t , and i n the c a l c u l a t i o n of gas/bed c o e f f i c i e n t s i t s area i s taken equal t o the  113  600  n  r Run No. AI3 Run No. AI4  550 h  Air Flow Rate = 2 4 . 6 kg/hr Sand Throughput = 2 5 . 0 kg/hr Rotational Speed = 3.0 rpm Inclination Angle = 1.36 degree Degree of Fill  .0  500 UJ  or  ZD -  or  w  450  UJ H  400  350  0.5  1.0  1.5  2.0  DISTANCE FROM CHARGE END , m  F i g u r e 6-24  E f f e c t of A i r I n l e t Temperature on Temperature D i s t r i b u t i o n  2.5  chord  l e n g t h times t h e bed l e n g t h . The  above a s s u m p t i o n s  the k i l n except fall In  from  this  arevalid  t h e zone o f t h e s o l i d  t h e f e e d i n g chute  f o r t h e whole l e n g t h o f i n l e t , where t h e p a r t i c l e  and shower t h r o u g h  r e g i o n the temperature  of the p a r t i c l e s  the a i r stream. rises  rapidly.  From a n e n t h a l p y b a l a n c e t a k e n o v e r a n i n c r e m e n t a l  axial  l e n g t h o f k i l n a s i l l u s t r a t e d i n F i g u r e 6-25, t h e f o l l o w i n g e q u a t i o n s c a n be e a s i l y d e r i v e d : / . 1  Gas  phase  dH  Solid  = <WX>  + q  gw(K)  = ^gs  " sw  (6  '4)  phase  dH  The  second  term  ( x )  q  6  5  i n e q u a t i o n 6-5 i s w r i t t e n w i t h t h e s i g n  a p p r o p r i a t e t o t h e c a s e where T is  <->  ( x )  > T .  g  H i s t h e e n t h a l p y and  d e f i n e d as  H  = W C 9  (T  g pg.  - T  )  (6-6)  gr  g  and  H  s  =  W  s  C P  s  (  T  s - s ' T  r  <-> 6  7  zzzzzzzzzzz  n w » ) f { m u m n  in  GAS  SOLIDS  '//////////.  Tviyi I I 11 I 1 TTTT I  F i g u r e 6-25  Differential  S e c t i o n o f Rotary  Kiln.  f  116  where T g , T r  S  are r e f e r e n c e temperatures  r  respectively  and q r e p r e s e n t s a h e a t  substitution  o f equations  6-5 r e s p e c t i v e l y ,  dH : _ g dx  dH  S  air The defined  C  ^  C  W  dT  -PS- s  The  6-6 and 6-7 i n t o e q u a t i o n s 6-4 a n d  , _„x fi  ( 6  8  )  s  dx~  ( - ) 6  transfer  terms,  V(x)  V(x)  9  q (x), q (x) and q (x) a r e ^gs ^gw ^sw i n terms o f heat t r a n s f e r c o e f f i c i e n t s ,  *sw  With  length.  W dT p g .g _ a dx  P  heat  flow per unit  gives  =  =  f o r gas and s o l i d  =  ( x )  =  h  sw  V V  ( x )  T  g "w  (T  ' s " w)  T  (e- )  }  1 1  < " >  T  6  12  e q u a t i o n s 6-8 t o 6-12, e q u a t i o n s 6-4 a n d 6-5 become  C pg  W g  c\ T g =  dx  ( x ) i (T - T  h  gs  s  g  ( x ) i (T--T, <)  )+h  s'  7  gw  w  s  w'  (6-13)  ps *  C  W  S  d  s — dx  =h  T  ( x ) l (T-T.')-h gs s g s  ( x ) l , (T • -T. ) sw w s w 1  (6-14)  In  these  two  equations,  measurements lated  from  of  spline  h  (x), h  gs  to  the  gas ^  gw  (x)  these  and  the  from  transfer  However,  h  one  must  solid  i s known,  i s calculated  then  to  i s used  wall, q (x) ' ^sw  kiln  three  6-13  unknown  and  sw  (x), the  heat  available  been  i s given  heat  transfer  gas  rate  variables order  solid,  transfer  co-  bed-wall  literature  under  i n the  use  In to  solid  i n the  correlated  6-14.  by  the  next from  and  frame  of  section. gas  to  solid  =  + d  to  (6-i5)  q sw( x ) q w  x  calculate  heat  transfer  rate  from  gas  1  q (x), q ^gs ^gw transfer  the  calcu-  by  V(x)  heat  are  by  a s  i n turn,  are  experimental  dTs -=—  F o r t u n a t e l y the  result  q g s( x )  that,  know h  have  The  from  c o e f f i c i e n t s from  c o e f f i c i e n t s are  Once bed  there  to wall.  data  obtained  i n equations ^  transfer  model.  (x)  (x)  sw  penetration sw  are  dTcj gradients, — — and x d i s t r i b u t i o n along  axial  heat  experimental  h  Ts  temperature  to wall,  efficient heat  the  functions.  evaluate  and  and  T^,  rate  (x) per  =  are  ^  -  local  unit  q  g s  (  x  heat  length of  )  (  transfer kiln  can  rates. be  The  6  -  1  6  )  averag ^  calculated  as  11H  <3gs  )  =  X  l  *  ( g  X  )  d  X  7  2  U  s  " l X  }  (6-17)  and  V  = /X\w(x)dX /  (X  2  " l> X  ( 6  "  1 8 )  The l o g a r i t h m i c mean heat t r a n s f e r c o e f f i c i e n t s f o r gas t o s o l i d s and gas t o w a l l are r e p r e s e n t e d by  h  h  s'  •= q / 1 (T - T-) , gs ^gs ' s g lm  gw  = q / 1 (T - T ) . ^gw w y lm v/w  CT  r e s p e c t i v e l y , where  (  V T s>lm " ( V ^ x z " < g " Vx,; T  In  ( T  g~ s)x2 T  (T -T )  and  (Tg -TV) 'W^x,, - (T g J-T' V ' x•)i v x  (  V T w)lm  In-'  v ±  ? (T -T ) 9  W  g  x  w  x  (6-19)  (6-20)  119  The heat l o s t through the k i l n w a l l to the surroundings can be estimated by the heat conduction equation f o r the i n s u l a t i o n material  , , q-^x) =  where k.: l D^ , n  2 k.(T -T. ) a. v i n In  (D. / D ) m w  (6-21)  thermal c o n d u c t i v i t y of i n s u l a t i o n m a t e r i a l .  Dw ,  J  diameters where temperature  probes f o r w a l l and i n s u l a t i o n  material. - , . . . > . From experimental measurements of w a l l temperature the temperature the w a l l may  and  of i n s u l a t i o n m a t e r i a l the heat l o s s through  be c a l c u l a t e d .  A heat balance over a s e c t i o n of the w a l l y i e l d s  q  The  l  (  x  = V(X)  )  +  s u b t r a c t i o n of e q u a t i o n 6-4  q  sw  ( x )  ( 6  from equation 6-5  "  2 2 )  a l s o g i v e s the  sum of q ix) + q (x) ^gw ^sw x  ^  "  =  q  ^  i  X  )  +  q  S  w  U  )  (  6  "  These two equations are used to check the heat l o s s through the w a l l .  A l o c a l heat balance d e v i a t i o n was  defined:  2  3  )  120  Local  Deviation =  Thus n e g a t i v e the  100  Bed t o W a l l  In o r d e r bed  and w a l l ,  solids  heat  transfer  Although  lost  through  from  the w a l l .  data.  s o l i d s bed t o w a l l o r v i c e  An a t t e m p t  data  f o r wall proposed  represents a l l the p u b l i s h -  was made t o c o r r e l a t e  I.C. and B.C. as g i v e n  6-26..plots  gas t o s o l i d s  i n t h e l i t e r a t u r e , ,.as d e s c r i b e d i n C h a p t e r  k  k  was  (3, 42, 4 3 ) , t o g e t h e r w i t h  =  1 , sw w  g  some e x p e r i m e n t a l  to the f o l l o w i n g dimensionless  h  from  t h e frame o f t h e p e n e t r a t i o n m o d e l .  t i o n model w i t h  Figure  and l o s t  model y e t s a t i s f a c t o r i l y  ed e x p e r i m e n t a l  / q (x)  t h a t more h e a t  transfer  from  transfer  models a r e a v a i l a b l e  within  (x)-q„(x)  1  by t h e s o l i d s  t o evaluate heat  bed heat  2 no p r o p o s e d  (x)+q  Heat T r a n s f e r  v e r s a must be known. to  s  deviations indicated  gas t h a n was g a i n e d  6.9  q  i n equations  penetra-  2-23  leads  equation  2  /nR^32_  ^  s  The s i m p l e  the data  ( 6  _  2 4  ,  a  the p u b l i s h e d data  (3, 42, 43) i n t e r m s o f  nR g 2  versus  •  The c o r r e l a t i o n  i n the f i g u r e  shows  s  a very i n t e r e s t i n g r e s u l t . 3  The N u s s e l t number, h  1 , increases sw w  k  s  A Wachters v Wes  et  & al  Lehmberg 9 o  soda sand  •  m  "•  d«  Kramers  d p = 15 - 1 0 0 et al = 137 v 157 323 794  vm  m  1038  A A A M AA A _ BgBgsCiB B B  o•  30 10*  10'  Figure  6-26  10  10"  6x10  nR ^ 2  C o r r e l a t i o n of S o l i d s Bed-to-Wall Heat T r a n s f e r  Coefficient.  122  2 with i n c r e a s i n g nR B/a a c c o r d i n g to the f o l l o w i n g equation,  h  0.3  1 , sw w' k  nR B 2  =  l  x  -  2 nR I  n  < 10  6  (6-25)  4  s  2 4 At v a l u e s o f nR B/a > 10" the dependence o f h 1 ,/k on ^ sw w* s 2 nR 3/a becomes s t r o n g e r , then -'- i/approaches a l i m i t i n g n  s w  w  c  value which depends on p a r t i c l e s i z e s .  s  The data w i t h coarse 2  4  p a r t i c l e s tend to l e v e l o f f q u i c k l y beyond nR B/a = 10", whereas w i t h f i n e p a r t i c l e s , h 1 ,/k continues t o i n c r e a s e . The ^ sw w s v a l u e s o f h 1 ,/k estimated from equation 6-25 a r e lower than sw w' s ^ 1  those from the simple p e n e t r a t i o n model from-which equation 6-24 i s d e r i v e d .  The negative d e v i a t i o n can be r e a d i l y ex-  p l a i n e d by the presence  o f a gas f i l m near the -wall, as postu-  l a t e d by B o t t e r i l l e t a l (63) f o r the f l u i d i z e d bed, E p s t e i n and Mathur  (4 5)  f o r the spouted bed and Lehmberg e t a l (43)  f o r the r o t a r y k i l n . E r n e s t (64) c a r r i e d out experiments  on moving beds with  d e f i n i t e c o n t a c t time, t , u s i n g p a r t i c l e s i z e s 100 pm - 700 p . A l i m i t i n g value o f heat t r a n s f e r c o e f f i c i e n t between w a l l and bed was found a t very s h o r t c o n t a c t time, t l i m i t i n g value depended on p a r t i c l e s i z e .  < 0.1 second.  The  The c o n t a c t time  bet-  ween the w a l l and the p a r t i c l e s near the w a l l i s approximately of the order o f t e n seconds under c o n d i t i o n s o f t h i s study. 2 3 4 range o f nR B/a i s from 10 to 10 . is  The  T h e r e f o r e equation 6-25  used to c a l c u l a t e the heat t r a n s f e r c o e f f i c i e n t s  f o r the solids  bed and the w a l l . 6.10  Heat T r a n s f e r C o e f f i c i e n t s  6.10a  L o c a l Heat T r a n s f e r C o e f f i c i e n t The l e n g t h of the k i l n taken to be the t e s t s e c t i o n i n  t h i s study i s the c e n t r a l 0.53 of 2.78. = 6.56)  meters which g i v e s a x/D  The t e s t s e c t i o n i s s i t u a t e d between 1.25 from the s o l i d charge end and 0.66  m  m  ratio (L/D  ( L / n = 3.46)  from  the d i s c h a r g e end of the k i l n . The l o c a l heat flow per u n i t l e n g t h from the gas and to the s o l i d s was 6-3  c a l c u l a t e d as d e s c r i b e d i n S e c t i o n 6.8.  Table  shows the r e s u l t s of heat flow d e t e r m i n a t i o n w i t h i n the  t e s t s e c t i o n from a t y p i c a l experiment.  In the t e s t  the gas g i v e s up the o v e r a l l heat of 211.2 73% goes to heat up the s o l i d s .  section  W of which about  The heat flow from the  solids  to the w a l l accounts f o r the one t h i r d of the heat l o s t  through  the w a l l .  -5,9%  The l o c a l heat balance d e v i a t i o n v a r i e s from  towards the charge end to +5.1%  i n the middle of the t e s t sec-  t i o n , then to -12.4% near the hot end.  However the o v e r a l l  heat balance i n the t e s t s e c t i o n d e v i a t e s o n l y -1.4%. high temperature Watkinson  experiment  In t h e i r  i n the p i l o t k i l n , Brimacombe and  (4) r e p o r t e d the l o c a l heat balance d e v i a t i o n of  near the charge end to -20%  near the hot end.  m  he  change i n  d e v i a t i o n , i n t h e i r r e s u l t , from negative to p o s i t i v e  was  thought to be due to the n e g l e c t of downstream r a d i a t i o n . The  l o c a l heat t r a n s f e r c o e f f i c i e n t s from the gas t o  +20%  124  Table 6-3 L o c a l Heat Flows and Heat T r a n s f e r x (m)  1. 25  1. 30  1. 40  Coefficients 1.50  1. 60  1. 71  T  g  (K)  462. 0  464 .3  469 .3  474.6  480. 4  492. 0  T  s  (K)  374. 0  377. 0  384 .1  392.2  400. 9  417. 0  T  w  (K)  369 .2  372. 9  380. 3  388.0  395 .7  410. 5  T  c  (K)  343. 6  346. 1  351. 5  357.7  364 .7  380. 5  57. 2  50. 0  45. 1  50.1  61. 4  77. 9  169 .2  190. 8  226. 5  252.1  267 .3  26 8 .1  226. 4  240. 8  271. 7  302.2  328 .7  345. 9  322. 6  335. 0  361. 5  390.6  422. 2  485. 3  96. 3  94. 1  89. 9  88.4  93. 4  139. 4  153. 6  144. 1  135. 0  138.5  154. 8  217 .3  134. 0  140. 2  150. 7  158.6  162. 2  157  3  5.1  1. 3  -12. 4  25. 9  28 .9  q ^sw q  s  q  g s  q  g  q  g w  c  (W/m) ' (W/m) (W/m) (W/m) (W/m)  3gw 3 w +(  (W/m)  S  q  (W/m)  1  local h  d e v i a t i o n , -5. 9 ( % )  (W/m K) local h (W/m K) 9 local 2  16. 13  -1.. 2% 3 ... 17..  A.  '20 J0  .' 2 300  y  w  2. 53  2. 51  2. 47  2.49  2. 69  4. 1'  the s o l i d s and t o the w a l l were c a l c u l a t e d based on equations 6-10 and 6-11.  The c a l c u l a t i o n r e s u l t s are i n c l u d e d i n Table  6-3 and shown i n F i g u r e 6-27' i n which the l o c a l heat  transfer  c o e f f i c i e n t s are p l o t t e d a g a i n s t x, the d i s t a n c e from the charge end and a g a i n s t the r a t i o o f x/F). h  gs  As shown i n F i g u r e 6-27 both  (x) and h (x) i n c r e a s e as x i n c r e a s e s towards the hot end. gw 2 2  The h ( x ) g s  g r a d u a l l y i n c r e a s e s from 16.1 w/m K t o 28.9 W/m K.  The same t r e n d was a l s o o b t a i n e d hy Brimacombe and Watkinson (4) i n t h e i r p i l o t k i l n .  In a t y p i c a l run o f t h e i r  experiments  the l o c a l heat flow r e c e i v e d by the s o l i d s doubled from one end of the t e s t s e c t i o n to the another end. difference,  (T^-T^) remained  Since the temperature  the same over the t e s t s e c t i o n i n  t h e i r study, the l o c a l heat t r a n s f e r c o e f f i c i e n t s , thus, doubled from one end o f the t e s t s e c t i o n to another end. the i n c r e a s i n g h ( x ) g w  The shape o f  as shown i n F i g u r e 6-26 i s found  consistent  w i t h t h a t f o r hot gas f l o w i n g through a tube near the e n t r y region.  As r e p o r t e d by Rohsenow and Hartnett(65) the l o c a l Nus-  s e l t number i n c r e a s e s s h a r p l y towards the gas e n t r y r e g i o n . Comparisons o f the p r e s e n t r e s u l t s w i t h those i n the l i t e r a t u r e are g i v e n i n s e c t i o n 6-10h. The l o g a r i t h m i c mean heat t r a n s f e r c o e f f i c i e n t s h and gs h gw over the t e s t s e c t i o n are c a l c u l a t e d by r equations 6-19 and 6-20. The v a l u e s o f h and h are 22.4 W/m K and 3.0 W/m'K gs gw ' r e s p e c t i v e l y f o r the t y p i c a l run as g i v e n i n Table 6-3. 2  ?  126  DISTANCE 12 l <NJ  E  FROM  10 i  |  6  8 i  i  ENTRANCE  GAS  X D 0  2  4  1  l  L-  ,  1  1 1  1  1  1  40  -  * H Z Ul  30  —  o  20  —  s  —  —  U_ U.  8 O  y  o r  it! CO  1 0  Test  —  Section  z  /  <  _  5  RUN  AI6  /  /  —  —  / /  —  —  X  < o  —  Q  —  —  Q  > I  i 2  i  1  i  I 6  4  1  1  1  8  1 10  1  1  12  X/D 1  1  0  0.5 DISTANCE  Figure  6-27  1  Local  FROM  1.0 SOLID  Heat T r a n s f e r  1  1 15 CHARGE  ! 2  2 0 END  Coefficient  X  ,  m  127  6.10b  Effect  of A i r  F i g u r e .6-28 on  heat  transfer  tigation,  range  no  on  effect  Watkinson gas  from gas  kiln.  the  The  effect  F. t o  to  solids  average  570  (63)  r a n g i n g 650  of  average  a i r temperature  A i r temperatures,  350  Brimacombe  temperature,  tary  shows  coefficient.  the  and  Temperature  K.  bed  The  heat  reported K  to  830  convective  in this  a i r temperature  transfer a  has  coefficient.  significant  K,  inves-  effect  in a direct-fired  gas-solid  of ro-  coefficients,  in  2 their  results,  are  i n the  range  of  120  to  240  W/m  K.  These  2 values  a r e much  in  present study  the  shows of  h  gs  that are  difference  6-10c  about  was  of  Gas  effect  of  gas-solids  throughput, turn,  an  varied  has  little  the  W/m  K obtained  Figure  effect  on  6-28  also  h  . The v a l u e s gw higher than h . This ^ gw  below.  Flowrate  gas and  flowrate  on  g a s - w a l l was speed  and  i n constant degree  over  18-53  kiln.  order of magnitude •'  rotational  results  the values, non-fired  a i r temperature  Effect  both  for a  i s discussed  The for  higher than  range  of  18.6  heat  transfer  studied  inclination of to  f i l l .  at  coefficients  constant  solids  angle, which,  The  gas  flow  in  rate  95 k g / h r , o r 653 t o 3334  2 kg/hr-m (kiln cross section). The R e y n o l d s number i n t h e g a s phase v a r i e d f r o m 1600 t o 7800. The h e a t t r a n s f e r coefficients, h g s a n d h gw , a r e pf l o t t e d a-ga a i n s t g a s f l o w r a t e i n F i g u r e 6-29. As  expected,  solids  and  raising  gas  the  to wall  gas  heat  flow-rate transfer  increases  both  coefficients.  gas  to  128  30 CM  o  £  v.  •  •  20  10  •  •  o  Wg = 186 kg/hr  •  Ws =36.0 kg/hr  O Wg =24.6 kg/hr  Ws =14.2  kg/hr  A  Ws =25.0  kg/hr  Wg =24.6 kg/hr  10 CM  E  JC  •  •  O  0 350  400  450  500  550  AVERAGE GAS TEMPERATURE,  F i g u r e 6-28  600 K  E f f e c t of Gas Temperature on Heat T r a n s f e r Coefficient  129  1.0  20  40  GAS RATE Wg, F i g u r e 6-29  60 kg/hr  E f f e c t of Gas Flow Rate on Heat T r a n s f e r Coefficient  130  As  was n o t e d  of magnitude h i g h e r  above t h e v a l u e s o f h than  h  a r e about an o r d e r gs The h i g h e r v a l u e s o f h are ^ gs  . gw  attributed to  solids  bed  t o two r e l a t e d heat  surface.  transfer  factors.  i s based  contributing  lateral  direction,  viscous  layer  t h a t would e x i s t  w a l l s , and w o u l d p r e s e n t  heat  transfer.  pictured gas  the thermal  flow  g  g  Any  means t h a t c o u l d r e d u c e  greater  the heat  kiln  interface  on  surface  significant  p a r t i c l e motion i n  the development o f a  e v e n on a r o u g h p l a t e , an even l a r g e r  flow.  this  o r on t h e  surface area f o r  interface i s  bed s i d e ,  then  one on t h e the strong  the major r e s i s t a n c e  r e s i s t a n c e would  A t t h e normal r o t a t i o n a l roll  consists of a r o l l i n g  definitely speed  on t h e s u r f a c e a t s p e e d s  the c i r c u m f e r e n t i a l  create turbulence 6.10d  i s rapid  plane  t h e gas p h a s e t o t h e b e d i s on t h e g a s s i d e .  the p a r t i c l e s  than  The o t h e r  on g a s f l o w r a t e s u g g e s t s  heat  rotary  from  the plane  o f two r e s i s t a n c e s i n s e r i e s ,  for  increase  ; S  and t h e o t h e r on t h e s o l i d  dependence o f h  length of a  r e s i s t a n c e o f t h e gas/bed  as c o n s i s t i n g  side,  hg  which would p r o h i b i t  kiln  If  twice  arrangement.  to higher  f o r t h e gas  surface area o f p a r t i c l e s  b e d c a n be more t h a n  a r e a d e p e n d i n g on p a r t i c l e factor  on t h e c h o r d  However t h e t o t a l  top o f a s t a t i c  ^he c o e f f i c i e n t  speed  of the k i l n .  of the much  Thus, t h e  mass o f p a r t i c l e s w h i c h w o u l d  i n t h e gas phase near  Effect  o f R o t a t i o n a l Speed  Figure  6-30  shows t h e e f f e c t  t h e bed s u r f a c e .  of r o t a t i o n a l  speed  on t h e  131  8 6 in to  m d  J C  Degree of Fill •• A O Ws  A  0.8 0.6  If)  5  CP JC  d  f  6.5% 11.0%  : 5 8 - 66  X  kg/hr  0  0.4  0.2  0.4  J 0.6  I JL 08 I ROTATIONAL  F i g u r e 6-30  2  I 4 SPEED, rpm  E f f e c t o f R o t a t i o n a l Speed on Heat Transfer C o e f f i c i e n t .  l 6  132  heat t r a n s f e r c o e f f i c i e n t s , h and h . The e f f e c t of gs gw 5 7 5 and r a t e i s excluded by d i v i d i n g h and h with W 0 " gs gw g respectively.  gas flow ^ Wo 17^ g  As seen i n the f i g u r e r o t a t i o n a l speed has a s l i g h t l y p o s i t i v e e f f e c t on h , and a s i g n i f i c a n t n e g a t i v e e f f e c t on gs h . The s l i g h t l y p o s i t i v e e f f e c t o f N on h _ can be e x p l a i n e d gw u It gg tr J  as f o l l o w s .  3  When heat i s t r a n s f e r r e d from the gas t o a s t a t i o n -  ary bed, heat f i r s t has t o r e a c h the bed s u r f a c e by c o n v e c t i o n through a gas f i l m and then p e n e t r a t e i n t o the bed by c o n d u c t i o n . 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 t o a s t a t i o n a r y bed can be estimated by the equations (66,67) developed f o r gas f l o w i n g over a rough f l a t p l a t e o r through a rough empty tube. As the k i l n s t a r t s t o r o t a t e a t low speed, the bed slumps as d e s c r i b e d i n Chapter  2 .  In a slumping bed the bed s u r f a c e  remains t r a n q u i l between slumps.  On the t r a n q u i l s u r f a c e heat  i s t r a n s f e r r e d t o t h e exposed burden  s u r f a c e from the gas t o  c r e a t e a t h i n hot l a y e r of p a r t i c u l a t e m a t e r i a l .  When the bur-  den slumps the gas " f i l m " near the bed s u r f a c e i s suddenly a g i t a t e d and the hot s o l i d l a y e r would mix w i t h a l a y e r mass of c o o l e r m a t e r i a l , l e a v i n g a f r e s h top s u r f a c e t o absorb heat d u r i n g the next slump p e r i o d .  m  h e p e r i o d i c f u n c t i o n o f gas  " f i l m " d i s t u r b a n c e and s o l i d mixing c e r t a i n l y i n c r e a s e s the heat t r a n s f e r r a t e from the gas t o the s o l i d bed compared w i t h t h a t i n a s t a t i o n a r y bed.  