UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

An investigation of heat transfer in spray cooling Prabhakar, Balasubramaniam 1980

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1981_A1 P73.pdf [ 12.36MB ]
Metadata
JSON: 831-1.0078747.json
JSON-LD: 831-1.0078747-ld.json
RDF/XML (Pretty): 831-1.0078747-rdf.xml
RDF/JSON: 831-1.0078747-rdf.json
Turtle: 831-1.0078747-turtle.txt
N-Triples: 831-1.0078747-rdf-ntriples.txt
Original Record: 831-1.0078747-source.json
Full Text
831-1.0078747-fulltext.txt
Citation
831-1.0078747.ris

Full Text

AN I N V E S T I G A T I O N OF HEAT T R A N S F E R IN SPRAY COOLING by B A L A S UB RAMAN I AM PRABHAKAR B . S c , O s m a n i a U n i v e r s i t y , I n d i a , 1 9 6 7 B . E . ( M e t a l ! urgy- ) , I n d i a n I n s t i t u t e o f S c i e n c e , 1 9 7 0 M . A . S c , The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1 9 7 3 A T H E S I S S-UBMITTED IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR THE D E G R E E OF DOCTOR OF PHILOSOPHY i n THE F A C U L T Y OF GRADUATE S T U D I E S D e p a r t m e n t o f M e t a l l u r g i c a l E n g i n e e r i n g We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE U N I V E R S I T Y OF B R I T I S H C O L U M B I A N o v e m b e r 1980 Q B . P r a b h a k a r , 1980 In present ing t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e fo r reference and study. I fur ther agree that permission for extensive copying of t h i s t h e s i s fo r s c h o l a r l y purposes may be granted by the head of my department or by h i s or her representa t i ves . It i s understood that copying or p u b l i c a t i o n of t h i s thes is for f i n a n c i a l gain s h a l l not be allowed without my wr i t ten permiss ion . Department of The Un ivers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date DE-6 (2/79) ABSTRACT S p r a y w a t e r f l u x e s .and h e a t - t r a n s f e r c o e f f i c i e n t s h a v e b e e n m e a s u r e d f o r some c o m m e r c i a l s p r a y n o z z l e s , w i t h a v i e w t o g e n e r a t i n g r e l i a b l e a n d a c c u r a t e d a t a f o r t h e d e s i g n o f s p r a y c h a m b e r s o f c o n t i n u o u s c a s t i n g m a c h i n e s . S p r a y s p r o d u c e d by b o t h f u l l c o n e and v e e - j e t n o z z l e s have b e e n i n v e s t i g a t e d . The d i s t r i b u t i o n o f w a t e r i n t h e s p r a y s has been m e a s u r e d f o r d i f f e r e n t s p r a y p r e s s u r e s and d i s t a n c e s f r o m t h e n o z z l e , by m e a s u r i n g t h e amoun t o f w a t e r a r r i v i n g a t c o l l e c t o r t u b e s i n s e r t e d i n t h e s p r a y s . T h e r m o c o u p l e s e m b e d d e d i n a h e a t e d s t a i n l e s s ' h e a t t r a n s f e r p r o b e ' a l l o w e d t h e t e m p e r a t u r e t r a n s i e n t s w i t h i n t h e p r o b e t o be m e a s u r e d d u r i n g t h e s p r a y c o o l i n g o f t h e s e p r o b e s . A n a l y s i s o f t h e s e t r a n s i e n t s by a s o l u t i o n t o t h e ' I n v e r s e B o u n d a r y V a l u e P r o b l e m ' a l l o w e d t h e c a l c u l a t i o n o f t h e h e a t -t r a n s f e r c o e f f i c i e n t s a n d s u r f a c e h e a t f l u x e s as a f u n c t i o n o f t h e s u r f a c e t e m p e r a t u r e o f t h e c o o l e d s u r f a c e o f t h e p r o b e The r e s u l t s o f t h i s i n v e s t i g a t i o n i n d i c a t e t h a t t h e m o s t i m p o r t a n t v a r i a b l e a f f e c t i n g t h e he a t - 1 r a n s f e r c o -e f f i c i e n t i s t h e l o c a l w a t e r , f l u x a t t h e c o o l e d s u r f a c e . The c o e f f i c i e n t s have a l s o been d e t e r m i n e d t o be t e m p e r a -t u r e s e n s i t i v e e v e n a t s u r f a c e t e m p e r a t u r e s in e x c e s s o f i i 800 ° C . F o r t h e same v a l u e o f w a t e r f l u x , n e i t h e r t h e n o z z l e t y p e n o r t h e s p r a y p r e s s u r e has a s t r o n g i n f l u e n c e on t h e h e a t - t r a n s f e r c o e f f i c i e n t s . C o r r e l a t i o n s o f t h e f o r m h = P ( l ) rh P ( 2 ) h a v e been o b t a i n e d b e t w e e n t h e h e a t - t r a n s f e r c o e f f i c i e n t s and s p r a y w a t e r f l u x e s f o r d i f f e r e n t s u r f a c e t e m p e r a t u r e s The f o r o f t h e c o r r e l a t i o n o b t a i n e d when t h e e f f e c t o f s u r f a c e t e m p e r a t u r e b e t w e e n 800 and 1000°C was i n c l u d e d i s f T o o o w h e r e p ( 3 ) i s n e g a t i v e . T h i s showed t h a t t h e o p e r a t i n g b o i l i n g p r o c e s s i n t h e p r e s e n t s p r a y c o o l i n g e x p e r i m e n t s was u n s t a b l e f i l m b o i l i n g , c a u s i n g s c a t t e r i n t h e d a t a . i i i T A B L E OF CONTENTS Page A b s t r a c t •• 1 1 Table o f Contents i v L i s t o f Tables • i x L i s t o f F igu res • • x i i l i s t o f Symbols x x i Acknowledgements x x i i Chapter 1 INTRODUCTION 1 1.1 Secondary Coo l i ng and Crack Format ion 5 1.1.1 Spray Re la ted Defects i n B i l l e t s 8 1 .1 .2 Spray Re la ted Defects i n S l a b s 11 1.2 Spray Chamber Design and Cont ro l 16 1.3 Scope o f the Presen t Work 18 2 REVIEW OF THE LITERATURE 20 2.1 I n t r o d u c t i o n . . , 20 2.2 S i n g l e Drop le t S t u d i e s 25 2.2.1 Dynamics o f D rop le t Impact 25 2 . 2 . 2 Heat T r a n s f e r to S e s s i l e Drops 26 2 . 2 . 3 Heat T r a n s f e r to Impinging Drops 28 2 . 2 . 4 Ex tens ion o f S i n g l e Drop Exper iments to 33 C h a r a c t e r i z a t i o n o f Spray H e a t - T r a n s f e r 2 . 3 Heat T r a n s f e r i n Sprays . . . 34 2.3.1 T r a n s i e n t Methods . . .„ 35 2 . 3 . 2 S t e a d y - S t a t e Methods . . . 51 2 . 3 . 3 I n - p l a n t Measurements 55 2.4 Summary 56 i v Chapter Page 3 EXPERIMENTAL 62 3.1 I n t r o d u c t i o n 62 3.2 Spray Nozz les 63 3 .3 Water Supply System 65 3.4 Spray Nozz le Mounting 68 3.5 Measurement o f Spray Water F luxes 68 3.5.1 Fac to rs A f f e c t i n g Spray F lux Measurements . . . 70 3 . 5 . 2 Apparatus 70 3 . 5 . 3 Exper imenta l Procedure 72 3.6 Spray H e a t - T r a n s f e r Measurements 74 3.6.1 Requirements f o r the Measurement o f Temperature T rans ien t s 74 3 .6 .2 S e l e c t i o n o f S tee l f o r the Probe M a t e r i a l . . . 82 3 . 6 . 3 Probe F a b r i c a t i o n 83 3 .6 .4 S e l e c t i o n o f the Thermocouple M a t e r i a l . 85 3 . 6 . 5 Thermocouple I n s t a l l a t i o n 86 3 .6 .6 Lead Wires and Connect ions 90 3 .6 .7 The High Speed Recorder 92 3 .6 .8 Mounting o f the Heat T r a n s f e r Probe f o r Heat ing 93 3 .6 .8 .1 Type I Exper iments . . . . . . . . . . . . . . . . . 93 3 . 6 . 8 . 2 Type II Exper iments . . . . . . 96 4 ANALYSIS OF THE MEASURED TRANSIENTS 102 4.1 D i g i t i s i n g and Smoothing of the T r a n s i e n t s 102 4 .2 A n a l y s i s o f the Temperature T r a n s i e n t s 103 v Chapter P a 9 e 4.2 .1 Prev ious S o l u t i o n s to the Inve rse , Q 5 Boundary Value Problem 4 . 2 . 1 . 1 A n a l y t i c a l and Analog Methods 1.05 4 . 2 . 1 . 2 Numerical Methods 108 4 . 2 . 1 . 3 Other Re la ted S o l u t i o n s ... 109 4 . 2 . 2 Method Employed i n the P resen t felork 110 4 . 2 . 2 . 1 The D i r e c t Problem T13 -4 .2 .2 .2 The Inverse Problem 117 4 . 3 V a l i d a t i o n o f the Mathemat ical Fo rmu la t i on Used . . . . 119 5 RESULTS AND DISCUSSION • 1 2 6 5.1 Spray F lux Measurements 126 5.1.1 Spray F luxes f o r a 1/4 GG 10 N o z z l e 127 5 .1 .1 .1 H o r i z o n t a l C e n t r e l i n e Spray P r o f i l e s - Type A C o l l e c t o r s 127 5 . 1 . 1 . 1 . 1 D i f f e r e n c e s Between S i m i -l a r Spray N o z z l e s 129 5 . 1 . 1 . 1 . 2 E f f e c t o f V i b r a t i n g the C o l l e c t o r s 132 5.1 . 1 . 1 . 3 E f f e c t o f D i f f e r e n t P r e s -s u r i z i n g Gases 132 5 . 1 . 1 . 1 . 4 E f f e c t o f Spray P ressu re a t Constant D i s t ance 133 5 . 1 . 1 . 1 . 5 E f f e c t o f Spray D is tance at Constant P r e s s u r e 133 5 . 1 . 1 . 2 Spray F lux Map f o r the 1/4 GG 10 Nozz le . . . 137 5 . 1 . 1 . 2 . 1 Water F luxes Obta ined w i t h Type A C o l l e c t o r s 143 5 . 1 . 1 . 2 . 2 Water F luxes Obtained w i th Type B C o l l e c t o r s 148 v i 5 . 1 . 2 Other F u l l Cone Nozz les - Spray F luxes w i t h Type A C o l l e c t o r s 5 . 1 . 3 V e e - j e t or F l a t - j e t N o z z l e s ; Measurements Made w i t h Type A C o l l e c t o r s 5.2 Measurements o f H e a t - T r a n s f e r C o e f f i c i e n t s 5.2.1 General Observa t ions o f the C o o l i n g P r o c e s s . . 5 . 2 . 2 V a l i d a t i o n o f the Exper imenta l Technique Used 5 . 2 . 3 De te rmina t ion o f the I n i t i a l Temperature P r o f i l e s 5 .2 .4 R e s u l t s o f Type I Exper iments 5 . 2 . 5 R e s u l t s o f Type II Exper iments 5 .2 .5 .1 Average o f Spray F luxes Over the Area of the Probe Face 5 . 2 . 5 . 2 Comparison o f Data f o r Peak and Average F luxes 5 . 2 . 5 . 3 R e s u l t s from Exper iments Per formed w i th Other Nozz les 5 .3 E f f i c i e n c y o f Spray Coo l i ng 5.4 C a l c u l a t i o n o f D rop le t V e l o c i t i e s and D rop le t Momenta W i t h i n the Sprays 5 . 5 . The N a t u r e o f t h e B o i l i n g P r o c e s s 5 . 6 T e m p e r a t u r e D e p e n d e n c e o f t h e H e a t -T r a n s f e r C o e f f i c i e n t 5 . 7 C o m p a r i s o n w i t h t h e R e s u l t s o f O t h e r W o r k e r s 5 . 8 P r o b l e m s L i m i t i n g t h e M e a s u r e m e n t s 5 . 9 A p p l i c a t i o n o f t h e D a t a f o r S p r a y C h a m b e r D e s i g n 6 . 0 SUMMARY AND CONCLUSIONS B I B L I O G R A P H Y v i i Appendi ces Page I Measured Spray F luxes f o r the Var ious Nozz les Used in t h i s I n v e s t i g a t i o n 255 II H o r i z o n t a l C e n t r e l i n e Spray F lux P r o f i l e s , Spray F lux Contour Maps and Three Dimensional Represen ta t i ons o f Spray F luxes 276 v i i i LIST OF TABLES Tables • Page I Spray r e l a t e d d e f e c t s 15 I l a Summary o f s t u d i e s on heat e x t r a c t i o n i n sprays -t r a n s i e n t measurements 59 l i b Summary o f S tud ies on heat e x t r a c t i o n i n sprays -s teady s t a t e measurements 60 l i e Summary o f s t u d i e s on heat e x t r a c t i o n i n sprays -i n - p l a n t measurements 61 I I I C a p a c i t i e s and spray ang les f o r the n o z z l e s i n v e s t i g a t e d i n t h i s work^O 64 IV C o e f f i c i e n t s o f the f i t t e d power curves c o r r e l a t i n g the h e a t - t r a n s f e r c o e f f i c i e n t s to the peak va lues o f spray water f l u x a t d i f f e r e n t s u r f a c e tempera tu res . 187 V C o e f f i c i e n t s o f the f i t t e d power curves c o r r e l a t i n g the h e a t - t r a n s f e r c o e f f i c i e n t s to water f l u x e s averaged over the area of the probe f a c e , f o r d i f f e r e n t s u r f a c e temperatures 195 VI L i s t o f n o z z l e s o the r than 1/4 GG 10 and o p e r a t i n g spray p ressu res used i n the measurement of spray h e a t - t r a n s f e r c o e f f i c i e n t s 197 VII C o e f f i c i e n t s o f the curves f i t t e d to c o r r e l a t e spray e f f i c i e n c y to the peak va lue of the spray water f l u x e s f o r d i f f e r e n t s u r f a c e temperatures 211 V I I I C o e f f i c i e n t s o f the curves f i t t e d to c o r r e l a t e the spray e f f i c i e n c y to the va lue o f spray water f l u x averaged over the area of the probe f a c e , f o r d i f f e r e n t s u r f a c e temperatures 212 IX C a l c u l a t e d d r o p l e t v e l o c i t i e s and d r o p l e t momenta i n the sprays produced by the n o z z l e s s t u d i e d i n t h i s i n v e s t i g a t i o n 215 X M u l t i p l e r e g r e s s i o n c o e f f i c i e n t s f o r the water f l u x and temperature dependence of the h e a t - t r a n s f e r c o e f f i c i e n t s . 222 XI B a s i s f o r the method used f o r the de te rm ina t i on of water f l u x e s by d i f f e r e n t i n v e s t i g a t o r s of spray heat e x t r a c t i o n 224 XII _ C o e f f i c i e n t s o f power curves f i t t e d to the v a r i a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s w i th water f l u x e s averaged over the whole sprayed a r e a , f o r d i f f e r e n t s u r f a c e temperatures 234 i x Appendix I  Tab les 1-1 Spray f l u x map f o r the 1/4 GG 10 nozz le a t a spray p ressure o f 0 .13 MPa f o r a nozz le d i s t a n c e o f 10.16 cm (Type A c o l l e c t o r s ) 1 - 2 Spray f l u x map f o r the 1/4 G G 10 nozz le a t a spray p ressu re o f 0 .13 MPa f o r a n o z z l e d i s t a n c e of 15.24 cm (Type A c o l l e c t o r s ) 1 - 3 Spray f l u x map f o r the 1/4 GG 10 nozz le at a spray p ressure o f 0.13 MPa f o r a n o z z l e d i s t a n c e of 20.32 cm (Type A c o l l e c t o r s ) 1 - 4 Spray f l u x map f o r the 1/4 G G 10 n o z z l e a t a spray p ressure o f 0 .13 MPa f o r a nozz le d i s t a n c e of 10.16 cm (Type B. c o l l e c t o r s ) 1 - 5 Spray f l u x map f o r the 1/4 GG 10 nozz le at a . sp ray p ressure o f 0.27 MPa f o r a nozz le d i s t a n c e of 10.16 cm (Type A c o l l e c t o r s ) 1 - 6 Spray f l u x map f o r the 1/4 GG 10 n o z z l e a t a spray p ressu re o f 0.27 MPa f o r a n o z z l e d i s t a n c e of 15.24 cm (Type A c o l l e c t o r s ) 1 - 7 Spray f l u x map f o r the 1/4 GG 10 nozz le a t a spray p ressu re o f 0.27 MPa f o r a n o z z l e d i s t a n c e of 20.32 cm (Type A c o l l e c t o r s ) 1 - 8 Spray f l u x map f o r the 1/4 GG 10 n o z z l e a t a spray p ressure o f 0 .27 MPa f o r a n o z z l e d i s t a n c e o f 10.16 cm (Type B c o l l e c t o r s ) '. 1-9 Spray f l u x map f o r the 1/4 GG 10 nozz le a t a spray p ressure o f 0.41 MPa f o r a nozz le d i s t a n c e o f 10.16 cm (Type A c o l l e c t o r s ) 1-10 Spray f l u x map f o r the 1/4 G G 10 n o z z l e a t a spray p ressure o f 0.41 MPa f o r a nozz le d i s t a n c e of 15.24 cm (Type A c o l l e c t o r s ) 1-11 Spray f l u x map f o r the 1/4 GG 10 nozz le a t a spray p ressure o f 0.41 MPa f o r a nozz le d i s t a n c e of 20.32 cm (Type A c o l l e c t o r s ) 1 -12 Spray f l u x map f o r the 1/4 G G 10 n o z z l e a t a spray p ressu re o f 0.41 MPa f o r a nozz le d i s t a n c e of 10.16 cm (Type B c o l l e c t o r s ) Page 256 257 258 259 260 261 262 263 264 265 266 267 x Appendix I Tables Page 1-13 H o r i z o n t a l c e n t r e l i n e spray water f l u x d i s t r i b u t i o n f o r the 1/8 GG 5 nozz le 268 1-14 H o r i z o n t a l c e n t r e l i n e spray water f l u x d i s t r i b u t i o n f o r the 1/8 GG 6 SQ nozz le 269 1-15 H o r i z o n t a l c e n t r e l i n e spray water f l u x d i s t r i b u t i o n f o r the 1/4 GG 6.5 SQ n o z z l e 270 1 -16 H o r i z o n t a l c e n t r e l i n e spray water f l u x d i s t r i b u t i o n f o r the 1/4 GG 12 SQ n o z z l e 271 1 -17 H o r i z o n t a l c e n t r e l i n e spray water f l u x d i s t r i b u t i o n f o r the 1/4 GG 14.5 n o z z l e 272 1 -18 H o r i z o n t a l c e n t r e l i n e spray water f l u x d i s t r i b u t i o n f o r the 1/4 GG 14 W nozz le 273 1 -19 H o r i z o n t a l c e n t r e l i n e spray water f l u x d i s t r i b u t i o n f o r the 1/4 U8020 nozz le 274 1 - 20 H o r i z o n t a l c e n t r e l i n e spray water f l u x d i s t r i b u t i o n f o r the 3/8 U5060 n o z z l e 275 x i LIST OF FIGURES Fi gures Page 1 Schemat ic diagram of a b i l l e t c a s t e r showing the d i f f e r e n t heat e x t r a c t i o n zones 3 2 Spray r e l a t e d c racks i n c o n t i n u o u s l y c a s t b i l l e t s and s l a b s - - . . 6 3 T y p i c a l b o i l i n g curves f o r a w i r e , t u b e , o r h o r i z o n t a l s u r f a c e i n a pool o f water a t a tmospher ic p r e s s u r e 5 2 . . 21 4 V a r i a t i o n o f heat f l u x w i t h s u r f a c e temperature i n spray c o o l i n g 5 3 24 5 E f f e c t o f d r o p l e t v e l o c i t y on the heat t r a n s f e r r e d to the d r o p l e t 6 5 31 6 Non we t t i ng d r o p l e t heat t r a n s f e r e f f i c i e n c y 6 5 32 53 7 Dependence o f spray e f f i c i e n c y on water f l u x 37 8 V a r i a t i o n o f spray h e a t - t r a n s f e r c o e f f i c i e n t s w i t h s u r f a c e temperature 38 9 Dependence o f the h e a t - t r a n s f e r c o e f f i c i e n t s on wa te r f l u x and s u r f a c e t e m p e r a t u r e 7 0 . 41 10 E f f e c t o f water temperature on spray h e a t - t r a n s f e r c o e f f i c i e n t s 43 11 V a r i a t i o n o f spray h e a t - t r a n s f e r c o e f f i c i e n t w i t h water f l u x as repor ted i n va r i ous s t u d i e s on spray heat e x t r a c t i o n 45 12 V a r i a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s w i t h s u r f a c e tempera tu re , from va r i ous s t u d i e s on spray heat e x t r a c t i o n 46 13 V a r i a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s w i t h water f l u x f o r d i f f e r e n t d r o p l e t v e l o c i t i e s * * ! 53 14 Schemat ic diagram o f the water supply sys tem 66 15 Schemat ic diagram o f the mount f o r the sp ray n o z z l e . . . 69 16 Schemat ic diagram o f the apparatus used f o r the measurement o f spray water f l u x e s 71 xi i F igu re Page 17 Dependence o f the mean e r r o r i n c a l c u l a t e d h e a t -t r a n s f e r c o e f f i c i e n t s on the d i s t a n c e o f the p o i n t o f measurement below the coo led s u r f a c e ^ ' 78 18 Three a l t e r n a t i v e c o n f i g u r a t i o n s f o r thermocouple placement i n the heat t r a n s f e r probe 81 19 Schemat ic diagram o f the h e a t - t r a n s f e r probe w i t h i n s t a l l e d thermocouples 84 20 Schemat ic diagram o f the c a p a c i t o r d i scha rge we ld ing apparatus 88 21 E l e c t r i c a l connec t ions to the reco rd i ng equipment 91 22 Schemat ic d iagram o f the probe i n s t a l l a t i o n f o r the Type I heat t r a n s f e r exper iments . . . . . 94 23 Schemat ic diagram o f the probe i n s t a l l a t i o n f o r the Type I Ia heat t r a n s f e r exper iments . . 97 24 Photograph of the hea t i ng p l a t e mounted on the t i l t a b l e mount 99 25 Schemat ic diagram o f the probe i n s t a l l a t i o n f o r the Type l i b heat t r a n s f e r exper iments 102 26 D i v i s i o n o f the heat t r a n s f e r probe i n t o nodes 113 27 Comparison o f b a c k - c a l c u l a t e d va lues o f hea t -t r a n s f e r c o e f f i c i e n t s and s u r f a c e temperatures w i t h expected v a l u e s , f o r h= 2.094 kw/m 2h 122 .28 Comparison o f b a c k - c a l c u l a t e d va lues o f the h e a t -t r a n s f e r c o e f f i c i e n t and s u r f a c e temperatures w i t h expected v a l u e s , f o r h = 4 .19 kW/m^h 123 29 Comparison of b a c k - c a l c u l a t e d va lues o f the h e a t -t r a n s f e r c o e f f i c i e n t w i th expected v a l u e s , f o r h va ry i ng w i th su r f ace temperature 125 30 Comparison of b a c k - c a l c u l a t e d va lues o f the h e a t -t r a n s f e r c o e f f i c i e n t , us ing t r a n s i e n t s ob ta ined a t d i f f e r e n t d i s t a n c e s from the coo led face 125 x i i i F igu re Page 31 T y p i c a l h o r i z o n t a l c e n t r e l i n e p r o f i l e ob ta i ned w i t h the 1/4 GG 10 n o z z l e , f o r a spray d i s t a n c e o f 15.24 cm and a spray p ressure o f .41 MPa 128 32 V a r i a t i o n i n the measured spray water f l u x e s f o r f ou r d i f f e r e n t 1/4 GG 10 n o z z l e s 130 33 R e p r o d u c i b i l i t y o f the spray f l u x measurements f o r a 1/4 GG 10 n o z z l e (Number 9 ) 130 34 R e p r o d u c i b i l i t y o f the spray f l u x measurements f o r a 1/4 GG 10 n o z z l e (Number 4) 131 35 E f f e c t o f v i b r a t i n g the c o l l e c t o r s on the sp ray water f l u x measurements 131 36 E f f e c t o f spray p ressure a t cons tan t d i s t a n c e f o r a 1/4 GG 10 n o z z l e a t a d i s t a n c e of 15.24 cm . . 134 37 E f f e c t o f spray p ressure a t cons tan t d i s t a n c e f o r a 1/4 GG 10 n o z z l e , a t a d i s t a n c e o f .10.16 cm 135 38 E f f e c t o f spray p ressure a t cons tan t d i s t a n c e f o r a 1/4 GG 10 n o z z l e , at a d i s t a n c e o f 20.32 cm 136 39 E f f e c t o f d i s t a n c e a t cons tan t p ressure f o r a 1/4 GG 10 n o z z l e , f o r a spray pressure o f 0 .27 MPa 138 40 E f f e c t o f d i s t a n c e a t cons tan t p ressure f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressure o f 0 .13 MPa 139 41 E f f e c t o f d i s t a n c e a t cons tan t p ressure f o r a 1/4 GG 10 n o z z l e , f o r a spray pressure o f 0.41 MPa 140 42 V a r i a t i o n o f spray water f l u x w i th p ressu re and d i s t a n c e a t the cen t re o f the spray produced by a 1/4 GG 10 n o z z l e 141 43 V a r i a t i o n o f spray water f l u x w i th p ressu re and d i s t a n c e 5.08 cm from the cen t re o f the spray produced by a 1/4 Gg 10 n o z z l e . : 142 44 Spray f l u x contour maps f o r a 1/4 GG 10 n o z z l e f o r a n o z z l e d i s t a n c e o f 10.16 cm and sp ray p ressure o f 0.41 MPa (Type A c o l l e c t o r s ) 144 x i v F igu re Page 45 Spray f l u x con tour maps f o r a 1/4 GG 10 n o z z l e f o r a n o z z l e d i s t a n c e o f 15.24 cm and spray p r e s s u r e o f 0.41 MPa (Type A c o l l e c t o r s ) 145 . 46 Spray f l u x con tour maps f o r a 1/4 GG 10 n o z z l e f o r a n o z z l e d i s t a n c e of 20.32 cm and spray p r e s s u r e o f 0.41 MPa (Type A c o l l e c t o r s ) 146 47 Three d imens iona l r e p r e s e n t a t i o n o f the sp ray f l u x e s f o r the 1/4 GG 10 n o z z l e f o r a nozz le d i s t a n c e of 15.24 cm and spray p ressure o f 0.27 MPa . . 147 48 Spray f l u x con tour map f o r a 1/4 GG 10 n o z z l e f o r a spray p ressu re o f 0.41 MPa and nozz le d i s t a n c e o f 10.16 cm (Type B c o l l e c t o r s ) 149 49 Three d imens iona l r e p r e s e n t a t i o n o f the sp ray f l u x e s f o r a 1/4 GG 10 n o z z l e , f o r a spray p r e s s u r e o f 0 .13 MPa and a nozz le d i s t a n c e of 10.16 cm (Type B c o l l e c t o r s ) 150 50 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/8 GG 5 n o z z l e , a t a nozz le d i s t a n c e o f 10.16 cm 152 51 H o r i z o n t a l c e n t r e l i n e 1 spray f l u x p r o f i l e s f o r a 1/8 GG 5 n o z z l e , a t a n o z z l e d i s t a n c e o f 15.24 cm 153 52 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 GG 6 .5 n o z z l e , a t a n o z z l e d i s t a n c e o f 10.16 cm . . . 155 53 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 GG 6 .5 n o z z l e , a t a n o z z l e d i s t a n c e o f 15.24 cm . . . 156 54 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/8 GG 6 SQ n o z z l e , a t a n o z z l e d i s t a n c e o f 10.16 cm . . 157 55 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 HH 14.5 SQ nozz le a t a n o z z l e d i s t a n c e o f 1 0 . 1 6 c m . 159 56 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 HH 14.5 SQ nozz le a t a nozz le d i s t a n c e o f 15 .24cm . 160 57 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 GG 14 W n o z z l e , a t a n o z z l e d i s t a n c e o f 10.16 cm . . 161 58 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 U8020 n o z z l e , a t a n o z z l e d i s t a n c e o f 15.24 cm . . . 162 xv F igu re Page 59 Comparison of c a l c u l a t e d and measured t e m p e r a t u r e s , f o r an average h e a t - t r a n s f e r c o e f f i c i e n t o f 1.05 kW/rrrK 168 60 Comparison of c a l c u l a t e d and measured t e m p e r a t u r e s , f o r an average h e a t - t r a n s f e r c o e f f i c i e n t o f 1.-88 kW/m^K 169 61 V a r i a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s w i t h water f l u x f o r a s u r f a c e temperature of 850°C (Type I exper iments) 172 62 V a r i a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s w i t h wa te r f l u x f o r a. s u r f a c e temperature o f 1000°C (Type I and Type I Ia exper iments) 174 63 V a r i a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s w i t h s u r f a c e temperature (Type I exper iments) 175 64 V a r i a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s w i t h s u r f a c e temperature (Type I Ia exper iments ) 178 65 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h peak va lues water f l u x f o r a s u r f a c e temperature o f 1000°C 180 66 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h peak va lues water f l u x f o r a s u r f a c e temperature o f 800°C 181 67 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h peak va lues water f l u x f o r a s u r f a c e temperature o f 850°C 182 68 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h peak va lues water f l u x f o r a s u r f a c e temperature o f 900°C 183 69 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h peak va lues water f l u x f o r a s u r f a c e temperature o f 950°C 184 70 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h peak va lues water f l u x f o r a s u r f a c e temperature o f 1050°C 185 71 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h va lues o f water f l u x averaged over the probe f a c e , f o r a su r f ace temperature o f 800°C 189 xv i F igu re Page 85 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h va lues o f water f l u x averaged over the probe f a c e , f o r a s u r f a c e temperature o f 900°C 207 86 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i th va lues o f water f l u x averaged over the probe f a c e , f o r a s u r f a c e temperature o f 950°C 208 87 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i th va lues o f water f l u x averaged over the probe f a c e , f o r a s u r f a c e temperature o f 1000°C 209 88 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h va lues o f water f l u x averaged over the probe f a c e , f o r a s u r f a c e temperature o f 1050°C 210 89 V a r i a t i o n o f c r i t i c a l temperature w i t h water f l u x 217 90 V a r i a t i o n o f the heat f l u x w i t h s u r f a c e temperature o f r d i f f e r e n t water f l u x e s 219 91 Curves f i t t e d to the measured v a t i a t i o n of hea t -t r a n s f e r c o e f f i c i e n t s w i t h peak va lues o f water f l u x e s . 226 92 Curves f i t t e d to the measured v a r i 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 w i th va lues o f water f l u x averaged over the probe f a c e . . . . 227 93 Curves f i t t e d to the measured v a r i a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s w i t h va lues o f water f l u x averaged over the whole sprayed area 235 Appendix II  F i g u r e 11-1 Spray f l u x con tour map f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressu re of 0.13 MPa at a n o z z l e d i s t a n c e of 10.16 cm (Type A c o l l e c t o r s ) 277 xv i i i Appendix II Fi gure Page 1 1 - 2 Spray f l u x con tour map f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressu re o f 0 .13 MPa a t a nozz le d i s t a n c e o f 15.24 cm (Type A c o l l e c t o r s ) 11 - 3 Spray f l u x contour map f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressure of 0.27 MPa at a nozz le d i s t a n c e of 10.16 cm (Type A c o l l e c t o r s ) 1 1 - 4 Spray f l u x con tour map f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressure o f 0.27 MPa at a n o z z l e d i s t a n c e of 15.24 cm (Type A c o l l e c t o r s ) 1 1 - 5 Spray f l u x con tour map f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressu re o f 0 .13 MPa a t a n o z z l e d i s t a n c e o f 20.32 cm (Type A c o l l e c t o r s ) 1 1 - 6 Spray f l u x con tour map f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressu re o f 0.27 MPa a t a nozz le d i s t a n c e o f 20.32 cm (Type A c o l l e c t o r s ) 1 1 - 7 Spray f l u x con tour map f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressure o f 0 .13 MPa a t a n o z z l e d i s t a n c e of 10.16 cm and Type B c o l l e c t o r s , I1-8 Spray f l u x con tour map f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressu re o f 0.27 MPa at a nozz le d i s t a n c e of 10.16 cm Type B c o l l e c t o r s 1 1 - 9 Three d imens iona l r e p r e s e n t a t i o n o f the spray f l u x d i s t r i b u t i o n f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressu re o f 0 .13 MPa and a nozz le d i s t a n c e o f 10.16 cm (Type A c o l l e c t o r s ) 1 1 - 1 0 Three d imens iona l r e p r e s e n t a t i o n o f the sp ray f l u x d i s t r i b u t i o n f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressu re o f 0.27 MPa and a nozz le d i s t a n c e o f 10.16 cm (Type A c o l l e c t o r s ) 11 - 1 1 Three d imens iona l r e p r e s e n t a t i o n o f the sp ray f l u x d i s t r i b u t i o n f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressure o f 0.13 MPa and a nozz le d i s t a n c e of . 15.32 cm (Type A c o l l e c t o r s ) 1 1 - 1 2 Three d imens iona l r e p r e s e n t a t i o n o f the spray f l u x d i s t r i b u t i o n f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressu re o f 0.27 MPa and a n o z z l e d i s t a n c e of 20.32 cm (Type A c o l l e c t o r s ) 278 279 280 281 282 283 284 285 286 287 288 x i x Appendix II Fi gure Page 1 1 - 1 3 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 GG 10 SQ nozz le at a nozz le d i s t a n c e of 10.16 cm 289 1 1 - 1 4 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 GG 10 SQ n o z z l e a t a nozz le d i s t a n c e o f 15.24 cm 290 1 1 - 1 5 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 GG 10 SQ nozz le a t a nozz le d i s t a n c e o f 20.32 cm 291 11 - 1 6 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 GG 12 SQ nozz le a t a nozz le d i s t a n c e of 10.16 cm 292 1 1 - 1 7 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 GG 12 SQ nozz le a t a nozz le d i s t a n c e o f 15.24 cm 293 11 - 1 8 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 GG 12 SQ nozz le a t a nozz le d i s t a n c e o f 20.32 cm 294 1 1 - 1 9 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 3/8 HH 18 SQ nozz le a t a nozz le d i s t a n c e of 10.16 cm \ 295 11 - 2 0 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 3/8 HH 18 SQ nozz le a t a nozz le d i s t a n c e o f 15.24 cm 296 11 - 2 1 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 3/8 HH 18 SQ nozz le a t a nozz le d i s t a n c e o f 20.32 cm 297 1 1 - 2 2 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 U8020 n o z z l e a t a nozz le d i s t a n c e of 20.32 cm 298 1 1 - 2 3 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 3/8 U5060 n o z z l e a t a n o z z l e d i s t a n c e of 17.78 cm 299 xx L I S T OF SYMBOLS Q H e a t f 1 u x • k W / r / 2 h H e a t - t r a n s f e r c o e f f i c i e n t k W / m K 2 m W a t e r f l u x z/m s T g S u r f a c e t e m p e r a t u r e ° C T w W a t e r t e m p e r a t u r e ° C T A m b i e n t t e m p e r a t u r e ° C a r Q D r o p l e t r a d i u s cm d D r o p l e t d i a m e t e r m n S p r a y c o o l i n g e f f i c i e n c y v D r o p l e t v e l o c i t y m/s V 1 , V 2 V e l o c i t y m/s k T h e r m a l c o n d u c t i v i t y W/mK p D e n s i t y k g / m Cp H e a t c a p a c i t y W s / k g A h v H e a t o f v a p o r i z a t i o n Ws a S u r f a c e t e n s i o n N/m P.j , P ^ P r e s s u r e Pa A X Node s p a c i n g m At T i m e i n c r e m e n t s T.j T e m p e r a t u r e a t t h e i t h node ° C * T. T e m p e r a t u r e a t t h e i t h n o d e , a t t i m e t + 0 . 5 At ° C P ( l ) , P ( 2 ) , P ( 3 ) C o e f f i c i e n t s o f f i t t e d c u r v e s We Weber Number xx i ACKNOWLEDGEMENTS The a u t h o r w i s h e s t o e x p r e s s h i s , s i n c e r e g r a t i t u d e t o h i s r e s e a r c h s u p e r v i s o r s , D r . J . K . B r i m a c o m b e a n d D r . F . W e i n b e r g , f o r t h e i r h e l p a n d g u i d a n c e t h r o u g h t h e c o u r s e o f t h i s w o r k . The d i s c u s s i o n s and a s s i s t a n c e o f f e l l o w g r a d u a t e s t u d e n t s , f a c u l t y members a n d t e c h n i c i a n s h a v e b e e n i n v a l u a b l e . F i n a n c i a l a s s i s t a n c e i n t h e f o r m o f a K i l l a m P r e d o c t o r a l F e l l o w s h i p , a n d a r e s e a r c h g r a n t f r o m t h e A m e r i c a n I r o n and S t e e l I n s t i t u t e ( G r a n t N o . 3 6 - 3 3 7 ) i s g r a t e f u l l y a c k n o w l e d g e d . i x x i i C h a p t e r 1 INTRODUCTION C o n t i n u o u s c a s t i n g i s g a i n i n g a p o s i t i o n o f e v e r i n -c r e a s i n g i m p o r t a n c e i n t h e s t e e l i n d u s t r y w i t h i t s c a p a b i l i t y o f b e i n g a b l e t o p r o d u c e b l o o m s , b i l l e t s a n d s l a b s o f d i f -f e r e n t c r o s s s e c t i o n s and a w i d e v a r i e t y o f s t e e l g r a d e s . C o m p a r e d t o c o n v e n t i o n a l i n g o t c a s t i n g , c o n t i n u o u s c a s t i n g o f s t e e l r e s u l t s i n a s i g n i f i c a n t r e d u c t i o n i n p r o c e s s i n g c o s t s b y : 1 i ) I n c r e a s i n g t h e y i e l d o f b l o o m s and s l a b s by a b o u t 10% i i ) R e d u c t i o n i n t h e e n e r g y c o n s u m p t i o n by a s u b s t a n t i a l amoun t i i i ) I m p r o v i n g p r o d u c t q u a l i t y a n d h o m o g e n e i t y i v ) R e d u c i n g o p e r a t i n g c o s t s v ) R e d u c i n g c a p i t a l i n v e s t m e n t by e l i m i n a t i n g i n g o t t e e m i n g , s o a k i n g p i t s , a n d p r i m a r y r o l 1 i ng m i l l s . H i g h e r p r o d u c t i v i t y has a l s o b e e n e n h a n c e d , e s p e c i a l l y w i t h t h e i n t r o d u c t i o n o f BOF c o n v e r t e r f a c i l i t i e s , t h e use o f s e q u e n t i a l c a s t i n g , and t h e u s e o f h i g h e r c a s t i n g s p e e d s . 1 M o r e o v e r , c o s t r e d u c t i o n s a r e e f f e c t e d by t h e s t r a n d c a s t i n g o f many s e m i f i n i s h e d s h a p e s , i n c l u d i n g beam b l a n k s a n d r o u n d s . S i n c e q u a l i t y r e q u i r e m e n t s a r e c o n t i n u a l l y b e i n g u p -g r a d e d , t h e p r o d u c t i o n t e c h n o l o g y o f a p r o c e s s l i k e c o n t i n -uous c a s t i n g m u s t a l s o be i m p r o v e d , a t l e a s t a t t h e same p a c e , i n o r d e r t o p r o d u c e an a c c e p t a b l e a n d m a r k e t a b l e p r o -d u c t . The i n f l u e n c e o f t h e p r o d u c t i o n p a r a m e t e r s on t h e q u a l i t y o f t h e c a s t p r o d u c t h a s t h e r e f o r e b e e n t h e o b j e c t o f much s c r u t i n y . The r e s u l t s o f a l a r g e n u m b e r o f i n v e s t i -g a t i o n s , b o t h t h e o r e t i c a l and e x p e r i m e n t a l , h a v e c l a r i f i e d , t o a r e a s o n a b l e e x t e n t , t h e e f f e c t o f t h e m a j o r p r o d u c t i o n 2 p a r a m e t e r s on t h e q u a l i t y o f t h e s t e e l p r o d u c e d . H o w e v e r , many f a c t o r s , s u c h as s p r a y c o o l i n g , r e q u i r e a t t e n t i o n , s i n c e i t h a s b e e n shown t h a t i m p r o p e r s p r a y c o o l i n g l e a d s t o a l a r g e number o f c a s t i n g d e f e c t s as d e s c r i b e d i n a f o l l o w -i n g s e c t i o n . The l o c a t i o n o f t h e s p r a y h e a t e x t r a c t i o n z o n e s i n r e l a t i o n t o t h e o t h e r h e a t e x t r a c t i o n z o n e s i n a ' c o n t i n u o u s b i l l e t c a s t i n g m a c h i n e c a n be s e e n f r o m an o b s e r v a t i o n o f F i g u r e 1 . T h r e e m a i n s t a g e s f o r t h e h e a t e x t r a c t i o n f r o m t h e s t r a n d c a n be o b s e r v e d f r o m t h i s F i g u r e : i ) i i ) t h e m o u l d r e g i o n t h e s p r a y z o n e s b e l o w t h e m o u l d input Stream From Tundr Figure 1 Schemat ic diagram o f a b i l l e t c a s t e r showing the d i f f e r e n t heat e x t r a c t i o n zones . i i i ) t h e r a d i a t i v e c o o l i n g z o n e a f t e r t h e s t r a n d e m e r g e s f r o m t h e s p r a y z o n e s . The w a t e r c o o l e d c o p p e r m o u l d s e r v e s t o f o r m a t h i n s k i n o f s o l i d i f i e d s t e e l , w h i c h s u p p o r t s t h e c o r e o f l i q u i d m e t a l . Much o f t h e h e a t r e m o v e d i n t h e s t r a n d ( 5 0 t o 65% i n t h e c a s e o f s l a b s ) i s e x t r a c t e d by t h e w a t e r s p r a y s i n t h e s p r a y c o o l -i n g z o n e s , a l s o : r e f e r r e d t o a s t h e s e c o n d a r y c o o l i n g z o n e . I n t h i s z o n e , the" c o o l i n g o f t h e s t r a n d s u r f a c e n o t o n l y p r o m o t e s s o l i d i f i c a t i o n , b u t a l s o p r o v i d e s t h e s o l i d i f i e d s h e l l w i t h e n o u g h s t r e n g t h t o s u p p o r t t h e l i q u i d c o r e , a n d a l s o s e r v e s t o a v o i d r e m e l t i n g o f t h e s h e l l . I n t h e t h i r d c o o l i n g r e g i o n , h e a t i s l o s t by t h e s t r a n d t o t h e s u r r o u n d -i n g s by t h e p r o c e s s o f r a d i a t i v e h e a t t r a n s f e r . S l a b c a s t e r s a r e s i m i l a r , e x c e p t t h a t a number o f s u p p o r t and d r i v i n g r o l l s a r e p r e s e n t t h r o u g h t h e l e n g t h o f t h e m a c h i n e , f r o m j u s t b e l o w t h e m o u l d t o t h e c u t - o f f s e c t i o n . In t h e e a r l y d a y s o f c o n t i n u o u s c a s t i n g , t h e d e s i g n o f t h e s p r a y c o o l i n g s y s t e m was b a s e d p r i m a r i l y o n two r e -q u i r e m e n t s : h i g h h e a t e x t r a c t i o n r a t e s f o r max imum p r o -d u c t i v i t y , a n d . s i m p l i c i t y f o r e a s e , o f o p e r a t i o n a s w e l l a s m a i n t e n a n c e . The use o f h i g h h e a t e x t r a c t i o n r a t e s i n t h e s p r a y r e g i o n s m u s t be t e m p e r e d by t h e f a c t t h a t , a s m e n t i o n e d b e f o r e , many o f t h e t y p e s o f c r a c k s i n t h e c a s t p r o d u c t a r e s p r a y r e l a t e d , and as s u c h , c a r e f u l c o n s i d e r a t i o n m u s t be 5 g i v e n t o t h e d e s i g n o f t h e s e c o n d a r y c o o l i n g z o n e i n o r d e r t o m i n i m i z e c r a c k f o r m a t i o n . 1.1 S e c o n d a r y C o o l i n g and C r a c k F o r m a t i o n D e f e c t s h a v e b e e n l i n k e d t o s p r a y p r a c t i c e i n t h e c o n t i n u o u s c a s t i n g o f b i l l e t s and s l a b s and a r e shown s c h e m a t i c a l l y i n F i g u r e 2. C r a c k s f o r m d u r i n g t h e c a s t i n g p r o c e s s when s u f f i c i e n t l y h i g h t e n s i l e s t r a i n s a r e g e n e r a t e d i n t h o s e p o r t i o n s o f t h e s t r a n d t h a t p o s s e s s l o w d u c t i l i t y . The o r i g i n o f t h e s e s t r a i n s c a n be t r a c e d b a c k b o t h t o t h e r m a l a n d m e c h a n i c a l f a c t o r s . When t h e s t r a n d s u r f a c e i s b e i n g c o o l e d , s t e e p t e m p e r a t u r e g r a d i e n t s a r e s e t up i n t h e s o l i d i -f y i n g s h e l l . When t h e r e i s a c h a n g e i n t h e r a t e o f h e a t e x t r a c t i o n a t t h e s u r f a c e , t h e s e t e m p e r a t u r e g r a d i e n t s c h a n g e r a p i d l y , g e n e r a t i n g d i f f e r e n t i a l t h e r m a l e x p a n s i o n and t h e r m a l s t r a i n s i n t h e s h e l l . C r a c k f o r m a t i o n t h e n o c c u r s when t h e m a g n i t u d e o f t h e s t r a i n s i s g r e a t e r t h a n t h e d u c t i l i t y o f t h e m a t e r i a l . In some c a s e s , t e m p e r a t u r e e x c u r s i o n s o f t h e s o l i d s h e l l due t o v a r i a t i o n s i n t h e c o o l i n g r a t e o f t h e s u r f a c e p r o m o t e t h e f o r m a t i o n o f p h a s e s l i k e A 1 N , w h i c h c a n r e d u c e t h e h i g h t e m p e r a t u r e d u c t i l i t y and l e a d t o c r a c k f o r m a t i o n . M e c h a n i c a l s t r a i n s c a n be g e n e r a t e d by one o r a c o m b i n a t i o n o f t h e f o l l o w i n g : f e r r o s t a t i c p r e s s u r e o f t h e l i q u i d p o o l , m o u l d f r i c t i o n , m a c h i n e m i s a l i g n m e n t , and b e n d i n g a n d 3-9 s t r a i g h t e n i n g o p e r a t i o n s . Many r e v i e w s d e a l c o m p r e h e n s i v e l y w i t h t h e t y p e s and m o r p h o l o g i e s o f d e f e c t s , t h e i r c a u s e s , and Billet (1) Midway cracks (2) R h o m b o i d i t y / diagonal cracks Slab (1) Transverse surface cracks (2) Longitudinal , m i d - f a c e cracks (3) T r i p l e - p o i n t cracks (4) Midway cracks (radial streaks) (5) Centre- l ine cracks (6) Centre segregation F i g u r e 2 S p r a y r e l a t e d c r a c k s i n c o n t i n u o u s l y c a s t b i l l e t s and s l a b s o 7 m e t h o d s f o r t h e i r p r e v e n t i o n i n s t r a n d c a s t p r o d u c t s . F rom t h e l i t e r a t u r e , t h e f a c t e m e r g e s t h a t s p r a y r e l a t e d c r a c k s ( w i t h t h e e x c e p t i o n o f t r a n s v e r s e c r a c k s i n s l a b s ) f o r m c l o s e t o t h e s o l i d i f i c a t i o n f r o n t , i n a t e m p e r a -t u r e r a n g e w i t h i n r o u g h l y 50 t o 75°C o f t h e s o l i d u s . I n -v e s t i g a t i o n o f t h e h i g h t e m p e r a t u r e m e c h a n i c a l p r o p e r t i e s o f s t e e l ^ 0 - ^ 5 h a v e shown t h a t t h e d u c t i l i t y o f t h e s t e e l a t t e m p e r a t u r e s c l o s e t o t h e s o l i d u s t e m p e r a t u r e i s v e r y l o w -o f t h e o r d e r o f 0 .2 to 0.3%. . T h i s l o w d u c t i l i t y r e s u l t s f r o m t h e p r e s e n c e o f 1 ow m e l t i n g - p o i n t 1 i q u i d f i l m s e n r i c h e d w i t h p o s i t i v e l y s e g r e g a t e d e l e m e n t s l i k e s u l p h u r a n d p h o s p h o r u s , s e p a r a t i n g a d j a c e n t d e n d r i t e s . F rom t h e f o r e g o i n g s t a t e m e n t s , i t c a n be g e n e r a l i z e d , t h a t m o s t t y p e s o f c r a c k i n g i n c o n -t i n u o u s l y c a s t p r o d u c t s c a n be p r e v e n t e d i f t h e m a g n i t u d e o f t h e t e n s i l e s t r a i n s , i m p o s e d e i t h e r t h e r m a l l y o r m e c h a n i c a l l y , c a n be r e d u c e d t o l e s s t h a n a b o u t 0 , .2%. F rom F i g u r e 2 , i t c a n be s e e n t h a t s l a b s h a v e a l a r g e r n u m b e r o f s p r a y r e l a t e d d e f e c t s , as c o m p a r e d t o b i l l e t s . T h i s i s b e c a u s e s l a b s a r e p r o n e t o b u l g i n g o f t h e b r o a d f a c e due t o f e r r o s t a t i c p r e s s u r e e x e r t e d by t h e l i q u i d c o r e . S p r a y c o o l -i n g a f f e c t s b u l g i n g , b e c a u s e i t c h a n g e s t h e t e m p e r a t u r e g r a d i -e n t s i n t h e s o l i d s h e l l , and t h u s t h e r e s i s t a n c e o f t h e s h e l l t o d e f o r m a t i o n u n d e r t h e i n f l u e n c e o f t h e f e r r o s t a t i c p r e s s u r e . B u l g i n g i s a l s o a f f e c t e d by r o l l p i t c h , d i s t a n c e b e l o w t h e 8 m e n i s c u s , and t h e c a s t i n g s p e e d . * 1 . 1 . 1 S p r a y R e l a t e d D e f e c t s i n B i l l e t s The m o s t common d e f e c t l i n k e d t o i m p r o p e r s p r a y c o o l i n g p r a c t i c e i n b i l l e t s i s t h e m i d w a y o r h a l f w a y c r a c k . T h e s e h a v e a l s o b e e n r e f e r r e d t o as r a d i a l s t r e a k , o r g h o s t l i n e s . T h e s e c r a c k s c a n be s e e n i n t r a n s v e r s e s e c t i o n s , a n d l i e n o r m a l t o t h e f a c e s o f t h e b i l l e t . T h e i r p o s i t i o n i n t h e t r a n s v e r s e s e c t i o n i s a p p r o x i m a t e l y h a l f w a y b e t w e e n t h e s u r -f a c e s and t h e c e n t r e o f t h e s e c t i o n . T h i s t y p e o f c r a c k i s c a u s e d by r e h e a t i n g o f t h e b i l l e t s u r f a c e when t h e r a t e o f h e a t e x t r a c t i o n a t t h e s u r f a c e i s s u d d e n l y r e d u c e d . T h i s may o c c u r when t h e b i l l e t p a s s e s f r o m o n e s p r a y c o o l i n g z o n e t o a n o t h e r o r f r o m t h e s p r a y c o o o l i n g z o n e t o t h e r a d i a t i o n c o o l i n g z o n e b e l o w t h e s p r a y s . 1 6 - 2 0 The s u d d e n r e d u c t i o n o f t h e s u r f a c e h e a t e x t r a c t i o n r a t e s c a n be c a u s e d by e x c e s s i v e s p r a y c o o l i n g i n some s p r a y c o o l i n g z o n e s , o r by a s p r a y c o o l i n g z o n e o f i n s u f f i c i e n t l e n g t h . T h e s u r f a c e r e h e a t i n g r e s u l t s i n t h e g e n e r a t i o n o f c o m p r e s s i v e s t r a i n s on t h e o u t -s i d e o f t h e s t r a n d , and t e n s i l e s t r a i n s n e a r t h e s o l i d i f i c a -t i o n f r o n t . C r a c k i n g t h e n o c c u r s i f t h e s t r a i n s e x c e e d t h e c r i t i c a l s t r a i n s o f 0 . 2 t o 0 . 3 % i n t h e r e g i o n s o f l o w d u c t i l i t y . T h u s , t o p r e v e n t t h e f o r m a t i o n o f m i d w a y c r a c k s t h e s u r f a c e r e h e a t i n g m u s t be m i n i m i z e d by p r o p e r s p r a y c o o l i n g d e s i g n . A maximum l i m i t on t h e s u r f a c e r e h e a t i n g o f 1 0 0 ° C h a s b e e n 9 21 p r o p o s e d t o p r e v e n t t h e o c c u r r e n c e o f t h e s e c r a c k s . T h i s 22 c r i t e r i o n has b e e n u s e d by A g a r w a l i n h i s r e d e s i g n o f t h e s p r a y s y s t e m i n an o p e r a t i n g b i l l e t c a s t e r , and he h a s d e m o n -s t r a t e d t h a t p r o p e r s p r a y c o o l i n g c a n a l l e v i a t e t h e f o r m a -t i o n o f s u c h c r a c k s . In an i n d i r e c t w a y , a h i g h c a s t i n g t e m p e r a t u r e a l s o has b e e n l i n k e d t o t h e f o r m a t i o n o f m i d w a y c r a c k s b e c a u s e v h i g h c a s t i n g t e m p e r a t u r e s l e a d t o t h e f o r m a t i o n o f l o n g , c o l u m n a r z o n e s d u r i n g s o l i d i f i c a t i o n . M i d w a y c r a c k s a r e a b l e t o f o r m more e a s i l y b e t w e e n t h e d e n d r i t e s i n t h e c o l u m n a r z o n e w h i c h r u n s p e r p e n d i c u l a r t o t h e t e n s i l e s t r e s s , as c o m p a r e d t o t h e e q u i a x e d z o n e . T h e r e f o r e , i t i s a d v a n t a g e o u s t o h a v e a p r e d o m i n a n t l y e q u i a x e d s t r u c t u r e i n t h e c a s t i n g t o r e d u c e c r a c k i n g . H o w e v e r , t h i s i s n o t o f t e n a p r a c t i c a b l e s o l u t i o n , s i n c e t h e s t e e l may become t o o c o l d t o w a r d t h e end o f t h e c a s t i n g , s u c h t h a t s k u l l s f o r m i n t h e t u n d i s h a n d l a d l e , and n o z z l e s become b l o c k e d . T h e r e f o r e i t i s a d v a n t a g e o u s t o c o n t r o l t h e f o r m a t i o n o f m i d w a y c r a c k s by p r o p e r d e s i g n o f t h e s p r a y c o o l i n g z o n e s . A f i n a l m e a s u r e i s t h e r e d u c t i o n o f s u l p h u r a n d p h o s p h o r u s l e v e l s ( t o b e l o w 0.02%), w h i c h i m p r o v e s t h e h i g h t e m p e r a t u r e m e c h a n i c a l p r o -p e r t i es o f t h e s t e e l . The o t h e r s p r a y r e l a t e d d e f e c t s - d i a g o n a l c r a c k i n g and r h o m b o i d i t y , a r e a s s o c i a t e d w i t h u n s y m m e t r i c a l c o o l i n g TO o f t h e b i l l e t f a c e s . T h o u g h i n some c a s e s t h e s e d e f e c t s h a v e t h e i r o r i g i n i n t h e m o u l d , t h e y c a n a l s o a r i s e i n t h e u p p e r s p r a y r e g i o n s i f t h e w a t e r p r e s s u r e i n a l l t h e s p r a y r i s e r s i s n o t e q u a l , o r i f some o f t h e n o z z l e s a r e p l u g g e d . T h u s , i f two a d j a c e n t f a c e s a r e c o o l e d m o r e r a p i d l y t h a n 3 2 3 o t h e r f a c e s ' i n t h e m o u l d o r i n t h e s e c o n d a r y c o o l i n g z o n e , t h e b i l l e t c o n t r a c t s t o g e n e r a t e a d i a g o n a l t e n s i l e s t r a i n b e t w e e n t h e c o l d e r f a c e s . I f t h e s t r a i n i s l a r g e , t h e b i l l e t d i s t o r t s and t a k e s on a r h o m b o i d s h a p e w i t h an a c u t e a n g l e b e t w e e n t h e c o l d e r f a c e s . A c r a c k may t h e n f o r m n e a r t h e s o l i d i f i c a t i o n f r o n t a l o n g t h e d i a g o n a l j o i n i n g t h e o b t u s e c o r n e r s , t h a t i s , p e r p e n d i c u l a r t o t h e t e n s i l e s t r a i n . U n i f o r m c o o l i n g on a l l f a c e s m i n i m i z e s t h e f o r m a t i o n o f s u c h c r a c k s . The o c c u r r e n c e o f c e n t r e l i n e c r a c k i n g i n b i l l e t s h a s b e e n a t t r i b u t e d t o t h e s u d d e n d r o p i n t h e c e n t r e l i n e t e m p e r a -17 t u r e a t t h e c o m p l e t i o n o f s o l i d i f i c a t i o n , s i n c e t h e r e i s no more l a t e n t h e a t b e i n g r e l e a s e d . T h u s , t h e c o o l i n g r a t e a t t h e c e n t r e b e c o m e s h i g h e r t h a n t h e r a t e a t t h e s u r f a c e . T h i s c a u s e s a r a p i d r e a r r a n g e m e n t o f t h e t e m p e r a t u r e g r a d i e n t s i n t h e b i l l e t , a n d i m p o s e s a t e n s i l e s t r a i n a t t h e c e n t r e , c o n t r i b u t i n g t o c e n t r e l i n e c r a c k i n g . By a p p l y i n g w a t e r s p r a y s t o t h e p o i n t c o r r e s p o n d i n g t o t h e b o t t o m o f t h e l i q u i d p o o l , t h e s u r f a c e c a n a l s o be made t o c o o l r a p i d l y so t h a t t h e d i f -f e r e n c e i n t h e c o o l i n g r a t e s b e t w e e n t h e c e n t r e a n d t h e 11 s u r f a c e i s d e c r e a s e d . As a c o n s e q u e n c e , t h e t e n s i l e s t r a i n s 7 4 a r e r e d u c e d , and c e n t r e l i n e c r a c k i n g a v o i d e d . 