Under the slumping c o n d i t i o n , the  bed mixing i s then expected t o c o n t r o l the heat uptake by the bed.  F i g u r e 6-31 i l l u s t r a t e s the expected e f f e c t o f N on h _  13 3  F i g u r e 6-31  E f f e c t of FI on h and R o l l i n g B e d s  i n Both Slumping g  w i t h s e v e r a l types of bed movement. ^ J  expected to i n c r e a s e s u b s t a n t i a l l y  The c o e f f i c i e n t h is gs  with i n c r e a s i n g  a speed i s reached where r o l l i n g s t a r t s .  M u n t i l at  Once r o l l i n g begins  the  dominating thermal r e s i s t a n c e i s thought to s h i f t to the  gas  side.  P a r t i c l e l a t e r a l v e l o c i t y on the bed s u r f a c e i s h i g h  enough to convey any heat r e c e i v e d through the gas " f i l m " as described before.  In the r o l l i n g bed an i n c r e a s e o f r o t a t i o n a l  speed i n c r e a s e s the l a t e r a l v e l o c i t y o f s u r f a c e p a r t i c l e as  <* N  as  shown i n F i g u r e 6-6.  Since r o t a t i o n a l  speeds i n t h i s study  range from 1 to 6 rpm, the l a t e r a l v e l o c i t y  i n c r e a s e s by about  2.5 times, which a p p a r e n t l y does not a l t e r the gas s i d e r e s i s t ance markedly.  As a r e s u l t i n c r e a s i n g  rotational  r o l l i n g bed i n c r e a s e s the heat t r a n s f e r  speed i n the  coefficients  from gas  to s o l i d s bed only s l i g h t l y . The on  negative e f f e c t of i n c r e a s i n g  the r o t a t i o n a l  the gas to w a l l c o e f f i c i e n t appeared somewhat  speed  surprising.  However, Cannon (68) r e p o r t e d the same e f f e c t of r o t a t i o n a l speed on c o n v e c t i v e g a s - w a l l beat t r a n s f e r . were c a r r i e d rotating  His experiments  out w i t h a i r f l o w i n g through an 1.52 m long empty  p i p e , 0.0254 m i n diameter.  r e g i o n s of gas flow were i n v e s t i g a t e d . e f f e c t of r o t a t i o n  Laminar and t r a n s i t i o n The most s i g n i f i c a n t  was found to be i n the t r a n s i t i o n  He concluded t h a t pipe r o t a t i o n  region.  tends t o s t a b i l i z e the laminar  flow so t h a t t r a n s i t i o n occurs a t higher Reynolds numbers.  135  This-: w o u l d  suggest that, at constant  R e y n o l d s number), the  increasing rotational  heat t r a n s f e r c o e f f i c i e n t  nolds  number i n gas  o f w h i c h most d a t a not  i n the By  is  fully  6.10e  i n the  are  i n the  turbulent  that of h  Effect  conditions  speed would  transition  phase v a r i e d from  1600  range of  to  (same  decrease  region.  Rey-  7800 i n t h i s  2000 t o  study,  4000 w h i c h i s  region.  r e g r e s s i o n a n a l y s i s the  0.091, and  flow  /w gw' g  o f Degree o f  0 , 4 7 5  slope of vs. N  n  0.575 g /^g*  -  v s  S  N  i s -0.297.  Fill  The  e f f e c t s o f d e g r e e o f f i l l on h and h are qiven ^ gs gw 0 575 0 091 i n F i g u r e 6-32. The.ordinate are h /W ' N and h / ^ gs' g gw 0475—0297 W ' M " w h i c h e x c l u d e t h e e f f e c t s o f gas f l o v ; r a t e and g J  rotational very  speed.  slightly  as  independent of The follows. of heat  I t appears i n the the  the  degree of  negative  effect  J  As  described  from the  comprising  degree of  two  gas  p a r t i c l e s w h i c h mix  with  will  remain This  bed  gs  particles i n t o the  until  they  can  h^  w  is  be  explained  as  bed,  be  the  transfer  thought of  t r a n s f e r r e d to the  of other bed.  The  surface mixed  emerge a g a i n  ratio  o f bed  on  surface  as surface  layers  the  bed  sur-  t o bed  vol-  i s an  bed  s u r f a c e a v a i l a b l e f o r gas-bed heat t r a n s f e r i n c r e a s e s s i z e of k i l n  as  the  be-  particles  ume  a given  f a c t o r i n the  can  rolling  s o l i d s bed  suggests t h a t the  important  h  Heat i s f i r s t  the m i x t u r e r e t u r n s  face.  n on  above, i n t h e  fore  i n the  increases while  decreases  s  fill.  of  to the  steps.  fill  figure that h^  heat t r a n s f e r process.  holdup i n c r e a s e s according  to  The at  6.0 o d  z  5.0  —  4.0  —  10  8 . 30  —  Gas to Solid Bed o o o  18.6 ~ 95.5 kg/hr. 0.9 ~ 6.0 rpm I. 4 ^ 4.|°  N  a  Ws  II. 3 — 66.3  2.0 Gas to Wall  o  OJ  i  d  en  1.0 0.9 0.8 0.7 0.6  8  o  8  8  0.4 0.3  12  18  DEGREE OF F I L L , % F i g u r e 6-32  E f f e c t o f Degree of . F i l l on Heat T r a n s f e r  Coefficient.  kg/hr  137  A a  0. 27  0.04 < n < 0.30  n  however, the r a t i o of bed s u r f a c e to bed volume decreases s i g n i f i c a n t l y as  Bed s u r f a c e  _ -.^ n  U• /J  QC  Bed volume  Although the heat t r a n s f e r r a t e , q g , i s d i r e c t l y proS  p o r t i o n a l t o the bed s u r f a c e area, experimental data i n Table 6-4 for'  v a r i o u s degrees o f f i l l  a t the same o p e r a t i n g c o n d i t i o n s  show a much weaker dependence of q temperature in  differences,  these t h r e e runs.  (T  -  T s  )  l m  g g  "/  on A . g  In a d d i t i o n , the  were found about the same  Thus, the heat t r a n s f e r  coefficients,  according to  h  q —!S«. -gs A AT, s lm  have a s l i g h t l y n e g a t i v e dependence on the degree of f i l l . slope o f hg /W * ^^^N^" ^9''" S  g  The  v s . n i n the l o g - l o g p l o t as shown i n  F i g u r e 6-32 i s -0.171. It  i s expected t h a t the gas to w a l l heat t r a n s f e r c o e f -  f i c i e n t s are independent o f the degree o f f i l l , 6.10f  E f f e c t o f . S o l i d Throughput  and I n c l i n a t i o n  e oo F i g u r e 6-33 p l o4.t s the 4-term, uh n  Angle  0. 0. 091 /W ^ 575 -0 n .171 N  /r7  a g a i n s t s o l i d s throughput w i t h i n c l i n a t i o n angle as parameter,  Table 6-4 E f f e c t o f Degree o f F i l l on Heat T r a n s f e r Rate and Bed Surface  n, % A (m ) 2  s  q  A36  17  11  0.084  0.075  A47 6.5 0.065  165  150  147  A T ( K)  65  63  66  h„„  30.2  31.7  34.4  gt> r T C  (W)  A22  l m  W  g  34 ~ 36 kg/hr  N  3 rpm  W  34 ~ 36 kg/hr  139  inclination Angle  8.0  A 1.36° O 2.6° • 4.1°  6.0 o  4.0  m m en  • •  __  2.0  10  20  40 Ws ,  F i g u r e 6-33  60  80  kg/hr  F f f e c t s of S o l i d Throughput and I n c l i n a t i o n Angle on G a s - S o l i d s Bed Heat T r a n s f e r Coefficient  0 ^75 -0 297 w h i l e the p l o t o f  n g w  /  w  g i v e n i n F i g u r e 6-34.  g  "~  N  " '  v s . s o l i d throughput i s  The r e s u l t s o f r e g r e s s i o n a n a l y s i s  show  that both s o l i d throughput and i n c l i n a t i o n angle have i n s i g n i cant e f f e c t s on h „ and h gs gw  In a r o l l i n g bed, i n c l i n a t i o n ' 3  angle would be expected to have no e f f e c t on heat S o l i d p a r t i c l e s move through a r o t a r y  transfer.  k i l n as a r e s u l t of cont-  inuous a x i a l movements o f p a r t i c l e s on the bed s u r f a c e .  Axial  v e l o c i t y o f p a r t i c l e s i s about one order o f magnitude l e s s  that  l a t e r a l v e l o c i t y as seen i n F i g u r e 6-6 when p a r t i c l e s r o l l on the  bed surface,.  transfer  The e f f e c t o f t h i s slow a x i a l movement on heat  i s negligible  compared w i t h r a p i d  of p a r t i c l e s , which are caused by the k i l n s The r e g r e s s i o n a n a l y s i s for gas-solids  l a t e r a l movements rotation.  l e a d s t o the f o l l o w i n g  heat t r a n s f e r , h = 2.44 W 0.575 -0.171 0.091 gs g n  N  equations  ( 6  _  2 6 )  and f o r gas t o w a l l ,  h gw = 0.822 Wg ° '  6.10g  E f f e c t of P a r t i c l e  4 7 5  N  0  ,  2  9  (6-27)  7  Size  Limestone w i t h t h r e e d i f f e r e n t p a r t i c l e s i z e s was used to study the e f f e c t o f p a r t i c l e s i z e .  The t h r e e s i z e s  used  were 10-20, 20-38 and 28-35 T y l e r mesh which corresponds to  141  1 — r  Inclination A O  V  Angle 1.36° 2.6° 4.1 °  2.0 CM  b i sz  m  b  1.0 0.8 o o o  0.6 0.4  0.251  10  20  30  40  60  100  Ws , kg/hr  F i g u r e 6-34  E f f e c t of S o l i d Throughput and I n c l i n a t i o n Angle on Gas-Wall Heat T r a n s f e r C o e f f i c i e n t  average Three  particle  s i z e s o f 1.26,  runs o f experiments  ferent a i r flow rates, ments were c a r r i e d conditions.  0.72 and 0.51 mm,  were c a r r i e d  18.6 k g / h r  o u t f o r e a c h o f two d i f -  and 34.0 k g / h r .  out a t temperatures  During  the experiments  r a t e was o r i g i n a l l y  The e x p e r i -  much below  calcining  a l a r g e amount o f f i n e  was c r e a t e d when l i m e s t o n e was f e d i n t o feed  respectively.  the k i l n .  s e t a t 34 k g / h r ,  The s o l i d  however t h e s o l i d  p u t a t d i s c h a r g e e n d was m e a s u r e d o n l y 24-27 k g / h r . accounts  f o r 20-30% o f f e e d r a t e .  mediately  carried  the e f f e c t  away when l i m e s t o n e d r o p p e d  ficant  as seen  of particle  i n Table  may be t h e r e a s o n  s i z e on h e a t  6-5.  effect  on h e a t  particle  size  f o r the i n s i g n i f i c a n t  by a f a c t o r lence actual heat  (h = 20 W/m p  temperature one  second  within  2  K, k  s  the p a r t i c l e s  o f exposure  Heat t r a n s f e r  t o heat  effect.  reported  little  calciner  further  significant  over size  turbu-  increase i n  surface area a v a i l a b l e f o r The B i o t numbers f o r  are very small,  = 0.692 W/m  of p a r t i c l e s  Change i n p a r t i c l e  i n a closed-packed array.  the t h r e e s i z e s o f p a r t i c l e s  i s insigni-  size  kiln  generates  nor produces  surface area per plane chord  transfer  0.015  (69) have a l s o  o f 2.5 a p p a r e n t l y n e i t h e r  t h e bed from  range  particle  o f 0.75 t o 2.65 mm.  i n t h e gas " f i l m " ,  into  transfer  flow to limestone i n a rotary range  The d u s t  Over t h e r a n g e c o -  The n a r r o w s i z e  However Brimacombe and W a t k i n s o n  out-  Most o f t h i s d u s t was i m -  t h e c h u t e and t h e n d i d n o t e n t e r t h e k i l n . vered,  dust  0.036,  0,021 a n d  2  K assumed), t h e r e f o r e t h e  becomes u n i f o r m a f t e r  about  transfer.  coefficients  from  a i r t o t h e l i m e s t o n e bed  143  Table  6-5  Gas to S o l i d s Heat T r a n s f e r C o e f f i c i e n t  Ottawa Sand  -  d  (mm)  0.7 3  Limestone 1.26  0.73  0.5  P W  g  (kg/hr)  18.6  20.6-21.6 *  28.9  23.7  22.4  34  30.6-34.6  34.1  34.7  31.4  W  (limestone)  24.4 - 2 7  kg/hr  W  (Ottawa Sand)  34  kg/hr  g  s  N : *  3 rpm  W/m K 2  -36  are  about the same as the case o f Ottawa sand.  6.10h  Comparison w i t h P r e v i o u s Work A comparison was made o f the e x p e r i m e n t a l d a t a i n the  p r e s e n t study on the e f f e c t o f gas f l o w r a t e w i t h two equations recommended i n P e r r y ' s Chemical E n g i n e e r i n g  h = 0.0981 G g  0  and  6  7  h = 0.0608 G ° '  4 6  g  G of  ,  Handbook:  (2-32)  /D  (2-33)  r e p r e s e n t s t h e gas f l o w r a t e p e r c r o s s s e c t i o n  g  the k i l n .  Equations  2-32 and 2-33 a r e p l o t t e d  6-35 w i t h t h e e x p e r i m e n t a l d a t a o b t a i n e d i n t h i s cluded (49) no  i n a rotary  f l i g h t s were  dryer.  >  used.  heat  transfer  Equation  coefficients  2-32 was g i v e n b a s e d  h i g h temperature transfer point  from  the w a l l - f i l m  p r e d i c t e d by e q u a t i o n s  heat  equations transfer,  s o l i d s bed.  resistance  approaches  forh  on t h e assumption  In f a c t ,  s  the wall  and  that at  and t h a t  heat a t any  temperature.  2-32 a n d 2-33 were recommended these  g  to convection  t h e gas t o t h e w a l l i s l i m i t i n g  t h e bed temperature  Although wall  study.- I n -  The d a t a were f o r t h e c o n d i t i o n s t h a t  2-32 and 2-33 l i e between t h e e x p e r i m e n t a l d a t a g w  i n Figure  i n F i g u r e 6-35 a r e t h e d a t a o f F r i e d m a n a n d M a r s h a l l  The  h  area  f o r gas t o  e q u a t i o n s have been u s e d  t h e p r e s e n t work shows t h a t h  f o r gas t o  g  g  i s about  F i g u r e 6-35  Comparison o f Experimental Data on Heat T r a n s f e r  Coefficients.  one  order  Although is  o f magnitude hg  W  shows more  t h e same a s t h a t  Figure air of  higher  scatter  L/D o f t h e t u b e  h  w  S  data  a t temperature  kiln  o f 0.19 m I D (G  = 1200 k g / h r - m ) ,  results  i n a gas-to-wall  1.7  W/m  K according  calculated  ever,  lower  Figure the  than  6-35.  short  compared  of h  i -  gw  s  with  three  runs  were  g w  ,  tube  section  ( L / D = 60) u s e d  effect  carried  three  i nthis  o f 0.53 m l o n g ,  runs,  flow  rates  for thetest  the transition  4140.  runs  region with  The t r a n s i t i o n  used  i n this  This  as,  may r e s u l t  how-  empty  work were  0.66 m f r o m  study  Reynolds  trans 6-6  the data  drum.  calculated  The over  the gas entry end. thedistance o f The a i r  a n d Wes e t a l w e r e  number,  f l o w may c o m p l i c a t e  Table  with  t h e end o f t h e k i l n .  of this  from  i n the kiln,  kiln.  together  was l o c a t e d b e t w e e n  = 3.47 a n d x/D =6.25 f r o m  x/D  in  coefficients  section  a n empty  length on heat  o u t i n t h e empty  transfer  thetest  an a i r  by K r e i t h .  of the short  heat  Thus,  f o r  K, a s g i v e n i n  ( L / D =2.8)  Wes, e t a l f o r a 0.6-m-ID, 9 . 0 - m - l o n g  section  case  o f magnitude  values  from  test  tube.  coefficient  2~4.7 W/m  experimental  shows t h e r e s u l t s f r o m t h e s e  a  w  2  The h i g h e r  rationalize the  transfer  t h e same o r d e r  the experimental h  the long  the size  g  The r a t i o  6-36 (Nu = 10, Re = 2900).  to Figure  length of the test  To fer  value  heat  (55)  tube.  400 K t h r o u g h 2  2  by K r e i t h  In a t y p i c a l  r a t e o f 34 k g / h r  of h  a non-rotating  1.52-m-long  w a s 60.  i n F i g u r e 6-35.  t h emagnitude  through  flow  study,  a s seen  hg '  transfer  a 25.4-mm-ID, he used  g  than  for a i r flowing  6-36 d e p i c t s t h e h e a t  flowing through  than  ranging from  2160  the explanation of  3.0xl0  2  5  7  i  o  5  2  3  4  5 6 7 8  I0  2  4  Re F i g u r e 6-36  Gas-to-Wall Heat T r a n s f e r C o e f f i c i e n t Empty K i l n  i n an  3  Table 6-6  Comparison o f A i r - W a l l Heat T r a n s f e r C o e f f i c i e n t s i n Empty K i l n s  W  T h i s work***  Wes e t a l * *  G  kg/hr  kg/hr-m'  34.0  Re  Nu  gw  Nu gw  ( - )  W/m K  1193  2647  5.40  ( - ) 32,2  34.0  1193  2980  5,66  50.5  1772  4140  2  f  ( - )  Nu  gw  Nu,  8.2  3.9  34 .2  10.2  3.4  6,67  39.8  15.0  2.7  95.0  336. 3  2160  4.9 '  80.1  5.5  14.6  155.0  548 . 5  3520  5.1  83.4  12.5  6.7  Taken from K r e i t h (58) f o r a i r flowing through a 25.4-mm-IP, 1.52-m-long heated tube  (L/D = 60)  For a 0.6-m-ID, 9-m-long empty drum  (L/D = 15)  For a t e s t s e c t i o n o f 0.53-m-long  00  the  effect  fer  coefficients  this  of the entry  study, because  NUj  i n Table from  found  about  number the  of larger 6-6  2.7  i s mainly  thermal  constant  heat  flow  this  (Re  study  6-37.  This  value  of kiln  times  falls  Nu^.  effect.  number entry  of length.  The t e s t  b e t w e e n x/D  numbers  =  e t a l and  Nusselt  num-  The v a l u e s  in this  The r e a s o n  Nusselt  and hydrodynamic  = 2100).  higher  trans-  of  f o r a fully-developed flow  due t o t h e e n t r a n c e  rate per unit  heat  f o r Wes,  diameter.  The N u s s e l t  of the l o c a l  combined  t h e same  e t a l h a d t h e much  6-36.  t o 3.9  The g a s t o w a l l  about  are considered  Figure  variation  nar  found  h o w e v e r Wes  ber  taken  were  section.  section 3.47  Figure  The c u r v e  gives  an average  Nusselt  i s 2.6  times  the Nusselt  number,  i n a tube.  This  plots  i n the tube  with  i s f o r lami-  of the k i l n  region  were  higher  6-37  x/D  region of a  a n d 6.25  study  for this  versus  and  shown number  used  in  i n Figure of  11.3  2 W/m  K which  the  fully-developed flow  Nu  /Nu, i s f o r t h e l a m i n a r f .  gw  the  same  flow  Nu  f  number,  =  4.36, 2.6,  h o w e v e r , i t may w e l l -  multiple exists, f o r the transition  flow.  for  of b e t h a t «-  X/D  "Figure  6-37  V a r i a t i o n of L o c a l N u s s e l t Number i n Thermal Entry Region o f a Tube w i t h Constant Heat Rate Per U n i t of Length (65)  151  6.11  C o r r e l a t i o n of Heat T r a n s f e r Cannon  (68) s t u d i e d  the heat t r a n s f e r from f l u i d flow-  i n g through a r o t a t i n g p i p e . fer  Coefficients  In h i s a n a l y s i s the heat  c o e f f i c i e n t i s a f u n c t i o n of the v a r i a b l e s l i s t e d  following  transi n the  equation  h = f  l  ( a,, - L, u , g  y , g  p , C , g  D,  p g  k ) g  Dimensional a n a l y s i s of t h i s group of v a r i a b l e s  Nu = f2  2 = D Wp /y  where Re  y  (Re, Re , w  L/D,  yields  Pr)  , the r o t a t i o n a l Reynolds  number.  y  In a r o t a r y k i l n heat t r a n s f e r i s more complicated than t h a t i n an empty tube.  The heat t r a n s f e r c o e f f i c i e n t i s expected  to depend on the f o l l o w i n g h  =  f  (D,  3  L,  N,  W, g  y  g f  group of v a r i a b l e s C ,  k ,  p g  g  p , g  W, s  d , p  k , s  C  p s  ,p ,n,a) s  Dimensional a n a l y s i s leads to the f o l l o w i n g e q u a t i o n , 2 hD _ jr / D p.t* VI L C y _® - *l_B. _2 > __r Pg 9, k V D y D k g g eg fl  g  where D  g  i s the e q u i v a l e n t  diameter  W k p • C \ n , a , _ s , _ s , l s , _^s \ _ W k C g g g p g ( 6  p  2 8 )  152  4A-- ."  _  D  ..  , , 2TT- 3 + sin 3  -  cross section  H (  g  Wetted P e r i m e t e r  e  S i n c e o n l y one of  variables  fluid  slightly different ^ 2  experiments,  are o f major  ( a i r ) and  pg be  neglected i n equation  were c a r r i e d that  W  out  and  g  equation  6-28  Nu  tion  i s applicable  6-30  a ,  l f  2  a • 3  interest  and  single on  1  K  p /p s g  size,  heat  a 2  o  a  Q  of  = a Re . Re>  where a ,  s i n | -  in this  (Ottawa sand  and  the  and  C  i n the  /C ps  can pg  experiments  the r e s u l t s  show  Therefore  6-30.  (6-30)  a 3 T 1  are c o e f f i c i e n t s to both  study.  limestone)  were u s e d  transfer.  to equation  a  g  In a d d i t i o n ,  effects  i s simplied  (6-29)  u /k , k /k , p / p ' and g g s g s g  6-28.  in a kiln  a have no  solids  k /k. , C /C s g ps pg  the terms, C  .  y +  TT-  Operating  .  j  t o be  gas-solid  determined.  and  gas-wall  Equaheat  transfer. Multiple  linear  experimental  data.  tion  to s o l i d  f o r gas  In Nu  that  gs  r e g r e s s i o n was  The  data  of  N  u  g  S  used  to c o r r e l a t e  y i e l d the  following  the equa-  bed,  = -0.777+0.535.'lnRe+0.104 InRe -0.341 l n a) •  n  (6-31)  is  Nu  gs  n ACT, 0.535,, •= 0.46Re Re  ui  0.104  n  -0.341  (6-32)  153  "The Table  6-7.  data with bed  heat  result  of regression analysis  F i g u r e 6-38 calculations  shows t h e c o m p a r i s o n o f t h e e x p e r i m e n t a l based  on e q u a t i o n  same p r o c e d u r e  was c a r r i e d  o f g a s - t o - w a l l N u s s e l t number.  Nu  , _ 0.575 _ 1.54 Re Re  gw  regression analysis  The  degree o f f i l l  The  comparison o f the experimental  the  The d a t a  i s not s u r p r i s i n g transition  out f o r the c o r r e l a t i o n equation i s  -0.292  ,, (6-33)  6-33  i s given i n Table  f o r a 95% c o n f i d e n c e data with equation  for  N  u  g  f o r experiments  W  6-8.  limit.  6-33 i s  i s relatively scattered. i n a flow range c o v e r i n g  region.  Scaleup For purposes  o f d e s i g n and m o d e l l i n g ,  t o examine p r e d i c t e d h e a t size kilns obtained  from  from  jection larger  transfer  using equations experimental  0.191m. . i n d i a m e t e r . size  forgas-solids  w  f o r equation  i s insignificant  i n F i g u r e 6-39.  6.12  6-32  The r e s u l t a n t  The  This  i s given i n  transfer.  The  given  f o r Hu  these  coefficients  6-32 and 6-33. results  for larger  Both equations  in a kiln  of single  The p r e d i c t i o n o f t h e e f f e c t  two e q u a t i o n s  were  size,  of k i l n  s h o u l d be c o n s i d e r e d a s a p r o -  o n l y , and i s s u b j e c t t o e x p e r i m e n t a l size  i t i s of interest  verification in  kilns.  Equation  6-32  f o r Nu  may  gs  be r e w r i t t e n i n t h e form,  Table 6-7  R e s u l t o f Regression A n a l y s i s J  1  f o r Nu gs  Equation 6-31 In Nu „ = bn+bi lnRe+b2lnRe t b ^ l n gs u). u  1  tbi+lna  95% confidence i n t e r v a l  1.  For In Nu gs R  2  = 0.9185  Standard e r r o r = 0.1063  F - p r o b a b i l i t y = 0.00  2.  For independent Significant  constant  variables  variables  Coefficients  Standard  '•'  t e r r o r ./  "• ....  F-ratio  F-probability  -0.777  0.356  4.769  0.033  In Re  0.535  0.039  185.4  0.000  In Re  0.104  0.031  11.25  0.002  In n  -0.341  0.057  35.8  0.000  Insignificant  variable  Partial In a  correlation 0.054  F-ratio 0.1137  F-probability 0.7344  155  ^0  60 70 80 90100  150  200  250 300  400  NUSSELT NUMBER. PREDICTED F i g u r e 6-38  Comparison of Experimental Data w i t h P r e d i c t e d Values f o r N ugs  500  156  Table 6-8  R e s u l t o f Regression A n a l y s i s  f o r Nu  gw  Equation 6-33  In Nu gw = a u+aiInRe+aolnRe +a^ln •n + a l n a i 0) n  For  3  H  u  In Nu gw R  2  = 0.6390  Standard e r r o r = 0.2624  F - p r o b a b i l i t y = 0.00 Significant  variables  Coefficient  Standard error  F-ratio  constant  0.432  0.8779  0.2426  0.6303  In Re  0.575  0.0807  50.79  0.000  In Re  -0.292  0.0731  15.91  0.003  Insignificant  F-probability  variables Partial correlation  F-ratio  F-probability  In n  0.1322  0.7118  0.4085  In a  0.1465  0.8769  0. 3575  157  NUSSELT NUMBER. PREDICTED F i g u r e 6-39  Comparison of Experimental Data w i t h P r e d i c t e d Values f o r N ugw  whence the dependence of h .-on D i s ^ gs e . gs  ^ -0.257 " e  h  D  S i m i l a r l y the dependence of h  h  gw  « e D  _  ( f i  g w  on D  g  "  ... 3 4 )  i s given as  ( " )  1  6  3 5  Since the e q u i v a l e n t diameter i s d i r e c t l y p r o p o r t i o n a l to the k i l n  D —  diameter,  2TT - 3 + sing  G  D  =  = constant  for fixed  n  TT- J + sinf  t h e r e f o r e , the p r e d i c t e d dependence of h and h on the k i l n ^ gs gw L  diameter are  . n  h  n  gs  gw  • cc  -  For f o r c e d c o n v e c t i o n  -0.257 D  D  -  1  i n an empty n o n - r o t a t i n g  tube, the  heat t r a n s f e r c o e f f i c i e n t s are dependent on the tube diameter  h « D  -0 2 f o r t u r b u l e n t flow  (6-36)  — 0 67 h oc D " f o r laminar flow  F i g u r e 6-40 6-32  and 6-33  p l o t s h - and h gs  (6-37)  versus D based on  g w  a t constant mass f l u x and temperature.  equations The  mass f l u x i s t y p i c a l of i n d u s t r i a l k i l n s , where w i t h diameters,  as  gas  larger  the gas flow i s i n the f u l l y t u r b u l e n t r e g i o n .  In-  cluded i n the p l o t are the equations recommended i n P e r r y ' s handbooks  (14,  15)  h = 0.0981 G ° '  (2-33)  6 7  g  and  The above two  h = 0.0608 G  n  y  Af  .  /D  (2-32)  equations were given to p r e d i c t the heat  t r a n s f e r c o e f f i c i e n t from gas to r e f r a c t o r y w a l l i n i n d u s t r i a l k i l n s , and have subsequently been used f o r gas to s o l i d bed many i n v e s t i g a t o r s .  As seen i n F i g u r e 6-40  about one order higher than equation 2-32 kilns.  equation 2-33  for industrial  The p r e d i c t e d gas to s o l i d s c o e f f i c i e n t s by  2-32 and by equation 2-33  by  is scale  equation  are c l o s e to each o t h e r a t l a r g e diameter,  The p r e d i c t e d gas to w a l l c o e f f i c i e n t by equation 6-33 about one h a l f those p r e d i c a t e d by equation  6-32.  are  160  0.2  0.5  1.0  2.0  5.0  KILN DIAMETER, m  Figure  6-40  P r e d i c t e d Heat T r a n s f e r C o e f f i c i e n t s f o r Scaleup  CHAPTER 7 A MODEL FOR  GAS  TO BED  HEAT TRANSFFR  The experimental r e s u l t s show t h a t 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 from the gas to s o l i d s i s about one order of magnitude higher than t h a t from gas to w a l l . c o e f f i c i e n t s are a t t r i b u t e d to two  factors:  The higher  the motion of  p a r t i c l e s on the bed s u r f a c e and the use of a plane s u r f a c e area r a t h e r than the t r u e s u r f a c e used i n the c a l c u l a t i o n of the heat transfer 7.1  coefficient.  True Surface Area F i g u r e 7-1  the s o l i d bed.  shows the heat t r a n s f e r path from the gas to  The heat t r a n s f e r r a t e i s d e f i n e d as  Q = h A (T -T ) gs. gs s g s'  (7-1)  v  where A  s  i s the plane area of bed s u r f a c e and. T  temperature. A  g  In t h i s equation T  and T  g  g  s  i s the bed  are measurable  and  i s o n l y f u n c t i o n of k i l n r a d i u s and the degree of s o l i d  Therefore, h g  g  i s calculated i f Q  g s  can be measured.  fill,  However,  t h i s equation expresses o n l y an i n d i r e c t r e p r e s e n t a t i o n o f the a c t u a l heat t r a n s f e r mechanism.  A d i r e c t e x p r e s s i o n f o r gas-  .162  F i g u r e 7-1  Heat T r a n s f e r from Gas to S o l i d s Bed  solid  heat t r a n s f e r r a t e should  Q  where A  gs  = h  •  i  i  A (T -T ) gs s g s' v  i s the t r u e exposed  g  be  v  surface  area  (7-1A) ;  o f t h e bed, which i s  i function of particle surface  size,  temperature.  shape and a r r a y ,  Since  T  present  experiments as w i l l • h „ and h „ becomes gs gs  and T  g  i s t h e bed  i s a b o u t t h e same a s T  g  be s e e n l a t e r ,  g  i n the  the r e l a t i o n s h i p of  •  h  The  ratio  i  A  = h — gs  gs  (7-2) s  i  o f A /A i n equation s s  7-2 i s o b v i o u s l y  important •  in  determining  heat t r a n s f e r c o e f f i c i e n t .  depend on t h e t y p e s a cubic array  of particle  as i n F i g u r e  shown i n F i g u r e  7-2B.  Figure  7-2B c a n b e s t  ticles  of d  o f A /A s s  and i s a b o u t 1.78 f o r  7-2A t o 2.42 f o r a s t r u c t u r e a s  The f i l m  describe  = 6 . 3 5 mm.  arrays,  The v a l u e s  study  ( S e c t i o n 5.2) shows t h a t  the array o f l a r g e r alumina  par-  However a c u b i c a r r a y mav be u s e d t o  p a p p r o x i m a t e t h e c o n d i t i o n f o r Ottawa The solid cles. the  As d e s c r i b e d  velocity. layer  mm.  second f a c t o r which c o n t r i b u t e s t o the higher gas-  heat t r a n s f e r c o e f f i c i e n t  surface  sand o f 0.7 3  i n Chapter  i s the motion o f s u r f a c e 6, t h e p a r t i c l e s  a t a s p e e d much h i g h e r The m o v i n g p a r t i c l e s  adjacent  roll  parti-  down on  than the k i l n c i r c u m f e r e n t i a l  not only  a g i t a t e t h e gas boundary  t o t h e bed s u r f a c e , b u t a l s o c o n t i n u o u s l y  remove  If  (a)  Side View  F i g u r e 7-2  A r r a y of Surface  Particles  the heat r e c e i v e d by the p a r t i c l e s themselves. are  expected to i n c r e a s e the heat t r a n s f e r c o e f f i c i e n t from the  gas to the bed over t h a t of a f l a t 7.2  These phenomena  p l a t e f o r example.  I n d i v i d u a l P a r t i c l e Feat T r a n s f e r F i r s t c o n s i d e r an i n d i v i d u a l p a r t i c l e i n the f i r s t  j u s t coming out of the bed w i t h a temperature,  T .  I t receives  heat from the gas w h i l e i t i s r o l l i n g on the s u r f a c e . the r e c e i v e d heat may  layer,  P a r t of  be t r a n s f e r r e d by conduction to the par-  t i c l e s of the a d j a c e n t l a y e r s . the conduction heat may  In a low temperature  process  compose o n l y a small f r a c t i o n of the  t o t a l heat r e c e i v e d by the p a r t i c l e . The equation governing the heat balance of a s i n g l e p a r t i c l e r o l l i n g down the s u r f a c e i s g i v e n ,  V P C p p p  dT ' • — = h S. (T -T) - h,S, (T-T ) p i g d i s v  p  d  (7-3)  ;  t  where V , p , C P P P  are volume, d e n s i t v and s p e c i f i c heat of  y  p  particle, respectively. • S-^ and S^ are exposed and covered s u r f a c e area of part i c l e i n the f i r s t  layer,  The l a s t term of Equation fer  to p a r t i c l e s below.  (7-3) accounts f o r heat t r a n s -  Since the experiments  were c a r r i e d out a t low temperature,  in this  study  the conduction term i s  n e g l e c t e d r e l a t i v e t o the gas to p a r t i c l e c o n v e c t i o n . I t i s of i n t e r e s t the  to know whether the temperature w i t h i n  p a r t i c l e becomes uniform a f t e r  t u r e suddenly changes.  the p a r t i c l e s u r f a c e  tempera-  The thermal d i f f u s i v i t y o f Ottawa sand  — 6 2 i s 0.277 x 10 m /s and the p a r t i c l e diameter i s 0.73 mm. time  (surface time, t_ ) f o r the p a r t i c l e exposed to the gas s  l  stream i s about one second. 2 a t  / p r  s l  The  i s 2.08.  Thus, the v a l u e of F o u r i e r modulus  T h i s v a l u e shows the p a r t i c l e c e n t e r tempera-  t u r e i s immediately r a i s e d to the s u r f a c e temperature a c c o r d i n g to Carslaw and Jaeger (70). ^Let T' : be the p a r t i c l e temperature b e f o r e i t r e t u r n s !  "Sl  .  c  i  to the bed, and t  i s the s u r f a c e time o f the p a r t i c l e s i n s  the  first  i  layer.  I n t e g r a t i o n of equation 7-3 w i t h the f o l l o w i n g  conditions, t = 0  T = T s  t  (7-4)  T = T si  si  gxves  = 1 " exp T  -  - T g  V  t V  p  P^P  s  C  (7-5) 1  P  '  P  -3 Ottawa sand used f o r the experiments has a diameter o f o.73 10 x  which g i v e s V values of C  P  = 0.204xl0~  m  3  and S T = 0.837xl0~ 1  6  m. 2  The  3 f o r the sand are 0.603 J/gK and 2527 kg/m ,  , and p P  9  m  P  respectively.  The gas to p a r t i c l e heat t r a n s f e r  hp, and the s u r f a c e time, t (Section 7.4)  g i  coefficient  are reasonably assumed a t 15  and 1 second r e s p e c t i v e l y .  W/m  The s u b s t i t u t i o n of  the above v a l u e s y i e l d s  h S, P 1  t.  s  si  0.04  p p Pp  Thus, equation 7-5  T T  and equation 7-6  V  p p  p p  C  si  - T - T  g  can be approximated as  s  s  =  h S,t p 1 si V p C-o P P  (7-6)  i s r e w r i t t e n as  (T - T ) = h S,t (T - T ) Pp' s i s' p 1 si g s ;  n  v  (7-7) ;  The l e f t - h a n d s i d e o f t h i s equation r e p r e s e n t s the heat accumulated by a p a r t i c l e w h i l e i t stays on the a e r a t e d bed s u r f a c e , and the r i g h t - h a n d s i d e r e p r e s e n t s the heat r e c e i v e d by the p a r t i c l e by c o n v e c t i o n from the gas. driving force, g T  r a i s e d o n l y 2 K.  ~  T  = s  For a temperature  50 K, the p a r t i c l e temperature i s  C o n s i d e r i n g the low thermal c o n d u c t i v i t y of  Ottawa sand and the temperature d i f f e r e n c e of 2 K heat t r a n s f e r to the p a r t i c l e s underneath by conduction w i l l be  insignificant  1 6 8  However, high  conduction  thermal  ture  should  not  conductivity,  be  such  neglected  as  metal  for material  pellets  in high  of tempera-  processes. A  similar derivation  of  the  surface  by  conduction  region  for  which  results  particles  ignores  heat  h §•  The surface  time  and  =  received  and  layer  transferred  S_  - exp ( - -2-1  1  V  s  particles  secondary  in  T - T T - T g  i n the  t  ( 7 - 8 )  P C P  P  ?  /  p  tr  in  the  exposed  second  surface  layer  area  will  from  have  that  different  in  the  first  layer.  7.3  Gas  to  It aerated from  Bed  Heat  i s assumed  layers  the  gas,  particles  Transfer  of  the  where  are  that  to  T  , and  T  S 1  cles  then  they  from  the  mix  with  return  to  bed  to  F  where M the  region  temperatures  ^  as  particles  surface  the  raised  no  Coefficient  m  i s the  thickness  the the  the  bed.  surface  number of  the  The  ( l  of  2 s  the  from  T  -  first  heat  by  aerated .  The  surface  heated  per  8 R K C O S |  per  region.  surface  particles  unit  time  layers  emerging  is  )  ( 7 - 9 )  unit Ax  parti^  other of  two convection  S  number  particles  surface  of  i n the  region  the  receive  S2  particles  ^AX-n  =  below  volume  is a  short  and  •< i s  distance  of  k i l n length. The d e t a i l e d d e r i v a t i o n o f equation 7-9 i s g i v e n i n the  appendix.  I f the r o l l i n g r a t e s o f p a r t i c l e s i n the f i r s t and  second l a y e r s r e s p e c t i v e l y a r e expressed as,  F = m A cV 1  3  11  (7-10)  and F~= 2  m.AxV 2 12 n  then a thermal balance of the mixing process can be expressed as  F  where T  m  sm  (T - T ) = F,(T - T ) + F„(T - T ) sm s 1 si s 2 s2 s  i s the temperature  A f t e r rearrangement, equation 7-11 becomes,  T  The  o f the mixture b e f o r e i t r e t u r n s  c  to the bed.  (7-11)  F F 1 2 - T •= — ( T -T ) + — (T -T ) sm s „ s i s _ S 2 S F F m m v  ;  V  ;  f o l l o w i n g equation i s o b t a i n e d a f t e r s u b s t i t u t i n g equations  7-4 and 7-8 i n the above equation,  T  -T s T -T g s sm  1-exp m  , h S V  1  p c p p p  .0 r  i | l-exp.(f m W f  + r  k  h S_ P  2  p C P P P  (7-12)  T  Therefore, i s represented  the heat absorbed by the r o l l i n g  by  Q „ = F p C V gs nrp Pp P  Combining equations Ax'l , one w i l l  h  gs  =  P P  P  1  s  +  m  7-1,  7-9,  (T  sm  7-12  and  h  1-exp ^ _  S. P 1  V p Cp p p p p  1-exp  2 l2 V  - T ) s  7-13,  (7-13)  and  letting  A  £  obtain  m-V. [ 1l i  p  particles  ^_  h  P  'si  S. 2  (7-14)  S2  V p C p p Pp D  In order to e v a l u a t e h gs determined.  , V. (or t„) and h must be I s p  U n f o r t u n a t e l y t h e r e i s no i n f o r m a t i o n i n the  l i t e r a t u r e on the r e l a t i o n s h i p o f meters.  to other o p e r a t i n g  For an i d e a l system the f o l l o w i n g equation  para-  i s derived  (see Appendix)  K  V  ll  =  ^~  n ( 1  s  "  8RKCO£  4  )  (7-15)  where < i s the t h i c k n e s s of s u r f a c e r e g i o n .  The  velocity,  of p a r t i c l e s i n the second l a y e r can be approximated  V  l 2  =  d ( 1 - -£ ) V K  1 1  by  (7-16)  ,  a c c o r d i n g to F i g u r e 5-2.  In equation 7-15,  K and V  to r o t a t i o n a l speed N and the degree of f i l l . experimental r e s u l t s i n F i g u r e 5-5  V_ ]  However, there i s s t i l l  Furthermore,  (7-17)  a need to know K , which i s a l s o u n a v a i l -  able i n the l i t e r a t u r e .  Based on the f i l m study V^ =  was  sphere a t 4.78  observed  1  f o r alumina  rpm.  0.24  7.4  Gas No  ori  . this  to P a r t i c l e Heat T r a n s f e r C o e f f i c i e n t i n f o r m a t i o n on the heat t r a n s f e r c o e f f i c i e n t from  to r o l l i n g p a r t i c l e s , h , p  was  m/s  I t seems reason-  a b l e to assume V,, , . _ - _ , , .11 = 0.20 m/s a t 3 rpm f o r Ottawa sand and value w i l l be used t o c a l c u l a t e K and h gs n  the  show  - JN  1  are r e l a t e d  f o r a system s i m i l a r to r o t a r y k i l n  r e p o r t e d i n the l i t e r a t u r e .  i s c l o s e to the f i x e d bed  gas  Since the bed i n r o t a r y k i l n  system, heat t r a n s f e r data f o r the  f i x e d bed w i l l be used as a guide, although the gas flow p a t t e r n i s d i f f e r e n t as d e s c r i b e d below. K u n i i and L e v e n s p i e l (71) r e p o r t e d a c o r r e l a t i o n of heat t r a n s f e r data f o r f i x e d bed i n terms of Nu which i s reproduced  i n F i g u r e 7-3. u  p o.  Re  = P  d g p  Nu^  versus Re , P P and R e are d e f i n e d as, p  F i g u r e 7-3  Reported R e s u l t s f o r G a s - t o - P a r t i c l e Heat T r a n s f e r i n F i x e d Bed. (Kunii & L e v e n s p i e l , 71).  and  Nu  = - i £k g  p  respectively. and  the  i n the cular  U  i s the  q  fluid.  To  use  k i l n where the to the  gas  (7-18)  r e l a t i v e v e l o c i t y between the  t h i s approach f o r the aerated p a r t i c l e s are  flow, U  i n equation 7-18  q  particle  s u r f a c e of the rolling  bed  perpendi-  i s defined  as  2 . 2 U  where u  i s the  g  space of the  gas  TTR2(1  value of u  gas  v e l o c i t y near the gas  whereas i n the  kiln  the  +  l i  V  y  -  n  through the  "  1 9 )  empty  )  i s expected to be bed  higher than t h a t of the  i s f l o w i n g over the f i x e d bed  i s expected to be  the  gas  bed  i n the  rotary  kiln  i s f l o w i n g through the heat t r a n s f e r  bed.  in a rotary  lower than t h a t i n a f i x e d bed.  value of t h i s e f f e c t i v e n e s s i s not adjacent p a r t i c l e s  r o t a r y k i l n about the  half  i s exposed to the  stream.  gas  true  surface.  e f f e c t i v e n e s s of g a s - p a r t i c l e  p a r t i c l e has  ( 7  superficial velocity  The  So,  o  kiln.  G  The  V g U  known.  ^he  In a f i x e d bed  each  surrounding i t , however, i n  s u r f a c e area of the  aerated  It i s , therefore, l i k e l y  particles that  hp f o r the aerated p a r t i c l e i n a r o t a r y k i l n i s roughly a f r a c t i o n o f h , i n a f i x e d bed. pf Chen e t a l (50) r e p o r t e d the gas to p a r t i c l e heat t r a n s fer i n a rotary dryer.  In t h e i r experiments  of f l o w i n g through the d r y e r , was passed  hot a i r , i n s t e a d  through the bed from  the w a l l which was made o f p l a t e with holes and p i t c h w i t h a screen.  covered  The data of the heat t r a n s f e r c o e f f i c i e n t s bet  ween gas and p a r t i c l e s were found to be i n the range of .fixed bed. 7.5  The data are a l s o shown i n F i g u r e 7-3. Comparison w i t h Experimental  Data  The comparison o f the experimental data w i t h equation 7-14 i s g i v e n i n F i g u r e 7-4 where h ^  s  i s p l o t t e d versus  A l l the experimental data are i n c l u d e d .  W^.  The i n p u t data f o r  c a l c u l a t i o n f o r equation 7-14 a r e g i v e n i n ^ a b l e 7-1 and the c a l c u l a t e d r e s u l t s are g i v e n i n Table 7-2. h  P  are taken as h,  Three curves w i t h  h and 1 times t h a t f o r a f i x e d bed.  The  curve w i t h % h f i t s the data b e t t e r than the other two. The Pf value o f h taken as one h a l f o f h seems reasonable s i n c e P Pf c  c  o n l y h a l f of s u r f a c e area o f the aerated p a r t i c l e i s exposed to the gas stream. i s taken from Nu  g  I f the value o f h^ f o r the a e r a t e d = 2 which corresponds  to an i s o l a t e d  particl sphere  at low Reynolds number t h i s r e s u l t s i n a much higher v a l u e of heat t r a n s f e r c o e f f i c i e n t than h , and the p r e d i c t i o n o f h pf gs would be c o n s i d e r a b l y h i g h e r . c  r  In equation 7-14 the e x p o n e n t i a l terms are found to be  —I  20  1  30  Wg,  —  I  40  I  I  50 60  I I  80  kg/hr  Comparison of T h e o r e t i c a l w i t h Experimental Data.  Curve  Table 7-1 Input data f o r Equation 7-14  For P a r t i c l e  (Ottawa sand) d P  C  P  P ' PP  V  0.73 x 10  -  2527.3 kg/m  =  0.603 J/gK  —  0.204 x 10  P  S  l  S  2 l  m  —  0.837 x 10  =  m  3  3  -9 -6  -  0.042 x 10"~  m  - 2.17 x 1 0  2  6  6  m m  3 2 2  no. o f p a r t i c l e s / i  For a i r (at 422 K) 2.369 x 1 0 0.833 kg/m 0.031  Operating  v  3 rpm .11%  n  li =  3  W/m-K  conditions N  _ J  0.20 m/s  kg/m-s  Table 7-2 C a l c u l a t i o n s f o r G a s - P a r t i c l e Heat T r a n s f e r  W  kg/hr  18.6  34  50  V  g  m/s  0.245  0.447  0.657  0.92  V  1  0.20  0.20  0.20  0.20  0.316  0.490  0.687  8.1  12.6  17.6  g  m/s  +  V  m/s  Q  Re  p  N U  h h  =  N  U  p  0  ,  W/m K  gs  W  /  m  2  °'  4  9.3  2  p  4  R  1  7  •  7  6 2  13.1 24.8  °-  9 0  19.1 35.8  70  0.942 24.2  1-4 29.3 55,2  Nu  - JsNu *  0.22  0.31  0.45  0.70  h  W/m K  4.65  6.55  9.55  14,65  W/m K  8.85  12.4  17.9  27.6  = i;Nu * 2  0.11  0.16  0.23  0.35  W/m K  2.33  3.28  4.28  7.33  2  p  h  2  y  &  Nu h h  p  p  gs  p  w  /  m  2  R  3 K x 10- m  4  -  4  3  0.369  +  assumed  *  taken from F i g u r e 7-3  6.2 0.369  8.95 0.369  13.8 0.369  quite small.  Thus,  1 V 11  = 0.042  1 p p Pp  for  V 12  '= 0.20 m/s a t N= 3 rpm.  = 0.005  The r a t i o o f these two terms  i n d i c a t e s t h a t the top l a y e r probably r e c e i v e s about 8 times as much as heat from the gas than does the second the second  l a y e r , and  l a y e r c o u l d probably be ignored i n the above a n a l y -  sis. The e f f e c t o f r o t a t i o n a l speed on h equation 7-14 i s shown i n F i g u r e 7-5. are g i v e n i n Table 7-3.  c a l c u l a t e d from gs The c a l c u l a t e d r e s u l t s  The slope o f h versus N i s 0.1 gs  which c o i n c i d e s roughly with the experimental The mathematical  data.  model f o r g a s - s o l i d heat t r a n s f e r has  been e s t a b l i s h e d from a s i n g l e p a r t i c l e .  