1 . 1 . 2 S p r a y R e l a t e d D e f e c t s i n S l a b s B u l g i n g c a u s e d by f e r r o s t a t i c p r e s s u r e , as m e n t i o n e d e a r l i e r , i s t h e c a u s e o f m o s t t y p e s o f c r a c k s i n 2 5 s l a b s . T h e s e i n c l ude t r i p i e p o i n t c r a c k s , c e n t r e l i n e c r a c k s , 26 2 7 31 r a d i a l s t r e a k s and c e n t r e l i n e s e g r e g a t i o n . " The t e n d e n c y f o r b u l g i n g c a n be r e d u c e d by i n c r e a s i n g t h e s e c o n -d a r y c o o l i n g i n t h e u p p e r s p r a y z o n e s , w h i c h p r o v i d e s a s t r o n g e r 2 7 28 s h e l l . ' In a d d i t i o n , p r o p e r a d j u s t m e n t o f r o l l g a p s and r o l l f o r c e s a l s o r e d u c e s b u l g i n g . T h o u g h s p r a y c o o l i n g i s n o t t h e p r i m a r y c a u s e f o r t h e f o r m a t i o n o f l o n g i t u d i n a l , m i d - f a c e c r a c k s , s p r a y i n g c o n d i t i o n s i n t h e u p p e r s p r a y z o n e s a r e known t o e x a c e r b a t e t h e c r a c k i n g p r o b l e m . T h e s e c r a c k s i n i t i a t e i n t h e m o u l d , and c a n b r e a k t h r o u g h t o t h e s u r f a c e d e p e n d i n g on t h e s e c o n d a r y c o o l i n g and 4 7 32 33 t h e s t r a n d s u p p o r t s y s t e m . ' ' ' R e d u c t i o n i n t h e c o o l i n g p r o v i d e d i n t h e u p p e r s p r a y z o n e s has b e e n f o u n d t o h a v e a b e n e f i c i a l i n f l u e n c e on t h e s u r f a c e q u a l i t y , and t o r e d u c e t h e i n c i d e n c e o f t h i s t y p e o f c r a c k . H o w e v e r , i t s h o u l d be n o t e d t h a t i f t h e s p r a y c o o l i n g i n t h e t o p z o n e i s i n a d e q u a t e , t h e s u r f a c e o f t h e s l a b may become t o o h o t and l e a d t o l a r g e s t r a i n s due t o b u l g i n g . On t h e o t h e r h a n d , e x c e s s i v e w a t e r c o o l i n g 12 i n t h e s p r a y z o n e s r e s u l t s i n r a p i d c o o l i n g o f t h e s u r f a c e , g e n e r a t i n g l a r g e t r a n s v e r s e t e n s i l e s t r a i n s , w h i c h c a n o p e n up s m a l l c r a c k s f o r m e d i n t h e m o u l d . T h u s , an o p t i m u m v a l u e o f s p r a y c o o l i n g m u s t be c h o s e n , t o c o m p r o m i s e b e t w e e n o v e r c o o l i n g and b u l g i n g . T r a n s v e r s e s u r f a c e c r a c k s r e s u l t i n g f r o m i m p r o p e r s p r a y p r a c t i c e c a n be a s e r i o u s p r o b l e m i n s l a b s c a s t f r o m s t e e l c o n t a i n i n g >.02% A l , >1 % Mn , o r Nb a n d V . T h e s e c r a c k s o c c u r a l m o s t e x c l u s i v e l y on t h e i n n e r r a d i u s s u r f a c e o f s t r a n d s p r o d u c e d i n a r c t y p e c o n t i n u o u s c a s t i n g m a c h i n e s . S i n c e t h e s e c r a c k s l i e a t t h e b a s e o f o s c i 1 1 a t i o n m a r k s , a n d a r e q u i t e f i n e , t h e y a r e d i f f i c u l t t o d e t e c t e x c e p t w i t h t h e a i d o f a c o n t r o l - p a s s s c a r f . The f o r m a t i o n o f t h e s e c r a c k s 4 16 34 has b e e n a t t r i b u t e d l a r g e l y t o s t r a i g h t e n i n g o f t h e s i ab's, ' ' when t h e t e m p e r a t u r e o f t h e t o p s u r f a c e , w h i c h i s u n d e r a x i a l t e n s i o n , i s b e t w e e n 700 and 9 0 0 ° C . In t h i s t e m p e r a t u r e r a n g e , t h e s t e e l i s shown t o h a v e a l o w d u c t i l i t y as t h e r e s u l t o f t h e p r e c i p i t a t i o n o f A l N ( o r p r e s u m a b l y , t h e n i t r i d e s a n d c a r b i d e s o f Nb and V , i f p r e s e n t ) a t g r a i n b o u n d a r i e s . Al .N p r e c i p i t a t i o n h a s b e e n f o u n d t o be e n h a n c e d by c o o l i n g -24 35 r e h e a t i n g c y c l e s i n t h e same t e m p e r a t u r e r a n g e . ' R e -d u c t i o n o f s p r a y c o o l i n g i n t h e u p p e r s p r a y z o n e s h a s b e e n u s e d t o a l t e r t h e c o o l i n g - r e h e a t i n g c y c l e s , t h u s r e d u c i n g t h e A1N p r e c i p i t a t i o n and i m p r o v i n g t h e d u c t i l i t y o f t h e 13 35 36 \ s t e e l a t t h e s t r a i g h t e n e r . ' The b r i t t l e z o n e h xas b e e n a v o i d e d d u r i n g s t r a i g h t e n i n g by one o f t w o s p r a y p r a c t i c e s : by k e e p i n g t h e s u r f a c e t e m p e r a t u r e o f t h e s l a b a b o v e t h e 24 o n , 3 5 , 3 8 700 t o 9 0 0 ° C r e g i o n , 2 4 ' 3 6 ' 3 7 o r by k e e p i n g i t b e l o w t h i s t e m p e r a t u r e r a n g e A l l r e m a i n i n g d e f e c t s shown i n F i g u r e 2 a r e t h e r e s u l t o f b u l g i n g o f t h e b r o a d f a c e o f t h e s l a b . T r i p l e p o i n t c r a c k s , r u n n i n g p e r p e n d i c u l a r t o t h e n a r r o w f a c e , l i e w i t h i n t h e V s h a p e d r e g i o n f o r m e d by t h e m e e t i n g o f t h e t h r e e s o l i d i f i c a t i o n f r o n t s . B u l g i n g o f t h e b r o a d f a c e r e s u l t s i n an o u t w a r d r o t a t i o n o f t h e c o l d c o r n e r s , c a u s i n g a s l i g h t c o n c a v i t y o f t h e n a r r o w f a c e . T h u s , t e n s i l e s t r e s s e s a r e g e n e r a t e d n e a r t h e s o l i d i f i c a t i o n f r o n t i n a d i r e c t i o n p a r a l l e l t o t h e n a r r o w f a c e . I f t h e r e s u l t i n g t e n s i l e s t r a i n s e x c e e d t h e d u c t i l i t y o f t h e m a t e r i a l i n t h i s a r e a , t r i p l e p o i n t c r a c k s a r i s e . M i d w a y c r a c k s o r r a d i a l s t r e a k s i n s l a b s a r e s e e n r u n n i n g n o r m a l t o t h e b r o a d f a c e i n l o n g i t u d i n a l s e c t i o n s , as c a n be s e e n f r o m F i g u r e 2 . I n s u f f i c i e n t s p r a y w a t e r a n d h i g h c a s t i n g s p e e d a r e t h e m o s t i m p o r t a n t f a c t o r s c o n t r i b u t -39 i n g t o t h e f o r m a t i o n o f t h i s t y p e o f c r a c k . T h e c r a c k s a r e c a u s e d by t h e s q u e e z i n g a c t i o n o f s u p p o r t r o l l s on a b u l g e d r e g i o n o f s l a b , g e n e r a t i n g t e n s i l e s t r a i n s a t t h e s o l i d i f i c a t i o n f r o n t . 14 C e n t r e l i n e c r a c k s a r e t h e r e s u l t o f b u l g i n g c l o s e t o t h e b o t t o m o f t h e l i q u i d p o o l . C r a c k i n g c a n be r e d u c e d by r e g a p p i n g t h e r o l l s c o r r e c t l y , r e d u c i n g c a s t i n g s p e e d , o r i n c r e a s i n g s p r a y c o o l i n g t o r e d u c e b u l g i n g . C e n t r e s e g r e g a t i o n i s a f f e c t e d p r i m a r i l y by b u l g i n g 27 28 29 40 a n d s u p e r h e a t , ' ' ' B u l g i n g n e a r t h e b o t t o m o f t h e p o o l c a u s e s t h e r e m a i n i n g l i q u i d , e n r i c h e d i n s o l u t e s s u c h as M n , C , S and P , t o be d r a w n down i n t o the b u l g e d a r e a . S p r a y c o o l i n g a n d c a s t i n g s p e e d a r e f a c t o r s a f f e c t i n g c e n t r e s e g r e g a t i o n i n s o f a r as t h e y a f f e c t t h e s l a b s u r f a c e t e m p e r a -t u r e , and c o n s e q u e n t l y , t h e r e s i s t a n c e t o b u l g i n g . In t h e c o n t r o l o f b u l g i n g o f t h e b r o a d f a c e s o f t h e s l a b , t h e r o l l p i t c h and r o l l g a p s i n t h e s u p p o r t a s s e m b l y a r e o f p r i m a r y i m p o r t a n c e . S p r a y p r a c t i c e p l a y s a s m a l l e r p a r t , by i n c r e a s i n g t h e b u l g i n g r e s i s t a n c e i f t h e s l a b s u r -f a c e t e m p e r a t u r e i s m a i n t a i n e d a t a l o w e n o u g h t e m p e r a t u r e . H o w e v e r , s i n c e s p r a y s p l a y an i m p o r t a n t r o l e i n t h e p r e -v e n t i o n o f d e f e c t s s u c h as t r a n s v e r s e c r a c k s , a d e g r e e o f f r e e d o m i s l o s t i f t h e s p r a y s m u s t be t i e d t o b u l g i n g c o n -t r o l . I t s h o u l d be e m p h a s i z e d t h a t , w i t h i n r e a s o n a b l e l i m i t s , t h e u s e o f s p r a y s s o l e l y t o l i m i t b u l g i n g i s an i n d i c a t i o n 9 o f d e f e c t s i n t h e m a c h i n e d e s i g n o r p o o r m a i n t e n a n c e . The c a u s e s f o r t h e d e f e c t s d i s c u s s e d i n t h i s s e c t i o n TABLE I Spray Related Defects Crack Type Spray Related Cause Other Factors Corrective Action BILLETS Midway Cracks Reheating of surface below spray chamber High casting temperature S and P >.02% Adjust sprays to minimize reheating, lower pouring temperature, S and P levels. Rhomboidity/Di agonal Cracks Centreline Cracking Asymmetrical cooling Rapid cooling of centre region below pool See Ref. 4 Severe secondary cooling and high pouring temperature Ensure uniform spray cooling on all four faces. Adjust:secondary cooling near the bottom of the pool. SLABS Transverse,Surface Cracks Precipitation of A1N and straightening with surface between 700 and 900°C. Steel composition >0.02% Al >U Mn, Nb, V Adjust sprays to prevent reheating from below 700°C,or maintain slab surface outside 700-900°C range at straightener. Longitudinal, Midface Cracks Overcooling in upper spray zones - Bulging See Ref. 4 Reduce cooling in upper spray zones. Check for bulging. Triple Point Cracks Bulging See Ref. 4 Regap rolls. Midway Cracks Bulging High casting speed Increasing S,C Check roll gaps. Increase spray cooling. Reduce casting speed. Centreline Cracks Bulging High casting speed As above. Centreline Segregation Bulging High casting speed High superheat As above. Reduce superheat. 16 and m e t h o d s f o r a l l e v i a t i n g t h e c r a c k i n g p r o b l e m s a r e s u m -m a r i z e d i n T a b l e I. 1 .2 S p r a y Chamber D e s i g n and C o n t r o l F rom t h e f o r e g o i n g d i s c u s s i o n , i t i s c l e a r t h a t c o o l i n g i n t h e s e c o n d a r y c o o l i n g z o n e s m u s t be p r o p e r l y d e s i g n e d and c o n t r o l l e d i n o r d e r t o a v o i d d e f e c t s i n t h e c a s t p r o d u c t s . The d e s i g n o f s p r a y c h a m b e r s f r o m t h e s t a n d p o i n t o f r e d u c t i o n o f t h e r m a l s t r a i n s i n t h e s t r a n d 9 21 41 has b e e n d e a l t w i t h i n t h e r e c e n t l i t e r a t u r e ' f o r t h e c a s e o f b i l l e t s . The v a r i a t i o n o f s p r a y c o o l i n g i n v a r i o u s z o n e s o f a s l a b c a s t e r t o m i n i m i z e f o r m a t i o n o f t r a n s v e r s e 9 35 c r a c k s h a s a l s o b e e n d i s c u s s e d . ' T h e s e d e s i g n s a r e a r r i v e d a t f r o m a k n o w l e d g e o f t h e h e a t t r a n s f e r c o e f f i c i e n t s a t v a r i o u s p o i n t s i n t h e s p r a y c h a m b e r t h a t w o u l d be n e c e s s a r y t o ' m a i n t a i n t h e s t r a n d s u r f a c e t e m p e r a t u r e s a t l e v e l s t h a t w o u l d m i n i m i z e t h e f a c t o r s l e a d i n g t o c r a c k f o r m a t i o n . T h e s e h e a t t r a n s f e r c o e f f i c i e n t s a r e t h e n u s e d i n c o n j u n c t i o n w i t h d a t a r e g a r d i n g t h e i r v a r i a t i o n w i t h s p r a y i n g , p a r a m e t e r s i n o r d e r t o a r r i v e a t t h e f i n a l d e s i g n o f t h e s p r a y c h a m b e r -t h e n o z z l e t y p e s t o be u s e d , n o z z l e - t o - n o z z l e s p a c i n g , n o z z l e -t o - s t r a n d d i s t a n c e a n d w a t e r p r e s s u r e i n t h e r i s e r s f e e d i n g t h e n o z z l e s . I t i s a s s u m e d i n t h e s e d e s i g n s t h a t t h e c a s t e r i s 17 o p e r a t i n g a t s t e a d y s t a t e . In r e a l i t y , h o w e v e r , c h a n g e s o c c u r d u r i n g t h e c a s t i n g o f a s i n g l e h e a t o r a s e q u e n c e o f h e a t s s u c h t h a t t r u e s t e a d y s t a t e i s r a r e l y a c h i e v e d . V a r i a -t i o n s i n c a s t i n g s p e e d i n p a r t i c u l a r a r e u n a v o i d a b l e as a r e s u l t o f n o r m a l o p e r a t i n g p r o c e d u r e s s u c h as s t a r t - u p , c a p p i n g o f f , t u n d i s h o r s h r o u d c h a n g e s , o r due t o u n p l a n n e d e v e n t s s u c h as n o z z l e b l o c k a g e . The p r o b l e m t h e n a r i s e s o f a d j u s t i n g t h e s p r a y s t o m i n i m i z e d e l e t e r i o u s e f f e c t s o n p r o d u c t q u a l i t y a n d m a c h i n e o p e r a t i o n . I t h a s b e e n common p r a c t i c e t o v a r y t h e s p r a y w a t e r t h r o u g h o u t t h e s e c o n d a r y c o o l i n g z o n e i n d i r e c t p r o p o r t i o n t o t h e c h a n g e i n c a s t i n g s p e e d ( w i t h i n p r e d e t e r m i n e d l i m i t s ) s u c h t h a t t h e s p e c i f i c w a t e r f l o w ( a / k g ) r e m a i n s t h e s a m e . H o w e v e r , s i n c e i t i s d e s i r a b l e t o k e e p t h e t h e r m a l h i s t o r y o f a n y g i v e n s l i c e o f m a t e r i a l p a s s i n g t h r o u g h t h e c a s t i n g m a c h i n e s i m i l a r t o t h a t w h i c h w o u l d be o b t a i n e d u n d e r s t e a d y s t a t e c o n d i t i o n s , s u c h a m e t h o d i s u n s a t i s f a c t o r y . The s p r a y c o o l i n g m u s t be a l t e r e d , n o t i n p r o p o r t i o n t o t h e c a s t i n g s p e e d , b u t a c c o r d -i n g t o t h e t i m e t h a t t h e s l i c e has s p e n t i n t h e m a c h i n e p r i o r t o r e a c h i n g any g i v e n l o c a t i o n , i . e . , a c c o r d i n g t o t h e a g e a t e a c h l o c a t i o n i n t h e s t r a n d . The a d j u s t m e n t o f t h e s p r a y s a c c o r d i n g t o t h e p r i n c i p l e o f c o o l i n g - w i t h - t i m e r e -q u i r e s t h r e e t y p e s o f i n f o r m a t i o n : i ) The age o r r e s i d e n c e t i m e s o f s l i c e s p a s s i n g s e l e c t e d p o i n t s a t any t i m e . 18 i i ) The d e s i r e d r e l a t i o n s h i p b e t w e e n s p r a y h e a t -t r a n s f e r c o e f f i c i e n t s and t i m e . 111 ) The r e l a t i o n s h i p s b e t w e e n t h e s p r a y h e a t -t r a n s f e r c o e f f i c i e n t s a n d t h e s p r a y p a r a -m e t e r s . B a p t i s t a 42 has d e t e r m i n e d s p r a y a d j u s t m e n t s t o be made t o a s l a b : c a s t e r d u r i n g t r a n s i e n t s i n t h e c a s t i n g p r o c e d u r e c a u s e d - by s p e e d c h a n g e s , b a s e d on s u c h r e s i d e n c e t i m e c a l c u l a t i o n s . T h e r e a r e d i s a d v a n t a g e s t o t h e m a n u a l a d j u s t m e n t o f 4 3 - 5 1 s p r a y s , a n d t h u s a u t o m a t i c c o n t r o l has b e e n d e v e l o p e d . T h i s c a n be a c h i e v e d t h r o u g h t h e a p p l i c a t i o n o f a u t o m a t i c c o n t r o l t h e o r y and m a t h e m a t i c a l m o d e l s o f t h e c o n t i n u o u s c a s t i n g p r o c e s s . C o n t r o l i s p e r f o r m e d by a r e a l - t i m e p r o -c e s s c o n t r o l c o m p u t e r , w h i c h c o n s t a n t l y m o n i t o r s t h e v a r i o u s o p e r a t i n g c o n d i t i o n s o f t h e c a s t i n g m a c h i n e , a n d w h i c h a u t o -m a t i c a l l y c o n t r o l s t h e w a t e r f l o w s i n t h e s e c o n d a r y c o o l i n g z o n e t o a d j u s t f o r c h a n g e s i n t h e o p e r a t i n g c o n d i t i o n s . 1.3 S c o p e o f t h e P r e s e n t Work I t b e c o m e s o b v i o u s f r o m t h e f o r e g o i n g d i s c u s s i o n t h a t f o r d e s i g n i n g t h e s p r a y c h a m b e r s i n c o n t i n u o u s c a s t i n g m a c h i n e s , a d e q u a t e and r e l i a b l e d a t a i s r e q u i r e d 1 i n k i n g 1 9 t h e v a r i o u s s p r a y p a r a m e t e r s ( f o r i n s t a n c e s p r a y p r e s s u r e , s p r a y w a t e r f l u x ) t o h e a t - t r a n s f e r c o e f f i c i e n t s . The p u r p o s e o f t h i s w o r k t h e r e f o r e was t o g e n e r a t e s u c h d a t a , a n d t o i n v e s t i g a t e t h e r e l a t i o n s h i p s b e t w e e n t h e s p r a y p a r a m e t e r s a n d h e a t - t r a n s f e r c o e f f i c i e n t s a t t h e h i g h s u r f a c e t e m p e r a -t u r e s t h a t p r e v a i l i n t h e s p r a y c h a m b e r s o f c o n t i n u o u s c a s t i n g m a c h i n e s . L a b o r a t o r y s t u d i e s w e r e p e r f o r m e d t o d e t e r m i n e t h e d i s t r i b u t i o n o f t h e w a t e r i n t h e s p r a y s p r o -d u c e d by s e v e r a l c o m m e r c i a l n o z z l e s u n d e r v a r i o u s o p e r a t i n g c o n d i t i o n s , a n d h e a t - t r a n s f e r c o e f f i c i e n t s w e r e m e a s u r e d f o r t h e s e s p r a y s u n d e r c o r r e s p o n d ! * ng c o n d i t i ons . C h a p t e r 2 HEAT FLOW IN SPRAY COOLING REVIEW OF THE L I T E R A T U R E 2 .1 I n t r o d u c t i o n In t h e c o n t i n u o u s c a s t i n g p r o c e s s , t h e s t r a n d e m e r g e s f r o m t h e m o u l d a t t e m p e r a t u r e s e x c e e d i n g 1 2 5 0 ° C . The c o o l i n g a p p l i e d b e l o w t h i s p o i n t m u s t n o t o n l y e x t r a c t h e a t f r o m t h e c a s t i n g t o p r o m o t e s o l i d i f i c a t i o n a t r e a s o n -a b l e r a t e s , b u t s h o u l d do s o a t a r a t e t h a t m a i n t a i n s t h e s u r f a c e t e m p e r a t u r e s o f t h e s t r a n d w i t h i n c l o s e l i m i t s . W a t e r j e t s c a n be u s e d t o p r o v i d e h i g h h e a t e x t r a c t i o n r a t e s , b u t c o n t r o l l i n g t h e s u r f a c e t e m p e r a t u r e s w i t h i n t h e l i m i t s d e s i r e d w o u l d be a d i f f i c u l t t a s k . S p r a y c o o l i n g w i t h a t o m i z e d w a t e r s p r a y s p r o v i d e s a b e t t e r s o l u t i o n , n o t o n l y by p r o v i d i n g c o n t r o l l a b l e c o o l i n g o f t h e s t r a n d , b u t a l s o by p r o v i d i n g a c c e p t a b l e h e a t e x t r a c t i o n r a t e s f o r e c o n o m i -c a l p r o d u c t i o n o f c o n t i n u o u s l y c a s t p r o d u c t s . The p h y s i c s o f s p r a y c o o l i n g i n v o l v e s a c o m b i n a t i o n o f b o i l i n g h e a t t r a n s f e r a n d d r o p l e t d y n a m i c s . A s h o r t d e s c r i p t i o n o f t h e b o i l i n g p r o c e s s f o l l o w s , t o c l a r i f y t h e r o l e o f t h e d i f f e r e n t b o i l i n g r e g i m e s i n t h e c o o l i n g o f h o t s u r f a c e s . 20 F 1 Q U R E 3 T y p i c a l b o i l i n g curves f o r a w i r e , t u b e , o r h o r i z o n t a l surface In a pool of water at atmospheric pressure. 5 2 22 A t y p i c a l e x a m p l e o f t h e h e a t f l u x o b t a i n e d d u r i n g t h e c o o l i n g o f a h o t s u r f a c e i m m e r s e d i n a p o o l o f w a t e r a t 52 s a t u r a t i o n t e m p e r a t u r e i s i l l u s t r a t e d i n F i g u r e 3 . T h u s , when t h e t e m p e r a t u r e d i f f e r e n c e b e t w e e n t h e s u r f a c e a n d t h e w a t e r i s w i t h i n a f ew d e g r e e s , t h e p r o c e s s o f f r e e c o n v e c t i o n t r a n s f e r s h e a t t o t h e l i q u i d s u r r o u n d i n g t h e s u r f a c e . C o n -v e c t i o n c u r r e n t s t h e n c i r c u l a t e t h e s u p e r h e a t e d f l u i d , a n d e v a p o r a t i o n o c c u r s - a t t h e s u r f a c e o f t h e f l u i d . As t h e t e m p e r a t u r e d i f f e r e n c e i n c r e a s e s , v a p o u r b u b b l e s a r e f o r m e d a t v a r i o u s n u c l e a t i o n s i t e s on t h e h o t s u r f a c e , a n d a s t h e t e m p e r a t u r e o f t h e h o t s u r f a c e i n c r e a s e s f u r t h e r , t h e s e b u b -b l e s become l a r g e r and more n u m e r o u s and r i s e up t o t h e s u r -f a c e . T h i s r e g i o n o f t e m p e r a t u r e i n w h i c h t h e f o r m a t i o n o f r i s i n g v a p o u r b u b b l e s i s t h e m e c h a n i s m o f h e a t t r a n s f e r , i s known as t h e " n u c l e a t e b o i l i n g r e g i m e " , a n d t h e h e a t f l u x i n c r e a s e s r a p i d l y as t h e s u r f a c e t e m p e r a t u r e i n c r e a s e s . A f u r t h e r i n c r e a s e o f t h e s u r f a c e t e m p e r a t u r e c a u s e s t h e a p p e a r -a n c e o f c o n t i n u o u s c o l u m n s o f b u b b l e s . The " t r a n s i e n t b o i l i n g r e g i o n " w i t h c o r r e s p o n d i n g l o w e r i n g o f t h e h e a t f l u x t h e n a p p e a r s a t h i g h e r s u r f a c e t e m p e r a t u r e s , s i n c e t h e r e i s a l i m i t t o t h e number o f v a p o u r c o l u m n s t h a t c a n be g e n e r a t e d a t t h e s u r f a c e . T h i s i s b e c a u s e t h e s p a c e b e t w e e n t h e c o l u m n s b e c o m e s t o o s m a l l t o a c c o m m o d a t e t h e s t r e a m s o f l i q u i d w h i c h m u s t move t o w a r d t h e h o t s u r f a c e t o r e p l a c e t h e l i q u i d e v a p o r a t e d t o f o r m t h e v a p o u r c o l u m n s . 23 A f u r t h e r i n c r e a s e o f s u r f a c e t e m p e r a t u r e b e y o n d t h i s r e g i o n l e a d s t o a p h e n o m e n o n known as " s t a b l e f i l m b o i l i n g " . In t h i s f o r m o f b o i l i n g , a v a p o u r f i l m c o m p l e t e l y b l a n k e t s t h e h e a t e d s u r f a c e , and h e a t i s t h e n t r a n s f e r r e d a c r o s s t h e v a p o u r f i l m by t h e p r o c e s s o f c o n d u c t i o n a n d r a d i a t i o n . As c a n be s e e n f r o m F i g u r e 3 , t h e h e a t f l u x i n t h i s r e g i m e i s l o w , and i n c r e a s e s a t h i g h e r t e m p e r a t u r e s d u e t o t h e i n -c r e a s e d r o l e o f r a d i a t i o n i n t h e h e a t t r a n s f e r p r o c e s s . The t e m p e r a t u r e a b o v e w h i c h s t a b l e f i l m b o i l i n g o c c u r s i s known a s t h e " L i e d e n f r o s t p o i n t " , and i s a l s o r e f e r r e d t o a s t h e " c r i t i c a l p o i n t " i n t h e h e a t t r a n s f e r l i t e r a t u r e . S i m i l a r r e g i m e s a r e a l s o o b s e r v e d i n t h e s p r a y c o o l -53 i n g o f h o t s u r f a c e s as c a n be s e e n f r o m F i g u r e 4 . S p r a y c o o l i n g c a n be u s e d t o a u g m e n t c o o l i n g i n t h e r e g i o n c o r -r e s p o n d i n g t o s u r f a c e t e m p e r a t u r e s a b o v e t h e L i e d e n f r o s t , o r c r i t i c a l , p o i n t . T h i s i s p o s s i b l e b e c a u s e t h e momentum o f t h e d r o p l e t s i n t h e s p r a y a l l o w s them t o p e n e t r a t e t h e v a p o u r l a y e r and a i d i n t h e h e a t e x t r a c t i o n f r o m t h e s u r f a c e . Many s t u d i e s h a v e b e e n u n d e r t a k e n t o c l a r i f y t h e r o l e o f t h e d i f f e r e n t v a r i a b l e s a s s o c i a t e d w i t h t h e h e a t t r a n s f e r b e t w e e n a h o t s u r f a c e a n d l i q u i d d r o p l e t s i m p i n g i n g on t h e s u r f a c e . The f o l l o w i n g d i s c u s s i o n d e a l s w i t h t h e v a r i o u s a s p e c t s o f t h e i n t e r a c t i o n s o f t h e i m p i n g i n g d r o p l e t s w i t h t h e h o t s u r f a c e . Surface Temperature *C Surface Temperature *F F igure 4 V a r i a t i o n o f heat f l u x w i th s u r f a c e temperature  i n spray c o o l i n g . 25 2 . 2 S i n g l e D r o p l e t S t u d i e s B e c a u s e o f t h e c o m p l e x n a t u r e o f s p r a y s a n d s p r a y c o o l i n g , some i n v e s t i g a t o r s h a v e t a k e n t h e a p p r o a c h o f s t u d y i n g t h e e f f e c t o f s i n g l e d r o p l e t s i m p i n g i n g on a h o t s u r f a c e , w i t h a v i e w t o b u i l d i n g up a p i c t u r e o f s p r a y c o o l i n g by summing t h e e f f e c t s o f a l l t h e d r o p s i n t h e s p r a y . Two d i f f e r e n t s i t u a t i o n s h a v e b e e n c o n s i d e r e d - a s e s s i l e d r o p r e s t i n g on a h o t s u r f a c e , and a s i n g l e d r o p i m p i n g i n g on a h o t s u r f a c e . 2 . 2 . 1 D y n a m i c s o f D r o p l e t I m p a c t 54 55 Heymann ' has p r e s e n t e d an a n a l y t i c a l m o d e l o f t h e c o l l i s i o n p r o c e s s b e t w e e n a l i q u i d d r o p a n d a s o l i d s u r f a c e , a n d o b t a i n e d q u a n t i t a t i v e r e s u l t s f o r t h e i m p a c t p r e s s u r e g e n e r a t e d a t t h e s u r f a c e by t h e i m p i n g i n g d r o p l e t s . T h i s a n a l y s i s was d e v e l o p e d f o r t h e c a s e o f h i g h s p e e d i m -p a c t b e t w e e n t h e d r o p and t h e s o l i d s u r f a c e , and s p e c i f i -c a l l y , was u n d e r t a k e n t o c l a r i f y t h e e f f e c t o f t h e c o l -l i s i o n s on t h e e r o s i o n p r o c e s s on t h e s u r f a c e . As s u c h , t h e a n a l y s i s d e a l t w i t h c o l d s u r f a c e s i n t h e a b s e n c e o f h e a t t r a n s f e r . i n v e s t i g a t e d t h e f l u i d l i q u i d d r o p l e t s on a 56 S a v i c a n d B o u l t h a v e a l s o f l o w a s s o c i a t e d w i t h t h e i m p a c t o f 26 s o l i d s u r f a c e . In a d d i t i o n t o t h e c a l c u l a t i o n o f t h e d i s t r i -b u t i o n o f p r e s s u r e i n t h e a r e a o f i m p a c t , t h e y h a v e c a l c u l a -t e d t h e s h a p e o f t h e d r o p a s i t s p r e a d s o n i m p a c t . H i g h s p e e d p h o t o g r a p h y was u s e d t o c o n f i r m t h e r e s u l t s o f t h e i r c a l c u l a t i o n s f o r t h e c a s e o f d r o p l e t s o f w a t e r o f . 4 7 6 cm ( 3 / 1 6 " ) d i a m e t e r i m p i n g i n g on a c o l d s u r f a c e . When t h e s u r -f a c e t e m p e r a t u r e was i n c r e a s e d t o 7 0 0 ° C , s p r e a d i n g o f t h e d r o p on t h e s u r f a c e was o b s e r v e d , a f t e r w h i c h v a p o u r b u b b l e s c a u s e d by t h e b o i l i n g p r o c e s s c a u s e d d i s i n t e g r a t i o n o f t h e d r o p s . No q u a n t i t a t i v e h e a t t r a n s f e r r e s u l t s w e r e p r e s e n t e d , b u t t h e i n t e r a c t i o n o f f l u i d f l o w and h e a t f l o w was s h o w n . 2 . 2 . 2 H e a t T r a n s f e r t o S e s s i l e D r o p s 57 5 8 G o t t f r i e d and W a c h t e r s e t a l . h a v e s t u d i e d t h e o r e t i c a l l y t h e h e a t t r a n s f e r t o s e s s i l e w a t e r d r o p l e t s on a h o t s u r f a c e ( 3 0 0 ° C t o 4 0 0 ° C) . The a s s u m p t i o n s u s e d i n t h e i r w o r k i n c l u d e t h e f o l l o w i n g : i ) The d r o p s a r e n e a r l y s p h e r i c a l e x c e p t f o r t h e l o w e r p a r t n e a r t h e h o t s u r f a c e ( s p h e r o i d a l ) i i ) The d r o p s a r e n e a r l y s e s s i l e u n t i l c o m p l e t e e v a p o r a t i o n t a k e s p l a c e i i i ) A t h i n f i l m o f v a p o u r i n s u l a t e s t h e d r o p f r o m t h e s u r f a c e i v ) R a d i a t i o n h e a t t r a n s f e r b e t w e e n t h e s u r f a c e and t h e d r o p s i s n e g l i g i b l e . 27 The a i m was t o c a l c u l a t e t h e v a p o u r f i l m t h i c k n e s s b e l o w t h e s e s s i l e d r o p , and t h e s h a p e o f t h e d r o p as i t e v a p o r a t e d due t o h e a t f l o w i n t o t h e d r o p f r o m t h e h o t s u r f a c e . F rom p h o t o g r a p h s o f t h e s e s s i l e d r o p s d u r i n g e v a p o r a t i o n , W a c h t e r s 58 e t a l . d e t e r m i n e d t h e e v a p o r a t i o n r a t e s o f t h e d r o p s . A s s u m i n g t h a t h e a t i s t r a n s f e r r e d t o t h e d r o p t h r o u g h t h e v a p o u r c u s h i o n a n d a l s o due t o v a p o u r f l o w a r o u n d t h e d r o p , t h e e v a p o r a t i o n r a t e s o f t h e d r o p s w e r e t h e o r e t i c a l l y c a l -c u l a t e d . The e x p e r i m e n t a l r e s u l t s i n d i c a t e d t h a t t h e b o t t o m o f t h e d r o p s a s s u m e d a f l a t s h a p e p a r a l l e l t o t h e h o t s u r -f a c e . W a t e r d r o p s on h e a t e d g o l d s u r f a c e s w e r e u s e d i n t h e e x p e r i m e n t s . D rop d i a m e t e r s w e r e v a r i e d b e t w e e n 0 . 2 5 mm t o 2 . 7 mm, a n d s u r f a c e t e m p e r a t u r e s f r o m 1 0 0 ° t o 4 0 0 ° C . F rom o b s e r v a t i o n s o f e v a p o r a t i o n t i m e s , M o r i y a m a 5 9 ' 6 0 o b t a i n e d h e a t - t r a n s f e r r a t e s b e t w e e n a h o t l o w c a r b o n s t e e l s u r f a c e ( s u r f a c e t e m p e r a t u r e s b e t w e e n 3 0 0 ° t o 8 0 0 ° C) and w a t e r d r o p s ( 2 . 4 5 mm t o 5 . 2 9 mm i n d i a m e t e r ) a n d h a s p r o -p o s e d a c o r r e l a t i o n o f t h e f o r m . Q = 8 4 9 . 9 2 e x p ( 0 . 0 0 2 1 6 T + 8 . 8 2 1 . r ) . . . 2 -1 f o r t h e h e a t t r a n s f e r t o a s i n g l e d r o p o f r a d i u s r Q c m s . The h e a t t r a n s f e r r e d t o t h e d r o p l e t i s s e e n t o r i s e as t h e s u r f a c e t e m p e r a t u r e a n d t h e d r o p r a d i u s i n c r e a s e . T h i s c o r -r e l a t i o n f i t s G o t t f r i e d ' s d a t a w e l l . 28 2 . 2 . 3 H e a t T r a n s f e r t o I m p i n g i n g D r o p s 6 1 6 2 W a c h t e r s and h i s c o - w o r k e r s ' h a v e c o m p a r e d t h e h e a t t r a n s f e r b e t w e e n h o t s u r f a c e s (up t o 4 0 0 ° C) a n d i m p i n g i n g d r o p l e t s ( d i a m e t e r s b e t w e e n 6 0 u a n d 2 m m ) . W i t h 5 8 p r e d i c t i o n s made f r o m t h e i r e a r l i e r w o r k f o r s e s s i l e d r o p s , t h e y f o u n d a l a r g e d i s c r e p a n c y e x i s t e d b e t w e e n t h e o b s e r v e d v a l u e s a n d t h e t h e o r e t i c a l p r e d i c t i o n s . T h i s h a s b e e n a t -t r i b u t e d t o two f a c t o r s : i ) The d r o p s t a y s i n t h e v i c i n i t y o f t h e h o t s u r f a c e f o r a r e l a t i v e l y s h o r t t i m e b e f o r e r e b o u n d i n g i i ) The s p h e r o i d a l s t a t e was n o t a t t a i n e d i n t h e i r e x p e r i m e n t s u n t i l t h e s u r f a c e t e m p e r a -t u r e e x c e e d e d 4 0 0 ° C . W i t h t h e u s e o f h i g h s p e e d p h o t o g r a p h y , t h e y f o u n d t h a t t h e l a r g e (2 mm d i a . ) d r o p s d i s i n t e g r a t e d a b o v e a c r i t i c a l Webe r Number o f 8 0 . F o r Weber n u m b e r s b e l o w 3 0 , no d r o p d i s i n t e -g r a t i o n was o b s e r v e d . F rom p h o t o g r a p h i c o b s e r v a t i o n s , t h e v o l u m e r e d u c t i o n o f t h e d r o p s due t o e v a p o r a t i o n was f o u n d t o d e c r e a s e as t h e s u r f a c e t e m p e r a t u r e i n c r e a s e d . T h e v o l u m e l o s s was l e s s t h a n 0 .5% o f t h e o r i g i n a l d r o p v o l u m e when t h e s u r f a c e t e m p e r a t u r e i n c r e a s e d b e y o n d 2 0 0 ° C . H e a t - t r a n s f e r r a t e s f o r a s e r i e s o f i m p i n g i n g d r o p l e t s 29 w e r e o b t a i n e d by M c G i n n i s and H o l m a n 6 3 a n d H o l m a n e t a l . 6 4 The e x p e r i m e n t a l t e c h n i q u e u s e d was t o h a v e t h e d r o p l e t s f a l l i n g v e r t i c a l l y on a p o l i s h e d n i c k e l p l a t e d c o p p e r p l a t e , m a i n t a i n e d a t c o n s t a n t t e m p e r a t u r e , and i n c l i n e d a t 2 7 ° t o t h e h o r i z o n t a l . A p e a k i n t h e h e a t - t r a n s f e r r a t e s was f o u n d f o r v a r i o u s l i q u i d s , a t a s u r f a c e t e m p e r a t u r e o f a p p r o x i m a t e l y 1 5 0 ° C . The maximum h e a t f l u x a t t h e s e t e m p e r a t u r e s was a t t r i b u t e d t o t h e o p p o s i n g e f f e c t s o f t h e t h e r m a l g r a d i e n t i n t h e v a p o u r f i l m b e l o w t h e d r o p a n d t h e d e c r e a s i n g d r o p l e t c o n t a c t t i m e as t h e s u r f a c e t e m p e r a t u r e i n c r e a s e d . The e x p e r i m e n t s w e r e c a r r i e d o u t f o r s u r f a c e t e m p e r a t u r e s b e l o w 3 0 0 ° C . 65 66 P e d e r s e n ' has p e r f o r m e d e x p e r i m e n t s w i t h m o v i n g d r o p s o f w a t e r p r o p e l l e d h o r i z o n t a l l y t o w a r d a v e r t i c a l h e a t e d t a r g e t . The t a r g e t m a t e r i a l was a s m a l l s t a i n l e s s s t e e l c y l i n d e r 6 mm i n l e n g t h w i t h a d i a m e t e r o f 6 mm, h e a t e d by r a d i a t i o n i n a r e s i s t a n c e h e a t e d f u r n a c e . The h e a t f l u x c a u s e d by t h e i m p i n g i n g d r o p l e t s was d e t e r m i n e d f r o m t h e m e a s u r e d t e m p e r a t u r e t r a n s i e n t e x p e r i e n c e d by t h e t a r g e t when t h e d r o p l e t s w e r e a l l o w e d t o i m p i n g e on i t . P h o t o g r a p h i c o b s e r v a t i o n s w e r e a l s o made o f t h e c o l l i s i o n o f t h e d r o p l e t s w i t h t h e p l a t e , t o d e t e r m i n e t h e d r o p l e t v e l o c i t y . The d r o p l e t s i z e s u s e d i n t h i s s t u d y w e r e 2 0 0 , 300 a n d 400 m i c r o n s i n d i a m e t e r , w i t h d r o p v e l o c i t i e s up t o 9 m e t r e s p e r s e c o n d . T a r g e t t e m p e r a t u r e s up t o 7 0 0 ° C w e r e u s e d . 30 As c a n be s e e n f r o m t h e r e s u l t s o f h i s e x p e r i m e n t s p r e s e n t e d i n F i g u r e 5 , an i n c r e a s e i n t h e d r o p l e t v e l o c i t y i n c r e a s e s t h e h e a t t r a n s f e r r e d t o e a c h d r o p l e t . D e f i n i n g t h e h e a t - t r a n s f e r e f f i c i e n c y as t h e r a t i o o f t h e h e a t t r a n s -f e r r e d t o t h e d r o p l e t t o t h e t o t a l h e a t r e q u i r e d f o r t h e e v a p o r a t i o n o f t h e d r o p l e t , h i s r e s u l t s s h o w an e f f i c i e n c y t h a t i n c r e a s e s w i t h i n c r e a s i n g a p p r o a c h v e l o c i t y a s shown i n F i g u r e 6 . The u s e o f h e a t - t r a n s f e r e f f i c i e n c y s e r v e s t o e l i m i n a t e t h e e f f e c t o f d r o p l e t s i z e . P h o t o g r a p h i c s t u d i e s o f t h e d r o p l e t i m p i n g e m e n t show t h a t t h e d i f f e r e n c e i n t h e b e h a v i o u r o f t h e d r o p l e t d u r i n g c o l l i s i o n w i t h t h e t a r g e t d e p e n d s on t h e t a r g e t s u r f a c e t e m p e r a t u r e . The d i f f e r e n t h e a t - t r a n s f e r r e g i m e s e n c o u n t e r e d h a v e b e e n l a b e l l e d as " w e t t i n g " , " t r a n s i t i o n " and " n o n w e t t i n g " , c o r r e s p o n d i n g t o t h e d r o p l e t b e h a v i o u r on i m p a c t . T h e s e r e g i m e s g e n e r a l l y c o r r e s p o n d t o t h e n u c l e a t e b o i l i n g , t r a n s i t i o n a n d f i l m b o i l i n g r e g i o n s r e s p e c t i v e l y , as n o t e d i n F i g u r e 3 . When t h e s u r f a c e t e m p e r a t u r e i s i n t h e r e g i o n c o r r e s p o n d i n g t o t h e n u c l e a t e b o i l i n g z o n e , i t was f o u n d t h a t t h e d r o p s s p r e a d o u t on t h e s u r f a c e on i m p a c t , a n d t h a t e v a p o r a t i o n t a k e s p l a c e m a i n l y by n u c l e a t e b o i l i n g w i t h i n t h e d r o p . T h i s h a s b e e n t e r m e d t h e " w e t t i n g " r e g i m e . H i g h h e a t f l u x e s and e f f i c i e n c i e s h a v e b e e n f o u n d i n t h i s r e g i o n . The e f -f i c i e n c y d e c r e a s e s as t h e s u r f a c e t e m p e r a t u r e i n c r e a s e s and t h e d r o p b e h a v i o u r on i m p a c t c h a n g e s . I n t h e " n o n w e t t i n g " r e g i o n , t h e d r o p l e t s b r e a k up i n t o s m a l l e r d r o p l e t s a f t e r W/ h B 0 o 8 400/im droplets • IL50°F surfoce o I300°F surface 0 " 10 15 20 25 30 35 Approach velocity, ft/'s 1 B.T.U. = 1055.56 Ws 1 f t / s = 0.3048 m/s E f f e c t o f d r o p l e t v e l o c i t y on the heat t r a n s f e r r e d to the d r o p l e t . 30 r 20 k S u r f a c e t e m p . « l l 5 0 ° F A p p r o x , d r o p l e t d i o . ^ m • 4 0 0 - 3 3 0 ? 2 9 0 a 2 7 0 '-• 2 0 0 V <7 Q • 10 O o o 12 16 2 0 24 App roach ve loc i ty , f t / s 28 32 36 4 0 1 f t / s = 0.3048 m/s 65 Figure 6 Non wetting droplet heat transfer e f f ic iency . rv> 33 i n i t i a l l y s p r e a d i n g o u t on t h e s u r f a c e on i m p a c t . The s m a l l e r d r o p l e t s t h e n r e b o u n d f r o m t h e s u r f a c e . 2.2.4 E x t e n s i o n o f S i n g l e Drop E x p e r i m e n t s t o C h a r a c t e r i z a t i o n o f S p r a y H e a t T r a n s f e r 5 9 U s i n g t h e a s s u m p t i o n s n o t e d b e l o w , M o r i y a m a has o b t a i n e d a c o r r e l a t i o n f o r s p r a y c o o l i n g b a s e d on t h e r e s u l t s o f h i s s i n g l e d r o p l e t e x p e r i m e n t s . The a s s u m p t i o n s u s e d i n h i s a n a l y s i s f o r d r o p l e t s i n t h e s p r a y a r e : i ) The d r o p l e t s a r e s p h e r i c a l a n d o f c o n s t a n t d i a m e t e r i i ) T h e r e i s no i n t e r a c t i o n o f d r o p l e t s i i i ) The d r o p l e t s b e h a v e i n t h e same m a n n e r as q u i e s c e n t d r o p l e t s on a h o t s u r f a c e i v ) T h e r e i s no d i s i n t e g r a t i o n o f d r o p l e t s on t h e h o t s u r f a c e . I t i s t o be n o t e d t h a t i n an a c t u a l p h y s i c a l s i t u a t i o n o f s p r a y c o o l i n g , none o f t h e s e a s s u m p t i o n s w o u l d h o l d . U s i n g a v a l u e o f d r o p l e t r e t e n t i o n t i m e ( p r o p o r t i o n a l t o d r o p 5 2 r a d i u s ) as p r o p o s e d by W a c h t e r s and W e s t e r l i n g t h e c o r -r e l a t i o n f o u n d f o r t h e s p r a y c o o l i n g h e a t f l u x Q i n t h e f i l m b o i l i n g r e g i on was Q = 586.1 5 m r o ~ 1 , 5 exp(0.00216 T s +8.821 r ) . . . 2.2 34 T h i s c o r r e l a t i o n h o w e v e r , p r e d i c t s much l o w e r h e a t - t r a n s f e r c o e f f i c i e n t s i n s p r a y s when c o m p a r e d t o t h e r e s u l t s o f o t h e r w o r k e r s w h i c h w i l l be p r e s e n t e d i n t h e f o l l o w i n g s e c t i o n . 2 . 3 H e a t T r a n s f e r i n S p r a y s L a b o r a t o r y e x p e r i m e n t s u s i n g e i t h e r s t e a d y s t a t e o r t r a n s i e n t m e a s u r e m e n t t e c h n i q u e s h a v e a l s o b e e n p e r f o r m e d t o c h a r a c t e r i ze - t he h e a t t r a n s f e r b e t w e e n c o m m e r c i a l w a t e r s p r a y s a n d h o t s u r f a c e s . S t e a d y s t a t e e x p e r i m e n t s h a v e b e e n c a r r i e d o u t by s u p p l y i n g a h o t m e t a l s a m p l e w i t h an e n e r g y i n p u t e q u i v a l e n t t o t h a t e x t r a c t e d f r o m t h e s a m p l e by t h e s p r a y d i r e c t e d o n t o i t . The m e a s u r e d v a l u e f o r t h e e n e r g y i n p u t a n d t h e s a m p l e t e m p e r a t u r e a l l o w t h e c a l c u l a t i o n o f t h e s u r f a c e h e a t f l u x e s a n d t h e h e a t - t r a n s f e r c o e f f i c i e n t s . T r a n s i e n t m e t h o d s u s e d f o r t h e e v a l u a t i o n o f t h e h e a t -t r a n s f e r c o e f f i c i e n t s f a l l i n t o two c a t e g o r i e s : i ) In t h e f i r s t c a t e g o r y , t e m p e r a t u r e t r a n s i e n t s w i t h i n t h e h o t m e t a l s a m p l e a r e r e c o r d e d d u r i n g t h e s p r a y i n g i n t e r v a l , a n d m a t h e m a t i -c a l m e t h o d s u s e d t o c a l c u l a t e t h e h e a t - t r a n s f e r c o e f f i c i e n t s . 35 i i ) In t h e s e c o n d c a t e g o r y , p y r o m e t e r s a r e u s e d t o m o n i t o r t h e s u r f a c e t e m p e r a t u r e o f t h e h o t s u r f a c e b e i n g s p r a y e d . The m e a s u r e d v a r i a t i o n o f s u r f a c e t e m p e r a t u r e a n d t h e , known i n i t i a l c o n d i t i o n o f t e m p e r a t u r e d i s t r i b u t i o n i n t h e s a m p l e , when u s e d i n t h e s o l u t i o n o f t h e c o n -d u c t i o n e q u a t i o n i n t h e s o l i d , y i e l d t h e r e -q u i r e d h e a t - t r a n s f e r c o e f f i c i e n t s . I n - p l a n t m e a s u r e m e n t s on o p e r a t i n g c o n t i n u o u s c a s t i n g m a c h i n e s h a v e a l s o been u s e d t o o b t a i n h e a t - t r a n s f e r c o e f -f i c i e n t s i n t h e s e c o n d a r y c o o l i n g z o n e . T h e s e c o e f f i c i e n t s c a n be o b t a i n e d by p e r f o r m i n g h e a t b a l a n c e s on t h e s t r a n d u s i n g m e a s u r e d v a l u e s o f t h e s t r a n d s u r f a c e t e m p e r a t u r e s a t v a r i o u s p o s i t i o n s . The d i f f e r e n t t e c h n i q u e s u s e d a n d t h e e x p e r i m e n t a l f i n d i n g s a r e d e a l t w i t h i n more d e t a i l b e l o w . 2 . 3 . 1 T r a n s i e n t M e t h o d s F o r s p r a y s p r o d u c e d by c o m m e r c i a l f u l l c o n e s p r a y n o z z l e s ( S p r a y i n g S y s t e m s C o . 1 /8 GG 1 and 1 / 8 GG 3 0 0 1 . 4 ) , s p r a y i n g downwards o n t o t h e f a c e o f a r e s i s t a n c e 53 h e a t e d c h r o m e p l a t e d c o p p e r b a r , G a u g l e r c a l c u l a t e d t e m p e r a t u r e d e p e n d e n t h e a t - t r a n s f e r c o e f f i c i e n t s f o r v a r i o u s 36 s p r a y i n g c o n d i t i o n s f r o m t e m p e r a t u r e t r a n s i e n t s m e a s u r e d i n s i d e t h e b a r w i t h C h r o m e ! - A l u m e l t h e r m o c o u p l e s . As m e n t i o n e d i n an e a r l i e r s e c t i o n , he o b s e r v e d t h r e e d i s t i n c t r e g i o n s i n t h e h e a t f l u x v s . s u r f a c e t e m p e r a t u r e r e l a t i o n -s h i p ( F i g u r e 4 ) . The r e s u l t s o f h i s e x p e r i m e n t a l w o r k a r e p r e s e n t e d i n F i g u r e s .7 and 8 ( C u r v e 1 ) . The e x p e r i m e n t a l c o n d i t i o n s u s e d i n h i s w o r k w e r e : I n i t i a l s u r f a c e t e m p e r a t u r e 4 0 0 ° C 2 W a t e r f l u x e s F rom 0 . 7 1 6 t o 3 . 7 Ji/m s D r o p l e t v e l o c i t i e s F rom 16 t o 26 m/s The f i l m b o i l i n g r a n g e i n h i s w o r k was f o u n d t o e x i s t a t t e m p e r a t u r e s g r e a t e r t h a n 2 5 0 ° C , a n d a c o r r e l a t i o n o f t h e f o r m u = 1 .031 x 1 0 ' 2 ( T s - T w ) ( m ) ~ ° ' 6 7 + 10% . . . 2 . 3 was f o u n d f o r t h e e f f i c i e n c y f o r a l l d r o p s i z e s a n d v e l o c i -t i e s . T h i s r e l a t i o n s h i p , p r e s e n t e d i n g r a p h i c a l f o r m i n F i g u r e 7 , shows t h e i n f l u e n c e o f t h e l o c a l w a t e r f l u x on t h e e f f i c i e n c y . The c o r r e s p o n d i n g c o r r e l a t i o n o f t h e h e a t f l u x t o t h e s p r a y i s Q = 3 . 6 9 5 2 (T - T ) m ° ' 3 3 + 10% . . . 2 . 4 s w — The h e a t f l u x t o t h e s p r a y i n c r e a s e d w i t h an i n c r e a s e i n t h e c o n c e n t r a t i o n o f d r o p l e t s i n t h e s p r a y ( d r o p s p e r u n i t v o l u m e ) a n d a l s o as t h e d r o p l e t momentum i n c r e a s e d . H o w e v e r , 37 CM E " $ •JC c 0> o X 50 40 £ 30 41 o o £ 201 c o 10 1 r Line Reference 1 Gaugler^ 2 Corman67 Water flux(l/m2s) 1-95 23-44 57 12 X X X X 100 200 300 400 500 Surfoce Temperature °C 600 Figure 8 V a r i a t i o n o f spray h e a t - t r a n s f e r c o e f f i c i e n t s w i th  su r face temperature. CO CO 39 the heat t ransfer red to each droplet decreased with i n -creasing water f1ow. Curves 2, 3 and 4 in Figure 8 are resul ts obtained by 6 7 5 3 Corman, who used the same equipment as Gaugler to extend the range of the measurements to higher temperatures and higher water f l u x e s . The resu l ts presented are for the Spraying Systems Co. 1/8 GSS nozz le . Increasing the water f lux not only increased the heat - t ransfer c o e f f i c i e n t s , but also s h i f t e d the c r i t i c a l point to higher temperatures. In the i r study of s t r i p cool ing on runout t a b l e s , Auman et a l . 6 ^ determined the quanti ty of heat removed from an instrumented s t a i n l e s s steel plate (AISI 304,15 cm by 20 cm by 2 cm t h i c k ) , which was heated to about 1100° C and passed through a spray of water d i rected v e r t i c a l l y downward. Ful l cone sprays and fan sprays were used in the i r experiments, with spray water f luxes as high as 217 £/m s . In agreement with other i n v e s t i g a t o r s , the three regimes of heat t ransfer corresponding to d i f f e ren t surface temperatures were observed. The heat f lux to the sprays was found to increase as the water f lux increased. However the rate of increase of heat f lux was found to decrease with increas ing water f l u x . The spray cool ing e f f i c i e n c y was also found to decrease with increasing water f l u x . 40 M e a n i n g f u l c o m p a r i s o n o f t h e s e o b s e r v a t i o n s w i t h t h e r e -s u l t s o f o t h e r w o r k e r s i s n o t p o s s i b l e b e c a u s e t h e s u r f a c e t e m p e r a t u r e s a t w h i c h t h e s e h e a t f l u x e s w e r e o b t a i n e d a r e n o t r e p o r t e d . C y l i n d r i c a l n i c k e l p r o b e s h e a t e d t o 8 0 0 ° C a n d t h e n 6 9 s p r a y c o o l e d w e r e u s e d by L a m b e r t a n d E c o n o m o p o u l o s i n t h e i r s p r a y h e a t - t r a n s f e r s t u d i e s . T h e i r r e s u l t s s h o w q u a l i t a t i v e a g r e e m e n t w i t h t h e wo rk o f Auman e t a l . In t h i s c a s e t o o , s i n c e o n l y t h e s p r a y p r e s s u r e o f 0 . 0 9 8 MPa ( 1 4 . 2 p s i ) , a n d t h e n o z z l e t o p r o b e d i s t a n c e s ( 1 0 - 2 0 cms) w e r e r e p o r t e d , c o m p a r i s o n w i t h o t h e r r e s u l t s i s n o t f e a s i b l e . The e f f e c t o f s p r a y v a r i a b l e s on t h e L i e d e n f r o s t t e m p e r a t u r e was i n v e s t i g a t e d by H o o g e n d o o r n and D e n H o n d 7 0 u s i n g f u l l c o n e a t o m i z e r n o z z l e s a t p r e s s u r e s o f up t o 1.1 MPa ( 1 6 0 p s i ) . S p r a y d r o p l e t s o f 0 . 2 t o 1 mm d i a m e t e r , w i t h v e l o c i t i e s o f 10 t o 30 m / s , w e r e d i r e c t e d d o w n w a r d o n t o a h e a t e d ( A I S I 321) s t a i n l e s s s t e e l p l a t e i n s t r u m e n t e d w i t h t h e r m o c o u p l e s . The s p r a y w a t e r f l u x e s u s e d i n t h i s 2 s t u d y v a r i e d f r o m 0 . 6 t o 25 a/m s . F i g u r e 9 s h o w s some o f t h e r e s u l t s o b t a i n e d f r o m t h i s s t u d y . C u r v e s 1 a n d 2 r e p r e s e n t t h e v a r i a t i o n o f t h e h e a t - t r a n s f e r c o e f f i c i e n t as a f u n c t i o n o f t h e s u r f a c e t e m p e r a t u r e f o r a w a t e r t e m p e r a t u r e o f 2 0 ° C . I t c a n be o b s e r v e d t h a t t h e c r i t i c a l p o i n t i s Figure 9 Dependence o f the h e a t - t r a n s f e r c o e f f i c i e n t s on water f l u x  and su r face t e m p e r a t u r e 7 0 42 2 b e l o w 6 0 0 ° C f o r t h e c a s e o f a l o w w a t e r f l u x ( 0 . 6 z/m s ) as shown by C u r v e 1 , w h e r e a s , f o r a much h i g h e r w a t e r f l u x o f 25 (J l /m s ) , t h i s t e m p e r a t u r e l i e s a b o v e 9 0 0 ° C ( C u r v e 2 ) . The i n c r e a s e o f t h e h e a t - t r a n s f e r c o e f f i c i e n t s w i t h i n c r e a s e o f s p r a y f l u x f o r a s u r f a c e t e m p e r a t u r e o f 9 0 0 ° C i s i l l u s t r a t e d by C u r v e 3 o f t h i s F i g u r e . A f a i r l y w i d e s c a t t e r o f + 20% i n t h e i r r e s u l t s h a s b e e n r e p o r t e d . Com-p a r i s o n o f t h e ; h e a t - t r a n s f e r c o e f f i c i e n t s o b t a i n e d by s p r a y -i n g d o w n w a r d on t h e h o t s u r f a c e w i t h t h o s e f r o m s p r a y i n g o n t o a v e r t i c a l p l a t e s h o w e d no s i g n i f i c a n t d i f f e r e n c e s . 71 72 M i t s u t s u k a a n d h i s c o - w o r k e r s ' c a r r i e d o u t e x p e r i -m e n t s u s i n g a h o r i z o n t a l p l a t e o f l o w c a r b o n s t e e l , h e a t e d i n a f u r n a c e t o 9 3 0 ° C , and c o o l e d by s p r a y i n g b o t h t h e t o p a n d t h e b o t t o m s i m u l t a n e o u s l y . The c o r r e l a t i o n f i t t i n g t h e i r r e s u l t s i s o f t h e f o r m h = A rfi n ( 1 - b T ) . . . 2 . 5 w w h e r e A , b a n d n a r e c o n s t a n t s . The e x p o n e n t n v a r i e d f r o m 2 0 . 3 t o 0 . 8 f o r w a t e r f l u x e s g r e a t e r t h a n 0 . 0 8 a/m s . The v a l u e o f b v a r i e d b e t w e e n 0 . 0 0 5 t o 0 . 0 0 8 f o r ifi o f a b o u t 10 2 Z/m s . The e f f e c t o f t h e w a t e r t e m p e r a t u r e on t h e h e a t -2 t r a n s f e r c o e f f i c i e n t f o r a s p r a y w a t e r f l u x o f 10 i/m s i s shown i n F i g u r e 1 0 , C u r v e 3 . I t c a n be o b s e r v e d f r o m t h i s c u r v e t h a t t h e w a t e r t e m p e r a t u r e e x e r t s a l a r g e i n f l u e n c e Woter Temperature °C Figure 10 E f f e c t o f water temperature on spray h e a t - t r a n s f e r c o e f f i c i e n t s . ^ 44 on t h e h e a t - t r a n s f e r c o e f f i c i e n t , w h i c h d e c r e a s e s r a p i d l y . by a p p r o x i m a t e l y 1% f o r e v e r y 1 ° C r i s e i n t h e w a t e r t e m p e r a t u r e . The h e a t - t r a n s f e r c o e f f i c i e n t c o r r e l a t i o n h a s 35 73 b e e n u s e d w i t h m o d i f i c a t i o n by o t h e r w o r k e r s , * a n d a 35 v a l u e f o r b o f 0 . 0 0 7 5 h a s b e e n a d o p t e d . N o z a k i f o r i n -s t a n c e , h a s f o u n d t h a t t h e h e a t - t r a n s f e r c o e f f i c i e n t s o b -t a i n e d f r o m M i t s u t s u k a ' s c o r r e l a t i o n w e r e t o o h i g h when a p p l i e d t o s l a b c a s t e r s , i n w h i c h t h e r e a r e a l a r g e n u m b e r o f r o l l s i n t h e s e c o n d a r y c o o l i n g c h a m b e r . He h a s t h e r e -f o r e i n c o r p o r a t e d an a c c o m m o d a t i o n c o e f f i c i e n t w h i c h was d e t e r m i n e d by m e a s u r e m e n t s on an o p e r a t i n g c a s t e r , and h a s p r o p o s e d a c o r r e l a t i o n o f t h e f o r m h = 1 . 5 7 m 0 ' 5 5 ( l - 0 . 0 0 7 5 T w ) / o . . . 2 . 6 w h e r e a i s t h e a c c o m m o d a t i o n c o e f f i c i e n t w i t h a v a l u e o f 4 . The h e a t - t r a n s f e r c o e f f i c i e n t v s . w a t e r f l u x r e l a t i o n s h i p s 73 u s e d by I s h i g u r o and N o z a k i c o r r e s p o n d i n g t o a l t e r e d f o r m s o f M i t s u t s u k a ' s c o r r e l a t i o n a r e p r e s e n t e d i n F i g u r e 1 1 , C u r v e s 1 a n d 2 r e s p e c t i v e l y . U s i n g a v e r t i c a l s t a i n l e s s s t e e l p l a t e , h e a t e d t o 74 1 1 0 0 ° C b e f o r e s p r a y c o o l i n g , S u g i t a n i d e t e r m i n e d t h a t t h e h e a t - t r a n s f e r c o e f f i c i e n t s d r o p p e d r a p i d l y w i t h i n c r e a s i n g s u r f a c e t e m p e r a t u r e , as shown i n F i g u r e 1 2 , C u r v e s 10 a n d 1 1 . I t m u s t be o b s e r v e d , t h a t f o r C u r v e 11 i n t h i s F i g u r e , i n 0 10 20 30 4 0 Water flux, l / m s F igure 11 V a r i a t i o n o f spray h e a t - t r a n s f e r c o e f f i c i e n t w i th water f l u x  as repor ted in va r ious s t u d i e s on spray heat e x t r a c t i o n - . Figure 11a Variation of spray heat-transfer coefficient with water flux as reported in various studies on spray heat extraction - Transient measurements cu o CO c 92 o CD O O CD < 4 — cn c D D CD X 0 0 Steady state measurements Curve Author Reference 6 Muller & Jeschar 81 7 Bolle 8 Moreau 83 8 II I I II 10 20 2 Water flux ( l / m s) 30 4 0 Figure lib Variation of spray heat-transfer coefficient with water flux as reported in spray heat extraction studies - - Steady state measurements F igu re 12 V a r i a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s w i t h s u r f a c e tempera tu re , from v a r i o u s s t u d i e s on spray heat e x t r a c t i o n . 47 w h i c h t h e r e i s no r e d u c t i o n i n t h e s l o p e o f t h e c u r v e e v e n a t s u r f a c e t e m p e r a t u r e s o f 1 0 0 0 ° C , t h e w a t e r f l u x i s v e r y 2 h i g h , w i t h a v a l u e o f 5 6 . 7 z/m s . S p r a y h e a t - t r a n s f e r c o e f f i c i e n t s w e r e m e a s u r e d f o r 14 f u l l c o n e and f l a t j e t s p r a y n o z z l e s by K i l l e s e t a l . a n d 75 E t i e n n e e t a l . S p r a y s i m p i n g i n g v e r t i c a l l y d o w n w a r d o n t o a p o l i s h e d f a c e o f a r e s i s t a n c e h e a t e d , p l a t i n u m r o d o f 1 cm d i a m e t e r w e r e u s e d f o r t h e h e a t t r a n s f e r m e a s u r e m e n t s . T h e y f o u n d t h a t f o r s p r a y s p r o d u c e d by f u l l c o n e n o z z l e s , t h e r e was no e f f e c t o f s u r f a c e t e m p e r a t u r e on t h e h e a t t r a n s f e r c o e f f i c i e n t s , as l o n g as t h e w a t e r f l u x e s a t t h e s u r f a c e 2 w e r e l e s s t h a n 5 t/m s . When h i g h e r w a t e r f l u x e s w e r e u s e d , s u r f a c e t e m p e r a t u r e p l a y e d a g r e a t e r r o l e i n t h e v a r i a t i o n o f t h e h e a t - t r a n s f e r c o e f f i c i e n t s : a d e c r e a s e o f t h e s u r -f a c e t e m p e r a t u r e f r o m 9 0 0 ° t o 8 0 0 ° C c a u s e d an i n c r e a s e i n t h e h e a t f l u x by 10 t o 15%. S p r a y e f f i c i e n c y was f o u n d t o d e c r e a s e w i t h i n c r e a s e i n t h e w a t e r f l u x . The m a j o r p a r a -m e t e r t h a t was f o u n d t o a f f e c t t h e h e a t - t r a n s f e r c o e f -f i c i e n t s , h o w e v e r , was f o u n d t o be t h e w a t e r f l u x . No e f f e c t o f t h e t y p e o f s p r a y , o r o f t h e d i s t a n c e b e t w e e n t h e n o z z l e and t h e p r o b e was f o u n d on- t h e h e a t - t r a n s f e r . c o e f f i c i e n t , s o l o n g as t h e w a t e r f l u x r e m a i n e d t h e s a m e . A s c a t t e r i n t h e r e s u l t s o f 12% i s r e p o r t e d f o r m e a s u r e m e n t s a t 9 0 0 ° C , and t h e s c a t t e r was o b s e r v e d t o i n c r e a s e as t h e s u r f a c e t e m p e r a t u r e d e c r e a s e d . A t 7 0 0 ° C , t h e s c a t t e r i n 48 t h e r e s u l t s was f o u n d t o be 25%. The c o r r e l a t i o n s o b t a i n e d b e t w e e n h e a t f l u x e s and w a t e r f l u x e s f o r d i f f e r e n t t e m p e r a -t u r e s a r e : Q = - 8 7 . 7 + 3 1 3 . 5 r f t 0 ' 5 4 ( 9 0 0 ° C ) '•' . . . 2 . 7 Q = - 3 5 6 . 0 + 4 9 2 . 4 m° * 1 8 ( 8 0 0 ° C ) . . . 2 . 8 Q = - 7 9 3 . A + 8 2 0 . 3 m ° ' 4 ( 7 0 0 ° C ) . . . 2 . 9 F o r s p r a y s p r o d u c e d by f l a t j e t n o z z l e s , i t was o b s e r v e d t h a t t h e s u r f a c e t e m p e r a t u r e h a d l i t t l e e f f e c t on t h e h e a t f l u x when t h e w a t e r f l u x was l e s s t h a n 4 £/m s . On i n c r e a s i n g t h e w a t e r f l u x b e y o n d t h i s l i m i t , i t was f o u n d t h a t a l o w e r -i n g o f t h e s u r f a c e t e m p e r a t u r e a g a i n c a u s e d an i n c r e a s e i n t h e h e a t f l u x - i n c r e a s i n g i t by 10 t o 15% when t h e s u r f a c e t e m p e r a t u r e was l o w e r e d f r o m 9 0 0 ° C t o 8 0 0 ° C . A l a w o f t h e f o r m Q = C o n s t a n t m n , . . . 2 . 1 0 was o b s e r v e d t o c o r r e l a t e t h e h e a t f l u x e s t o w a t e r f l u x e s a t 9 0 0 ° C , w i t h t h e e x p o n e n t n d e c r e a s i n g f r o m a v a l u e o f 1 t o 2 0 . 5 when t h e w a t e r f l u x i n c r e a s e d f r o m 2 t o 20 £/m s . D e -c r e a s i n g t h e s u r f a c e t e m p e r a t u r e was f o u n d t o i n c r e a s e t h e s c a t t e r i n t h e r e s u l t s o b t a i n e d . F o r o v e r l a p p i n g s p r a y s f r o m two f l a t j e t n o z z l e s , i t i s r e p o r t e d t h a t a n o t i c e a b l e e f f e c t o f t h e t y p e o f s p r a y a n d o f t h e d i s t a n c e b e t w e e n t h e s p r a y a n d t h e c o o l e d s u r f a c e was o b s e r v e d . H e a t f l u x 49 c o r r e l a t i o n s o b s e r v e d f r o m t h e i r e x p e r i m e n t s f o r f l a t j e t s p r a y s and a s u r f a c e t e m p e r a t u r e o f 9 0 0 ° C a r e : 0 93 Q = 182.4 + 77.2 m n o z z l e - t o - n o z z l e spac ing 8 cm probe to nozz le d i s t a n c e 11 cm . . . 2.11 0 81 Q = 80 + 2 1 8 . 8 iii n o z z l e - t o - n o z z l e spac ing 20 cm probe to n o z z l e d i s t a n c e 35 cm . . . 2 .12 M i z i k a r 7 6 e m p l o y e d a s t a i ri.'l e s s s t e e l p l a t e , h e a t e d t o a b o u t 1 0 0 0 ° C and f i x e d v e r t i c a l l y , i n h i s l a b o r a t o r y e x p e r i m e n t s . He f o u n d t h a t s u r f a c e t e m p e r a t u r e s i n e x c e s s o f 6 0 0 ° C d i d n o t i n f l u e n c e t h e h e a t - t r a n s f e r c o e f f i c i e n t s . F o r a 1 / 4 GG10 S p r a y i n g S y s t e m s Co. n o z z l e , he o b t a i n e d l i n e a r r e l a t i o n s h i p s b e t w e e n t h e h e a t - t r a n s f e r c o e f f i c i e n t s and t h e w a t e r f l u x e s f o r two d i f f e r e n t w a t e r p r e s s u r e s . The r e l a t i o n s h i p s o b t a i n e d w e r e h = 0.0776 m + . 0 . 2 2 f o r a p ressure o f 0.276 MPa . . . 2 .13 h = 0.1 m + . 0 . 2 2 f o r a p ressure o f 0.620 MPa . . . 2.14 The c o n s t a n t o f 0 . 2 2 r e p r e s e n t s t h e c o n t r i b u t i o n due t o r a d i a t i o n h e a t t r a n s f e r . T h e s e r e l a t i o n s h i p s a r e shown g r a p h i c a l l y i n F i g u r e 1 1 , C u r v e s 3 and 4 , r e s p e c t i v e l y , a f t e r s u b t r a c t i n g t h e r a d i a t i o n c o n t r i b u t i o n . The a n g l e o f i m p i n g e m e n t o f t h e d r o p s d i d n o t a f f e c t t h e h e a t - t r a n s f e r c o e f f i c i e n t s , b u t an i n c r e a s e i n t h e d r o p l e t momentum c a u s e d 50 an i n c r e a s e i n t h e s e c o e f f i c i e n t s . 7 7 78 S a s a k i e t a l . and S u g i t a n i ' u s e d a n o v e l a p p r o a c h i n t h e d e t e r m i n a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s i n s p r a y c o o l i n g . A v e r t i c a l s t a i n l e s s s t e e l p l a t e ( T y p e 1 8 - 8 ) w a s h e a t e d t o a b o u t 1 2 0 0 ° C i n a r e s i s t a n c e f u r n a c e a n d was s p r a y e d f r o m b o t h s i d e s f o r s h o r t p e r i o d s o f t i m e ( 0 . 3 t o 1 s e c ) w i t h f u l l c o n e and f l a t j e t n o z z l e s . D u r i n g t h e s p r a y c o o l i n g i n t e r v a l , t h e s u r f a c e t e m p e r a t u r e was m o n i t o r e d by o p t i c a l p y r o m e t e r s s i g h t e d on t h e s u r f a c e . From t h e c h a n g e i n s u r f a c e t e m p e r a t u r e w i t h t i m e , t h e h e a t - t r a n s f e r c o -e f f i c i e n t s w e r e c a l c u l a t e d . W a t e r f l u x e s w e r e v a r i e d f r o m 2 . 6 7 t o 4 1 . 8 £./m s a n d s p r a y p r e s s u r e s f r o m 0 . 1 4 MPa t o 0 . 3 5 M P a . The s u r f a c e t e m p e r a t u r e o f t h e p l a t e was f o u n d t o a f f e c t t h e h e a t - t r a n s f e r c o e f f i c i e n t s , and a c o r r e l a t i o n o f t h e f o r m -h = 708 m° - 7 5 T _ 1 ' 2 + 0 . 1 1 6 . . . 2 . 1 5 s was p r o p o s e d f o r t h e r a n g e o f s u r f a c e t e m p e r a t u r e s b e t w e e n 7 0 0 ° and 1 2 0 0 ° C . T h i s e q u a t i o n , f o r a s u r f a c e t e m p e r a t u r e o f 1 1 5 0 ° C , i s shown i n F i g u r e 1 2 , C u r v e 5 . The e f f e c t o f w a t e r t e m p e r a t u r e was n o t as g r e a t as t h a t o b s e r v e d by M i t s u t s u k a , as c a n be o b s e r v e d f r o m F i g u r e 1 0 , C u r v e s 1 a n d 2 . 51 79 B a m b e r g e r e t a l . c a r r i e d o u t u n s t e a d y - s t a t e h e a t - t r a n s f e r s t u d i e s t o m e a s u r e t h e h e a t - t r a n s f e r c o -e f f i c i e n t s f o r t h e s p r a y c o o l i n g o f n o n - f e r r o u s m a t e r i a l s ( n i c k e l , a l u m i n i u m , and c o p p e r ) , w i t h s u r f a c e t e m p e r a t u r e s b e t w e e n 250 a n d 1 0 0 0 ° C , and f o r w a t e r f l u x e s v a r y i n g f r o m 10 t o 100 £,/m s . The m e a s u r e m e n t s i n d i c a t e a d e p e n d e n c e o f t h e h e a t - t r a n s f e r c o e f f i c i e n t s on t h e t h e r m o p h y s i c a 1 p r o -p e r t i e s o f t h e m a t e r i a l . The m o s t i m p o r t a n t p a r a m e t e r a f f e c t i n g t h e h e a t - t r a n s f e r c o e f f i c i e n t s was f o u n d t o be t h e s p r a y w a t e r f l u x and t h e c o e f f i c i e n t s w e r e a l s o f o u n d t o be a f u n c t i o n o f t h e s u r f a c e t e m p e r a t u r e . The c o r r e l a t i o n o b t a i n e d f r o m t h e r e s u l t s o f t h e i r wo rk i s h = 0.1 m 0 - 5 5 ( 0 . 0 7 / T ^ ~p ( -0 .0049 T g + 28)) . . . 2 . 1 6 + ^ r a d i a t i o n T h e y h a v e r e p o r t e d t h a t t h e y h a v e o b t a i n e d a l a r g e s c a t t e r i n t h e i r r e s u l t s , e s p e c i a l l y when t h e s u r f a c e t e m p e r a t u r e s w e r e b e t w e e n 250 and 7 0 0 ° C . 2 . 3 . 2 S t e a d y - S t a t e M e t h o d s From t h e m e a s u r e d v a l u e s o f e l e c t r i c a l e n e r g y r e q u i r e d t o m a i n t a i n t h e t e m p e r a t u r e o f t h e m e a s u r i n g Q A s e c t i o n c o n s t a n t d u r i n g s p r a y i n g , J u n k e v a l u a t e d t h e h e a t -t r a n s f e r c o e f f i c i e n t s d u r i n g s p r a y i n g w i t h o v a l n o z z l e s . The 52 r e s u l t s o f h i s e x p e r i m e n t s a r e shown i n F i g u r e 1 2 , C u r v e s 7 , 8 and 9 , f o r d i f f e r e n t s p r a y p r e s s u r e s . F l a t t e n e d p i p e s made o f h e a t and s c a l e r e s i s t i n g s t e e l s h e a t e d by e l e c t r i c a l c u r r e n t s p a s s i n g t h r o u g h them w e r e u s e d a s t h e m e a s u r i n g s e c t i o n . The s u r f a c e t e m p e r a t u r e s w e r e c a l c u l a t e d f r o m a m e a s u r e d t e m p e r a t u r e w i t h i n t h e p i p e . J u n k h a s p r o p o s e d s e v e r a l f u n c t i o n a l r e l a t i o n s h i p s b e t w e e n t h e h e a t f l u x a n d c e r t a i n p a r a m e t e r s , e . g . t h e s p r a y p r e s s u r e , s p r a y d i s t a n c e , t h e s p r a y w a t e r f l u x , and t h e a v e r a g e i m p i n g e m e n t p r e s s u r e . H o w e v e r , s i n c e t h e c o e f f i c i e n t s i n t h e r e l a t i o n s h i p s a r e n o t g i v e n , t h e r e l a t i v e e f f e c t s o f t h e s e p a r a m e t e r s c a n n o t be e v a l u a t e d . From t h e r e s u l t s o f t h e i r e x p e r i m e n t s u s i n g s t e e l 81 p l a t e s ' , M u l l e r a n d J e s c h a r f o u n d t h a t t h e h e a t - t r a n s f e r c o e f f i c i e n t s a r e f u n c t i o n s o f b o t h t h e w a t e r f l u x a n d t h e d r o p l e t v e l o c i t y a t t h e e x i t f r o m t h e n o z z l e . The m e a s u r e -m e n t s , e x c l u d i n g t h e r a d i a t i o n c o m p o n e n t a r e d e s c r i b e d by t h e e q u a t i o n h = 0.01 V + (0.107 + 6 .8 x 1 0 " 4 V ) m . . . 2 .1 7 The e x p e r i m e n t a l r e s u l t s a r e shown i n F i g u r e s 11 a n d 1 3 . Fan j e t n o z z l e s , and f u l l c o n e n o z z l e s o p e r a t e d a t p r e s -s u r e s o f up t o 1 MPa w e r e u s e d t o e x t r a c t h e a t f r o m v e r t i c a l , r e s i s t a n c e h e a t e d s t e e l p l a t e s , w i t h s u r f a c e a r e a s v a r y i n g f r o m 20 t o 65 s q . cm- W a t e r f l u x e s u s e d i n t h e e x p e r i m e n t s Fiqure 13 V a r i a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s w i t h water f l u x 2 — g^ j ' ' f o r d i f f e r e n t d rop le t v e l o c i t i e s . 54 2 v a r i e d f r o m 3 t o 9 i/m s , w i t h d r o p l e t v e l o c i t i e s r a n g i n g b e t w e e n 10 a n d 35 m / s . P l a t e s u r f a c e t e m p e r a t u r e s w e r e v a r i e d b e t w e e n 7 0 0 ° a n d 1 2 0 0 ° C . The e r r o r s i n t h e h e a t -t r a n s f e r c o e f f i c i e n t s a r e r e p o r t e d t o be l e s s t h a n 15%. T h e s e c o e f f i c i e n t s w e r e f o u n d t o be i n s e n s i t i v e t o s u r f a c e t e m p e r a t u r e i n t h e r a n g e s t u d i e d . The s p r a y c o o l i n g e f f i c i e n c y was f o u n d t o d r o p w i t h an i n c r e a s e i n t h e w a t e r f l u x . 8 2 - 8 4 E x p e r i m e n t s by B o l l e a n d M o r e a u w e r e c o n d u c t e d w i t h f a n t y p e s p r a y s , s i m i l a r t o t h o s e u s e d by M u l l e r and J e s c h a r , s p r a y i n g d o w n w a r d s o n t o a r e s i s t a n c e h e a t e d , f l a t p l a t e , c o n t a i n i n g i m b e d d e d t h e r m o c o u p l e s . W a t e r p r e s s u r e s o f 0 .1 MPa t o 0 . 5 MPa w e r e u s e d i n t h e i r s t u d i e s , and t h e 2 w a t e r f l u x e s u s e d r a n g e d f r o m 1 t o 7 £/m s - The h e a t f l u x e s o b t a i n e d f r o m t h i s w o r k w e r e h i g h e r t h a n t h o s e o b t a i n e d by M u l l e r and J e s c h a r i n t h e s u r f a c e t e m p e r a t u r e r a n g e s t u d i e d ( 5 0 0 ° t o 1 0 0 0 ° C ) . In a g r e e m e n t w i t h M u l l e r and J e s c h a r , t h e s p r a y h e a t e x t r a c t i o n e f f i c i e n c y was f o u n d t o d r o p as t h e w a t e r f l u x o r s p r a y p r e s s u r e i n c r e a s e d , and t h e h e a t -t r a n s f e r c o e f f i c i e n t s i n c r e a s e d w i t h i n c r e a s i n g w a t e r f l u x , as r e p r e s e n t e d by t h e c o r r e l a t i o n h = 0 . 4 2 3 ( m ) 0 , 5 5 6 + 17% . . . 2 . 1 8 f o r s u r f a c e t e m p e r a t u r e s b e t w e e n 6 0 0 ° a n d 9 0 0 ° C a n d w a t e r 55 2 f l u x e s b e t w e e n 1 a n d 7 i / m s . I t was a l s o f o u n d t h a t c o o l -i n g by s p r a y i n g u p w a r d s f r o m b e l o w t h e h o t s u r f a c e y i e l d e d h e a t - t r a n s f e r c o e f f i c i e n t s t h a t w e r e a b o u t 15% l o w e r t h a n t h o s e o b t a i n e d f r o m t h e a b o v e c o r r e l a t i o n . The r e s u l t s f r o m t h e two c o r r e l a t i o n s a r e shown i n F i g u r e 1 1 , C u r v e s 7 and 8 . 2 . 3 . 3 I n - p l a n t M e a s u r e m e n t s H e a t b a l a n c e s on an o p e r a t i n g c a s t e r h a v e b e e n • a numer-1 4 , 8 8 , 8 9 85—87 p e r f o r m e d u s i n g e i t h e r a n a l y t i c a l m e t h o d s ~ o r a n u m e r i c a l s o l u t i o n o f t h e m a t h e m a t i c a l m o d e l o f t h e p r o c e s s . The m e a s u r e d s u r f a c e t e m p e r a t u r e s a t v a r i o u s p o s i t i o n s i n t h e c a s t e r w e r e u s e d as i n p u t i n t h e c a l c u l a t i o n s , w h i c h y i e l d t h e a v e r a g e h e a t - t r a n s f e r c o e f f i c i e n t s i n d i f f e r e n t c o o l i ng z o n e s . 8 5 - 8 7 A k i m e n k o e t a l . ~ d e t e r m i n e d t h a t t h e h e a t - t r a n s f e r c o e f f i c i e n t s i n c r e a s e as t h e w a t e r f l u x i n c r e a s e s , u n t i l a 2 w a t e r f l u x o f 8 . 5 a/m s was r e a c h e d . Any f u r t h e r i n c r e a s e i n t h e w a t e r f l u x d i d n o t a f f e c t t h e h e a t - t r a n s f e r c o -e f f i c i e n t s . A s l i g h t d e p e n d e n c e , o f t h e h e a t - t r a n s f e r c o -e f f i c i e n t s on t h e w a t e r t e m p e r a t u r e h a s b e e n r e p o r t e d , w i t h t h e c o e f f i c i e n t s d e c r e a s i n g as t h e w a t e r t e m p e r a t u r e i n -c r e a s e s . 56 The r e s u l t s o f t h e w o r k o f A l b e r n y e t a l . 0 0 ' 0 3 a r e p r e s e n t e d i n F i g u r e 1 1 , C u r v e s 9 , 10 a n d 1 1 . T h e s e w e r e o b t a i n e d f o r d i f f e r e n t s p r a y c o n f i g u r a t i o n s on a c e n t r i -f u g a l c o n t i n u o u s c a s t e r . The s u r f a c e t e m p e r a t u r e f o r w h i c h t h e s e c o e f f i c i e n t s w e r e o b t a i n e d v a r y f r o m 1050 t o 1 2 5 0 ° C . From t h i s F i g u r e , i t i s s e e n t h a t t h e r e i s a l e v e l l i n g o f f o f t h e h e a t - t r a n s f e r c o e f f i c i e n t b e y o n d a c e r t a i n v a l u e o f t h e w a t e r f l u x . I t i s i n t e r e s t i n g t o n o t e t h a t t h e i n -s e n s i t i v i t y o f t h e h e a t - t r a n s f e r c o e f f i c i e n t s t o w a t e r f l u x b e y o n d a l i m i t i n g v a l u e has b e e n o b s e r v e d o n l y i n t h e c a s e s w h e r e t h e s e c o e f f i c i e n t s h a v e b e e n o b t a i n e d f r o m h e a t b a l a n c e s on o p e r a t i n g c a s t e r s . 2 . 4 Summary From t h e p r e c e d i n g d i s c u s s i o n o f t h e v a r i o u s i n -v e s t i g a t i o n s o f h e a t - t r a n s f e r i n w a t e r s p r a y s , i t c a n be s e e n t h a t t h e m a i n v a r i a b l e s t h a t h a v e b e e n s t u d i e d a r e t h e f o l 1 o w i n g : i ) L o c a l w a t e r f l u x e s a t t h e c o o l e d s u r f a c e i i ) The s u r f a c e t e m p e r a t u r e i i i ) W a t e r p r e s s u r e s a t t h e n o z z l e i v ) D r o p l e t s i z e v ) D r o p l e t v e l o c i t i e s i n t h e s p r a y v i ) W a t e r p r e s s u r e a t t h e s p r a y n o z z l e v i i ) T e m p e r a t u r e o f t h e s p r a y w a t e r 57 A wide range of resu l ts has been obtained, as re-ported in th is chapter . In many cases , d i f f e r e n t i n -vest igat ions show c o n f l i c t i n g r e s u l t s , and, in a d d i t i o n , in many cases , lack of data regarding the experimental con-d i t ions makes meaningful comparisons impossib le . In genera l , however, some conclusions may be arr ived at from the mass of data ava i lab le regarding spray c o o l i n g . i ) In strand c a s t i n g , the temperature of the strand surface as i t passes through the sprays is greater than 900° C and is higher than the " c r i t i c a l point" beyond which a phenomenon akin to f i lm b o i l i n g takes p lace . A vapour cushion ex is ts next to the strand s u r f a c e , but the momentum of the water droplets in the spray allow them to penetrate th is cushion increasing the heat flow from the sur face . Nonwetting behaviour takes place on impact. i i ) Increasing the droplet momentum in the spray, e i ther by increas ing the droplet s ize or the v e l o c i t y , increases the heat - t ransfer co-e f f i c i e n t . i i i ) At constant drop s ize and v e l o c i t y , increas ing the water f lux to the surface increases the heat t ransfer c o e f f i c i e n t . 58 i v ) A p p l i c a t i o n o f t h e r e s u l t s o f s i n g l e d r o p l e t e x p e r i m e n t s t o g r o s s s p r a y s l e a d s t o i n c o r r e c t h e a t t r a n s f e r c o e f f i c i e n t p r e d i c t i o n s , b e c a u s e o f i n t e r a c t i o n s i n t h e s p r a y s . v ) The e x t e n t o f t h e e f f e c t o f t h e w a t e r t e m p e r a -t u r e on t h e h e a t - t r a n s f e r c o e f f i c i e n t s i s u n c l e a r . v i ) The e f f i c i e n c y o f t h e s p r a y i s u s u a l l y l o w , l e s s t h a n 10%, a n d t h i s i s d e c r e a s e d i f t h e f l o w r a t e i s i n c r e a s e d . v i i ) I n c r e a s i n g t h e d r o p l e t v e l o c i t y o r t h e w a t e r f l u x s h i f t s t h e " c r i t i c a l p o i n t " t o h i g h e r t e m p e r a t u r e s . A summary o f t h e e x p e r i m e n t a l m e t h o d s a n d e x p e r i m e n t a l c o n d i t i o n s u s e d , as w e l l as t h e r e s u l t s o f v a r i o u s i n v e s t i -g a t i o n s on s p r a y h e a t t r a n s f e r d i s c u s s e d i n t h i s c h a p t e r a r e p r e s e n t e d i n T a b l e I I . TABLE H a Summary of" Studies on Heat Extraction in Sprays - Transient Measurements Investigator & Reference No. Nature of the Heated Surface Direction of Spraylnq In i t ia l Temperature °C Spray Nozzle Type Spray Fluxes l/mZs Comments Gaugler 5 3 Horizontal upper face of chrome plated copper cylinder heated In a furnace, Surface area 112 sq cm Downwards 400 Full cone 1/8 GG 1 1/8 GG 3001.4 .716 to 3.7 n = 1.487 X 10" 3 ( T s - T w) m - ° - 6 6 ± 1 0 X h = 3.695 m 0 - 3 3 ± 1 0 % Increasing droplet momentum increasesh. Heat transfer-red te each drop decreases as iti Increases. r 67 Gorman Same as Gaugler. Downwards 900 Ful l cone 1/8 GSS Up to 57 Increasing ifi increases h and moves c r i t i c a l point to hiqher temperatures. , . 68 Aunan et a l . A1S1 304 stainless s t e e l , furnace heated. Area 300 sq cm. Downwards 1100 Ful l cone and fan je t . Up to 217 Increasing it) Increases n and h. Lambert and Economopoul OS Cyl indrical nickel probes. Area 3.1 sq cm. Horizontal 800 Only spray pressure of 0.098 'VPa reported. Results s imi lar to that of Gaugler. Hoogendoom and den Hond70 Horizontal stainless steel plate (AISI 321), furnace heated. Area 269 sq cm. Downwards 1000 Shlck 0.6 to 25 Increasing m and drop veloci ty increases c r i t i c a l j temperature, to as much as 900°C scat ter t 20%. No difference in h when a vert ical plate was used. Mitsutsuka Shimada?!.72 Horizontal low carbon steel plate, heated in a resistance furnace. Area 484 sq cm. Upwards and downwards simultaneous-l y . 930 Full cone 1 to 50 h = A mn (1-b T w ) 0.5 < n < 0.8 0.005 < b < .008 for ifi - 10.3 t / m 2 s . h decreases as T w increases. 74 Sugitanl et a l . Vertical stainless steel plate heated 1n a resistance furnace. Surface area 500 sq cmj Horizontal 1000 to 1200 Full cone and f l a t j e t . Up to 60 h Is a strong function of T $ even above 700° C. N i l l es et al . 1 4 , 5 Etlenne et a l . Polished surface of a platinum rod, heated by a resistance wire wound around i t . Sur-face area 0.79 s q . cm. Downwa rd 1050 Ful l cone and f l a t j e t . 1.5 to 50 h is a function of T s even above 700°C . h increases as T s decreases, n decreases with increasing m. Scatter Increases as T s decreases for fu l l con ' nozzles: Q = -36.7 + 313.5 m 0 , 5 4 (900°C) Q = -356.0 + 492.4 i i " ' ' 8 (800°C) 0 = -793.4 + 492.4 m (700°C) M i z i k a r 7 6 Stainless steel plate (AISI 304) heated in a resistance furnace. Area 161 sq cm. Horizontal 1000 Full cone 1/4 GG 10 1/4 GG 6.5 3/8 GG 15 0 to 20 h constant above T. of 600°C. h increases as m in -creases. Increasing spray pressure increases h for the same m. h = 0.0776 m + 0.22 at 0.276 MPa h = 0.1 m + 0.22 at 0.620 MPa. S a s a k i e t a l 7 7 Sugitanl 78 18-8 stainless steel plate heated in a resistance furnace. Horizontal sprayed on bopn sides 700 to 1200 Full cone and fan let h 1s a function of T s . h = 708 m 0 - 7 5 Is" 1 " 2 + 0.116 for 700°C < T s < 1200 °C 79 Bamberger et a l . Nonferrous materials N i , A l , Cu Various, depending on material 10 to 100 h = 0 . 1 m0 - 5 5 ( 0 . 0 7 APCp exp (0.0049 Ts+ 28))+h radiat ion Large scat ter 1n results at lower surface temperatures. Table l ib Summary of Studies on Heat Extraction in Sprays - Steady State Measurements Investigator & Reference No. Mature of the Heated Surface Direction of Spraying In i t ia l Temperature °C Spray Nozzle Type Spray Fluxes i /m 2 s Comments Junk Resistance heated flattened steel pipes. Area 33 to 207 sq cm. Horizontal Oval Correlations obtained between spray pressure, nozzle distance, m values of the coef f ic ients are not given. Muller and Jeschar81 Resistance heated steel plates. Area 20 to 65 sq cm. Horizontal 700 to 1200 Full cone and fan je t . 0.3 to 9 Drop ve loc i t ies 10 to 35 m/s. Scatter + 15%. h i s a function of droplet ve loc i ty . h » O.Olv + (0.107 + 6.8 x 10" 4 v) m h Is independent of T $ n decreases as m increases. Bolle and„. Moreau8Z-84 Resistance heated f l a t stainless steel plate (AISI 309) Area 128 sq cm. Vert ica l ly downwards and upwards 500 to 1000 Fan type simi lar to Muller and Jeschar 1 to 7 Heat fluxes higher than those of Bolle and Moreau. n decreases as m or spray pressure increases. When spraying v e r t i c a l l y downwards. h - 0.423 m 0 - 5 5 6 + 1755 Cooling by spraying ve r t i ca l l y upwards decreased h by about 15* when compared with spraying ver t ica l ly downwards. CTl, o Table l i e Summary of Studies on Heat Extraction in Sprays - In-plant Measurements Investigator & Reference No. Nature of the Heated Surface Direction of Spraying In i t ia l Temperature °C Spray Nozzle Type Spray Fluxes t/m2s Comments Nozaki 3 5 Measurements on slab casters . Altered form of Mitsutsuka's equation: h = 1.57 n-,0-S5 ( ] _ Q 0 Q 7 5 T j / o d = 4 (Nozaki) . • . , , 85-8) Akimenko et a l . Up to 15 h increases with increasing id, but remains constant i f m > 8.5 h decreases as T,, increases w » , 88,89 Alberny et a l . Up to 56 Measurements on centrifugal caster . h increases with Increasing m to a certain value of m and then stays constant beyond this value. C h a p t e r 3 E X P E R I M E N T A L 3.1 I n t r o d u c t i on The m e a s u r e m e n t s c a r r i e d o u t i n t h i s i n v e s t i g a t i o n f a l l i n t o two c a t e g o r i e s : i ) M e a s u r e m e n t s o f l o c a l w a t e r f l u x e s w i t h i n t h e s p r a y s i i ) M e a s u r e m e n t s o f h e a t - t r a n s f e r c o e f f i c i e n t s . i ) F o r t h e m e a s u r e m e n t s o f l o c a l w a t e r f l u x e s , s e v e r a l i n d u s t r i a l s p r a y n o z z l e s w e r e u s e d , and t h e s e w e r e s u p p l i e d w i t h w a t e r a t c o n s t a n t p r e s s u r e ( w i t h i n a r a n g e f r o m 70 k P a t o 700 k P a ) . L o c a l w a t e r f l u x e s w e r e m e a s u r e d i n v a r i o u s p o s i t i o n s w i t h i n t h e s p r a y s a t d i f f e r e n t d i s t a n c e s ( 1 0 t o 25 cm) f r o m t h e s p r a y n o z z l e , f o r t h e d i f f e r e n t s p r a y p r e s s u r e s u s e d . I t was f o u n d t h a t some w a t e r f l o w e d d o w n -w a r d t h r o u g h t h e s p r a y c o n e a d j a c e n t t o t h e v e r t i c a l p l a t e on w h i c h t h e s p r a y i m p i n g e d . T h i s a m o u n t o f w a t e r was a l s o m e a s u r e d . i i ) H e a t - t r a n s f e r m e a s u r e m e n t s . w e r e c a r r i e d o u t f o r t h e c o n d i t i o n s c o r r e s p o n d i n g t o t h o s e f o r w h i c h t h e w a t e r f l u x e s w e r e m e a s u r e d . In t h e h e a t - t r a n s f e r m e a s u r e m e n t s , a 62 63 s t a i n l e s s s t e e l " h e a t - t r a n s f e r p r o b e " , w i t h t h e r m o c o u p l e s embedded i n i t , was f i r s t h e a t e d t o t e m p e r a t u r e s i n t h e o r d e r o f 1 1 5 0 ° C . T h i s was t h e n s p r a y e d w i t h w a t e r , and t h e t e m p e r a t u r e - t i m e t r a n s i e n t s d u r i n g t h e c o o l i n g w e r e r e c o r d e d on an o s c i l l o g r a p h i c r e c o r d e r . A n a l y s i s o f t h e s e t r a n s i e n t s t h e n y i e l d e d t h e r e q u i r e d h e a t - t r a n s f e r c o -e f f i c i e n t s , and t h e i r v a r i a t i o n w i t h t h e s u r f a c e t e m p e r a t u r e o f t h e h e a t - t r a n s f e r p r o b e . 3 . 2 S p r a y N o z z l e s The f o l l o w i n g c o m m e r c i a l s p r a y n o z z l e s , p r o v i d e d by S p r a y i n g S y s t e m s C o . ( M i s s i s s a u g a , O n t a r i o ) w e r e u s e d i n t h i s i n v e s t i g a t i o n . 1 /8 GG 5 1 /8 GG 6 SQ 1 /4 GG 6 . 5 1 /4 GG 10 1 / 4 GG 10 SQ 1 /4 GG 12 SQ 1 /4 HH 1 4 . 5 SQ 3 / 8 HH 18 SQ 1 /4 U 8020 3 / 8 U 5060 The f i r s t number i n t h e d e s i g n a t i o n r e p r e s e n t s t h e p i p e TABLE III Capacities and Spray Angles for the Nozzles Investigated in this work. Capacity l i t res/sec Spray Angle(d< jgrees) Pressun ; psi 5 10 20 30 40 60 80 100 7 20 80 N o z z l e ^ ^ \ _ ^ Number 1 MPa 0.03 0.07 0.14 0.21 0.28 0.41 0.55 0.69 0.05 0.14 0.55 1/8 GG 5 0.023 0.032 0.045 0.053 0.061 0.077 0.084 0.097 52 65 69 1/8 GG 6 SQ 0.028 0.039 0.054 0.065 0.071 0.090 0.103 0.116 60 66 60 1/4 GG 6.5 0.030 0.042 0.057. 0.071 0.084 0.097 0.110 0.123 45 50 46 1/4 GG 10 0.047 0.065 0.090 o.no 0.122 0.155 0.174 0.194 58 67 61 1/4 GG 10 SQ 0.047 0.065 0.090 0.110 0.122 0.149 0.168 0.187 62 67 61 1/4 GG 12 SQ 0.056 0.077 0.110 0.129 0.149 0.181 0.207 0.226 70 75 68 1/4 GG 14 W 0.646 0.090 0.123 0.149 0.168 0.200 0.226 114 120 103 1/4 HH 14.5 SQ 0.071 0.094 0.129 0.155 0.181 0.213 0.245 0.271 78 82 85 1/4 U 8020 0.046 0.065 0.090 0.110 0.129 0.161 0.181 0.207 74 83 3/8 U 5060 0.136 0.194 0.271 0.387 0.471 0.549 0.614 0.865 43 53 cn 65 t h r e a d s i z e o f t h e n o z z l e s . The s e c o n d n u m b e r i s a m e a s u r e o f t h e n o z z l e c a p a c i t y ( f l o w r a t e t h r o u g h t h e n o z z l e ) . The l e t t e r s GG a n d HH i n d i c a t e n o z z l e s p r o d u c i n g f u l l c o n e s p r a y s . The n o z z l e n u m b e r s c o n t a i n i n g U i n d i c a t e t h a t t h e s e n o z z l e s p r o d u c e v e e - j e t s p r a y s . The c a p a c i t i e s a n d s p r a y 9 a n g l e s o f t h e d i f f e r e n t n o z z l e s a r e p r e s e n t e d i n T a b l e I I I . F u l l c o n e n o z z l e s , as t h e name i n d i c a t e s , p r o v i d e s p r a y s w h i c h a r e c o n i c a l i n s h a p e . V e e - j e t n o z z l e s p r o d u c e a f l a t , w i d e s p r a y , and i n t h e c a s e s o f t h e n o z z l e s u s e d , t h e w i d t h o f t h e s p r a y s was b e t w e e n 2 . 5 t o 5 c m . 3 . 3 W a t e r S u p p l y S y s t e m A s t a b l e s o u r c e o f p r e s s u r i z e d w a t e r a t t h e p r e s -s u r e s a n d f l o w r a t e s n e e d e d f o r t h e s t u d y was r e q u i r e d . The r a n g e o f p r e s s u r e s r e q u i r e d was b e t w e e n 6 9 . 5 t o 6 9 5 k P a ( 1 0 t o 100 p s i ) , t o be c o n s t a n t w i t h i n 3 . 5 k P a ( 0 . 5 p s i ) . F i g u r e 14 shows a s c h e m a t i c d i a g r a m o f t h e e q u i p m e n t c o n s t r u c t e d t o mee t t h i s r e q u i r e m e n t . A 1 5 0 l i t r e ( 3 3 g a l l o n ) d o m e s t i c h o t w a t e r t a n k r a t e d f o r a p r e s s u r e o f 1048 k P a ( 1 5 0 p s i ) was u s e d t o p r o v i d e t h e p r e s s u r i z e d r e s e r v o i r s u p p l y . The t a n k was f i l l e d w i t h w a t e r f r o m t h e m a i n s s u p p l y , and was t h e n p r e s s u r i z e d w i t h c o m p r e s s e d 66 Nozzle Figure 14 Schemat ic diagram o f the water supp ly sys tem. 67 n i t r o g e n f r o m a gas c y l i n d e r t o a p r e s s u r e o f 8 2 0 k P a ( 1 2 5 p s i ) . The p r e s s u r i z e d w a t e r f r o m t h e t a n k was p a s -s e d t h r o u g h e i t h e r o f two w a t e r p r e s s u r e r e g u l a t o r s (CASHCO T y p e D 1 / 2 ) w i t h 103 t o 276 k P a ( 1 5 t o 40 p s i ) o r 276 k P a - 522 k P a (40 t o 80 p s i ) r a n g e s d e p e n d i n g on t h e p r e s s u r e r e q u i r e d a t t h e s p r a y n o z z l e . The w a t e r p r e s s u r e i m m e d i a t e l y b e h i n d t h e s p r a y n o z z l e was m o n i t o r e d by b o t h a M a r s h 15 cm (6 i n ) d i a . B o u r d o n t y p e p r e s s u r e g u a g e w i t h a r a n g e o f 0 t o 1100 k P a (0 - 160 p s i ) , and a CEC p r e s s u r e t r a n s d u c e r . The o u t p u t f r o m t h e t r a n s d u c e r w e n t t o a W h e a t s t o n e B r i d g e c i r c u i t , and r e c o r d e d on a H o n e y w e l l E l e k t r o n i k 194 c h a r t r e c o r d e r . By m o n i t o r i n g t h e p r e s s u r e t r a c e on t h e r e c o r d e r , i t was e s t a -b l i s h e d t h a t t h e w a t e r p r e s s u r e a t t h e n o z z l e c o u l d be k e p t c o n s t a n t w i t h i n t h e r e q u i r e d r a n g e f o r a p e r i o d o f n e a r l y 10 m i n u t e s , w h i c h was much l o n g e r t h a n t h a t u s e d e i t h e r f o r t h e w a t e r f l u x o r h e a t - t r a n s f e r m e a s u r e m e n t s . R e f e r r i n g t o F i g u r e 1 4 , e l e c t r i c a l l y s w i t c h e d s o l e -n o i d v a l v e s ( m a r k e d A) w e r e i n s t a l l e d i n t h e f l o w s y s t e m t o t u r n t h e w a t e r o r gas s u p p l i e s on o r o f f , a n d t o i n i t i a t e o r s t o p t h e s p r a y . In t h i s w a y , a q u i c k r e s p o n s e o f t h e s p r a y s y s t e m was e n s u r e d . T y p i c a l l y , t h e s p r a y s t a b i l i z e d w i t h i n 0 . 2 s e c o n d s o f t h e s t a r t o f s p r a y i n g . T h i s was 68 d e t e r m i n e d by m o n i t o r i n g t h e o u t p u t o f t h e CEC p r e s s u r e t r a n s d u c e r on a c a t h o d e r a y o s c i 1 1 o s c o p e . 3 . 4 S p r a y N o z z l e M o u n t i n g E a c h n o z z l e was m o u n t e d on a f r a m e , s u c h t h a t t h e n o z z l e a x i s was h o r i z o n t a l . A s c h e m a t i c o f t h e m o u n t i n g s e t - u p i s shown i n F i g u r e 1 5 . The m o u n t h a d t h e c a p a b i l i t y o f a l l o w i n g t h e n o z z l e t o be moved o v e r a r a n g e o f 1 5 . 2 4 cm (6 i n ) i n t h e v e r t i c a l d i r e c t i o n a n d an e q u i v a l e n t a m o u n t i n t h e h o r i z o n t a l d i r e c t i o n . L a r g e r m o v e m e n t s i n t h e h o r i z o n t a l d i r e c t i o n w e r e p o s s i b l e by u n c l a m p i n g a n d m o v i n g t h e m o u n t i n g i t s e l f . 3 . 5 M e a s u r e m e n t o f S p r a y W a t e r F l u x e s D a t a r e p o r t e d by M i z i k a r 7 6 f o r t h e 1 / 4 GG 10 f u l l c o n e n o z z l e i n d i c a t e d t h a t t h e s p r a y w a t e r f l u x w i t h i n t h e s p r a y e d c o n e was n o n u n i f o r m . T h i s n o n u n i f o r m i t y i n t h e d i s t r i b u t i o n o f w a t e r f l u x e s i n t h e s p r a y l e d t o t h e n e c e s -s i t y o f d e t e r m i n i n g t h e l o c a l w a t e r f l u x e s i n d i f f e r e n t p o s i t i o n s w i t h i n t h e s p r a y . O n l y i n t h i s way c o u l d w a t e r f l u x e s be r e l a t e d t o t h e h e a t - t r a n s f e r c o e f f i c i e n t s a t c o r r e s p o n d i n g p o s i t i o n s i n t h e s p r a y . M e a s u r e m e n t s w e r e made by i n s e r t i n g c o l l e c t o r t u b e s i n t o t h e s p r a y a t f i x e d p o i n t s a n d d e t e r m i n i n g t h e amoun t o f w a t e r a r r i v i n g a t t h e c o l l e c t o r s i n a f i x e d t i m e . 6 9 Adjusting screws Moveable base Post guides Retaining screw Slotted rail Mounting ring l j ± / Spray nozzle Nozzle holder ^Slotted rail Sliding posts Moveable {as^mount Retaining bolt Front view Moveable mount Support rails ( bolted to frame ) Slotted rail Plan view ( nozzle mount removed ) ( not to scale ) Figure 15 Schemat ic diagram of the mount f o r the spray n o z z l e . 70 3 . 5 . 1 F a c t o r s A f f e c t i n g S p r a y F l u x M e a s u r e m e n t s The f o l l o w i n g f a c t o r s w e r e c o n s i d e r e d t o be i m p o r t a n t i n t h e c h o i c e o f t h e e x p e r i m e n t a l m e t h o d u s e d f o r t h e m e a s u r e m e n t s : i ) C o l l e c t i o n t i m e : S h o r t c o l l e c t i o n t i m e s c o u l d g i v e r i s e t o m i s l e a d i n g v a l u e s o f f l u x e s due t o t h e n o n - s t a b i l i z e d n a t u r e o f t h e s p r a y i m m e d i a t e l y a f t e r i n i t i a t i o n o r t e r m i n a t i o n o f s p r a y i n g . i i ) C o l l e c t o r t u b e s i z e : Use o f v e r y s m a l l c o l -l e c t o r t u b e s , c o u l d c a u s e t h e l a r g e r d r o p l e t s i n t h e s p r a y t o r e b o u n d f r o m t h e s e t u b e s , a n d l e a d t o t h e m e a s u r e m e n t o f l o w e r s p r a y f l u x e s t h a n w o u l d a c t u a l l y be p r e s e n t . i i i ) S p r a y a x i s a l i g n m e n t : A l i g n m e n t o f t h e s p r a y a x i s i n a v e r t i c a l p o s i t i o n s u c h t h a t t h e s p r a y f a c e d d o w n w a r d , m i g h t n o t i n d i c a t e t h e d i s t r i b u t i o n s p r a y f l u x e s a c t u a l l y p r e s e n t d u r i n g o p e r a t i o n o f t h e s p r a y s i n t h e c a s t i n g p r o c e s s w h e r e t h e s p r a y a x i s i s n o r m a l l y h o r i z o n t a l . 3 . 5 . 2 A p p a r a t u s The a p p a r a t u s u s e d t o m e a s u r e t h e s p r a y w a t e r f l u x d i s t r i b u t i o n i s shown i n F i g u r e 1 6 . I t c o n s i s t e d o f a 71 3 Copper collector tube ( n o t t o S C Q | e } 4 Plastic tube 5 Water receptacle Figure 16 Schemat ic diagram of the apparatus used f o r the  measurement o f spray water f l u x e s . 72 1 .6 mm ( 1 / 1 6 " ) t h i c k a l u m i n i u m s h e e t h e l d i n a v e r t i c a l p l a n e , i n w h i c h 13 h o l e s i n a h o r i z o n t a l l i n e w e r e d r i l l e d on 2 5 . 4 mm (1 i n ) c e n t r e s . C o p p e r t u b e s w i t h an O . D . o f 1 2 . 8 mm ( 0 . 5 in ) "and I . D . o f 1 0 . 6 mm ( 0 . 4 1 5 i n ) w e r e i n -s e r t e d t h r o u g h t h e h o l e s a n d a n c h o r e d s o t h a t t h e i r a x e s w e r e h o r i z o n t a l . B e h i n d t h e s h e e t , t h e t u b e s w e r e a n g l e d downward a t a b o u t 4 5 ° t o t h e h o r i z o n t a l . P l a s t i c h o s e s c o n n e c t e d t o t h e s e t u b e s c a r r i e d t h e w a t e r c o l l e c t e d t o a s e t o f p r e w e i g h e d g l a s s b e a k e r s w i t h a c a p a c i t y o f 250 m l . 3 . 5 . 3 E x p e r i m e n t a l P r o c e d u r e The s p r a y n o z z l e a x i s was a l i g n e d p a r a l l e l t o t h e a x i s o f t h e c o l l e c t o r t u b e s , and t h e n o z z l e was f i x e d a t a known d i s t a n c e f r o m t h e f r o n t o f t h e t u b e s . N o r m a l l y , t h e t u b e s w e r e a n c h o r e d s o t h a t t h e y p r o j e c t e d a d i s t a n c e o f 6 mm ( 1 / 4 i n ) f r o m t h e f r o n t o f t h e a l u m i n i u m s h e e t ( T y p e A e x p e r i m e n t , F i g u r e 1 6 a ) . The s p r a y was t h e n t u r n e d on and t h e w a t e r i n t e r c e p t e d by i n d i v i d u a l c o l l e c t o r t u b e s f l o w e d i n t o t h e g l a s s b e a k e r s . D e p e n d i n g on t h e s p r a y p r e s s u r e and t h e d i s t a n c e o f t h e n o z z l e t i p f r o m t h e p l a t e s u r f a c e , t h e s p r a y t i m e was c h o s e n s u c h t h a t a t l e a s t 200 g . o f w a t e r was c o l l e c t e d i n t h e b e a k e r c o r r e s p o n d i n g t o t h e c e n t r a l c o l l e c t o r t u b e . T h i s e x p e r i -ment was r e p e a t e d , s t a r t i n g w i t h e m p t y b e a k e r s , s o t h a t t h e c u m u l a t i v e s p r a y i n g t i m e f o r any s e t o f s p r a y c o n d i t i o n s was 73 a b o u t 10 m i n u t e s . T h i s p r o c e d u r e was f o l l o w e d t o r e d u c e t h e e f f e c t o f r a n d o m e r r o r s i n t h e m e a s u r e m e n t s . W h i l e s p r a y i n g on t h e p l a t e s u r f a c e , i t was o b s e r v e d t h a t a l a r g e q u a n t i t y o f w a t e r f l o w e d d o w n w a r d a l o n g t h e s u r f a c e o f t h e v e r t i c a l p l a t e . T h i s w i l l be r e f e r r e d t o as t h e " w a t e r c u r t a i n " . F o r t h e e v a l u a t i o n o f t h e e f f e c t o f t h e " w a t e r c u r t a i n " , t h e c o l l e c t o r t u b e s w e r e p l a c e d f l u s h w i t h t h e p l a t e s u r f a c e ( T y p e B e x p e r i m e n t , F i g u r e 1 6 b ) . T h u s , when t h e m e a s u r e m e n t s w e r e p e r f o r m e d , t h e m e a s u r e d w a t e r f l u x e s w e r e t h e sum o f t h e w a t e r a r r i v i n g a t t h e c o l -l e c t o r t i p s d i r e c t l y f r o m t h e s p r a y , and a l s o t h e w a t e r a r r i v i n g a t t h e c o l l e c t o r s as a c o n s e q u e n c e o f t h e p r e s e n c e o f t h e w a t e r c u r t a i n . F o r m o s t o f t h e n o z z l e s i n v e s t i g a t e d , w a t e r f l u x e s w e r e o b t a i n e d o n l y i n a h o r i z o n t a l l i n e p e r p e n d i c u l a r t o and c o i n c i d i n g w i t h t h e s p r a y a x i s ; h o w e v e r , i n t h e c a s e o f t h e 1 /4 GG 10 n o z z l e , more e x t e n s i v e m e a s u r e m e n t s w e r e p e r -f o r m e d . By m o v i n g t h e s p r a y n o z z l e a x i s i n 2 5 . 4 mm (1 i n ) i n c r e m e n t s i n t h e v e r t i c a l d i r e c t i o n , w i t h r e s p e c t t o t h e c o l l e c t o r t u b e s , a " m a p " o f t h e ' s p r a y f l u x e s t h r o u g h o u t t h e s p r a y c o n e was o b t a i n e d , w i t h and w i t h o u t t h e w a t e r c u r t a i n i . e . , b o t h w i t h c o l l e c t o r s f l u s h w i t h t h e p l a t e s u r f a c e , and c o l l e c t o r s p r o t r u d i n g f r o m t h e s u r f a c e . 74 The w a t e r f l u x e s i n s p e c i f i c p o r t i o n s o f t h e s p r a y w e r e c a l c u l a t e d f r o m t h e w e i g h t o f w a t e r c o l l e c t e d a t t h a t p o s i t i o n i n t h e s p r a y d u r i n g t h e s p r a y i n g p e r i o d . 3 . 6 S p r a y H e a t - T r a n s f e r M e a s u r e m e n t s The e s t i m a t i o n o f t h e h e a t - t r a n s f e r c o e f f i c i e n t s f o r d i f f e r e n t s p r a y i n g c o n d i t i o n s r e q u i r e s a k n o w l e d g e o f t h e s u r f a c e t e m p e r a t u r e o f t h e s o l i d b e i n g s p r a y e d a n d t h e t e m p e r a t u r e g r a d i e n t a t t h e s u r f a c e . S i n c e t h e d i r e c t m e a s u r e m e n t o f s u r f a c e t e m p e r a t u r e s p o s e s many p r o b l e m s , s u b s u r f a c e t e m p e r a t u r e m e a s u r e m e n t s w e r e made d u r i n g t h e s p r a y i n g i n t e r v a l and u s e d i n t h e c a l c u l a t i o n o f t h e h e a t -t r a n s f e r c o e f f i c i e n t s . T h i s s e c t i o n d e a l s w i t h t h e r e q u i r e m e n t s o f t h e t e m p e r a t u r e m e a s u r e m e n t s y s t e m , c r i t e r i a f o r t h e s e l e c t i o n o f t h e t e c h n i q u e u s e d , and t h e e x p e r i m e n t a l m e t h o d e m p l o y e d . 3 . 6 . 