In the model two f a c -  t o r s which s i g n i f i c a n t l y a f f e c t the gas t o s o l i d bed heat t r a n s f e r are the p a r t i c l e a r r a y on the top bed l a y e r and the gas to r o l l i n g p a r t i c l e heat t r a n s f e r c o e f f i c i e n t .  The c u b i c  packing a r r a y was assumed f o r Ottawa sand bed.  The gas-to-  r o l l i n g p a r t i c l e heat t r a n s f e r c o e f f i c i e n t , taken as one-half value o f t h a t f o r f i x e d bed, y i e l d s a reasonable p r e d i c t i o n f o r the r o t a r y k i l n .  To make the model more adaptable  further  179  10 9  T  8 7 6 50  CVI  A Calculated from Equation  7—14  Tf = 11%  Wg = 3 4 k g / h r hp =1/2 h p f  40  E to  ?  30 2.5 2.0h 1.5  .0  1  1  2  3  4  1  5  6  ROTATIONAL SPEED, rpm  Figure  7-5  E f f e c t of R o t a t i o n a l Speed on T h e o r e t i c a l Gas-Solids 'Bed Heat T r a n s f e r C o e f f i c i e n t  Table 7-3 C a l c u l a t i o n of h  from Equation 7-14 gs  N (rpm)  1.0  3.0  6. 0  V  m/s  0.447  0.447  0.447  m/s  0.116  0.20+  0.283  m/s '  0.462  0 . 490  0.529  11.8  12.6  13.6  0.60  0.62  0.66  0.30  0.31  0. 33  12.7  13.1  14 . 0  0.221  0.369  0.5 04  23.8  2 4.8  26.5  g V 1  V  o  Re P Nu * P Nu = h Nu * P P h W/m K P K x 10"^, m 2  h  W/m K 2  gs  +  assumed  *  taken from F i g u r e 7-3  n = 11% W  =34.0 kg/hr  181  , work on the t h i c k n e s s of the mixing zone and the p a r t i c l e l a t e r a l velocity i s required.  Both K and  are used to determine the  temperature of the mixing p a r t i c l e s i n the s u r f a c e  region.  182  CHAPTER 8 MODELLING OF ROTARY KILN HEAT EXCHANGER  As noted i n the f i r s t two c h a p t e r s a number o f s t u d i e s on r o t a r y k i l n m o d e l l i n g have been p u b l i s h e d (5-14), however, there was a l a c k o f experimental data on heat t r a n s f e r to i n c o r p o r a t e i n t o the models.  Although Watkinson and  Brimacombe  (4) r e p o r t e d some r e s u l t s on heat t r a n s f e r i n a d i r e c t - f i x e d kiln,  0.406 m i n s i d e diameter, t h e i r data are s t i l l  form r e a d i l y adapted f o r scaleup to i n d u s t r i a l s i z e Kern  not i n a kilns.  (15) e s t a b l i s h e d a model f o r heat t r a n s f e r i n a  r o t a r y heat exchanger.  In h i s model , the r o t a t i n g w a l l  e r a t u r e i s formulated i n terms of gas and s o l i d  temp-  temperatures  by t a k i n g i n t o account the p e r i o d i c c o o l i n g and h e a t i n g o f the wall.  By e l i m i n a t i n g the w a l l temperature, he o b t a i n e d  dT "g _ a i T dx  dT, dx  = biT  s  + a T  g  + a  3  s  + b T  g  + b  3  2  2  183  where a  n  and b  n  are f u n c t i o n s of the mass flow r a t e s ,  speed and the heat t r a n s f e r c o e f f i c i e n t s . e f f i c i e n t s were assumed, h  21  = 5 W/m'K  Q  The heat t r a n s f e r _  , h g  _  g  s o l i d bed to gas), and h /h =3. ^ ' sw' wg  rotational  1.5 W/m  2  co-  K (for  The assumed v a l u e s of heat  t r a n s f e r c o e f f i c i e n t s do not seem to be r e l i a b l e i n terms of the measured v a l u e s r e p o r t e d i n the p r e s e n t study. A model of a r o t a r y k i l n heat exchanger  i n the low temp-  e r a t u r e range where r a d i a t i o n e f f e c t s can be n e g l e c t e d i s p r e sented here. Chapter  6  The heat t r a n s f e r c o e f f i c i e n t s ' e s t a b l i s h e d i n  can be used i n the model.  Thus, the equations used  e a r l i e r to c a l c u l a t e heat t r a n s f e r c o e f f i c i e n t s from p r o f i l e s are j u s t i n v e r t e d  temperature  to c a l c u l a t e temperature p r o f i l e s  from heat t r a n s f e r c o e f f i c i e n t s .  The equations governing the  heat balances on gas and s o l i d phases over a s m a l l d i f f e r e n t i a l d i s t a n c e are given as dT W C — g pg  a  d  x  dT W C s ps  = h 1 (T -T ) + h 1 (T -T ) gs s g s' gw w g w  (8-1)  , = h 1 (T -T ) - h 1 (T -T ) gs s g s sw w s w  (8-2)  v  v  v  d  x  ;  The heat c a p a c i t i e s , C  y  and C pg  temperature  ;  , are assumed c o n s t a n t over the P  range of i n t e r e s t .  s  The w a l l temperature,  T , is  assumed c i r c u m f e r e n t i a l l y constant a t a p a r t i c u l a r l o c a t i o n . T h i s s i m p l i f y i n g assumption r e s u l t s g i v e n i n Chapter  6,  i s j u s t i f i e d by the experimental and by those of r e f e r e n c e (4).  The i n s i d e r e f r a c t o r y temperature  ( i f there i s a l i n i n g  m a t e r i a l i n the k i l n ) , T , i n eguations 8-1 and 8-2 must be w known i n order t o o b t a i n the gas and s o l i d temperature  profiles  Therefore a heat balance over the w a l l i s s e t up to o b t a i n T"v/ t  Gas to Wall convection  S o l i d s t o Wall +  Feat l o s s  convection  through  Wall by Conduction 2irk (T -T  h i (T -T ) + h 1 (T -T ) = gw w g w' sw w s w^  where T  w Q  W  (  R  (8-3) ^  )  i s the o u t s i d e l i n i n g temperature.  assumed t h a t there i s no temperature kiln shell. to  )  W  I t i s further  drop a c r o s s the metal  T h e r e f o r e , the heat l o s s through the k i l n  shell  the surroundings i s g i v e n by  2fTk (T -T ) w w wo (R2/R±)  In  = h 1 (T - T ) o o wo o  (8-4)  S u b s t i t u t i o n o f equations 8-3 and 8-4 i n t o equations 8-1 and 8-2 y i e l d s two f i r s t order l i n e a r equations f o r gas and s o l i d s temperatures which can be r e w r i t t e n as;  dT -2.  =  D l  T  g  - D T 2  s  - D T 3  o  (8-5)  and = E,T  - E„T  +  E„T  (8-6)  185  where z = x / L , and t h e c o e f f i c i e n t s D mass f l o w r a t e and h e a t 8-1. and  Kern  transfer  temperatures  In t h i s  as g i v e n i n T a b l e  e q u a t i o n s f o r t h e gas  study both the i n l e t  0  T  z =  1  T = T _ g gL  from  i, h  = T  s  heat t r a n s f e r  calculated  the f o l l o w i n g  gs  n AC =0.46  R  g r, ° — a - Re  n  = 11.e- -, w  i s further  (  a  assumed t h a t  F o r a non-uniform  developed  a formula  "  7  )  i n Table 8-1 are  T>  Re  w  „  Re  °'  ° -  1  0  1  -0.34 ri  ,, (6-31)  -0.29  (6-32)  w  3  )  (6-26)  t h e bed h e i g h t a l o n g t h e k i l n  bed system,  Kramers and C r o o c k e w i t  f o r bed h e i g h t a l o n g t h e k i l n  o f o p e r a t i n g parameters.  coefficients  nR B 2  3  w  4  e  k s  5  g „ -58 Re  CA  used  8  equations,  e i  h  (  D  i T  and  s o  coefficients  h„ = 1.54 gw  uniform.  g a s and s o l i d  a r e f i x e d as  z =  The  ion  coefficients  are functions of  8 - 5 and 8 - 6 c a n be s o l v e d i f a s e t o f b o u n d a r y  conditions are given.  (29)  n  temperature.  Equations  is  and E  ( 1 5 ) o b t a i n e d somewhat s i m i l a r  solids  It  n  Since the g a s - s o l i d  depend on t h e d e g r e e  of f i l l ,  heat  as f u n c t transfer  the assumption o f  186  Table 8-1 The C o e f f i c i e n t  l -  D  l  =  B  +  B ] l  B  D  2  =  D  3  = A A B  E  x  = B  E  2  E  3  =  B  3  A  + A A B 2  5  2  2  4  +  5  4 " 2 5 4  B  A  = 4 4 B  5  + B A  3  8-5 and 8-6  2 ~ 2 5  B  4  f o r Equations  A  A 5  A  B  '  where h l o  Q  ln(R / ) 2  R l  A l  1  A  3  A 4  2 k w h i '  1 + A1  1 '  1  V  '2 A  2 k A  w  3 h  1 ln(R„/R, ) gw w T 1'  v, i T as s h  1  L  = -S2-§_  B  B  w g cpg h  B  2  =  2  1 L gw. v/ — Wg C pg  B  4  3  =  h 1 L 9S s  ws cps , . h SW 1'w L WsCps *>^\?o  + *4  187  uniform  bed  parameters uniform  depth (N,  bed  a,  makes  the  problem  n , D)  are  fixed,  system  W  where  T  and  n  s  =  T  can  5-  gas  by  solving  8-7  gives  the  at  boundary at  given not  0 and  conditions T  equal  to  T g  L  '  to  flow  g -  8-1. end  A  L  If both of  the  and  kiln,  8-6  and  following  a  equation:  (2-12)  s  profiles  with  error  equations =  T  so  equation  value the  equations  used.  and  8-6  T„„ go  at  and  for T  8-7.  g o  gas  was  of  the  kiln,  Therefore,  Runge  0.  Gas  with  tempera-  and  temperature  set be  as  g L  temperature  i s given  can  T  assumed  gas  c o n d i t i o n s are 8-6  Equation  ends  compared  program  and  obtained  L  calculated  8-5  be  First, T was ' go were s o l v e d w i t h  z =  calculated  f o r computer  boundary  opposite  was  . T^ = g  I f the  can  difficult.  8-5  calculated  until  chart the  for  (2-13)  solution  another  repeated  the  )  conditions at  8-7.  procedure T  8-5  then  i n equation  from  operating  throughput  tana/sanO -  temperature  trial  1 was  solid  the  IT  solid  with  ;  s  Once  cos-t- )  analytical  z =  z =  -  sing  boundary  an  method  assumed  ture  and  ND p 2  •L  =1(3-  equations  w h i c h makes Kutta  ( 1  the  calculated  =.77. 7i,  2  The  be  simpler.  at  in  the  solved  was  the , equal Figure  same analytic-  ally. A  kiln,  3 m  I.D.  by  80  m  long  with  0.15  m  thick  refract-  F i g u r e 8-1  Flow Chart o f Computer Program f o r Temperature P r o l i l e s  ( START  T  go  )  assumed  Calculate W s 2-12  Equation  Calculate D , 1 e w 1', l . Re, Re w s w e  h  o  assumed T  C a l c u l a t e h's equations 6-31,32,33 Calculate D i n Table  n 8-1  [Solve equations  & E  8-5  8-6 by KK method o b t a i n T' 9l±  Yes PRINT T , T g s, vs x ( STOP ~~)  n  go  = T + go -  T  go  ory  lining  speed, that  i s selected  inclination  the solids  trial  angle  and t h e degree  throughput  lime k i l n .  collected  to i l l u s t r a t e the model.  The  i n Table  i s about  of f i l l  The  inlet  the  kiln  i s fixed  Equations with  a t 350 8-5  coefficients while  solid  results solid  f o r gas and  lines  8-6  8-1  dimensionless  form,  from  with  heat  8-2.  The  (T-T  recommended  profile  y i  8-2  from  coefficients  equation  profiles  A  As  expected  considerably gas  the local  as the heat  temperature  drops  transfer  and  32,  2-12.  The  are depicted  in  ). bu  calculated  from  profiles  the equations  E n g i n e e r i n g Handbook  (46,  47).  (.2-32)  c -  h = 0.061 I -3- j A  solved  are expressed i n  h = 0.0981 ( -3- )  1  31  are the temperature  i n Perry's Chemical  and  at  end o f  are  Heat  6-26,  temperatures  ) / ( T .-T  i n Figure  transfer  equations  temperature  ou  Included  i s kept  at the other  f o r temperature  i s calculated  solid  i n Figure  indus-  f o r modelling are  f o r the c o e f f i c i e n t s .  are calculated throughput  so  K.  and  the a i d of Table  as an  gas temperature  500° K, w h i l e t h e i n l e t s o l i d t e m p e r a t u r e  rotational  are chosen  t h e same o r d e r  necessary parameters  8-2.  The  /  c  solids  transfer  accordingly.  (2-33)  /  temperature  coefficients  increases increase.  The  Table 8-2  M o d e l l i n g Parameters  S o l i d phase  : Ottawa sand  Gas phase  :  Air  D=3m  L = 80 m  T _ = 500 K gL  T so  h  k = 0.043 W/m K w '  = 10 W/m K ' 2  o  N = 1 rpm n =" 11%  350 K 2  a  W S —  =.  0.7° A  = 2130 kg/hr-m  (kiln cross section)  191  hgs =11.1 (W/m K) hgw = 1.84 ( W / m K) from Equations 6 - 3 1 and 6 - 3 2 2  2  hgs = hgw = 16.6 (W/m K) from Equation 2-32 2  X/L  F i g u r e 8-2  E f f e c t o f Heat T r a n s f e r C o e f f i c i e n t Temperature P r o f i l e s  on  F i g u r e 8-3 g i v e s the e f f e c t o f gas flow r a t e on the i temperature p r o f i l e .  The r e s u l t s a r e a l s o as expected.  :  In-  c r e a s i n g gas flow r a t e i n c r e a s e s both g a s - s o l i d and g a s - w a l l heat t r a n s f e r c o e f f i c i e n t .  As a r e s u l t , the s o l i d  temperature  i n c r e a s e s r e p i d l y , however, the gas temperature drops a r e small due t o the h i g h gas flow r a t e . The w a l l temperature f o r the o p e r a t i n g c o n d i t i o n s g i v e n i n Table 8-2 i s i l l u s t r a t e d  i n F i g u r e 8-4.  Wall temperatures  are c o n s i s t e n t l y h i g h e r than the s o l i d temperatures along the k i l n due to the presence o f the t h i c k r e f r a c t o r y l i n i n g , and low heat l o s s .  For comparison, a r o t a r y k i l n of the same  dimension having no r e f r a c t o r y l i n i n g i s assumed.  The k i l n wal  i s 0.051 m i n t h i c k n e s s , made of m i l d s t e e l having thermal c o n d u c t i v i t y 45.2 W/m-K.  In t h i s case, the w a l l  temperature  drops below the s o l i d temperature, and the gas temperature a l s o drops due t o h i g h heat l o s s through the w a l l .  T h i s type  of behaviour was found i n the p r e s e n t experimental study. The e f f e c t o f k i l n l e n g t h on the temperature p r o f i l e i s g i v e n i n F i g u r e 8-5 .  For a lime k i l n equipped w i t h a p r e h e a t e r ,  the k i l n l e n g t h of the 3 m I.D. k i l n i s t y p i c a l l y about 50 m. For a s h o r t k i l n ,  the e x i t gas temperature i s e x p e c t e d l y ,  h i g h e r than t h a t f o r a long k i l n  i f the e n t e r i n g gas tempera-  t u r e s are maintained the same for, both cases. The e f f e c t o f k i l n diameter i s o f most i n t e r e s t to the designer o f the k i l n .  The s w i t c h o f k i l n diameter i n v o l v e s a  change o f heat t r a n s f e r c o e f f i c i e n t s and s o l i d throughput.  It  may a l s o a l t e r the flow p a t t e r n i f the r o t a t i o n a l speeds are  193  X/L  F i g u r e 8-3  E f f e c t of Gas Flow Rate on M o d e l l i n g of Rotary K i l n .  X/L  F i g u r e 8-4  E f f e c t of R e f r a c t o r y I n s u l a t i o n on M o d e l l i n g of Rotary K i l n .  X/L  F i g u r e 8-5  E f f e c t of K i l n Length on M o d e l l i n g of Rotary K i l n .  maintained diameter  the same.  the s o l i d  In order to compare the e f f e c t of  flow p a t t e r n i n k i l n s of d i f f e r e n t  should be kept the same, which can be accomplished  kiln  diameters  by  maintain-  ing the same Froude number,  N N - = — N N c c 1  . , = constant or  1  D  1 :  ^ ^ constant  D  Therefore, the r o t a t i o n a l if  speed must be a d j u s t e d a c c o r d i n g l y  the change of the k i l n s i z e i s necessary.  t o r t h a t should be taken i n t o account per k i l n c r o s s area.  The  second  i s the s o l i d  throughput  T h i s f a c t o r w i l l govern the r e s i d e n c e  time i n k i l n s of the same l e n g t h .  In t h i s c a l c u l a t o n ,  throughputs  are maintained  per k i l n c r o s s s e c t i o n  v a r y i n g k i l n diameters.  the  According to equation 2-12,  the  angle must be adjusted to keep the same degree of  fill.  F o r t u n a t e l y , the e f f e c t of i n c l i n a t i o n angle on  inclinsolid  heat  is n i l .  F i g u r e 8-6 diameters, of N/N  solid  constant a t  ation  transfer  fac-  3 m,  and  efficiency.  2 m and  solid  i n the f i g u r e ,  1 m f o r a 50 m long k i l n .  T h i s i s due  F i g u r e 8-7  ratio.  k i l n s show high heat  to higher heat t r a n s f e r  Although  kiln  Both the r a t i o  r e s i d e n c e time are kept c o n s t a n t .  small diameter  f o r small k i l n s . at f i x e d L/D  shows the e f f e c t of three d i f f e r e n t  As  seen  transfer  coefficients  g i v e s the e f f e c t of k i l n  diameter  small k i l n s have a s h o r t e r k i l n  i g u r e 8-6  E f f e c t of K i l n Diameter on M o d e l l i n g of Rotary K i l n Heat Exchanger  X/L  Figure 8 - 7  F f f e c t of K i l n Diameter on Temperature P r o f i l e at F i x e d L/D r a t i o  l e n g t h , the s t r o n g e f f e c t on heat t r a n s f e r c o e f f i c i e n t s o v e r comes the n e g a t i v e e f f e c t of s h o r t  length.  The model of the r o t a r y k i l n heat exchanger has been developed f o r low temperature and n o n - r e a c t i n g systems.  The  h i g h temperature process r e q u i r e s a r a d i a t i v e term added  into  Equations 8-1 and 8-2 which w i l l r e s u l t i n n o n - l i n e a r  first-  order e q u a t i o n s .  term,  the  For a r e a c t i o n system an a d d i t i o n a l  heat of r e a c t i o n , should be added, and the e q u a t i o n f o r  m a t e r i a l balance should be supplemented  as w e l l .  CHAPTER 9 CONCLUSIONS Convective heat t r a n s f e r  from gas to s o l i d s bed and  wall  has been s t u d i e d e x p e r i m e n t a l l y as a f u n c t i o n of o p e r a t i n g parameters.  The parameters covered i n c l u d e d temperature  flow r a t e ,  s o l i d throughput,  speed, degree of f i l l  i n c l i n a t i o n angle,  and p a r t i c l e s i z e .  both limestone and Ottawa sand. transfer  I t was  l e v e l , gas  rotational  T e s t s were done on found t h a t the heat  c o e f f i c i e n t from the gas to s o l i d s bed based  on  plane chord area i s roughly an order of magnitude h i g h e r that from gas to w a l l . s o l i d throughput transfer  The experimental r e s u l t s  than  show t h a t  both  and i n c l i n a t i o n angle have no i n f l u e n c e on  c o e f f i c i e n t s and the e f f e c t of degree of f i l l  gas to w a l l heat t r a n s f e r  which p o s s i b l y  from the narrow range of p a r t i c l e s i z e s t e s t e d . dimensional equations have been obtained f o r the of experimental data f o r Ottawa sand.  gs  = 2.44 0  on  coefficient i s insignificant.  e f f e c t of p a r t i c l e s i z e i s n e g l i g i b l e ,  . h  the  T7  W  0 . 575 ...0.091 -0.171 N g . n  The  heat  the The  results following  correlation  v, gw  and  h  The  higher  gas  - n - °-  8 2  W  w 0-475. -0.297 g N  to s o l i d s bed  heat t r a n s f e r c o e f f i c i e n t s  p a r t l y r e s u l t from the underestimation  of the t r u e s u r f a c e  used i n the c a l c u l a t i o n of the c o e f f i c i e n t . s u r f a c e area i s  The  a c t u a l exposed  about^ twice as much as the plane chord  Rapid p a r t i c l e v e l o c i t y on the bed c a n t l y to high g a s - s o l i d s bed ates the gas adjacent  surface contributes  heat t r a n s f e r .  to the bed  area  area.  signifi-  I t not o n l y  agit-  s u r f a c e , but a l s o convects heat  by v i r t u e of mixing of the f a s t - r o l l i n g p a r t i c l e s i n t o the. bed. A mathematical model has been developed to d e s c r i b e the i n f l u e n c e of p a r t i c l e movement f o r a r o l l i n g  bed.  Since the motion of aerated p a r t i c l e s was  thought to  be  important f o r heat t r a n s f e r , e x p l o r a t o r y experiments on measurements of s u r f a c e time and r o l l i n g bed  s u r f a c e v e l o c i t y were made.  In  the l a t e r a l v e l o c i t y of p a r t i c l e s on the bed  i n c r e a s e s with  surface  the square r o o t of the r o t a t i o n a l speed.  Residence time d i s t r i b u t i o n i n a r o t a r y k i l n was briefly.  The  the  studied  r e s u l t s show t h a t the s o l i d flow i n a r o t a r y  ,can be assumed as. a plug flow a x i a l l y and-well-mixed  radially.  A simple model of a r o t a r y k i l n heat exchanger was t r u c t e d to i l l u s t r a t e the e f f e c t s of k i l n parameters on ture p r o f i l e s i n a low temperature  kiln.  kiln  cons-  tempera-  CHAPTER  RECOMMENDATION  should -  Future  work  entail  g a t h e r i n g more  particularly  rotational surface ness its  time,  associated  tigated  FUTURE  data  on  of f i l l  may  of surface  layers. particle  The  WORK  transfer  relating  velocity  degree  ratio  of surface  FOR  on c o n v e c t i v e h e a t  particle  speed,  10  time  i n a rotary  to p a r t i c l e  to retention  to thoroughly understand  i n each  Besides  be a m a j o r  layer  the heat  factor  time  thickness of surface  velocity  mechanics  the bed s u r f a c e . also  and  layers  on  thickand  s h o u l d be  transfer  kiln  inves-  mechanism,  •  particularly  i n high  fired  The e x p e r i m e n t s  kiln  kiln.  using a high In  ment bed heat  may  surface  the  the heat  influence  could  be  such  carried  the slumping  Since  type  i t has been  as the  direct-  out i n a  lucite  mode.  that  move-  increased  factors  that  enhances  i t i s t o be e x p e c t e d  that  gas t o  will  increase mass  significantly  increases  F u r t h e r work  transfer  o f slumping  of particle  indicated  i s one o f t h e major  of particle  the r o l l i n g  investigate  kilns  transfer  frequency  processes  camera.  coefficients,  bed heat  slumping reaches  occur.  