1 R e q u i r e m e n t s f o r t h e M e a s u r e m e n t , o f . T e m p e r a t u r e T r a n s i e n t s The m e a s u r e m e n t s y s t e m s h o u l d i n d i c a t e f a i t h -f u l l y and a c c u r a t e l y , t h e c h a n g e i n t h e t e m p e r a t u r e w i t h t i m e as t h e p o i n t o f m e a s u r e m e n t . The i n t r o d u c t i o n o f a t e m p e r a t u r e s e n s o r , i n t h i s c a s e , t h e r m o c o u p l e s , i n t o t h e 75 s o l i d , c a n a f f e c t t h e t h e r m a l f i e l d and t h e f l o w o f h e a t t h a t w o u l d be p r e s e n t i n t h e a b s e n c e o f t h e s e n s o r . P r o p e r p r e c a u t i o n s a r e t h u s n e c e s s a r y t o e n s u r e t h a t t h i s d i s r u p t i o n i s as s m a l l as p o s s i b l e , a n d a c o m p r o m i s e r e a c h e d b e t w e e n t h e d e s i r e d a c c u r a c y o f m e a s u r e m e n t and t h e i n t e r a c t i o n o f t h e m e a s u r i n g s e n s o r w i t h t h e h e a t f l o w . The m e t h o d s o f m i n i m i z i n g t h e e r r o r s i n m e a s u r e -m e n t s o f t h e t y p e u n d e r d i s c u s s i o n i n c l u d e t h e f o l l o w i n g : i ) U s i n g s m a l l i n s t a l l a t i o n s i z e s - i . e . s m a l l d i a m e t e r t h e r m o c o u p l e w i r e , w i t h a s s o c i a t e d s m a l l s i z e s o f i n s u l a t i n g t u b e s , a n d c o r -r e s p o n d i n g l y s m a l l h o l e s d r i l l e d f o r t h e i n -s e r t i o n o f t h e t h e r m o c o u p l e s . i i ) L o c a t i o n o f t h e s e n s o r ( t h e r m o c o u p l e ) as c l o s e as p o s s i b l e t o t h e s u r f a c e l o s i n g h e a t . i i i ) R e d u c t i o n o f t h e t h e r m a l r e s i s t a n c e b e t w e e n t h e s e n s o r a n d t h e p o i n t o f t e m p e r a t u r e m e a s u r e m e n t t o a m i n i m u m . i v ) L o c a t i n g t h e s e n s o r w i r e s i n an i s o t h e r m a l 91 92 r e g i o n f o r a t l e a s t 20 w i r e d i a m e t e r s . ' v ) U s i n g t h e r m o c o u p l e s w i t h a f a s t r e s p o n s e t o c h a n g i n g t e m p e r a t u r e s . T h e s e f a c t o r s a r e d e a l t w i t h i n d e t a i l b e l o w . 7 6 As m e n t i o n e d e a r l i e r , t h e i n t e r a c t i o n o f t h e s e n s o r s w i t h t h e h e a t f l o w m u s t be m i n i m i z e d , a n d as s u c h , t h e u s e o f s m a l l d i a m e t e r t h e r m o c o u p l e s , i n s u l a t i n g t u b e s , a n d s m a l l h o l e s b e c o m e s m a n d a t o r y i n m e a s u r e m e n t s o f t h e t y p e u n d e r d i s c u s s i o n . T h i s h o w e v e r i s o f f s e t by c o n s i d e r a t i o n s o f t h e e a s e o f p l a c e m e n t and t h e r e d u c t i o n o f t h e r m o c o u p l e l i f e a t h i g h t e m p e r a t u r e s as t h e w i r e s i z e i s r e d u c e d . E v a l u a t i o n o f t h e m e a s u r e m e n t e r r o r s r e s u l t i n g f r o m t h e i n t e r a c t i o n o f t h e t h e r m o c o u p l e s w i t h t h e h e a t f l o w h a s b e e n a t t e m p t e d , u s i n g b o t h n u m e r i c a l a n d a n a l y t i c a l t e c h n i -9 3 - 9 6 q u e s . T h e s e m e t h o d s i n v o l v e t h e s o l u t i o n o f t h e c o n -d u c t i o n e q u a t i o n i n t h e s o l i d a r o u n d an " i d e a l i z e d " t h e r m o -c o u p l e e m b e d d e d i n i t , u s i n g a p p r o p r i a t e b o u n d a r y c o n d i t i o n s . S i n c e t h e s e b o u n d a r y c o n d i t i o n s c a n be d e f i n e d o n l y f o r c e r t a i n i d e a l i z e d c o n d i t i o n s n o t met w i t h i n p r a c t i c e , an u n c e r t a i n t y i s i n t r o d u c e d r e g a r d i n g t h e e f f e c t i v e u s e o f t h e s o l u t i o n s o b t a i n e d by t h e s c h e m e s p r o p o s e d f o r t h e e s t i m a t i o n o f t h e e r r o r s . A l l t h e s o l u t i o n s p r o p o s e d a s s u m e t e m p e r a t u r e i n -d e p e n d e n t t h e r m o p h y s i c a l p r o p e r t i e s , b o t h o f t h e t h e r m o -c o u p l e , and o f t h e m a t e r i a l i n w h i c h t h e t e m p e r a t u r e i s m e a s u r e d . The t h e r m o c o u p l e i s c o n s i d e r e d t o be a homo-g e n o u s c y l i n d r i c a l m a t e r i a l , embedded i n a s e m i - i n f i n i t e 77 b o d y w i t h p e r f e c t t h e r m a l c o n t a c t , and p l a c e d n o r m a l t o a s e m i - i n f i n i t e s u r f a c e t h r o u g h w h i c h a t i m e v a r i a b l e h e a t f l u x p a s s e s . The c o n d i t i o n s i n v e s t i g a t e d i n c l u d e b o t h t h e c a s e s w h e r e t h e t h e r m o c o u p l e m a t e r i a l e i t h e r h a s a h i g h e r o r l o w e r t h e r m a l c o n d u c t i v i t y t h a n t h e s u r r o u n d i n g m a t e r i a l . 9 3 As p o i n t e d o u t by S p a r r o w , t h e c a l c u l a t i o n s o f e r r o r s i n t h e m e a s u r e m e n t s o f t e m p e r a t u r e t r a n s i e n t s i s a f o r m i d a b l e p r o b l e m , e v e n f o r r e l a t i v e l y s i m p l e p h y s i c a l s i t u a t i o n s , b e c a u s e t h e m a t h e m a t i c a l f o r m u l a t i o n r e q u i r e s t h e s o l u t i o n o f c o u p l e d p a r t i a l d i f f e r e n t i a l e q u a t i o n s . The m e t h o d s r e c o m m e n d e d t o r e d u c e t h e e r r o r s i n t r o d u c e d a r e t o u s e s m a l l d i a m e t e r t h e r m o c o u p l e w i r e , and t o use t h e r m o c o u p l e m a t e r i a l s w h o s e t h e r m o p h y s i c a l p r o p e r t i e s a p p r o x i m a t e c l o s e l y t h o s e o f t h e m a t e r i a l i n w h i c h t h e t e m p e r a t u r e s a r e t o be m e a s u r e d . When t h e s u r f a c e t e m p e r a t u r e a t t h e s u r f a c e o f a s o l i d b o d y i s s u b j e c t e d t o c h a n g e s o r p e r t u r b a t i o n s , t h e s e c h a n g e s a r e p r o p a g a t e d i n t o t h e s o l i d , b u t a r e p r o g r e s s i v e l y damped as t h e d i s t a n c e f r o m t h e s u r f a c e i n c r e a s e s . The p r o b l e m b e c o m e s more a c u t e as t h e t h e r m a l c o n d u c t i v i t y o f t h e s o l i d d e c r e a s e s . The e f f e c t o f t h e p o i n t o f m e a s u r e m e n t b e l o w t h e s u r f a c e on t h e e r r o r i n t h e c a l c u l a t e d h e a t - t r a n s f e r 97 c o e f f i c i e n t s h a v e b e e n c o m p u t e d by E c o n o m o p o u l o u s a n d p r e s e n t e d i n F i g u r e 1 7 . E x a m i n a t i o n o f t h e F i g u r e r e v e a l s t h a t t h e e r r o r d e c r e a s e s as t h e t h e r m o c o u p l e i s p l a c e d c l o s e r t o t h e s u r f a c e w h o s e t e m p e r a t u r e i s c h a n g i n g . 73 100 Figure 17 Dependence of the mean error in calculated heat-transfer coefficients on the distance of the _ — point of measurement below the cooled surface. 79 M e a s u r e d t e m p e r a t u r e s c o u l d be i n e r r o r when t h e r e i s a t h e r m a l r e s i s t a n c e b e t w e e n t h e m e a s u r i n g j u n c t i o n a n d t h e p o i n t a t w h i c h t h e s e m e a s u r e m e n t s a r e m a d e . T h i s i s i l -l u s t r a t e d i n t h e c a s e o f s p r i n g l o a d e d t h e r m o c o u p l e s by 91 O t t e r , who shows t h a t as t h e s p r i n g p r e s s u r e on t h e t h e r m o -c o u p l e a s s e m b l y i s i n c r e a s e d , b r i n g i n g t h e t h e r m o c o u p l e i n more i n t i m a t e c o n t a c t w i t h t h e p o i n t o f m e a s u r e m e n t , t h e m e a s u r e m e n t e r r o r d e c r e a s e s . E l i m i n a t i o n o r r e d u c t i o n o f t h i s c o n t a c t r e s i s t a n c e c a n be e f f e c t e d by p r o p e r w e l d i n g o f t h e t h e r m o c o u p l e j u n c t i o n t o t h e m a t e r i a l i n w h i c h m e a s u r e m e n t s a r e m a d e . An i s o t h e r m a l r e g i o n i n t h e t h e r m o c o u p l e w i r e c l o s e t o t h e m e a s u r i n g j u n c t i o n p r e v e n t s t h e g e n e r a t i o n o f a n y e . m . f . c a u s e d due t o t e m p e r a t u r e g r a d i e n t s i n t h e w i r e . T h e r m o c o u p l e r e s p o n s e t i m e b e c o m e s a v e r y i m p o r t a n t f a c t o r when f a s t t e m p e r a t u r e t r a n s i e n t s a r e b e i n g m e a s u r e d . As t h e mass o f t h e t h e r m o c o u p l e m e a s u r i n g j u n c t i o n i n -c r e a s e s , t h e t h e r m a l i n e r t i a o f t h e t h e r m o c o u p l e i n c r e a s e s , r e s u l t i n g i n an i n c r e a s e i n t h e r e s p o n s e t i m e o f t h e t h e r m o -c o u p l e t o a c h a n g i n g t e m p e r a t u r e i n i t s e n v i r o n m e n t . R e -d u c t i o n o f t h i s r e s p o n s e t i m e c a n be e f f e c t e d e i t h e r by r e d u c i n g t h e t h e r m a l mass o f t h e m e a s u r i n g j u n c t i o n ( b y u s i n g f i n e t h e r m o c o u p l e w i r e s w i t h s m a l l w e l d e d j u n c t i o n s ) , 80 9 8 99 o r by t h e u s e o f " i n t r i n s i c " t y p e t h e r m o c o u p l e s . ' T h i s i s b e c a u s e t h e l a t t e r t y p e o f t h e r m o c o u p l e h a s an i n s t a n t a n e o u s s t e p o u t p u t f o r a s t e p i n p u t . In s p i t e o f t h e l o w e r i n g o f t h e r e s p o n s e t i m e , t h e u s e o f s m a l l w e l d e d b e a d j u n c t i o n s i s d i s a d v a n t a g e o u s i n t h a t an u n -c e r t a i n t y a r i s e s as t o t h e e x a c t p o i n t c o n t r i b u t i n g t o t h e p r o d u c t i o n o f t h e t h e r m o e l e c t r i c e . m . f . H o l e s d r i l l e d f o r t h e i n s e r t i o n o f t h e t h e r m o c o u p l e s c o u l d be p l a c e d i n t h e c y l i n d r i c a l m e a s u r i n g p r o b e i n t h e t h r e e a l t e r n a t i v e c o n f i g u r a t i o n s i l l u s t r a t e d i n F i g u r e 1 8 . In t h e e x p e r i m e n t s p e r f o r m e d i n t h i s s t u d y , s e p a r a t e w i r e s w e l d e d t o t h e s t e e l h e a t - t r a n s f e r p r o b e w e r e u s e d t o o b t a i n t h e t e m p e r a t u r e t r a n s i e n t s w i t h i n t h e p r o b e . When" t h e t h e r m o c o u p l e h o l e s a r e p l a c e d p a r a l l e l t o t h e p r o b e a x i s , t h e e x a c t p o i n t w h e r e t h e t h e r m o c o u p l e s c o n t a c t t h e s t e e l p r o b e c a n be d e t e r m i n e d . On t h e o t h e r h a n d , i t h a s b e e n 9 5 r e p o r t e d t h a t t h i s g e o m e t r y i s l i k e l y t o c a u s e t h e l a r g e s t m e a s u r e m e n t e r r o r . P l a c i n g t h e t h e r m o c o u p l e s p e r p e n d i c u l a r t o t h e p r o b e a x i s , h o w e v e r , a i d s i n o b t a i n i n g an i s o t h e r m a l r e g i o n i n t h e t h e r m o c o u p l e w i r e a d j a c e n t t o t h e j u n c t i o n . U n f o r t u n a t e l y , when t h i s m e t h o d ' i s e m p l o y e d , t h e p o i n t a t w h i c h t h e m e a s u r e d t h e r m o e l e c t r i c e . m . f . i s b e i n g g e n e r a t e d i s u n c e r t a i n . R e f e r r i n g t o F i g u r e 1 8 , t h i s p o i n t c o u l d be a n y w h e r e b e t w e e n x and x + 2 r , w h e r e r i s t h e r a d i u s o f Cooled surface •Type 2 -I2r| Type I ( not to scale ) Figure 18 Three a l t e r n a t i v e c o n f i g u r a t i o n s f o r thermocouple  placement i n the heat t r a n s f e r probe. CO 82 t h e t h e r m o c o u p l e w i r e . A n g l i n g t h e h o l e t o t h e p r o b e a x i s a l s o has t h i s d i s a d v a n t a g e . S i n c e t h e e x a c t l o c a t i o n o f t h e p o i n t o f m e a s u r e -m e n t i s an i n p u t f o r t h e m e t h o d u s e d f o r t h e d a t a a n a l y s i s , t h i s was t h e o v e r r i d i n g c r i t e r i o n i n t h e c h o i c e o f l o c a t i n g t h e t h e r m o c o u p l e h o l e s p a r a l l e l t o t h e c y l i n d e r a x i s . In a d d i t i o n , t h e i n s t a l l a t i o n o f t h e t h e r m o c o u p l e w i r e s a n d i n s u l a t i o n , a n d s u b s e q u e n t w e l d i n g o f t h e t h e r m o c o u p l e w i r e t o t h e b o t t o m o f t h e b l i n d h o l e was f a c i l i t a t e d i n t h i s c a s e . E x p e r i m e n t s p e r f o r m e d u s i n g t h i s m e t h o d f o r d i f -f e r e n t h e a t - t r a n s f e r c o n d i t i o n s e s t a b l i s h e d t h e v a l i d i t y o f t h e u s e o f t h i s t e c h n i q u e f o r t h e r a n g e o f h e a t ^ t r a n s f e r c o e f f i c i e n t s o b t a i n e d i n t h i s w o r k . T h i s w i l l be d i s c u s s e d i n a l a t e r s e c t i o n . 3 . 6 . 2 S e l e c t . i on o f the S t e e l f o r t h e P r o b e M a t e r i a l In s e l e c t i n g t h e m o s t s u i t a b l e s t e e l f o r t h e p r o b e , t h e f o l l o w i n g f a c t o r s w e r e c o n s i d e r e d : i ) No s o l i d - s t a t e t r a n s f o r m a t i o n s s h o u l d o c c u r i n t h e s t e e l b e t w e e n room t e m p e r a t u r e and 1 1 0 0 ° C . i i ) T h e r e s h o u l d be m i n i m a l s c a l i n g d u r i n g h e a t i n g a n d s p r a y c o o l i n g . 83 i i i ) The s t e e l s h o u l d be s i m i l a r t o s t e e l s u s e d i n c o n t i n u o u s c a s t i n g . i v ) The t h e r m o p h y s i c a l p r o p e r t y d a t a f o r t h e s t e e l s h o u l d be a v a i l a b l e i n t h e t e m p e r a t u r e r e g i o n up t o a r o u n d 1 1 0 0 ° C f o r t h e h e a t - t r a n s f e r c a l c u l a t i o n s . On t h e b a s i s o f t h e f a c t o r s l i s t e d a b o v e , A I S I 304 s t a i n -l e s s s t e e l a p p e a r e d t o be m o s t s u i t a b l e . I t i s an a u s t e n i -t i c s t a i n l e s s s t e e l a t a l l t e m p e r a t u r e s , s h o w s an a c c e p t -a b l e s c a l i n g r e s i s t a n c e , h a s w e l l d o c u m e n t e d t h e r m o p h y s i c a l c h a r a c t e r i s t i c s , and i s c a s t c o n t i n u o u s l y i n b i l l e t a n d s l a b f o r m . 3 . 6 . 3 P r o b e F a b r i c a t i o n A 2 5 . 4 mm (1 i n ) d i a m e t e r r o d o f t h e s t a i n -l e s s s t e e l m a t e r i a l was u s e d t o make t h e p r o b e s , w h i c h w e r e e i t h e r 2 5 . 4 mm o r 31 mm ( 1 . 2 5 i n ) i n l e n g t h . T h i s l e n g t h was c u t f r o m b a r s t o c k and t h e s e c t i o n e d f a c e t o be s p r a y e d was t h e n p o l i s h e d t o 4 / 0 e m e r y g r i t . F i n e p o l i s h -i n g was s u b s e q u e n t l y p e r f o r m e d w i t h 5 m i c r o n d i a m o n d p a s t e t o g i v e t h e s a m p l e a s m o o t h , r e p r o d u c i b l e s t a r t i n g s u r f a c e . A s c h e m a t i c r e p r e s e n t a t i o n o f t h e s a m p l e i s shown i n F i g u r e .19. T h r e e s e t s o f two h o l e s e a c h w e r e d r i l l e d f r o m T C # I T C # 3 T C # 2 (a ) Face Polished With 5 Micron Diamond Paste. (t>) T C # Distance From Front Face 1 0-040 in. I mm 2 0 0 8 0 in. 2 mm 3 0-75 in. 1875mm Positions of holes for thermocouple Installation m/l 304 Stainless. Steel Figure 19 Schematic diagram o f the h e a t - t r a n s f e r probe w i th I n s t a l l e d thermocouples. 85 t h e r e a r o f t h e p r o b e ( t h e f a c e away f r o m t h e s p r a y e d f a c e ) so t h a t t h e e n d s o f e a c h s e t o f h o l e s t e r m i n a t e d a t 1 mm, 2 mm, a n d 19 mm ( 0 . 0 4 0 , 0 . 0 8 0 and 0 . 7 5 i n ) f r o m t h e s p r a y e d f a c e . The d i a m e t e r o f t h e h o l e s was 1 . 8 mm, a n d t h e b o t t o m o f t h e h o l e s w e r e made f l a t w i t h a f l a t t i p p e d d r i l l o f t h e same d i a m e t e r . As shown i n F i g u r e 1 9 b , t h e h o l e s w e r e p l a c e d w i t h i n a r a d i u s o f 4 mm o f t h e a x i s o f t h e c y l i n d e r . The h o l e s w e r e t h e n c l e a n e d o f c u t t i n g s w a r f a n d c u t t i n g f l u i d by i n j e c t i n g d e n a t u r e d a l c o h o l w i t h a h y p o -d e r m i c s y r i n g e . A f t e r e t c h i n g t h e i n s i d e o f t h e h o l e s w i t h a s o l u t i o n o f M a r b l e ' s e t c h (10 g . C u S Q 4 , 50 m l . H C 1 , 50 m l . w a t e r ) , t h e h o l e s w e r e t h e n c l e a n e d a g a i n w i t h a l c o h o l . The p r o b e , a f t e r b e i n g d r i e d , was t h e n r e a d y f o r t h e i n -s e r t i o n a n d w e l d i n g o f t h e t h e r m o c o u p l e l e a d s f o r t h e t e m -p e r a t u r e m e a s u r e m e n t s . The c a r e f u l c l e a n i n g d e s c r i b e d a b o v e was f o u n d t o be a b s o l u t e l y n e c e s s a r y , as t h e p r e s e n c e o f d i r t o r m o i s t u r e i n s i d e t h e h o l e s e i t h e r p r e v e n t e d t h e t h e r m o c o u p l e w i r e f r o m f u s i n g w i t h t h e s t e e l d u r i n g w e l d i n g , o r p r o d u c e d w e l d s t h a t f a i l e d p r e m a t u r e l y i n s e r v i c e . 3 . 6 . 4 S e l e c t i o n o f t h e T h e r m o c o u p l e M a t e r i a l The f o l l o w i n g c r i t e r i a w e r e s e l e c t i o n o f t h e t h e r m o c o u p l e m a t e r i a l : u s e d i n t h e 86 i ) The u p p e r o p e r a t i n g r a n g e o f t h e t h e r m o c o u p l e r e q u i r e d i s t o be g r e a t e r t h a n 1 1 5 0 ° C . i i ) The t h e r m o e l e c t r i c o u t p u t o f t h e t h e r m o c o u p l e s h o u l d be l a r g e t o o b t a i n max imum s e n s i t i v i t y i n t h e t e m p e r a t u r e m e a s u r e m e n t . i i i ) The t h e r m o c o u p l e m a t e r i a l s h o u l d h a v e t h e r m o -p h y s i c a l p r o p e r t i e s s i m i l a r t o t h o s e o f t h e p r o b e m a t e r i a 1 • i v ) The w e l d i n g o f t h e t h e r m o c o u p l e w i r e s t o t h e s t e e l p r o b e s h o u l d be e f f e c t e d e a s i l y . Of t h e m a t e r i a l s r e a d i l y a v a i l a b l e a n d o f t e n u s e d , C h r o m e l - A l u m e l t h e r m o c o u p l e s s a t i s f y t h e a b o v e c r i t e r i a , a n d t h e s e w e r e a d o p t e d i n t h e p r e s e n t w o r k . The u p p e r o p e r a t i n g t e m p e r a t u r e l i m i t o f t h i s t y p e o f t h e r m o c o u p l e i s a r o u n d 1 2 5 0 ° C , and t h e r e f o r e c a r e was t a k e n n o t t o e x c e e d a t e m p e r a t u r e o f 1 1 7 5 ° C d u r i n g t h e h e a t i n g c y c l e o f t h e p r o b e . The t h e r m o c o u p l e w i r e u s e d h a d a n o m i n a l d i a m e t e r o f 0 . 6 mm ( 0 . 0 2 5 i n ) . 3 . 6 . 5 T h e r m o c o u p l e i n s t a l l a t i o n S i n g l e b o r e m u l l i t e t u b e s w i t h an O . D . o f 1 .6 mm ( 1 / 1 6 i n ) and an I . D . o f 0 . 7 6 mm ( 0 . 0 3 0 i n ) w e r e c u t t o t h e r e q u i r e d l e n g t h s , s u c h t h a t t h e i r e d g e s w e r e r e a s o n a b l y f l a t . T h e s e w e r e t h e n i n s e r t e d i n t o t h e d r i l l e d 87 holes ; the thermocouple wires were inser ted into these tubes and spark welded into p lace , using the capac i tor discharge apparatus shown schemat ical ly in Figure 20. Experiments were f i r s t car r ied out to e s t a b l i s h the welding condit ions and procedure which would y i e l d s a t i s -factory welds at the bottom of a hole . These tests consisted of spark welding 0.6 mm thermocouple wires- of chromel and alumel onto cleaned and pol ished 304 s t a i n l e s s steel p l a t e s , such that the wire axis was perpendicular to the p l a t e . The wire was then pul led along i t s a x i s , and then bent at an angle to the axis to see whether f a i l u r e occurred at the weld. Though the welds withstood .the t e n s i l e forces along the axis of the wire very w e l l , any twist ing or bend-ing of the wire about i t s axis resul ted in a greater sus-c e p t i b i l i t y of the weld to f a i l . The procedure was re-peated at d i f f e r e n t values of capac i t ies and vo l tage , to e s t a b l i s h optimum values. Optimum condi t ions were obtained with a tota l capacity of 6950 MFD in the capac i tor bank, and voltages of 40 vol ts and 50 vol ts for alumel and chromel r e s p e c t i v e l y . The decay of voltage across the capaci tor bank during the welding was found to be d i f f e r e n t for welds that f a i l e d e a s i l y and those tha't did not. This decay was there-fore monitored with a Tektronix storage o s c i l l o s c o p e during welding. If the trace indicated that a poor weld had been D.C. Power Supply Charging switch Electrical lead Thermocouple w l r e Mullite tube Heat-transfer probe Capacitor bank Figure 20 Schematic diagram o f the c a p a c i t o r d i scha rge  we ld ing appara tus . CO CO 89 f o r m e d , t h e n t h e s a m p l e was n o r m a l l y d i s c a r d e d , s i n c e r e w e l d i n g was u s u a l l y f o u n d t o g i v e i n f e r i o r w e l d s t h a t f a i l e d q u i c k l y u n d e r s e r v i c e c o n d i t i o n s . In a d d i t i o n t o s e t t i n g up t h e v o l t a g e s and c a p a c i -t a n c e s i n t h e w e l d i n g c i r c u i t , c a r e h a d t o be t a k e n t h a t t h e e n d s o f t h e t h e r m o c o u p l e w i r e s p e r p e n d i c u l a r t o t h e w i a x i s w e r e f l a t - t h i s was done by f i l i n g o f f t h e e n d w i t h a j e w e l l e r s f i l e . The t h e r m o c o u p l e w i r e s a l s o h a d t o be p u s h e d i n t o t h e h o l e s i n a r e p r o d u c i b l e m a n n e r . W e l d s o f g o o d q u a l i t y w e r e o b t a i n e d when t h e n e g a t i v e t e r m i n a l f r o m t h e c a p a c i t o r bank was c o n n e c t e d t o t h e t h e r m o c o u p l e w i r e , w i t h t h e p o s i t i v e l e a d a t t a c h e d t o t h e s t a i n l e s s s t e e l . S i n c e n o n d e s t r u c t i v e p o s t - w e l d e x a m i n a t i o n was i m p o s s i b l e , g r e a t c a r e had t o be e x e r c i s e d d u r i n g t h e w e l d i n g o f t h e t h e r m o c o u p l e w i r e s t o t h e b o t t o m o f t h e b l i n d h o l e s . D u r i n g h a n d l i n g o f t h e p r o b e s a f t e r t h e t h e r m o c o u p l e w i r e s h a d b e e n w e l d e d i n p l a c e , any t w i s t i n g o f t h e w i r e was a v o i d e d t o r e d u c e t h e c h a n c e o f w e l d f a i l u r e . The t h e r m o c o u p l e w i r e s o u t s i d e t h e p r o b e w e r e e l e c t r i c a l l y i n s u l a t e d w i t h 3 mm ( 1 / 8 i n ) m u l l i t e ' d o u b l e b o r e t u b i n g f o r a d i s t a n c e o f 1 . 2 5 m e t r e s ( a b o u t 3 . 7 5 f t ) . 90 The e n d s o f t h e t h e r m o c o u p l e w i r e s w e r e c o n n e c t e d t o a t e r m i n a l b l o c k . 3 . 6 . 6 L e a d W i r e s a n d C o n n e c t i o n s The e l e c t r i c a l c o n n e c t i o n s made f r o m t h e t h e r m o c o u p l e s a r e shown i n F i g u r e 2 1 . F r o m t h e e n d o f t h e t e r m i n a l b l o c k , w h i c h was a s s u m e d t o be i s o t h e r m a l , 0 . 6 mm d i a m e t e r f i b r e g l a s s s h e a t h e d c h r o m e ! - a l u m e l t h e r m o c o u p l e w i r e s w e r e u s e d t o make c o n n e c t i o n s t o t h e c o l d j u n c t i o n . T h i s was an i c e - w a t e r m i x t u r e m a i n t a i n e d a t 0 ° C i n a Dewar f l a s k . The c o l d j u n c t i o n s w e r e made by w e l d i n g c o p p e r w i r e s t o t h e e n d s o f t h e t h e r m o c o u p l e l e a d s . From t h e c o l d j u n c t i o n , a l l l e a d w i r e s w e r e made o f c o p p e r , and t h r e e s e t s o f c o n n e c t i o n s w e r e t h e n made - t o a m u l t i p o i n t s w i t c h , a d i g i t a l v o l t m e t e r a n d a h i g h s p e e d r e c o r d e r . C o n n e c t i o n s t o t h e m u l t i p o i n t s w i t c h a l l o w e d t h e o u t p u t f r o m a n y t h e r m o c o u p l e t o be m o n i t o r e d c o n t i n u o u s l y d u r i n g t h e h e a t i n g c y c l e on a H o n e y w e l l E l e k t r o n i k 194 c h a r t r e c o r d e r . A s p e c i a l f i l t e r was u s e d i n t h e s e r e -c o r d e r s when i n d u c t i o n h e a t i n g was e m p l o y e d , t o f i l t e r o u t any e . m . f . p i c k e d up by t h e t h e r m o c o u p l e due t o i n d u c t i o n f r o m t h e c o i l . A m u l t i c h a n n e l d i g i t a l v o l t m e t e r (HP 2 0 7 0 A D a t a l o g g e r ) w i t h a v i s u a l d i g i t a l d i s p l a y m e a s u r e d t h e m i l l i v o l t o u t p u t f r o m t h e t h e r m o c o u p l e s . Heat- t ransfer probe Thermocouples Copper leads Spray nozzle N / 0 ° C Co ld junction Multipoint switch. Honeywell 1 5 0 8 C VISICORDER c Honeywell Accudata 106 Honeywell Electronik 194 H P 2 7 0 8 A Datalogger F igu re 21 E l e c t r i c a l connect ions to the reco rd ing equipment, AO 92 T e m p e r a t u r e t r a n s i e n t s d u r i n g t h e c o o l i n g o f t h e p r o b e f a c e by t h e s p r a y w e r e m o n i t o r e d on a h i g h s p e e d r e c o r d e r t o be d e s c r i b e d b e l o w . 3 . 6 . 7 The H i g h S p e e d R e c o r d e r A h i g h s p e e d r e c o r d e r w i t h a l o w i n e r t i a i n t h e r e c o r d i n g s y s t e m was n e c e s s a r y i n t h e e x p e r i m e n t s , b e c a u s e t h e t h - e r m o c o u p l e o u t p u t s c o u l d v a r y by a s much as 10 m V / s e c o n d . The e q u i p m e n t u s e d was a f i v e c h a n n e l H o n e y w e l l 1508C " V I S I C O R D E R " , w h i c h was an u l t r a v i o l e t r e c o r d e r . The t h e r m o c o u p l e o u t p u t s w e r e f e d i n t o H o n e y w e l l "ACCUDATA 1 0 6 " s i g n a l c o n d i t i o n e r s w h i c h t h e n p r o d u c e d d e f l e c t i o n s i g n a l s t o t h e g a l v a n o m e t e r s i n t h e V i s i c o r d e r . I t was n e c e s s a r y t o c a l i b r a t e t h e s i g n a l c o n d i -t i o n e r s s o t h a t a c h a n g e o f 1 mV i n t h e i n p u t c o r r e s p o n d e d t o a 1 cm d e f l e c t i o n on t h e c h a r t . The o u t p u t f r o m t h e s i g n a l c o n d i t i o n e r s was d e p e n d e n t n o t o n l y on t h e m i l l i v o l t i n p u t , b u t a l s o on t h e e x t e r n a l r e s i s t a n c e o f t h e c i r c u i t . T h e r e f o r e , t h e r e s i s t a n c e o f t h e t h e r m o c o u p l e s a n d l e a d w i r e s ( t y p i c a l l y 25 ohms) w e r e m e a s u r e d , u s i n g a K e i t h l e y O h m m e t e r , a c c u r a t e t o 0 . 5 ohm. A p r e c i s i o n r e s i s t a n c e b o x , w i t h c o r r e s p o n d i n g r e s i s t a n c e s s e t on i t was t h e n c o n n e c t e d 93 t o t h e s i g n a l c o n d i t i o n e r s , a n d u s i n g an i n t e r n a l l y g e n e r a t e d e . m . f . o f 1 t o 10 m i l l i v o l t s , t h e d e f l e c t i o n s o f t h e g a l v a n o m e t e r s w e r e a d j u s t e d t o t h e r e q u i r e d v a l u e s w i t h t h e h e l p o f a c a l i b r a t i o n p o t e n t i o m e t e r b u i l t i n t o t h e s i g n a l c o n d i t i o n e r s . S i n c e f u l l s c a l e d e f l e c t i o n on t h e c h a r t c o r -r e s p o n d e d o n l y t o 16 m i l l i v o l t s , and t h e t h e r m o c o u p l e s p r o d u c e d o u t p u t s o f a b o u t 45 m i l l i v o l t s a t 1 1 0 0 ° C , i n t e r n a l l y g e n e r a t e d s i g n a l s o f 30 m i l l i v o l t s f r o m t h e s i g n a l c o n d i t i o n e r s w e r e u s e d t o o f f s e t t h e s c a l e . 3 . 6 . 8 M o u n t i n g o f t h e H e a t - T r a n s f e r P r o b e s  f o r H e a t i n g E i t h e r o f two m e t h o d s , i n d u c t i o n h e a t i n g o r h e a t i n g i n a g a s f i r e d f u r n a c e , was u s e d t o h e a t t h e p r o b e s t o 1 1 0 0 ° C . The two s e t s o f e x p e r i m e n t s c o r r e s p o n d i n g t o t h e two t y p e s o f h e a t i n g a r e l a b e l l e d T y p e I a n d T y p e I I e x p e r i m e n t s , r e s p e c t i v e l y . S i n c e t h e a p p a r a t u s u s e d f o r e a c h t y p e was d i f f e r e n t , t h e s e w i l l be d i s c u s s e d s e p a r a t e l y . 3 . 6 . 8 . 1 Type I E x p e r i m e n t s A d i a g r a m o f t h e p r o b e i n s t a l l a t i o n u s e d i n t h i s s e r i e s o f e x p e r i m e n t s i s s h o w n i n F i g u r e 2 2 . •:'-:'::::'| Fiberfrax Insulation \ ^ 316 Stainless Steel Heater Block y//A 304 Stainless Steel Heat Transfer Sample Asbestos Sheet A l 2 0 3 Powder O Induction Coil o o o o o o da T C # 4 £ TC's # 1 , 2 8 3 F i g u r e 22 Door S c h e m a t i c d i a g r a m o f t h e p r o b e i n s t a l l a t i o n f o r t h e Type I h e a t t r a n s f e r e x p e r i m e n t s . 95 R e f e r r i n g t o t h i s F i g u r e , t h e i n s t r u m e n t e d p r o b e , A , was s h r i n k f i t t e d i n t o a A I S I 316 s t a i n l e s s s t e e l h o l l o w c y l i n d r i c a l h e a t e r b l o c k . w i t h 6 mm ( 1 / 4 i n ) o f t h e l e n g t h o f t h e p r o b e e x t e n d i n g f r o m t h e h e a t e r b l o c k . The c y l i n d r i c a l h e a t e r b l o c k was 75 mm (3 i n ) i n d i a m e t e r , 100 mm (4 i n ) i n l e n g t h and had an a x i a l h o l e B o f 20 mm d i a . ( 3 / 4 i n ) , e x c e p t f o r a l e n g t h o f a b o u t 19 mm ( 3 / 4 i n ) i n t h e r e g i o n w h e r e t h e p r o b e was i n s t a l l e d . H e r e t h e d i a m e t e r was a b o u t 25 mm (1 i n ) . The a x i a l h o l e s e r v e d as a p a s s a g e f o r t h e t h e r m o c o u p l e w i r e s . T h i s h o l e was t h e n f i l l e d w i t h a l u m i n a p o w d e r f o r i n s u l a t i n g p u r p o s e s a f t e r t h e i n s t a l l a t i o n o f t h e p r o b e . The p o r t i o n o f t h e h e a t t r a n s f e r p r o b e p r o t r u d i n g f r o m t h e h e a t e r b l o c k was t h e n c e m e n t e d w i t h a l u m i n a c e m e n t i n t o a 2 5 . 4 mm (1 i n ) h o l e i n a v e r t i c a l a s b e s t o s p l a t e , C , w h i c h was 6 mm ( 1 / 4 i n ) t h i c k , s u c h t h a t t h e p o l i s h e d f a c e o f t h e p r o b e was f l u s h w i t h t h e s u r f a c e o f t h e a s b e s t o s s h e e t . An a s b e s t o s d o o r , D, was t h e n hung i n f r o n t o f t h e b l o c k . T h i s d o o r was s u s p e n d e d f r o m a s o l e n o i d a r r a n g e m e n t , w h i c h c a u s e d t h e d o o r t o f a l l when t h e s o l e n o i d was t r i p p e d . An i n s u l a t i n g l a y e r o f F i b r e f r a x w a s t h e n w r a p p e d a r o u n d t h e h e a t e r b l o c k , and t h e a s s e m b l y e n c l o s e d i n an i n d u c t i o n c o i l . 96 P o w e r t o t h e c o i l was p r o v i d e d f r o m an I n d u c t o t h e r m m o t o r g e n e r a t o r u n i t . The t e m p e r a t u r e o f t h e h e a t e r b l o c k was m o n i t o r e d w i t h a t h e r m o c o u p l e m a r k e d TC #4 i n t h e F i g u r e . The p o w e r i n p u t t o t h e c o i l was b e t w e e n 1 a n d 2 KW, w h i c h h e a t e d t h e p r o b e t o 1 0 0 0 ° C i n a b o u t 40 t o 60 m i n . S l o w h e a t i n g was u s e d t o m i n i m i z e t h e t e m p e r a t u r e g r a d i e n t a l o n g t h e a x i s o f t h e p r o b e . The t h e r m a l g r a d i e n t s e x i s t i n g i n t h e p r o b e a t t h e i n s t a n t o f t h e i n i t i a t i o n o f s p r a y c o o l i n g was l e s s t h a n 1 0 ° C p e r c m . When t h e t e m p e r a t u r e o f t h e p r o b e r e a c h e d t h e r e -q u i r e d s t a r t i n g t e m p e r a t u r e , t h e V i s i c o r d e r was t u r n e d o n , t h e s p r a y was s t a r t e d a n d s t a b i l i z e d , a n d w i t h i n 2 s e c o n d s , t h e s o l e n o i d h o l d i n g up t h e d o o r was t r i p p e d . When t h e s p r a y i m p i n g e d on t h e s a m p l e , t h e p r o b e c o o l e d r a p i d l y , and t h e t r a n s i e n t s m e a s u r e d by t h e t h e r m o -c o u p l e s w e r e r e c o r d e d on t h e V i s i c o r d e r . 3 . 6 . 8 . 2 Type I I E x p e r i m e n t s In t h i s c a s e , t h e p r o b e was m o u n t e d i n a 304. s t a i n l e s s s t e e l p l a t e , - and t h e w h o l e a s s e m b l y h e a t e d i n a gas f i r e d f u r n a c e b e f o r e s p r a y i n g w a t e r on t h e p r o b e f a c e . A d i a g r a m o f t h e i n s t a l l a t i o n i s s h o w n i n F i g u r e 2 3 . A 2 5 . 4 mm (1 i n ) d i a m e t e r h o l e was d r i l l e d i n 97 AISI 3 0 4 Stainless steel plate Spray nozzle Heat - transfer probe Fibref rax insulation Thermocouples ( not to scale ) F igure 23 Schemat ic diagram of the probe i n s t a l l a t i o n f o r the Type I Ia heat t r a n s f e r expe r imen t s . 98 t h e m i d d l e o f t h e A I S I 304 s t a i n l e s s s t e e l p l a t e , o f d i m e n s i o n s 406 mm x 203 mm x 2 5 . 4 mm (16 i n x 8 i n x 1 i n ) . The p r o b e was t h e n p r e s s f i t t e d i n t o t h e h o l e , w i t h i t s p o l i s h e d s u r f a c e f l u s h w i t h t h e p l a t e f a c e . The i n s u l a t i n g t u b e s s u r r o u n d i n g t h e t h e r m o c o u p l e s i n t h e v i c i n i t y o f t h e p r o b e w e r e a n c h o r e d t o t h e p l a t e w i t h s c r e w s a n d s t r a p p i n g . The end o f t h e p r o b e , a t t h e t h e r m o c o u p l e e x i t , a n d i t s s u r r o u n d i n g s w e r e i n s u l a t e d w i t h " F i b r e f r a x " i n s u l a t i n g w o o l . (_ Type I Ia exper iments ) As shown i n F i g u r e 2 4 , t h e p l a t e was t h e n a t t a c h e d by b o l t s t o a t i l t a b l e m o u n t B m o u n t e d on a m o v a b l e t r o l l e y C . The s p r a y h o l d e r was a l s o m o u n t e d on t h e t r o l l e y s w i t h t h e s p r a y a x i s h o r i z o n t a l . The t i l t a b l e m o u n t a l l o w e d t h e p l a t e t o be p o s i t i o n e d i n a h o r i z o n t a l p o s i t i o n i n t o a gas f i r e d f u r n a c e D. When t i l t e d 9 0 ° f r o m t h i s p o s i t i o n , t h e p l a t e was b r o u g h t i n t o a v e r t i c a l p o s i t i o n , w i t h t h e p o l i s h e d p r o b e s u r f a c e f a c i n g t h e s p r a y . The p l a t e was f i r s t h e a t e d up i n t h e g a s f i r e d f u r n a c e i n w h i c h t h e a t m o s p h e r e was k e p t n e u t r a l o r s l i g h t l y r e d u c i n g , i n o r d e r t o m i n i m i z e - the o x i d a t i o n o f t h e p r o b e s u r f a c e . In m o s t o f t h e e x p e r i m e n t a l r u n s , a s t a i n l e s s s t e e l c a p , a b o u t 15 cm (6 i n ) s q u a r e and 2 . 5 cm (1 i n ) d e e p was p l a c e d o v e r t h e f a c e o f t h e p r o b e , a n d n i t r o g e n was p a s s e d i n t o t h e c a p , t o f u r t h e r r e d u c e t h e o x i d a t i o n o f t h e Figure 24 Photograph of the heating plate mounted on the ti ltable mount. 100 p r o b e f a c e i n t h e f u r n a c e . When t h e p l a t e r e a c h e d t h e d e s i r e d t e m p e r a t u r e , t h e c a p was r e m o v e d , t h e moun t moved away f r o m t h e f u r n a c e , and t h e p l a t e t i l t e d up i n t o t h e v e r t i c a l p o s i t i o n . The V i s i c o r d e r was a c t i v a t e d , and a f t e r t u r n i n g on t h e s p r a y , t h e o u t p u t o f t h e t h e r m o c o u p l e s m o n i t o r e d on t h e h i g h s p e e d r e c o r d e r . In o r d e r t o i n v e s t i g a t e t h e c o o l i n g e f f e c t o f w a t e r f l o w i n g down t h e p l a t e s u r f a c e , e x p e r i m e n t s w e r e c a r r i e d o u t u s i n g 31 mm (1 1 /4 i n ) l o n g p r o b e s m o u n t e d i n t o t h e p l a t e . The f i r s t 6 mm ( 1 / 4 i n ) was t h e n f i t t e d w i t h a s t a i n l e s s s t e e l r i n g as shown i n F i g u r e 2 5 . I n t h i s c o n f i g u r a t i o n , t h e e n d o f t h e p r o b e was c o o l e d o n l y by t h e d r o p s o f w a t e r i m p i n g i n g on i t . ( T y p e l i b E x p e r i -m e n t ) \ 101 AISI 3 0 4 Stainless steel plate Stainless steel ring H e a t - transfer probe Fibrefrax insulation II It |«-25>|««—I •] Thermocouples ( not to scale ) F igure 25 Schemat ic diagram o f the probe i n s t a l l a t i o n f o r the Type l i b heat t r a n s f e r expe r imen t s . C h a p t e r 4 A N A L Y S I S OF THE MEASURED TEMPERATURE T R A N S I E N T S T h i s c h a p t e r p r e s e n t s t h e c o n v e r s i o n o f t h e t e m -p e r a t u r e - t i me c u r v e s o b t a i n e d f r o m t h e V i s i c o r d e r i n t o m a c h i n e r e a d a b l e f o r m , - a s w e l l as t h e m a t h e m a t i c a l m e t h o d e m p l o y e d t o c a l c u l a t e t h e h e a t - t r a n s f e r c o e f f i c i e n t v s . s u r f a c e t e m p e r a t u r e r e l a t i o n s h i p s f r o m t h e m e a s u r e d t r a n s i e n t s . 4 . 1 D i g i t i s i n g a n d S m o o t h i n g o f t h e T r a n s i e n t s The f i r s t s t e p i n t h e a n a l y s i s o f t h e m e a s u r e d d a t a was d i g i t i s i n g t h e t i m e - m i l l i v o l t t r a c e s o b t a i n e d on t h e V i s i c o r d e r . The c h a r t t r a c e s w e r e d i g i t i s e d e i t h e r u s i n g e i t h e r a " G r a d i c o n " d i g i t i s e r b e l o n g i n g t o t h e M e c h a n i c a l E n g i n e e r i n g D e p t . , U . B . C , o r a " T a l o s C y b e r -g r a p h " d i g i t i s e r l o c a t e d i n t h e C o m p u t e r C e n t r e , U . B . C . The f o r m e r d i g i t i s e r p r o v i d e d p u n c h e d c o m p u t e r c a r d s w i t h t h e x and y c o o r d i n a t e s ( w i t h r e g a r d t o a s e t o r i g i n ) o f t h e p o i n t b e i n g d i g i t i s e d . The l a t t e r m a c h i n e d i r e c t l y e n t e r e d t h e s e c o o r d i n a t e s i n t o a m a g n e t i c d i s c s t o r a g e u n i t . B o t h d i g i t i s e r s had a r e s o l u t i o n o f 0 . 0 0 1 i n c h . The d i g i t i s e d p o i n t s w e r e t h e n r e a d i n t o a d i g i t a l 102 103 c o m p u t e r ( i n i t i a l l y an IBM 3 7 0 / 1 6 8 and l a t e r an A m d a h l V6) and t h e m i l l i v o l t r e a d i n g s w e r e c o n v e r t e d t o t e m -p e r a t u r e s u s i n g a c o m p u t e r p r o g r a m w r i t t e n f o r t h e c o n -v e r s i o n s . The t i m e c o r r e s p o n d i n g t o e a c h d i g i t i s e d v a l u e o f v o l t a g e was o b t a i n e d u s i n g a c o n v e r s i o n f a c t o r d e p e n d -i n g on t h e c h a r t s p e e d i n t h e r e c o r d e r a n d t h e d i s t a n c e c o o r d i n a t e o f t h e d i g i t i s e d p o i n t . The t e m p e r a t u r e - t i m e t r a n s i e n t s w e r e t h e n s m o o t h e d by f i t t i n g a p o l y n o m i a l o f maximum d e g r e e 7 , w i t h t e m p e r a -t u r e as t h e d e p e n d e n t and t i m e as t h e i n d e p e n d e n t v a r i a b l e . The n e c e s s i t y o f s m o o t h i n g t h e t r a n s i e n t s h a s b e e n p o i n t e d 97 o u t by E c o n o m o p o u l o s . The d i f f e r e n c e b e t w e e n t h e d i g i -t i s e d a n d t h e f i t t e d v a l u e s w a s , i n m o s t c a s e s , l e s s t h a n 1° C . The f i t t e d v a l u e s w e r e t h e n u s e d a s i n p u t t o t h e c o m p u t e r p r o g r a m u s e d t o c a l c u l a t e t h e h e a t - t r a n s f e r c o -e f f i c i e n t s . T h i s p r o g r a m w i l l be d e s c r i b e d i n a l a t e r s e c t i o n o f t h i s c h a p t e r . 4 . 2 A n a l y s i s o f t h e T e m p e r a t u r e T r a n s i e n t s T h i s s e c t i o n d e s c r i b e s t h e s t e p s i n v o l v e d i n t h e a n a l y s i s o f t h e t e m p e r a t u r e t r a n s i e n t s m e a s u r e d i n s i d e t h e h e a t - t r a n s f e r p r o b e d u r i n g c o o l i n g by t h e w a t e r s p r a y . I n i t i a l l y , a d i s c u s s i o n o f t h e s o l u t i o n o f t h e c o n d u c t i o n e q u a t i o n t o c a l c u l a t e t h e v a r i a t i o n o f t h e t e m p e r a t u r e 104 w i t h i n a b o d y , u n d e r g o i n g h e a t i n g o r c o o l i n g u n d e r t h e i n -f l u e n c e o f known b o u n d a r y c o n d i t i o n s i s p r e s e n t e d . The m o d i f i c a t i o n o f t h i s s o l u t i o n t o t h e c a s e w h e r e t h e b o u n d a r y c o n d i t i o n s a r e t h e u n k n o w n s , a n d a r e t o be e v a l u a t e d , i s s u b s e q u e n t l y d i s c u s s e d . In t h e c a s e o f a s o l i d b o d y w h i c h i s l o s i n g h e a t t o i t s e n v i r o n m e n t , a t a r a t e t h a t i s p r o p o r t i o n a l t o t h e d i f f e r e n c e i n t h e t e m p e r a t u r e b e t w e e n t h e s u r f a c e o f t h e body and t h a t o f t h e e n v i r o n m e n t , t h e c o n t i n u i t y o f h e a t f l o w a t t h e s u r f a c e r e q u i r e s t h a t - k ST . = h (T - T ) . . . . . 4 . 1 ax 'g s a From t h i s e q u a t i o n , i t c a n be o b s e r v e d t h a t a k n o w l e d g e o f t h e s u r f a c e t e m p e r a t u r e a n d t h e t e m p e r a t u r e g r a d i e n t a t t h e s u r f a c e i s n e c e s s a r y i n o r d e r t o e v a l u a t e t h e h e a t - t r a n s f e r c o e f f i c i e n t . A c c u r a t e m e a s u r e m e n t s o f t h e s u r f a c e t e m p e r a t u r e , e s p e c i a l l y when t h e t h e r m a l e v o l u t i o n i s r a p i d , a n d i n t h e p r e s e n c e o f an a d v e r s e e n v i r o n m e n t , a r e e x t r e m e l y d i f -f i c u l t , a n d i n many c a s e s , i m p o s s i b l e . T h i s d i f f i c u l t y i s a v o i d e d by m e a s u r i n g s u b s u r f a c e t e m p e r a t u r e s w i t h i n t h e s o l i d a n d r e c o n s t r u c t i n g t h e v a r i a t i o n o f t h e s u r f a c e t e m p e r a t u r e s w i t h t i m e , by c a l c u l a t i o n . 105 As o p p o s e d t o t h e " D i r e c t P r o b l e m " , i n w h i c h t h e t e m p e r a t u r e v a r i a t i o n s i n a b o d y u n d e r g o i n g c o o l i n g o r h e a t i n g w i t h known b o u n d a r y c o n d i t i o n s c a n be c a l c u l a t e d u s i n g t h e l a w s o f u n s t e a d y s t a t e h e a t c o n d u c t i o n , t h e p r e s e n t p r o b l e m r e q u i r e s t h e s o l u t i o n o f t h e " I n v e r s e B o u n d a r y V a l u e P r o b l e m " i n h e a t c o n d u c t i o n t o d e t e r m i n e t h e s u r f a c e t e m p e r a t u r e s a n d s u r f a c e h e a t f l u x e s u s i n g m e a s u r e d v a l u e s o f t e m p e r a t u r e t r a n s i e n t s w i t h i n t h e b o d y . B o t h a n a l y t i c a l and n u m e r i c a l m e t h o d s h a v e b e e n p r o p o s e d t o a t t a c k t h i s p r o b l e m , as d i s c u s s e d b e l o w . I t m u s t be n o t e d , t h a t a l t h o u g h i n m o s t c a s e s , t h e t r e a t m e n t o f t h i s p r o b l e m i s w i t h r e s p e c t t o t h e c o o l i n g o f a b o d y , i t i s e q u a l l y a p p l i c a b l e t o t h e c a s e o f h e a t i n g o f s o l i d s . 4 . 2 . 1 P r e v i o u s S o l u t i o n s t o t h e I n v e r s e  B o u n d a r y V a l u e P r o b l e m v 4 . 2 . 1 . 1 A n a l y t i c a l and A n a l o g M e t h o d s S h u m a k o v 1 ^ has p r e s e n t e d a m e t h o d . o f s t e p - b y - s t e p c a l c u l a t i o n a p p l i c a b l e t o t h e h e a t i n g o f p l a n e p l a t e s , b a s e d on t h e a s s u m p t i o n t h a t t h e . b o u n d a r y c o n d i t i o n s r e m a i n c o n s t a n t f o r e a c h t i m e i n c r e m e n t . I n t h i s m e t h o d , t h e t e m p e r a t u r e d e p e n d e n c e o f t h e t h e r m o -p h y s i c a l p r o p e r t i e s o f t h e s o l i d c a n be t a k e n i n t o a c c o u n t . 97 H o w e v e r , i t has b e e n r e p o r t e d t h a t t h i s m e t h o d p r e s e n t s a s e v e r e l i m i t a t i o n when h i g h c o o l i n g o r h e a t i n g r a t e s a r e e n c o u n t e r e d , a n d i n m a t e r i a l s whose t h e r m a l d i f f u s i v i t i e s a r e r a t h e r l o w , as i n t h e c a s e o f s t e e l s . P a s c h k i s and S t o l t z 1 0 1 ' 1 0 2 h a v e m e a s u r e d t r a n s i e n t t e m p e r a t u r e s i n q u e n c h e d s a m p l e s o f s i l v e r a n d s t e e l , a n d h a v e u s e d an a n a l o g c o m p u t e r f o r t h e d e t e r m i n a t i o n o f t h e b o u n d a r y c o n d i t i o n s . 103 M i r s e p a s s i h a s r e p o r t e d a g r a p h i c a l m e t h o d f o r t h e s o l u t i o n o f t h e i n v e r s e p r o b l e m f o r s e m i - i n f i n i t e b o d i e s , b u t t h i s r e l a t e s t o s o l i d s i n w h i c h t h e t h e r m o -p h y s i c a l p r o p e r t i e s a r e t e m p e r a t u r e i n d e p e n d e n t . S t o l t z ^ 0 4 has u s e d a n u m e r i c a l i n v e r s i o n o f t h e a n a l y t i c a l s o l u t i o n o f t h e s i m p l i f i e d ' d i r e c t p r o b l e m ' , u s i n g t h e a s s u m p t i o n s o f c o n s t a n t t h e r m o p b y s i c a l p r o p e r t i e s a n d no i n t e r n a l h e a t g e n e r a t i o n . T h o u g h d e v e l o p e d f o r t h e c a s e o f s p h e r e s , i t c a n be e x t e n d e d t o s l a b s a n d c y l i n d e r s . He p o i n t s o u t t h a t i n t h e s o l u t i o n o f t h e p r o b l e m , c a l c u l a -t i o n s a r e b a s e d on t h e use o f t r u n c a t e d d a t a w h i c h h a v e b e e n d a m p e d , and t h a t u s i n g t o o s m a l l a t i m e s t e p i n t h e c a l c u l a t i o n s l e a d s t o o s c i l l a t i o n s i n t h e s o l u t i o n . An a d d i t i o n a l c o n s t r a i n t , w h i c h .a l s o ' a p p l i es t o some o f t h e o t h e r m e t h o d s i s t h a t t h e i n i t i a l t e m p e r a t u r e t h r o u g h t h e s o l i d i s a s s u m e d t o be u n i f o r m . 1 07 S p a r r o w e t a l . I U 0 h a v e p r e s e n t e d ~a more g e n e r a l , c o m p u t a t i o n a l l y s i m p l e t e c h n i q u e , w h i c h m a k e s i t p o s s i b l e t o u t i l i z e , i n some c a s e s , t h e g r a p h i c a l m e t h o d o f 103 M i r s e p a s s i t o s i m p l i f y m a j o r p a r t s o f t h e c a l c u l a t i o n s . The e q u a t i o n s h a v e been d e v e l o p e d f o r s p h e r e s , c y l i n d e r s a n d s l a b s , i n c l u d i n g c a s e s i n w h i c h t h e i n i t i a l t e m p e r a -t u r e s may be n o n - u n i f o r m w i t h i n t h e b o d y . B a s i c a l l y , t h e s o l u t i o n i n v o l v e s o b t a i n i n g a L a p l a c e t r a n s f o r m o f t h e u n -s t e a d y s t a t e c o n d u c t i o n e q u a t i o n , a n d u p o n s u b s t i t u t i o n o f t h e m e a s u r e d t e m p e r a t u r e s a t a p o i n t w i t h i n t h e b o d y , t h e s u r f a c e t e m p e r a t u r e c a n be c a l c u l a t e d as a c o m b i n a t i o n o f two t e r m s - - - an i n t e g r a l a n d t h e i n v e r s e L a p l a c e t r a n s f o r m o f a f u n c t i o n . The i n t e g r a t i o n i s e a s i l y p e r f o r m e d u s i n g n u m e r i c a l t e c h n i q u e s on a d i g i t a l c o m p u t e r . Once t h e s u r -f a c e t e m p e r a t u r e i s k n o w n , t h e a p p l i c a t i o n o f t h e s o l u t i o n o f t h e d i r e c t p r o b l e m y i e l d s t h e t e m p e r a t u r e d i s t r i b u t i o n i n t h e b o d y , a n d f r o m t h i s , t h e s u r f a c e h e a t f l u x e s a n d t h e s u r f a c e h e a t t r a n s f e r c o e f f i c i e n t s a r e e x t r a c t e d . , T h e m e t h o d i s r e p o r t e d t o p r o d u c e s m o o t h , n o n - o s c i l l a t i n g r e -s u l t s , b u t i s l i m i t e d t o t h e u s e ' o f c o n s t a n t t h e r m o p h y s i c a l p r o p e r t i e s . The u s e o f t h i s t e c h n i q u e i s f u r t h e r e l a b o r a t e d u p o n 108 CO c i by G a u g l e r and Corman i n t h e t r e a t m e n t o f t h e i r h e a t t r a n s f e r d a t a . The l a t t e r a u t h o r r e p o r t s t h a t t h e u s e . o f s m a l l t i m e s t e p s d i c t a t e d by t h e r a p i d c o o l i n g t r a n s i e n t s • o b t a i n e d i n h i s s t u d y , t e n d e d t o c a u s e s t a b i l i t y p r o b l e m s i n t h e s o l u t i o n . O t h e r t r e a t m e n t s o f t h e i n v e r s e p r o b l e m a r e a l s o a v a i l a b l e , ^ 0 6 " 1 0 9 b u t t h e y a r e l i m i t e d i n t h a t t h e y c a n n o t d e a l w i t h v a r i a b l e t h e r m o p h y s i c a l p r o p e r t i e s . 4 . 2 . 1 . 2 , N u m e r i c a l M e t h o d s U n l i k e t h e p r e v i o u s i n v e s t i g a t i o n s i n w h i c h t h e c a l c u l a t i o n s w e r e done by e i t h e r o n e o r a c o m b i n a t i o n o f a n a l o g c o m p u t e r s , a n a l y t i c a l s o l u t i o n s , a n d n u m e r i c a l i n t e g r a t i o n s o f p a r t s o f t h e s o l u t i o n , a p u r e l y n u m e r i c a l m e t h o d f o r t h e s o l u t i o n o f t h e i n v e r s e p r o b l e m h a s b e e n p r o p o s e d by E c o n o m o p o u l o s , L a m b e r t a n d G r e d a y . 6 9 ' 9 ^ ' ^ 1 ^ T h i s m e t h o d i n v o l v e s t h e r e p l a c e m e n t o f t h e p a r t i a l d e r i v a t i v e s i n t h e u n s t e a d y s t a t e c o n d u c t i o n e q u a t i o n w i t h f i n i t e d i f f e r e n c e s . No a s s u m p t i o n r e g a r d i n g t h e f u n c t i o n e x p r e s s i n g t h e v a r i a t i o n o f t h e s u r f a c e t e m p e r a t u r e o r h e a t f l u x i s m a d e , and t h i s t e c h n i q u e l e n d s i t s e l f t o t h e u s e o f v a r i a b l e t h e r m o p h y s i c a l p r o p e r t i e s . A s e t o f a l g e b r a i c e q u a t i o n s w h i c h a r e o b t a i n e d f o r t h e h e a t b a l a n c e s a t d i f f e r e n t 1 0 9 portions of the s o l i d is solved by the Gauss-Sie'del i t e r a t i v e technique to y i e l d the temperature d i s t r i b u t i o n in the body at a given time, and from t h i s , the surface heat f luxes and surface heat - t ransfer c o e f f i c i e n t s can be obtained. This method is useful even for the ana lys is of fast t ransients within the s o l i d which would ar ise from the presence of high heat f l u x e s . The e f fec ts of the inf luences of various parameters e . g . the distance of the point of temperature measurement below the sur face , the values of the space and time i n -crements used in the d i s c r e t i s a t i o n of the par t i a l der iva -t i v e s , the degree of accuracy of the i t e r a t i o n s e t c . on the computed resu l ts have been examined. 4 . 2 . 1 . 3 Other Related Solut ions A numerical s o l u t i o n of the inverse problem has been proposed for the determination of thermal c o n d u c t i v i t i e s of s o l i d s . ^ While a l l the above-mentioned methods for the so lu t ion of the inverse problem deal only 11 2 with un id i rec t iona l conduct ion, Imber has worked out a method for the so lu t ion of the problem in two dimensions. Both the above methods involve the simultaneous determination of temperature t ransients at various posi t ions in the body being heated or cooled. n o 4 . 2 . 2 M e t h o d E m p l o y e d i n t h e P r e s e n t Work A p u r e l y n u m e r i c a l t e c h n i q u e i s e m p l o y e d t o a n a l y z e t h e m e a s u r e d t e m p e r a t u r e t r a n s i e n t s , s i n c e t h i s m e t h o d has t h e f o l l o w i n g c a p a b i l i t i e s : i ) The p r e s e n c e o f n o n - u n i f o r m t e m p e r a t u r e s i n t h e h e a t - t r a n s f e r p r o b e as t h e i n i t i a l c o n d i -t i o n c o u l d be t a k e n i n t o a c c o u n t . i i ) The t e m p e r a t u r e d e p e n d e n t v a r i a t i o n o f t h e t h e r m o p h y s i c a 1 p r o p e r t i e s c a n be a c c o m m o d a t e d . i i i ) The e q u a t i o n s o b t a i n e d a r e e a s i l y s o l v e d i n a f a i r l y s i m p l e manne r on a d i g i t a l c o m p u t e r . The a p p r o a c h i n v o l v e s t h e d i v i s i o n o f t h e m e a s u r i n g s e c t i o n i n a d i r e c t i o n p e r p e n d i c u l a r t o t h e h e a t -f l o w d i r e c t i o n , p e r f o r m i n g h e a t b a l a n c e s on e a c h s l i c e , and t h e s i m u l t a n e o u s s o l u t i o n o f t h e s e t o f e q u a t i o n s o b t a i n e d t o y i e l d t h e v a l u e s o f t h e r e q u i r e d p a r a m e t e r s . The a s s u m p t i o n s u s e d i n t h e f o r m u l a t i o n o f t h e s o l u t i o n a r e : i ) The e x i s t e n c e o f . u n i d i r e c t i o n a l c o n d u c t i o n i n t h e s o l i d i n a d i r e c t i o n o u t o f , a n d p e r -p e n d i c u l a r t o , t h e f a c e o f t h e p r o b e b e i n g s p r a y e d . i i ) A b s e n c e o f s h a p e o r v o l u m e c h a n g e s i n t h e I l l h e a t - t r a n s f e r p r o b e due t o t e m p e r a t u r e c h a n g e s . i i i ) The t e m p e r a t u r e o f t h e s p r a y w a t e r i m p i n g -i n g on t h e p r o b e i s a s s u m e d t o be c o n s t a n t , e q u a l t o t h e m e a s u r e d t e m p e r a t u r e o f t h e w a t e r i n t h e s p r a y w a t e r d e l i v e r y s y s t e m . S i n c e t h e m a t e r i a l o f t h e p r o b e u s e d i n t h e m e a s u r e -m e n t s was A I S I 304 g r a d e s t a i n l e s s s t e e l , no h e a t e v o l u t i o n o c c u r s due t o p h a s e t r a n s f o r m a t i o n s . F i g u r e 26 shows t h e d i v i s i o n o f t h e h e a t - t r a n s f e r p r o b e i n t o n o d e s so t h a t h e a t b a l a n c e s c a n be p e r f o r m e d . S i n c e o n l y u n i d i r e c t i o n a l c o n d u c t i o n i s b e i n g c o n s i d e r e d , t h e c r o s s s e c t i o n o f t h e n o d e s i n t h e d i r e c t i o n p e r p e n d i -c u l a r t o t h e p a p e r i s c o n s i d e r e d t o be u n i t y , AX i s t a k e n as t h e s p a c i n g b e t w e e n t h e n o d e s i n t h e d i r e c t i o n o f h e a t c o n d u c t i o n . H o w e v e r , i t c a n be n o t e d t h a t t h e s u r f a c e node has o n l y h a l f t h i s t h i c k n e s s . The same h o l d s f o r t h e t h i c k n e s s o f t h e node a t t h e r e a r end o f t h e s a m p l e away f r o m t h e s p r a y e d f a c e , a t w h i c h t h e t e m p e r a t u r e was a l s o b e i n g m o n i t o r e d . To p e r f o r m t h e h e a t b a l a n c e s , t h e d i s -c r e t i s e d t r e a t m e n t o f t h e c o n d u c t i o n e q u a t i o n a s s u m e s t h a t t h e node s i z e s , a r e s m a l l e n o u g h t h a t t h e p o i n t a t t h e c e n t r e o f e a c h n o d a l v o l u m e h a s a t e m p e r a t u r e t h a t i s r e p r e s e n t a t i v e o f t h a t o f t h e w h o l e n o d a l v o l u m e . The node number n n-l n-2 n-3 m+l m m-l surface node 7 6 5 4 thermocouple positions Figure 26 D i v i s i o n o f the heat t r a n s f e r probe i n t o nodes. 113 , t i m e v a r i a b l e i s a l s o d i s c r e t i s e d i n t o s m a l l i n c r e m e n t s , and t h e h e a t b a l a n c e s a r e p e r f o r m e d f o r a l l n o d e s f o r e a c h t i m e i n c r e m e n t . 4 . 2 . 2 . 1 The D i r e c t P r o b l e m In o r d e r t o s i m p l i f y t h e p r e s e n t a -t i o n o f t h e e q u a t i o n s u s e d f o r t h e i n v e r s e p r o b l e m , t h e f o r m u l a t i o n f o r t h e ' d i r e c t p r o b l e m ' i s p r e s e n t e d f i r s t and t h e c h a n g e s s u b s e q u e n t l y made t o t h i s f o r m u l a t i o n to y i e l d t h e s o l u t i o n t o t h e ' r e v e r s e p r o b l e m " a r e t h e n d i s -c u s s e d . The t o t a l number o f n o d e s i s t a k e n t o be n , w i t h t h e node number i n c r e a s i n g f r o m t h e i n t e r i o r to t h e s u r f a c e l o s i n g h e a t . A s s u m i n g f o r t h e moment t h a t t h e t h e r m a l c o n -d u c t i v i t y r e m a i n s c o n s t a n t , a n d t h a t t h e r e i s no i n t e r n a l h e a t g e n e r a t i o n o r c o n s u m p t i o n w i t h i n t h e s o l i d , an i m p l i c i t f i n i t e d i f f e r e n c e s c h e m e c a n be u s e d t o p e r f o r m t h e h e a t b a l a n c e s on e a c h n o d e . I t i s t o be n o t e d t h a t t h e i n i t i a l t e m p e r a t u r e a t e a c h node i s a known q u a n t i t y . T h e n a f t e r an i n t e r v a l o f t i m e At t h e h e a t b a l a n c e f o r t h e i t h i n t e r i o r node y i e l d s k(T*_i - V - k(T* - T * + i } = p i C p i A x (T* - V ••• 4-2 A X " AX A t 114 The i n t e r f a c i a l a r e a b e t w e e n t h e n o d e s , a s m e n t i o n e d e a r 1 i e r , i s u n i t y . R e a r r a n g i n g t h i s e q u a t i o n and m o v i n g a l l t h e known v a l u e s t o t h e r i g h t h a n d s i d e o f t h e e q u a t i o n a n d t h e u n -knowns t o t h e l e f t , an e q u a t i o n o f t h e f o r m ic ic ic a . T. , . + b. T. + c T . . , = d . . . . 4 . 3 i l - T i i i i+ l i r e s u l t s , w h e r e t h e a , b , c r e p r e s e n t t h e c o e f f i c i e n t s o f t h e unknown t e m p e r a t u r e s . S i m i l a r e q u a t i o n s a r e o b t a i n e d f o r t h e o t h e r i n t e r i o r n o d e s . I f t h e t e m p e r a t u r e - t i m e r e l a t i o n s h i p f o r n o d e 1 i s k n o w n , t h e n t h e e q u a t i o n f o r t h e s e c o n d n o d e w i l l be o f t h e f o r m a 2 T 3 + b 2 T 2 = d 2 . . . 4 .4 F o r t h e s u r f a c e node n u m b e r e d n , i f t h e b o u n d a r y c o n d i t i o n i s o f t h e f o r m shown i n e q u a t i o n 4 . 1 , t h e n t h e h e a t b a l a n c e y i e l d s b T* + c T* = d . . . 4 . 5 . n n-1 n n n T h u s , c o n s i d e r i n g a l l t h e n o d e s , a s e t o f n-1 a l g e b r a i c e x p r e s s i o n s i s o b t a i n e d w h i c h a r e t o be s o l v e d s i m u l t a n e o u s l y i n o r d e r t o y i e l d t h e n-1 u n k n o w n t e m p e r a t u r e s , 115 as shown b e l o w . b c n n a n - l b n - l c n - l a n - 2 b n - 2 q n - 2 a 3 b 3 C 3 a 2 b 2 The r i g h t h a n d s i d e m a t r i x i s c o m p l e t e l y d e f i n e d , a s i s t h e c o e f f i c i e n t m a t r i x c o n t a i n i n g t h e a ' s , b ' s , and c * s . I t c a n be o b s e r v e d a b o v e , t h a t t h e c o e f f i c i e n t m a t r i x on t h e l e f t h a n d s i d e , c o r r e s p o n d s t o t h e f o r m o f a ' t r i - d i a g o n a l m a t r i x ' . B e c a u s e o f t h e s p e c i a l n a t u r e o f s u c h a m a t r i x , G a u s s i a n ' e l i m i n a t i o n o r c o m p l e x i t e r a t i o n s c h e m e s ( e . g . t h e G a u s s - S i e d e l i t e r a t i v e t e c h n i q u e ) n e e d n o t be u t i l i z e d t o s o l v e t h i s s e t o f e q u a t i o n s t o , o b t a i n t h e unknown t e m -p e r a t u r e s . I n s t e a d , a s i m p l e r e c u r s i v e m e t h o d , s o m e t i m e s 52 r e f e r r e d t o as t h e ' T h o m a s M e t h o d c a n be u s e d f o r t h e s o l u t i o n , a t a s a v i n g o f a c o n s i d e r a b l e a m o u n t o f c o m p u t a -t i o n . U s i n g t h e t e m p e r a t u r e s o l u t i o n t h u s o b t a i n e d , t h e * T n d n * V 1 d n - 1 * T n - 2 d n - 2 • • * T 3 • * T 2 . . . 4.6 116 p r o g r e s s i v e l y w i t h t i m e . 1 1 3 O t h e r n u m e r i c a l m e t h o d s a r e a l s o a v a i l a b l e t o p e r f o r m s u c h c a l c u l a t i o n s f o r t h e d i r e c t p r o b l e m , b u t t h e ' i m p l i c i t f i n i t e d i f f e r e n c e m e t h o d ' j u s t d i s c u s s e d h a s t h e a d v a n t a g e o f y i e l d i n g s t a b l e , n o n - o s c i l l a t i n g s o l u t i o n s f o r a w i d e r a n g e o f A t a n d A x . D e t a i l e d t r e a t m e n t s o f t h e n u m e r i -c a l s t a b i l i t y o f t h i s and o t h e r p r o c e d u r e s a r e a v a i l a b l e e l s e w h e r e . 1 1 3 - 1 1 6 The t r e a t m e n t o f v a r i a b l e t h e r m o p h y s i c a l p r o p e r t i e s i s a l s o s i m p l e i n t h e a b o v e m e t h o d . In p e r f o r m i n g t h e h e a t b a l a n c e s , a v e r a g e v a l u e s o f t h e t h e r m a l c o n d u c t i v i t i e s a r e u s e d f o r t h e c o n d u c t i o n t e r m b e t w e e n a n y two a d j a c e n t n o d e s b e i n g c o n s i d e r e d . T h e s e a r e b a s e d on t h e v a l u e o f t h e t h e r m a l c o n d u c t i v i t i e s c a l c u l a t e d f o r e a c h n o d e a t t h e t i m e a t w h i c h t h e t e m p e r a t u r e o f t h e node i s k n o w n . T h e v a l u e o f t h e s p e c i f i c h e a t i s a l s o c a l c u l a t e d f o r e a c h i n d i v i d u a l n o d e , d e p e n d i n g on t h e t e m p e r a t u r e o f t h e n o d e . To r e f i n e t h e s o l u t i o n f u r t h e r , i t e r a t i v e t e c h n i q u e s a r e u s e d , w h i c h i n -v o l v e s r e c a l c u l a t i n g t h e t h e r m o p h y s i c a l p r o p e r t i e s f o r t h e n o d e s u s i n g t h e t e m p e r a t u r e s c o m p u t e d a t t h e end o f t h e t i m e s t e p , a n d s o l v i n g t h e s e t o f s i m u l t a n e o u s e q u a t i o n s a g a i n . The p r o c e s s i s r e p e a t e d u n t i l t h e t e m p e r a t u r e s o l u t i o n s c o n v e r g e t o s p e c i f i e d l i m i t s . p r o c e s s i s r e p e a t e d f o r t h e n e x t t i m e s t e p , b u i l d i n g up t h e c h a n g e i n t h e t h e r m a l f i e l d 117 4 . 2 . 2 . 2 The I n v e r s e P r o b l e m M o v i n g on t o t h e p r o b l e m a t h a n d , t h e s u r f a c e t e m p e r a t u r e and t h e c o n v e c t i v e t y p e b o u n d a r y c o n d i -t i o n i . e . t h e h e a t - t r a n s f e r c o e f f i c i e n t , a r e u n k n o w n . How-e v e r , t h e t e m p e r a t u r e h i s t o r y o f an i n t e r i o r n o d e , s a y t h e mth n o d e , c l o s e t o t h e s u r f a c e , i s t h e m e a s u r e d i n p u t . The e q u a t i o n s d i s c u s s e d f o r t h e d i r e c t p r o b l e m s t h u s h a v e t o be r e s t r u c t u r e d t o p r o v i d e t h e v a l u e s o f t h e s e u n k n o w n s . A t t h e s u r f a c e n o d e , t h e a p p l i c a t i o n o f t h e h e a t b a l a n c e y i e l d s a non l i n e a r e q u a t i o n o f t h e f o r m a T* , + (b . + h) T* + h T = d . . . 4 .7 n n-1 n n a n * s i n c e b o t h h a n d T a r e u n k n o w n s . n The t h r e e o t h e r e q u a t i o n s t h a t n e e d c h a n g i n g i n v o l v e t h e b a l a n c e s f o r node m and t h e n o d e s f l a n k i n g n o d e m i . e . , n o d e s n u m b e r e d m-1 and m+1. The r e f o r m e d e q u a t i o n s w o u l d be a T* , + c T* , = d . . . 4 .8 m m-1 m m+1 m V l T m-2 + b m - l V l = d m - l 4 ' 9  bm+l C l + Cm+1 Tm+2 = dm+l . . . . 4 .10 The e n d r e s u l t i s t h a t , o n c e a g a i n , n-1 e q u a t i o n s i n 118 n-1 u n k n o w n s i s o b t a i n e d . H o w e v e r , t h e s y s t e m o f a l g e b r a i c e q u a t i o n s t o be s i m u l t a n e o u s l y s o l v e d i n c l u d e s o n e n o n -l i n e a r e q u a t i o n . The s o l u t i o n o f s u c h a s e t i s c o m p l e x , •and i s n o t p o s s i b l e w i t h t h e u s e o f t h e r e c u r s i v e f o r m u l a m e n t i o n e d e a r l i e r i n c o n n e c t i o n w i t h t r i d i a g o n a l m a t r i c e s . S i m p l i f i c a t i o n o f t h i s s y s t e m , h o w e v e r , i s e a s i l y e f f e c t e d u s i n g t h e o b s e r v a t i o n t h a t f o r n o d e s 1 t o m, t h e i n i t i a l a n d b o u n d a r y c o n d i t i o n s a r e c o m p l e t e l y d e f i n e d . As s u c h , t h e t h e r m a l f i e l d f o r t h i s s e c t i o n o f t h e s y s t e m c a n be o b t a i n e d e a s i l y by t h e use o f t h e s o l u t i o n t o t h e d i r e c t p r o b l e m . * From E q u a t i o n 4 . 8 , t h e v a l u e f o r T -j i s o b t a i n e d by s u b s t i t u t i o n o f t h e v a l u e o f Tm_-j> w h i c h h a s b e e n p r e v i o u s l y c a l c u l a t e d by s o l v i n g t h e s e t o f a l g e b r a i c e q u a t i o n s f o r n o d e s 1 t o m. S i m i l a r s u b s t i t u t i o n s made f o r t h e d i f f e r e n c e e q u a t i o n s f o r n o d e s m+2 t o n y i e l d t h e t e m p e r a t u r e s a t t h e s e n o d e s . S u b s t i t u t i o n o f t h e s e known t e m p e r a t u r e s i n t o E q u a -t i o n 4 . 7 y i e l d t h e h e a t - t r a n s f e r c o e f f i c i e n t s , a n d w i t h a s i m p l e f u r t h e r c a l c u l a t i o n , t h e s u r f a c e h e a t f l u x i s o b t a i n e d . The t i m e i s t h e n i n c r e m e n t e d and t h e o p e r a t i o n i s r e p e a t e d , y i e l d i n g t h e s u r f a c e t e m p e r a t u r e s and c o r r e s p o n d i n g h e a t -t r a n s f e r c o e f f i c i e n t s a n d s u r f a c e h e a t f l u x e s a s a f u n c t i o n o f t i m e . 119 4 . 3 V a l i d a t i o n o f t h e M a t h e m a t i c a l F o r m u l a t i o n U s e d As a f i r s t s t e p , a c o m p u t e r p r o g r a m b a s e d on u n i -d i r e c t i o n a l c o n d u c t i o n was w r i t t e n f o r t h e g e o m e t r y u s e d i n t h e p r e s e n t e x p e r i m e n t s , a s s u m i n g c o n s t a n t t h e r m o p h y s i c a l p r o p e r t i e s . The t h e r m a l h i s t o r y w i t h i n t h e s o l i d was t h e n c a l c u l a t e d f o r known b o u n d a r y c o n d i t i o n s , c h o s e n s u c h t h a t t h e a n a l y t i c a l s o l u t i o n s a v a i l a b l e c o u l d be u s e d t o c h e c k t h e c a l c u l a t i o n s - . T h i s s t e p was n e c e s s a r y s i n c e a n a l y t i c a l s o l u t i o n s f o r t r a n s i e n t h e a t c o n d u c t i o n a r e n o r m a l l y u n -a b l e t o h a n d l e v a r i a b l e t h e r m o p h y s i c a l p r o p e r t i e s o r c o m p l e x b o u n d a r y c o n d i t i o n s . Once t h e c o m p u t e r p r o g r a m w a s d e b u g g e d , so t h a t t h e n u m e r i c a l c a l c u l a t i o n s m a t c h e d t h e a n a l y t i c a l s o l u t i o n , i t was m o d i f i e d t o a c c e p t a v a r y i n g i n i t i a l t e m -p e r a t u r e d i s t r i b u t i o n i n t h e s o l i d , a n d t o a c c o m m o d a t e v a r i -a b l e t h e r m o p h y s i c a l p r o p e r t i e s . C a l c u l a t i o n s w e r e t h e n p e r -f o r m e d u s i n g t h i s p r o g r a m w i t h d i f f e r e n t h e a t - t r a n s f e r c o -e f f i c i e n t s as b o u n d a r y c o n d i t i o n s . A n o t h e r p r o g r a m , u s i n g t h e m a t h e m a t i c a l f o r m u l a t i o n d i s c u s s e d i n S e c t i o n 4 . 2 . 2 . 2 was t h e n w r i t t e n , a n d t h e t e m -p e r a t u r e t r a n s i e n t s o b t a i n e d f r o m t h e c a l c u l a t i o n s i n v o l v i n g t h e " d i r e c t p r o b l e m " w e r e s u p p l i e d as i n p u t , i n o r d e r t o b a c k - c a l c u l a t e t h e s u r f a c e t e m p e r a t u r e s a n d h e a t - t r a n s f e r c o e f f i c i e n t s . The t e m p e r a t u r e t r a n s i e n t s a t a d e s i g n a t e d p o s i t i o n was f i r s t s m o o t h e d u s i n g t h e p o l y n o m i a l f i t t i n g r o u t i n e m e n t i o n e d i n S e c t i o n 4 . 1 , s o as t o m a i n t a i n s i m i -l a r i t y b e t w e e n t h e h a n d l i n g o f t h e t e s t d a t a w i t h t h a t o f t h e e x p e r i m e n t a l d a t a . I n i t i a l t e s t s w e r e c a r r i e d o u t f o r t h e c a s e o f c o n s t a n t h e a t - t r a n s f e r c o e f f i c i e n t s . A s l i g h t l y d i f f e r e n t i n i t i a l c o n d i t i o n ( t e m p e r a t u r e d i s t r i b u t i o n i n t h e s o l i d ) t h a n t h a t u s e d t o c a l c u l a t e t h e t e m p e r a t u r e t r a n s i e n t s u s i n g t h e s o l u t i o n t o t h e ' d i r e c t p r o b l e m ' was t h e n i n t r o d u c e d i n t o t h e s o l u t i o n f o r t h e ' i n v e r s e p r o b l e m ' . T h i s was done t o o b s e r v e t h e s e n s i t i v i t y o f t h e s o l u t i o n t o t h e ' i n v e r s e p r o b l e m ' . The b a c k - c a l c u l a t e d h e a t - t r a n s f e r c o e f f i c i e n t s w e r e t h e n c o m p a r e d w i t h t h e v a l u e s u s e d t o g e n e r a t e t h e t e m p e r a t u r e t r a n s i e n t s . The r e s u l t s , f o r two 2 v a l u e s o f h e a t - t r a n s f e r c o e f f i c i e n t s , 2 . 0 9 4 a n d 4 . 1 9 kW/m K.. 2 ( 0 . 0 5 and 0 .1 c a l / c m s °C ) a r e shown i n F i g u r e s 27 a n d 28 r e s p e c t i v e l y . I t c a n be o b s e r v e d f r o m t h e s e F i g u r e s , t h a t t h e b a c k - c a l c u l a t e d h e a t - t r a n s f e r c o e f f i c i e n t s m a t c h t h e e x p e c t e d v a l u e s t o w e l l w i t h i n 5% a f t e r t h e f i r s t two o r t h r e e t i m e s t e p s ( o f 0 . 1 s d u r a t i o n ) , a n d t h a t t h e c a l -c u l a t e d s u r f a c e t e m p e r a t u r e s m a t c h t h e e x p e c t e d s u r f a c e t e m p e r a t u r e s v e r y W e l l . S u b s e q u e n t l y , t h e s u r f a c e h e a t -2 t r a n s f e r c o e f f i c i e n t was a l l o w e d t o v a r y f r o m 1 . 6 7 5 kW/m K a t 8 0 0 ° C t o 2 . 0 9 4 k W / m 2 K a t 1 0 0 0 ° C i n t h e s o l u t i o n s t o t h e ' d i r e c t p r o b l e m ' . The c a l c u l a t e d t e m p e r a t u r e t r a n -i e n t s a t 0 . 1 cm f r o m t h e s u r f a c e w e r e t h e n u s e d t o b a c k -c a l c u l a t e t h e s e c o e f f i c i e n t s i n t h e ' i n v e r s e p r o b l e m ' . 121 _ 1-47 CM j£ 2-09 1-88 h-1000 • 900 3 O o. E • 1 o a w 3 CO 800 — Expected • Obtained I Time (seconds) Figure 27 Comparison o f b a c k - c a l c u l a t e d va lues o f h e a t - t r a n s f e r c o e f f i c i e n t s and s u r f a c e tempera tu res  w i th expected v a l u e s , f o r h = 2.094 kW/m h. 122 2 5-02 E v. * 4-19] 3-35 lOOOh-u 0 €> 3 O © CL E © 900 800H © o o 3 CO 700 i i i • • — i i i Expected • Obtained — •\ — ^ 4 1 Time 2 (seconds) Figure 2.8 Comparison of back-calculated values of the heat- transfer coefficient and.surface temperatures  with expected values, for h = 4.19.kw7m2h. .123 The r e s u l t s p l o t t e d i n F i g u r e 2 9 , show v e r y g o o d a g r e e m e n t b e t w e e n t h e e x p e c t e d and c a l c u l a t e d v a l u e s . The e f f e c t o f u s i n g t r a n s i e n t s a t l a r g e r d i s t a n c e s f r o m t h e c o o l e d f a c e i s shown i n F i g u r e 3 0 . H e r e , t h e d i s t a n c e s u s e d w e r e 0 . 1 7 5 and 0 . 2 0 cm r e s p e c t i v e l y . A g a i n , v e r y g o o d a g r e e m e n t b e -t w e e n t h e c a l c u l a t e d a n d e x p e c t e d v a l u e s i s o b s e r v e d a f t e r t h e f i r s t two t i m e s t e p s . T h u s , i t was e s t a b l i s h e d w i t h t h e t e s t d a t a t h a t t h e m a t h e m a t i c a l f o r m u l a t i o n o f t h e ' I n v e r s e ' B o u n d a r y V a l u e P r o b l e m ' u s e d i n t h i s w o r k i s v a l i d , a n d p r e d i c t s t h e e x p e c t e d h e a t - t r a n s f e r c o e f f i c i e n t s w i t h a n a c c u r a c y o f w e l l w i t h i n 5% when u s e d w i t h t h e t e s t d a t a . i l 1 1 2-09 — • — - "~ ~ " — • ^ — • — * — • — " ~ % 1-88 — — „ - - . • — E x p e c t e d . •— ' 5 % limit w 1-67 ^ — - • Obtained — JZ 1-47 -i i l - —1 I I I I I 8 0 0 8 5 0 9 0 0 9 5 0 Surface Temperature °C F i g u r e 2 9 C o m p a r i s o n o f b a c k - c a l c u l a t e d v a l u e s o f t h e h e a t - t r a n s f e r c o e f f i c i e n t w i t h  e x p e c t e d v a l u e s , f o r h v a r y i n g w i t h s u r f a c e t e m p e r a t u r e . ro 2-30 (VI E J 1-88 1-67 1-47 I —- Expected - - 5 % limits o Distance below surface 0175 cm. 0-20 cm. „ - -cr • o • o — X 800 850 900 Surface Temperature *C 950 F i g u r e 30 C o m p a r i s o n o f b a c k - c a l c u l a t e d v a l u e s o f t h e h e a t - t r a n s f e r  c o e f f i c i e n t , u s i n g t r a n s i e n t s o b t a i n e d a t d i f f e r e n t d i s t a n c e s f r o m t h e c o o l e d f a c e . Chapter 5 RESULTS AND DISCUSSION The experimental f indings reported in th is chapter include measurements of spray water f luxes for various spray nozzles enumerated in Section 3.2, under a range of operat ing c o n d i t i o n s , and measurements of corresponding hea t - t rans fer c o e f f i c i e n t s . 5.1 Spray f lux measurements As described e a r l i e r in Chapter 3 on experimental methods, two types of spray c o l l e c t o r s were used in the charac te r i za t ion of the spray water d i s t r i b u t i o n . The Type A c o l l e c t i n g system measured the spray f lux a r r i v i n g at the t ips of the c o l l e c t o r s d i r e c t l y from the spray nozz le , while measurements with the Type B c o l l e c t o r s gave a measure of the combined volume of water a r r i v ing at the c o l l e c t o r s d i r e c t l y from the spray, and that flowing down-ward adjacent to the sprayed face under the inf luence of g r a v i t y . In this s e c t i o n , spray prof i les- obtained with both c o l l e c t i o n systems are presented. These correspond to the spray f luxes obtained with the hor izonta l ser ies of c o l l e c t o r tubes, with the axis of the middle tube being al igned with that of the spray nozzle . Measurements of spray f luxes were car r ied out for most of the sprays at 126 127 d i s t a n c e s o f 1 0 . 1 6 , 1 5 . 2 4 and 2 0 . 3 2 cm ( 4 , 6 a n d 8 i n ) r e s p e c t i v e l y f r o m t h e t i p o f t h e n o z z l e , a n d a t s p r a y p r e s s u r e s o f 0 . 1 3 , 0 . 2 7 a n d 0 . 4 1 MPa ( 2 0 , 40 a n d 60 p s i ) r e s p e c t i v e l y . 5 . 1 - 1 S p r a y F l u x e s f o r a 1 /4 GG 10 N o z z l e The m a j o r i t y o f t h e s p r a y f l u x m e a s u r e m e n t s w e r e made w i t h a 1 /4 GG 10 n o z z l e . T h i s n o z z l e p r o v i d e s a c o n i c a l s p r a y p a t t e r n , a n d i s known as a " f u l l c o n e " t y p e n o z z l e , i n w h i c h w a t e r e n t e r i n g t h e n o z z l e i s i m p a r t e d a s w i r l i n g m o t i o n by a s p e c i a l l y s h a p e d v a n e w i t h i n t h e n o z -z l e . 5 . 1 . 1 . 1 H o r i z o n t a l C e n t r e l i n e S p r a y P r o f i l e s -Type A C o l l e c t o r s A t y p i c a l h o r i z o n t a l c e n t r e l i n e s p r a y f l u x p r o f i l e o b t a i n e d f o r t h e 1 /4 GG 10 n o z z l e , a t a d i s t a n c e o f 1 5 . 2 4 cm (6 i n ) and f o r a s p r a y p r e s s u r e o f .41 MPa (60 p s i ) i s shown i n F i g u r e 3 1 . I t i s s e e n t h a t t h e s p r a y d i s t r i -b u t i o n i s n o t u n i f o r m , and i s c h a r a c t e r i z e d by a h i g h w a t e r f l u x i n t h e c e n t r e o f t h e s p r a y , and a r a p i d l y d e c r e a s i n g f l u x t o w a r d s t h e e d g e s o f t h e s p r a y p a t t e r n . A l t h o u g h t h e p u b l i s h e d s p r a y a n g l e f o r t h i s n o z z l e i s b e t w e e n 6 0 ° a n d 7 0 ° f o r t h i s s p r a y i n g c o n d i t i o n , i t c a n be o b s e r v e d t h a t t h e s p r a y c o v e r s a l a r g e r a r e a , c o r r e s p o n d i n g t o t h e i n c l u d e d a n g l e o f t h e s p r a y c o n e o f a b o u t 8 0 ° . Distance from centre (In) 6 4 2 0 2 ~i 1 1 « ~ " ' Distance from centre (cm) Figure 31 Typ i ca l h o r i z o n t a l c e n t r e l i n e p r o f i l e ob ta ined w i t h the 1/4 GG 10 n o z z l e , f o r a spray d i s tance of 15.24 cm and a spray p ressure o f .41 MPa. ro CO 129 5 . 1 . 1 . 1 . 1 D i f f e r e n c e s B e t w e e n S i m i l a r  S p r a y N o z z l e s D i f f e r e n c e s i n t h e s p r a y f l u x p r o f i l e s w e r e o b s e r v e d when d i f f e r e n t 1 /4 GG 10 s p r a y n o z z l e s w e r e u s e d u n d e r t h e same s p r a y i n g c o n d i t i o n s . The s p r a y f l u x p r o f i l e s w e r e n o t a l w a y s s y m m e t r i c a l a b o u t t h e c e n t r e l i n e , as c a n be s e e n f r o m t h e s p r a y f l u x p r o f i l e s i n F i g u r e 3 2 , f o r f o u r 1 /4 GG 10 n o z z l e s . T h e s e n o n - s y m m e t r i c a l s p r a y p a t t e r n s w e r e o b t a i n e d w i t h t h e s p r a y n o z z l e a x i s a c c u r a t e l y a l i g n e d w i t h t h e a x i s o f t h e c e n t r a l c o l l e c t o r t u b e . T h r e e s e t s o f m e a s u r e m e n t s o f s p r a y f l u x e s f o r o n e o f t h e 1 /4 GG 10 n o z z l e s a r e shown i n F i g u r e 3 3 . The r e -p r o d u c i b i l i t y o f t h e m e a s u r e m e n t s i s s e e n t o be e x c e l l e n t f r o m t h i s F i g u r e . T h i s was t y p i c a l o f m o s t o f t h e n o z z l e s , b u t i n a few c a s e s some s c a t t e r o f t h e m e a s u r e m e n t s was o b s e r v e d ( F i g u r e 3 4 ) , i n s p i t e o f g r e a t c a r e t o m e a s u r e w a t e r f l u x e s u n d e r i d e n t i c a l e x p e r i m e n t a l c o n d i t i o n s . I n v i e w o f t h e v a r i a b i l i t y b e t w e e n s i m i l a r n o z z l e s , s p r a y f l u x p r o f i l e s w e r e o b t a i n e d f o r e l e v e n 1 /4 GG 10 n o z z l e s . T h e a v e r a g e o f t h e e l e v e n s e t s o f m e a s u r e m e n t s i s p l o t t e d i n F i g u r e 3 1 . The e r r o r b a r s p l o t t e d on t h i s F i g u r e c o r -r e s p o n d t o l a l i m i t s on t h e a v e r a g e v a l u e s . The r e s u l t s o f t h i s s e r i e s o f m e a s u r e m e n t s d e m o n s t r a t e s t h a t t h e r e i s a m a n u f a c t u r i n g v a r i a b i l i t y i n t h e n o z z l e s , w i t h r e l a t i v e l y l a r g e v a r i a t i o n s , o f t h e o r d e r o f 30%, a n d as s u c h , t h e m e a s u r e d s p r a y f l u x e s f r o m any n o z z l e c o r r e s p o n d o n l y t o t h e s p r a y s o b t a i n e d f o r t h a t p a r t i c u l a r n o z z l e . T h i s i s an 130 from centre (In) 0 2 15-24 5 0 8 0 5 08 1016 Distance from centre (cm) 15-24 F i g u r e 32 V a r i a t i o n i n t h e m e a s u r e d s p r a y w a t e r f l u x e s f o r f o u r d i f f e r e n t 1 /4 GG 10 n o z z l e s . F i g u r e 33 R e p r o d u c i b i l i t y o f t h e s p r a y f l u x m e a s u r e -m e n t s f o r a 1 /4 GG 10 n o z z l e ( N o . 9 ) . 131 Distance from centre (In) 4 2 0 2 15-24 1016 5 0 8 0 5 0 8 (0-16 Distance from centre (cm) 15-24 F i g u r e 34 R e p r o d u c i b i l i t y o f t h e s p r a y f l u x m e a s u r e m e n t s f o r a 1 /4 GG 10 n o z z l e ( N u m b e r 4 ) . Distance from centre (in ) 4 2 0 2 10 E • vibrator In a vibrator out - L . _1_ 1524 1016 5 08 0 5 08 Distance from centre (cms.) 1016 15-24 F i g u r e 35 E f f e c t o f v i b r a t i n g t h e c o l l e c t o r s on t h e s p r a y w a t e r f l u x m e a s u r e m e n t s . 132 i m p o r t a n t p o i n t t o n o t e when a t t e m p t s a r e made t o c o r r e l a t e s p r a y h e a t - t r a n s f e r c o e f f i c i e n t s w i t h t h e s p r a y v a r i a b l e s . V e r y l i t t l e d a t a has b e e n r e p o r t e d i n t h e l i t e r a t u r e r e -g a r d i n g t h e v a r i a t i o n o f t h e s p r a y f l u x e s w i t h i n t h e s p r a y e d a r e a . The p o s s i b i l i t y o f v a r i a b i l i t y b e t w e e n s i m i l a r s p r a y n o z z l e s has a l s o n e v e r b e e n r e p o r t e d . F o r t h e r e m a i n d e r o f t h e m e a s u r e m e n t s , a n o z z l e e x h i b i t i n g t h e m o s t s y m m e t r i c a l s p r a y f l u x p r o f i l e was u s e d . 5 . 1 . 1 . 1 . 2 E f f e c t o f V i b r a t i n g t h e  C o l 1 e c t o r s A s i x t y h e r t z v i b r a t o r was c o n n e c t e d t o t h e p l a t e h o l d i n g t h e s p r a y c o l l e c t o r s i n o r d e r t o c h e c k w h e t h e r t h e r e was any r e s i s t a n c e t o t h e f l o w o f w a t e r t h r o u g h t h e c o l l e c t o r t u b e s . The d i f f e r e n c e o b t a i n e d w i t h a n d w i t h o u t t h e v i b r a t o r was s m a l l , a s shown i n F i g u r e 3 5 , o b t a i n e d f o r a n o z z l e o p e r a t e d a t a s p r a y p r e s s u r e o f 0 . 4 1 MPa ( 4 0 . p s i ) . In v i e w o f t h e s m a l l d i f f e r e n c e , v i b r a -t i o n o f t h e p l a t e was d i s c o n t i n u e d f o r a l l f u r t h e r m e a s u r e -m e n t s . 5 . 1 . 1 . 1 . 3 E f f e c t o f D i f f e r e n t  P r e s s u r i z i n g G a s e s S i n c e t h e r e was a p o s s i -b i l i t y t h a t t h e gas u s e d t o p r e s s u r i z e t h e w a t e r s y s t e m c o u l d d i s s o l v e i n t h e w a t e r and s u b s e q u e n t l y be r e l e a s e d 133 a t a t m o s p h e r i c p r e s s u r e a t t h e n o z z l e o r i f i c e , a f f e c t i n g t h e s p r a y s p r o d u c e d , t h r e e d i f f e r e n t g a s e s ( n i t r o g e n , a r g o n a n d a i r ) w e r e u s e d i n t h e p r e s s u r i z i n g s y s t e m . S p r a y f l u x p r o f i l e s w e r e t h e n m e a s u r e d , b u t no s i g n i f i c a n t d i f -f e r e n c e s i n t h e s p r a y p r o f i l e s w e r e o b t a i n e d due t o t h e d i f f e r e n t g a s e s . 5 . 1 . 1 . 1 . 4 E f f e c t o f S p r a y P r e s s u r e  a t C o n s t a n t D i s t a n c e F i g u r e 36 shows t h e s p r a y f l u x p r o f i l e s o b t a i n e d a t a d i s t a n c e o f 1 5 . 2 4 cm (6 i n ) f r o m t h e s p r a y n o z z l e ^ f o r t h r e e d i f f e r e n t s p r a y p r e s s u r e s o f 0 . 1 3 , 0 . 2 7 and 0 . 4 1 MPa ( 2 0 , 40 a n d 60 p s i ) r e s p e c t i v e l y . An i n c r e a s e i n t h e s p r a y p r e s s u r e i n c r e a s e s t h e s p r a y f l u x a t any p o i n t i n t h e s p r a y , b e c a u s e o f t h e i n c r e a s e i n t h e f l o w -r a t e o f w a t e r t h r o u g h t h e n o z z l e . The m a g n i t u d e o f t h e i n -c r e a s e , h o w e v e r , i s s m a l l e s t i n t h e c e n t r a l p o r t i o n o f t h e s p r a y , and b e c o m e s l a r g e r t o w a r d s t h e e d g e o f t h e s p r a y p a t t e r n . S i m i l a r r e s u l t s o b t a i n e d f o r s p r a y d i s t a n c e s o f 1 0 . 1 6 cm a n d 2 0 . 3 2 cm (4 a n d 8 i n ) a r e s h o w n i n F i g u r e s 37 and 3 8 . 5 . 1 . 1 . 1 . 5 E f f e c t o f S p r a y D i s t a n c e  a t C o n s t a n t P r e s s u r e The e f f e c t o f i n c r e a s i n g n o z z l e d i s t a n c e a t c o n s t a n t p r e s s u r e on t h e s p r a y f l u x 134 DISTANCE FROM CENTRE (INI 0 - 6 . O - 4 . 0 - 2 . 0 0 . 0 2 . 0 I 1 I ! I 4 . 0 6 . 0 o o . n CM O CM UJco. on-es CO NOZZLE 1/4GG10 DISTANCE 15.24 CMS PRESSURE PS 3 MPA. • 20 v 0 .13 A 40 0.27 O 60 /0 . 41 T - 3 5 . 2 4 - 1 0 . J 6 - 5 . 0 B 0 . 0 . 5 . 0 B DISTANCE FROM CENTRE KCM) ( N l O f M O 00 o n a r-' f M a in o CM o 1 0 . 1 6 1 5 . 2 4 Figure 36 E f f e c t o f spray p ressure a t cons tan t d i s t a n c e f o r a 1/4 GG 10 n o z z l e a t a d i s t a n c e o f 15.24 cm 135 o - 6 . 0 - 4 . 0 DISTANCE FROM CENTRE UN) - 2 0 0 . 0 2 . 0 i J J 4 . 0 _ J 5 . 0 = ea-rn o r-\ f M o ^ » , CM NOZZLE 1/4GG10 DISTANCE20.32 CMS PRESSURE PSI MPA • 20 0.'13 A 40 0 . 27 O 60. 0 .41 t o -es CO dirt". X ZD cn" Q_ CO o o o F igu re 38 E f f e c t o f spray p r e s s u r e a t c o n s t a n t d i s t a n c e f o r a 1/4 GG 10 n o z z l e , a t a d i s t a n c e o f 20 .32 cm. 136 o - 6 . 0 - 4 . 0 o . CO cv CM o — ^ . CM C O -O CO C C f ^ • o_ CO o C D ' o DISTANCE - 2 . 0 i • FROM CENTRE ( IN I 0 . 0 2 . 0 4 . 0 _ J 6 . 0 = N0Z2LE 1/4GG10 DISTANCE 1 0 . 1 6 CMS. PRESSURE PS I MPA CD. 20 0 . 1 3 A 40 0 . 2 7 O 60 0 . 4 ] CM CM o ' CM - 3 5 . 2 4 o n - 3 0 . 3 6 - 5 . 0 8 0 . 0 5 . 0 B DISTANCE FROM CENTRE (CMO -m—m a . in o . CM" o ' C5 O ' I D O 1 0 . 1 6 1 5 . 2 4 F i g u r e 37 E f f e c t o f sp ray p r e s s u r e a t c o n s t a n t d i s t a n c e f o r a 1/4 GG 10 n o z z l e , a t a d i s t a n c e o f 1 0 . 1 6 cm. 137 p r o f i l e s i s shown i n F i g u r e 39 f o r a s p r a y p r e s s u r e o f 0 . 2 7 MPa (40 p s i ) . As t h e d i s t a n c e i n c r e a s e s , i t c a n be o b s e r v e d t h a t , as e x p e c t e d , t h e a r e a o f t h e s p r a y c o v e r a g e i n c r e a s e s . The l a r g e s t e f f e c t , h o w e v e r i s t h e m a r k e d d r o p i n t h e s p r a y f l u x i n t h e c e n t r e o f t h e s p r a y as t h e s p r a y d i s t a n c e i n -c r e a s e s . The s p r a y p r o f i l e a l s o t e n d s t o b e c o m e more u n i f o r m as l a r g e r d i s t a n c e s , as s e e n f r o m t h e p r o f i l e o b t a i n e d a t a d i s t a n c e o f 2 0 . 3 2 cm (8 i n ) f r o m t h e n o z z l e . R e s u l t s p u b l i s h e d by M i z i k a r 7 6 f o r n o z z l e d i s t a n c e s o f 2 0 . 3 2 cm (8 i n ) a n d 1 0 . 1 6 cm (4 i n ) a r e a l s o p l o t t e d on t h i s F i g u r e , and a r e s e e n t o be l o w e r t h a n t h o s e o b t a i n e d i n t h i s i n -v e s t i g a t i o n . S i m i l a r r e s u l t s o b t a i n e d f o r s p r a y p r e s s u r e s o f 0 . 1 3 MPa a n d 0 . 4 1 MPa (20 a n d 60 p s i ) a r e g i v e n i n F i g u r e s 40 a n d 41 r e s p e c t i v e l y . The v a r i a t i o n o f t h e s p r a y w a t e r f l u x w i t h p r e s s u r e a n d d i s t a n c e a t t h e a x i a l c e n t r e l i n e o f t h e s p r a y , and a p o s i t i o n 5 . 0 8 cm (2 i n ) f r o m t h e c e n t r e l i n e a r e p l o t t e d i n F i g u r e s 42 a n d 43 f o r s p r a y p r e s s u r e s o f 0 . 1 3 , 0 . 2 7 a n d 0 . 4 1 MPa ( 2 0 , 40 and 60 p s i ) r e s p e c t i v e l y . I t s h o u l d be n o t e d t h a t t h e s p r a y f l u x a t t h e c e n t r e o f t h e s p r a y was a l w a y s h i g h e s t when t h e s p r a y n o z z l e was o p e r a t e d a t 0 . 2 7 MPa ( 4 0 p s i ) . 5 . 1 . 1 . 2 S p r a y F l u x Map f o r t h e 1 / 4 GG 10 N o z z l e S p r a y f l u x maps o f t h e s p r a y e d a r e a w e r e o b t a i n e d by m o v i n g t h e n o z z l e i n v e r t i c a l i n c r e m e n t s 138 . DISTANCE FROM CENTRE (IN) a - 6 . 0 - 4 . 0 - 2 . 0 0 . 0 2 . 0 _ ^ i i : 4 . 0 _l 6 . 0 o NOZZLE 1/4GG10 PRESSURE 0.27 MPA Mizikar7 5 DISTANCE IN CM • • 4 30 ..16 A 6 15.24 • O 6 20.32 . r-o O . GO T - 3 5 . 2 4 - ] 0 . ] 6 - S . 0 B 0 . 0 5 . 0 6 DISTANCE FROM CENTRE (CM) 10. 16 1 5 . 2 4 Figure 39 Effect of distance at constant pressure for a 1/4.GG 10  nozzle, for a spray pressure of 0.27 MPa. 139 o-6.0 -4.0 DISTRNCE -2.0 FROM CENTRE (IN) 0.0 2.0 4.0 _ l 6.Do r- -i CM CM O CM " NOZZLE 1/4GG10 PRESSURE 0.13 MPR DISTRNCE IN CM • 4 10.16 A 6 15.24 O 8 2.0.32 CM CM O CM O o in o m -35.24 -30.36 -5.08 0.0 5.08 DISTANCE FROM CENTRE (CM) 10. 16 15.24 Figure 40 E f f e c t o f d i s t ance a t cons tan t p ressure f o r a 14 GG 10 n o z z l e , f o r a spray p ressure o f 0 .13 MPa, 140 o - 6 . 0 -4 .0 DISTANCE FROM CENTRE (IN) -2 .0 0.0 o . m T -I o (M 2.0 JL 4.0 _ l 6 . 0 o NOZZLE 1/4GG10 PRESSURE 0 . 4 ] MPA - J S . 2 4 DISTANCE IN CM • 4 1 0 . 1 6 A 6 1 5 . 2 4 <3> 8 2 0 . 3 2 -30.16 - S . 0 6 0.0 5.08 DISTANCE FROM CENTRE (CM) . o ro o 10.16 Figure 41 E f f e c t o f d i s t a n c e at cons tan t p ressu re f o r a 1/4 GG 10 n o z z l e , f o r a spray p r e s s u r e o f 0.41 MPa, 141 Nozzle 2 18 16 to CM 14 £ | I2h u_ I 10 a CO 81 T to collector distance (In) 4 6 8 1 1/4 GG 10 Pressure psi MPa 5-08 10-16 15-24 20-32 Nozzle to collector distance (cm) F i g u r e 42 V a r i a t i o n o f s p r a y w a t e r f l u x w i t h p r e s s u r e and  d i s t a n c e a t t h e c e n t r e o f t h e s p r a y p r o d u c e d by  a 1 /4 GG 10 n o z z l e . \ 1 42 Nozzle 2 1 to collector distance (in) 4 6 8 T 16 14 F T 7 1/4 GG 10 Pressure psi MPa A 20 0-13 • 40 0-27 • 60 0-41 m <\> 12 E _J I I I  5-08 1016 15-24 20-32 Nozzle to collector distonce (cm) F i g u r e 43 V a r i a t i o n o f s p r a y w a t e r f l u x w i t h p r e s s u r e a n d  d i s t a n c e 5 . 0 8 cm f r o m t h e c e n t r e o f t h e s p r a y p r o d u c e d by a 1 /4 GG 10 n o z z l e . 143 o f 2 . 5 4 cm (1 i n ) a b o v e a n d b e l o w t h e a x i s o f t h e c e n t r a l c o l l e c t o r t u b e . The r e s u l t s o f t h e s e m e a s u r e m e n t s h a v e b e e n t a b u l a t e d i n A p p e n d i x I. C o n t o u r maps a n d t h r e e - d i m e n s i o n a l r e p r e s e n t a t i o n s o f t h e s p r a y f l u x p a t t e r n s a r e g i v e n i n t h i s s e c t i o n . 5 . 1 . 1 . 2 . 1 W a t e r F l u x e s O b t a i n e d w i t h Type A C o l l e c t o r s S p r a y f l u x c o n t o u r maps f o r a c o n s t a n t s p r a y p r e s s u r e o f 0 . 4 1 MPa ( 6 0 p s i ) a n d f o r n o z z l e d i s t a n c e s o f 1 0 . 1 6 c m , 1 5 . 2 4 c m , a n d 2 0 . 3 2 cm ( 4 , 6 a n d 8 i n ) a r e shown i n F i g u r e s 4 4 , 45 a n d 4 6 , r e s p e c t i v e l y . The m a r k i n g s on t h e c o n t o u r s r e p r e s e n t 10 t i m e s t h e s p r a y 2 f l u x i n 1/m s . An i n c r e a s e i n t h e s p r a y c o v e r a g e a s t h e n o z z l e d i s t a n c e i s i n c r e a s e d c a n be o b s e r v e d f r o m t h e s e F i g u r e s . In a d d i t i o n , i t c a n be s e e n t h a t t h e c o n t o u r s show a c o n s i d e r a b l e a m o u n t o f c i r c u l a r s y m m e t r y a b o u t t h e c e n t r e l i n e o f t h e s p r a y . C o n t o u r maps o f t h e s p r a y f l u x e s f o r t h e o t h e r c o n d i t i o n s u n d e r w h i c h t h e m e a s u r e m e n t s w e r e c a r r i e d o u t a r e g i v e n i n A p p e n d i x I I . T h r e e d i m e n s i o n a l r e p r e s e n t a t i o n s o f t h e d a t a h a v e a l s o b e e n p r o d u c e d , a n d one s u c h r e p r e s e n t a t i o n o f t h e s p r a y map f o r a n o z z l e d i s t a n c e o f 1 5 . 2 4 cm (6 i n ) a n d a s p r a y p r e s s u r e o f 0 . 2 7 MPa (40 p s i ) i s shown i n F i g u r e 4 7 . The s h a r p p e a k i n t h e m i d d l e o f t h e s p r a y i s e v i d e n t i n t h e F i g u r e , a s a r e t h e p l a t e a u s i n t h e d i s t r i b u t i o n s a t a d i s t a n c e a p p r o x i m a t e l y 144 •12.7 , V E R T I C A L D I S T A N C E FROM CENTRE t'CMS.l -10.16 -7.62 -5.08 -2.54 0.0 2.54 5.08 "7.G2 10.16 12. 7 -vJ - 5 .0 - 4 . 3 - 3 . C - 2 . 0 - 1 . 0 0 . 0 1.0 -2 0 V E R T I C A L D I S T A N C E FROM CENTRE f ' l N . i 3.0 r 4 . 0 5 . 0 F igure 44 Spray f l u x contour maps f o r a 1/4 GG 10 n o z z l e f o r a n o z z l e  d i s t a n c e of 10.16 cm and spray p r e s s u r e o f 0.4-1 MPa  (Type A c o l l e c t o r s ) . -12. ° i X) o n —(Ul JO* m o -3D.56 I . VERTICAL DISTRNCE FROM CENTRE (C.MS.l -T.62 -5.08 -2.54 0.0 2 . H S.C8 _ J J I 1 1 1 "1.62 IC. 16 _ J ^ -5.0 -4.0 -3.0 -2 0 -J .0 0.0 ! .0 2.'. VERTICAL DISTRNCE FROM CENTRE. (IN.I ~ l — 3.0 4.0 Figure 45 Spray f l u x contour maps f o r a 1/4 GG 10 n o z z l e f o r a n o z z l e  d i s t a n c e o f 15.24 cm and spray p r e s s u r e o f 0.41 MPa  (Type A c o l l e c t o r s ) . 146 VERTICAL DISTANCE FROM CEN1RE (CMS.1 -12.1 - l i ) . ]6 --7.62 -S.08 -2.54 0.0 2.54 5.08 7.52 10.16 12.7 _i : 1 1 1 1 1 1 1 1 ; Li, VERTICAL DISTANCE FROM CENTRE S IN . ) Figure 46 Spray f l u x contour maps f o r a 1/4 GG 10 n o z z l e f o r a n o z z l e  d i s t a n c e of 20.32 cm and spray p ressu re o f 0.41 -MPa (Type A c o l l e c t o r s ) . Figure 47 Three dimensional representation of the spray fluxes for the 1/4 GG 10 nozzle for  a nozzle distance of 15.24 cm and spray pressure of 0.27 MPa. 148 h a l f w a y b e t w e e n t h e c e n t r e a n d t h e e d g e o f t h e s p r a y . F u r t h e r on t o w a r d s t h e e d g e o f t h e s p r a y , a s h a r p d r o p i n t h e s p r a y f l u x i s o b s e r v e d . T h i s F i g u r e c a n be c o m p a r e d t o F i g u r e 31 e f f e c t i v e l y r o t a t e d a b o u t t h e c e n t r a l a x i s i n t h e f o r m o f a c o n e . S p r a y f l u x r e p r e s e n t a t i o n s s i m i l a r t o F i g u r e 47 f o r o t h e r s p r a y c o n d i t i o n s a r e g i v e n i n A p p e n d i x I I • 5 . 1 . 1 . 2 . 2 W a t e r F l u x e s O b t a i n e d w i t h  T y p e B C o l l e c t o r s From an e x a m i n a t i o n o f t h e T a b l e s i n A p p e n d i x I, i t c a n be s e e n t h a t t h e r e i s c o n s i d e r a b l y more w a t e r c o l l e c t e d by t h e T y p e B c o l l e c t o r s t h a n w i t h t h e T y p e A c o l l e c t o r s , u n d e r i d e n t i c a l s p r a y i n g c o n d i t i o n s . T h i s i s a d i r e c t r e s u l t o f t h e w a t e r f l o w i n g d o w n w a r d t h r o u g h t h e s p r a y , a d j a c e n t t o t h e s p r a y e d f a c e . In a d d i t i o n , a r i n g o f w a t e r s u r r o u n d s t h e s p r a y e d a r e a a n d f l o w s downward j u s t o u t s i d e t h e a r e a b e i n g d i r e c t l y s p r a y e d . A c o n t o u r map o f t h e s p r a y f l u x e s o b t a i n e d f o r t h e 1 /4 GG 10 n o z z l e f o r a s p r a y p r e s s u r e o f 0 . 4 1 MPa ( 6 0 p s i ) and a t a d i s t a n c e o f 1 0 . 1 6 cm (4 i n ) i s g i v e n i n F i g u r e 4 8 . C o m p a r i n g t h i s F i g u r e ' w i t h F i g u r e 44 shows t h a t t h e r e i s a h i g h e r w a t e r f l u x i n t h e m i d d l e o f t h e s p r a y . A d d i t i o n a l l y , t h e r e a r e a l a r g e n u m b e r o f c l o s e l y s p a c e d c o n t o u r s n e a r t h e t o p and t h e s i d e s o f t h e c o n t o u r m a p . T h e s e c o r r e s p o n d t o t h e w a t e r f l o w i n g down o u t s i d e 149 F igure 48 Spray f l u x contour map f o r a 1/4 GG 10 n o z z l e f o r a sp ray p ressure o f 0.41 MPa and n o z z l e d i s t a n c e o f 10.16 cm (Type B c o l l e c t o r s ) . Figure 49 Three dimensional representation of the spray fluxes for a 1/4 GG 10 nozzle, for a spray pressure of 0 .13 MPa and a nozzle distance of 10.16 cm (Type B collectors). en O 151 t h e s p r a y e d a r e a . T h i s e f f e c t i s g r a p h i c a l l y i l l u s t r a t e d ( F i g u r e 4 9 ) by a t h r e e d i m e n s i o n a l v i e w o f t h e s p r a y f l u x map o b t a i n e d f o r a s p r a y p r e s s u r e o f 0 .1 .3 MPa (20 p s i ) a t a d i s t a n c e o f 1 0 . 1 6 cm (4 i n ) f r o m t h e n o z z l e . The s m a l l p e a k i n t h e c e n t r e c o r r e s p o n d s t o t h e p e a k i n t h e s p r a y e d c o n e d i s c u s s e d e a r l i e r . The much h i g h e r p e a k s t o w a r d t h e o u t s i d e o f t h e s p r a y r e p r e s e n t t h e r e g i o n s o f w a t e r f l o w i n g d o w n w a r d , s u r r o u n d i n g t h e s p r a y e d c o n e . S p r a y f l u x c o n t o u r maps and t h r e e d i m e n s i o n a l r e p r e s e n t a t i o n s o b t a i n e d f o r o t h e r s p r a y i n g c o n d i t i o n s a r e g i v e n i n A p p e n d i x I I . 5 . 1 . 2 O t h e r F u l l Cone N o z z l e s - S p r a y F l u x e s w i t h  Type A C o l l e c t o r s O t h e r f u l l c o n e n o z z l e s f o r w h i c h s p r a y f l u x m e a s u r e m e n t s w e r e made i n c l u d e some w i t h a h i g h e r c a p a c i t y , a n d some w i t h l o w e r c a p a c i t i e s t h a n t h e 1 /4 GG 10 n o z z l e f o r t h e same s p r a y p r e s s u r e . N o z z l e s w i t h t h e l o w e r c a p a c i t i e s w e r e t h e S p r a y S y s t e m s , C o . 1 / 8 GG 5 , 1 / 8 GG 6 SQ a n d t h e 1 / 4 G G . 6 . 5 n o z z l e s , a n d f o r t h e s e n o z z l e s , m e a s u r e -m e n t s w e r e made a t f o u r d i f f e r e n t s p r a y p r e s s u r e s . The h o r i z o n t a l c e n t r e l i n e s p r a y f l u x e s m e a s u r e d f o r t h e 1 / 8 GG 5 n o z z l e , a t s p r a y d i s t a n c e o f 1 0 . 1 6 a n d 1 5 . 2 4 cm (4 a n d 6 i n ) r e s p e c t i v e l y a r e g i v e n i n F i g u r e s 50 a n d 5 1 . The d i s t r i -b u t i o n o f t h e s p r a y w a t e r f l u x e x h i b i t s a s h a r p p e a k i n t h e c e n t r e , p a r t i c u l a r l y a t p r e s s u r e s up t o 0 . 4 1 MPa ( 6 0 p s i ) . In F i g u r e 5 1 , f o r a n o z z l e - c o l l e c t o r d i s t a n c e o f 152 DISTRNCE FROM CENTRE (IN) o - B . O -4.0 -2.0 0.0 2.0 4.0 I I I 1 L _ 6.0= a en. o to . to-o l to d o - . >-Q to a co' N0Z2LE 1/BGG5 DISTANCE 10.16 CMS, PRESSURE PSI MPA LTJ O CD 20 40 60 100 0 .13 0.27 0.41 0 .68 a a ' $ 85--15.24 a -10.16 -5.06 0.0 5.08 DISTANCE FROM CENTRE [CM) B-10.16 a 03 a to" a 15.24 Figure 50 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/8 GG 5 n o z z l e , a t a nozz le d i s t a n c e o f 10.16 cm. DISTANCE FROM CENTRE (IN) a - 6 . 0 - 4 . 0 - 2 . 0 0 . 0 2 . 0 4 . 0 1 1 1 1 L _ 153 6.0= Q 0 3 . U J r J . C O -a to Q_ to a a a rJ' a NOZZLE 1/8GG5 DISTANCE 15.24 CMS. PRESSURE PSI MPA • 20 0 . K A 40 0 .27 O 60 0.41 CD 100 0 .68 .a m a .03 C 3 - U 3 a a a a ' to" a a - 1 5 . 