velocity  transfer  solids  speed  industrial also  temperature  until  i s also  i n the slumping  f r e q u e n c i e s which  as the t h e bed  suggested  bed,  i n turn  to  particularly are  affected  by r o t a t i o n a l  speed.  Although the c o r r e l a t i o n transfer  equations f o r c o n v e c t i v e heat  c o e f f i c i e n t s f o r both gas to bed and gas t o w a l l have  been o b t a i n e d i n the p r e s e n t study, i t i s s t i l l scaleup and d e s i g n f o r i n d u s t r i a l k i l n s . t h a t the k i l n s of a t l e a s t two  inadequate f o r  I t i s thus,  sizes larger  suggested  than one used i n  the present study be t e s t e d , so t h a t the e f f e c t s of diameter, and l e n g t h to diameter r a t i o can be  demonstrated.  204  NOMENCLATURE 2  A  area  s A ' s n a  plane area  n C  constants,  dimensionless  Cp  specific  c  number o f p a r t i c l e s  D  kiln  A  A  B  o f bed s u r f a c e  a c t u a l area constants, heat  m m m  o f bed s u r f a c e defined  i n Table  8-1  diffusivity  axial  d  2  i n Table  8-1  -  concentration  heat  j/gK per u n i t weight  diameter  D  kg"  defined  dispersion  i n Table  8-1  coefficient  m /s 2  distance  per cycle  m  particle  diameter  m  d'  thickness  E  exit n  F m g g G  defined  volumetric  m s-  i n Table  flow  region gas  to surface  mass f l u x  acceleration  8-1  rate  emerging r a t e o f p a r t i c l e s  heat  flow  h  heat  transfer  region  s-1  b a s e d on empty  kiln  m/s  coefficient  2  coefficient  gas-to-bed heat t r a n s f e r  coefficient  b a s e d on a c t u a l s u r f a c e k  thermal  L  kiln  It  length  Is  bed  1 w  exposed w a l l  heat t r a n s f e r  area  coefficient  conductivity  surface  W/m ] 2  W/m ] 2  m-1 W/mK  length  m  of test  2  W/m ]  transfer  relative  kg/h: W  heat  h'  -  from bed  rate  conductive  1  m^/s  of gravity  H  hgs'  layer  gas d i s t r i b u t i o n  solid  F  of wall  constants,  1  m  a dp  E  2  m /s  defined  constants,  2  section  area area  per u n i t per u n i t  m length length  m /m 2  m /m 2  205  covered w a l l area per u n i t l e n g t h  m^/m  M  number of p a r t i c l e s per u n i t volume  m~3  m  number of p a r t i c l e s per u n i t area  m~2  N  rotational  rpm  V  N n  C  speed  c r i t i c a l r o t a t i o n a l speed rotational  rpm rps  speed  Q  heat t r a n s f e r r a t e  W  q R  heat t r a n s f e r r a t e per u n i t l e n g t h  W/m  kiln  m  r  radius position  S  exposed area of p a r t i c l e  surface  m2  S'  covered area o f p a r t i c l e  surface  m  T  temperature  K  e n t e r i n g gas temperature  K  T  go  radius  m  gi sm t  e x i t gas temperature  K  p a r t i c l e mixing temperature  K  t  b  bed time  t  c  t  s  t  t  T  r e t e n t i o n time or r e s i d e n c e contact  time  2  S  s time  s  s u r f a c e time.  s  c y c l e time  s  tx  r e t e n t i o n time  s  U  average a x i a l v e l o c i t y  m/s  v e l o c i t y d e f i n e d i n equation Uo  7-19  o v e r a l l g a s - s o l i d heat t r a n s f e r coefficient  v  a  m/s W/m K 3  a x i a l v e l o c i t y on bed s u r f a c e  m/s  Vl V  l a t e r a l v e l o c i t y on bed s u r f a c e  m/s  r a d i a l v e l o c i t y i n the bed r e g i o n  w  mass flowrate  m/s kg/hr  X  distance  m  z  x/L  -  r  206  Greek l e t t e r s a a  0  Kiln inclination  angle  radian  Kiln inclination  angle  degree  C e n t r a l angle of the s e c t o r  3  occupied  by the s o l i d bed  radian  e  s t a t i c angle o f repose  radian  e•  dynamic angle of repose  radian  e  dynamic angle of repose  degree  ?  dimensionless  n  degree of s o l i d  -  X  Angle between i n c l i n e d bed & h o r i z o n t a l  radian  Ug  gas absolute  Ns/m  vg  gas kinematic  viscosity  m /s  Ps  p a r t i c l e bulk  density  kg/m^  PP  p a r t i c l e true density  kg/m^  gas d e n s i t y  kg/m^  bed  height  m  T  bed  h e i g h t a t x=L  m  ,  Stefan-Boltzmann (5.67xl0 )  0  g T  p  L a  time fill  viscotiy  2  2  W/m K4  constant  2  -8  °e  absolute  variance  s  relative  variance  -  shearing  angle  radian  Angle between bed s u r f a c e and kiln angular  axis  radian  velocity  radian/s  u  c  c r i t i c a l angular  6  U  parameter d e f i n e d i n Equation  e  g s  e  w K e  velocity  radian/s 2-31  m  gas e m i s s i v i t y  -  solid emissivity  -  wall emissivity Thickness o f s u r f a c e  region  m  Dimensionless Groups  Bi  hD/k  Fo  at/r P  Fr  N  B i o t number  s  F o u r i e r number  / c  Froude number  N  d p g 1— a  G a  G a l l i l e o number  y  R cos  Nj,  L  9  d e f i n e d i n Chapter 2  tana  N,  — 3  F sm0 nR tana  d e f i n e d i n Chapter 2  Nu  hD k~  Nusselt  NUp  ^Pf^P  p a r t i c l e Nusselt  Pe  uL/D  P e c l e t number  Pr  C y/k P 9  P r a n d t l number  Re  uDp^/y  R e  p  u  o g^p P  g  number  number  Reynolds number p a r t i c l e Reynolds number  2  Re^,  D ojp _J;—9 y y  R o t a t i n g Reynolds number T a y l o r number  208  Subscripts: g  gas  p  particle  s  bulk s o l i d m a t e r i a l ,  w  exposed w a l l  w  covered  gs  gas t o s o l i d  gw  gas t o w a l l  sw  s o l i d bed to covered w a l l p a r t i c l e i n the f i r s t exposed l a y e r  1  bed  wall bed  p a r t i c l e i n the second  layer  209 REFERENCES 1.  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( E d i t o r - i n - C h i e f ) Chemical E n g i n e e r i n g Handbook, 3rd E d i t i o n , p. 831, McGraw-Hill, New York 1950.  series.  48^:, Gygi, H. ,  'The Thermal E f f i c i e n c y o f the Rotary Cement Kiln'. Cement and Lime Manufacture, p. 82, A p r i l , 1938.  49.  Friedman,  S.J. and. M a r s h a l l , W.R.J., 'Studies i n Rotary Drying, P a r t I I Heat and Mass T r a n s f e r ' , Chemical E n g i n e e r i n g Progress, 45(9), 573 (1949).  50.  Chen, C.C., Lu, W.M. and Teng, L.T., 'Heat T r a n s f e r i n the Through Flow Rotary Dryer', J . o f Chinese I n s t i t u t e of Chemical Engineers, 5, 1-6 (1974).  213  51.  K a i s e r , V.A. and Lane,J.W., correspondence t o Saas 'Simul a t i o n o f the Heat T r a n s f e r Phenomena i n a Rotary K i l n ' , I & EC Process Design and Development, 1_ (2) 318 (1968).  52.  E c k e r t , E.R.G., and Drake,. R.M., 'Heat and Mass T r a n s f e r ' , McGraw H i l l , New York, 1959, p. 405.  53.  Luethge, J.A., 'Measurement and C o n t r o l o f Temperatures i n Rotary K i l n s ' , Instrumentation Technology, 46, March 1968.  54.-  Venkateswaran,V.,. M.A.Sc. Thesis, 1976, British  The U n i v e r s i t y o f  Columbia.  55.  1974 ASTM Standard book, E-220 and E-230.  56.  H i l l s , A.W.D. and P a u l i n , A., 'The C o n s t r u c t i o n and C a l i b r a t i o n o f an Inexpensive M i c r o s u c t i o n Pyrometer', J o u r n a l o f S c i e n t i f i c Instruments (J. o f P h y s i c s E) 2, 713 (1969). B r i n n , M.S., Friedman, S.J., G l u c k e r t , F.A. and P i g f o r d , L.R., 'Heat T r a n s f e r t o Granular M a t e r i a l s ' , Ind. Eng. Chem., 4£, 1050 (1948).  57.  58.  K r e i t h , F., ' P r i n c i p l e s o f Heat T r a n s f e r , I n t e r n a t i o n a l Textbook Co., Scranton, Pa. (1969).  59.  I r v i n e , T.F. J r . and H a r t n e t t , J.P., 'Steam and A i r Tables i n SI U n i t s ' , Hemisphere Pub. Co., Washington (1976)  60.  Friedman,  61.  Shevtsov, B.I., Kubyshev, N.N., C h e r e p i v s k i i , A.A. and Bogdanov, Yu.Yu., 'Determination o f the Rate o f Movement o f the Charge i n Rotary K i l n by means of R a d i o a c t i v e Isotopes', I n t e r n a t i o n a l Chemical E n g i n e e r i n g , .11(2) , 252 (1971) .  62.  M i s k e l l , F., and M a r s h a l l , J r . , W.R., 'A Study o f R e t e n t i o n Time i n a Rotary Dryer', Chemical E n g i n e e r i n g Progress, 5_2(1) , 35 (1956).  63.  B o t t e r i l l , J.S., B u t t , M.H.D., C a i n , G.L. and Redish, K.A., Proc. Eindhoven F l u i d i z a t i o n Symposium, p.442 (1967) .  64.  E r n e s t , R. , 'Warmeubergang anJ'.Warmeaustauschern i n Moving Bed', Chem, Ing. Techn. 3j2, 17 (1960).  1  S.J. and M a r s h a l l , J r . , W.R., 'Studies i n Rotary Drying - P a r t I - Holdup"arid;Dusting', Chemical E n g i n e e r i n g P r o g r e s s , 45(3), 482 (1949).  214  65.  Rohsenow W.M. and H a r t n e t t , J.P. ( E d i t o r s - i n - C h i e f ) , 'Handbook o f Heat T r a n s f e r ' , McGraw-Hill Inc., N.Y., N.Y. (1973).  66.  McAdams,  67.  S c h l i c h t i n g , H., 'Boundary Layer Theory', p. 407, McGrawH i l l Book Co. Inc., N.Y., 1957.  68.  Cannon, J.N'.., 'Heat T r a n s f e r from a f l u i d flow i n s i d e .a R o t a t i n g C y l i n d e r ' , Ph.D. d i s s e r t a t i o n , S t a n f o r d U n i v e r s i t y , 1965.  69.  Brimacombe and Watkinson, ' C a l c i n a t i o n o f Limestone i n a Rotary K i l n ' , 17th Conference o f M e t a l l u r g i s t s , CIM, Vancouver, August,•1977.  70.  Carslaw, H.S. and Jaeger, J . c , 'Conduction o f Heat i n S o l i d s ' . 1947, Oxford.  71.  Kunii  'Heat T r a n s m i s s i o n ' , McGraw-Hill Book Co., 1954.  D. & L e v e n s p i e l , O, ' F l u i d i z a t i o n Engineering', Hohn Wiley & Sons, Inc., New York. 1969.  APPENDIX  CALIBRATION  1..  Thermocouple  The an  Calibration  equipped  temperatures  recorded  up  with  Haake  t o 400  on Watanabe  K.  the thermocouples  eratures,  the melting points  692.75 K ) .  couple  was  readings Figure for  The m e t a l  they melted then  were  A - l .  t i n and  The  Figure  into  shows  of  300  fitted  by  the metal  heated  shut  bath.  and  baths  The m i l l i v o l t  least  were  641) .  In  a t two  temp-  i n the  off. The  The  were  23.00 mV,  bath thermo-  millivolt shown i n  were  squares  o f thermocouple  obtained  over  calibration  the temperature  readings  f o r each  = a + b  range  thermocouple  to a quadratic equation of the  form,  T  FS)  (504.8 K a n d  The r e s u l t s  the results  the constant temperature  were  then  in  respectively.  A-2  K.  was  (Model  zinc  first  (Model  readings  calibrated  f o r t i n and  12.60 mV  in  t o 700  also  and r e c o r d e d .  readings  zinc  were  calibrated  regulator  recorder  g r a n u l e s were  dipped  were  The m i l l i v o l t  and the heat  taken  thermo  Multicorder  addition,  until  EQUIPMENT  iron-constantan thermocouples  o i l bath  for  OF  A  (millivolts)  + c  (millivolts)  Figure A - l  C a l i b r a t i o n of Thermocouple i n Metal  Baths.  217  F i g u r e A-2  C a l i b r a t i o n of Iron-Constantan Thermocouples.  The constants f o r the above equation are given i n Table A - l , along w i t h the d e v i a t i o n s of the c a l i b r a t e d v a l u e s from measured v a l u e s a t two temperatures.  The measured v a l u e s were a l s o  compared w i t h those t a b l e d i n the ASTM Standard manual w i t h the maximum d e v i a t i o n of + 1.8 F.  (55)  The thermocouple data  i n the manual are given i n Table A-2.  2.  C a l i b r a t i o n of Rotameter  The rotameters were c a l i b r a t e d a g a i n s t gas meters, The c a l i b r a t i o n curves are g i v e n i n F i g u r e s A-3  and A - k .  \  219  Table A - l Calibration  THERMOCOUPLE NO.  o f Thermocouples  Deviation a  b  K  c 34 3°K  504.  A  279.21  17.9 61  o.oooo  . 0.36  0.70  B  279.55  17.935  0.0003  0.08  0.79  C  278.11  18.187  -0.0111  0.29  0 .35  D  277.72  18.197  -0.0108  0.30  0.39  E  277.75  18.425  -0.0224  0.27  0. 65  F  280.03  17.875  0.0020  -0.53  G  278.08  18.158  0.0005  0.30  0 .33  H  280.32  17.327  0.0324  0.32  0.80  I  279.87  17.553  0.0062  0.17  0.87  J  277.55  18.189  -0.0101  0.29  0.33  K  279.12  17.681  0.0266  -0.03  0.41  L  276.28  18.736  -0.0346  0.14  0.28  M  278.38  18.047  -0.0022  0.71  0.61  N  269.60  20.980  -0.1348  0.23  -0>.-81  0  282.91  16.707  - 0.0367  0.71  0.92  P  277.70  18.104  -0.0034  0.58  0 . 47  Q  284.13  16.078  0.0910  0.54  0.98  R  273.89  19.869  -0.0529  0.61  -0.10  S  277.80  17.931  0.0108  0.06  0.65  T  268.41  20.874  -0.1174  -0.11  -1.00  T  (K) = a + b ( m i l l i v o l t s )  0.78  + c(millivolts)  Table A-2 Thermocouple Data Reference Temperature at 0 ' C. Voltage millivolt  Temperature C  Temperature K  1. 019  20  293.15  1.536  30  303.15  2. 058  40  313.15  2.585  50  323.15  3.116  60  333.15  3.649  70  343.15  4.186  80  353.15  4.725  90  363.15  5.268  100  373.15  6 . 359  120  393.15  7.457  140  413.15  8.560  160  433.15  9.667  180  453.15  10.777  200  473.15  12.998  240  513.15  15.217  280  553.15  16.325  300  573.15  18.537  340  613.15  SCALE OF ROTAMETER, gure A-3  %  A i r Flow Rate versus Reading on Rotameter Scale  (Rotameter 2854).  0  20  40  60  80  100  120  140  160  180  200  220  240  260  READINGS F i g u r e A-4  S u c t i o n Rate versus  Reading on Rotameter Scale  (Rotameter 2487).  APPENDIX B SURFACE  1.  Determination  AREA  transfer surface  ratio  s  The  t o gas stream.  of  A /A ,  t h e exposed  in  each  of the f i r s t  differential  surface  However, o n l y  exposed s  i s important  1  be  g  s  of A /A  coefficient. layers.  SURFACE V E L O C I T Y  o f A'/A /  The  AND  surface  region  the f i r s t  In order  surface  area  two  layers  area  of a  d = -P— 4  i n determining  have  heat  comprises  several  two l a y e r s  seem t o  to calculate the of individual  ratio  particles  t o be d e t e r m i n e d .  The  spherical particle i s  2  dS  The a  cubic  given the  of particles  arrangement  i n Figure  first  surface the  array  as given  7-2A.  layers  desinc  i n Figure  In the l a t t e r  a r e shown  equation.  (B-l)  i n the f i r s t  i n Figure  of individual particle  following  dt,  two  7-2B,  array, B-l.  layers  or a  i s either  structure  as  the particles i n Therefore,  c a n be o b t a i n e d  the exposed  by i n t e g r a t i n g  225  2  r  5  2TT  S, =  f V*  de 0  sin? d.c,  J 0  TTd  1 +  I T  (R-2)  S i m i l a r l y , the exposed area of the second l a y e r  par-  ticle is 2ir  d 2 2-n  r  r  S-, =  T  de  4  J  0  J  0  s i n ? d?  3 ir , 2 —• d 8 P  (B-3)  Consider a plane s u r f a c e with dimension  2  as shown i n F i g u r e 7-2A. first  3d^ by ( 1 + -Jf_ )d P  There are two p a r t i c l e s i n the  l a y e r and 6 p a r t i c l e s i n the second l a y e r .  Thus, the  r a t i o of A ' / A i s s s  AJ 3  2S  A  3d (1-^") d P T' p  s o  + 6S  1  2  = 2.42  (B-4)  v  In a c u b i c a r r a y as shown i n F i g u r e 7-2A the aerated area o f i n d i v i d u a l p a r t i c l e i n the f i r s t  l a y e r i s represented by  S  It  n  1  = L  d  2  p  (B-5)  2  i s assumed t h a t a l l the space other than t h a t occupied  by the f i r s t particles.  l a y e r p a r t i c l e s are aerated by the second l a y e r T h e r e f o r e , the t o t a l exposed area of the f i r s t  layer  p a r t i c l e s i n a plane area, 4 d x 4d i s P P  ^d  x  2 p  16  =  8ird  CB-6)  2 p  and t h a t of the second l a y e r p a r t i c l e s are  4d  P  x 4d  - 16 - d P 4 P  The r a t i o of A /A s s  A'  -2. = s  A  2.  8ird  +  2  )d  2  P  (B-7)  J  -  4 (4  IT ) d  P_ 16  TT  f o r a cubic array i s  P.  e  = 4(4 -  d  p  =  1  >  7  8  ( B  _  8 )  2  P a r t i c l e exchange r a t e between the bed r e g i o n and the surface region The temperature of the a e r a t e d s u r f a c e p a r t i c l e s  be r a i s e d from T gion.  g  to T  will  before they r e t u r n i n t o the bed r e -  J u s t before they r e t u r n t o the bed the heated  particles  227  mix  with the p a r t i c l e s i n the other s u r f a c e l a y e r s , which  r e c e i v e no heat from the gas  stream.  In order to f i n d  the  temperature of the mixture the r a t e of the p a r t i c l e s emerging out of the bed r e g i o n must be determined. Assume the k i l n r o t a t e s a t a speed, JI, as shown i n F i g ure B-2. The  The  angular  v e l o c i t y w i l l be  w  = 2im  v e l o c i t y of the p a r t i c l e s normal to the bed  V  N  (radians/s). surface i s  = ur s i n ?  (B-9)  L e t l ' be the l e n g t h of the boundary between the s  face r e g i o n and  the bed,  and M,  the number of p a r t i c l e s  1' For a plane area, Ax — 2 the p a r t i c l e s i s represented by  u n i t volume.  s  surper  , the emerging r a t e of  V/2 V dy  (B-10)  0  where y i s the d i s t a n c e from the c e n t r a l l i n e , OA 1 i n F i g u r e B-2. L e t h^, be equal to OA'. Then  y = h '  tan? •  r = h '  sec?  R  and  The  f i r s t equation  f o l l o w i n g equation  R  1  i s d e r i v e d with r e s p e c t to ? and i s obtained  as shown  (B-ll)  the  Figure  B-2  Emerging Rate of P a r t i c l e s from Bed Region to Surface Region  229  dy  Therefore,  =  equation  F_ m  =  h  ' sec  B-10  f  MAx  ?  d?  (B-12)  i s rewritten  2  wh'"  7  tan?  sec  and  2  t,  integrated  as  follows:  d?  0  ,2  =  MAxuh  =  JsMAxcjh'  1  7  —4  term,  to  kiln  of  the  l  s  ' ,  diameter surface  By  2  s  and  2  (B-13)  length degree  region.  taking  o  A T ' n M. A/ x. l cS  i s the  ?  tan -^-'  2  B  -T£1AXUV1  The  3s s e c  B  of  the  boundary  f i l l .  Let  line,  K be  the  and  related  thickness  Then  hg  = h  square  on  '2  of  B  + K  both  sides,  equation  B-14  is  obtained  2  (B-14)  Since v., 2  2  and  equation B-14 can be r e w r i t t e n as  l ' s  2  = Is -  8RKCOS-| +  K  (B-15)  2  2 By n e g l e c t i n g K , equation B-13 f o r F  F  M  = - MAxn(l  2  4  -  8RKCOS|-  m  becomes-  )  (B-16)  As i n d i c a t e d i n F i g u r e 6-3, the p a r t i c l e v e l o c i t y i n the s u r f a c e r e g i o n can be approximated by a l i n e a r f u n c t i o n as  V =  V, <  (B-17)  x  where t, i s the d i s t a n c e outv/ard  from the boundary between two  r e g i o n as shown i n F i g u r e B-3, and of p a r t i c l e s i n the f i r s t  layer.  i s the s u r f a c e  velocity  For a width Ax o f the k i l n  the r a t e of the p a r t i c l e s r o l l i n g on the bed s u r f a c e i s r e presented by  F i g u r e B-3  Particle Velocity Region.  P r p f i l e i n Surface  2.32  F,. = m  =  By a  KV  a  function  is  then  by  the  K  0  kMAxKV  (B-18)  x  e q u a t i n g e q u a t i o n B-16  relationship  In  MAx  f  of  n  ( l  addition,-  the  of  =  K and  2  square  depending following  on  as  -  2 s  the  K  of  (B-19)  rotational  rotational  obtain  n.  velocity,  — + 8Rcos^ l Un s  of  one  8RKCOS|)  equation  1  e q u a t i o n B-18,  functions  surface  root  and  was  speed,  speed  and  found  the  as  thickness  degree  of  f i l l  APPENDIX C SAMPLE CALCULATIONS 1.  C a l c u l a t i o n o f r e s i d e n c e time d i s t r i b u t i o n The sample c a l c u l a t i o n s f o r mean r e s i d e n c e time, v a r i -  ance, P e c l e t number and d i s p e r s i o n c o e f f i c i e n t are presented. The experimental data f o r run R2 i s given i n the f i r s t two columns i n Table C - l .  The c o n c e n t r a t i o n , C ( t ^ ) r e p r e s e n t s  no. o f t r a c e r i n the sample C(t )  no. o f t o t a l t r a c e r used  =  ±  wt. o f sample wt. o f bed  In t h i s run, the weight o f t o t a l c o l o r t r a c e r used was 13.7 gm (939  individual tracers).  t = 8 minute.  The f i r s t  sample was c o l l e c t e d a t  A f t e r the t r a c e r s were f e d .  The weight of the  sample was 243.9 g i n which 5 t r a c e r s were found. weight was 9.4 kg.  C(t.) 1  =  Thus C ( t ^ ) f o r the f i r s t  —  5  /  9  3  9  The bed  sample i s  = 0.205  243.9/9^00  With the same procedure the v a l u e s o f C ( t . ) , i = 2,  3  M  234  Table C - l T a b u l a t i o n of t.  1  (min)  c(t ) i  ( - )  C a l c u l a t i o n f o r RTD run (R2) F(t )  F(t.)t.At.  1 1  ±  (min)"  l  E(t ) ( t i  ±  1  8. 00  0.205  2.09xl0  0.042  0.0072  8. 25  2. 300  23.40  0.483  0 . 0495  8.50  5.159  54.58  1.158  0.0612  8 . 75  6.731  6 8.47  1.498  0.0302  9. 00  9 . 571  97.37  2.190  0.0703  9 . 25  5.924  60.26  1. 394  0.OHIO  9.50  3.543  36.04  0.859  0.0098  9. 75  1.582  16.09  0.392  0.0135  10.00  1.360  13.84  0 . 346  0.0238  10.25  0.622  6.33  0.162  0.0185  10.50  0.580  5.9 0  0.155  0.0261  10.75  0.402  4.09  0.102  0.0255  11. 00  0 . 360  3.66  n. i n i  0.0307  11.25  0.345  3.51  0.099  0,0380  11.50  0.268  2.73  0.079  0.0371  11. 75  0.194  1.97  0.058  0.0328  12. 00  0.160  1.63  0.041  0.0326  -2  9.17  (min)  0.453 (min)  are c a l c u l a t e d equation 5-5, defined  and  the r e s u l t s are  the e x i t age  l i s t e d i n Table C - l .  d i s t r i b u t i o n function  E(t^)  From is  as  E(t )  C(t. ) = — EC ( t . ) A t . 1 l l  =  i  where  Therefore F(t.) I  EC(t.)At i  = 9.83  f o r the  first  E(t.)  =  0  ,  and  E(t^)  i n the  f o r a l l the  2  0  sam.Dle i s  = 0.0209  5  9.83  1  (min)  samples are  calculated  second column i n Table C - l .  time and  v a r i a n c e can  be  a  2 t  and  tabulated  from  M t - E t.E(t.)At i=l and  1  Then the mean r e s i d e n c e  calculated  1  (min)  (5-3)  1  M = Z ( t - t ) F, ( t ) At i=l 2  ±  ±  (5-4)  The v a l u e s o f E ( t ^ ) t ^ A t ^ f o r each sample i s c a l c u l a t e d and t a b u l a t e d i n the f o u r t h column i n Table C - l .  Since the  time i n t e r v a l f o r each sample At^ = 0.25 min, the summation of the v a l u e s i n the f o u r t h column g i v e s n  t = E F, (t. ) t. At i=l 1  1  = 9.17 (min)  _ 2 The mean r e s i d e n c e time allows the c a l c u l a t i o n of (t^-.t) E ( t ^ ) f o r each sample.  The r e s u l t s are l i s t e d i n the same t a b l e .  Therefore, 6  2  = 0.453  (min)  2  The r e l a t i v e v a r i a n c e and P e c l e t number a r e then as j 6„ =  6 -A, 2  =  0.453 (9.17)  = 5.39x10 2  and Pe = ^  = 371  Then the a x i a l d i s p e r s i o n c o e f f i c i e n t , D i s  calculated  Pe  2 44^"  =  2.  tPe  9.17x60x371  -S  2  m/s  C a l c u l a t i o n o f the heat t r a n s f e r C o e f f i c i e n t The computer  program  c a l c u l a t i o n s i s appended. run  = 2.91x10  t h a t was  used r o u t i n e l y f o r these  The sample c a l c u l a t i o n i s done f o r  A16. The a i r flow r a t e and the s o l i d feed r a t e f o r the run  were 24.6 kg/hr and 14.2 kg/hr r e s p e c t i v e l y . speed was the  1.5 rpm,  the i n c l i n a t i o n angle was  s o l i d holdup was  17%.  1.2 degree and  The temperatures o f a i r , sand and  w a l l were measured a t x= 1.25 m and 1.78 entrance .end.  The r o t a t i o n a l  m from the solid,  The temperature were then i n t e r p o l a t e d and g i v e n  i n the t a b l e i n Appendix E.  The l o c a l heat flows f o r s o l i d s  to w a l l , gas to s o l i d s and gas to w a l l a t a given a x i a l l o c a t i o n are c a l c u l a t e d . s o l i d s to bed r e q u i r e s  The d e t e r m i n a t i o n of heat flow from the knowledge of s o l i d s to bed heat  t r a n s f e r c o e f f i c i e n t which are o b t a i n e d from F i g u r e 6-26. -6 d i f f u s i v i t y of Ottawa sand, a = 0.225x10 conductivity  of Ottawa sand, k  g  value of  2 m / s , the thermal  = 0.268 W/mK.  angle f o r occupied s o l i d s i s g = 1.98  The  radians.  The c e n t e r Thus, the  238  ^ r  2  =  5  - x  ( 0 . 0 9 5 2 5 )  22  1 0 . 2 2 6  a  1 . 9 8  x  2  x  =  1 9 8 7  1 0  From equation 6-25, the N u s s e l t number i s  hswi ' w k  0 3 = 11.6 ( 1 9 8 7 ) ' = 113.2 J  J  s  and  1 = BR = 0.189 m. w  h  Thus, the value o f h i s ' sw  = 113.2 x 0.268/0.189 = 160.5 W/m K 2  g w  Since there i s a l a y e r o f cement about 1 mm t h i c k on the w a l l , and i t s thermal c o n d u c t i v i t y valent  heat t r a n s f e r c o e f f i c i e n t across t h i s l a y e r i s 0.294/ -3  1.0x10  i s 0.294 W/mK the equi-  2 = 294 W/m K.  The o v e r a l l heat t r a n s f e r c o e f f i c i e n t  is h  =  = 103.8 W/m K 2  sw,o  1  1605  1  2940  Then the l o c a l heat flow from s o l i d s bed can be c a l c u l a t e d a t a given a x i a l l o c a t i o n by  <W  x )  = ^w^w  ( T  s-  V  239  For i n s t a n c e a t x = 1.25 m, T the value o f q  g  = 374.0 K and  = 369.2 K,  (x) a t x = 1.25 ni i s 57.2 W/m.  The heat re-  c e i v e d by the s o l i d s i s c a l c u l a t e d by  dH (x) s _  C  ps  W  s  dx  C  Thus  C  s  dx  j  where  dT  = 0.653 + 0.215xlO" T 3  ps p  (J/gK)  = 0.733. . '  The v a l u e o f  dT /dx was o b t a i n e d by the S p l i n e f u n c t i o n g  dT -- dx  = 57.3 K/m  S  T h e r e f o r e , the heat r e c e i v e d by the s o l i d s i s  dH (x) kg 1000 |L —= 14.2 — x dx hr 3600 =hr = 16 6.  x  0.733 J/gK x 57.3 K/m  W/m  From equation 6-15, the heat t r a n s f e r r e d from the gas to the s o l i d s i s dH (x) g (x) = " " " -gs 5  d  x  + q  (x)  240  = 223.2  W/m  Then, the heat which the gas g i v e s up i s c a l c u l a t e d  from  equation 6-8  dH (x) g _ dx  G  W pg  g  dT g dx  where C  = 1.0017 + 0.042 T/lfffco pg . '  C  =1.0 21 J/gK pg  and by the S p l i n e  function,  dT —2- = 4 5.9 K/m dx  Therefore,  dH (x) —2  , 1000 = 24.6^ x : £2. 3600 p^r  x  dx  n  =  320.4  r  W/m  1.021  J/gK x 45.9 K/m  From e q u a t i o n 6-16, the l o c a l heat flow from the gas t o the w a l l a t x = 1.25 m i s dH (x) g  q  gw  - q (x) ^gs  dx  = 320.4-223.2=97.2  W/m  With the same procedures, the l o c a l heat flows a t x = 1.30, 1.40, 1.50, 1.60 and 1.78 m are a l s o c a l c u l a t e d .  The r e s u l t s  are given i n the t a b l e on page 261. The average heat t r a n s f e r r a t e per u n i t l e n g t h f o r the test section, q and q can be c a l c u l a t e d from equations ^gs ^gw ^ 6-17 and 18, r e s p e c t i v e l y .  r 2 x  = 291.5 W/m  and q gw M  =  r  x  2  I J  x  q (x)dx/(x~ - x, ) gw ' 2 1  J  i  = 10 7.0 where x^, x x  0  2  W/m  a r e l o c a t i o n s f o r two ends o f the t e s t  - x-, = 0.53 m.  section.  T h e r e f o r e , the l o g a r i t h m i c  mean heat t r a n s f e r  coeffi-  c i e n t s f o r gas t o s o l i d s and gas t o w a l l are r e p r e s e n t e d by  h  and  h  gs  = q / l (T - T J , ^gs s g s lm  gw  = q / l (T - T ) ^gw w g w lm n  r e s p e c t i v e l y , where  ( T  g  T  s lm ;  (462.0 - 374.0) - (492.0 - 417.0) 462.0 - 374.0 492.0 - 417.0  = 81.3 K and 1  g  _  . _ (462.0 - 369.2) - (492.0 - 410.5) w'lm 462.0 - 369.2 492.0 - 410.5  8 7.0 K  In  addition,  1  = 2R sin-?1  no  = 2 x 0.09525 s i n i ^ - =0.175 m 2  243  and 1 = w  (2TT -g)R  = (6.28 - 1.98)x0.09525 = 0.410 m  Thus, the heat t r a n s f e r  coefficients  from gas t o s o l i d s and gas  to w a l l are  h  = 291.5/0.175/81.3 = 22.5 W/m K 2  g s  and h  = 107.0/0.41/87.0 =3.0  W/m K 2  COMPUTER PROGRAMS  THIS PROGRAM MODELS THE ROTARY K U N BASED ON EQUATIONS 8-1 AND 8-2, USING THE CORRELATED HEAT TRANSFER COEFFICIENTS. N U ( G S I = 0 . 4 6 « R E * * { 0 . ! 3 5 ) * R E W * * ( 0. 104)*FI L L * * (-0.341) NU(GWI=1.54*RE**(0.575)*REW**(-0.292) THE CHARGE TEMPERATURE TEMPERATURE IS 500 K  IS FIXED AT 350 K WHILE AIR INLET  DIMENSION Y ( 3 ) , F ( 3 1 , 0 ( 3 ) , T G ( 1 0 0 ) , T S t 1 0 0 ) , T W ( 1 0 C ) , Z ( I O C I COMMON D 1 , 0 2 , D 3 , E 1 , E 2 , E 3 , T 0 REAL L , K W , K S , N , L l . L 2 , L S , L 0 PI=3.14159 Y(1)=0.0 JJ = 10 STFP=0.01 M=10  11*0.0  C C C  NN = 3 J=0 KILN DIMENSION R0=1.15 RI=1.0 D=2.C*Rl L=r/3.0*50. KS KW DIFF DENS  .  SOLID THERMAL CONDUCTIVITY, W/M K. REFRACTORY THERMAL CONDUCTIVITY. DIFFUSIVITY, M2/SEC SCLIO BULK DENSITY, KG/M3  KS=0.268 KW=0.043 0TFF=0.225E-C6 0ENS=1.602E+03 N ROTATIONAL SPEED, RFM. FILL OEFREE OF F I L L . ALPH INCLINATICN ANGLE, DEGREE. BETA CENTRAL ANGLE OF THE OCCUPIED BED, RADIAN. N=1.225 FILL=0.11 ALFH=0.B570  C C C C C  C C C C C C  C C C  cc c  BETA=1.68 WRITE(6,149) 149 FCPVATP READY FOR TGO, TSO IN FCRMAT 2 F 5 . 1 ' ) PF»(M5.151> Y(2),Y(3) TS1=Y(3) 151 F O F « A T ( 2 F 5 . 1 l « l P t - » = ALPH/57.32 BEE=BETA/2. BE E=COS(BEE• HP=RI*(1.0-BEE) WS : SOLID THROUGHPUT, CALCULATED BY WS=1.295*HB*D**2*ALPHA*DENS*N/SIN(THETA) WS*1.295*HB*D**2.0 VS = t « S * A L P H A / 0 . 4 5 4 KS=WS*nENS*60.*N APE»=PT*R1*RI WG = WS PPf=PFTA/2.0 BP E = SIN(BBE) CE: EOUIVALENT  DIAMETER.  DE-(2.*PI-BETAI*RI*2.*RI*BBE DF=P!*RI*Rt*(1.0-FILL)/DE DE=4.*DE T0=2S3. CALCULATE THE CCNTACT AREA PER UNIT LENGTH. L i : EXPOSED AREA. 12: COVERED AREA. L S : BED SURFACE AREA. L1-(2.*PI-RETA)*R! L2=PET8*RI  LS=2.0*RI*eEE  CALCULATE OF HEAT TRANSFER  COEFFICIENTS  HOMC.O  NNNN=3 24 IF(NNNN-IO) 21.21,22 21 T=(Y(2)-273.)/10C0. TT=(Y(3)-273.1/1000.  NO  n  x o  z  U-  Ul a O  II •-4 CJ LU * a 0 * II Ul z UJ . 0  •  II IL a II -  •  PI  00  •  * u. rvi *  • 0 to z LU UJ * c * • II O LO CL LU O » LO II » O et 0 » to a Cf (_> UJ • 0. O «— 0 «-< 0 CC LU 0 a • ru • II tn «e  PI  • PI • II gj • _ J u. u. •> »  -J  • • • ft m pi * *  • a  * *v O • a z  •  PI  * *  (-0 a o o o K . "V. v. >s. Ul ui IT* <\J JE QU o 2 Jt a o  D. O-  e* v.  _J - J  "N.  *  # CP Ul CM 1 (M * » Ul + t/i o o o V) X X X cu H H n II II pi CC CO a. o #  *  -J  —1  •  «  *«  or  <i CD *  «  + a)  3  <  < *  *  < l  *  •4a" •  •M  o  *  #  H  <  *  j z n LU • — X o o LL o o  m m * pi to  +  t—i  *  >  ••  •I•I  II — K CC C LU <2 -J  < # o  m Pi ca < a; CD cu it I I li It II rsj p. <M pi c UJ Hi LU  •LUII o  -> «-> UL ^*  t— (X a o 2 UP>  m  •  o o  w U.  *  _J  »>  •  - J C"i U. z * LU 1— — • v- II I a: a. — LU _j O CL O O m •  O w •  w *LU «t  3L • «— CC a. 0 U. LL  O  c 0 m  O CM  »4  P-4 *• —  LU  I <I — a -J cr  2 U. Ct LJ LL.  •  • 0  LU  w tn CO  3: • II » to Li-i j * CD  •  ^  •  II z  •»t LU  0 3:  m  m  •  •  *  •  », X fSJ  — — X n  CO  »  PvJ CD  LU  UJ  •  •  •  zr  •  k-  ^~  Ql 3E  z <r  O >f  »-*  LU  ^:  O tn  CJ to  0  <  *  *  u  -az z  X 1Ui 2.  • LU LU m  •  ~- II O UJ O a CC  0 0 «o  in  t-  CC  LU • cr 0 CL  UJ  >  LU  z <i * •.  0  O  O  1<I =3  II Ul*. JE u> UJ  — *0 w K >— «l LU <k u, <i LU 2' t— 3'. X 1iXCL »—• u. • U cx l _ a 0 O. LL 2 LL V u. 3  *c0  w LU  z  •  ••  in UJ w LU m ul » < m » • x x X. » ro X LU 0, rg •v. O X LL. < * * a I/) •. Ul LU or rvj » e L.« LU O X LJ t• LU O < X <i LU — a — < 0 <x O in O LLl O a O O X •«• in X <NJ  to z 0  • 0 jr O  • •> «-i • m 0 CC 0 LU  •  t  * • tl CO  +  * a Ul  <r  to  =>  0 -3 • —) U-  »-K  ^:  KI  •  _1 * a LU K — CO (NI * —  ^It > —  CC tJ a. ^ —J + -> 11 11 0 u - j Ki  0: LU UJ  O  O CD  Ul  MM  » B  LU O z  < < • 2 0 a. "-• LJ UJ LL •  «  * eg <  +  w KI II 11 II II — — to-. —' c ; Ui JK K!  •-  m  uuuuu  UJ  < o I  X  u 3 (M  rg  >  # •  l / l ^<  K U =) o 2  - *  UJ ^« t- t- - J  1 l~ *  3 «  0 u> go <\ 1 v f~ • UJ c * m 0 it tr  0 1 u* 0  r~  ^4  t/> C C I U VJ c/1 (/) — >  »  *  Q u i V z u.  I  4  « x: t-  v i t/i < < c  u  e  -r  <  o —fc-JJt  . V) *  > > <  O  O  O  O  •  O  •  —  n * r* ui • > II (1 to 1/1 >  .  1•-• P z • 3 — II 1  Ul  > ^  o  2  +  l*  +  0 3  •  ^4 + a  Ul  9-1  CD  <  «  *  00 p-  rg  c  C  *  CM rg  z «  « ru  *  •  «  •4"  LU CO 0 Ul 0 1 •v. « LU X r\l O V. X + m ^4 »~ rg •It  • <.^II  z -> =1 rg tl at ac u*— > > >  o  O  CC _ J  LU 1<I -J z> c —1  • It•  < <  o  LU « l  o  Ul CL u  0  l_> -J «t  •  CJ  z  U  X H  0  0  <l 0 in l  © •-•«•«  0  •  CD  *-  K- UJ  O CC rg  •  O  O  O II  JE  Ul X  31 ^  #CL LU # LU *  # * LU LU  »- ^1 a -J  0  -J  "V — JX —  ' .  1  a  V  . O a. I II I <  JE  0  0  0  -4-  O < < + 4(M O N • rg S I J < « X • * rg » • < CJ - J • — P I — _j • a. *s o # J t t v O u Wi • • -J X X CM <l ~* • - i it tt 11 it 11 l) rt IM CI 4 <f> < <1 <t < < <I N»  •J I  JE .JL JC JE JK Ul V I u« X St U l JC UJ LU k. Z 0 O O Ul Ul Ul u. Ul CC Ct < « X X O X X X X X X X X X  0  ^  • ~* •  -v  tn 0  • * cr + CC LU • * 0 • OI •-• CJ rg * 0 0 * —1 • cc a m * • » toO O CL 0 - J * JK a • lO ">V "V JT •—• O• • • # * * * *z 0• Ul gj LL m Ul * •• *v • • C) O *. Ul > O <-> ^ « u> « ("gCG * **JC « O 7 tn • II II -1 z O O O 0Ul Ul • Ul CD U) 3 0 rg• X X • X I X W; X JX n o w II II II II II II 11 ^ II It II X II  II  UJ  4  O  UJ UJ CC CL * *  *3" 00 • m m m LU • • ^ 0 0 0 0 0 UJ  UJ  Pi rg i_> m 11 c? a u  0 z  <  LU X Ct  • • 4  O X.  • #Z # UJ 0 £  LL U-  •v * Jt  » Ul  •  z"  *  JK O  # *r  — O • 1. O ~  — * » ># t  * 0 X  WRTTF(6,7C0) Z U l . T G t H , T S ( I » t T H ( t » IF f I . N E . J J ) GO TO 24 700 FCOWMI I X , F 1 0 . 3 , 3 ( 5 X , F 1 0 . 2 > ) 10 CONTIK'U? TTT»TG(JJ)-TS1 or 11 1=1,JJ  Zt I » = ZtI>/L  TC(TI=(TG(I)-TS1)/TTT TS(II»(TS(II-TSl)/TTT TW»I)=(TW(I1-TS1)/TTT V.PITF (6,701 ) It 1 ).TG( I ) , T S U J . T W U ) 701 F O B M A T ( I X , « F 1 0 . « » 11 CTNTINUE STOP ENO SUBRCUTIKE  AUXRKs EQUATIONS  SURfCUTTNE AUXRKtY.F) DIHEKSICN Y(3) ,F<3> COMMON 0 1 , D 2 , D 3 i E l . E 2 , F 3 , T 0 F(2)«D1*Y(2»-D2*Y<3)-D3*T0 F(3>«El*Y<2)-E2*Y(3>*E3*TO FETUfN  FNC  EXECUTIC* TERMINATED  *SIGNCFF  FOR RK CALAUIATION  c  C C C C C C C C C C C C C C C C  THIS PROGRAM IS WRITTEN FOR HEAT TRANSFER IN ROTARY KILN. A KILN OF 8 INCHES 00, T . 5 ID IS USEO FOR EXPFRIMENT TO OBTAIN TEMPERATURE PROFILES OF AIR SANC AND WALL ALONG THE KILN. THE MAIN OBJECTIVE IS TO EVALUATE HEAT TRANSFE COEFFICIENTS RASED ON EXPERIMENTAL DATA. NU SSELT AND REYNOLDS NUMBERS ARE ALSO CALULATED.  INPUT  C C C C C C C C  01 MENS ION X(30),LW(7),L<(7) , T WE ( 7 J , T ! E« 7) ,T SE (7) . TAE (7) DIMENSION T W I 3 0 ) , T ! t 3 0 ) , T S ( 3 0 ) , T A t 3 0 l . T S O I 3 0 ) , T A 0 I 3 0 I OIMENSION 51(30),S2<30),S3(30 I DIMENSION QSW(3C),0GS(30),0GW(30) DIMENSION OA(30),0S(30I,HTCGS(30),HTCGW(30) EOUIVALENCEISl,0A) ECUIVALENCEtS2,0S) ECU I VALENCE(S3,CGW) COMMON / A / L W , L S » T W E » T I E « T S E « T A E REAL K,LW,LS,NU EXTERNAL FCT TATA D f l T / l H . / , C0R/1HI/ RUN RUN NUMBER WA AIR FLOW RATE THROUGH K I L N , VS SAND FEED RATE, ROT ROTATATtONAL SPEED, RPM BIN INCLI NAT ICNAL ANGLE, DEGREE HCLDUP T  KG/HR KG/HR  DC 1111 1111=1,44 R E A D I S . l l l ) RUN,WA,ROT,WS , R IN , HCLDUP FORMAT( I X , A 4 , F 5 . 1 , F 6 . 2 . F 4 . I , ? X , F 4 . 2 , F 4 . I » WRITE(6,112) RUN»WA,ROT,WS»"IN,HOLDUP 112 FCPMAT(1H1//////22X,7HRUN N O . , 2 X , A 5 / / 4 X , 1 6 H A I R FLOW RATE 1 . F 5 . 1 . 6 H KG/HR, 10X, 17HR0TAT IONA L SPEED , F 4 . 1 , 4 H RPM/4X, 216HSAN0 FEED RATE . F 5 . 1 . 6 H KG/HR,10X,19HINCLI NATION ANGLE 3 . F 4 . 1 . 7 H DEGREE/4X.16HHCLDUP , F5 .1 , IX , 1H J / ) PER=H0LDUP/100. 111  C C C  LS THERMOCOUPLE tOCATlCN FOR AIR AND SOLIDS TEMPERATURES, M TfcE MEASURED WALL TEMPERATURE TIE MEASURED INSULATION TEMPERATURE TSE MEASURED SANO TEMPERATURE TAE MEASURED AIR TEMPERATURE LW(2)=0.31 LW(3)=0.91 LW»4)=1.52 LW<5)=2.13 LSt2) = 0.21 IS(3)=0.72 LS(4I=1.25 LS(5) = 1.78 LS(6I=2.32  CATA: RUN,WA,ROT,WS.RIN,HCLDUP MEASURED TEMPERATURES.  THE INTERPOLATED TEMPERATURES ARE CALCULATED BY THE USE OF SPLINE FUNCTIONS.  c  C C C C C C C  LW THERMOCOUPLE LOCATION FOR WALL TEMPERATURE FROM CHARGE END, M.  C C C  READ MEASURED TEMPERATURES . RFADI5.10) ( T W E ( I ) , 1 = 2 , 5 ) , ( T I E ( I ) , 1 = 2 , 5 I PEAC(5,10) ( T S F ( I ) . I = ? , 6 ) , t T A E ( I ) , I = 2 . 6 ) RE AD(5,10) TA0.TA6.TSO,TS6.TW0.TW5 00 16 l=?,6 WRITE(6, 171) LSI I ) , D O R , T A E ( I ) , T S E ( I ) , D O R 171 F C R M 6 T ( 7 X , F 4 . 2 , 2 X , A 1 , 2 ( F 6 . 0 , 2 X 1 , 1 6 X , A 1 ) I F d . E 0 . 6 t GO TO 16 WRITFI6.172) LW(I) ,DOR,TWE( I) ,T IE( I l.DOR 172 F C R M A T ( 7 X , F 4 . 2 , 2 X , A l , 1 6 X , 2 ( F 6 . 0 , 2 X l f A l > 16 CCNTINUE WRITE(6,173) 173 FORMAT!/) Xtl)=0.0 X125I=2.4 11 = 24 IM=II+I DO 200 1=1,5 52 tIt = L St 1*1) 200 TAC(I)=TAE(I*1) DO 201 1=1,5 201 TSniIt=TSE(1*1) T A E t l )=TAO TSEtl)=TSO TSE(7)=TS6 T«E(7)=TA6 DO 202 1=1,4 53 (I ) = LH (1 + 1 >  -  202 ThCl I I= TWE( 1*1 ) 203  00 2C3 1=1,4 TSOtI)=TIF(1*1 ) TfcE(l)=TWO  ho -P> 00  TWE(6)=»TW5 TIE(l)=SAINT(4,S3.T$D,Xll),3,Sl) TIE161=SAINTI4,S3,TSD,XI25) ,3,S1> LSI1I=XI1 ) LSI7)=XI25) LM1)=XI1I LWI6) = XI25> A= 0 . l DC 11 1=1,11 I F I t . E O . 1 3 ) GO TO 11 I F I I . E C . l f l ) GO TO 11 1 F M . E 0 . 1 2 ) 00 TO 204 IF II . E 0 . 1 7 ) GO TO 205 " XII»I)=XIII*A GO TO 11 204 XI 1*1 ) = 1.25 • • XI1*2)=1.3 GO TO 11 205 XII*1I=1.78 XII*2)=1.8 II CONTINUE C C C C  C C  C C C C C C C C  TO FIND INTERPOLATED TEMPERATURES BASED ON MEASURED DATA CALL CALL CALL CALL  SPLINE(LW,TWE,S2.6,X,TW,S1 , I f , 1 0 0 1 I SPLINE(LW,TIE,S2.6,X,TI,S1,IM,1001) SPLINEILS,TSF,S2,7,X,TS,TSD,IM,1001) S P L I N E I L S . T A E , S 2 . 7 , X , T A , T A C , I M , 1 001 I  SLNA=0. SUMB=0. SUf1=0.0 SUM2=0.0 SUM3=0.0 EPS=l.0E-C5 XST=1.0 IFND=50  C C C C C C  c  C C C  C C  '  CALCULATE THE CENTRAL ANGLF OF THE BED WITH SUBROUTINE THETA. CALL THETAIZ t F i D E R F , F C T , X S T , E P S , I E N D . I E R , P E R > KILN RADIUS IS 0.09525 M RAC=C.CS525 CE SGI  C  EQUIVALENT DIAMETER, M CONTACT LENGTH BETWEEN GAS ANO SOLIO BED, M  C C  C  C C C  .SGL=RA0*SINIZ)*2.0 ARC=2.*I3.142-Z)*RA0 *RE*=3.142*RA0*RAD DE=4.*AREA*I1.-PER I/1SGL+ARC) CALCULATE HEAT TRANSFER COEFFICIENTS FROM BED TO WALL» HTCSW. A HEAT DIFFUSIVITY OF SOLID, 0.225X10E-6 M2/SEC FOR OTTAWA SAND .  A=C.225E-06 AA = R 0 T / 6 C . * R A D * * 2 / A * 2 . * Z AA = A A * * 0 . 3 AA=11.6*AA TK  THERMAL CONDUCTIVITY,  0.268 W/M K FOR OTTAWA SAND  TK=0.268 EL=?.*Z*RA0 HTCSW=AA*TK/EL AAA=HTCSW ASSUME THERMAL CONDUCTIVITY OF CEMENT 0.294 W/M K ANO ITS THICKNESS IS 2 MM. ECHTC=0.294/1.0*1000. HTCSW=1./HTCSW*1./ECHTC HTCSW=1./HTCSW WRITEI6.175) Z.SGL,ARC,OE,EL,AAA,EOHTC,HTCSW 175 F O R M A I I ^ X , 1 l = ',*S.2,' SGL = ' . F 5 . 2 . < ARC='.F5.2, 1' nE=',F5.2,< EL=',F5.2/' HTCSW=',F6.1, 2« FOHTC-',F6.1,• HTCSW OVER ALL = ' , F 6 . 1 / / / ) DC 150 MM=1,IM OA IS AMOUNT OF HEAT RELASED BY AIR , W/M T=TAIMM»/1000. CP=1.0017*0.042*T TCP=C.C42»(T-0.2S8) SA=(CP*TCP)*TAi:(MM) CA ( M V ) = 1 . / ? . 6 * S « * W A OS IS T HF AMOUNT OF HEAT RECEIVED BY SOLIDS. W/M T=TS(MM)/1000. CP=0.t?3*0.?15*T TCP=C2l5*!T-0.298> SS=ICP*TCPI*TSD(MM| 0S(MMI=1./3.6*SS*WS TO CALCULATE HEAT FLUX FROM BED TO WALL.OSW OSMMM)=HTCSW*FL*(TS(MMI-TWIMM) ) TO CALCULATE HE'T FLUX FROM GAS TO BED, 0G3IMM)  K3  C C C C C  C C  C  OGS|MM»=OSWIMM»*OSIMM1 TO CALCULATE HEAT FLUX FROM GAS TO WALL. OGWI»<M)=QAIMM|-QGS(MM)  OGW(MM)  TO CALCULATE HTC HTCGS LCCAL HEAT TRANSFER COEFFICIENTS. W/M2 K HTCGW HEAT TRANSFER COEFFICIENT, W/M2 K HTCGS(MM)=QGSIMM)/SGL/(TA(MM)-TSIMM)I HTCGW|MM)=QGW(MMI/ARC/(TAI MM)-TW(MM II J = MM WPITE(6,115> XIJI,TA1JI,TS< J),TW( J ) , T I C J l . Q S W U I , K S ( J ) ,OGS(JI l.CMJl.CGWU ) 115 FCPMATI2X.F4. 2, 4(F6 . 1 . 2 X 1 , 5 1 - 0 P F 7 . 1,2X11 150 CONTINUE 10 FORMAT!10F8.31 11 = 1 JJ = 25 *PITEt6,1831 183 FCRMATI1H1///1 00 500 1 = 11 .JJ TSDII l = O S ( I > / < T A U t - T S t l l l / S G L T«P(I1=0AIIl-QSIII TAC! I ) = T A D ( I » / ( T A ( I ) - T w m i / A R C WPITE(6,116» X!It.HTCGS(Il,HTCGWCI),TSOIIl,TAOUl 500 CCNTINUE 116 F r F M A T I 2 X , F 4 . 2 . 4 F 1 2 . 2 l KK=IE 11 = 13 KKK=KK-1 SUM4=0.0 SU*5=0.0 SUM6 = C.C CO 153 I=II,KKK SEG=»t1*11-X!I1 «VG=(HTCGSIII+HTCGSI1*111/2.0 SUM«=SUMA*AVG*SEG AVG = (HTCGW(II*HTCGW(l + lI 1/2.0 SUM6=SUME*AVG*SEG AVC=(0GS(Il+OGS!1*111/2.0 SLM1=SUM1*AVG*SEG AVG=IOGW!Il+QGW!1*1(1/2.0 SUM2=SUM2*AVC*SEG AVG = ( C S U ) *CSI 1*11 I/2.0 SUM4=SUM4*AVC*SEG C = ( C M I I * O a ( I + l ) 1/2. SL'M5 = SUM5*C.*SEG  A«OA(Il-OS!11 B=0ACl+l l-OSI 1 * 1 » AVG=(A»P»/2.0 SUM3=SUM3+AVG*SEG 153 CCNTINUF OSWT = HTCSW*EL*(TSU 6 »-TW(16 11*0.53 SU«7=QSV.T*SUM4 SUM8=SUM5-SUM7 WRITE!6,176 1 QSViT,SUM4,SUMT,SUM5,SUV8 176 FCRMAT!/2X, , 0SWT=',E10.4,> OST= • , E 1 0 . 4 , ' 1E10.4,' OGT=-,E10.4,» OGWT=«.E10.4) AHA AHB  *EAN PAS/SCLID HTC DERIVED FROM INTEGRATION OF LOCAL HTC DIVIOEO BY KILN TEST SECTION LENGHT. MEAN GAS/WALL HTC DERIVED FROM INTEGRATION CF LOCAL HEAT TRANSFER COEFFICIENTS.  JJ = KK PP = X ( J J 1 - X H I ) AHA=SUMA/BB AHP=SUMR/9B A = TA!UI-TS f i l l B=TA( J J l - T S ! JJ1 C*«-P D = A/B IF1A.E0.BI GO TO 161 T=C/«LOGID) GC TC 162 161 T= A HRS LOGARITHM MEAN GAS/SOLID HTC HBW LOGARITHM MEAN GAS/WALL HTC. 162 HPS=SUM1/T/SGL/BB HP S2=SUM4/1/SGL/BB HBS7=SUM7/T/SGL/BB WRITE(6,177) A.B.T.HBS7 177 FCRMAT(/2X,'AIR - SCLIO: DEL T l - ' . F S . l , * 1' LOG T * » , F 5 . 1 , » AIP-SCLIO H T C = « . F 5 . 2 1 A=TA(JJ)-TW(JJ) R=TMI! l-TW! II 1 C = A-B  c=A/e  OGST»»,  IFfA.EO.BI GO TO 163 T=C/ALOG(D» GC TO 164 163 T = A 164 HBW3=SUM3/T/ARC/BB HPV=SUM2/T/ARC/BB  DEL T 2 » « , F 5 .  PATSUM=SUM4/SUM5 HPW8=SUH8/T/ARC/BB WRITEI6.178) A , 8 , T , H B H 8 178 FCPMATI/2X,*AIR - WALL I OEF T l = • f F 5 . 1 , • OEL T 2 » « , F 5 . 1 1' LCG T = ' , F 5 . l , « AIR - WALL H T C » ' , F 5 . 2 ) WRITEI6.173) WRTTFI6.10I HBS,HBW,«HA,AHB,HBS2,H8W3,RATSUM,HBS7,HBW8 C C C C C C C C C C C C C C  CALL 1001  C  c  C C  c  AK VIS T PE NU DE  AIR THERMAL CONDUCT!VITY, J/S M K AIR VISCOSITY, N S/M2 AIR AVERAGE TEMPERATURE IN TEST SECTION REYNOLDS N O . , V*OEN*DE/VIC = WA/VIC/DE/4./PIE/1600. NUSSELT N C . , HETRA*OE/AK EQUIVALENT DIAMETER OF KILN, M  1 2  T=(TA( JJ (*TA(II M / 2 . 0 TAA = T TSS = ( T S < H ) + T S ( J J ) ) / 2 . 0 TWW=tTW(11)*TW(JJ I I / 2 . C T=ITAA*TSS)/2.0 CALL PROPTYtT,AK.VIS.OEN)  126 121 122 1111 129  PIE=3.142 REW=E./6C.*PIE*DE *OE *ROT*DEN/V!S RE = WA/VIS/P ! E / O E / 3 * 6 0 0 . * 4 . NU = I-PS*CE/AK TTT=(TAA*TWW»/2.0 CALL PRrPTY(TTT,AK,VIS,DENl WNU=HBW*OE/AK WRITEI6.126I P.E.NU.WNU FCPMAT(///5X,12HREYNOLOS N 0 . . 1 P E 1 2 . 3 / 15X,12HNUSSELT NO.,1PE12.3,1PE12.31 WPITEIIO,121) RUN,WA,ROT,WS.RIN,HCLDUP FOP«AT(lX,A5,F5.1,F6.2,3X.3F?.l) WP.ITFI 11,122) RUN,HBS7,HBW8,RE,NU,WN'U,REW F0PMAT(1X,A5,6F12.2) CONTINUE WRITEI6.129) FORMAT 11H1) PICT  TEMPERATURE PROFILES V S . KILN LENGTH.  