2 4 - 1 0 . 1 6 - 5 . 0 8 0 . 0 5 . 0 8 DISTANCE FROM CENTRE (CM) 10.16 -SB-—j£ 1 5 . 2 4 Figure 51 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/8 GG 5 n o z z l e , a t a n o z z l e d i s t a n c e o f 15.24 cm. 154 1 5 . 2 4 c m , t h e s p r a y w a t e r f l u x i s m a r k e d l y l o w e r . I n t h e c e n t r a l p o r t i o n s o f t h e s p r a y , t h e s p r a y f l u x t e n d s t o be more u n i f o r m f o r t h e h i g h e r p r e s s u r e s o f 0 . 4 1 MPa a n d 0 . 6 8 MPa ( 6 0 a n d 100 p s i ) . The r e s u l t s o f m e a s u r e m e n t s made w i t h t h e 1 / 4 GG 6 . 5 and 1 /8 GG 6 SQ n o z z l e s a r e g i v e n i n F i g u r e s 5 2 , 5 3 a n d 5 4 . P e a k s i n t h e s p r a y f l u x d i s t r i b u t i o n s a r e p r e s e n t i n a l l t h r e e F i g u r e s . P l a t e a u s a p p e a r i n t h e d i s t r i b u t i o n s a t t h e l a r g e r d i s t a n c e s . E v e n a t t h e n o z z l e d i s t a n c e o f 1 5 . 2 4 cm (6 i n ) , t h e d i s t r i b u t i o n o f t h e s p r a y w a t e r i s u n e v e n i n t h e c e n t r a l p o r t i o n o f t h e s p r a y . The r e s u l t s o b t a i n e d f o r t h e n o z z l e s i n v e s t i g a t e d w i t h f l o w r a t e s h i g h e r t h a n t h o s e o f t h e 1 / 4 G G 1 0 n o z z l e now f o l l o w . S p r a y c h a r a c t e r i s t i c s f o r t h e 1 /4 GG 10 SQ a n d t h e 1 /4 GG 12 SQ n o z z l e s , w h i c h show c h a r a c t e r i s t i c s e s s e n t i a l l y t h e same as t h o s e o b t a i n e d f o r t h e 1 /4 GG 10 n o z z l e , a r e t a b u l a t e d i n A p p e n d i x I. The h o r i z o n t a l c e n t r e l i n e s p r a y p r o f i l e s o b t a i n e d a r e g i v e n i n A p p e n d i x I I . When h i g h e r c a p a c i t y f l o w n o z z l e s w e r e b e i n g s t u d i e d , t h e h i g h f l o w r a t e s i n v o l v e d c a u s e d l a r g e p r e s s u r e d r o p s i n t h e w a t e r d e l i v e r y s y s t e m . As a c o n s e q u e n c e , t h e maximum a v a i l a b l e p r e s s u r e a t t h e n o z z l e was l o w e r e d , a n d t h e m e a s u r e m e n t s w e r e c a r r i e d o u t o n l y a t l o w p r e s s u r e s . The 155 a - 6 . 0 i-4-9 to™ a to a~to ce-Q_ to 03 DISTANCE FROM CENTRE (IN) - 4 . 0 - 2 . 0 0 . 0 2 . 0 4 . 0 J I 1 1 — J — 6.0= •4 NOZZLE 1/4GG6.5 DISTANCE 10.16 CMS PRESSURE PSI MPA CD 20 0 .13 A 40 0 .27 <!> 60 0.41 CD 90 0 .62 •R .03 fM fM a . a CM o . to" t - C M a "oo - 1 5 . 2 4 - 1 0 . 1 6 - 5 . 0 8 0 . 0 5 . 0 3 DISTANCE FROM CENTRE (CM) — B -1 0 . 1 6 1 5 . 2 4 F igure 52 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 GG 6.5 n o z z l e , a t a nozz le d i s t a n c e o f 10.16 cm, 9-03. UJrf. CO CM C3 CO DISTANCE FROM CENTRE tIND i - B . D - 4 . 0 - 2 . 0 0 . 0 2 . 0 4 . 0 I I I 1 1 156 (X io . o_ to • ro . 6.0=> "9 NOZZLE 1/4GG6.5 ' DISTANCE 15.24 CMS, PRESSURE PSI MPR CD 20 0.13 A 40 0.27 <!> 60 0.4] h i * . 0 3 .v CM - 3 5 . 2 4 - 3 0 . 1 6 - 5 . 0 8 0 . 0 5 . 0 8 DISTANCE FROM CENTRE ICMJ 10.16 1 5 . 2 4 re 53 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 GG 6 .5 n o z z l e , a t a nozz le d i s t a n c e o f 15.24 cm. 157 DISTANCE FROM CENTRE ( IN) a - 6 . 0 - 4 . 0 - 2 . 0 0 . 0 - 2 . 0 4 . 0 ) l I I I 6.0=> C3 . CM Q 0 0 . a I D * . a £_)<=> C3 to Q . CO a C D a ru" a NOZZLE 1/FJGG6SQ DISTANCE 1 0 . 1 6 CMS, PRESSURE P S I MPA a 20 A 40 <!> 60 O 90 0.13 0.27 0.41 0.62 $ H --15.24 -8S © - 1 0 . 1 6 - 5 . 0 8 0 . 0 5 . 0 8 1 0 . 1 6 DISTANCE FROM CENTRE (CM) a ru a co" a to a a a a o to" a a "rJ 1 5 . 2 4 Figure 54 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/8 GG 6 SQ n o z z l e , a t a nozz le d i s t a n c e o f 10.16 cm. 1 58 r e s u l t s o f m e a s u r e m e n t s made on t h e 3 / 8 HH 18 SQ n o z z l e a t 0 . 1 3 a n d 0 . 2 MPa (20 and 30 p s i ) a r e i n c l u d e d i n A p p e n d i c e s I a n d I I . The s p r a y c h a r a c t e r i s t i c s o f t h e s e n o z z l e s a r e s i m i l a r t o t h o s e o f t h e f u l l c o n e n o z z l e s d i s c u s s e d e a r l i e r . From m e a s u r e m e n t s made o n t h e 1 /4 HH 1 4 . 5 SQ n o z z l e s , as shown i n F i g u r e s 55 a n d 5 6 , i t i s o b s e r v e d t h a t e v e n a t n o z z l e d i s t a n c e s o f o n l y 1 5 . 2 4 cm (6 i n ) , t h e m a j o r i t y o f t h e s p r a y e d a r e a h a s an e v e n d i s t r i -b u t i o n o f t h e s p r a y f l u x , . U n i f o r m s p r a y f l u x d i s t r i b u t i o n s cam a l s o be o b s e r v e d w i t h w i d e a n g l e n o z z l e s , as e v i d e n c e d by m e a s u r e m e n t s made on t h e 1 /4 GG 14 W n o z z l e , shown i n F i g u r e 5 7 . A t t h e l o w e r p r e s s u r e , t h e s p r a y f l u x d i s t r i b u t i o n b e c o m e s u n e v e n , p r o b a b l y due t o t h e l a c k o f e n o u g h p r e s s u r e d r i v i n g f o r c e t o b r e a k up t h e w a t e r f l o w i n t o u n i f o r m d r o p l e t s . • 5 . 1 . 3 V e e - j e t o r F l a t - j e t N o z z l e s ; M e a s u r e m e n t s Made w i t h T y p e A C o l l e c t o r s The n o z z l e s p r o v i d e a f l a t s p r a y p a t t e r n (2 t o 5 cm t h i c k f o r t h e s m a l l e r n o z z l e s ) a n d a r e p r i m a r i l y u s e d i n s l a b c a s t i n g a p p l i c a t i o n s ' . A f e w o f t h e s e n o z z l e s w e r e i n v e s t i g a t e d t o d e t e r m i n e t h e i r s p r a y c h a r a c t e r i s t i c s . Due t o t h e h i g h f l o w r a t e s i n v o l v e d , m e a s u r e m e n t s w e r e made o n l y a t l o w e r p r e s s u r e s . In m o s t c a s e s , f i n e s p r a y d r o p l e t s w e r e n o t f o r m e d due t o l o w o p e r a t i n g p r e s s u r e s , DISTANCE FROM CENTRE (IN) - 2 . 0 0 . 0 2 . 0 J 1 L 159 - 1 5 . 2 4 - 1 0 . 1 6 - 5 . 0 8 0 . 0 5 . 0 8 DISTANCE FROM CENTRE (CM) iS | o 1 0 . 1 6 1 5 . 2 4 F igure 55 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 HH 14.5 SQ n o z z l e a t a nozz le d i s t a n c e o f 10.16 cm, 160 - 6 . 0 DISTRNCE FROM CENTRE (IN) - 2 . 0 0 . 0 2 . 0 4 . 0 i i 1 : 1— 6.0=1 o CM NOZZLE 1/4HH14.5SQ DISTRNCE15.24 CMS. PRESSURE PSI MPA • 2 0 0.13 A 40 0.27 O 50 0.34 l-to a | _ ( D a a a to o 1 1 - 1 5 . 2 4 - 1 0 . 1 6 - 5 . 0 8 0 . 0 5 . 0 8 DISTANCE FROM CENTRE (CM) 1 0 . 1 6 1 5 . 2 4 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 HH 14.5 SQ nozz le a t a nozz le d i s t a n c e o f 15.24 cm. 161 a - 6 . 0 a. a a i ' o oo' U J . COW O to —J°. > - o CO DISTANCE FROM CENTRE (IN) „ n c • - 4 . 0 - 2 . 0 0 . 0 2 . 0 4 . 0 6.0=) _ J I I 1 1 U a NOZZLE 1/4GG14V DISTANCE 1 0 . 1 6 CMS, PRESSURE PS I MPA • 20 0 . 1 3 A 40 0 . 2 7 a a I D a in a 1 r— 1 1 - 1 5 . 2 4 - 1 0 . 1 6 - 5 . 0 8 0 . 0 5 . 0 8 DISTANCE FROM CENTRE (CM) 10.16 1 5 . 2 4 Figure 57 H o r i z o n t a l c e n t r e ! i n e spray f l u x p r o f i l e s f o r a 1/4 GG 14 W n o z z l e , a t a nozz le d i s t a n c e o f 10.16 cm. 162 Q-6 .0 9-DI5TRNCE FROM CENTRE (IN) -4.0 -2.0 0.0 2.0 4.0 _J I I I L_ 6.0= •4-NOZZLE 1/4U8020 D I S T R N C E 2 0 . 3 2 CMS, Pi-PRESSURE PSI MPA • 20 0 . 1 3 A 40 0 . 2 7 <!> 60 0 .41 a o ' . . 1 1 -15.24 -10.16 -5.08 DISTANCE ir, t= "I <=' 15.24 0.0 5.08 FROM CENTRE (CM) 16 F igu re 58 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 1/4 U8020 nozz le a t a nozz le d i s t a n c e o f 20.32 cm. 163 a n d t h e r e f o r e , no m e a n i n g f u l m e a s u r e m e n t s c o u l d be o b t a i n e d , p a r t i c u l a r l y f o r t h e s m a l l n o z z l e t o c o l l e c t o r d i s t a n c e s u s e d i n t h i s w o r k . The h o r i z o n t a l c e n t r e l i n e s p r a y f l u x d i s t r i b u t i o n s o b t a i n e d f o r t h e 1 /4 U 8020 n o z z l e i s g i v e n i n F i g u r e 5 8 , f o r a n o z z l e t o c o l l e c t o r d i s t a n c e o f 2 0 . 3 2 cm (8 i n ) . I t c a n be o b s e r v e d f r o m t h i s F i g u r e t h a t i n t h e c e n t r a l r e g i o n o f t h e s p r a y p a t t e r n , t h e r e i s a f a i r l y u n i f o r m d i s t r i b u t i o n o f t h e s p r a y f l u x , t a p e r i n g o f f t o w a r d s the e d g e s . T h i s f e a t u r e i s u s e f u l when o v e r l a p p i n g s p r a y s a r e u s e d t o c o o l s l a b s o f l a r g e w i d t h s . 5 . 2 M e a s u r e m e n t s o f H e a t - T r a n s f e r C o e f f i c i e n t s The h e a t - t r a n s f e r c o e f f i c i e n t s r e p o r t e d i n t h i s s e c t i o n p e r t a i n t o t h e h e a t t r a n s f e r b e t w e e n w a t e r s p r a y s d i s c u s s e d i n t h e p r e v i o u s s e c t i o n a n d a h e a t e d A I S I 304 s t a i n l e s s s t e e l s u r f a c e a t t e m p e r a t u r e s i n e x c e s s o f 8 0 0 ° C . The m a j o r i t y o f t h e r e s u l t s r e p o r t e d w e r e m e a s u r e d d u r i n g t h e c o o l i n g o f t h e h e a t e d s t e e l s u r f a c e f r o m an i n i t i a l t e m p e r a t u r e o f a b o u t 1 1 0 0 ° C . 5 . 2 . 1 G e n e r a l O b s e r v a t i o n s o f t h e C o o l i n g P r o c e s s V i s u a l and a u r a l o b s e r v a t i o n s o f t h e c o o l e d s u r f a c e w e r e made d u r i n g t h e s p r a y c o o l i n g and a r e d i s c u s s e d b e ! o w . 164 In t h e e a r l y s t a g e s o f c o o l i n g o f t h e p r o b e s u r f a c e , when t h e " f i l m b o i l i n g " r e g i m e was p r e s e n t , t h e r e , was- a l o w h i s s i n g n o i s e e m a n a t i n g f r o m t h e s u r f a c e . V i s u a l o b s e r v a -t i o n s s h o w e d t h a t t h e s u r f a c e was d r y and d r o p l e t s c o u l d be s e e n b o u n c i n g away f r o m i t . On f u r t h e r c o o l i n g , when t h e t r a n s i t i o n p o i n t was r e a c h e d , t h e h i s s i n g n o i s e r o s e v e r y s h a r p l y i n i n t e n s i t y . P a t c h e s o f 1 i q u i d c o u l d be s e e n r e m a i n i n g on t h e s u r f a c e a n d v o l u m i n o u s a m o u n t s o f s t e a m w e r e p r o d u c e d . On c o o l i n g f u r t h e r , t h i s s t a g e was f o l l o w e d by a s t a g e w h e r e i n t h e e n t i r e s p r a y e d s u r f a c e s h o w e d a w e t t e d a p p e a r a n c e and t h e amoun t o f s t e a m p r o d u c t i o n d e -c r e a s e d , w i t h a c o r r e s p o n d i n g l o w e r i n g o f t h e i n t e n s i t y o f t h e h i s s i n g n o i s e . U n d e r n o r m a l c o n d i t i o n s , t h e w e t t i n g o f t h e s p r a y e d s u r f a c e s p r e a d o u t f r o m t h e r e g i o n o f t h e h i g h e s t s p r a y w a t e r f l u x i n t h e c e n t r a l r e g i o n o f t h e s p r a y , t o w a r d s t h e e d g e s o f t h e s p r a y c o n e i n a s y m m e t r i c a l f a s h i o n . The p r e s e n c e o f any s e m i - a d h e r e n t s c a l e o r f o r e i g n m a t t e r on t h e s u r f a c e c a u s e d a d r a s t i c c h a n g e i n t h e p a t t e r n . When t h e s c a l e was n o t c o m p l e t e l y d e t a c h e d f r o m t h e s u r f a c e , t h e a r e a i m m e d i a t e l y a r o u n d i t t u r n e d b l a c k a n d was w e t t e d s o o n e r t h a n t h e o t h e r r e g i o n s . W h e n e v e r s u c h m a t t e r was p r e s e n t on t h e s u r f a c e o f t h e m e a s u r i n g p r o b e , t h i s c h a n g e i n c o l o u r was a l s o r e f l e c t e d i n h i g h c o o l i n g r a t e s b e i n g r e c o r d e d by t h e t h e r m o c o u p l e s c l o s e . t o t h e c o o l e d s u r f a c e . 165 S u c h c o n d i t i o n s w e r e o b s e r v e d t o h a v e a h i g h e r ; f r e q u e n c y o f o c c u r r e n c e when t h e m e a s u r i n g p r o b e h a d u n d e r -g o n e a number o f h e a t i n g - c o o l i n g c y c l e s . When s u c h o c c u r -r e n c e s w e r e o b s e r v e d , t h e m e a s u r i n g p r o b e w a s d i s c a r d e d ( a s w e r e t h e r e s u l t s o f t h a t r u n a n d a f ew b e f o r e i t ) , a n d a new p r o b e made and i n s t a l l e d f o r s u b s e q u e n t m e a s u r e m e n t s . I n i t i a l l y , a new p r o b e had a h i g h l y p o l i s h e d s u r f a c e . H o w e v e r , a f t e r one h e a t i n g a n d c o o l i n g c y c l e , t h e p r o b e s u r f a c e was c o v e r e d by a t h i n , s m o o t h , g r a y i s h o x i d e l a y e r . S u b s e q u e n t h e a t i n g and c o o l i n g c y c l e s s l o w l y c a u s e d t h i s l a y e r t o c h a n g e c o l o u r t o a b l a c k i s h - g r a y i n n o n - u n i f o r m p a t c h e s . W i t h a b l a c k i s h - g r a y o x i d e c o v e r i n g , h i g h c o o l i n g r a t e s o f t h e s u r f a c e w e r e o b s e r v e d when s p r a y c o o l i n g f r o m h i g h t e m p e r a t u r e s . W e t t i n g o f t h e s u r f a c e was a l s o s e e n t o o c c u r e a r l i e r a t t h e s e s p o t s as c o m p a r e d w i t h o t h e r r e g i o n s . S u c h o c c u r r e n c e s w e r e c o n s i d e r e d s u f f i c i e n t c a u s e t o d i s c a r d t h e p r o b e . T h e s e o b s e r v a t i o n s d e m o n s t r a t e d t h a t c h a n g e s i n t h e a p p e a r a n c e o f t h e p r o b e s u r f a c e r e s u l t e d i n v a r i a t i o n s i n c o o l i n g r a t e s u n d e r i d e n t i c a l s p r a y i n g c o n d i t i o n s , a n d t h u s c o n t r i b u t e d t o t h e s c a t t e r o f t h e d a t a . G r o s s v a r i a t i o n s i n t h e h e a t - t r a n s f e r c o e f f i c i e n t s (up t o a f a c t o r o f 10 ) w e r e o b s e r v e d w i t h l a r g e c h a n g e s i n t h e s u r f a c e c o n d i t i o n s o f t h e m e a s u r i n g p r o b e . G r e a t c a r e was t h e r e f o r e n e c e s s a r y i n 166 t h e m e a s u r e m e n t s t o o b t a i n d a t a w i t h s m a l l s c a t t e r . 5 . 2 . 2 V a l i d a t i o n o f t h e E x p e r i m e n t a l T e c h n i q u e U s e d An i m p o r t a n t p o i n t t o n o t e when i n t r o d u c i n g a m e a s u r i n g s e n s o r i n t o a s y s t e m t o m e a s u r e t r a n s i e n t s i s t h a t i t c o u l d c h a n g e t h e ^ s t a t e o f t h e s y s t e m . The p r o b l e m c a n a r i s e i n t h e s y s t e m u s e d i n t h i s i n v e s t i g a t i o n , w h e r e t h e r m o c o u p l e s a r e i m b e d d e d i n a s o l i d t o m e a s u r e t h e h e a t f l o w w i t h i n i t . I f s u f f i c i e n t c a r e i s n o t t a k e n t o m i n i m i z e t h e e f f e c t o f t h e t h e r m o c o u p l e i n s t a l l a t i o n on t h e h e a t f l o w , a p p r e c i a b l e e r r o r s c o u l d d e v e l o p i n t h e m e a s u r e m e n t s . F o r t h i s r e a s o n , t h e t h e r m o c o u p l e w i r e s i z e s a n d h o l e s d r i l l e d f o r t h e i r i n s t a l l a t i o n w e r e k e p t s m a l l . In o r d e r t o e n s u r e t h a t t h e i m b e d d e d t h e r m o c o u p l e s had no s i g n i f i c a n t e f f e c t on t h e h e a t f l o w , a s e t o f e x p e r i -m e n t s was c o n d u c t e d i n w h i c h f o u r s e t s o f t h e r m o c o u p l e w i r e s w e r e i n s t a l l e d i n t h e h e a t t r a n s f e r p r o b e . The e n d s o f t h e s e t h e r m o c o u p l e s w e r e p l a c e d a t d i s t a n c e s o f 1 . 0 2 , 2 . 0 3 , 3 . 0 5 and 1 9 . 0 5 mm ( 0 . 0 4 , 0 . 0 8 , 0 . 1 2 and 0 . 7 5 i r r e s p e c t i v e l y f r o m t h e s p r a y e d f a c e o f t h e p r o b e . The t e m p e r a t u r e t r a n s i e n t s o b t a i n e d f r o m t h e t h e r m o c o u p l e c l o s e s t t o t h e s p r a y e d f a c e w e r e t h e n u s e d t o c a l c u l a t e t h e t e m p e r a t u r e -t i m e r e l a t i o n s h i p w i t h i n t h e p r o b e d u r i n g c o o l i n g . The c a l c u l a t e d v a l u e s w e r e t h e n c o m p a r e d t o t h e m e a s u r e d v a l u e s o f t e m p e r a t u r e a t t h e p o s i t i o n s o f t h e t h e r m o c o u p l e s r e m o t e 167 f r o m t h e s u r f a c e as s p e c i f i e d a b o v e . The r e s u l t s a r e s h o w n i n F i g u r e s 59 a n d 6 0 , i n w h i c h t h e c a l c u l a t e d a n d m e a s u r e d v a l u e s o f t e m p e r a t u r e w i t h i n t h e h e a t - t r a n s f e r p r o b e a r e p l o t t e d a t d i f f e r e n t t i m e s f r o m t h e s t a r t o f c o o l i n g . E x c e l -l e n t a g r e e m e n t was o b t a i n e d b e t w e e n t h e c a l c u l a t e d and m e a s u r e d v a l u e s . The a v e r a g e h e a t - t r a n s f e r c o e f f i c i e n t s f o r t h e s e r u n s w e r e 1 . 0 5 k w / m 2 K and 1.8.8 k W / m 2 K ( 0 . 0 2 5 a n d 0 . 0 4 5 c a l s / c m s e c 0 C) r e s p e c t i v e l y . T h e s e f a l l i n t h e r a n g e o f h e a t - t r a n s f e r c o e f f i c i e n t s m e a s u r e d i n t h i s s t u d y . The t h e r m o c o u p l e c l o s e s t t o t h e s p r a y e d f a c e w o u l d be e x p e c t e d t o i n f l u e n c e t h e h e a t f l o w t o t h e c o o l e d s u r f a c e t h e m o s t as c o m p a r e d t o t h e o t h e r s . T h i s w o u l d l e a d t o a s i t u a t i o n i n w h i c h t h e v o l u m e o f m a t e r i a l a h e a d o f t h i s t h e r m o c o u p l e w o u l d c o o l r a p i d l y , c a u s i n g t h e t h e r m o c o u p l e t o e x h i b i t f a s t e r c o o l i n g t h a n w o u l d be t h e c a s e i f t h e r e w e r e no b a r r i e r t o t h e h e a t f l o w . U s i n g t h e c o o l i n g c u r v e o b t a i n e d f r o m t h i s t h e r m o c o u p l e t o c a l c u l a t e t h e t h e r m a l h i s t o r y o f t h e p r o b e w o u l d c a u s e l o w e r t e m p e r a t u r e s t o be c a l c u l a t e d a t t h e o t h e r p o s i t i o n s o f t h e o t h e r t h e r m o c o u p l e s as w e l l . S u c h i s c e r t a i n l y n o t t h e c a s e , as c a n be o b s e r v e d f r o m F i g u r e s 59 and 6 0 . T h i s p h e n o m e n o n o f t h e d i s t u r b a n c e o f t h e h e a t f l o w by t h e m e a s u r i n g s e n s o r c o u l d be e x p e c t e d t o h a v e l a r g e r e f f e c t s as t h e h e a t - t r a n s f e r c o e f f i c i e n t a t t h e s u r f a c e i n c r e a s e s i . e . , w i t h h i g h h e a t f l u x e s . T h e r e f o r e , when much h i g h e r h e a t f l u x e s a r e e n c o u n t e r e d , 900 Thermocouple I 2 3 i i Distance From Front Face 0 0 4 0 in. 0 0 8 0 in. 0-120 in. Imm 2mm 3mm 700 Average Heat Transfer Coefficient 0-025 cals./cm2sec P C 105 k W / m 2 K Measured Calculated * T C # 3 T C # 2 ^ T C # I Measured Surface Temperature 0 5 10 1-5 2 0 Time (Seconds) 2-5 3 0 F igu re 59 Comparison o f c a l c u l a t e d and measured tempera tu res , f o r an average h e a t - t r a n s f e r c o e f f i c i e n t o f 1.05 kW/m 2K. oo 880 840 800 o o £ 760 0) C L £ 720 640 600 1 1 1 1 1 S^s^-v. Thermocouple Distance From _ Front Face 0040in. Imm ~ 0080 in. 2mm _ 0120 in. 3 mm A Measured Calculated \ ^ ^ T C # 2 • \ \ -\ . ^ - T C # I Measured — ^ Surface Temperature Average Heat Transfer Coefficient « 0 045 cal/cm 2/sec/°C 1-88 kW/m 2 K i i i i i -0-5 10 1-5 20 Time (sec) 2-5 Figure 60 Comparison o f c a l c u l a t e d and measured tempera tu res , f o r an average — — : 2 h e a t - t r a n s f e r c o e f f i c i e n t o f 1.88 kW/m K. CD VO 170 t h i s m e t h o d o f m e a s u r e m e n t m u s t be r e v a l i d a t e d , a s was d o n e i n t h i s w o r k . 5 . 2 . 3 D e t e r m i n a t i o n o f t h e I n i t i a l T e m p e r a t u r e  P r o f i 1 e s T e m p e r a t u r e g r a d i e n t s o f up t o 1 0 ° C / c m ( 2 5 ° C / i n ) e x i s t e d w i t h i n t h e p r o b e d u r i n g h e a t i n g , w i t h t h e l o w e r t e m p e r a t u r e a t t h e s p r a y e d f a c e . T h e s e g r a d i e n t s w e r e m i n i m i z e d p r i o r t o s p r a y c o o l i n g by s o a k i n g t h e p r o b e a t t e m p e r a t u r e s w i t h m in imum h e a t i n p u t . H o w e v e r , s i n c e t h e t e m p e r a t u r e s w i t h i n t h e p r o b e w e r e m e a s u r e d a t d i f f e r e n t p o i n t s by t h e e m b e d d e d t h e r m o c o u p l e s , t h e t e m p e r a t u r e g r a -d i e n t s w i t h i n t h e p r o b e c o u l d be i n c o r p o r a t e d i n t o t h e m a t h e m a t i c a l a n a l y s i s o f t h e t e m p e r a t u r e t r a n s i e n t s as t h e i n i t i a l c o n d i t i o n . In t h e i n i t i a l s p r a y c o o l i n g r u n s , t h e t e m p e r a t u r e g r a d i e n t i n t h e s a m p l e was a s s u m e d t o be l i n e a r a l o n g t h e p r o b e a x i s . T h i s c a u s e d a n a m o l o u s h e a t - t r a n s f e r c o e f f i c i e n t s t o be d e t e r m i n e d f o r t h e f i r s t f ew t i m e s t e p s u s e d i n t h e c a l c u l a t i o n s . T h i s was a t t r i b u t e d t o t h e r e -a r r a n g e m e n t o f t e m p e r a t u r e s a t v a r i o u s p o i n t s w i t h i n t h e p r o b e i n o r d e r t o mee t t h e r e q u i r e m e n t s o f t h e g o v e r n i n g c o n d u c t i o n e q u a t i o n . S u b s e q u e n t ' m e a s u r e m e n t s w e r e t h e n p e r f o r m e d w i t h f o u r t o f i v e t h e r m o c o u p l e s i n s e r t e d a t v a r i o u s p o s i t i o n s w i t h i n " " " t h e m e a s u r i n g p r o b e t o e s t a b l i s h t h e i n i t i a l c o n d i t i o n s . T h e s e m e a s u r e m e n t s s h o w e d t h a t h a l f o f t h e m a g n i t u d e o f t h e t e m p e r a t u r e g r a d i e n t was c o n f i n e d t o t h e 171 f i r s t o n e - t h i r d o f t h e l e n g t h o f t h e p r o b e ( t o w a r d s t h e f r o n t f a c e ) . U s i n g t h i s i n f o r m a t i o n t o s e t up t h e i n i t i a l t e m p e r a t u r e s w i t h i n t h e p r o b e as a f u n c t i o n o f t h e a x i a l d i s t a n c e f r o m t h e s p r a y e d f a c e r e d u c e d t h e a n a m o l o u s bumps i n t h e c a l c u l a t e d h e a t - t r a n s f e r c o e f f i c i e n t v s . s u r f a c e t e m p e r a t u r e r e l a t i o n s h i p . 5 . 2 . 4 R e s u l t s o f Type I E x p e r i m e n t s The e x p e r i m e n t a l r e s u l t s p r e s e n t e d i n t h i s s e c t i o n w e r e o b t a i n e d w i t h t h e s p r a y e d s t e e l s u r f a c e m o u n t e d f l u s h w i t h t h e f r o n t o f a v e r t i c a l a s b e s t o s s h e e t . A l l t h e r e s u l t s p r e s e n t e d i n t h i s s e c t i o n p e r t a i n t o m e a s u r e m e n t s made u s i n g a 1 /4 GG 10 n o z z l e . The v a r i a t i o n o f t h e h e a t -t r a n s f e r c o e f f i c i e n t s as a f u n c t i o n o f t h e s p r a y w a t e r f l u x f o r t h e 1 /4 GG 10 n o z z l e i s p r e s e n t e d i n F i g u r e 61 f o r a s u r f a c e t e m p e r a t u r e o f 8 5 0 ° C . T h e s e r e s u l t s a r e f o r m e a s u r e -m e n t s p e r f o r m e d w i t h o p e r a t i n g s p r a y p r e s s u r e s o f 0 . 1 3 , 0 . 2 7 a n d 0 . 4 1 MPa ( 2 0 , 40 a n d 60 p s i ) . I n o r d e r t o o b t a i n d i f f e r e n t s p r a y w a t e r f l u x e s a t t h e p r o b e s u r f a c e , t h e n o z z l e was t r a n s l a t e d n o t o n l y i n a d i r e c t i o n a l o n g t h e s p r a y n o z z l e a x i s , b u t a l s o i n a d i r e c t i o n p e r p e n d i c u l a r t o i t . T h i s a p p r o a c h was t a k e n i n v i e w o f t h e f a c t t h a t M i z i k a r 7 ^ h a s r e p o r t e d t h a t t h e a n g l e o f i m p i n g e m e n t o f t h e s p r a y d r o p l e t s on t h e c o o l e d s u r f a c e h a d no e f f e c t on t h e h e a t - t r a n s f e r c o e f f i c i e n t f o r t h e same s p r a y w a t e r f l u x . The r e s u l t s r e p o r t e d by M i z i k a r f o r t h i s n o z z l e f o r two Spray heat-transfer coefficient,kW/m °C — ro • • • T Q ro = o X 3. ro O o 9 0 ? ^ = OJ o o r o o o o o ro o o o cn O O Spray heat - t ransfer coefficient (Btu/hr ft °F) 1 7 3 d i f f e r e n t s p r a y p r e s s u r e s o f 0 . 2 7 a n d 0 . 6 2 MPa ( 4 0 a n d 90 p s i ) r e s p e c t i v e l y a r e a l s o p l o t t e d i n F i g u r e 61 a s t h e two s t r a i g h t 1 i nes . W h e r e a s M i z i k a r ^ o b t a i n e d a d i f f e r e n c e i n t h e h e a t -t r a n s f e r c o e f f i c i e n t s f o r t h e two s p r a y p r e s s u r e s s h o w n i n t h i s F i g u r e , no s u c h d i f f e r e n c e due t o t h e e f f e c t o f p r e s -s u r e i s o b s e r v e d f r o m t h e r e s u l t s o f t h e p r e s e n t w o r k . The p r e s e n t r e s u l t s g i v e h e a t - t r a n s f e r c o e f f i c i e n t s w h i c h a r e much h i g h e r , and h a v e a much g r e a t e r v a r i a b i l i t y f o r t h e same s p r a y f l u x t h a n w o u l d be e x p e c t e d f r o m t h e r e s u l t s o f M i z i k a r . F i g u r e 62 p r e s e n t s r e s u l t s o b t a i n e d f o r a s u r f a c e t e m p e r a t u r e o f 1 0 0 0 ° C . The h e a t - t r a n s f e r c o e f f i c i e n t i s a g a i n o b s e r v e d t o be i n d e p e n d e n t o f t h e s p r a y p r e s s u r e . In a d d i t i o n , t h e h e a t - t r a n s f e r c o e f f i c i e n t s f o r a n y g i v e n s p r a y w a t e r f l u x a r e much h i g h e r t h a n t h o s e r e p o r t e d by M i z i k a r f o r t h e h i g h e s t s p r a y p r e s s u r e u s e d i n h i s w o r k -0 . 6 2 MPa (90 p s i ) . A w i d e v a r i a b i l i t y o f t h e h e a t - t r a n s f e r c o e f f i c i e n t s i s a g a i n o b s e r v e d . A c o m p a r i s o n o f t h e v a r i a t i o n o f t h e h e a t - t r a n s f e r c o e f f i c i e n t s w i t h s u r f a c e t e m p e r a t u r e s f o r d i f f e r e n t s p r a y f l u x e s i s p r e s e n t e d i n F i g u r e 6 3 . From t h i s F i g u r e , i t c a n be o b s e r v e d t h a t t h e v a r i a t i o n o f t h e h e a t - t r a n s f e r Water flux (gal / f t miri) 10 2 0 3 0 4 0 5 0 6 0 0 1 1 1 1 1—J o 0 10 2 0 3 0 4 0 2 Water flux, l / m s F i g u r e 62 V a r i a t i o n o f h e a t - t r a n s f e r . c o e f f i c i e n t s w i t h w a t e r f l u x f o r a s u r f a c e t e m p e r a t u r e o f 1 000°C ( T y p e I and Type 11 a E x p e r i m e n t s ) . 0 0 6 0 0 0 4 8 0 0 3 6 0 0 2 4 c a> "o O % <» o a) v. . w £ CM o | 0012 0 700 Water flux(IAn2s) 19-3 n - e F i g u r e 63 V a r i a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s w i t h s u r f a c e t e m p e r a t u r e ( T y p e I E x p e r i m e n t s ) . CM G c 0J O o c o o 800 900 Surface Temperature ( °C) 1000 tn 176 c o e f f i c i e n t s w i t h t e m p e r a t u r e i s s m a l l , b u t t h a t a t t h e 2 h i g h e r s p r a y f l u x o f 1 9 . 3 1/m s , t h e h e a t - 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 s l o w l y as t h e s u r f a c e t e m p e r a t u r e d r o p s b e l o w 8 5 0 ° C . The r e l a t i v e i n s e n s i t i v i t y o f t h e h e a t - t r a n s f e r c o e f f i c i e n t s t o t h e s u r f a c e t e m p e r a t u r e a t t h e l o w e r w a t e r f l u x e s i s i n a g r e e m e n t w i t h t h e r e s u l t s r e p o r t e d by M i z i k a r . The h i g h e r h e a t - t r a n s f e r c o e f f i c i e n t s o b t a i n e d i n t h e p r e -s e n t w o r k a r e a t t r i b u t e d t o t h e p r e s e n c e o f t h e " w a t e r c u r t a i n " f l o w i n g down t h e c o l d s u r f a c e s u r r o u n d i n g t h e h e a t -t r a n s f e r p r o b e . The p r e s e n c e o f t h i s " w a t e r c u r t a i n " h a s b e e n o b s e r v e d i n t h e p r e v i o u s m e a s u r e m e n t o f s p r a y f l u x e s as r e p o r t e d i n a p r e v i o u s s e c t i o n . 5 . 2 . 5 R e s u l t s o f T y p e I T E x p e r i m e n t s F u r t h e r m e a s u r e m e n t s w e r e t h e n c o n d u c t e d u s i n g t h e m e a s u r i n g p r o b e i m b e d d e d i n a s t e e l p l a t e . F o r t h e s e e x p e r i m e n t s , t h e f a c e o f t h e m e a s u r i n g p r o b e was p r o t e c t e d by a m e t a l l i c s h r o u d p u r g e d w i t h n i t r o g e n , d u r i r i g h e a t i n g i n a gas f i r e d f u r n a c e . In t h e f i r s t s e r i e s o f e x p e r i m e n t s , t h e s u r f a c e o f t h e m e a s u r i n g p r o b e was f l u s h w i t h t h e s u r f a c e o f t h e s t a i n l e s s s t e e l p l a t e ( T y p e M a E x p e r i m e n t , F i g u r e 2 3 ) . T h e s e t e s t s w e r e done t o c o n f i r m t h a t t h e wa te r 177 f l o w i n g down t h e c o o l e d s u r f a c e c o u l d c a u s e an i n c r e a s e o f t h e h e a t - t r a n s f e r c o e f f i c i e n t s . The r e s u l t s o f t h i s s e r i e s o f t e s t s , p l o t t e d i n F i g u r e 62 show t h a t t h e r e i s a d e c r e a s e i n t h e s c a t t e r o f r e s u l t s , as w e l l as a g e n e r a l d e c r e a s e i n t h e h e a t - t r a n s f e r c o e f f i c i e n t s f o r a g i v e n w a t e r f l u x , when c o m p a r e d t o t h e T y p e I m e a s u r e m e n t s p r e s e n t e d i n F i g u r e s 61 a n d 6 2 . S i n c e t h e r e i s a l a r g e s u r f a c e a r e a c a p a b l e o f e x t r a c t i n g h e a t f r o m t h e i m p i n g i n g s p r a y s i n t h e T y p e I I e x p e r i m e n t s , t h e q u a n t i t y o f w a t e r f l o w i n g downward a d j a c e n t t o t h e s p r a y e d s u r f a c e w o u l d be d r a s t i c a l l y r e d u c e d , a n d t h u s w o u l d n o t i n t e r f e r e as much w i t h t h e d i r e c t s p r a y c o o l i n g o f t h e m e a s u r i n g p r o b e , when c o m p a r e d t o t h e c o n d i t i o n s o b t a i n e d i n t h e Type I e x p e r i m e n t s . In t h e s e Type 11 a e x p e r i m e n t s , t h e h e a t - t r a n s f e r c o e f f i c i e n t s w e r e f o u n d t o be s u r f a c e t e m p e r a t u r e s e n s i t i v e . From t h e r e s u l t s p r e s e n t e d i n F i g u r e 6 4 , i t c a n be o b s e r v e d t h a t t h e h e a t - t r a n s f e r c o e f f i c i e n t s d e c r e a s e as t h e s u r f a c e t e m p e r a t u r e i n c r e a s e s . In a d d i t i o n , i t c a n be s e e n t h a t i n c r e a s e o f t h e s p r a y w a t e r f l u x s h i f t s t h e c u r v e s u p w a r d s t o h i g h e r h e a t - t r a n s f e r c o e f f i c i e n t s . The e f f e c t o f s p r a y p r e s s u r e on t h e h e a t - t r a n s f e r c o e f f i c i e n t s c o u l d n o t b e d i s t i n g u i s h e d . 1 78 CM E c .2 o o o to c t>-5 o X Water flux ( l/m2s) 800 9 0 0 1000 Surface Temperature ° C F i g u r e 64 V a r i a t i o n o f h e a t - t r a n s f e r c o e f f i c i e n t s w i t h s u r f a c e t e m p e r a t u r e ( T y p e 11 a E x p e r i m e n t s ) 1 79 A l l fur ther runs of the Type II experiments were car r ied out with heat - t ransfer probes of length 3.18 cm (1.25 in) f i t t e d with a ring around the front of the probe so that only the water d i r e c t l y impinging on the probe surface from the spray nozzle would be used to cool the surface of the probe (Type l i b Experiments, Figure 25). Henceforth, spray water f luxes at the probe were varied only by movement of the nozzle along i t s a x i s , and by changing the spray pressure. The va r ia t ion of the heat - t ransfer c o e f f i c i e n t s with spray water f lux at 1000° C for th is set of experiments is presented in Figure 65. Spray pressures employed for th is set of resu l ts were 0.14, 0.28, and 0.41 MPa (20, 40 and 60 p s i ) . S imi lar resu l ts obtained for surface tempera-tures of 800, 850, 900, 950 and 1050° C are given in Figures 66 to 70. The heat - t ransfer c o e f f i c i e n t s p lot ted in these Figures do not include the rad ia t ion c o n t r i b u t i o n . It can be observed from these Figures that as the tempera-ture decreases, there is an increase both in the value and the v a r i a b i l i t y of the heat - t ransfer -coeff i ci ent. In genera l , the hea t - t rans fer c o e f f i c i e n t s increase as the spray f lux increases . Since i t has been demonstrated that Type I experiments do not measure just the heat t rans fer from the^ impinging sprays , only the resu l ts of the Type II experiments have been used in further analyses. The results of the type.IIa experiments fell within the limits of the variability of the data obtained from Type lib experiments. 180 U3 CD " U J O s a I — o to \ • L U i 0 » »—i_" u_ u_ U J -o <->OJ U J u_ to " z cr X A Q NOZZLE 1/4G630 1/4GGJ0 1/4GG10 OTHER PRESSURE PSI MPA 20 . 0.13 40 0.21 60 0.41 SEE TABLE VI Fitted curve ± 25 % CD PEAK FLUXES SURFACE TEMP. (DEG. CJ 1000 i i i i I 1 1 1 1 1 r 0.0 4.0 S:0 J2.D 16.0 20.0 SPRAY FLUX L / S 0 . 24.0 2B.0 METRE SEC 32.0 36.0 40.0 F i g u r e 65 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s  w i t f i peak va lues water f l u x f o r a s u r f a c e tempera tu re o f 1000°C. 181 to CD • IxJ Oeo en t— . U J O CO V . • : * UJ •—1 o<°. U."" u. UJ -O <-i(S UJ u. . CO cc°o cr UJ, NOZZLE PRESSURE PSI MPfl 1/4GG10 20 0.13 1/4GG10 40 0,27 1/4GG10 60 0.41 OTHER SEE TABLE VI IS Fitted curve ± 2 5 % PEAK FLUXES SURFRCE TEMP. (DEG. C) 800 — i 1 — i — i 1 — i — ~ ~ i — i — i — i — 0.0 4.0 S.O 32.0 16.0 20.0 SPRAT FLUX L/SQ 24.0 28.0 METRE SEC 32.0 36.0 F igure 66 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s  w i t h peak va lues water f l u x f o r a s u r f a c e tempera tu re of 800°C. 182 to • UJ Ooo oc UJ o CO \ • I — z . U J •—i <_)U> UJ • O UJ U_ CO (X°Q ex UJ, + X • NOZZLE 1/4GG10 1/4GG10 1/4GG10 OTHER PRESSURE PSI MPA 20 0.13 40 0.27 60 0.41 "SEE TABLE VI CD Fitted curve PEAK FLUXES SURFACE TEMP. (DEG. C) 850 o.o 4 . 0 —f— BJO T T i 1 1 1 1 r 3 2 . 0 1 6 . 0 2 0 . 0 2 4 . 0 2 8 . 0 SPRAY FLUX L /SQ. METRE SEC i 1 1— 32.0 36.0 43.0 F i g u r e 67 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h peak va lues wa te r f l u x . f o r a s u r f a c e tempera tu re o f 850°C. 183 to CD " UJ Q c o U J ^ ' C£ I— . UJ •ex O CO \ -UJ UJ -o UJ -2 r x w CX UJ, + X • NOZZLE 1/4GG10 1/4GG10 1/4GG10 OTHER PRESSURE PSI MPA "20 40 60 SEE 0.13 0.27 0.41 TABLE VI Fitted curve ± 25 % CD PEAK FLUXES SURFACE TEMP. (DEG. C) 900 — i 1 1 1 1 1 1 1 1 1 1 1— i 1 r — i 1 1 r 0.0 4.0 6.0 12.0 16.0 20.0 24.0 2B.0 32.0 36.0 SPRAY FLUX L /SQ. METRE SEC 43.0 F i g u r e 68 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h peak va lues water f l u x f o r a s u r f a c e tempera tu re o f 900°C. 184 to CD -UJ Oeo UJ~' cc »— . UJ =T o to ^ -+ x (3 NOZZLE 1/4GG10 1/4GG10 1/4GG10 OTHER PRESSURE PSI > MPfl 20 40 60 0.13 0.27 0.41 SEE TABLE VI Fitted curve ± 25 % ts u_ u_ UJ • o <->fN UJ C C • PEAK FLUXES SURFACE TEMP. (DEG. C) 950 —i 1 1 1 1 1 1 r 0.0 4.0 8.0 12.0 16.0 SPRAY FLUX i 1 1 1 1 1— 20.0 24.0 26.0 L / S 0 . METRE SEC 32.0 36.0 40.0 F igu re .69 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h peak va lues water f l u x f o r a s u r f a c e tempera tu re o f 950°C. 185 I S CN CD 1 LU Qco en L U O CO N • L U »—i U . LU • O L U U_ CO e x + X D NOZZLE 1/4GG10 1/4GG10 1/4GG10 OTHER PRESSURE PSI MPA 20 40 60 SEE 0.13 0.27 0.41 TABLE VI Fitted curve + 25 % PERK FLUXES SURFACE TEMP. (DEG C) 1050 —i 1 1 1 1 1 1 1 r 0.0 4.0 B.O 32.0 16.0 SPRAT FLUX 20.0 24.0 28.0 L / S Q . METRE SEC 32.0 36.0 40.0 F igu re 70 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h  peak va lues water f l u x f o r a s u r f a c e tempera ture o f 1050°C, 186 T h r e e t y p e s o f c u r v e f i t s w e r e a t t e m p t e d t o c o r -r e l a t e t h e d a t a . T h e s e w e r e o f t h e f o l l o w i n g f o r m s : i ) h = P (1 ) rfi . . . 5 . 1 i i ) h = P ( l ) m P ( 2 ) . . . 5 . 2 i i i ) h = P ( l ) + P ( 2 ) rfi . . . 5 . 3 w h e r e P ( l ) and P ( 2 ) a r e f i t t i n g p a r a m e t e r s . The c o m p u t e r p r o g r a m u s e d f o r t h e f i t t i n g u t i l i z e d a d e r i v a t i v e f r e e n o n l i n e a r r e g r e s s i o n t e c h n i q u e . The powe r f i t ( i i ) was f o u n d t o c o r r e l a t e t h e d a t a b e s t a n d t h e v a l u e s o f t h e p a r a m e t e r s a r e g i v e n i n T a b l e l V . The w a t e r f l u x e s u s e d f o r t h e s e f i t s and f o r F i g u r e s 65 t o 70 a r e t h o s e m e a s u r e d by t h e c e n t r a l c o l l e c t o r s i n t h e s p r a y f l u x m e a s u r e m e n t s y s t e m u s i n g Type A c o l l e c t o r s . The f i t t e d c u r v e s t o t h e d a t a a r e d r a w n on t h e F i g u r e s and m o s t o f t h e d a t a f a l l w i t h i n 25% o f t h e s e v a l u e s . The f i t t e d p a r a m e t e r s a r e t a b u l a t e d i n T a b l e I V . 5 . 2 . 5 . 1 A v e r a g i n g o f S p r a y F l u x e s O v e r t h e  A r e a o f t h e P r o b e F a c e S i n c e t h e s p r a y f l u x d i s t r i b u t i o n s show a s h a r p p e a k i n t h e c e n t r e , a v e r a g e w a t e r f l u x e s o v e r t h e 2 5 . 4 mm d i a m e t e r p r o b e s u r f a c e s w e r e t h e n c a l c u l a t e d u s i n g t h e s p r a y f l u x e s o b t a i n e d a t t h e t h r e e c e n t r a l c o l -l e c t o r t u b e s ( T y p e A c o l l e c t o r s , 2 5 . 4 mm a p a r t ) f o r t h e a p p r o p r i a t e s p r a y i n g c o n d i t i o n s . T h i s , i n e f f e c t , l o w e r s 187 TABLE IV C o e f f i c i e n t s o f t h e F i t t e d P o w e r C u r v e s C o r - r e l a t i n g t h e H e a t - T r a n s f e r C o e f f i c i e n t s t o t h e  P e a k V a l u e s o f S p r a y W a t e r F l u x a t D i f f e r e n t  S u r f a c e T e m p e r a t u r e s . ' P ( 2) Form o f t h e c u r v e h = P ( l ) rii v ' S u r f a c e T e m p e r a t u r e °C P a r a m e t e r E s t i m a t e s S t a n d a r d E r r o r o f P(D P ( 2 ) P(D | p ( 2 ) _ 800 0.73 0. 38 0 . 14 j 0.08 • 850 0. 76 0.25 0 . 1 6 0.09 900 0.61 0. 23 0. 12 0. 08 950 0.40 0.31 0 . 08 0. 08 • 1000 0. 20 0.52 0.05 0.10 1050 0. 12 0.65 0 . 04 0 . 1 5 1 8 8 t h e v a l u e s o f t h e s p r a y f l u x a t t h e p r o b e f o r any g i v e n s p r a y i n g c o n d i t i o n , and y i e l d s a l a r g e r h e a t - t r a n s f e r c o -e f f i c i e n t f o r a g i v e n s p r a y f l u x when c o m p a r e d t o v a l u e s o b t a i n e d u s i n g t h e peak f l u x e s . The v a r i a t i o n o f h e a t -t r a n s f e r c o e f f i c i e n t s p l o t t e d as a f u n c t i o n o f t h e a v e r a g e s p r a y f l u x f o r d i f f e r e n t t e m p e r a t u r e s i s p r e s e n t e d i n F i g u r e s 71 t o 76 f o r s u r f a c e t e m p e r a t u r e s f r o m 800 t o 1 0 5 0 ° C i n 5 0 ° C i n c r e m e n t s . A g a i n , powe r c u r v e s o f t h e t y p e d i s c u s s e d i n t h e p r e v i o u s s e c t i o n w e r e f o u n d t o y i e l d t h e b e s t f i t s t o t h e d a t a . The v a l u e s o f t h e p a r a m e t e r s o b t a i n e d from t h e c u r v e f i t t i n g r o u t i n e s a r e p r e s e n t e d i n T a b l e V . 5 . 2 . 5 . 2 C o m p a r i s o n o f D a t a f o r P e a k and  A v e r a g e d F l u x e s The h e a t - t r a n s f e r c o e f f i c i e n t s m e a s u r e d i n t h i s s t u d y a r e s e e n t o h a v e a f a i r l y w i d e v a r i a b i l i t y as e v i d e n c e d by an e x a m i n a t i o n o f t h e p l o t s o f h e a t - t r a n s f e r c o e f f i c i e n t s v s . t h e s p r a y w a t e r f l u x . The v a r i a b i l i t y i s s e e n t o i n c r e a s e as t h e s u r f a c e t e m p e r a t u r e d e c r e a s e s , a n d as t h e s p r a y f l u x i n c r e a s e s . The h e a t -t r a n s f e r c o e f f i c i e n t s a r e a l s o f o u n d t o be s u r f a c e t e m p e r a t u r e d e p e n d e n t , w i t h t h e i r m a g n i t u d e s i n c r e a s i n g w i t h d e c r e a s i n g s u r f a c e t e m p e r a t u r e . As c a n be s e e n f r o m T a b l e s IV and V , i n g e n e r a l , t h e e x p o n e n t s o f t h e p o w e r c u r v e s i n c r e a s e f r o m 0 . 2 5 t o 0 . 9 9 as t h e s u r f a c e t e m p e r a t u r e 189 / Fitted curve 4 25 % NOZZLE PRESSURE PSI MPfl 1/4GG10 20 0.13 1/4GG10 40 0.27 1/4GG10 60 0.41 OTHER SEE TABLE VI AVERAGE FLUXES SURFACE TEMP. (DEG. C) 800 —i 1 1 1 j 1 j 1 1 1 — 0 . 0 4 . 0 8 . 0 3 2 . 0 1 6 . 0 2 0 . 0 SPRAY FLUX L/SO. . 2 4 . 0 2 S . 0 METRE SEC i r 32.0 36.0 40 F i g u r e 71 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h va lues o f water f l u x averaged over the probe f a c e , f o r a s u r f a c e temperature o f 800°C. 190 CD • LU O < o LU04"' I— LU T V o CO I— LU ' LU a or-LU U_ CO GC«0 <X LU, Fitted curve ± 25 % NOZZLE 1/4GG10 1/4GG10 1/4GG10 OTHER PRESSURE PSI MPfl 20 0 .13 40 0.27 60 0.41 SEE TRBLEVI RVERflGE FLUXES SURFACE TEMP. (DEG. C) 850 o.o 4.0 — J — 8.0 32.0 16.0 20.0 SPRAT FLUX L/SO, —i 1 1 — 24.0 28.0 METRE SEC 32.0 36.0 40 .0 F i g u r e 72 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h va lues o f water f l u x averaged o v e r the probe f a c e , f o r a s u r f a c e temperature o f 850°C. 191 C O C l " CD • U J a c o Q l t— . UJ • C N ' O CO ^ • i ' U_ U_ U J • o O r , C X " ' U J u_ . CO z fX Fitted curve i 25 % NOZZLE PRESSURE 1/4GG10 1/4GG10 1/4GG10 OTHER PSI 20 40 60 SEE MPR 0.13 0.27 0.41 TABLE V! AVERAGE FLUXES SURFACE TEMP. (DEG. C) 900 —i 1 1 1— i 1 1 — 2 0 . 0 2 4 . 0 2 B . 0 3 2 . 0 L /SQ. METRE SEC 0 . 0 4 . 0 —\— B.O 1 2 . 0 1 6 . 0 SPRAT FLUX 3 6 . 0 F i g u r e 73 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h vaoues o f water f l u x averaged o v e r the probe f a c e , f o r a s u r f a c e temperature o f 900°C. 192 to (*>" CM CD ' LU O c o LU 0 1 ' " LU T o CO \ • : * Fitted curve ± 25 % • — i „ U_ U-LU O O N LU U . CO C C « o NOZZLE 1/4GG10 1/4GG10 1/4GG10 OTHER PRESSURE PSI MPfl 20 40 60 SEE 0.13 0.27 0.41 TABLE VI AVERAGE FLUXES SURFACE TEMP. (DEG. C) 950 — % 1 1 1—~i 1 i i r n D 4 0 B .O 3 2 . 0 1 6 . 0 °- • SPRAY FLUX —i 1 1 1 i 2 0 . 0 2 4 . 0 2 8 . 0 L/SQ. METRE SEC 32.0 3 6 . 0 F i g u r e 74 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h va lues o f wa te r f l u x averaged over the probe f a c e , f o r a s u r f a c e temperature o f 950°C. 193 Fitted curve ± 25 % CD NOZZLE 1/4GG10 1/4GG10 1/4GG10 OTHER PRESSURE PSI MPR 20 0.13 40 0.27 60 0.41 SEE TABLE VI AVERAGE FLUXES SURFACE TEMP. (DEG. Cl 1000 i i i i i i i r 0.0 4.0 8.0 12.0 16.0 SPRRY FLUX 1 1 1 1 1 1 20.0 24.0 2B.0 L /SO. METRE SEC 32.0 36.0 40.0 F i g u r e 75 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s  w i t h v a l u e s o f water f l u x averaged o v e r the probe f a c e , f o r a s u r f a c e temperature o f 1000°C. 194 to (N O • UJ Oo U J ~ ' t— . UJ Fitted curve ± 25 % TM O to rJ" I — 2 . UJ <—• t_><°. u_ u_ UJ -o UJ u_ to tx» UJ, / NOZZLE 1/4GG10 1/4GG10 1/4GG10 OTHER PRESSURE PSI MPA 20 40 60 SEE 0.13 0.27 0.41 TABLE VI AVERAGE FLUXES SURFACE TEMP. (DEG. Cl 1050 — i 1 — i 1 1 — i — i — i — i — i — ~ i — i 1 — i — 0.0 4.0 8.0 32.0 16.0 20.0 24.0 28.0 SPRAT FLUX L /SQ. METRE SEC 32.0 36.0 40.0 F i g u r e 76 V a r i a t i o n o f the measured h e a t - t r a n s f e r c o e f f i c i e n t s w i t h va lues o f wa te r f l u x averaged Over the probe f a c e , f o r a s u r f a c e ' t e m p e r a t u r e ' O f 1 0 5 0 ° C . 195 TABLE V C o e f f i c i e n t s of the F i t ted Power Curves Corre la t ing the Heat-Transfer C o e f f i c i e n t s to Water Fluxes Averaged Over the Area of the  Probe Face, for D i f ferent Surface Temperatures. Form of the curve h = P(l) m v ' Surface Parameter Estimates Standard Error of Temperature °C P ( l ) P(2) P ( l - ) P(2) 800 0. 64 e . 50 0.13 0. 10 850 0.68 0. 34 0.16 0 . 1 1 . 900 0.55 0. 33 0.11 0. 10 950 ' 0. 34 0.43 0.07 0. 10 1 000 0.15 0.75 0. 04 0.13 1050 0.07 0.99 0.03 0. 19 196 i n c r e a s e s . The f r a c t i o n a l e x p o n e n t s i n d i c a t e t h a t t h e w a t e r f l u x h a s l e s s t h a n a p r o p o r t i o n a l e f f e c t on t h e h e a t - t r a n s f e r c o e f f i c i e n t . The e x p o n e n t s a r e , as e x p e c t e d , h i g h e r i n t h e c a s e s w h e r e t h e h e a t - t r a n s f e r c o e f f i c i e n t s h a v e b e e n r e l a t e d t o t h e a v e r a g e w a t e r f l u x e s t h a n when r e l a t e d t o t h e p e a k w a t e r f l u x e s . The g e n e r a l t r e n d o f t h e i n c r e a s e i n t h e e x p o n e n t w i t h i n c r e a s i n g t e m p e r a t u r e d o e s n o t h o l d when t h e s u r f a c e t e m p e r a t u r e i s 8 0 0 ° C , b u t t h i s may be due t o t h e l a r g e a m o u n t o f s c a t t e r p r e s e n t i n t h e r e s u l t s o b t a i n e d f o r t h i s t e m p e r a t u r e . 5 . 2 . 5 . 3 R e s u l t s f r o m E x p e r i m e n t s P e r f o r m e d  w i t h O t h e r N o z z l e s In o r d e r t o d e t e r m i n e w h e t h e r t h e s p r a y s o b t a i n e d f r o m o t h e r f u l l c o n e n o z z l e s b e h a v e d i n a s i m i l a r m a n n e r , h e a t - t r a n s f e r c o e f f i c i e n t s w e r e m e a s u r e d f o r s p r a y s p r o d u c e d by n o z z l e s l i s t e d i n T a b l e V I . The o p e r a t i n g c o n d i t i o n s u n d e r w h i c h t h e m e a s u r e m e n t s w e r e made a r e a l s o l i s t e d i n t h i s T a b l e . The r e s u l t s a r e p l o t t e d i n F i g u r e s 65 t o 76 a l o n g w i t h t h o s e o f t h e 1 /4 GG 10 n o z z l e s . The h e a t t r a n s f e r c o e f f i c i e n t s o b t a i n e d f o r t h e s e n o z z l e s a r e o b s e r v e d t o be s i m i l a r t o t h a t ' o f t h e 1 / 4 GG 10 n o z z l e f o r t h e same w a t e r f l u x . T h u s , t h e t y p e o f n o z z l e d o e s n o t h a v e a s t r o n g i n f l u e n c e on t h e h e a t - t r a n s f e r c o e f f i c i e n t . 197 T A B L E VI L i s t o f N o z z l e s O t h e r Than 1 / 4 GG 10 a n d O p e r a t i n g S p r a y P r e s s u r e s U s e d i n t h e  M e a s u r e m e n t o f S p r a y H e a t - T r a n s f e r C o e f f i c i e n t s . N o z z l e T y p e S p r a y P r e s s u r e s MPa p s i 3/8 HH 18 SQ 1/4 G.G 12 SQ 1/4 GG 6.5 •1/8 GG 5 0 .14 ,0 .21 0 . 1 4 , 0 . 2 8 , 0 . 4 1 0 . 1 4 , 0 . 2 8 , 0 . 4 1 , 0 . 6 9 0 . 1 4 , 0 . 2 8 , 0 . 4 1 , 0 . 6 9 20,30 20 ,40 ,60 2 0 , 4 0 , 6 0 , 1 0 0 20 ,40 ,60 ,100 198 5 . 3 E f f i c i e n c y o f S p r a y C o o l i n g Many a u t h o r s 5 3 , 6 5 - 6 7 ' 7 6 ' 8 1 " 8 4 h a v e u s e d t h e c o n c e p t o f s p r a y c o o l i n g e f f i c i e n c y , n , w h i c h i s d e f i n e d a s t h e r a t i o o f t h e a c t u a l h e a t e x t r a c t e d by t h e i m p i n g i n g , w a t e r , t o t h e t h e r m a l p o w e r r e q u i r e d t o h e a t a n d v a p o r i z e a l l t h e i m p i n g i n g w a t e r . n = h (T - T ) . . . 5 . 4 s w rfi U h + C_ (T, - T ) ] .. v p b w J S p r a y c o o l i n g e f f i c i e n c i e s a r e c a l c u l a t e d a n d t h e r e s u l t s a r e g i v e n f o r s i x s u r f a c e t e m p e r a t u r e s i n F i g u r e s 77 t o 88 r e s p e c t i v e l y , f o r t h e peak v a l u e s a n d a v e r a g e d v a l u e s o f w a t e r f l u x e s . E x a m i n a t i o n o f t h e F i g u r e s shows t h a t as t h e w a t e r f l u x i n c r e a s e s , t h e s p r a y c o o l i n g e f f i c i e n c y d r o p s , u n t i l a l i m i t i n g v a l u e i s r e a c h e d a t a b o u t 16 1/m s . B e y o n d t h i s v a l u e o f t h e w a t e r f l u x , no a p p r e c i a b l e d e c r e a s e o f t h e e f f i c i e n c y i s o b s e r v e d . In a d d i t i o n , t h e m a g n i t u d e s o f t h e e f f i c i e n c i e s i n c r e a s e as t h e s u r f a c e t e m p e r a t u r e i s l o w e r e d . T h i s i s c o n s i d e r e d t o be a m a n i f e s t a t i o n o f t h e i n c r e a s e o f t h e h e a t - t r a n s f e r c o e f f i c i e n t w i t h d e c r e a s i n g s u r f a c e t e m p e r a t u r e . R e f e r r i n g t o F i g u r e 8 8 , f o r a s u r f a c e t e m p e r a t u r e o f 1 0 5 0 ° C , i t c a n a l s o - be o b s e r v e d t h a t t h e s p r a y c o o l i n g e f f i c i e n c y d o e s n o t d e c r e a s e as much w i t h i n -c r e a s i n g w a t e r f l u x as c o m p a r e d t o e f f i c i e n c i e s a t l o w e r s u r f a c e t e m p e r a t u r e s . T h i s i s r e f l e c t e d i n t h e i n c r e a s e i n t h e e x p o n e n t i n t h e p o w e r c u r v e s f i t t e d t o t h e h e a t - t r a n s f e r 199 - * x NOZZLE PRESSURE cn _ \ PSI MPA - 1/4GG10 20 0.13 \ * 1/4GG10 40 0.27 \ a 1/4GG10 60 0.41 +\ CD OTHER SEE TABLE VI r- _ A x \ * PERK FLUXES «5 -X \ \ A SURFACE TEMP. (DEG. O 8 0 0 o z LU \ A tZ U- — UJ •sr -to -• \ 9 x • v X 4 + • • • • • • CM -— 1 1 1 1 1 1 1 1 r 1 ' 1 1 r i i i i i i 0.0 4.0 8 0 12 0 16.0 20.0 24.0 28.0 SPRAY FLUX (L 7 S 0 . M . SEC) 32.0 36.0 F i g u r e 77 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h peak va lues o f water f l u x , f o r a s u r f a c e temperature of 800°C. 40 .0 200 NOZZLE PRESSURE PSI MPfi 40 .0 F i g u r e 78 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h peak va lues df water f l u x , f o r a s u r f a c e temperature o f 850°C. 201 CO CO 1 o z UJ o 1 0 u. ro 1 CM -1 0.0 + X ts NOZZLE PRESSURE PSI MPA JV4GG30 20 0 .13 1/4GG30 40 0.27 1/4GG30 60 0.43 OTHER SEE TABLE VI PEAK FLUXES SURFACE TEMP. (DEG. C) 9 0 0 CD 4.0 8.0 T 1 1 71 1 J _ „ 1 Z : S P R A Y ' F L U X ( I ' 7 S Q . M ^ S E C ) ' F i g u r e 79 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h peak va lues o f water f l u x , f o r a s u r f a c e temperature o f 900°C. -1 1 "> 1 1 ^ 1 16.3 ' 2 0 . - 0 . ; . 2 4 . 0 _ „ _ . 2 8 . 0 32.0 36.0 40.0 202 cn oo N 4 + X a NOZZLE PRESSURE 1/4GG10 1/4GG30 1/4GG10 OTHER PSI 20 40 60 MPA 0 .13 0 .27 0.41 SEE TABLE VI u u. to H PEAK FLUXES SURFACE TEMP. (DEG. C) 950 CD • 0.0 4.0 B.O -l 1 1 1 I I ' * 1 12 0 16.0 20.CT 2 4 . 0 ^ 28.0 SPRAY FLUX (L / S Q . M . SEC) 32.0 36.0 40 .0 F i g u r e 80 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h peak v a l u e s o f wa te r f l u x , f o r a s u r f a c e temperature o f 950°C. 203 to J N -J «5 >-O z Ul Lu u. LU CM "I + X A O NOZZLE 1/4GG30 1/4GG10 1/4GG10 OTHER PRESSURE PSI MPR 20 0 .13 40 0 .27 60 ' 0.42 SEE TRBLE VI PERK FLUXES SURFRCE TEMP. (DEG. C) 1000 m O.D 4.0 B.O - i 1 1 1 r — i 1 1 i ]2 0 1-6.0 20.0 24.0; 28.0 SPRRY FLUX (L / S 0 . M . SEC) 32.0 36.0 F igu re 81 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h peak v a l u e s o f water f l u x , f o r a s u r f a c e tempera tu re o f 1000°C. 204 NOZZLE PRESSURE PSI MPfl + 1/4GGI0 20 0 . 1 3 x 1/4GGI0 40 0 . 2 7 A 1/4GG10 60 0.41 0 OTHER SEE TABLE VI PERK FLUXES SURFACE TEMP. (DEG. C) 1050 oo J o z UJ .UJ -1 A X A ro H + A CD ^ • + A ° & ° x * + AX CD Q ~ i i i r i i i i i i i 1 1 1 1 1 1 1 1 0.0 4.0 B.O ]2.0 16.0 20.0 24.0 2B.0 32.0 3 6 0 40 0 SPRAY FLUX (L / S Q . M . SEC) F i gu re 82 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h peak v a l u e s  o f water f l u x , f o r a s u r f a c e temperature o f 1050°C. 205 to o z Ul o <n 1 Lu U. Ul A v A W X NOZZLE PRESSURE PSI MPfl \ * + 1/4GG10 20 0 .13 x 1/4GG10 40 0 .27 \[D \ A £ 1/4GG10 60 0.41 •o OTHER SEE TABLE VI X \ CD _ \ + AVERAGE FLUXES \ + SURFRCE TEMP. (DEG. C) 8 0 0 • • o • ° CD a • — ^ — — i 1 1 1 — — — i • — i 1 r — — i 1 r — i r i i i i 0 .0 4.0 B.O J2.0 16.0 2D.D 24.0 2B.0 32.0 S P R A Y ' F L U X ( L ' 7 S 0 . M ' . " S E C ! " F igu re 83 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h va lues o f  water f l u x averaged over the probe f a c e , f o r a  s u r f a c e temperature o f 800°C. 36.0 40.0 2 0 6 CO o z ui u. IU CM H + NOZZLE 1/4GG10 1/4GG10 1/4GG10 OTHER PRESSURE PSI MPA 20 0 .13 40 0 .27 60 0.41 S E E TABLE VI AVERAGE FLUXES SURFACE TEMP. (DEG. CJ 850 • 0.0 4.0 6.0 - | 1 1 1 1 } 1 1 1 32 0 16.0 20.0 ' 24.0 2B.0 SPRAY FLUX (L / S 0 . M . SEC) 32.0 i r 36.0 40 .0 F igu re 84 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h v a l u e s o f wa te r f l u x averaged over the probe f a c e , f o r a s u r f a c e temperature o f 850°C. 207 cn J CO N -4 >• o Z ' UJ o m LL. UJ to 0 . 0 NOZZLE PRESSURE PSI MPA + 1/4GG10 20 0.13 X 1/4GG10 40 0.27' 1/4GG10 60 0.41 o OTHER SEE TABLE VI RVERRGE FLUXES SURFACE TEMP. (DEG. C) 900 CD 4 . 0 8 . 0 i 1 1 1 1 1 1 1 1 r 3 2 . 0 1 6 . 0 2 0 . 0 2 4 . 0 . 2 8 . 0 SPRAY FLUX (L / S 0 . M . SEC) 3 2 . 0 ^ r 3 6 . 0 4 0 . 0 F igu re 85 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h v a l u e s o f  water f l u x averaged over the probe f a c e , f o r a  s u r f a c e temperature o f 9 0 0 o C . 208 CO J o z U J iZ u. • NOZZLE PRESSURE PSI MPA + 1/4GG10 20 0.13 X 1/4GG10 40 0.27 1/4GG10 60 0.41 Q OTHER SEE TABLE VI AVERAGE FLUXES SURFACE TEMP. (DEG. C) 950 • —i 1 1 1 1 1 1 i 1 1 1 1 1 1 r 0.0 4.0 B.O 32.0 15.0 20.0 24.0 2B.0 . SPRAY FLUX (L / S Q . M . S E C ) — i 1 1 1— 32.0 36.0 40.0 F igu re 86 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h v a l u e s o f  water f l u x averaged over the probe f a c e , f o r a  s u r f a c e temperature o f 950°C. 209 NOZZLE PRESSURE PSJ MPfl • 1/4GG10 20 0 .13 X 1/4GG10 40 0.27 t 1/4GG10 60 0.41 a OTHER SEE TABLE VI AVERAGE FLUXES SURFACE TEMP. (DEG. C) 1000 + 28.0 32.0 36.0 40.0 l i re 87 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h va lues o f  wa te r f l u x averaged over the probe f a c e , f o r a 210 0) - NOZZLE PRESSURE PSI MPfl CO • 1/4GG10 20 0 .33 X 1/4GG10 40 0.27 A 1/4GG10 60 ." 0.41 a OTHER SEE TABLE VI AVERAGE FLUXES >-o z UJ u. WD ro H CM H A A X+ * + A + A + X A 3 + • CD CD SURFACE TEMP. (DEG. C) 1050 ED • "i 1 1 1 1 1 r 32.0 16.D 20.0 24.0 2B.0 SPRAY FLUX (L / S Q . M . SEC) . o.o 4.0 B.O ^ — ~ T 32.0 36.D 40.0 F igu re 88 V a r i a t i o n o f spray c o o l i n g e f f i c i e n c y w i t h v a l u e s o f wa te r f l u x averaged over the probe f a c e , f o r a s u r f a c e temperature o f 1050°C. T A B L E V I I C o e f f i c i e n t s o f t h e C u r v e s F i t t e d t o C o r r e l a t e S p r a y E f f i c i e n c y t o t h e P e a k V a l u e o f t h e S p r a y W a t e r F l u x e s f o r D i f f e r e n t S u r f a c e T e m p e r a t u r e s . Form o f t h e f i t t e d c u r v e : . P n (%) = P ( l ) + P ( 2 ) m S u r f a c e T e m p e r a t u r e ° c P a r a m e t e r E s t i m a t e s P ( l ) P ( 2 ) P ( 3 ) S t a n d a r d E r r o r o f P ( l ) P ( 2 ) P ( 3 ) 800 1 . 3 7 ~ 2 4 . 1 5 - 0 . 8 3 1 .60 7 . 36 0 . 34 850 0 . 2 9 1 9 . 6 1 - 0 . 6 8 1 .95 4 . 1 0 0 . 30 900 0 . 0 6 1 6 . 3C - 0 . 6 6 1 .51 2 . 74 0 . 26 950 0 . 4 3 1 2 . 5 0 - 0 . 6 9 1. 14 2 . 5 1 0 . 29 1000 1 .26 7 . 0 6 - 0 . 75 0 . 9 7 3 . 0 0 0 . 5 3 T A B L E V I I I C o e f f i c i e n t s o f t h e C u r v e s F i t t e d t o C o r r e l a t e t h e S p r a y E f f i c i e n c y t o t h e V a l u e o f S p r a y W a t e r F l u x A v e r a g e d O v e r t h e A r e a o f t h e P r o b e F a c e , f o r D i f f e r e n t S u r f a c e T e m p e r a t u r e s . Form o f t h e f i t t e d c u r v e : n (%) = P(l) + P(2) m SURFACE TEMPERATURE PARAMETER E S T I M A T E S STANDARD ERROR OF °C P(D P ( 2 ) P(3) P(D P (2) P (3) 800 2 . 9 2 2 2 . 4 8 - 0 . 8 9 2 . 3 5 8 . 7 5 0 . 5 2 850 2 . 0 2 2 0 . 3 2 - 0 . 8 4 2 . 2 9 6 . 6 0 0 . 4 7 900 1 .51 1 7 . 0 4 - 0 . 8 2 1 .72 4 . 5 2 0 . 39 950 1 .51 1 2 . 4 3 - 0 . 8 0 1 . 4 9 3 . 6 7 0 . 4 5 1000 2 . 5 4 5 . 8 9 - 0 . 9 5 1 .12 5 . 2 3 1 .10 ro i—• 213 c o e f f i c i e n t v s . s p r a y w a t e r f l u x d a t a ( T a b l e s IV and V ) . In F i g u r e 7 6 , t h e r e l a t i o n s h i p b e t w e e n t h e h e a t - t r a n s f e r c o e f f i c i e n t and t h e s p r a y w a t e r f l u x i s a l m o s t l i n e a r , and as c a n be s e e n f r o m F i g u r e 8 8 , t h e c h a n g e i n t h e e f f i c i e n c y w i t h w a t e r f l u x i s v e r y s m a l l . A n o t h e r p o i n t o f n o t e i s t h a t t h e d a t a f r o m o t h e r n o z z l e s a l s o f a l l s w i t h i n t h e v a r i a b i l i t y f o r t h e 1 /4 GG 10 n o z z l e . No e f f e c t o f t h e s p r a y p r e s s u r e on t h e e f f i c i e n c y i s o b s e r v e d . The v a r i a t i o n o f e f f i c i e n c y w i t h w a t e r f l u x f o r d i f f e r e n t s u r f a c e t e m p e r a t u r e s w e r e f i t t e d t o an e q u a t i o n o f t h e f o r m n% = P ( l ) + P ( 2 ) m P ( 3 ^ . . . 5 . 5 The c o e f f i c i e n t s P ( l ) , P ( 2 ) a n d P ( 3 ) f o r t h e s e f i t s u s i n g t h e p e a k and a v e r a g e d v a l u e s o f w a t e r f l u x a r e g i v e n i n T a b l e s V I I a n d V I I I . 5 . 4 C a l c u l a t i o n o f D r o p l e t V e l o c i t i e s and D r o p l e t Momenta W i t h i n t h e S p r a y s ' As a p r e l u d e t o t h e c o m p a r i s o n o f t h e r e s u l t s f r o m t h e p r e s e n t w o r k t o d a t a r e p o r t e d ' i n t h e l i t e r a t u r e , c a l c u l a t i o n s o f t h e d r o p l e t v e l o c i t i e s a t t h e n o z z l e e x i t and d r o p l e t momenta w e r e m a d e . D r o p l e t s i z e s r e q u i r e d f o r t h e c a l c u l a t i o n o f d r o p l e t momenta w e r e t h e m e d i a n d r o p s i z e s p u b l i s h e d by t h e m a n u f a c t u r e r o f t h e n o z z l e s . 214 D r o p l e t v e l o c i t y c a l c u l a t i o n s w e r e c a r r i e d o u t u s i n g 53 an e n e r g y b a l a n c e a p p r o a c h s u g g e s t e d by G a u g l e r . N e g l i -g i b l e e n e r g y l o s s e s a r e a s s u m e d f o r t h e c a l c u l a t i o n s . U p -s t r e a m f r o m t h e n o z z l e , t h e w a t e r h a s a v e l o c i t y , p r e s s u r e a n d f l o w s t h r o u g h a p i p e o f a r e a . D o w n s t r e a m , t h e f 1 o w . c o n s i s t s o f d r o p l e t s o f d i a m e t e r d a n d v e l o c i t y a t . a t m o s p h e r i c p r e s s u r e P g . I f t h e n e t r a t e o f p r o d u c t i o n o f t h e d r o p l e t s i s c o n s i d e r e d t o be N , t h e n t h e e n e r g y b a l a n c e c a n be w r i t t e n as p V ] A-j 2g P = N pud" 2 V + P V2 12 29 P + N a ud .. 5.6 S i n c e t h e s u r f a c e t e n s i o n term accounts f o r l e s s than 5% o f the e n e r g y , i t i s n e g l e c t e d . S u b s t i t u t i n g m = P V 1 A 1 = N TF d* 5.7 and s i m p l i f y i n g y i e l d s = + 2g (P2 - 5.8 S i n c e {? ^ - P | ) i s t h e p r e s s u r e g a u g e r e a d i n g , k n o w l e d g e o f t h e m a s s f l o w r a t e t h r o u g h t h e n o z z l e y i e l d s a v a l u e f o r t h e d r o p l e t v e l o c i t y V 2 < The r e s u l t s o f t h e c a l c u l a t i o n s a r e g i v e n i n T a b ! e I X . E x a m i n a t i o n o f t h i s T a b l e s h o w s t h a t a s t h e s p r a y T A B L E IX C a l c u l a t e d D r o p l e t V e l o c i t i e s a n d D r o p l e t Momenta i n t h e S p r a y s P r o d u c e d b y t h e N o z z l e s  S t u d i e d i n t h i s I n v e s t i g a t i o n . Nozz le Type Spray ps i P ressure MPa Drop le t V e l o c i t y cm/sec Mean Drop D iamete r , m ic rons Drop le t Momentum gm cm/sec 1/4 GG 10 20 0.14 1669 2420 12.39 40 0 .28 2359 2040 10.49 60 0.41 2889 1730 7.83 1/4 GG 12 SQ 20 0.14 1672 2540 14.35 40 0.28 2363 2120 11.79 60 0.41 2894 1800 8.84 1/4 GG 6 .5 20 0.14 1664 2120 8.30 40 0.28 2354 1800 7.19 60 0.41 2883 1520 5.30 90 0.66 3627 1120 2.67 3/8 HH 18 20 0.14 1673 2820 19.65 30 0.21 2049 2580 18.43 1/8 GG 5 20 0.14 1667 1900 5.99 40 0.28 2357 1580 4 .87 60 0.41 2888 1360 3.80 80 0.69 3728 970 1.78 216 pressure increases , there is a decrease in the droplet diameter. The ca lcu la ted exi t ve loc i ty of the droplets increases with the spray pressure. However, due to the rapid decrease of droplet diameter with increas ing spray pressure , the droplet momentum decreases as the spray pressure i n c r e a s e s , in the case of the nozzles inves t iga ted . It should be noted that these c a l c u l a t i o n s are ap-proximate and that the actual ve loc i ty of the droplet would decrease as i t moves away from the spray nozzle due to drag e f f e c t s . The range of droplet v e l o c i t i e s is seen to vary from about 16.5 to 30 m/s, and the droplet momentum from about 8 to. 20 gm cm/s - a factor of 2 to 2 .5 , for the resu l ts presented in th is t h e s i s . 5.5 The Nature of the Boi1ing Process C r i t i c a l , or L iedenfrost temperatures for the onset of stable f i lm b o i l i n g have been estimated from the res -u l ts of other studies on spray c o o l i n g , and have been p lot ted in Figure 89 as a funct ion of the spray water f l u x . It can be seen from th is Figure that the c r i t i c a l point is moved to higher surface temperatures as the spray water f lux is increased!, thus extending the region of un-stable f i lm b o i l i n g ,to higher surface temperatures, It 7 6 can also be observed that in the experiments of Miz ikar , stable f i lm b o i l i n g is present at surface temperatures o o CD CL E CD 1000 I 9001 o 8 0 0 S 7001 A • Legend Re fe rence A 7 0 • 7 4 o 7 6 o 7 7 # 8 8 CD O e to Ld A 6 0 0 500 9. 0 O 8 0 Water f lux (l/nri s) I 2 O t—1 F i g u r e 8 9 V a r i a t i o n o f c r i t i c a l t e m p e r a t u r e w i t h w a t e r f l u x 218 g r e a t e r t h a n 6 2 5 ° C e v e n a t w a t e r f l u x e s i n e x c e s s o f 10 Vm s . T h i s i s i n c o n t r a s t w i t h o t h e r r e s u l t s p r e s e n t e d i n t h i s F i g u r e , i n w h i c h t h e c r i t i c a l t e m p e r a t u r e e x c e e d s 2 950°C when t h e w a t e r f l u x i n c r e a s e s b e y o n d 6 £/m s . The v a r i a t i o n o f h e a t f l u x w i t h s u r f a c e t e m p e r a t u r e , as o b t a i n e d f r o m t h e p r e s e n t s t u d y f o r d i f f e r e n t w a t e r f l u x e s , i s p l o t t e d i n F i g u r e 9 0 . The r e s u l t s shown i n t h i s F i g u r e h a v e b e e n c a l c u l a t e d f r o m t h e d a t a shown i n T a b l e I V . The n e g a t i v e s l o p e s o f t h e c u r v e s i n t h e t e m p e r a t u r e r a n g e s t u d i e d i n d i c a t e t h a t t h e o p e r a t i n g b o i l i n g mode i s t r a n s i t i o n o r u n s t a b l e f i l m b o i l i n g m o d e . T h i s b o i l i n g mode has been o b t a i n e d i n t h i s s t u d y e v e n f o r t h e l o w w a t e r f l u x o f 2 £/m s . The m a g n i t u d e o f t h e h e a t f l u x e s p r e s e n t e d i n F i g u r e 90 i s i n r e a s o n a b l e a g r e e m e n t w i t h t h a t i n t h e h i g h t e m p e r a t u r e e n d ( j u s t b e l o w t h e c r i t i c a l p o i n t ) o f t h e u n s t a b l e f i l m b o i l i n g r e g i o n shown i n F i g u r e 3 . I t mus t be n o t e d i n c o m p a r i n g t h e s e F i g u r e s t h a t t h e d a t a i n F i g u r e 3 h a s been o b t a i n e d f r o m p o o l b o i l i n g s t u d i e s o f h e a t t r a n s f e r f r o m a h o t w i r e i m m e r s e d i n w a t e r a t i t s s a t u r a t i o n t e m p e r a t u r e . The e x i s t a n c e o f u n s t a b l e f i l m b o i l i n g s e r v e s t o e x p l a i n t h e o b s e r v a t i o n t h a t t h e h e a t - t r a n s f e r c o e f f i c i e n t s 219 2 0 0 0 h 1000 h CvJ X 3 O CD X 5 0 0 h 100 8 0 0 9 0 0 1000 Surface Temperature °C Figure 90 Var ia t ion of the he at f lux with surface temperature for d i f f e ren t water f l u x e s . 220 that were measured were inf luenced by the surface condi t ion of the heat - t ransfer probe. The extent of scat ter due to the presence of adherent scale on the surface i s , how-ever , l im i ted to that reported in Figures 65-76. This is in view of the fact that whenever the cool ing of the probe was af fected by the presence of semidetached s c a l e , (sect ion 5 .2 .1 ) , the data from such runs was not used in the c a l c u l a t i o n of the heat - t ransfer c o e f f i c i e n t s . In Figure 12, i t can be observed that only the 74 resu l ts of Sugitani show any s i g n i f i c a n t temperature dependence of the heat - t ransfer c o e f f i c i e n t s for surface temperatures greater than 700°C. His spray cool ing studies employed a t rans ient method for the determination of the heat - t ransfer c o e f f i c i e n t s . The other resu l ts p lot ted in Figure 12 were obtained using s teady-s ta te measurement techniques. The resu l ts of Mul ler and Jeschar 81 , obtained from steady-state measurements, a lso did not ind ica te .any s i g n i f i c a n t temperature dependence of the hea t - t rans fer c o e f f i c i e n t s for surface temperatures between 700 and 1200°C. In contrast with these r e s u l t s , recent spray cool ing s t u d i e s , u t i l i s i n g t rans ien t meas-14 74 75 7 7 - 7 9 urements ' ' ' have shown that the heat - t ransfer c o e f f i c i e n t s decrease as the surface temperature increases between 700 and 1000°C. In summary, these f ind ings i n -dicate that , while for the steady-state measurements stable f i lm b o i l i n g is achieved above a surface temperature of 221 .6 0 0 0 C , unstable f i lm b o i l i n g is the operat ing b o i l i n g phenemenon in t rans ien t type s t u d i e s , even at sur face temperatures much in excess of 600°C,. (except in the case of Mi 'z ikar 's study) . 5 . 6 Temperature Dependence of the Heat -Trans fer C o e f f i c i e n t s -P(?)l r i P 3 ) Curves of the type: h = P( l ) m [ '_£_] . . 5 . 9 \1000f were f i t t e d to the h e a t - t r a n s f e r data obtained for the k GG 10 nozzle using a mul t ip le regress ion t e c h n i q u e ^ 7 ' The r e s u l t s of the regression are presented in Table 'X. Thus large values of P(3) can be seen which shows the s i g n i f i c a n t temperature dependence of h, as reported in the previous s e c t i o n . These values for P(3) are much higher than the value of 1.2 reported by S a s a k i 7 7 . The values of P(2) f a l l wi thin the range reported in other spray c o o l i n g s t u d i e s . 5 .7 Comparison with the Results of Other Workers Since laboratory i n v e s t i g a t i o n s on spray heat t rans fe r have been ca r r i ed out using a va r ie ty of e x p e r i -mental methods and condi t ions (Table I I ) , there is a large v a r i a t i o n i n the publ ished s p r a y - h e a t t r a n s f e r d a t a , as can be seen i n Figure 1 1 . In many cases , a l l the re levant experi mantal d e t a i l s are not p u b l i s h e d , w h i c h makes comparison between the r e s u l t s of d i f f e r e n t w o r k e r s uncer ta in . The b a s i s on which the s p r a y w a t e r f l u x e s have been c a l c u l a t e d i s by f a r the most i m p o r t a n t f a c t o r , because t h i s has been found to be the v a r i a b l e t ha t p l a y s the l a r g e s t r o l e i n the T A B L E X M u l t i p l e R e g r e s s i o n C o e f f i c i e n t s f o r t h e W a t e r F l u x and T e m p e r a t u r e D e p e n d e n c e o f t h e H e a t - T r a n s f e r C o e f f i c i e n t s • . P (2 ) / \ P ( 3 ) Form o f t h e F i t : h = P ( l ) m T s | V Too ol ( k GG10 n o z z l e ) S u r f a c e T e m p e r a t u r e : 800 t o 1050°C Wa t e r f 1 u x P a r a m e t e r E s t i m a t e s P ( l ) P ( 2 ) P ( 3 ) S t a n d a r d P(2) E r r o r o f P(3) M u l t i p l e R S q u a r e d P e a k 0 . 239 0 . 4 1 7 - 4 . 7 3 6 0 . 034 0 . 190 0 . 7 8 3 4 A v e r a g e d O v e r 25mm D i a m e t e r 0 . 2 1 4 0 . 5 3 7 - 4 . 7 3 3 0 . 0 4 1 0 . 1 8 5 0 . 7 9 6 1 A v e r a g e d O v e r S p r a y e d A r e a 0 . 403 0 . 323 - 4 . 8 0 7 0 . 031 0 . 203 0 . 7 5 4 6 1X3 r o 223 var ia t ion in the heat - t ransfer c o e f f i c i e n t s . A summary of the d i f f e ren t ways in which the spray f luxes have been obtained is given in Table XI It can be observed from this Table that a number of workers have used average values of spray water f l u x . These have been ca lcu la ted e i ther from data on water flow rates through the spray nozzle and the spray angle , o r , in the case of in -p lan t measurements, from the water flows in d i f fe ren t spray zones in the cas te r . In a d d i t i o n , where local water f luxes have been measured,, d i f -ferent c r o s s - s e c t i o n a l areas of the c o l l e c t o r s have been us,ed. It becomes evident from the resu l ts of the measure-ments made on the f u l l cone nozzles in the present work, that when peaks are present in the spray water f lux d i s t r i -but ions , the value of the average water f lux would change by a substant ia l amount depending on the area used for the c a l c u l a t i o n s . T h i s , as has been shown in a previous sect ion ( 5 . 2 . 5 . 2 ) , changes the r e l a t i o n s h i p between the heat - t ransfer c o e f f i c i e n t s and the spray water f l u x . As mentioned e a r l i e r , use of averaged water f luxes (when peaked f lux d i s t r i b u t i o n s are present) would y i e l d higher hea t - t rans fe r c o e f f i c i e n t s for the same value of water f l u x , when compared with those ca lcu la ted using peak f l u x e s . Thus, a cons is tent approach to the c a l c u l a t i o n of the spray water f luxes becomes mandatory i f the heat - t ransfer c o e f f i c i e n t vs. spray f lux cor re la t ions obtained by d i f f e ren t workers are to be in terpreted in a meaningful f ash ion . Since most workers have not reported any 224 Table XI Basis for the Method Used for the Determination  of Water Fluxes by Di f ferent Invest igators of  Spray Heat Extract ion Invest igator 71 ,72 75 Mi tsutsuka Ishi g u r o 7 3 Etienne et al Auman 35 Nozaki Akimenko et a l . 8 5 8 7 A-IK + i 88,89 Alberny et al . Hoogendoorn and den Hond70 M- - i , 76 Mi zl ka r Sugitani et al J u n k 8 0 74,78 81 Muller and Jeschar Bol le and Moreau 8^ 8 4 Basis for the Ca lcu la t ion of Water Fluxes Average, over the sprayed area Average, over the sprayed area Average, depending on nozzle p o s i t i o n , for veejet nozz les . Average, over the sprayed area Average, i n -p lan t measurements Average, in -p lan t measurements Average, in -p lan t measurements Peak water fluxes,unknown c o l -l e c t o r area. Peak water f l u x e s , 6mmdia. col 1ectors. Peak water f l u x e s , 6mmdia. col 1ectors. Peak water f l u x e s , unknown c o l -l e c t o r area . 2 Peak water f l u x e s , 120mm to 600 mm2 col 1ector area. Peak water f l u x e s , 40mm x 20mm c o l l e c t o r s . 2 2 5 data regarding the d i s t r i b u t i o n of water f luxes in the sprays produced by the nozzles employed in the i r measurements, i t becomes impossible to reconstruct the values of the local water f luxes in the sprays for which the measurements of hea t - t rans fer c o e f f i c i e n t s have been reported. To aid in the comparison of the heat t ransfer resu l ts obtained in this study with those of other i n v e s t i g a t o r s , the power curves f i t t e d to the data (Tables IV and V) have been p lot ted in Figures 91 and 92. Peak values of water f lux have been used for Figure 91 and water f luxes averaged over the cooled surface of the heat t ransfer probe have been used in Figure 92. The ran<ge of water f luxes for which the f i t t e d curves are v a l i d representat ions of the data are shown in the Fi gures . The present resul ts can be compared most read i ly to 7 5 those reported by Miz ikar , since the nozzles and exper i -mental condi t ions employed by him are s i m i l a r to those used in the present i n v e s t i g a t i o n . Comparison of Miz ikar 's re-su l ts (Figure l la )and the resu l ts in Figure 91 show that for the higher surface temperatures (>900° C) the present resu l ts are lower than the heat - t ransfer c o e f f i c i e n t s re-2 ported by him for m greater than 2 to 14 l/m s , with the agreement being better for a larger range of water f luxes as the surface temperature decreases. While he has found 9ZZ S p r a y heat-transfer coe f f i c i en t , kW/m °C — ro oj J > on o o o o o o o o o o o S p r a y heat - t r a n s f e r c o e f f i c i e n t ( B t u / h r ft °F) LZ Z 228 that the heat - t ransfer c o e f f i c i e n t s are f a i r l y independent of surface temperature when the surface temperatures are in excess of about 600 to 700°C, the present resu l ts indicate that these c o e f f i c i e n t s are temperature sens i t i ve even when the surface temperatures are in excess of 800°C. In con-t ras t with the resu l ts of the present study, very l i t t l e scat ter is evident in M i z i k a r ' s work. This is surpr is ing in view of the fact that even with the great care used to perform the experiments reported in th is t h i e s i s under s imi la r c o n d i t i o n s , a considerable amount of scat ter in the data was obtained. There was also no evidence of pressure on the heat-t ransfer c o e f f i c i e n t s as was reported in his work. Compar-ison of the resurts shown in Figure 92 with those reported by him (Figure 11a) show that for surface temperatures in excess of 950°C, the agreement between the two sets of 2 resu l ts is f a i r l y good for m < 15 a/m s . Although there is no mention of average water f luxes in his work, the fact that the present resu l ts are c loser to his resu l ts when average f luxes are used may be due to the lower water f luxes used by him for the % GG 10 nozzle . Examination of Figures 11, 91 and 92 show that the present inves t iga t ion y i e l d s the lowest heat - t ransfer 229 c o e f f i c i e n t s for any given water f l u x , when compared to other laboratory heat t ransfer measurements for surface temperatures of 1000 and 1050° C. While th is could be a t t r i -buted to the d i f f e ren t methods used for the c a l c u l a t i o n of the water f lux by various Inves t iga tors , i t must be noted that the' experimental technique used also appears to strongly a f fec t the measured hea t - t rans fer c o e f f i c i e n t s . In genera l , the hea t - t rans fer c o e f f i c i e n t s measured by spraying v e r t i -c a l l y downward upon a hor izonta l heated plate are higher than those obtained by spray cool ing a v e r t i c a l p la te . This o p 0 4 can be seen by comparing the resul ts of Bo l le and Moreau 81 and Muller and Jeschar . Bol le and Moreau, spraying down-ward onto a hor izonta l p l a t e , found that t h e i r s teady-state experiments y ie lded hea t - t rans fer c o e f f i c i e n t s that were 20% higher than those obtained by Muller and Jeschar , who used v e r t i c a l p l a t e s . For the range of water f luxes used in these two sets of invest iga t ions (up to 12 z/m s ) , i t is seen from Figure 11 that both show the highest hea t - t ransfer 7 3 c o e f f i c i e n t s (except for the resul ts of Ishiguro ). Spraying downward onto hor izontal heated surfaces would be expected to ra ise the hea t - t rans fe r c o e f f i c i e n t s because of e i ther of the fol lowing reasons: i ) Spray droplets impinging on t h e surface and rebounding from i t a f ter impact would f a l l 230 back onto the sur face , thus e f f e c t i v e l y i n -creasing the actual water f lux on the sprayed surface and increasing the e f f i c i e n c y of spray coo l i ng. i i ) A hor izonta l layer of water held up by a vapour cushion could ex is t above the s u r f a c e , and be forced against the surface by the im-pinging spray. This again would have the e f fec t of increas ing the spray cool ing e f f i c i e n c y , with a corresponding increase in the heat-t rans fer c o e f f i c i e n t . 81 The resu l ts reported by Muller and Jeschar show that the v e l o c i t y of the impinging droplets exerts an inf luence on the hea t - t rans fer c o e f f i c i e n t s (Eq. 2.17), which increase with increasing droplet v e l o c i t y . For a water f lux of 10 n/m s , an increase in the droplet ve loc i ty from 15 to 30 m/s (a fac tor of 2) causes a 25% increase in the heat-t ransfer c o e f f i c i e n t s . Increases of the heat - t ransfer co-e f f i c i e n t s have also been l inked to increasing droplet momenta. Due to the scat ter of the resu l ts in th is study, no e f fec ts due to the dynamic droplet propert ies could be d i s -cerned. The very high heat - t ransfer c o e f f i c i e n t s reported 71 7? by Mitsutsuka are probably due to a combination of a number of e f f e c t s . Pla in carbon stee ls were used in 231 his experiments, and these s tee ls tend to scale e a s i l y . The h o r i z o n t a l , 28 mm t h i c k , heated plates were sprayed both from the bottom and top s imultaneously , and the t ran-s ient temperatures at distances between 5 and 23 mm from the top surface of the plate were monitored. These temperatures were then used to ca lcu la te the surface temperatures and heat - t ransfer c o e f f i c i e n t s . It has been mentioned in Chapter 3 that increasing the distance of the point of measurement below the surface could lead to gross errors in the ca lcu la ted heat - t ransfer c o e f f i c i e n t s . In a d d i t i o n , the heat-transfer c o e f f i c i e n t s have been estimated for s p e c i f i c temperature d i f ferences at the sur face . Since i t has been shown from the present resul ts that the heat- . t ransfer c o e f f i c i e n t s increase rapid ly with decreasing sur-face temperatures, the average values of the ca lcu la ted heat - t ransfer c o e f f i c i e n t s would be expected to have higher values than those obtained for higher surface temperatures. Another point to note is that even though f u l l cone nozzles were employed in his work, the spray water f luxes used in his cor re la t ions were averaged over the plate area , thus e f f e c t i v e l y y i e l d i n g higher hea t - t rans fer c o e f f i c i e n t s for the same value of water f l u x , when compared to local water f1uxes. Among the invest igators report ing the dependence of heat - t ransfer c o e f f i c i e n t s on surface temperature, only 232 74 77 t h e r e s u l t s o f S u g i t a n i , S a s a k i e t a l . and E t i e n n e 75 e t a l . show any s i g n i f i c a n t d e p e n d e n c e i n t h e h i g h t e m -p e r a t u r e r a n g e a b o v e 7 0 0 ° C . S a s a k i e t a l . 7 7 o b t a i n e d t h e i r h e a t - t r a n s f e r c o e f f i c i e n t s u s i n g o p t i c a l p y r o m e t r i c m e a s u r e -m e n t s o f t h e h e a t e d p l a t e s u r f a c e d u r i n g s p r a y c o o l i n g . S i n c e no m e n t i o n i s made o f t h e use o f two c o l o u r p y r o m e t e r s i n t h e i r w o r k , i t w o u l d a p p e a r t h a t t h e p r e s e n c e o f w a t e r i n t h e s i g h t i n g p a t h c o u l d l e a d t o e r r o r s i n t h e c a l c u l a t e d h e a t - t r a n s f e r c o e f f i c i e n t s . The c o r r e l a t i o n o f S a s a k i ( E q . 2 . 1 5 ) p r e d i c t s a 13% d i f f e r e n c e ( a s a g a i n s t a 11% d i f -f e r e n c e f r o m t h e r e s u l t s o f t h e p r e s e n t s t u d y ) i n t h e h e a t -t r a n s f e r c o e f f i c i e n t s as t h e s u r f a c e t e m p e r a t u r e f a l l s f r o m 1 0 0 0 ° C t o 9 0 0 ° C. f o r a w a t e r f l u x o f 10 £ / m 2 s . The f a c t t h a t s u r f a c e c o n d i t i o n s c o u l d a f f e c t t h e h e a t - t r a n s f e r c o n d i t i o n s i s m e n t i o n e d i n h i s w o r k . When c o m p a r i n g t h e h e a t t r a n s f e r c o r r e l a t i o n o b t a i n e d 75 by E t i e n n e e t a l . , f o r a s u r f a c e t e m p e r a t u r e o f 9 0 0 ° C , w i t h t h e p r e s e n t r e s u l t s , i t i s f o u n d t h a t t h e p r e s e n t r e -s u l t s a r e l o w e r t h a n t h e p r e d i c t i o n s f o r t h e i r c o r r e l a t i o n s a b o v e rfi o f a b o u t 10 fc/m s . Even t h o u g h p l a t i n u m r o d s w i t h a h i g h r e s i s t a n c e t o s c a l i n g h a v e b e e n e m p l o y e d i n t h e i r e x p e r i m e n t s , t h e y h a v e f o u n d t h a t a f a i r a m o u n t o f s c a t t e r was p r e s e n t i n t h e i r m e a s u r e m e n t s , a n d t h a t t h e s c a t t e r i n -c r e a s e d a t l o w e r s u r f a c e t e m p e r a t u r e s . The d i f f e r e n c e b e -t w e e n t h e r e s u l t s o f t h e p r e s e n t s t u d y a n d t h e i r r e s u l t s 233 could be •attr ibuted p a r t i a l l y to the d i f f e ren t surface condit ions of the i r measuring probe, and p a r t i a l l y to the fact that the measurements were made while spraying downward onto the probe sur face . As a f i n a l step in the comparison of the present resul ts with those of other workers, water f luxes were averaged over the whole sprayed area ( for the 1/4 GG 10 nozzle) and power curves of the form given in Equation 5.2 were then f i t t e d to the var ia t ion of the heat - t ransfer c o e f f i c i e n t s with the averaged water f l u x e s . The coef-f i c i e n t s of the f i t t e d curve are given in Table XII and 2 are va l id for rfi between 1 and 10 £/m s . These f i t t e d curves are plot ted in Figure 93. Comparison of this Figure with Figure 11 shows that for surface temperatures in excess of 900° C, the present resul ts f a l l within the range of heat-t ransfer c o e f f i c i e n t s reported by other i n v e s t i g a t o r s . T h i s , again re in forces the necessi ty of using a consistent basis for the c a l c u l a t i o n of water f l u x e s , so that meaningful in te rpre ta t ions of the data can be made. The form of the power curves f i t t e d to the var ia t ion of hea t - t rans fer c o e f f i c i e n t s with water f lux is in agree-ment with those proposed from several of the studies on spray heat ex t ract ion (Table II). Several of the i n -vest igators have also reported that the exponent of the 234 T a b l e X I I C o e f f i c i e n t s o f P o w e r C u r v e s F i t t e d t o t h e V a r i a t i o n o f He a t - T r a n s f e r C o e f f i c i e n t s w i t h  W a t e r F l u x e s A v e r a g e d o v e r t h e W h o l e S p r a y e d  A r e a , f o r D i f f e r e n t S u r f a c e T e m p e r a t u r e s . Form o f t h e c u r v e : h = P ( l ) rfi P ^ S u r f a c e T e m p e r a t u r e °C P a r a m e t e r E s t i m a t e s S t a n d a r d E r r o r o f P ( l ) P ( 2 ) P ( D P ( 2 ) 800 1 . 2 2 0 . 2 7 0 . 1 3 0 . 0 8 850 1. 14 0 . 1 3 0 . 12 0 . 0 8 900 0 . 86 0 . 15 0 . 08 0 . 0 7 950 0 . 5 9 0 . 25 0 . 0 5 0 . 06 1000 0 . 36 0 . 4 9 0 . 0 4 0 . 0 7 1050 0 . 1 8 0 . 7 5 0 . 04 0 . 1 2 1 — J . : -5 Ira C 2 1 -> QJ j -s < - s - h - h C —»• X <-+ <-+ ( OJ ro V < Q . - s c+ fl) O L O fD !-+ Q - 3 " O fD < 3 a CD ro -5 01 CD — i <-l- c 3 - - s —K fD ra c Q . X 3 " < o ai \ fD s r-t-• a —'-- s O OJ 3 fD O a . - h O i 3 " -5 r + r o O OJ • r + < Q) C fD V) O Spray heat-transfer coe f f i c ien t . kW/m °C _ r o OJ ro o o o cool 4^  OJ ro — r o A 3 -A i n O O C D CD CO GO o o ° o ° ° o o o o o o OO O O O O o c < CD CO c - I —h a o CD C^ 3 T3 CD CCD O CD C a - i -+ < \ CD -+ CO Q cn -+> CD ro o 04 o CD CL 2 o 2. 3 I * CD O Q CD* 3 Cf) c J_ X o Q CD i Q ro 3. 3 o CT) O O O ro o o 04 o o o o cn O O S p r a y h e a t - t r a n s f e r coef f ic ient (Btu /hr ft °F) 9 £ 2 power curve changes with the surface t e m p e r a t u r e . T h e f r a c t i o n a l values of the exponent in the curves is l inked to the reduction in the e f f i c i e n c y of spray cool ing as the water f lux inc reases . The decrease in the e f f i c i e n c y can be a t t r ibu ted to the in te rac t ions between the droplets propel led towards the cooled surface and those rebounding away from i t . 5 . 8 Problems Limit ing the Measurements Of the many problems encountered in the course of the measurements of heat - t ransfer c o e f f i c i e n t s , the most troublesome were the problems of f a i l u r e of the measure-ment systems and non-reproducib i1 i ty of cool ing rates under s i m i l a r spraying c o n d i t i o n s . The high temperatures and repeated thermal cyc l ing of the measuring probe were the main contr ibutors to the problems with the measuring systems. The thermocouples in the measuring probe were being operated at temperatures close to the i r maximum operating range. In a d d i t i o n , the thermocouple wires were welded in the bottom of b l ind holes and there fore , as mentioned e a r l i e r , examination of these welds before s t a r t i n g the measurements was impract icab le . These f a c t o r s , inc luding thermal cyclings were very d e t r i -mental to the useful l i f e of the probe under serv ice con-d i t i o n s , and led to frequent f a i l u r e s of the temperature 237 measurement system. In the i n i t i a l experiments, the welds between the thermocouple wire and the AISI 304 s t a i n l e s s steel of the heat t ransfer probe were, in most ins tances , the s i t e of f a i l u r e . Careful control of the welding procedure tended to reduce the incidence of such f a i l u r e s , but did not e l iminate the problem. The thermocouple wires subsequently f a i l e d at other locat ions as w e l l . The useful l i f e t ime of the probes could not be estimated - the probes might l a s t anywhere from 1 to 15 thermal c y c l e s . The only remedy found to prevent such occurrences was to use lower operating temperatures, and to use slow heating and cool ing ra tes . Since the cool ing rates were the parameters being measured, and thus not amenable to c o n t r o l , slow heating rates were employed to even out the temperature gradients associated thermal stresses which could contr ibute to the f a i l u r e s of the thermocouples. Non-reproducibi1 i ty of the cool ing rates under s i m i l a r external cool ing condi t ions was another pers is tent problem, and could occur due to a var ie ty of reasons, the most important of which was the surface condi t ion of the probe. Due to th is problem, the probe surfaces to be sprayed were i n i t i a l l y p o l i s h e d . However, repeated heating and b l a s t i n g with water soon marred the surface f i n i s h . Oxida-t ion of the probe surface was minimized by the choice of a scale r e s i s t a n t s t e e l , but the harsh condit ions imposed on 238 t h e p r o b e c h a n g e d t h e p r o b e s u r f a c e c o n d i t i o n , a n d c h a n g e d t h e c o o l i n g r a t e s . T h e r e f o r e , many r e p e a t e d m e a s u r e m e n t s w e r e made f o r ' e a c h s p r a y i n g c o n d i t i o n , and t h e p r e s e n c e o f a n y f a c t o r t h a t c o u l d a d v e r s e l y a f f e c t t h e m e a s u r e m e n t s was r e a s o n f o r d i s r e g a r d i n g t h e r e s u l t s o f t h a t p a r t i c u l a r r u n . O n l y t h e c o o l i n g c u r v e s f r o m r e p r o d u c i b l e r u n s w e r e u s e d f o r t h e a n a l y s i s a n d c a l c u l a t i o n o f h e a t - t r a n s f e r c o e f -f i c i e n t s . T e s t s w e r e r e p e a t e d a t f r e q u e n t i n t e r v a l s w i t h s i m i l a r s p r a y i n g c o n d i t i o n s t o d e t e r m i n e t h a t r e p r o d u c -i b i l i t y was b e i n g m a i n t a i n e d . T h e s e two p r o b l e m s made t h e a c q u i s i t i o n o f d a t a w i t h s m a l l s c a t t e r a l o n g and a r d u o u s t a s k . E l e c t r i c a l n o i s e r e a c h i n g t h e r e c o r d i n g e q u i p m e n t was a p r o b l e m more e a s i l y d e a l t w i t h , by i n s t a l 1 i n g f i 1 t e r c a p a c i t o r s a t t h e t e r m i n a l s o f t h e s i g n a l c o n d i t i o n i n g e x p e r i m e n t s . The use o f a m p l i f i e r s w i t h n o i s e s u p p r e s s i o n c i r c u i t s w o u l d be a g r e a t a s s e t i n p e r f o r m i n g t h e m e a s u r e -m e n t s o f t h e f a s t t r a n s i e n t s i g n a l s . T h e s e w e r e n o t a v a i l -a b l e i n t h e c o u r s e o f t h e p r e s e n t i n v e s t i g a t i o n . 5 . 9 A p p l i c a t i o n o f t h e D a t a f o r S p r a y C h a m b e r D e s i g n S i n c e , i n an a c t u a l c a s t i n g o p e r a t i o n , e s p e c i a l l y f o r t h e c a s t i n g o f c a r b o n s t e e l s , a r e a s o f s e m i d e t a c h e d s c a l e , may e x i s t on t h e s t r a n d s u r f a c e , t h e h e a t - t r a n s f e r c o e f f i c i e n t s b e t w e e n t h e s p r a y and t h e s t r a n d s u r f a c e c o u l d be much h i g h e r t h a n t h o s e r e p o r t e d i n t h i s t h e s i s . As s u c h , t h e s u r f a c e t e m p e r a t u r e o f t h e s t r a n d w o u l d be l o w e r t h a n t h a t c a l c u l a t e d u s i n g t h e r e s u l t s o f t h i s l a b o r a t o r y s t u d y . E v a l u a t i o n o f t h e e f f e c t o f t h i s s c a l e on t h e h e a t - t r a n s f e r c o e f f i c i e n t s w o u l d t h e r e f o r e h a v e t o be done w i t h t h e a i d o f i n - p l a n t m e a s u r e m e n t s o f t h e s t r a n d s u r f a c e t e m p e r a t u r e u s i n g o p t i c a l p y r o m e t r i c d e v i c e s . C h a p t e r 6 SUMMARY AND CONCLUSIONS M e a s u r e m e n t s have b e e n c a r r i e d o u t t o c h a r a c t e r i z e t h e w a t e r d i s t r i b u t i o n i n t h e s p r a y s p r o d u c e d b y - s e v e r a l c o m m e r c i a l s p r a y n o z z l e s as a f u n c t i o n o f t h e s p r a y p r e s s u r e a n d d i s t a n c e f r o m t h e n o z z l e . I t has b e e n f o u n d t h a t , when s p r a y i n g o n t o a v e r t i c a l , c o l d s u r f a c e , t h e r e i s a s u b -s t a n t i a l a m o u n t o f w a t e r f l o w i n g downward a d j a c e n t t o t h e s p r a y e d s u r f a c e , d e s i g n a t e d as t h e ' w a t e r c u r t a i n ' . T h e r e -f o r e , two t y p e s o f m e a s u r e m e n t s h a v e b e e n made t o d e t e r m i n e : i ) The amoun t o f w a t e r a r r i v i n g a t any p o i n t i n t h e s p r a y d i r e c t l y f r o m t h e s p r a y n o z z l e . i i ) The c o m b i n e d v o l u m e o f w a t e r a r r i v i n g a t t h i s p o i n t i n t h e s p r a y d i r e c t l y f r o m t h e s p r a y n o z z l e , as w e l l as t h a t f l o w i n g d o w n -w a r d a d j a c e n t t o t h e s p r a y e d s u r f a c e u n d e r t h e i n f l u e n c e o f g r a v i t y . The m e a s u r e m e n t s i n d i c a t e d t h a t t h e r e i s a f a i r d e g r e e o f v a r i a b i l i t y i n t h e s p r a y s p r o d u c e d by s i m i l a r n o z z l e s , y i e l d i n g a v a r i a t i o n i n t h e w a t e r f l u x o f a b o u t 30% u n d e r s i m i l a r o p e r a t i n g c o n d i t i o n s . S p r a y f l u x ' m a p s ' a n d c o n t o u r s o v e r t h e w h o l e s p r a y e d a r e a show t h a t , f o r t h e f u l l cone n o z z l e s , t h e r e i s a r e a s o n a b l e amoun t o f 240 241 c i r c u l a r s y m m e t r y o f t h e s p r a y f l u x e s a b o u t t h e s p r a y a x i s . The h o r i z o n t a l c e n t r e l i n e s p r a y f l u x p r o f i l e s f o r t h e s p r a y s f r o m f u l l c o n e n o z z l e s show t h a t s h a r p p e a k s a r e p r e s e n t i n t h e s p r a y f l u x d i s t r i b u t i o n s a t t h e c e n t r e o f t h e s p r a y s . R e d u c t i o n i n t h e s p r a y p r e s s u r e s and i n c r e a s i n g t h e d i s t a n . e e f r o m t h e s p r a y n o z z l e s t e n d t o y i e l d more e v e n d i s t r i b.utj o.n.s i n t h e s p r a y f l u x e s a t t h e c e n t r e o f t h e s p r a y e d c o n e . H e a t - t r a n s f e r c o e f f i c i e n t s h a v e b e e n m e a s u r e d f o r t h e s e s p r a y s i m p i n g i n g on h e a t e d , v e r t i c a l s u r f a c e s o f s t a i n l e s s s t e e l " h e a t t r a n s f e r p r o b e s " . M e a s u r e m e n t o f t e m p e r a t u r e t r a n s i e n t s w i t h i n t h e p r o b e d u r i n g s p r a y c o o l i n g ( w i t h t h e a i d o f t h e r m o c o u p l e s e m b e d d e d i n t h e m ) , and a n a l y s i s o f t h e s e t r a n s i e n t s y i e l d e d t h e r e q u i r e d h e a t -t r a n s f e r c o e f f i c i e n t s a n d h e a t f l u x e s as a f u n c t i o n o f t h e t e m p e r a t u r e o f t h e c o o l e d s u r f a c e . The t e m p e r a t u r e - t i m e t r a n s i e n t s w e r e a n a l y z e d u s i n g a s o l u t i o n t o t h e " I n v e r s e B o u n d a r y V a l u e P r o b l e m " . The r e s u l t s o f t h e m e a s u r e m e n t s show t h a t : i ) The m o s t i m p o r t a n t v a r i a b l e a f f e c t i n g t h e h e a t - t r a n s f e r c o e f f i c i e n t s i s t h e m a g n i t u d e o f t h e l o c a l w a t e r f l u x a t t h e p r o b e s u r f a c e . , i i ) The he a t - 1 r a n s f e r c o e f f i c i e n t s a r e s u r f a c e t e m p e r a t u r e d e p e n d e n t e v e n a t t e m p e r a t u r e s i n e x c e s s o f 8 0 0 ° C . The o p e r a t i n g b o i l i n g 242 phenomenon is unstable f i lm b o i l i n g up to the maximum surface temperature (1050°C) that was used. i i i ) The nozzle type does not st rongly a f fec t the measured heat - t ransfer c o e f f i c i e n t s for the same loca l water f l u x . iv) The spray pressure (within the range used in the measurements) does not have a strong inf luence on the heat - t ransfer c o e f f i c i e n t s . v) The presence of the "water cur ta in" was found to increase the heat - t ransfer co-e f f i c i e n t s . vi ) The spray cool ing e f f i c i e n c y decreases with increasing water f lux and increasing surface temperature. Cor re la t ions have been obtained l i n k i n g the spray hea,t-t ransfer c o e f f i c i e n t s and water f l x u e s , and are of the form: h • P(l) ft P ( 2 ) f T s \ P ( 3 ) • • • • 6 A U O O O I 243 The value of the exponent P(2) is f r a c t i o n a l , and ind icates that increase of the water f lux has less than a proport ional e f fec t on the heat - t ransfer c o e f f i c i e n t s . It has been determined that a consistent method must be used as the basis for the determination of the water f lux at the cooled sur face , in order to be able to make meaning-ful comparison with the resu l ts obtained by d i f f e r e n t work-ers . 244 BIBLIOGRAPHY 1. K u r z i n s k i , E . F . , "Continuous Casting Cooling Water Flow C o n t r o l " , Iron and Steel Engineer, October 1979, pp. 57-59. 2. Tay lo r , C . R . , "Continuous . Casting Update", Met. Trans. B, Vol. 6B, 1975, pp. 359-375. 3. Mor i , H . , "Causes and Prevention of Defects in Continuous Cas t ing , Part I", Tetsu-to-Hagane, V o l . 58, 1972, pp. 1511-1534, [HB T r a n s l . No. 9000-1 & I I ] . 4. Brimacombe, J . K . and Sor imachi , K., "Crack Formation in the Continuous Casting of S t e e l " , Met. T r a n s . - B , Vol . 8B, 1 977 , pp. 489-505. 5. Ushi j ima, K., "Continuous Casting of S t e e l " , IS I Speci al Report No.89, 1 965. 6. Ushi j ima, K., "Mechanism of Internal Crack Formation in Continuously Cast Steel B i l l e t s " , Tetsu-to-Hagane, V o l . 47, No. 2, 1961, pp. 116-124. [HB T r a n s l . No. 5220]. 7. Mor i , H . , "Causes and Prevention of Defects in Continuous Cast ing , Part II", Tetsu-to-Hagane, V o l . 60, 1974, pp. 784-806. [HB T r a n s l . No. 9355-1 & I I ] . 8. De f in i t ions and Causes of Continuous Casting Defects ISI Pub. 106, 1967. 9. Brimacombe, J . K . , Agarwal, P . K . , B a p t i s t a , L . A . , H ibb ins , S . , and Prabhakar, B . , "Spray Cooling in the Continuous Casting of S t e e l " , Paper presented at the N0H-B0S Conference, Washington, 1980. 10. Adams, C . J . , "Hot D u c t i l i t y and Strength of Strand Cast Steels up to the i r Melting Points" Open Hearth P r o c , TMS- Al ME, V o l . 54 , 1 971 , pp. 290-302. 11. Wray, P . J . and Holmes, M.F . , " P l a s t i c Deformation of Austen i t i c Iron at Intermediate Stra in Rates", Met. Trans. A, Vo l . 6A, No. 6, 1975, pp. 1189-1196. 12. Fuchs, A . , "Untersuchung der Hochtemperaturzahigkeit von Stahlen mit der Gleeble -apparatur" , ESTEL-Berichte aus Forschung und Entwicklung Unserer Werke, No. 3, 1975, pp. 127-135. 245 13. Nadai, A. and Manjoine, M . J . , "High Speed Tension Tests at Elevated Temperatures", J . App l . Mech. V o l . 53, No . 6 , 1941 , pp. A77-91 . 14. N i l l e s , P . , Dauby, P.,. Et ienne, A . , Mairy, B. and Palmaers, A . , "Qual i ty Improvements of Continuously Cast Products" , Proc. Open Hearth C o n f . , Chicago, ISS-AlME, V o l . 61, 1978, pp. 399-410. 15. Weinberg, F. , "The D u c t i l i t y of Continuously . Cast Steel Near the Melting Point - Hot T e a r i n g " , Met. Trans. B, Vol . 10B, 1 979 , pp. 21 9-227. 16. Vom Ende, H. and Vogt, G . , "Comparison of the Influence of St ra ight and Curved Mould Continuous Casting Machines on Product Q u a l i t y " , J . Iron Steel I n s t . , Vo l . 210, No. 12, 1972, pp. 889-894. 17. Van Drunen, G . , Brimacombe, J . K . and Weinberg, F . , "Internal Cracks in Strand-cast B i l l e t s " , Ironmaking Steelmaking, Vo l . 2, No. 2, 1975, pp. 125-133. 18. Backer, L. and G o s s e l i n , P . , "Continuous Cast ing: Its Meta l lu rg ica l Aspects Relat ive to High-Grade Al loy and Carbon S t e e l s " , Open Hearth P r o c , TMS-AIME, Vo l . 