3 4 5 6 . 7 8 C C C C C  C C C C  KILNPLOT(RUN,WA,ROT.WS,RIN,HOLOUP)  STOP END SUBROUTINE THETA TO CALCULATE CENTRAL ANGLE OF THE BED.  TFE FOLLCWING IS TO CALCULATE NUSSELT NUMBER ANC PFYNCLCS NUMBER.  C  C C C C  C  SUBROUTINE THETAIX,F,DERF.FCT,XST,EPS,I IFR = 0 X=XST TCL=X CALL FCTITOL,F,OERF,PER I TOLF=100.*EPS CC 6 I=1,1END IF(F) 1,7,1 IF(DERF)2,8,2 C X = F/PER F X=X-0X TOL = X CALL FCT(TCL,F,DERF,PER) TCl=EPS A=A8<(X ) IF(A-l.O) 4,4,3 TCl=TCL*A !FtARS(nx>-TOL) 5 , 5 , 6 IFI«eS(F)-TOLF) 7 , 7 , 6 CCNTINUE IFR=1 RETURN IFR = ? RETURN END  END,IER,PER)  FUNCTION FOR CENTRAL ANGLE CALCULATION. SUBROUTINE FCTIX,F,DERF,PER) PIE=3.14159 F=X-SIN(2.*X)/2.0-PER*P!E DERF=1.-C0S(2.*X) RETURN END SUBROUTINE  PROPTY TO CLACULATE AIR PROPERTY.  c  NO  20 22  25  30  C C  c C C  SUBROUTINE PROPTYIX,AKK,AVIS,ADEN I DI»"ENSICN TI2Ol,OENI2O),CPGI2OI,VIS(20l,VKS(20) CIMENSION PI2O),AKl20l,PRI2C>.YF(2O) DC 20 1=1,11 REACI7,22I TI I 1 ,DE M J ) ,CPG (f I , VIS I I » ,VKS I I ) , AK (I » , PR FCFMATI7F10.4) DC 25 1=1,11 VI S(It = VI SI I l » 1 . 0 E - C 5 VKS( I ) = V K S ( I ) * l . 0 E - 0 3 CONTINUE CO 3C 1=1,12 Tl H = (T( I 1*460.1/1.8 OEM T)=OEN(ll*16.018 CPCII)=CPG(I)*0.41B68E*C4 V IS II I = VIS111*1.4882 VKSI II =V*S( I )*0.C929C3 AK 11 )= AK 11 1*1.7308 CONTINUE AKK=5A!NT{11,T,AK,X,5,YF1 AV!S=SAINTIll,T,VIS,X,5,YFI ADEN=SA!NTI11,T,DEN,X.5.YF) RETURN . END  C C  C  C  THIS SUBROUTINE PLOTS THE TEMPERATURE PROFILES FOR AIR, SANO AND WALL VS. KILN LENGTH POSITION. SUBROUTINE KILNPLOT(RUN,WA.ROT,WS,RIN.HOLDUPI  C C  1002  C  . DIMENSION XI301,TAI301,TSI30I.TWI301,T!1301 CCMMCN / A / L W , L S , T W E , T I E , T S E , T A E DI"ENSIGN TAEI 81 ,TSE181,TWE18 I,TIEI 81,LSI 81,LWI 8 I DIMENSION S1I30I ,521301 REAL LS.LW ILM = 1 A=2.C B = 0.0 CCC=7.0 CCC=CCC+A CALL PLOT ( 8 . 0 , 0 . 0 , - 3 1 CALL P L O T I C . C , 2 . 0 , * 1 I CALL PL0TI5.0.A.+21 CALL F L C T ( 5 . C , C C C , * l I CALL PL0T(B,CCC, + 1 I CALL P L 0 T I R , A , * 1 1 00 1 1 1 = 1 , 6 XX=I-1  C  c  C  c  CALL SYMBOL I X X , A , 0 . 1 4 , 1 4 , 1 8 0 . 0 , - 1 1 Z=XX*0.5 *>*=XX-0.15 CALL NUMBER I X X X , I . 7 , 0 . 1 4 , Z . 0 . 0 . 1 ) 11 CONTINUE Z=250. DC 20 1=1,7 Y=t*l CALL SYMBOL 1 0 . 0 , Y , 0 . 1 4 , 1 5 , 1 8 0 . 0 , - 1 1 Z=Z+50. IFI I . F O . l 1 GO TO 20 Y=Y-0.14 CALL N U M B E R ( - 0 . 1 5 , Y , 0 . 1 4 , Z . 9 0 . . - 1 1 20 CONTINUE CALL P L 0 T I C . 4 0 , 1 . 5 , * 3 ) CALL SYMBOL 1 0 . 4 0 , 1 . 2 . C . 1 4 , ' D I S T A N C E FROM SOLID FEED END,' 1' METER',0.0,351 CALL S P L I N E ( L S , T S E , S 2 , 7 , X , T S , S 1 , I P , 1 0 0 1 1 CALL S P L ! N F ( L S , T A E , S 2 , 7 , X , T A , S 1 , I M , 1 0 0 1 1 AAAA=3CC. DC 5C 1 = 1.25 XII ) = X ( I ) « X ( I ) TAII ) = ( T A U )-AAAA)/50.*A TS 111=(TS!I1-AAAA1/50.+A T M I > = ( TWII I-AAAA1/50. + A T i l I l = ITI(Il-AAAAI/50. + A 50 CONTINUE OC 40 1=2,6 LSIII=LS(I)+LSII1 TAE I 11 = 1TAEI 1 l-AAAA I/50.+A TSE 111=(TSEI I l - A A A A 1 / 5 0 . * A CALL S Y V B O L I L S I 1 1 , T A E ( 1 1 , 0 . 1 4 , 3 0 , 0 . 0 , - 1 I CALL SYMROLILSIIl.TSEII 1 . 0 . 1 4 , 3 , 0 . 0 , - 1 1 I F I I . E Q . 6 I GO TO 40 LW(II=LW(I)*LW(I) TWEI 11=1TWEIIl-AAAA1/50.*A CALL SYMBOL(LWII 1 .TWEII 1 , 0 . 1 4 , 2 , 0 . 0 , - 1 ) 40 CONTINUE CALL CALL CALL CALL  PL0T(0.0,TA(l),+3) LINE(X,TA,25,-l) PLOT(0.0,TS(11,+3) L!NEIX,TS,25,-1)  N3  CALL PLOT(0.0,TW(1),*3) CALL LlNF(X,TW,25,-l)  C  WWW=B.S CALL SYMPOL(0.5,WWW,0.14,'RUN N O . 1,0.0,31) CALL SYMBOL(2.96,WWW, 0.14.RUN,0.0,4) www*www-o.2 C A I L SY"BCL(C.5,WWW,0.14,'AIR FLCW RATE l.C.0,31) CALL MJMBER(2.96.WWW.0.14,WA,0.0.1I WWW=WWW-0.2 CALL SY*ROL(0.5,WWW,0.14,'SAND THROUGHPUT 1.0.C.31) CALL NUMBER I 2. <36, WWW. 0. 14 . VS ,0. C , I ) WWV=WWW-0.2 C A I L SY"B0L(0.5.WWW,0.14,'ROTATICKAL SPEED 1,0.0,31) CALL MIMRER(2.96,WWW,0.14,ROT,0.0,1) WWV<=WWW-0. 2 CALL SYMPOHO.5,WWW,0.14,'INCLINATION ANCLE 1.0.C31 ) CALL N , U M BFR(2.96,WWW, 0. 14 , RI N , 0 .0 , I ) WWW=WWW-0.2 CALL JY W BOL (0.5,WWW,0.14,'DEGREE CF F I L L 1 .C.C.31I CALL Nll»PER (2.96,WWW, 0. 14, HOLDUP, 0.0, 11 WH.-WWW-0.4 VVV'C.5 VVW=0.9 CALL SYMROL(VVV,WWW,0.14,30,0.0,-1) CALL SYMBOL ( W W , WNW.O. 14, ' A IR ',0.0,41 VWW=WWW-0.2 CALL SYMBOL!VVV,WWW,0.14,3,0.0,-1) CALL SYMROL(VVW,WWW,0.14.'SANO',0.0,4) WWW»WV>W-0.2 CAIL SYMBOL!VVV,WVW,0.14,2,0.0,-11 . CALL SYMBOLIVVW.WWW.O.H.'WALL'fO.O,*)  KC/HR •  KG/HR •  RPM  •  DEGREE'  X  •  c c c  IF(ILH.EC.4( GO TO 1001 1LP«ILM*1 CC TO 1002 1001 CALL PLOTNO STOP ENO EXECUTION TERMINATED  '  • '  tSIGNOFF K3  VL=VL3*BATIO**0.5 . K=PI/4.0»SN*L**2 K=F/(VL*2.*PI*SN*BETC*R) VLL=VL  THIS PBCGBAB PREDICTS GAS-TO-BED BEIT TRAHSFER COIPIICIEHTS BASED OR TBEOHETICAL EQOATIOH 7-14. C  c  PEJI KA,H1,B2,K,»,L,R0P AIR TEN PERATORE AT 422 K, AIR PEOPERTIES ARE AS FOLLOWS... PI = 3.14159 PR=0.71 VISA=2. 369E-05 KG/B S DE»A=0.833 KG/H3 KA=0.O31 , W/fl K PHTSTCAL PROPERTIES OP OTTAWA SARC ARE AS FOLLOBS.... F=0.09525 DP=0.73E-03 VP=PI/6.0*DP**3 DEKF=2527.3 KG/B3 CPP=0.603 J/G K  VDC=VP*DEHP*CPP*1.0E*03 S1=PI/2.0*DP*DP S2= (1.-PI*DP*DP/«.0*B1)/B2 C VL=VL**2+VG**2 VL=VL**0.5 RE=CF*VL*DENA/VISA SRITE(6,10) RE,VG,VLL,VL 10 F C F B A T f REP=',F5. 1,3E14.4) KRITE (6,23) 23 FOBBATC RHAC NOP IN F5.2, VALUE TAKER FROH KBHII S • 1'LEVENSPIET. BOOK, P. 212') PEAC(5,11) NOP 11 FCRHAT(F5.2) HF=NOP*KA/DP C C  CALCOIATE PARTICLE VELOCITY AT SECOHD LATER UI=VLL* (1.-DP/K)  C FItI.=0.065 EETA=1.535 BETB=BETA/2. BETC=COS(BETB) BETD=SIN (BETB) . H1=2.17E*06 . B2 = B T DBIT OP B1, B2 , RO. OP PARTICLES / H2 ASSURE B=3BPS, R=5.0E-03 B AT 11* OP FILL WRITE(6,21) FORMAT {• BEAD B Ig RPfl ARD RG IH KG/HR , BOTH I f FORHAT P5i READ (5, 22) N.SG FORB AT ( 2F5. 2) SR=N/60.0 I=2.*R*8ETD VL3=0.20 AREA=PI*R*R AREA=AREA*( 1 .-FILL) HG=SG/DESA/3600. VG=»G/ARIA  A1=-HP*S1*L/VDC/VLL B1=-HP*S2*L/VDC/OL A=EXP(A1) B=EXP(P1) «BITE(6,15) A1,E1,A,B 15 EORHAT(HE12.U) A=1.-A E=1.TB  A=B1*VLL*A B=B2*0L*B  ')  HGS=VDC/L*(A+B) WRITE(6,12) N.K.BP.HGS 12 FOBBATC H=',F4.1,« ^'.EIO.*,' STOP END EXECOTICK TERBINATED  HP« • ,E10. 4 , •  HGS=« ,E10.4)  SSIGHOF?  RAlIC=H/3.0  to  c c  C C C  C  THIS PHOGHAH I S POH & PLOT OF MtJGS(EXP) VS. AND FOB HUGH(EXP) VS. NUGW (PP.ED) . THB PLOTS ARE SHOIIH IB FIGURES 6-34 6 6-35.  TT=CC-0.20 CALL BOBBER (TX.TY.O. 14,ZZ,0.0,-1) 7 SS ( I ) - S S ( I ) »CC CALL STHBOL(A,SS (I) ,0. 14,15,180.0,-1) GO TO (3,3,3,3,3,3,5,5,5,5,3,5,5,5,5,3,3,3,3.3) ,I 5 GO TO 90 3 TX=A-0.14 TY = S S ( I ) - 0 . 1 4 CALL NUMBER (TX,TY,0. 14,ZZ, 90. ,-1) 90 CONTINUE CALL SYHBOL(-0. 60,3.0,0.11,'NUSSELT NUMBER, EXPERIMENTAL' 1,90.,28) CALL SYMBOL (1.0,1.2,0. 11,'NUSSELT BOMBER, PHEDICTED',0. 0 ,25)  HOGS(PRBD)  DI HENSION Y (50) ,X (50) , AA (50) , SS (50) BEAD<5,11) (Y (I) , X ( I ) .1=1,44) 11 FORMAT(6X,E12. 4, 12X,B12. 4) CC=2.0 A=0.0 B=5.757 C=0.0 D=5.757 C=C*CC D=D+CC CALL PL0T{3.0,2.0.-3) C A I L PLOT(»,C,*3) CALL PLOT(B,C,*2) C A L L PLOT(B,D,*2) CALL PLOT (A, D,*2) CALL PLOT(A,C,»2) AA(1)=5.0 DO 21 1=1,15 AA (1*1) = AA(I) • 1. 0 21 CONTINUE A» ( 17) =25.0 AA (18)=30.0 AA(19) = 40.0 AA(20) = 50.0 AA(21) = 60.0 AA(22)=70.0  95  96  97  DO 85 1=1,»a  C  c  T(I)=I<I)/50. Y (I) =ALOG (Y (I) ) *2. 5*CC X(I)=X(I)/50. 1 ( 1 ) =ALOG (X ( I ) ) »2.5 85 CONTINUE DO 80 1=1,20 SS(I)=AA(I)/AA(1) SS(I)=AL0G(SS(I))*2.5 80 CONTINUE DO 90 1=1,20 CALL S I B B O L ( S S ( I ) , C , O . ia,ia,180.0,-1) ZZ = » A ( I ) * 1 0 . GO TO (2,2,2,2,2.2.4,4,4,4,2,4,4,4,4,2,2,2.2.2>.I 4 GO TO 7 2 T X = S S ( I ) - 0 . ia  12  AA(1)=AA(1) *10.0 DO 95 1=1,15 CALL SYMBOL ( X ( I ) ,1(1) ,0. 14, 1,0. 0,-1) CONTINUE DO 96 1=16,34 CALL SYMBOL (X (I ) , Y ( I ) , 0 . 1 4 , 0 , 0 . 0 , - 1 ) CONTINUE DO 97 1=35,44 CALL SYMBOL(X(I) ,Y(I) ,0. 14,2,0.0,-1) CONTINUE CALL PLOT(A,C, »3) CALL PLOT(B,D,*2) DD=C»2.0 BB=B-2.0 EE=EB»0.20 CALL SYMBOL(BB.DD.O.14,1,0.0,-1) CALL SYHBOL.(EE, DD,0. 14, • 17X F I L L ',0.0,10) DD=DD-0.25 CALL SYNBOL(BB,DD,0. 14,0,0.0,-1) CALL SYMBOL (EE,DD,0. 14 , ' 1 U • ,0.0,3) DD=DD-0.25 CALL SYMBOL(BB,DD,0.14,2,0.0,-1) CALL SYMBOL (EE, DD, 0. 1 4, ' 6. 5* ' , 0. 0, 4) CALL SYMBOL(0.5,6.8,0. 14,'GAS/SOLID HEAT TR ANSFER " , 0. 0, 23 ) FEAD(5,12) (Y (I) ,X (I) ,1=1,44) FORHAT(42X,E12. 4, 12X.E12.4) '  C C CC=2.0 A=0.0 B=6.2 C=0.0 D=6.2 C=C*CC D=D*CC  NO  c  C  C  CALL PLOT(3.0,2.0,-3) CALL PLOT (A, C, • 3) CALL PLOT(B.C.*2) CALL PLOT(B,D, *2) CALL PLOT (A,D,+ 2) CALL PLOT (A.C, *2) AA (1) =5.0 DO 22 1=1,15 AA (I*1)=AA(I)+1.0 22 CONTINUE AA (17)=25.0 AA(18) = 30.0 AA (19)=«0.0 AA(20)=50.0 AA (21) =60.0 AA(22)=70.0 DO 81 1=1,20 SS (I) =AA (I) /AA (1) SS (I) = ALOG(SS(I)) * 2 . 5 81 CONTINUE DO 91 1=1,20 ZZ=AA(I) CA LL SYBBOL (SS (I),C,0.11,11,180.0,-1) GOTO (1, 1, 1, 1, 1, 1, 6,6,6*6, 1,6,6,6,6,1,1,1,1,1) ,I 6 GO TO 10 1 TI=SS(I) TY=CC-0.20 CALL NUMBER(TI,TY,0.14,ZZ,0.0,-1) 10 SS (I) =SS (I) *CC . CALL SY NBOL (A,SS(I) ,0. 14,15,1 80.0,-1) GO TO (8,8,8,8,8,8,9,9,9,9,8,9,9,9,9,8,8,8,8,8),I 8 GO TO 91 8 TX=A-0. 14 TY = SS(I) CALL NUBBBR(TX,TY,0.14,ZZ,90. ,-1) 91 CONTINUE CALL SYBBOL (-0. 60,3.0,0. 14,'NUSSELT HOHBEB, EXPERIMENTAL' 1,90.,28) CALL SYMBOL (1.0,1.2,0. 14,' NL3SELT BDHBEH, PBEDICTED', 0. 0, 25) DO 94 1=1,44 X(I)=X (I)/AA(1) Y(I)=Y(I)/AA(1) X (I)=ALOG (X (I) ) *2.5 I (I) = ALOG (Y (I) ) *2. 5+CC 94 CONTINUE DO 99 1=1,44 CALL SYBBOL (X(I) , 1 ( 1 ) , 0.14,2,0.0,-1)  99 CONTINUE CALL PLOT(A,C,*3) CALL PLOT(B, D,*2) CALL SYBBOL (0.5,6. 8,0.11,'GAS/WALL HEAT TBAHSPEB'.0. 0,23) CALL PLOTND STOP END EXECUTION TERMINATED  $COPY *SKIP  EXPERIMENTAL  DATA  Run No. . A1 1 A 1 2 A 1 3 A 1 4 A 1 5 A 1 6 A 1 7 A 1 8 A 1 9 A 2 0 A 2 1 A 2 2 A2 3 A 2 4 A 2 5 A 2 6 A 2 7 A 2 8 A 2 9 A 3 0 A3 1 A 3 2 A 3 3 A 3 4 A3 5 A 3 6 A 3 7 A 3 8 A 3 9 A 4 0 A 4 1 A 4 2 A4 3 A 4 4 A 4 5 A 4 6 A 4 7 A 4 8 A 4 9 A 5 0 A51 A 5 2 A 5 3 A 5 4  W 2 4 . 6 2 4 . 6 2 4 . 6 2 4 . 6 2 4 . 6 2 4 . 6 2 4 . 6 18. 6 1 8 . 6 1 8 . 6 3 4 . 0 3 4 . 0 3 4 . 0 3 4 . 0 3 4 . 0 3 4 . 0 5 0 . 5 5 0 . 5 5 0 . 0 5 0 . 0 5 0 . 5 8 1 . 0 6 5 , 5 7 3 . 0 8 1 . 0 3 4 . 0 3 4 . 0 3 4 . 0 3 4 . 0 1 8 . 6 1 8 . 6 1 8 . 6 1 8 . 6 5 0 . 0 6 5 . 5 3 4 . 0 3 4 . 0 6 5 . 5 6 5 . 0 9 5 . 5 9 5 . 5 3 4 . 0 9 5 . 5 8 1 . 0  N 3 . 0 0 3 . 0 0 3 . 0 0 3 . 0 0 1. 5 0 1.50 1. 5 0 3 . 0 0 1. 6 0 1 . 6 0 1. 5 0 3 . 0 0 1. 5 0 6 , 0 0 1. 5 0 3. 20 3. 20 3. 10 3. 10 1 . 6 0 6 . 0 0 3 . 0 0 3 . 0 0 3 . 0 0 3 . 0 0 3 . 0 0 3 . 0 0 3 , 0 0 3. 0 0 3 . 0 0 3 . 0 0 3 . 0 0 3 . 0 0 3 . 0 0 0. 9 0 1 . 0 0 3 . 0 0 3 . 0 0 0. 90 3 . 0 0 1.00 1 . 0 0 1 . 0 0 0. 95  1 . 2 0 1 . 2 0 1 . 2 0 1,2 0 1 . 2 0 1 . 2 0 1 . 2 0 1 . 2 0 2 . 2 0 1 . 2 0 1 , 2 0 1 . 2 0 1 . 2 0 1 . 2 0 3 . 4 0 2 . 2 0 2. 2 0 3 . 0 0 1 . 2 0 2 . 2 0 2 . 2 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0  n  W  1 7 . 0 1 7 . 0 1 7 . 0 1 7 . 0 1 7 . 0 1 7 . 0 1 7 . 0 1 5 . 0 1 7 . 0 1 7 . 0 1 7 . 0 1 7 . 0 1 7 . 0 1 7 . 0 1 7 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 6 . 5 6.5 6 . 5 6 . 5 6.5 6.5 6.5 6 . 5 6.5 6.5  2 5 . 0 2 5 . 0 2 5 . 0 2 5 . 0 1 4 . 2 1 4 . 2 1 4 . 2 2 1 . 0 2 9. 1 1 5 . 0 1 5 . 0 3 4 . 0 1 5 . 0 5 0 . 5 3 9 . 0 3 4 . 6 3 4 . 0 5 2 . 7 1 9.4 18. 2 6 6 . 3 3 6 . 0 3 6 . 0 3 6 . 0 3 6 . 0 3 6 . 0 3 6 , 0 3 6 . 0 3 6 . 0 3 6 . 0 3 6 . 0 3 6 . 0 3 6 . 0 3 6 . 0 1 2 . 0 13. 3 3 5 . 8 3 5 . 8 1 1 . 7 3 5 . 8 1 5 . 8 1 1 . 3 16.1 1 2 . 0  Pun.No.  Ta]_  All A12 A13 A 14 A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 • A28 A29 A 30 A31 A3 2 A33 A34 A35 A36 A37 A38 A39 A40 A41 A42 A 43 A44 A45 A46 A47 A48 A49 A50 A51 A52 A53 A54  450.0 425.0 '402.0 372.0 330.6 414.0 470.0 351.5 350. 0 365. 0 380.0 368. 0 383.0 357.0 361.0 370.0 369.0 361.0 376.0 378. 0 353.0 407.0 393.0 396.2 396. 8 366. 7 420.0 395. 0 420.6 385.6 358.3 351.7 375. 6 3 98.0 412.0 382. 1 367.8 400.0 419.0 404.0 406. 6 384. 0 403,3 419.0  Ta  2  486.0 460.0 423.0 392.0 340.0 438.0 505.0 378.9 3 75.1 392.8 393 .0 388.0 400.8 374.0 377.2 385.0 380. 0 371.0 386 .0 388. 0 365.0 417 407 412 411 380 446 .4 417.0 446.5 417.0 376. 0 360.0 400.0 416.7 425.0 397.2 332.2 408.0 427.0 410.2 412 3 98 409 42 7  T a 3 524.0 489.0 457.0 411.0 348.3 462.0 543. 0 412.2 405.0 427.2 418.0 407.0 418.0 390 391 393 388 381 396 .0 399. 0 375.6 426.1 418. 3 423.3 422.2 395.6 476.7 44 0.6 475.0 461 .1 410. 6 384.4 440.0 433.9 434.4 413.3 398.9 420.6 435. 0 417.2 41 7.6 416.7 414.4 434.4  T3^ 574.0 535.0 493.0 436.0 358.8 494 594 44 5 44 3 464 435 428.0 437.0 407 .0 410.0 414.0 401 .0 395.0 405 .0 410.0 387.5 437 .5 431.0 436.0 433 .0 415.0 513.3 471 .0 512.3 510.0 447. 0 413.5 473 .3 452.5 441.1 427.3 416.0 432 .3 442.3 424.0 422 .3 428.0 413.5 442 . 0  T a  5  635.3 592.0 538.0 457.3 372.0 535 .0 652. 0 488.0 497 .3 507. 0 455.0 455.3 456.0 430.0 430.0 43 7.0 4L3.3 41 0.0 417.0 420.5 404. 5 45 0.0 445.0 44 8.9 4 4 4.4 441 .0 560.0 535.3 55 9. 0 550.0 505. 0 460.0 5 3 5.3 475.0 44 8.3 4*4.3 441. 0 447.0 44 8.0 431.0 42 7 .0 443. 0 422.8 45 0.0  T S 1 334.0 323.0 321.0 314.0 306. 7 341.0 364. 0 313.9 312.2 330.5 335.0 320.6 337. 8 308.3 305.6 313.8 316.7 312.8 328.9 329.4 308. 3 333 .3 326.1 3 31.7 326.7 311. 1 322.8 318.9 32 3.9 318.3 308.9 306. I 313.3 323.9 361. 1 333.3 312. 8 327.8 368.9 375.0 370.6 335.5 374.4 37 3.3  Ts  2  356.0 3 39.0 3 37.0 3 2 7.0 3 08.9 356.0 3 83.0 325. 6 322.2 3 40.3 346. 1 331.1 348.9 3 15.0 313.6 323. 3 326.1 318.9 339.4 341.1 3 13.9 350.6 341 .7 347. 2 348.9 322. 2 343. 3 334.4 343. 3 331.7 317.8 312. 2 325.0 3 38. 9 373.9 345.6 322.8 341.1 378.3 3 77. 8 3 77.2 348.9 375. 6 381.7  3 378.3 356.0 354.0 341.3 312.8 374.0 410.3 338. 9 332.2 352.8 360. 3 341 .7 365. 0 322.2 322 .2 333.3 334.4 327.9 353.9 357.2 321. 5 366.7 358 .3 362. 7 366.7 3 34.4 369.4 355 .0 369.4 352.0 3 32.2 321.7 345.0 360. 0 391.7 361.7 336.1 360 .0 397 .3 391. 7 390.6 368. 3 388.9 397 .2 T S  Ts  4  431.0 397. 0 392.0 368.0 326. 7 417.0 473.3 363. 9 355.5 3 83.3 384.4 363.3 385.6 3 36.7 333.9 350. 0 351.7 341. 370. 373, 331. 391.1 383. 6 385. 8 388.9 352.2 399.7 3 80.0 400.0 377.8 343.3 336. 1 365.0 384.2 416.7 385.7 352 . 8 332.0 419.4 407. 2 402.7 391.7 4 04.4 413.9  T s  5  521.0 473.3 447.0 405 .0 34S.3 473.0 554.0 402.8 391 .7 42 4.i 411.1 393 .0 412.3 360.0 352.1 376. 1 373 .9 358.9 391.1 394 .4 350.0 417.3 407 .2 412.2 414.2 378 .1 443.0 415.3 44 5.> 428.0 387 .2 366.7 412 .2 419.4 434.4 411.1 380.0 409.4 433 .3 418. 9 418.3 418.9 415.6 435 .3  TW  2  320.0 3 14 313 308 331 324 341.3 308.0 304.0 315.5 319.4 311.0 321.3 302. 0 330.0 306.0 3 06 . 8 304 320 323 332 321.1 3 13.3 315.8 3 15.8 304.5 312.6 312.4 312.3 311.0 333 .4 299.0 306.0 312.3 339.8 3 14.0 335.3 318.0 349 .6 355. 0 351.4 3 19.3 347.0 351.3  351.0 333.3 333.0 326.0 305 .3 347.0 373.3 3 2 3.0 317.0 331.3 336. 0 326.6 338 .3 311.6 313.4 321 .6 323.0 315.5 338.8 339.0 313.6 347.4 338 .4 344.0 345.0 321 .7 341 .1 335.4 344.0 333. 0 317.6 312.6 325.0 338 .3 365.0 338.4 323.6 340.2 374.4 374.0 372 .2 341 .5 369. 0 364.4  0V  TW  397.0 372 .3 353. 0 352.0 316.0 387. 5 425.0 349.0 341.0 363.0 355 .8 349. 6 365 . 3 330. 0 331.0 340.0 341.6 333.3 350.0 363.0 326.0 3 75. 5 367.4 370.0 375. 5 339.3 380. 4 361. 0 383.0 364. 0 335.0 3 2 7.0 352.0 371.3 400.0 369.4 344.2 369. 0 402 .5 395.0 393. 3 373.0 395.0 400.0  500.0 445 .3 429.3 395. 0 333 .0 447. 0 520.0 335 .3 377. 0 407.0 431 .3 378.0 43 0.0 355.0 360.0 354 .8 366. 0 353.0 330.0 387. 0 346.5 407.0 395.0 402 .3 404. 0 368.0 425. 5 401. 0 425 .5 413.0 372.8 35 5 .8 397. 5 437.0 428 .0 400. 370. 395. 430. 415 .0 413. 0 435.0 413.3 430.0  3  4  N3  260  RUN NO.  All  V*> 1.25 1.30 1.40 1.50 1.60 1. 7 8 5  520.0 524.4 534.2 544.9 556.0 76.04  T  s  (  x  )  378.0 381.5 389.5 398.9 409.5 31.04  V  X  )  373.2 377.0 385.4 394.9 405.9 30.41  dT  dT  g dx~  s dlT  34.8 91.9 103.0 109.9 112.6 06.81  q  «CX>  q  gs  ( K )  q  a  65.1 339.5 446.5 73.0 381.9 481.1 87.6 460.3 552.8 100.4 530.2 619.6 111.3 591.4 671.2 26.4679.5693. 5  (  x  )  q  gw  ( x )  598.4 151.3 649.0 167.3 728.0 175.1 777.4 157.8 797.1 125.3 757.463.9 I  Z = 0.99 SGL= 0.16 A R O 0.41 DE= 0.17 EL= 0.19 \ QSWT=0.4739E+02 QST=0.2801E+03 QGST=0.3275E+03 Q3T=0.3939E+03 0GWT=0.6641E+02 HTCGS=27.0 HTCGW= 2.1 ) RE=2.013F+03 NU=1.202E*02 NUW=1.048E+01 /  RUM NO. 1.25 1.30 1 . 40 1.50 1.60 1.78  A12  489.0 4Q2.5 500.0 503.4 517.4 535.0  356. 0 35 8. 5 364. 4 3 71.3 3 79.4 397. 0  353.9 356.8 363. 1 370.4 378.9 397. 5  66.9 71.4 79.6 8 6.9 93.2 102.2  48. 3 53.2 63.7 74. 8 86.7 109.7  248. 7 274. 7 329.7 389.0 452. 6 578.5  314. 3 359. 1 409. 2 46 1.9 566. 5  5C2.9 561.1 6 12.3 657.9 722.0  188. 6 202. 0 203. 5 195. 9 155.. 5  EL= 0. 19 0E= 0.17 ARC = 0.41 SGL = 0.16 Z= 0.99 QGT =0.3 240E+03 QGST=0.2248E+03 QST=0.2141E+03 QSWT =0. 1072F+02 HTCGW= 3.4 = 1 9. 6 HTCGS QGWT-0. 9912F+02 NUW=1.630E+01 NU=9 .350E+01 RE=2. 108E+03  RUN NO.  A13  1.25 452.0 1.30;455. 4 1.40 462.5 1.50 470.1 1.60 478.1 1.73 493.0  354.0 349.9 66.5 48.3 3 56. 5 3 5 2 . 9 6 9 . 1 5 3 . 5 2 362.4 359.3 73.8 63.2 369.1 366.5 77.7 71.3 376.7 374.4 8C.9 79.3 392.0 390.6 84.8 90.1  248.6 7 5 . 9 326.7 372.6 413.4 473.9  341.2 3 58. 5 395.4 432.2 465.1 506.3  466.4 435.C 518.2 546.2 569.0 596.9  125.2 12 6.5 122.8 114.1 103.9 90.7  Z = 0 . 9 9 S O T = 0 . 1 6 A R C =0.4 1 D E = 0 . 1 7 E L= 0.19 QSWT=0.3160E+02 QST=0.1974E+03 QGST=0.2 290E+03 QGT=0.2879E+03 QGWT=0.5891E+02 HTCGS=27.2 HTCGW= 2.7 * RE=2.181E+03 NU=1.354E+C2 NUN=1.325E+01  1  1  261  RUN NO. 1. 25 1 .30 1. 40 1. 50 1 .60 1 . 78  A14  411.0 413.1 417.4 422. 1 426.9 436.0  341. 0 342.9 347. 3 352. 2 357. 5 368. 0  33 8.7 340.9 345.6 350.9 356.6 368.7  40.5 42.1 45.0 47. 5 49.3 5 1 .5  36.8 40. 2 46.3 51.4 55.5 60.4  188. 1 205. 3 2 37.6 264. 5 286.4 313.3  220. 7 283.2 234. 8 294.8 261.0 3 15.3 282. 5 33 2.2 297.0 345.6  62 .5 60.0 54.3 49 .7 48. 7  EL = 0. 19 DE= 0. 17 ARC = 0.41 SGL = 0.16 z= 0 .99 QSWT=0. 9579E+01 QST=0. 1336E+03 QGST = 0.1482 E + 0.3 QGT=0. 1748E+03 QGWT=0.2658E+02 HTCGS=25.4 HTCGW= 1.8 \ RE=2.330E+03 NU = 1 .327F + 02 NUW=9.943E+00 / _ x  I  RUN NO.  /  A15 i  1.25 1.30 1 .40 1. 50 1.60 1.73  348 .3 349. 3 351 .6 354.0 356.6 361.0  312.8 313. 6 315.6 318.0 320. 8 326.7  310.4 311.3 313.2 315.5 318 . 2 324.0  19.8 2 1 .3 23.6 2 5.0 2 5.4 23.5  15.6 17.3 21.9 2 5.9 29.6 35 .9  44.6 50.8 62 .7 74.1 85.0 103. 3  73. 1 79. 1 91.6 104.2 115.9 135.0  137.7 14 3.4 164.6 1 74.0 176.6 1 c4.0  64. 6 69. 3 73.0 69.3 60.7 29.1  Z= 0.99 SGL= 0.16 ARC= 0.41 0E= 0.17 E L= 0.1.9 QSWT=0.1597F+02 QST=0.3979E+02 QGST=0.5576E+02 QGT=0.8792E+02 QGWT=0. 3216E+02 HTCGS=18.9 HTCGW=4.0 RE=2.593F+03 NU = 1.1 10E+02 NUW= 2•3 36E +01  RUN NO. 1. 1.30 1. 40 1. 50 1. 60 1. 78  A16  462.0 464. 3 469.3 474. 6 400.4 492. 0  374. 0 37 7.0 384. 1 392.2 400. 9 417. 0  369. 2 3 72 .9 3 80.3 333 .0 3 95 .7 410. 5  45.9 4 7.7 51.4 55.5 60.0 68.9  57.2 64.4 76.2 34.4 89.0 88.5  169. 2 226.4 190.8 271. 7 226.5 252. 1 302. 2 267.3 328.7 268. 1 345. 9  322.6  96.3  361.5 39.9 3, 0 . 6 33.4 422.2 93.4. 4 85.3 139 .4 c  Z = 6 . 9 9 S G L = 0 . 1 6 A R C = 6 . 4 1 D E = 0 . 17 EL= 0.19 QSWT = 0. 2655F+02 Q 5T = 0. 12 79E + 03 QGST = 0. 1545E+ 03 QGT=0.2 112E+03 QGWT=0. 5669E + 02 HTCGS = 22. 5 HTCGW= 3.0 RE=2.134E+03 NU=1.119E+02 NUW=1.368E+01  262  RUN  NO.  1 .25 1 .30 1 .40 1 . 50 1 . AO 1 .78  A17 543.0 547.2 5 56. 1 565.4 575.3 594.0  410.0 414.3 42 4. 1 435. 4 447. 9 473.0  395.9 400. 7 411.0 422 .5 435.3 461.2  82.5 85.6 9 1.3 96.3 10 0.7 106.7  81.5 90. 2 10 5.9 119.5 131.0 146. 2  246. 1 272.9 322. 2 365.9 403 .7 4 57.0  523. 3 540.9 579. 8 613.6 651.8 68 3. 3  5E3..5 605. 7 6 4 6.4 6 6 2.4 713.7 757.9  60.2 64.7 66.6 63. 8 61.8 69.6  E L= 0.19 DE = 0.I 7 ARC = 0.41 z = 0. 99 SGL = 0.16 QSWT = 0. 1.340E+03 QST=0. 19 3 1 E«-03 OG ST= 0. 3 2 70E +03 QG T =0. 3610 E+03 QGWT=0.3397E+02 HTCGS=30.5 HTCGW= 1.1 RE=1.930E+03 NU=1.323E+C2 NUW=4.959E+00  RUN  NO.  1.25 1 .30 1.40 1. 50 1.60 1.78  A18 410.0 413. 1 419.4 425. 9 432.6 445.0  338.9 340. 6 344.3 348. 6 3 53.4 363.9  336.3 338. 6 343.2 348.0 352.9 362.3  60.8 6 2. 1 64.3 66.2 67.7 69.6  32.1 34.6 39.9 45.7 52.0 64.6  137.5 143.2 171.4 196. 8 224.6 280.9  32 1 .6 193.0 191. 1 .3 2 8.3 ,137. 3 146. 3 194. 1 34G .4 350 .6 142 .3 208. 2 358 . 9 123. 2 235.7 53. 2 316.0 ,365 .2  EL = 0. 18 ARC = 0 .42 0E= 0. 17 SGL = 0.15 Z= 0.95 QST=0.1031E+03 QGST=0 .1 142E + 03 QGT = 0. 1.8 52E+03 QSWT =0. 6056E+01 HTCGS = 18.3 HTCGW= 4.1 QGWT = 0. 7107E+02 NUW=2.003E+01 NU = 1 .044E+02 RE=1.730E+03 /  RUN  1. 25 1. 30 1. 40 1. 50 1. 60 1. 78  NO.  A19 405.0 408.5 4 16.0 4 24.0 432.4 448.0  z= 0.99 i  3 32. 2 333.3 3 3 7. 5 341. 8 346.5 355. 5  329.2 331 .3 335. 6 340.1 344.7 353.9  68.5 7 1.9 77.8 82.3 85.3 87. 1  29.9 33.7 40. 1 45. 1 48.6 51.0  176.7 199.3 238.2 263. 3 289. 7 306.0  235. 9 249. 1 2 76-0 301. 8 323. 8 33 8. 0  36 1.9 380 .4 411 .7 435 .6 451 .9 462 .1  125 .9 131 .3 135 .7 133 .7 128 .0 124 .1  EL= 0. 19 DE= 0. 17 A R O 0.41 SGL = 0.16 0SWT=0.1778E+02QST=0.1381E*03 QGST = 0. 1559E + 03 QGT = 0.2 272E+03 QGWT=0.7127E+0? ' HTCGS=22.4 HTCGW= 3.9 ; •RE = 1. 776E + 03 NU=1.211E+02 NUW=2.006E+01  RUN NO. 1. 