53, 1 970 , -pp. 145-1 56. 19. M i l l e r , C . I . J r . , "Meta l lurg ica l Process Control Y ie lds Consistent Strand Cast B i l l e t Q u a l i t y " , Open Hearth P r o c , TMS-AIME, V o l . 54, 1 971 , pp. 316-321. 20. Donaldson, J . W . , "Qual i ty Control of Continuously Cast Steel B i l l e t s " , J . Metals, Vo l . 17, No. 12, 1965, pp. 1338-1343. 21. Brimacombe, J . K . , "Design of Cont inuous-Cast ing . Machines Based on a Heat Flow A n a l y s i s : A S ta te -o f -the-Art Review", Can. Met. Quar t . , V o l . 15, No. 2, 1976, pp. 163-175. 22. Agarwal, P . K . , "Case Study of Spray Design for a Continuous B i l l e t Caster" , M.A.Sc. T h e s i s , Univers i ty of B r i t i s h Columbia, 1979. 23. Schmidt, L. and Fredri ks'son, H . , "Formation of Macro-Segregation and Centre-Line Cracks in Continuously Cast S t e e l " , Ironmaking Steelmaking, V o l . 2, No. 1, 1 975 , pp. 61-67 . 24. Brovman, M. Ya. Stal in E n g l i s h , V o l . 1, 1967, p. 26. 246 25. Ozeki , R.K. and Duke, J . D . , "The Casting of High Qual i ty Plate Steel Slabs at Texas Works", Proc. Int. Conf. on Continuous Casting of S t e e l , B i a r r i t z , France, 1976, The Metals Society / IRSID, pp. 292-299. 26. Lankford, W.T. , "Some Considerations of Strength and D u c t i l i t y in the Continuous Casting Process" , Met. T r a n s . , V o l . 3, No. 6, 1972, pp. 1331-1357. 27. Myoshi, S . , "Influence of Operating Conditions and Mechanical Factors on C e n t r e Segregation of S l a b s " , Proc. Int. Conf. on Continuous Casting of S t e e l , B i a r r i t z , France, June 1976, The Metals Soc ie ty / IRSID, pp. 286-291. 28. Asano, K., Hiromoto, T. and Ohashi, T . , "Centre Segregation in Continuously Cast Steel S labs-Par ts I and II", Tetsu-to-Hagane, Vo l . 59, No. 4, 1973, pp. S82-S83 [HB Trans ! . No. 9099]. 29. Asano, K. , Hiromoto, T. and Ohashi, T . , "Study of Centre Segregation in Continuously Cast Slabs -Parts III, IV and V", Tetsu-to-Hagane, V o l . 60, No. 4, 1974, pp. S63-S64, and S65 [HB T r a n s l . No. 9320]. 30. Abe, Y'., Koike, A . , Sh ibu tan i , A . , and Shinoda, K., "Segregation in Continuously Cast High Carbon Steel Blooms", Tetsu-to-Hagane, V o l . 59, No. 4, Lecture 82, 1973, p. S84 [HB T r a n s l . No. 9108]. 31. Nashiwa, H . , Yasumoto, K., Tokuda, M. and Hirakawa, K., "E f fec t of Roll Alignment on the Centre Segregation in Continuously Cast S l a b s " , Tetsu-to-Hagane, V o l . 60, No. 4, Lecture 96, 1974, p. S96 [HB T r a n s l . No. 9374]. 32. I rv ing , W.R. and Perk ins , A . , "Basic Parameters A f fec t ing the Qual i ty of Continuously Cast S l a b s " , Proc. Int. Conf. on Continuous Casting of S t e e l , B i a r r i t z , France, 1 9 76 , The Metals Society /1RSID, pp. 107-115. 33. Brimacombe, J . K . , Weinberg, F. and Hawbolt, E . B . , "Formation of L o n g i t u d i n a l , Midface Cracks in Con-t inuously Cast S l a b s " , Met. Trans. B, Vo l . 10B, 1979, pp. 279-292. 34. Schmidt, L. and Jose fsson , A . , "On the Formation and Avoidance of Transverse Cracks in Continuously Cast Slabs from Curved Mould Machines", Scandinavian Journal of Meta l lurgy, Vo l . 3, No. 5, 1974, pp. 193-199. 247 35. Nozaki, T . , Matsuno, J . , Murata, K. , Odi , H. and Kodama, M., "A Secondary Cooling Pattern for Preventing Surface Cracks of Continuous Casting S l a b " , Trans. IS IJ , Vo l . 18, 1978, pp. 330-338. 36. F i s h e r , K., L i t t e r s c h e i d t , H . , Rudacks, W., Simon, R.W. and Weber, R .A . , " Industr ia l Experience with the Pro-duction of Continuously Cast S l a b s " , Proc. Int. Conf. on the Continuous Casting of S t e e l , B i a r r i t z , France, 1 976 , The Metals S o c i e t y - / 1 R S I D , pp. 280-285. 37. Eto , B . , Onozawa, M., Abe, M. and Aoyagi , T . , "Internal Cracks in Continuously Cast Blooms", Tetsu-to-Hagane, V o l . 58, No. 4, Lecture 111, 1972, p. S i l l [HB T r a n s l . No. 8830]. 38. Sakamoto, E . , Miyashi ta , Y . , Yano, K. and Ansa i , T . , "Avoidance of Surface Defects in Continuously Cast Slabs for P l a t e " , Tetsu-to-Hagans?, V o l . 60, No. 4, Lectures 37-39 , 1 974 , pp. S37-S39. [HB Transl. No. 9321 ] . 39. F u j i i , H . , Ohashi, T. and Hiromoto, T . , "On the Formation of Internal Cracks in Continuously Cast S l a b s " , Trans. IS IJ , V o l . 18, 1978, pp. 510-518. 40. G r a y , . R . J . , Perk ins , A. and Walker, B. , "Quality of Continuously Cast S l a b s " , Proc. Int. Conf. on S o l i d i f i c a -t ion and Casting of Metals, S h e f f i e l d , England, 1977, The Metals S o c i e t y , pp. 300-305. 41. G r i l l , A . , "Cooling System to Prevent Centre-Line Cracks, in Continuously Cast Steel B i l l e t s " , Ironmakin,g Steelmaking, No. 2, 1979, pp. 62-67. 42. B a p t i s t a , L . A . , "Control of Spray Cooling in the Continuous Casting of S t e e l " , M.A.Sc. T h e s i s , Univers i ty of B r i t i s h Columbia, 1979. 43. F o u s s a l , J . , "Model Pratique de Gestion et de Commande du Refroidissement Secondaire en Calculateur a la Coulee Continue de Solmer a Fos-Sur-Mer" , Rev. de Met. , Vol . 75 , 1 978 , pp. 403-41 4. 44. Et ienne, A . , "Method of Cont ro l l ing Continuous Casting of a Meta l" , U.S. Patent No. 4,073,332, 1978. 45. Adams, R .V . , "Method of Continuously Casting S t e e l " , U.S. Patent 3,478,808, November 18, 1969. • 46. Fekete, K. and Bruderer, W., "Method of Cont ro l l ing the Secondary Cooling of a Continuously Cast St rand" , U.S. Patent No. 3,915,216, 1975. 248 47. T i s k u s , J . R . , "Method and Apparatus for Contro l l ing the Rate of Heat Transfer to or From an Elongated Object" , B r i t i s h Patent No. 1 , 3 0 2 , 0 4 0 , 1 9 7 3 . 48. T iskus , J . R . , "Automation for High Tonnage Con-tinuous Cas t ing" , Iron and Steelmaking Automation Conference, V o l . IB , 1976, p. 4 .2 .2 . 49. Et ienne, A . , Mairy, B. and Dauby, P . , "Meta l lurg ica l Control and Automation for Continuous Casting Opera-t i o n " , Iron and Steelmaking Automation Conference, V o l . I B , 1976, p. 4 .2 .3 . 50. Et ienne, A . , "Reflexions sur le Controle du Refroidessement Secondaire des I n s t a l l a t i o n s de Coulee Cont inue", C i r c u l a i r e d 1 Informat ion-techniques, V o l . 34, No. 9, 1977, pp. 1929 - 1942. 51. Dewar, W.A.6. and P a t r i c k , B . , "Computer Control of Secondary Spray Cooling on an Eight -Strand Continuous Bloom Casting Machine", Iron and Steelmaking Automation Conference, V o l . IB , 1976, p. 4.2.1 . 52'. K r e i t h , F . a n d Black, W.Z. , "Basic Heat T rans fer" , Harper and Row P u b l i s h e r s , 1980. 53. Gaugler, R . E . , "An Experimental Study of Spray Cooling of High Temperature Sur faces" , Ph.D. T h e s i s , Department of Mechanical Engineer ing, Carnegie Inst i tu te of Technology, 1 966. 54. Heymann, F . J . , "High Speed Impact Between a Liquid Drop and a So l id Sur face" , Journal of Applied Phys ics , V o l . 40, No. 13, 1969, pp. 5113-5122. 55. Heymann, F . J . , "On the shock Wave Ve loc i ty and Impact Pressure in High Speed L i q u i d - S o l i d Impact", Trans. ASME, Journal of Basic Engineer ing, Paper No. 68 -FE-B , 1968, pp. 1-3. 56. S a v i c , P. and Boul t , G . T . , "The F lu id Flow Associated with the Impact of L iquid Drops with So l id Sur faces" , Report MT-26, 1955, National Research Council of Canada, Ottawa. 57. G o t t f r i e d , B . S . , "The Evaporation of Small Drops on a Flat Plate in the Film B o i l i n g Range", Ph.D. Thes is , Case Inst i tu te of Technology, 1962. 249 5 8 . W a c h t e r s , L . H . , B o n n e , H . and van N o u h i s , H . J . , " T h e H e a t T r a n s f e r From a Ho t H o r i z o n t a l P l a t e t o S e s s i l e W a t e r D r o p s i n t h e S p h e r o i d a l S t a t e " , Chem. E n g . S c i . , V o l . 2 1 , 1 9 5 6 , p p . 9 2 3 - 9 2 6 . 5 9 . M o r i y a m a , A . , " H e a t T r a n s f e r From a H o t S t e e l S u r f a c e t o a W a t e r D r o p l e t " , T r a n s . I S I J , V o l . 1 4 , 1 9 7 4 , p p . 2 8 5 - 2 8 9 . 6 0 . M o r i y a m a , A . , " E v a p o r a t i o n R a t e o f a S i n g l e W a t e r D r o p l e t on a H o t S u r f a c e " , T r a n s . I S I J , V o l . 1 4 , 1 9 7 4 , p p . 2 9 0 - 2 9 5 . 6 1 . W a c h t e r s , L . H . , S m u V d e r s , L . , V e r m e u l e n , J . R . and K l e i w e g , H . C . , " T h e H e a t T r a n s f e r F rom a Ho t W a l l t o I m p i n g i n g M i s t D r o p l e t s i n t h e S p h e r o i d a l S t a t e " , Chem. E n g . S c i . , V o l . 2 1 , 1 9 6 6 , p p . 1 2 3 1 - 1 2 3 8 . 6 2 . W a c h t e r s , L . H . a n d W e s t e r l i n g , N . A . , " T h e H e a t T r a n s f e r F rom a H o t W a l l t o I m p i n g i n g W a t e r D r o p s i n t h e S p h e r o i d a l S t a t e " , Chem. E n g . S c i . , V o l . 2 1 , 1 9 6 6 , p p . 1 0 4 7 - 1 0 5 6 . 6 3 . M c G i n n i s , F . K . and H o l m a n , J . P . , " I n d i v i d u a l D r o p l e t H e a t T r a n s f e r R a t e s f o r S p l a t t e r i n g on Ho t S u r f a c e s " , I n t . J . H e a t Mass T r a n s f e r , V o l . 1 2 , 1 9 6 9 , p p . 9 5 - 1 0 8 . 6 4 . H o l m a n , J . P . , J e n k i n s , P . E . a n d S u l l i v a n , F . G . , " E x p e r i m e n t s on I n d i v i d u a l D r o p l e t H e a t T r a n s f e r R a t e s " , I n t . J . H e a t Mass T r a n s f e r , V o l . 1 5 , 1 9 7 2 , p p . 1 4 8 9 -1 4 9 5 . 6 5 . P e d e r s e n , C O . , " A n E x p e r i m e n t a l S t u d y o f t h e D y n a m i c B e h a v i o u r a n d H e a t - T r a n s f e r C h a r a c t e r i s t i c s o f W a t e r D r o p l e t s I m p i n g i n g Upon a H e a t e d S u r f a c e " , I n t . J . H e a t Mass T r a n s f e r , V o l . 1 3 , 1 9 7 0 , p p . 3 6 9 - 3 8 1 . 6 6 . P e d e r s e n , C . O . , "The D y n a m i c s a n d H e a t - T r a n s f e r C h a r a c t e r i s t i c s o f W a t e r D r o p l e t s I m p i n g i n g on a H e a t e d S u r f a c e " , D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g , C a r n e g i e M e l l o n U n i v e r s i t y , 1 9 6 7 . 6 7 . C o r m a n , J . C . , " W a t e r C o o l i n g o f a M o v i n g , H i g h T e m p e r a t u r e M e t a l S t r i p " , P h . D . T h e s i s , D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g , C a r n e g i e I n s t i t u t e o f T e c h n o l o g y , 1 966 . 6 8 . A u m a n , P . M . , G r i f f i t h s , D . K . and H i l l , D . R . , " H o t S t r i p M i l l R u n o u t T a b l e T e m p e r a t u r e C o n t r o l " , I r o n and S t e e l E n g i n e e r , S e p t e m b e r 1 9 6 7 , p p . 1 7 4 - 1 8 1 . 250 6 9 . L a m b e r t , N . and E c o n o m o p o u l o s , M . , " M e a s u r e m e n t o f t h e H e a t - T r a n s f e r C o e f f i c i e n t s i n M e t a l l u r g i c a l P r o c e s s e s " , J o u r n a l o f t h e I r o n and S t e e l I n s t i t u t e , V o l . 10 , 1 9 7 0 , p p . 91 7 - 9 2 8 . 7 0 . H o o g e n d o o r n , C . J . a n d den H o n d , R . , " L i e d e n f r o s t T e m p e r a t u r e a n d H e a t - T r a n s f e r C o e f f i c i e n t s f o r W a t e r S p r a y s I m p i n g i n g on a Ho t S u r f a c e " , P a p e r B 3 . 1 2 , F i f t h I n t e r n a t i o n a l H e a t T r a n s f e r C o n f e r e n c e , T o k y o , 1 974 , p p . 1 35 -1 3 8 . 7 1 . S h i m a d a , M. and M i t s u t s u k a , M . , "On H e a t T r a n s f e r C o e f f i c i e n t by F o r c e d W a t e r C o o l i n g t o C a r b o n S t e e l " , T e t s u - t o - H a g a n e , V o l . 5 2 , 1 9 6 6 , p . 1 6 4 3 . 7 2 . M i t s u t s u k a , M . , " S t u d y on t h e W a t e r C o o l i n g o f S t e e l P l a t e a t H i g h T e m p e r a t u r e " , T e t s u - t o - H a g a n e , V o l . 5 4 , 1 9 6 8 , p p . 1 4 5 7 - 1 471 . 7 3 . I s h i g u r o , M . , I c h i h a r a , T . , e t . a l . , " S e c o n d a r y S p r a y C o o l i n g i n C o n t i n u o u s C a s t i n g " , T e t s u - t o - H a g a n e , V o l . 6 0 , N o . I T , L e c t u r e s 126 and 1 2 7 , 1 9 7 4 , p p . S 4 6 4 -S 4 6 5 [HB T r a n s l . N o . 8 7 3 5 ] . 7 4 . S u g i t a n i , Y . , T a k a s h i m a , K. and K a w a s a k i , S . , " S t u d y o f S e c o n d a r y C o o l i n g i n C o n t i n u o u s C a s t i n g " , T e t s u - t o -H a g a n e , V o l . 5 9 , N o . 1 1 , L e c t u r e s 12 a n d 1 3 , 1 9 7 3 , p p . S 3 8 8 - S 3 8 9 [HB T r a n s l . N o . 9 2 3 6 ] . 7 5 . E t i e n n e , A . a n d M a i r y , B . , " H e a t T r a n s f e r i n C o n t i n u o u s l y C a s t S t r a n d s " , C . N . R . M . R e p o r t 5 5 , N o v e m b e r 1 9 7 9 , p p . 3 - 1 3 . 7 6 . M i z i k a r , E . A . , " S p r a y C o o l i n g I n v e s t i g a t i o n f o r C o n t i n u o u s C a s t i n g o f B i l l e t s a n d B l o o m s " , I r o n a n d S t e e l E n g i n e e r , V o l . 4 7 , N o . 6 , 1 9 7 0 , p p . 5 3 - 6 0 . 7 7 . S a s a k i , K . , S u g i t a n i , Y . and K a w a s a k i , M . , " H e a t T r a n s f e r i n S p r a y C o o l i n g on H o t S u r f a c e " , T e t s u - t o -H a g a n e , V o l . 6 5 , 1 9 7 9 , p p . 9 0 - 9 6 . 7 8 . S u g i t a n i , Y . , " H e a t - T r a n s f e r C o e f f i c i e n t i n S p r a y C o o l i n g " , T e t s u - t o - H a g a n e , V o l . 6 1 , N o . 1 2 , 1 9 7 5 , p . S 5 1 3 . 7 9 . B a m b e r g e r , M . , J e s c h a r , R. and P r i n z , B . , " U n t e r s u c h u n g des W a r m e i i b e r g a n g s b e i m K u h l e n von Ni ch t e i s e n m e t a 11 en d u r c h W a s s e r " , Z e i t s . M e t a l l k u n d e , V o l . 7 0 , N o . 9 , 1 9 7 9 , p p . 5 5 3 - 5 6 0 . 251 8 0 . J u n k , J . , " H e a t T r a n s f e r I n v e s t i g a t i o n s i n a S i m u l a t e d S e c o n d a r y C o o l i n g Zone f o r t h e C o n t i n u o u s C a s t i n g o f S t e e l " , Neue H u t t e , V o l . 1 7 , N o . 1 , 1 9 7 2 , p p . 1 3 - 1 8 [HB T r a n s l . N o . 8 7 4 0 ] . 8 1 . M u l l e r , H . a n d J e s c h a r , R . , " U n t e r s u c h u n g des W a r m e L i b e r g a n g s an e i n e r s i m u l i e r t e n S e k u n d a r k ' u h 1 z o n e b e i m S t r a n g g i e s s v e r f a h r e n " , A r c h . E i s e n h u t t e n w e s . , V o l . 44 , 1 973 , p p . 5 8 9 - 5 9 4 . 8 2 . B o l l e , L . and M o u r e a u , J . C . , " S p r a y C o o l i n g o f Ho t S u r f a c e s : A D e s c r i p t i o n o f t h e D i s p e r s e d P h a s e and a P a r a m e t r i c S t u d y o f H e a t T r a n s f e r R e s u l t s " , P r o c . o f Two P h a s e F l o w s and H e a t T r a n s f e r , V o l . I l l , NATO A d v a n c e d S t u d y I n s t i t u t e , 1 9 7 6 , p p . 1 3 2 7 - 1 3 4 6 . 8 3 . B o l l e , L . and M o u r e a u , J . C . , " E x p e r i m e n t a l S t u d y o f H e a t T r a n s f e r by S p r a y C o o l i n g " , I n t . C o n f . on H e a t a n d Mass T r a n s f e r M e t a l l u r g i c a l P r o c e s s e s , D u b r o v n i k , Y u g o s l v i a , 1 9 7 9 . 8 4 . B o l l e , L . a n d M o r e a u , J . C . , U n i v e r s i t e C a t h o l i q u e de L o u v a i n , B e l g i u m , U n p u b l i s h e d w o r k . 8 5 . A k i m e n k o , A . D . , K o r o t k o v , K . P . , M a i o r o v , N . P . , S k v o r t s o v , A . A . a n d S h e n d e r o v , L . B . , " C o n t i n u o u s C a s t i n g o f S t e e l " , B I S I T S T r a n s l a t i o n N o . B I S I 2 3 8 0 , 1 9 6 2 , I r o n a n d S t e e l I n s t i t u t e , L o n d o n . 8 6 . A k i m e n k o , A . D . , K a z a n o v i c h , L . B . , S k v o r t s o v , A . A . a n d S l u t s k i i , B . I . , " I n v e s t i g a t i n g H e a t T r a n s f e r i n t h e S e c o n d a r y C o o l i n g Zone i n a C o n t i n u o u s C a s t i n g P l a n t " , S t e e l i n t h e U S S R , 1 9 7 2 , p p . 4 4 8 - 4 4 9 . 8 7 . A k i m e n k o , A . D . a n d S k v o r t s o v , A . A . , " H e a t T r a n s f e r i n Zone o f S e c o n d a r y C o o l i n g o f C o n t i n u o u s S t e e l C a s t i n g I n s t a l l a t i o n s " , N a u c h n . D o k l a d y V y s s h . S h k o l y -M e t a l 1 u r g i y a , A p r i l - J u n e 1 9 5 9 , N o . 2 , p p . 1 2 3 - 1 3 0 [HB T r a n s l . N o . 4 7 9 6 ] . 8 8 . A l b e r n y , R . , " H e a t T r a n s f e r and S o l i d i f i c a t i o n i n C o n t i n u o u s C a s t i n g " , I n f o . S y m p . on C a s t i n g a n d S o l i d i f i c a t i o n o f S t e e l , V o l . 1 , C o m m i t t e e o f E u r o p e a n C o m m u n i t i e s , L u x e m b o u r g , 1 9 7 7 , IPC S c i e n c e and T e c h n o l o g y P r e s s , p p . 2 7 8 - 3 3 5 . 8 9 . A l b e r n y , R . , L e c l e r q , A . and B a s i l i s , J . , " T h e r m a l S t u d y o f S e c o n d a r y C o o l i n g o f a C o n t i n u o u s C a s t i n g M a c h i n e " , C i r c u l a i r e d ' I n f o r m a t i o - t e c h n i q u e s , V o l . 3( 31 5) , 1 973 , p p . 7 6 3 - 7 7 6 . 252 9 0 . I n d u s t r i a l C a t a l o g 2 6 , S p r a y i n g S y s t e m s C o . , W h e a t o n , I l l i n o i s . 6 0 1 8 7 . 9 1 . O t t e r , A . J . , - . " T h e r m o c o u p l e s a n d S u r f a c e T e m p e r a t u r e M e a s u r e m e n t " , AECL R e p o r t 3 0 6 2 , M a r c h 1 9 6 8 , C h a l k R i v e r , O n t a r i o . 9 2 . B e n e d i c t , R . P . , C h a p t e r 1 2 , " F u n d a m e n t a l s o f T e m p e r a - t u r e , P r e s s u r e a n d F l o w M e a s u r e m e n t " , 2nd E d i t i o n , P u b . J . W i l e y and S o n s , p p . 2 3 8 - 2 6 4 . 9 3 . S p a r r o w , E . M . , " E r r o r E s t i m a t e s i n T e m p e r a t u r e M e a s u r e m e n t " , M e a s u r e m e n t T e c h n i q u e s i n H e a t T r a n s f e r , E d s . E c k e r t , E . R . G . and G o l d s t e i n , R . J . , P u b . T e c h n i v i s -i o n S e r v i c e s , S l o u g h , E n g l a n d , 1 s t . E d i t i o n , 1 9 7 0 , p p . 1 3 - 3 2 . 9 4 . B e c k , J . V . , " T h e r m o c o u p l e T e m p e r a t u r e D i s t u r b a n c e s i n Low C o n d u c t i v i t y M a t e r i a l s " , T r a n s . A S M E , J o u r n a l o f H e a t T r a n s f e r , May 1 9 6 2 , p p . 1 2 4 - 1 3 2 . 9 5 . B e c k , J . V . a n d H u r w i c z , H . , " E f f e c t o f T h e r m o c o u p l e C a v i t y on H e a t S i n k T e m p e r a t u r e " , T r a n s . A S M E , J o u r n a l o f H e a t T r a n s f e r , F e b r u a r y 1 9 6 0 , p p . 2 7 - 3 6 . 9 6 . M a s t e r s , J . I ' , and S t e i n , S . , " E f f e c t o f an A x i a l C a v i t y on t h e T e m p e r a t u r e H i s t o r y o f a S u r f a c e H e a t e d S l a b " , The R e v i e w o f S c i e n t i f i c I n s t r u m e n t s , V o l . 2 7 , N o . 1 2 , 1 9 5 6 , p p . 1 0 6 5 - 1 0 6 9 . 9 7 . E c o n o m o p o u l o s , M . , "New C a l c u l a t i o n M e t h o d o f t h e H e a t T r a n s f e r C o e f f i c i e n t s i n S t e e l M a k i n g P r o c e s s e s " , C . N . R . M . R e p o r t N o . 1 4 , 1 9 6 8 , p p . 4 5 - 5 8 . 9 8 . G a t , U . , K a m m e r , D . S . a n d H a h n , O . J . - , "The E f f e c t o f T e m p e r a t u r e D e p e n d e n t P r o p e r t i e s o f T r a n s i e n t s M e a s u r e -m e n t s w i t h I n t r i n s i c T h e r m o c o u p l e " , I n t . J . H e a t Mass T r a n s f e r , V o l . 18 , 1 975 , p p . 1 3 3 7 - 1 342 . 9 9 . H e n n i n g , C D . and P a r k e r , R . , " T r a n s i e n t R e s p o n s e o f an I n t r i n s i c T h e r m o c o u p l e " , T r a n s . A S M E , J o u r n a l o f H e a t T r a n s f e r , May 1 9 6 7 , p p . 1 4 6 - 1 5 4 . 1 0 0 . S h u m a k o v , N . V . , "A M e t h o d f o r t h e E x p e r i m e n t a l S t u d y o f t h e P r o c e s s o f H e a t i n g o f a S o l i d B o d y " , S o v i e t P h y s i c s , T e c h n i c a l P h y s i c s , V o l . 2 , 1 9 5 7 , p p . 7 7 1 - 7 8 1 . 1 0 1 . P a s c h k i s , V . and S t o l t z , G . , " Q u e n c h i n g as a H e a t T r a n s f e r P r o b l e m " , J o u r n a l o f M e t a l s , A u g u s t 1 9 5 6 , p p . 1 0 7 4 - 1 0 7 5 . 1 0 2 . P a s c h k i s , V . and S t o l t z , G . , "How M e a s u r e m e n t s L e a d t o E f f e c t i v e Q u e n c h i n g " , The I r o n A g e , N o v e m b e r 2 2 , 1 9 5 6 , p p . 9 5 - 9 7 . 253 1 0 3 . M i r s e p a s s i , T . , " G r a p h i c a l e v a l u a t i o n o f a C o n v o l u t i o n I n t e g r a l " , M a t h e m a t i c s o f C o m p u t a t i o n , V o l . 1 3 - 1 4 , 1 9 5 9 - 6 0 , p p . 2 0 2 - 21 2 . 1 0 4 . S t o l t z , J r . G . , " N u m e r i c a l S o l u t i o n s t o an I n v e r s e P r o b l e m o f H e a t C o n d u c t i o n f o r S i m p l e S h a p e s " , T r a n s . A S M E , J o u r n a l o f H e a t T r a n s f e r , F e b r u a r y 1 9 6 0 , p p . 2 0 - 2 6 . 1 0 5 . S p a r r o w , E . M . , H a j i - S h e i k , A . a n d L u n d g r e n , T . S . , " T h e I n v e r s e P r o b l e m i n T r a n s i e n t H e a t C o n d u c t i o n " , T r a n s . A S M E , J o u r n a l o f A p p l i e d M e c h a n i c s , S e p t e m b e r 1 9 6 4 , p p . 3 6 9 - 3 7 5 . 1 0 6 . K o l p , A . Y a . and L e b e d e e v , V . V . , " C o m p a r i s o n o f S o l u t i o n s o f t h e I n v e r s e T r a n s i e n t H e a t C o n d u c t i o n by t h e M e t h o d s o f T i k h o n o v a n d S p a r r o w " , T e p l o f i z i k a V y s s o k i k h T e m p e r a t u r , V o l . 1 1 , N o . 2 , 1 9 7 3 , p p . 3 6 9 - 3 7 4 . 1 0 7 . A l i f a n o v , O . M . , " R e g u l a r i s a t i o n o f S o l u t i o n s o f I n v e r s e P r o b l e m s o f H e a t C o n d u c t i o n " , H e a t T r a n s f e r , S o v i e t R e s e a r c h , V o l . 5 , N o . 4 , 1 9 7 3 , p p . 1 6 3 - 1 6 9 . 1 0 8 . M a k h i n , V . A . and S h m u k i n , A . A . , " I n v e r s e P r o b l e m s o f U n s t e a d y H e a t C o n d u c t i o n " , H e a t T r a n s f e r , S o v i e t R e s e a r c h , V o l . 5 , N o . 2 , 1 9 7 3 , p p . 1 6 0 - 1 6 5 . 1 0 9 . F r a n k , I . , "An A p p l i c a t i o n o f L e a s t S q u a r e s M e t h o d t o t h e S o l u t i o n o f t h e I n v e r s e P r o b l e m o f H e a t C o n d u c t i o n " , T r a n s . A S M E , J o u r n a l o f H e a t T r a n s f e r , S e p t e m b e r 1 9 6 3 , p p . 3 7 8 - 3 7 9 . 1 1 0 . L a m b e r t , N . and G r e d a y , T . , " D e t e r m i n a t i o n o f t h e H e a t - T r a n s f e r C o e f f i c i e n t " , C . N . R . M . R e p o r t N o . 4 4 , 1 9 7 5 , p p . 1 3 - 2 7 . 1 1 1 . T h a l e r , R . H . , "An I n v e r s e F i n i t e D i f f e r e n c e M e t h o d f o r t h e D e t e r m i n a t i o n o f T h e r m a l C o n d u c t i v i t y " , P a p e r Cu 2 . 8 , P r o c e e d i n g s o f t h e 5 t h I n t e r n a t i o n a l H e a t T r a n s f e r C o n f e r e n c e , T o k y o , 1 9 7 4 , p p . 2 0 2 - 2 0 4 . 1 1 2 . I m b e r , M . , " T h e Two D i m e n s i o n a l I n v e r s e P r o b l e m i n H e a t C o n d u c t i o n " , P a p e r Cu 2 . 2 , P r o c e e d i n g s o f t h e 5 t h I n t e r n a t i o n a l H e a t T r a n s f e r C o n f e r e n c e , T o k y o , 1 9 7 4 , p p . 1 7 4 - 1 7 8 . 1 1 3 . C a r n a h a n , B . , L u t h e r , H . A . and W i l k e s , J . O . , " A p p l i ed  N u m e r i c a l M e t h o d s " , J o h n W i l e y and S o n s , P u b l i s h e r s , 1 969 . / 254 1 1 4 . P r i c e , P . H . and S l a c k , M . R . , " S t a b i l i t y and A c c u r a c y o f N u m e r i c a l S o l u t i o n s o f t h e H e a t F l o w E q u a t i o n " , B r i t i s h J o u r n a l o f A p p l i e d P h y s i c s , V o l . 3 , 1 9 5 2 , p p . 3 7 9 - 3 8 4 . 1 1 5 . D o u g l a s , J . , "A S u r v e y o f N u m e r i c a l M e t h o d s f o r P a r a -b o l i c D i f f e r e n t i a l E q u a t i o n s " , A d v a n c e s i n C o m p u t e r s , V o l . 2 , 1 962 , p p . 1 - 5 4 . 1 1 6 . B a r a k a t , H . Z . and C l a r k , J . A . , "On t h e S o l u t i o n o f t h e D i f f u s i o n E q u a t i o n s by N u m e r i c a l M e t h o d s " , T r a n s . A S M E , J o u r n a l o f H e a t T r a n s f e r , V o l . 8 8 , November 1 9 6 6 , p p . 4 2 1 - 4 2 7 . 1 1 7 . B i o m e d i c a l C o m p u t e r P r o g r a m s , P S e r i e s , E d . W . J . D i x o n , 1 9 7 7 , U n i v e r s i t y o f C a l i f o r n i a P r e s s , p p . 4 8 4 - 4 9 8 . 1 1 8 . M a i r y , B . a n d R a m e l o t , D . , " S e n s o r f o r M e a s u r i n g t h e S u r f a c e T e m p e r a t u r e o f t h e S t r a n d i n a C o n t i n u o u s C a s t i n g M a c h i n e " , C . N . R . M . R e p o r t N o . 4 6 , M a r c h 1 9 7 6 , p p . 2 3 - 2 8 . A P P E N D I X I M e a s u r e d s p r a y f l u x e s f o r t h e v a r i o u s n o z z l e s u s e d i n t h i s i n v e s t i g a t i o n . T A B L E ' I - 1 NUZZLE m-E 1/4 CO 10 PRESSURE 20. PSI DISTANCE 10. 16 CM coi .Ltc ion IVPE A O. 14 ttf'A DISTANCE FROM CENTRE <CM> •10 It, -7 1,2 -5 OQ -2 34 O O 2. 54 5 00 7 fc2 10 16 15.24 -12.70 -10.16 -7.62 -3.08 -2 34 O. 0 2.54 3. OB 7.62 10.16 12.70 15.24 0 0 0 o 0 0 0 0 Q o 0. 0 0 0 0 o 0 0 0 0 O 0 0. 0 0. o o o 0. o 0 0 O 0 0. 0 0. 0 O. 0 o. o 0. 0 0. 0 1. 60 8. 60 0. 70 Q. O 1.43 0 0 o. o 2. eo 4. BO 3. 30 0. O 0 O 4. 70 0. 0 O. 6 O 0 O. O b. 60 6. 00 0. 0 O. 0 O. 0 0. 0 O. O O. 0 0. o o. o 0. o 0. 0 o. 0 0. o 0. 0 0. 0 5. 20 B. 00 3 20 3. 60 0. 0 6. 40 IB. 23 6. BO 6.00 2.00 0.0 1.40 6 30 3.90 7. BO 3.70 6.60 0.30 0.0 0. 70 2. 60 0. 0 0. 0 0. 0 0 0 3 60 0 O 0 0 3. 70 6. 70 0. 0 0. O 2 60 O. 10 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 o. o 0. 0 0. 0 0. 0 o. o o. o 0 o 0. o O. 0 0. o 0 0 0. 0 0. 0 o. o 0.0 0. 0 0.0 O. 0 0. 0 O. 0 0. 0 TABLE I - 2 c o 2 Ul u £ u. I l l U l »-• Q NOZZLE TYPE 1/4 CO 10 PRESSURE 20. PSI 01 STANCE 13 24 CM COLLECTOR TYPE A 0 II MPA DISTANCE FROM CENTRE (CM» . — — — — — 1 -15 24 -12 70 -10. 16 -7 62 -5 08 -2. 54 0. 0 54 3. 08 7. 62 10. 16 12. 70 13. 24 -10 16 0 io O. to 0. 0 0. 30 1. 50 1. 80 3. 20 2 OO O. O 0. 0 O. 0 O 0 o. o -7 62 0 10 0. 10 0. 30 0. 80 2 20 2. 70 3 10 2. 30 0. 0 0. 0 0. 0 0 0 0. 0 -5 06 0 10 0 30 0. 60 30 2 00 2. 30 2. 70 2. 40 0. 10 I. 50 0. 0 0. 0 0. 0 -2. 51 0. 10 0. 10 1. 70 3. 70 2. 00 2 60 3. 00 4. 40 2. 20 . 3. 20 0. 0 0. 0 0. 0 0 0 0. 0 0 30 .2. DO 3. 00 2. GO <t. 70 U. 90 ^. 80 2. 20 2. 60 0. 0 0. 20 0. 0 2 :>4 0. 0 0 0 1. 40 2 70 2. 00 3. 70 4 10 2. 00 2. 70 3. AO 0. 0 0 0 0. 0 3 00 0. 4'_- 0. 0 , 0. VO 3 00 3 10 60 2. 70 2 60 2. 70 2. 20 0. 0 0. 0 0 0 7 62 0 20 0. ib- 0. 0 0. 40 3. 10 2 40 3. 00 3. 00 1. 00 0. 0 0. 0 0.-0 0. 0 10 16 0 10 0. 0 0. 0 0. 0 0. 60 0 30 1. 70 1. 20 0. 0 0. 0 O. 0 0. 0 0. 0 ro cn T A B L E I - 3 NOZZLE TVPE 1/4 CC 10 PRESSURE 20 PSI DISTANCE 20. 32 CM COLLECTOR TYPE A 0. 1 4 MPA DISTANCE FROM CENTRE <CM> c z 11 o E cc IL in a -15 24 -12 70 -10 16 -7. 62 -5 OB 54 0 0 2. 54 5 00 7. 62 10. 16 12 70 13. 24 - 10 16 0. 10 0. 30 0. GO 1. 30 1. 40 1. 60 2. 00 2 00 0. 30 0. 80 0. 0 0. 0 0. 10 -7. 62 0. 20 0 50 1. 10 1. 30 i . 40 1 50 1. 70 i . BO 0. 40 1. 00 0. 0 0. 0 0. 0 -5 00 0. 40 O 50 1. 30 1 70 1. 60 1. 70 2. 30 t. BO 0. 0 1. 00 0. 0 0. 0 0. 0 54 1. 00 0. 50 1. 40 1. 40 1. BO 3. 10 3. 90 2. 20 0. 40 0. 90 0. 10 0. 30 0. 30 0. 0 0. 70 1. 20 1, BO 1 33 1. 73 3. 33 3, 40 3. 50 t. 60 1. 40 I. 40 1. IS 1. 20 2 34 0. 40 1. 20 a. 00 I 60 1. 70 2. SO 3. 70 S. 90 1. 60 1. 30 0. 00 1. 10 0. 60 5 00 0. 40 1 00 t. 90 1 90 1. 60 1. 70 1. 90 I. 70 1. 40 1. 60 0. 90 0. 60 0. 30 7. 62 0. 30 0 60 . i. 30 1 80 » 70 1. 60 1. 30 1. 40 1. 00 1. 70 0. 40 0. 30 0. 40 10 16 0 30 0 30 0. 60 1 00 1. 10 1 60 i. 30 60 1. 40 1. to 0. 0 0. 20 0. 30 cn co T A B L E I - 4 z I I I o 5 a ii N O Z Z L E TYPE 1/4 00 10 P R E S S U R E 20. P S I D I S T A N C E 10. 16 CM COLLECTOR TYPE B O. 14 MPA D I S T A N C E FROM CENTRE <CM) -13 24 -12. 70 -10. 16 -7. 62 -3. 00 -2. 34 - 1 0 16 0. 0 0. 0 0. 0 0 0 0. 0 0 0 - 7 o2 0 0 0. 0 O. 0 0 0 12: 30 ?. 30 -s 0 0 0 0 0. 0 0. 0 31. 00 9. 30 II. 60 -2. 51 0.0 0.0 04,40 4. 20 10. 40 9. 30 0 0 0 30 0. 30 31. 10 9. BO I.I. 70 13. 80 2 54 0 0 22 80 g . 40 B. 10 13. 10 12 70 5 OH 0 0 24 BO 0. so 6 20 10. 20 13. 30 7 6 ? 0. 0 27. 40 0. 10 2. 30 3 10 7. 10 10 16 0. 0 1?. 20 3. 30 1. 20 3. 20 4. 60 o o 2. 34 3. 00 7. 62 10. 16 12. 70 13. 24 O 0 0. 0 O. 0 0. 0 0. 0 O. 0 O. 0 0. O O. 0 0. 0 0. 0 O. 0 O. 0 0. 0 0.0 O. 0 0.0 H. 00 14 .00 0 .0 T A B L E I - 5 NOZZLE IVPE 1/4 CO 10 PRESSURE 40 PBI 0. 2B HP A OISIANCE 10. lb CM CULLEC TQH IYPE A DISTANCE FROM CENTRE (CM) -15 24 -12 70 -10. 16 -7 62 -5 . 00 -2 54 0. 0 54 3. OB 7. 62 10 16 12. 70 15. 24 c - 10 16 0. 0 0 0 0. 0 0. 0 0 0 0 0 0. 0 0 0 0. 0 0. 0 0. 0 0 0 0. 0 o -7 C3 0 0 0 0 0. 0 0 80 2 30 2 70 4. 60 20 0. 0 0. 0 0. 0 0. 0 0. 0 Ul a h-- b 00 0 0 0 0 0. 0 2 00 4. 30 6 30 9. 40 10 00 4. 00 0. 0 0. 0 0. 0 0 0 2 Ul o 34 0 0 0 0 0. 0 1. 70 7. 50 7. 30 10. 50 7. 00 7. 30 2. 10 0 .0 0. 0 0. 0 c o It u 111 0 0 0 0 0. 0 .0, 0 2 60 6, 70 e, SO 20. 20 9. SO 7. 10 3, 90 0. 0 0. 0 0. 0 2 54 0 0 0 20 0. 0 2. 60 8. 80 7 40 9. 10 7. 60 7. 30 2. 00 0. 0 0. 30 0. 0 •J z < 3 00 0 0 0 0 0. 0 0. 70 3 30 6. 30 6. 10 3. 90 4. JO 0. 0 0. 0 0. 0 0 0 h-m 7 62 0 0 0 0 0. 0 0. 0 1. 90 2. 00 3. 40 2. 40 0. 0 0. 0 0. 0 0 0 0. 0 10 16 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 o T A B L E I - 6 NOZZLE TYPE 1/4 CO 10 PRESSURE 40. PSI DISTANCE »5 24 CM COLLECTOR TYPE A DISTANCE FROM CENTRE (CM) n c o a U in -15 24 -12 70 -10. 16 -7. 62 -5 . OB -2. 54 0 0 -» 54 3. 08 7. 62 10. 16 12 70 15. 24 - IO 16 0 O 0 10 o. o 0. 40 1. 90 =• 10 3. 10 —» 30 0. 6 0. 0 0. O O. 0 0. 0 -7 62 0 0 0. 0 0. 40 1 00 3. 40 3. 10 3. 40 3 10 O. 10 0. 0 0. 0 0 0 0. 0 -3 . 00 0 0 0. 0 1. 00 3 00 3. 60 3. 40 4. 40 3. 40 2. 10 3. 90 0. 0 0 0 0. 0 -2 54 0 0 0. 0 2 10 4 40 4. 00 4. 00 6. 30 5. 40 3. 30 3. 50 1. 30 0. 0 0. 0 0 0 0 0 0. 0 3.30 3.,60 3. 70 6. 20 9. 20 b. 70 3. 70 3. 30 0. 0 0. 0 0. 0 2 34 0 0 0 0 2. 10 3. 40 3 40 4. 10 4. 90 4. 30 3. 60 4. 10 0. 10 0.0 0.0 3 00 0 0 0. 0 1. 00 3 30 3. 40 3 00 3. 20 3 to 3. 00 3. 20 I. 50 0 0 0. 0 1 62 0. 0 0. 0 0. 0 0.0 a. 00 a. 10 3, 10 4: 60 o, q 0.0 0, 0 0.0 0,0 10 16 0. 0 0 o" 0. 0 0. 0 0. 0 0. 0 0. 0 2. 20 0. 0 0. 0 0. 0 0. 0 0. 0 r\5 cn T A B L E I - 7 NOfZl.E TVPE 1/4 OC 10 PRESSURE 40 PSI DISTANCE 20 32 CM COLLECT OH TYPE A 0. 28 MPA DISTANCE FROM CENTRE (CM) 2 U l o n o a u I -Ul a - l b 24 -12 70 -10. 16 -7 62 -3 00 — 1 54 0 0 £1 54 5 00 7 62 10 16 12 70 15 24 - 10 16 0 40 0 70 1. 10 1 &o 1 60 1 70 2 40 50 1 70 2 10 0 0 0 10 0 0 -7 62 1 60 0 60 1. 50 1 80 1 70 00 2 60 50 1 50 2 40 0. 30 0 10 0. 20 -3 OB 0 70 0 70 2. 20 30 2 20 •"» 60 3. 00 30 0. 70 1. 70 0. 70 0 20 0. O -j :i4 0 50 1 50 2. 40 2 00 2 40 3. 30 4. 50 3. 30 1. 60 2. 00 1. 40 1. 60 0. 50 0 0 0. 50 1 60 2. 20 2 10 40 4 00 3. 90 4. 60 2. 70 2. 00 2. 10 2. 10 0 90 1 34 0 60 1 60 2 30 2 00 2. 10 3 00 4. 30 3 60 2. 30 1. 60 1. 90 1. 70 1. 10 5 00 0 00 1 70 2. 60 30 2. 20 2 40 2. 90 BO 2. 20 1. 90 1. 80 1 40 0 60 7 62 0 70 1. 30, 2 10 J 60 2. no 2. 20 2 20 2 50 2. 30 2. 10 1. 40 0 70 0. 60 10 16 0 30 0 50 1. 00 1. 60 2 00 1 90 1. no 2 00 90 1. 60 0. 0 0 30 0. 40 T A B L E I - 8 NOZZLE 1VPE 1/4 CO 10 PRESSURE 40 PSI OlSlANCC 1 0 l b C M C0LLKC10R TYPE D 0. 28 MPA DISTANCE FROM CENTRE (CM) -10 16 - 7 62 - 5 . 00 •2 34 0 0 2 54 3. 09 7 62 10 16 - 1 3 24 -12. 70 -10. 16 0. O O. 0 0 0 -7. 62 - 3 . Od 34 O O 2. 34 5. 08 7.62 10.16 12 70 13 21 O O O O 0 0 0 10 O O 1.70 11.60 8 00 13.00 O. O O. 0 0 O 0 .0 34. O O 0 0 O. 0 0. O O. O 0. 10 0. 60 11.40 9 40 15 40 11.40 13.10 29.90 0 .0 0 0 37.30 B 60 12.90 16 10 19.30 17.60 16 10 9.40 32 60 0 0 u i v 1.50 10.30 6.50 13.30 12 30 10.50 15 40 18.20 10.60 10.10 11.20 0 0 16 80 0 .0 6.40 12.20 13.10 23.30 15 50 11.90 9.10 0.0 32.60 10 00 14 10 • 3.00 10.70 17.00 14 BO 10 10 13 70 17.40 11.00 0.0 10.30 30.10 27.10 20.90 0.0 8 10 12.70 17.30 17.00 19.30 13. 10 8.30 0 0 12.30 43.00 33 40 I3 '30 2 .00 6 10 7.90 10.40 12.30 12.00 B. 00 0.30 0.0 6.10 43.60 23 20 0. 93 0. 0 0.0 0 80 3. 70 4 50 4. 90 0. 0 0. 0 0. 0 10. 10 24. 70 DISTANCE FRDn CENTRE (Cr,) o VI UJ IU o 1 u 1 u V s 0- o o c o e IE c-ro 0-o o o o 9 o o o o 1 v o o o o o o o o © ru 1. o p p p p , p 9 © o 1 IU o o o o o o o o o vl o o o o o «. W _ o o 1 o o o w o - e CJ vl o o o VI © o 0-p o »J <J> o © 1 •V o o o-o c o M o o VI 10 u © o IU p u ik V u o 1 Ul o PJ o o o VI l>J o •v' o VI c o © c CD p u u 0- u p 1 IU u o vl o o o VI u o o V V u o o u p u u VI -0 VI y> 01 _ 9 o Q o 03 c u u o o w M o o a o o p u V) l» J> y © IU o Q o o u VI o o u •0 V! o o o (J* J* o o — A — o V o o v; o u U) o u u u VI o o o CD p p ». * » u p 9 vl o o u o u w o vl u w ' VI © o 0-IU p p o o u p 9 9 p 9 o o o o o o o o o ? o o o o o o o o o IU o o o o o o o o o vl o 9 p 9 © o o o 9 o Ul o o o o o © © © o w o 3 r. •o 2 o — X r- m IV r — U) VI fr. > <n n z c r* 3 o IT m - i z VP -1 -o m - — m o- v i vO T A B L E I - 10 N O Z / L E T V P E 1/4 Cd 10 P R E S S U R E *o. P S I D I S 1 A N C E 20 32 CM C O L L E C T O R T Y P E A 0. 41 MPA DISTANCE FROM CENTRE (CMl - I D 24 - 10 16 0 60 - 7 62 0 60 hi a: - s OB 0 60 V-2 Id - 2 54 0. 40 U r. 0. 0 0. 50 o it u 2 54 0 10 Ul u i 3 00 0. VO 4 1" 0. 60 Ul 7 62 o 10 16 0. 2 0 o. o 2.54 5.08 7.62 10.16 12 7Q 15.24 , 40 0.50 2 00 2 70 3 20 0 70 1 6 0 3 1 0 3 40 2 VO 3 10 2 70 2.30 3.10 3 30 3 50 3.90 =• ™ 1.40 3 20 3 00 3.30 4.20 3 70 3 50 O. 20 O. 0 O 20 2 10 0 .0 0 0 0.0 O. 10 O 10 0. O 1.20 2.20 2. 50 2. 60 1. 3 0 O. 2 0 2. BO 2. 00 I. 00 3. "0 3 10 2 to «. oo 3 3 0 3. 20 4. 00 3. 70 , . 6 0 3. BO 4.80 3.20 2.70 3 00 2 .40 3 40 «.20 3.60 1 70 2 00 0 .0 3.IQ **> 3 30 3 70 3.70 I |0 2.00 3 « 0 3 = 0 3 . 0 3 10 3 30 3 . 0 2. 00 2. 30 2. *?0 2. 50 2.30 I. SO O. 10 0. 20 0. VO 1. 00 TABLE I - 11 NOZZLE IYPE 1/4 CO 10 PRESSURE 60. PSI DISTANCE 10 16 CM COLLECTOR TYPE A O. 41 MPA DISTANCE FROM CENTRE <CM» u l or r o E u Ul u z < t -(II a -13. 24 -12. 70 -10. 16 -7 . 62 -3 00 -2 34 0 0 2 34 3. OB 7 62 10. 16 12 70 13. 24 - IU 16 0. 0 0 o 0. 0 0. 0 0. O O. 0 . O. 0 0 O 0. 0 0 O O. 0 O. 0 0. O -7 . o2 0 0 0. 0 0. 0 0. 0 3. 10 3 90 7. 60 3. 70 0 O 0. 0 0. 0 0. 0 0. 0 -3 OB 0 0 0. 0 0. 30 0. 20 3 30 8 40 1 1. 70 12. 00 3. 30 0 0 0 0 0. 0 0. 0 -2 . 54 0 0 0 0 0. 0 0. 70 9. 20 10. 40 12. 00 9. 10 0 40 2. 60 0. 0 0. 0 0. 0 0,0 0, 0 0.Q Q; SO 2. IP 10, 3P I I , ? 0 1"?, 30 10, BO ?, po 3. $0 0. 0 o. 0 0. 0 2 54 0 0 0 0 0. 20 2. 00 9. 60 9 00 11 60 10. 30 9. 20 2. 60 0. 0 0 0 0. 0 5 00 0 0 0. 0 0. 0 0 10 3. 00 10. 10 9. 40 10. 30 4. 40 0. 0 0. 0 0. 0 0. 0 7 62 0 0 0 0 0. 0 0 0 0 0 0. 10 3. 30 2. 30 0. 0 0. 0 0. 0 0. 0 0. 0 10 16 0 0 0. 0 0. 0 0. 0 0. 0 0 0 0. 0 0 0 0. 0 0. 0 0. 0 0. 0 0. 0 PO CTi cn T A B L E I - 12 N U Z Z L E T Y P E 1/4 CO 10 P R E S S U R E 60. PSI D I S T A N C E 10. 16 CM C O L L E C T O R T Y P E U O 41 MPA DISTANCE FROM CENTRE < C M > l<i u »' t. Ul u b u ••I 4 I-a -15 i4 -12 70 -10 16 -7 62 -5 00 -2 54 0 0 2 54 5. on 7. 62 10. 16 12 70 15. 24 - 1 o 1 6 ' 0 0 0 0 0. 0 0 O IQ. f.0 IV. VO I'J. 3 t l 20. 70 12. 40 0. O o. 0 O. 0 0. 0 -7. 62 0 0 0. 0 0. 0 37 30 1 1. 60 11. 00 IB 00 13 10 12. 90 22. 60 0. 30 0. 0 0. 0 -5 00 0 0 0 0 37 40 10 00 13. 70 21 10 27. 00 23. 20 10. 40 10. 50 29. 30 10 40 0. 0 -3 34 0 0 14. 20 2 60 H. 10 11. /O 10 40 SS. 50 IQ, i'O 81, 40 11,00 0. 0 40. 00 0. 0 0 0 0 00 26 00 0. 0 7. 20 16. 60 10 20 26. 40 17. 30 16. HO 8. 60 0 0 22. 30 IB. 60 - 1 54 27 70 22. 40 0 0 13 10 23 00 21 40 20 10 19 70 21. 40 13. 70 0. 0 13 10 38. 40 5 00 26. VO 17 20 0. 0 10. 70 16. 20 23 VO 23. 60 23 10 19. 00 11. 40 0. 0 12. 10 33. 30 7 62 26 40 23 50' 0. 0 8. 10 9. 00 12. 90 13. 40 16. 30 11. 30 0. 50 0. 0 6. SO 31. 70 to 16 23 GO 9 10 0. 0 7. 20 4. 70 6. VO 9. 10 9. 20 2. 00 0. 0 o. 0 9. 00 23. 80 ro T A B L E I - 13 HORIZONTAL CENTRELINE SPRAY WATER FLUXES (L / S Q . M. B> 1/0 GO 5 NOZZLE SPRAY P R E S S U R E PSI MPA 20 40 60 |100 20 40 bO llOO 0. 14 O. 20 0. 41 0. 69 0. 14 0 20 0 41 0 69 SPRAY DIST. <CM> D I S T A N C E FROM C E N T R E <CM) 10 16 10. 16 10 16 10. 16 15. 24 15. 24 1 5 24 1 5 24 15 24 - 1 2 . 7 0 - 1 0 . 1 6 - 7 . 6 2 - 5 . 0 0 - 2 . 5 4 0 0 2 . 5 4 5, OB 7 . 6 2 1 0 . 1 6 1 2 . 7 0 13 24 0. 0 O. 0 0 O 0 O 0. 0 0. 0 0 0 0. 0 0. 0 0 , O 0. o 0. 0 0. 0 0. 0 0. o 0. 0 0. 0 O. 0 O. 0 0. 0 0. 0 0. 0 0 0 0. 0 O 0 O. O 0. 0 0. 0 0. 0 1. 12 2. 76 3 40 1 .67 3 . 3 c 8. 94 3. 54 3. 53 O. O 3 . 1 3 4 . 3 7 1 0 . 5 4 4. 7 0 5 . 3 7 O. O 5. 59 7. 13 1. 29 6. 04 10. 2 7 9. 2 6 12. 2 0 1 . 8 0 4 . 2 6 1 . 9 6 2 . 2 9 9 06 3 1 1 3. 29 4 B8 5 , 3 2 4 . 7 7 5 . 7 1 5. 9 0 6. 90 0. 0 8. BO 10. 29 0. O 0. 0 O. 0 0. 0 0. 0 2. 21 1. 00 0. 01 0. 0 3. 22 2. 02 3. 3 0 3. oa 4. 66 5. 67 2. 37 0. 0 2. 9 3 0. 0 4. 04 0. 0 0. 0 O. 0 0. 0 0. 0 0. 0 0. 0 O. O 0. 0 0. 0 o. o 0. 0 O. 0 0. 0 0. 0 0. 0 0. 0 T A B L E I - 1 4 H 0 R I 2 0 N 1 A L C E N T R E L I N E SPRAY WATER F L U X E S (L / S Q . M . B ) 1 /8 GO 6 SQ N O Z Z L E SPRAY P R E S S U R E SPRAY 01 ST . (CM) D I S T A N C E FROM C E N T R E (CM) 1 - 1 5 . 24 - 1 2 . 70 - 1 0 . 16 - 7 . 62 - 5 . 08 - 2 . 54 0. 0 2. 54 5. 08 7. 62 TO . 16 12. 70 15. 24 P S I MPA 20 • 0 14 10 16 0. 0 0. 0 0. 0 3 28 5. 27 4. 17 ? . 16 4. 00 n c. 05 0 0 0. 0 0 0 0. 0 40 0 28 10 16 0 O 0. O 0. o 5. •44. 5. 66 5. 03 11. 15 4. 77 3. 10 o. 0 O. O 0. O 0. O 60 0. 41 10 16 0 0 0. 0 0. 0 5. 57 6. 51 6. 70 12. 2 9 5. 85 3. 51 0. 0 0. 0 0. 0 0. 0 90 0. 62 10 16 0. 0 0. 0 0 0 6. 64 7 68 9. 36 13 72 6 72 4. 0 0 0. 0 0. 0 0. 0 0 0 T A B L E I - 15 HORIZONTAL CENTRELINE SPRAY WATER FLUXES (L / SQ.M. S) 1/4 CO 6 .5 SPRAY SPRAY PRESSURE DIS1 PSI HP A <CM> 20 0. 14 10. 16 40 0. 20 10 16 60 0 41 10 16 90 0 62 10. 16 20 0 14 13 24 40 0 20 15 24 60 0. 4 1 15. 24 90 0. 62 15 24 20 0. 14 20. 32 40 0. 20 20. 32 60 0. 41 20. 32 90 0. 62 20. 32 0 0 o-. o 0. 0 0 o 0. 0 0. 0 0. o 0. 0 0. o 0. 0 0. 0 0. o 0. 0 O. Q 0. o 0. o 0. 0 0. o o. o 0. 0 0. o 0. 0 0. 0 o. o 0. 0 o. 0 0. 0 0. 0 0 0 0. 0 0. 0 0. 0 O. 0 0. 0 0. 0 0. O 0. 0 O. O O. O 0. o 0. 0 0 0 0. o 0. o 0. o 1. 63 0. 96 3. 33 NOZZLE DISTANCE FROM CENTRE (CM) 15.24 - 1 2 . 7 0 - 1 0 . 1 6 - 7 . 6 2 -5 . 09 54 O. 0 2.54 5.00 7, 62 10. 16 12.70 15 2' 1 52 1. 03 1. 84 1. 05 2 76 4 71 5 29 6. 32 0. 15 2. 64 3. 51 3. 87 11.13 13. 11 17. 21 20. 29 3. 29 5. 15 9. 04 10. 59 2. 20 5. oa 5. 45 6. 26 29. B6 26 4 1 30. 39 33. 49 14. 17 17. 01 17. oa 19. 26 10. 31 10. 91 10. 95 12. 20 13. 06 lO. 77 13. 71 17. 04 5. 31 5. 20 7. 77 9. 91 5. 07 4. 49 5. 37 6. 54 60 2. 29 0. O O. 06 O. O 3. 49 O. O 4. 69 0 0 3. 73 0. O 4. 91 O. O 6. 13 0. O 7 .57 0.91 O. 17 0. 0 3. 53 2. 97 0 0 O. O 0. 0 O O 0. O 0. 0 O. 0 0. 0 0. O 2. 48 0. 0 0. 0 4. 19 4. 55 O. O 0. O O. O O. O O. O O. 0 0 0 0. O 0. 0 0. O 0. 0 0. 0 O. O 0. 0 O. o 0. 0 O. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 O. 0 T A B L E I - 16 HORIZONTAL CENTRELINE SPRAY WATER FLUXES <L / 1/4 GG 12 SQ NOZZLE f — — SPRAY PRESSURE SPRAY D1ST ( CM ) DISTANCE FROM CENTRE (CM) -15. 24 - 12. 70 -10 16 - 7 . 62 -5 . OQ _2 54 0. 0 2. 54 5. 08 7. 62 10 16 12. 70 15. 24 PS 1 M P A 20 0 14 10. 16 0. 0 0. 0 0. 0 2. 05 5. 1 5 5. 50 13. 30 5. 55 4. 45 4. 10 0. 0 0. 0 0 0 40 0 2.a 10. 16 0. ,0 O. 0 0. O 3 45 6 55 0. BO 17. 55 0. 50 6. 60 5. 20 o. 0 O. 0 0. O 60 0. 4 1 10. 16 0. 0 0 0 0. 0 4. 00 8 15 10 B5 19. 50 10. 65 8. 30 5. 95 0. 0 0. 0 0. 0 20 0 14 1 5 24 0 0 0. 0 0. 90 2. 55 "~1 C - 30 4 10 6. 65 3. 60 1. 40 2. 20 1 c. 50 0. 0 0. 0 40 0. 20 1 5 24 0 0 0. 0 2. 70 3 10 3 50 6. 00 8. 35 5. 20 3. 00 2 95 3. i o 0. 0 0. 0 60 0 4 1 1 5. 24 0 0 0. 0 3. 00 3 4 50 7. 05 10. 20 6. 45 4. 00 3 80 3. 55 0. 0 0. 0 20 0 14 20.32 0 0 0. 0 0 70 0. BO 1 50 2. 65 5 25 3. 65 0. Q3 0 0 0. 0 o. 0 0. 0 40 0. 28 20 .32 u 0 0 •jo I (30 t .60 2 .60 3 90 20 4. 00 2. 70 1 50 0. 70 1 20 0 0 60 0. 4 1 30. 32 0 0 0. 70 2 10 1. 95 2 .85 4 4.5 t BO 5. 30 3. 15 1 . 95 1. 30 1 65 0 15 TABLE I - 17 S P R A Y P H l l S S U K E . VSl 20 1 0 5 0 20 4 0 30 M P A O 14 0 . 2 8 0 . 3 1 0 H 0 . 2 0 0 3 4 HORIZONTAL CENTRELINE SPRAY WATER FLUXES (L / SQ. M. S) 1/4 HH 14. 5 SQ NOZZLE S P R A Y 0 I S T . ( C M ) lO. 1 6 1 0 1 6 1 0 1 6 15. 21 1 3 2 4 1 5 . 2 4 DISTANCE FROM CENTRE (CM) 15 -2.51 0 0 2.54 5.00 7.62 10.16 .2.70 ,5.24 O 0 0 . 0 0 0 o o 0. 0 0. 0 o. o 0. 0 0. 0 4 . 4 0 3. 5 0 4 . 6 1 7. 26 Q. 04 3. /13 8. 73 0. 15 0. 07 2. 30 2. 06 2. 61 0.0 ». «?7 3.32 0 0 0. 07 3. BO 6. 42 8 41 0. 41 10.35 7. 23 10 17 3, 64 1.12 3. 31 A. 30 6. 00 4. 84 4. 72 O. 0 7. 36 6. 36 O. O 8 67 7. 43 3. 83 O. 0 0. 61 2. 30 3. 33 3. 30 0. o 0. O O. O 1. 04 0. 0 4. 20 0. 0 3. 12 4. 26 4. 70 5. 0? 4.33 4.53 5.01 4.76 4.37 4.29 4. 70 3.60 0.0 0. 0 0. 0 O. 0 p. 0 0. 0 0. 0 T A B L E I - 18 / , / « GO H " N 0 Z I L E SPRAY PMt35Uf 'E CO 40 HP A 0 1 4 0 20 SPRAY D t S I . (CM> 10 lb 10. 16 " o T ^ ^ C E FROM C E N T R E (CM) 2 34 „ =oo o . » o.oo . . » . • « • ' • ' • » 0 ,..o ».» >=° '=-• 1 M ' T A B L E I - 19 £FRAY FRESSi . 'PE PS I 20 ••o 6 0 20 ' 10 6 0 HP A 0 1 4 0 . 2 8 0 . 4 1 0 . 1 4 0 . 2 8 0 4 1 HORIZONTAL CENTRELINE SPRAY WATER FLUXES (L / SQ. M. S) 1/4 U B020 NOZZLE SPRAY D IST . ( CM) 1 5 . 2 4 1 5 . 2 4 1 5 2 4 2 0 . 3 2 2 0 . 3 2 20. 32 DISTANCE FROM CENTRE (CM) -15.24 -12.70 -10.16 -7.62 -5. OB -2.54 0.0 2. 54 5.08 7.62 10. 16 12.70 15. 24 0 . 0 3 . 3 7 3 . 3 0 1 9 . 2 0 A. 4 2 o. o a. 6. 76 11. 16. 63 5.75 6.87 7.75 12.81 12.30 8.84 11.07 15.63 20.55 20.37 17. 10 13. 10 10. 40 0. 0 0. 0 25. 13 ia 71 1 1. 63 20. 12 0. 0 41. 16 28. 55 17. 24 16 88 0. 20 13. 63 8. ea 7. 31 5. 86 21. 80 21. G6 IS 01 11. 85 7. 12 6 67 30. 4? 21 27 16. 85 16. 05 12 18 T A B L E I - 20 HORIZONTAL CENTRELINE SPRAY WATER FLUXES (L / SQ. M. S) 3/8 U 5060 NOZZLE SPRAY | P R E S S U R E PS I MPA 10 5 0. 07 0. 03 SPRAY 01 S T . (CM) 17 78 17 70 D I S T A N C E FROM C E N T R E (CM) 1 5 24 -12. 70 -10. 16 -7. 6 2 -5. 08 - 2 54 0.0 2.54 5.08 7.62 10.16 12.70 15.24 0. 0 0. 0 0. 0 0. 0 0. 0 0 0 ,4.90 56.95 84.70 106.90 96.40 63.45 17.75 0 0 9.80 07.45 46.90 06.95. 69.55 104.75 OO O. 0 o. o 0. 0 o o ro • — i cn A P P E N D I X I I Horizontal cent re l ine spray f lux p r o f i l e s , spray f lux contour maps and three dimensional representat ions of spray f l u x e s . 277 VERTICRL DISTANCE FROM CENTRE (CMS.) -12.1 -50.16 -T.G2 -5.06 --'.54 0.0 2.54 5.08 _1_ '1.52 10.16 12.7 5.0 -2.0 -i V E R T I C R L D o.D i.o i TRNCE FROM CENTRE i Figure 11-1 Spray flux contour map for a 1/4 GG 10 nozzle, for a  spray pressure of 0.13 MPa at a nozzle distance of  10.16 cm (Type A collectors). 278 F i g u r e 11-2 Spray f l u x con tour map f o r a 1/4 GG 10 n o z z l e , f o r a  sp ray p ressu re o f 0 .13 MPa at a n o z z l e d i s t a n c e of  15.24 cm (Type A c o l l e c t o r s ) . 279 Figure 11-3 Spray flux contour map for a 1/4 GG 10 nozzle, for a  spray pressure of 0.27 MPa at a nozzle distance of  10.16 cm (Type A collectors). VFRTICRL DISTHNCE FROM CENTRE (CMS . 1 - 5 . 0 8 - : . 5 J 0 . 0 5 . 0 8 •7.62 10. IC 280 i: . i Figure 11-4 Spray flux contour map for a 1/4 GG 10 nozzle, for a  spray pressure of 0.27 MPa at a nozzle distance of  10.16 cm (Type A collectors). 281 F igu re 11-5 Spray f l u x con tour map f o r a 1/4 BB 10 n o z z l e , f o r a  spray p ressu re o f 0 .13 MPa at a n o z z l e d i s t a n c e o f  20.32 cm (Type A c o l l e c t o r s ) . 282 -12.1 VERTICAL DISTANCE FROM.CENTRE (CMS.) -10 16 -7.G2 -5.08 -2.54 0.0 2.54 5.08 J J 1 1 1 L. 1.62 10.1G i _ 12. J - 4 . 0 - 2 0 - 1 . 0 0 . 3 ! . 0 2 . 0 V E R T I C A L D I S T A N C E FROM CENTRE i I N . l F igu re H - 6 Spray f l u x con tour map f o r a 1/4 GG 10 n o z z l e , f o r a  spray p ressure o f 0.27 MPa a t a n o z z l e d i s t a n c e of  20.32 cm (Type A c o l l e c t o r s ) . 283 F igu re 11 - 7 Spray f l u x con tour map f o r a 1/4 GG 10 n o z z l e , f o r a  spray p ressu re o f 0 .13 MPa a t a n o z z l e d i s t a n c e o f  10.16 cm and Type B c o l l e c t o r s . 284 VFRT JCRL DISTRNCE FROM CcN' f tE (CMS.) -12.1 • ) 0 . ! G - I .C2 -5.08 O.U S.OB 7.62 10.16 12.7 F igure 11-8 Spray f l u x con tour map f o r a 1/4 GG 10 n o z z l e , f o r a  spray p ressure o f 0.27 MPa a t a. n o z z l e d i s t a n c e - o f  10.16 cm Type B c o l l e c t o r s . 2 8 5 Figure 11-9 Three dimensional representation of the spray flux  distribution for a 1/4 GG 10 nozzle, for a spray  pressure of 0.13 MPa and a nozzle distance of 10.16 cm (Type A collectors). Figure 11-10 Three dimensional representation of the spray flux distribution for a 1/4 GG 10 nozzle, for a spray pressure of 0.27 MPa and a nozzle distance of  10.16 cm (Type A collectors). Q5MI^IL:II Three d imens iona l r e p r e s e n t a t i o n o f the sp ray f l u x d i s t r i b u t i o n f o r a 1/4 GG 10 n o z z l e , f o r a spray p ressu re o f 0 .13 MPa and a n o z z l e <» d i s t a n c e o f 15.32 cm (Type A C o l l e c t o r s ) F igu re 11-12 Three d imens iona l r e p r e s e n t a t i o n o f the sp ray f l u x d i s t r i b u t i o n f o r a co spray p ressu re o f 0 .13 MPa and a n o z z l e d i s t a n c e o f 20.32 cm (Type A C o l l e c t o r s ) . o -6.0 DISTRNCE -2.0 FROM CENTRE UN) 0.0 2.0 j L 2 8 9 -35.24 -30 36 -5.06 0.0 5.08 ' DISTRNCE FROM CENTRE (CM) 10.36 Figure 11-13 Horizontal centreline spray flux profiles for a  1/4 GG 10 SQ nozzle at a nozzle distance of 10.16 cm. 290 o - 6 . D -4.0 DISTANCE FROM CENTRE UN) -2.0 a LUcc . C O -to Q_ CO o o ID ' a 2.0 _ L 4.0 i • 6 .Do NOZZLE I/4GGI0SQ. DISTANCE 15.24 CMS PRESSURE PSI MPA LTJ 20 0.13 A 40 0.27 <3> 60 0.41 m—i -35.24 a CO o a CM a ID -30.36 -5.0e 0.0 5.08 DISTANCE FROM CENTRE (CM) 30.15 15.24 Figure 11-14 Horizontal centreline spray flux profiles for a 1/4 GG 10 SQ nozzle at a nozzle distance of 15.24 cm, 291 -6.D -4.0 CN a UJOD C O -O CO G_ CO a c n ' DISTRNCE -2.0 I FROM CENTRE (IN) 0.0 ' 2.0 4.0 _J NOZZLE 1/4GG30S0. DISTANCE 20 . 32 CMS PRESSURE PSI MPfl • 2 0 0.13 A 40 0.27 O 60 0.41 -35.24 •30.36 -5.08 CD 5. OS DISTANCE FROM CENTRE. (CM) 10.16 6 . D o a . a m a CO in a cn 15.24 Figure 11-15 Horizontal centreline spray flux profiles for a 1/4 GG 10 SO nozzle at a nozzle distance of 20.32 cm. -292 a - 6 . 0 DISTRNCE FROM CENTRE U N ) -2.0 0.0 2.0 J _ 1 L 6 . 0 = -15.24 -10 16 -5.06 0.0 5.08 DISTANCE FROM CENTRE CCM3 10.16 15.24 Figure 11-16 Horizontal centreline spray flux profiles for a 1/4 GG 12 SQ nozzle at a nozzle distance of 10.16 cm, 29 3 DISTRNCE FROM CENTRE (IN) -6 0 - -4.0 -2.0 O.D 2.0 I I 1 1 -i.O 6.0=3 t o - 1 to _ | a (_><=> U J r J C O -NDZZLE 1/4GG125Q DISTANCE 1 5 . 2 4 CMS, PRESSURE • PSI MPA • 2 0 0 . 1 3 A 40 0 . 27 O 60 0 .41 o 03 a -15.24 -10.16 -5.08 0.0 5.08 DISTANCE FROM CENTRE [CK3 10:16 Figure 11-18 Horizontal centreline spray flux profiles for a 1/4 GG 12 SQ nozzle at a nozzle distance of 20.32 cm. 2.9'4 o - 6 . 0 CD . C D - J o o<=> UJoJ. c o -ca CO >-<= Q_ CO DISTRNCE FROM CENTRE U N ) -4.0 -2.0 0.0 2.0 4.0 J J I 1 1— 6 . 0 = NOZZLE 1/4GG12SQ D I S T R N C E 2 0 . 3 2 CMS, PRESSURE PSI MPA LTJ 20 0 . 1 3 A 40 0 . 2 7 O 60 0 . 4 1 o . S 3 a L - U 3 a o '-15.24 -10.16 -5.08 0.0 5.08 DISTANCE FROM CENTRE (CM) 10.16 o 03 15.24 Figure 11-18 Horizontal centreline'spray flux profiles for a • 1/4 GG 12 SQ nozzle at a nozzle distance of 20.32 cm. 29-5 DISTRNCE -2.0 FROM CENTRE (IN) 0.0 2.0 6.0= I -]0 ]6 -5.OB 0.0 5.08 • DISTRNCE FROM CENTRE (CM) 10.16 15.24 F igu re 11-19 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 3/8 HH 18 SQ n o z z l e at a n o z z l e d i s t a n c e o f 10.16 cm, 296 -6.0 -4.0 DISTANCE -2.0 o -CM FROM CENTRE (IN) 0 0 2.0 4,0 f __1 I 6.0a NOZZLE 3/8HH18SQ. DISTANCE 15.24 CMS PRESSURE PSI MPA • 3 0 0.20 A 20 0.13 a I D - J a UJrsi, a a a -15.24 -r r— r -10 16 -5.0B 0.0 5.08 DISTANCE FROM CENTRE (CM) 10.16 15.24 Figure 11-20 Horizontal centreline spray flux profiles for a 3/8 HH 18 SQ nozzle at a nozzle distance of 15.24 cm. 297 -6.0 -4.0 DISTRNCE -2.0 FROM CENTRE ( IN) 0.0 2.0 CM o to'_J a C O -O to d o . >-o Q_ CO o 4.0 l 6.0o NOZZLE 3/8HH3 8S0. DISTANCE 20.32 CMS PRESSURE PSI MPA • 3 0 0.20 A 20 0.13 i 1 i •35.24 -30.36 -5.08 0.0 5.08 DISTANCE FROM CENTRE (CM) o O | _ C Q Q L. a o CM' o o Q OO a 10.36 15.24 Figure 11-21 Horizontal centreline spray flux profiles for a 3/8 HH 18 SQ nozzle at a nozzle distance of 20.32 cm. 298 o-6.D -4.0 DISTRNCE -2.0 FROM CENTRE (IN) 0.0 2.0 4.0 _J 6.0° NOZZLE 1/4U8020 DISTRNCE15.24 CMS PRESSURE PSI MPfl -35.24 -30 36 -5.06 0.0 5.D8 DISTRNCE FROM CENTRE (CM) 10.36 F i g u r e 11-22 ' H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a - ! l / 4 U8020 n o z z l e , at a nozz le d i s t a n c e o f 15 .24 cm, 299 DISTANCE FROM CENTRE UN) -4.0 - 2 . 0 O . D 2 . 0 J L 6 . 0 " -io is -s.oa o.o s.oa DISTANCE FROM CENTRE (CM) 1 0 . 1 6 1 5 . 2 4 F igu re I1-23 H o r i z o n t a l c e n t r e l i n e spray f l u x p r o f i l e s f o r a 3/8 U5060 n o z z l e a t a n o z z l e d i s t a n c e o f 17.78 cm. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0078747/manifest

Comment

Related Items