25 1. 30 1.40 1. 50 1. 60 1. 78  A20 42 7. 2 430.7 43 7.6 444. 5 451.4 464.0  352.8 355.0 360.0 365. 6 371. 8 383.3  347.2 350.0 3 55.7 361.8 368.0 3 79.7  6 9.0 69. 1 69.1 69.3 69.6 70.2  41.1 45. 8 53.6 59.3 62. 9 64. 1  126.9 141. 6 166.2 1 84 . 4 196. 4 201.5  239. 1 241. 5 250. 1 261. 2 2 71. 8 272.2  365. 6 36 5. 8 3c6. 5 367. 6 369. 1 3 12.  126. 6 124. 3 116. 5 106. 5 97. 3 100. 6  0. 99 SGL = 0.16 ARC = 0.41 DF= 0. 1 7 FL = 0. 19 z = GSWT=0.4067F+02 QST = 0.9447E + 02 QGST=0.1351E+03 QGT^O. 1952E+03 QGWT=0.6008E+02 HTCGS=20.6 HTCGW= 3.4 PE=1.700E+03 NU=1.076E+02 NUW=1.656E+01  RUN NO. 1 . 25 1.30 1. 40 1.50 1.60 1. 78  A21 418.0 419.8 423. 2 426.6 430.0 436.0  360.3 351.2 362.2 353. 8 359. 1 366. 3 370. 8 364.7 3 75 . 5 370.4 384.4 380.9  3 5.8 35.2 3 4.3 33.7 33.3 3 3.6  36.3 38.8 43.0 46. 3 48.5 49.9  112. 6 120. 5 133.9 144.2 151.5 156. 8  29Q. 7 235. 1 27 4.6 263. 8 2 51.3 224.6  346.6 34C.9 331.3 32 5. S 322.9 3 25.4  55 .9 55 . 8 57 .3 62 .0 71 , 1 100 .8  EL= 0. 19 0E= 0.17 Z= 0.99 ARC = 0.41 SGL = 0.16 QSWT =0. 6 3 4 0 E + 0 2 Q ST =0.7490E+02 QGST = 0.1384E+03 QGT = 0.1745E+03 HTCGS =30. 0 HTCGW = 2.7 QGWT =0. 3 6 1 1 E + 0 2 550E+02 NUW=1.445E+01 RE = 3.15 1E+03 NU = 1 .  RUN NC.  A22  1.25 407.0 341.7 339.0 34.9 29.5 1 7 3 0 4 0 8. 3 3 4 3 . 3 3 4 1 . 0 3 5 . 5 3 2 . 7 2 1.40 412.4 346.3 344.9 36.9 33.1 1.50 416.2 350.3 343.8 33.8 42.0 1.60 420.1 355.2 352.7 41.1 44.5 1.78 428.0 363.3 359.8 46.4 45.1  204.8 264.7 337.5 2 7 . 6 2 7 8 . 5342.9 265.7 308.1 357.0 293.6 333.4 375.2 311.4 367.1 397.7 317.5 395.1 448.9  72.8 64 .4 48.9 36.8 30.6 53.9  Z = 0 . 9 9 S G L = 6.16 AR C = 6.41 0E= 0.17 EL= 0.19 QSWT=0.2375E+02 QST=0.1503E+03 QGST=0.1740E + 03 QGT = 0.2 035E+03 QGWT = Q.2941E+02 HTCGS =31. 7 HTCGW= 2.0 RE=3.247E+03 NU=1.737E+02 NUW=8.804E+00  \  Z04  RUN NO. 1.25 1.30 T740 1.50 1.60 1.78  A23  418.0 419.7 423.1 426.6 430.2 437.0  355.0 366.6 370.0 373.6 377.4 385.6  355.7 357.8 362.3 367.0 372.0 381.0  33.2 33.7 34.7 35.7 36.7 38.4  32.9 33.1 34.3 36.9 40.7 50.8  102.2 102.8 107.0 115.2 127.4 159.8  285.3 275.8 258.0 243.4 234.6 250.6  321.2 35.9 326.3 50.5 336.3 78.3 346.0 102.5 355.4 120.8  ARC= 0.41 DE= 0.17 EL= 0.19 SGL = 0.16 7= 0.99 QST =0.6471E+02 QGST=O.1327fE + 03 QGT=0.1839E+03 QSWT =0.6797E+0? HTCGS = 30. 1 HTCGW= 4.0 QGWT =0.5125E+02 NUW=2.050E+01 NU=1.562F+02 RE = 3.140E+03  RUN NO. 1.25 1. 30 1.40 1. 50 1. 60 1.78  A24  390.6 392. 6 396.9 401 .5 406. 1 414.0  322. 2 323. 2 325. 5 328.1 331.0 336.7  321 .1 322. 7 326.0 329 .3 332.6 338.9  38.6 41.1 44.7 46.3 46.0 4 0.6  21.1 215.6 24. 6 2 51.7 27.6 282.5 30. 0 307.9 33.0 340.0  227.9 2 38. 8 251.7 266. 6 285. 7  397.2 431.7 447.6 444 .9 3 92.7  169 .3 193 o, 195 .9 178 .3 107 .0 .  V.'  E L = 0. 19 0E= 0. 17 ARC = 0.41 SGL = 0.16 Z= 0. 99 1 QGT =0.2247E+03 GST=0. 1482E+03' QGST=0 . 1319E + 03 QSWT^-. 1634F+ 02 = 21.4 HTCGW= 5.9 HTCGS 0.9282E+02 QGWT = NUW=3.169E+0l RE=3.379E+03 NU=1 .212E+02  RUN MO.  A25  1.25 391.5 322.2 322.3 29.3 22.0 173.5 1 . 3 0 3 9 3 .0323.3 3 2 3 . 8 3 0 . 5 2 3 . 8187. 8 1.40 396.2 325.9 326.9 32.7 27.4 216.5 1.50 399.5 328.8 330.3 34.7 31.0 245.2 1.60 403.1 332.1 334.1 36.7 34.6 273.9 1.78 410.0 333.9 341.8 39.9 40.9 325.7  170.6 283.1 1 7 9. 1 2 9 4 . 2 197.5 315.5 216.3 335.6 235.5 354.6 263.1 385.9  112.5 1 15.1 118.0 116.8 119.1 117.8  1 = 0 . 9 9 S G L = 0 . 1 6 A R C = 0 . 4 1 0 E = 0 . 1 7 E L = 0.19 QSWT=~. 1507E+02 QST = 0. 1 323E+03 QGST = 0.1172E+03 QGT=0. 1786E+03 QGWT = 0.6144F+C2 HTCGS=19. 8 HTCGW= 4. 1 RE=3.331E + 03 NU=1 .084E + 02 NUW=2.313E + 01  265  RUN NO.  A26 A  1.25 1 . 30 1 .40 1 . 50  398.9 33 3. 3 400. 1 334.4 402.6 336.9 339.7 405.2  1 .78  414.0  350.0  331 .4 332. 9 336.0 339.3  24.6 24. 5 2 5.2 26.9  22. 1 23.3 26.2 29.9  155.7 164. 0 184. 9 211.5  349.6  37.4  44.6  317.2  195. 3 237.6 195.3 236.9 203. 0 24 3.2 219. 5 259.8 246.2 266.8  42.3 41 .1 40. 1 40.3 40.7  Z = 0.84 S C O 0.14 A R O 0.44 0E = 0.17 EL= 0.16 QSWT=0.4212E+01 QST=0.1185E+03 QGST=0.1228E+03 QGT=0.1467E+03 QGWT = 0.2396E+-02 HTCGS=25.1 HTCGW= 1.6 RO3.159E + 03 NU=1.472E+02 NUW= 7. 930E + 00  RUN NO. 1. 25 1. 30 1. 40 1. 50 1. 60 1. 78  A2T  388.9 390 .0 392.4 394.9 3 97.3 401.0  334.4 335.9 339. 2 342. 8 346. 4 351. 7  333.2 334.7 337.8 341.0 344. 1 350.3  2 1.3 22.7 24.5 24. 8 2 3.4 1.7.1  31.0 35.3 36. 5 34.4 22.7  214.8 245.3 253. 7 239.9 158,7  233. 0 273. 5 291.9 286. 3 188. 3  3 2 6.0 351.8 • 3 5 5.1 3 3 6.0 245.0  88. 1 78.3 63 .2 49. 7 56 .7  Z= 0.84 SGO 0.14 ARO 0.44 DE= 0.17 EL= 0.16 QSWT-0.2025E+02 QS T = 0. 1 1 87E + 03 QGST=0.1389E+03 QGT=0.1719E+0 3 QGWT=0.3295F+02 HTCGS=35.6 HTCGW= 2.7 RE=4.74?E+03 NU = 2 .024E + 02 NUW=1.643E+01  RUN NO.  1.30 1 .40 1 . 50 1.60 1 .78  A23  382.3 384.7 387.3 390. 0 395.0  329. 0 326.7 331. 3 329.5 332 .4 333.8 336. 4 335.5 341 . 3 341.7  23.5 25.1 26.4 2 7.4 28.5  23.9 25.6 27.4 31.2  38.9 49.6 66.0 2 55.9 293. 7 359.6 274.2 30 2. 6 3 7 8 .2 75.6 2 94. 4 314. 3 392.8 73 .5 335. 6 344. 7 4C8.6 64.0  Z=0. 8 4 S G l . = 0 . 1 4 A R O 0 . 4 4 6 . 6 = 0.17 E O 0.16 Q.SWT=0. 1505F + 02 QST=0. U 8 2 E + 03 QGST=0. 1633E+03 QGT = 0. 1989E+03 QGWT=0.356?F+02 HTCGS =40.7 HTCGW= 2.8 RE = 4. 81 7E+03 NU = 2 ..390E + 02 NUW= 1. 645E+ 01  zoo  RUN NO.  A29  1.25 396.0 1.30 397.0 1.40 398.9 1.50 400.7 1.60 402.6 1.73406.0  353.9 355.4 358.5 361.6 364.8 370.6  351.0 19.0 352.8 19.0 356.2 19.0 359.4 18.9 362.4 18.8 367.518.63  30.0 30.4 30.9 31.5 32.0 2.7,  119.9 178.4 121.3 174.9 123.9 170.3 126.3 171.5 128.5 177.6 132.0194. 6  270.4 92.0 270.3 95.4 269.6 98.8 263.6 97.2 267.3 39.7 264.069.4  Z= 0.84 SGl.= 0.14 ARO 0.44 0E= 0.17 E L= 0.16 QSWT=0.2393E+02 Q S T= 0 . 67 C0E + 02 QGST=0.9093E+02 QGT=0.1420E+03 0GWT=0.5110E+02 HTCGS=31.2 HTCGW= 5.3 RE=4.573E + 03 NU=1.824E+02 NUV* = 2 . 800E+ 01  RUN NU.  A~30  1. 2 5 3 9 9 . 0 3 1.30 400.1 1.40 402.3 T750 404.. 3 1.60 406.4 1.78 410.0  57. 2349.322.230.7115.12 353.7 351.5 21.8 30.2 113.6 361.7 355.1 21.2 30.0 112.7 364. 7 359. 1 2~077 30T5 114.8 367.8 363.6 20.3 31.7 119.9 373.9 372.1 19.9 36.0 136.5  4 9 . 8 3 1 5.465.6 244.6 310.2 65.5 232.1 3C1.1 69.0 216.3 2 9 3.3 77 .5 197.5 263.3 90.8 163.9 282.8 113.9  Z= 0.84 SGL= 0.14 A R O 0.44 DE = 0.17 EL= 0.16 QSttT = 0. 5376E+Q2 QS T^=0 .6322 E + 02 QGST = 0. 1 1 70E+03 QGT=0. 1 564E+03 QGWT = 0. 3947F. + 02 HTCGS=39.9 HTCGW= 3.9 RE=4.541E+03 NU=2.148E+02 N'JW= 2. 472E + 01  RUN NO. 1. ?5 i . 30 I . 40 i . 50 i . 60 I . 78  A31 375.6 3 76.7 3 79. 0 331.3 383.7 387. 5  321.5 322.4 324. 1 326.0 323.0 331. 7  320. 1 321.1 3 2 3.2 325. 5 3 23.0 33 3.2  2 1.3 22.2 23.4 23.6 22.9 19.3  16. 7 17. 3 18. 4 19. 3 20. 1 21. 0  223.9 232.2 247.0 259. 5 269. 7 282.3  255. 1  3 04.7  49.6  267. 5 271. 1 269. 1 247. 7  334.6 3 27.9 327.9 276.1  67.1 66.8 58.7 28 .4  2 = 0 . 3 4 S G L = 0 . 1 4 : A R C = 0 . 4 4 D E = 0 . 1 7 E L = 0 . 16 QSWT=0.6145E+0l QST=0.1363E+03 QGST=0.1430E+03 QGT=0.1695E+03 QGWT = 0.2649E + 02 HTCGS=34. 5 HTCGW= 2.1 RE=4.891L + 03 MU=2.011E + 02. NUW=1.392 E +01  267  RUN NO. 1. 25 1. 30 1. 40 1. 50 1. 78  A3?  426. 1 427.0 429.0 431. 1 43 3. 4 437.5  366. 7 368. 7 373.0 377. 6 382.4 391. 1  3 62.9 365. 2 369.9 374.6 3 79.3 3 88.2  17.8 1 8.9 20.7 2 1 .9 22.7 22.9  ARC = 0.4 4 SGL = 0.14 QSWT=0.3232E+02 QST=0.1026£ +03 QGWT=0.4671E+02 HTCGS=54.3 RE=7.053E+03 NJ = 2 .944E + 02  z= 0. 84  RUN NO. 1.25 1 .30 1. 40 1 . 50 1.60  38.3 40. 8 44.9 47. 5 48. 6  285.7 305.1 3 36. 1 3 56. 5 366.3  36 2. 2 375.2 399. 4 413.4 4 2 8. S  41 1.2 43 5.9 476.8 5 06.3 5 24.3  48 .9 60 .7 77 .4 37 .8 95 .3.  FL= 0. 16 DE = 0. 17 QGST=0.2155E+03OGT=0.2622E+03 HTCGW= 3.6 NUW=1.908E+01  A33  413.3 419.4 421.7 424. 1 426.5  358.3 360. 2 364. 1 363. 3 372.6 380. 6  3^4.8 357.2 3 61. 9 3 66. 5 371.0 370.9  2 1.8 22.5 23.5 24.3 24.7 24.6  36.4 37.9 282.2 302.6 40.6 42.6 313.2 43.9 329.2 44. 8 336.8  342.0 346.9 3 5 3. 9 362.2 371. 2  418.7 438.5 452.3 460. 1 459.1  76 .6 91 .6 9 3.4 97 .9 37 .9  DE= 0.17 EL= 0 . 16 SGL == 0.14 ARC = 0 .44 Z= 0.84 18 53E+03. QGT =0.2364E+03 QGST=0. 1890E+02 QST=0.1664E+03 QSWT =0. HTCGW= 3.8 =44. 7 HTCGS QGWT =0. 5106E+0 12 NUW=1.972E+01 NU= 2.487E+02 RE=5.803E + 03  RUN NO.  A34  1.25 423.3 362.7 358.4 21.1 35.7 266.2 354.5 437.6 1 . 3 0 4 24.4364."5360.422.637. 7281.1364.:9458 . 1 1.40 426.7 368.5 364.6 23.6 41.1 307.5 385.7 490.1 1.50 429.1 372.7 369.1 24.5 44.0 329.3 403.8 510.2 1.60 431.6 377.3 373.S 24.9 46.1 346.6 415.9 518.3 1.78 436.0 385.8 383.1 24.2 48.5 365.9 420.8 502.9  83.1 9 3 .2 104.4 106.3 102.4 82.1  Z = 0 . P 4 S G L = 0 . 1 4 A R C '=6' . 4 4 D F = 0 . 1 7 E L = 0 . 16 QS^T=0.3949E+02 QST=0. 1729E+03 QGST=0.2124E+03 QGT =0. 2631E+03 QGWT=0. 5078E+02 HTCGS = 51 . 0 HTCGW= 3.7 RE=6.404E+03 MU=2.756E+02 NUW=2.072E+01  268  RUN NO. 1.25 1.30 1.40 1.50 1.60 1. 7 8  •  A35  422.2 423.2 425.2 427.2 429.2 4 33. 0  366.7 362.3 368.5 364.8 372.2 369.7 376.2 374.5 380.5 379.3 3 8 8. 9 3 87. 7  19.7 19.8 20.1 20.3 20.6 2 1 . 1  34.4 256.6 346.0 35.9 268.3 342.9 38.8 290.9 341.5 41.6 312.6 346.7 44.3 333.4 353.3 4 8 . "7368. 5 3 9 3 .  454.5 108.5 457.1 114.2 462.5 121.0 468.5 121.8 474.9 116.7 0 4 8 7.894.8  Z = 0.84 SGL= 0.14 A R P 0.44 DE = 0.17 EL= 0.16 QSWT=0.1805F+02 QST=0. 1667E+03 QGST=0.1848E+03 QGT =0. 249 IE+ 03 QGWT=0.6435E+02 HTCGS=49.5 HTCGW= 5.3 RE=7.096E+03 NU=2.739E+02 NUW=2.706E + 01  RUN NO. 1.25  1.30 1.40 1 . 50 1 . 60 1.78  A36  395.6 397.2 400.6 404. 1 407. 3 415.0  334.4 335. a 338. 8 342. 1 345. 6 352.2  330.6 33 2.0 335.0 333.3 342. 0 349. 8  3 1.7 32.6 34.4 36.3 3 8.2 41.7  29. 0 31. 5 33. 7 35. 5 38. 0  212.3 2 89. 1 231. 4 309. 4 248.0 325. 3 262. 1 334.3 3 30. 9 281.2  314.8 332.3 3 5 0.3 368.9 403.8  25.7 22.9 25.0 34 .6 72.9  Z= 0.84 SGL= 0.14 ARC= 0.44 DF= 0.17 EL= 0.16 QSWT=0.409SE+02 QST=0.1309E+03 QGST = 0.17 19E+03 QGT=0. 1875E + 03 QGWT=0.1562E+02 HTCGS=36.8 HTCGW= 1.0 RE=3.157E+03 NU=2.066E+02 NUW=7.145E+00  RUN NO.  A37  1.25 476.7 369.4 362.1 62.1 52.1 390.0 537.2 1. 3 6 4 7 9 . 8 3 7 2 . 0 3 6 5 . 5 6 2 . 9 5 2 . 1 3 9 0 . 5 5 2 3 . 1 1.40 466.2 377.3 372.2 64.8 53.1 398.7 500.9 1.50 492.8 382.7 379.0 67.3 55.3 416.4 490.0 1.60 499.7 338.4 385.9 70.5 58.7 443.8 494.2 1.78 513.0 399.7 398.4 77.7 68.1 517.9 544.3  604.1 6 11 .4 630.4 655.4 686.5 757.5  66.9 33.3 129.5 165.4 192.3 213.2  Z=0.84SGL=6.14ARC =0.44DE=6.1 7 E L= 6.16 QSWT=0.3904E+0? 0ST=0.2293E+03 QGST=0.2683E+03 QGT=0.3538E+03 QGWT--=0.8550E + 02 hTCGS=32.3 HTCGW= 3.2 RE=2.789E+03 NU=1.650E+02 NUW=1.604E+01  269  RUN NO.  A33  1.25 1 .30 1.40 1 . 50  440. 6 44 3.2 448.5 454. 2  1. 78  471 .0  355. 0 357. 1 361.4 365. 9 370. 6 380.0  348.4 350. 5 355.0 359. 9 365.4 376.5  50.5 52.2 55.1 57.6 59.6 61.9  • 42. 1 42. 5 43.7 45.8 48.7  312.6 315.3 3 25. 5 342.0 364. 7  446.3 469.9 44 9. 2 506. 0 455. 6 534. 7 462. 5 558.8 470. 0 578.3  43 .6 56 .8 79 . 1 96 .2 108 .3  EL = 0. 16 DE= 0.17 SGL = 0.14 ARO 0.44 QGT= 0.2947E+03 GS T=O.1872E+03 QGST=0 .2511E+03 QSWT = 0.6391E+^2 HTCGW= 2.0 HTCGS = 37. 8 QG WT = 0.4353E+02 NUW=1.183E+01 NU = 1.980E + 02  z= o .84  RUN NO.  A39  1 . 2 5 4 7 5 . 0 3 6 9 . 4 3 6 3 . 2 5 T . ™ 5 4 9 . 3 3 7 2 . 1 4 9 3 . 3 5 6 3.5 1.30 477.9 371.9 366.2 59.4 49.2 368.8 484.9 577.2 1.40 484.0 376.8 372.3 62.4 50.2 377.1 469.5 6G6.6 1.50 490.5 382.0 378.7 67.0 53.8 405.6 473.1 652.3 1.60 497.5 387.7 385.4 73.3 60.1 454.4 500.2 714.1 1.78 512.0 400.0 393.4 88.9 78.2 594.8 626.6 866.6  70.3 92.3 137.1 179.2 214.0 240.0  Z= 0.84 SGL= 0.14 ARC= 0.44 DE= 0.17 EL= 0.16 QSWT=0.3579H+02 QST=Q.2324E+03 QGST=0.2632E+03 QGT=0.3614E+03 QGWT=0.9320E+02 HTCGS=32.7 HTCGW= 3.6 RE=2.792E+03 NU=1.672E+02 NUW=1.791E+01  RUN NO. 1. 25 1. 30 1. 40 1. 50 1. 60 1. 78  A40  461 .1 465. 7 47 5.7 486.4 497.2 515.0  352. 0 3 43.3 353. 9 350. 9 3 57.7 356.5 361 . 9 362 .7 366. 6 369.5 383.2 377.8  87.9 95.0 10 4 . 8 108.6 106. 5 87.6  38.2 39.3 44.0 51.9 74.0  353. 0 466.6 108.6 50 4.7 164.1 557.3 240.9 291. 8 316.4 267.4 327. 6 3 10.7 5 7 8.1 567.2 238.4 337.3 3 2 3. 8 20.0 556. 1 447. 1 4 6 7.1  282. 5  ARO 0.44 0. 16 SGL = 0.14 z = 0. 84 QSWT=-.R945E+01 QST=0.1942E+03 QGST=0.1853E+03 QGT=0.2845E+03 QGWT = 0.992 1E + 02 HTCGS=20. 1 HTCGW= 3.5 RE=1.558E+03 NU=1.032E+02 NUW=1.851E+01  270  RUN NO.  A41  1. 25 1.30 1 .40 1.50  410.6 332. 2 413.7 333. 3 419. 7 33 5.2 425.6 337.3  1.78  44 7.0  325.7 327.0 330. 2 334. 1  64. 1 60.9 5 8.6 6 1.6  22. 1 162. 1 147.6 20.2 19.7 144.2 23.9 175.2  294.5 338.9 273. 7 322.3 246.0 3 10.1 240.9 3 26.0  44 .4 48 .6 64 . 2 85 . 1  348. 3 349.7  EL = 0. 16 DE= 0. 17 ARC = 0.44 SGL = 0.14 Z= o .84 QGT — 3. 19 49 E+0 3 QST =0.1210L+03 QGST=0.1553E+03 QSWT =0.34836+02 HTCGW= 1.9 HTCGS = 23. 5 QGWT=0.3909E+02 NUW=1. 16 IE+ 01 NU=1 .277E+02  RUN NO. 1 .25 1.30 1.40 1.50 1.60  A42  384.4 3 37.1 392.4 3 97./ 403.1  321.7 322.7 324. 6 326.9 329. 5 336. 1  320.6 3 23.4 326.3 329.9 337.8  53.6 5 2.6 53.0 54.9 61.9  19. 1 20.7 24.3 29.7 44.2  139. 1 151. 1 177.0 216.8 324. 1  175.7 176.9 187. 7 209.2 289. 5  282.8 107 . 1 2 77.7 100 .8 2 6 0.3 92 . 5 290.3 31 . 1 327.5 38 .0  DE= 0.17 EL= 0 .16 ARC= 0.44 Z= 0.84 SGL = 0.14 QGST=0.1 119E+03 QGT =0.1543E+03 QSWT=0.5679F+01 Q ST=0.1062E+03 HTCGW= 2.6 HTCGS=21.3 QGUT=0.4242E+02 NUW=1.612E+01 RE=l.765E+03 NU= 1.216E+02  RUN NO.  A43  1.25 440.0 345.0 1. 3 0 4 4 3.7346. 6 1.40 450.7 349.5 1.50 457.6 352.6 1.60 464.5 356.2 1.73 478.0 365.0  338.4 74.3 32.4 239.2 372.2 3 4 0 . 7 7 2 . 3 3 0 . 5 2 2 5 .2344." 4 345.5 69.1 29.6 218.6 300.0 350.9 68.6 32.5 240.4 275.9 356.8 70.6 39.2 291.0 278.3 368.9 80.6 61.0 455.4 375.7  396.6 3 83.3 366.9 364.1 374.E 428.5  24.4 38. 9 66.9 88.2 96.5 52.8  Z = 6 . 8 4 S G L = 6 . 1 4 A R C = 6 . 4 4 D E = 6.17 EL= 0.16 QSWT=0.1880E+02 QST=0.1505E+03 QGST=0.1693E+03 QGT=0.20 28E+03 QGWT=0 . 3350F + 02 HTCGS = 21. 7 HTCGW= 1.4 RF = 1.616E + 03 NU=1. 139E + 02 NUW=8.217E+00  271  RUN NO. 1. 25 1. 30 1. 40 1. 50 1. 60 1. 73  A44  433.9 360. 0 356.1 435. 5 3 62. 0 353. 8 43 3.7 36 6.0 364.4 442. 1 370. 1 369 .9 445. 7 374. 6 3 75.3 452.5 334.2 385.2  3 1.6 32.0 33.1 3 4.5 3 6.2 40. 1  40.2 39.7 40. 1 42.7 47.3 60. 8  3 7 3. 9 298.9 295.2 359. 5 299. 5 331. 6 319.3 323.0 354.7 339.2 458. 5 439. 1  45C.4 4 5 6.4 4 71.7 49 1.6 516.C 571.5  71. 5 96.9 140.2 168.6 176.3 132.4  DE= 0. 17 E L = 0.16 ARC = 0.44 SGL = 0.14 z= 0.84 QSWT=0.1965E+01 QST=0.1824E+03 GGST=0.1844E+03 QGT=0.2655E+03 QGWT=0.3111E+02 HTCGS=34.4 HTCGw= 4.8 RF=4.33 7E+03 NU=1.896E + 02 NUW=2.449E+01  RUN NO. 1. 25 1 , 30 1 .40 1. 50 1 .60 1.78  A45  434. 4 435. 1 436.5 437. 8 439. 1 441 . 1  391.7 393. 9 398.5 403.4 40 8. 3 416. 7  3 83.7 386.7 392 .8 398. 8 404.7 414.5  14.0 14.0 13.7 13. 1 12.2 9.8  42.5 44.6 47.7 49.0 48. 8 44. 1  107.3 224. 3 1 12.8 217. 3 204. 8 120.8 124. 6 191. 3 124. 3 176. 5 145.1 112.9  262.0 261.6 2 5 6 .3 245.1 228.0 182.4  37.7 43.8 51.5 53.8 51.4 37.3  EL = 0. 13 DE= 0.18 ARC = 0.47 SGL = 0.12 Z= 0.70 QST =0.6325E+02 QGST=0 .9358E+02 QGT =0.1246E+03 QSWT =0.3534F+02 HTCGW= 2.3 QGWT =0.2605E+O2 HTCGS= 46. 6 NUW=1.499E+01 RE=5.345E+03 NU = 2.551E+0 2  RUN NO. 1. 25 1. 30 1. 40 1. 50 1. 60 1. 78  A46  413. 3 414.7 417.4 420.0 422.6 42 7.3  361. 7 363.8 368.4 373. 2 378. 2 386. 7  355.6 358.2 363.3 363.4 373.4 382. 2  28.2 27.6 26.5 2 5.9 2 5.8 26.7  40. 9 43.6 47.4 49.3 49.3 44. 4  112. 6 120.0 130.9 136.5 136.8 123.9  20 3. 5 204.0 206.4 203. 7 203. 5 190.8  273.2 266.5 2 56.4 250.8 249.7 2 58.9  69.7 62.5 50 .0 42. 1 41.2 68.1  DE= 0.18 EL = 0.13 ARC = 0.47 SGL = 0.12 1= 0.70 QSWT=0.3827F+02 QST=0.6386E+02 QGST=0.1071E+03 QGT=0.1358E+0 3 QGWT=0.2367E+02 HTCGS=36. 1 HTCGW= 2.3 RE=2.90 5E+03 NU=2.068E+02 NUW=1.245E+01  272  RUN NO. 1. 25 1. 30 1. 40 1. 50 1. fti  A47  398.9 400.4 403 .5 40 6.5 409.6 416.0  336. 1 337. 5 340. 3 343. 2 346.4 352. 6  334.9 336. 5 340 .0 3 43.5 347. i 354.0  31.1 30.5 30.1 30.8  3 2.6  27.3 199.4 27.6 201.2 28.6 208.8 30.3 2 2 2.0 32. 8 240. 7  222.0 300.0 217.9 294.2 214.1 290.6 217.0 297.5 227. 5 3 15.0  78.0 76.3 76.4 80.5 87.6  EL = 0. 13 0E= 0.18 ARC = 0.47 SGL = 0.12 QSWT=-.2667E+01 QST=0.1228 E + 03 QGST=0.1202E+03 QG T = 0. 1661E+03 QGWT=0.4592E+02 HTCGS=29.5 HTCGW=3.0 RF=3.036E+03 NU=1.751F + 02 NUH= 1 .JlJiEirtl  z= 0.70  RUN NO. 1.25 1.30 1.40 1.50 1.60 1. 73  A48  413.0 419.2 421. 8 424. 5 427.2 432.0  360. 0 362.0 366. 1 370. 3 374.4 382. 0  356. 5 359.0 3 63.7 363. 2 372.1 378.7  24. 1 25.1 26.5 27.2 27.2 25.5  40.4 40.6 41 .2 41.6 41.9 42.2  298.4 300.9 305.4 309. 3 312.4 316.2  356.0 46 7.4 343. 2 49 3.1 346. 9 5C6.3 354. 0 5G7. C 376. 6 476.7  111 .4 144 .9 159 .5 153 .0 100 .1  EL= 0. 13 0E= 0.18 4RC= 0.47 SGL = 0.12 Z = 0.70 QST=0.1637E+03 QGST=0 . 1836E+03 QGT =0.2 601E+0 3 QSWT =0. 1992E+02 HTCGW= 5.4 HTCGS = 52. 6 QGWT =0. 765 1F + 02 3.064E+02 NUW=2.870E+01 NU = RE=5.5 88E + 03  RUN NO.  1. 30 1. 40 1. 50 1. 60 1. 78  A49  435.0 397.8 399. 9 435.8 4 37.2 404. 1 438.7 408. 2 440. 1 412.3 442.3 419.4  390. 1 392.4 397. 1 401 .7 406.3 414.6  15.1 1 5.0 14.7 14.1 13.4 11.5  41.6  102.7  214.9  279.3  64.4  41. 7 41.3 40. 5 38.0  10 3.5 102. 7 100.9 95.0  206. 0 193. 5 189.0 165. 7  2 71.7 261.6 247.6 212.5  65.7 63.2 5 3.7 46.7  Z = 0 . 7 0 S G L = 0 . 1 2 A R C = 6 . 4 7 D E = 0 . 1 8 E L = 0.13 QSWT=0.5073F+02 QST=0.5360E+02 QGST=0.1044E+03 QGT=0.1349E+03 QGWT=0.3056E + 02 HTCGS =54. 7 . HTCGW= 3.5 RE=5.279E + 03 NU = 2.925E + 02 NUW=1.97 IE + 01  115  RUN NO.  ' A50  1.25 1 .30 1 .40 1.50  417.2 417.8 418.3 419.9  1. 73  423.0  391. 7 392.9 395. 1 397.0 398.8 402. 5  385.5 337.2 390.7 394. 3 398.0 4 04. 8  1 1.9 1 1.2 10.4 1 0.2 10.6 13.1  25. 1 23. 1 20. 1 18.7 18.8 22.7  189.4 174. 1 152.0 141.2 141.9 171.9  301.3 277. 1 231.2 190.4 156. 8  322.9 304.6 2*1.4 275.9 288.2  21.7 27.6 50.1 85.5131.4  EL = 0. 13 DE= 0.18 A R P 0.47 SGL = 0.12 Z = 0.70 QSWT=0. 2607E+02 QST = 0. 82 44E+ 02 QGST=0 . 1 085E +-03 QGT =0 . 1 590E+03 QGWT = 0. 5044E+02 HTCGS=73.1 HTCGW= 8.4 RE=7.978E+03 NU = 3 .903E+02 NUW=5.085E + 01  RUN NO. 1 .25 1 . 30 1 .40 1 . 50 1. 60 1. 78  A51  417.6 390. 6 333.9 418. 1 391. 8 385.7 389. 1 419.0 393.9 392 .6 396. 0 419.3 398. 1 396.2 420. 6 422.0 402. 7 402.6  9.5 9.2 8.6 8.2 7.9 7.8  24.2 22.6 20. 7 20.6 2 2.3 29.7  75. 1 69.0 68. 8 74.4 99. 3  166. 3 141. 1 119. 3 103. 4 101. 3  249. 1 233.8 222.4 2 14.9 211.3  82.8 92.8 103. 1 111.5 109.9  Z= 0.70 SGL= 0.12 ARC = 0.47 0E= 0.18 EL= 0.13 QSWT=0.2677F+0? QST=0.4077E +02 QGST = 0.6754E + 02 QGT =0.1 199E+03 QGWT=0.5232E+C2 HTCGS=45.5 HTCGW= 8.2 RE=7.933E+03 NU=2.495E+G2 NUW=4.643E+01  RUN NO. 1. 2 5 1 . 30 1 .40 1. 50 1 .60 1 .78  A52  414.0 415.6 413.7 421.8 424.9 430.0  368.3 370. 5 374.9 3 79. 4 383.8 391. 7  353.9 361. 6 366 .9 3 72 .0 376.9 385.5  31.4 31.5 31.4 30.9 2 9.8 2 6.7  42. 6 43. 5 44. 6 45. 1 44. 7 42. 1  99.9 239. 7 102. 1 105. 1 2 2 4.4 106.4 216.2 105. 8 209. 6 100.1 192. 7  63.8 70.6 3 C 4 . 2 79. 8 298.9 82.7 288.8 79.2 258.8 66. 1 3C3.4  Z = 6 . 7 0 S G L = 0.12 ARC= 6.47 DE= 0.18 EL= 0.13 QSWT=0.5821E+02 QST=0 . 55 12 E + 02 QGST=0 . 11 3 3 E+-03 QGT =0 . 1 545 E+0 3 QGWT=0. 411 5E + 0? HTCGS=41. 8 HTCGW= 3.4 RE=2.333F+03 NU=2.376E+02 NUW=1.862E+01  274  RUN MO.  ' A53  1.25 414.4 388.9 384.3 7.5 31.2 105.4 1.30 414.B 390.5 386.4 7.2 30.9 104.6 1.40 415.5 393.5 390.5 6.9 30.3 102.7 1.50 416.2 396.5 394.3 7.1 29.5 100.3 1.60 416.9 399.4 397.6 7.8 28.6 97.4 1 .'78413.5404.4402 . 6 1 0 . 4 2 6 . 6 9 C . 9  174.7 2G4.3 29.5 165.0 194.7 29.7 147.3 166.2 38.3 133.4 191.7 58.3 124.2 211.3 87.1 1 1 7 . 5 2 8 1 . 9 1 6 4 .4  Z = 0.70 SGL= 0.12 ARC= 0.47 DE = 0.18 EL = 0.13 QSWT=0.1750E+02 QST=0.5261E+02 QGST=0.7011E+02 QG T =0.1 124E+03 QGWT=0.4234E+02 HTCGS=56.3 HTCGW= 7.7 RE=8.910E+03 NU=3.259E+C2 NUW=4.040E+01  RUN NO.  A 54  1 7 2 5 4 35 . 6 3 9 7 7 2 3 8 2 . 4 1 3 . 6 3 3 . 9 9 8 . 4 316.7 1.30 435.7 399.2 385.6 13.3 40.6 103.0 303.3 1.40 437.0 403.4 392.1 12.9 42.3 103.8 275.3 243. 2 43.2 110.0 3 98.7 12.3 1. 50 438.3 40.7.7 207. 3 41.7 106.5 405.1 13.1 1.60 439.5 412.0 133. 3 34.5 88.4 14.4 1.78 442.0 418.9 415.9  314.7 2.0 306.9 3.1 297.2 21.9 295.4 52 .2 301.3 • 94 .0 3 31.7 198 .4  DE= 0.18 EL= 0. 13 Z= 0.70 SGL= 0.12 ARC = 0.47 QSWT=0.7056E+02 Q5T=0.5494E +02 QGST=0.1255E+03 QG T =0.1622E+03 HTCGS=64.9 HTCGW= 3-9 QGWT=0.3668E+02 3.463E+02 NUW=2.257E+01 RE=6.582E+03 NU=  RUN MO. 1 .25 1.30 1.40 1 . 50 1 .60 1.78  A55 431.1 432.0 43 3. 9 435 .7 43 7.3 440.0  394.4 396. 7 401. 1 405. 2 409. 1 415.6  3 8 3.5 3 86.3 393.3 399.4 405.0 413.9  18.9 18.3 1 8.2 17.3 16.1 13.2  46. 1 45.0 42.7 40.4 38.0 33. 8  56.4 55. 1 52.4 49.6 46.9 41.7  19 2. 9 269.6 149. 8 122.0 9 3.0 63.4  259.3 24 6.8 2 29.3 187.6  76.7 83.5 109 .6 124.8 131.3 124.2  Z=6.7 0 S G L = 6 7 1 2 A R C = 0 . 4 7 DE= 6.18 EL- 0.13 QSWT=0.3834E+02 QST=0.2606E+02 QGST=0.6440E+02 QGT=0.1265E+03 QGWT = 0.6206E + 02 HTCGS=33.0 HTCGW= 7.0 RE=4.085E+03 NU=1.809E+02 NUW=3.816E+01  

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