An experimental method of determining the mean heat transfer coefficient for the nozzle of a solid propellant rocket engine, by means of constant flow calorimetry

THE COLLEGE OF AERONAUTICS

C R A N F I E L D

AN EXPERIMENTAL METHOD OF DETERMINING THE

MEAN HEAT TRANSFER COEFFICIENT FOR THE NOZZLE

O F A SOLID PROPELLANT ROCKET ENGINE, BY MEANS O F

CONSTANT FLOW CALORIMETRY

by

THE C O L L E G E OF AERONAUTICS

CRANFIELD

An E x p e r i m e n t a l Method of Determining the Mean Heat T r a n s f e r Coefficient for the Nozzle of a Solid Propellant Rocket Engine,

by m.eans of Constant Flow Calorinaetry by

-A. G. Smithf B . S c . , A . R . C . S . . D . I . C . , A . F . R . A e . S . , and

T. A. C a r b e r r y , A. F , Inst. P e t .

SUMMARY

An investigation h a s been made into the feasibility of predicting m e a n convective heat t r a n s f e r coefficients for the nozzles of solid propellant rocket e n g i n e s . The principle of the method used was constant flow c a l o r i m e t r y ; the surface of a copper nozzle was heated with a flow of hot w a t e r , and cooled by a i r flow through the nozzle. Heat t r a n s f e r coefficients w e r e then derived from m e a s u r e m e n t s of w a t e r flow, w a t e r t e m p e r a t u r e drop and nozzle surface t e m p e r a t u r e s . F o r a range of Reynolds n u m b e r s , the m e a n convective heat t r a n s f e r for a star^shaped conduit could be e x p r e s s e d by the following

equation:-Nu = 0.1976 Re'-''' Pr^"^^^

F o r a c i g a r e t t e - b u r n i n g charge the m e a n convective heat t r a n s f e r could be e x p r e s s e d by the following equation :

-Nu = 0.7013 Re°-^^1 P r ^ ' ^ ^ ^

The flow pattern into the nozzle was studied using a w a t e r flow visualisation r i g involving both photographic and d i r e c t viewing techniques. In addition, investigations into the t e m p e r a t u r e and p r e s s u r e distributions along the nozzle surface at ambient conditions were c a r r i e d out using a p e r s p e x nozzle fitted with surface thermocouples and p r e s s u r e tappings.

Hives P r o f e s s o r and Head of Department of Mechanical Engineering, University of Nottingham.

F o r m e r l y P r o f e s s o r and Head of Department of Aircraft P r o p u l s i o n , The College of A e r o n a u t i c s .

Notation

1. Introduction 1 2. Mean Heat Transfer Determination 2

3. Nozzle Construction 3 4. T e m p e r a t u r e Measurement 3

5. Heat Leakage 4 8 , Treatment of Results 4

7. Flow Visualisation 8 8. Surface Temperature Measurement 7

9. Discussion 8 10. Conclusions 9 11. References 10 Notation to Appendix 1 11 Appendix 1 12 Results 13 Graphs F i g u r e s

A _ throat a r e a of n o z z l e , ft C s p e c i f i c heat of w a t e r at constant p r e s s u r e c a l . / g r m . C . *^w D_, throat d i a m e t e r of n o z z l e , ft. — , 2 o h a v e r a g e heat t r a n s f e r coefficient. C . H . U . / h r . f t . C .

h coefficient of heat leakage to surroundings. C . H . U . / h r . f t . C . h o b s e r v e d a v e r a g e heat t r a n s f e r coefficient. C . H . U . / h r . f t . C . Ah differential head a c r o s s m e t e r i n g o r i f i c e , i n s . w a t e r g a u g e .

K t h e r m a l conductivity of a i r . C . H . U . / h r . f t , C . Nu N u s s e l t Number I —=p— )

p p r e s s u r e of a i r at upstream tapping of o r i f i c e . "Hg. gauge. P a t m o s p h e r i c p r e s s u r e . "Hg. WD,j, Re Reynolds Number ( — - — ) T a i r t e m p e r a t u r e upstream of o r i f i c e . C. T s u r f a c e t e m p e r a t u r e of n o z z l e . C. T t e m p e r a t u r e of water at inlet to n o z z l e . C. T t e m p e r a t u r e of water at outlet from n o z z l e . C. AT t e m p e r a t u r e drop of water through n o z z l e . C .

3 V volume flow rate of w a t e r , cm / s e c .

w W a i r m a s s flow r a t e . l b . / s e c . c expansion coefficient U absolute v i s c o s i t y of a i r . lb. / h r . f t . 3 p d e n s i t y of w a t e r , g r m . / c m .

1. Introduction

The t e m p e r a t u r e of a rocket engine nozzle i s often a design limitation. In o r d e r to d e t e r m i n e t h i s t e m p e r a t u r e , a knowledge of the coefficient of heat t r a n s f e r by convection from the gas to the surface i s r e q u i r e d .

It h a s been noted that conditions u p s t r e a m of the nozzle, e. g. the geometry of the conduit of a solid propellant engine, influence the r a t e of heat t r a n s f e r to the nozzle. In the c a s e of s t a r - s h a p e d solid propellant c h a r g e s , t h e r e i s a tendency for the converging (upstream) surface of the nozzle to be eroded, thus affecting the p e r f o r m a n c e of the engine. This tendency i s m o r e m a r k e d with hot propellants than with cool; however, it h a s been noted a l s o that with c i g a r e t t e -burning c h a r g e s the e r o s i o n of this nozzle region i s often much l e s s m a r k e d .

C e r t a i n obvious hypotheses a r i s e : c l e a r l y when the jet issuing from a s t a r -shaped conduit s t r i k e s the nozzle e n t r y face, conditions a r e obviously favourable to the existence of m a r k e d secondary flows. In fact, each s t r e a m from a s t a r point of the conduit would be expected to impinge obliquely on the nozzle e n t r y face and then s p l a s h sideways, with consequent continued renewal of the hot s t r e a m on the nozzle s u r f a c e , hence giving r i s e to high heat t r a n s f e r , friction, and e r o s i o n .

In the case of the c i g a r e t t e - b u r n i n g c h a r g e , t h e r e would be no jet impingement action, no s e c o n d a r y flow, l e s s friction and heat t r a n s f e r , and l e s s tendency to e r o s i o n .

E x p e r i m e n t s on nozzle e r o s i o n could not be undertaken at Cranfield owing to the expense of the r o c k e t s and the requisite labour. However, investigations of heat t r a n s f e r coefficients by convection, both local and m e a n , have been c a r r i e d out. Local heat t r a n s f e r coefficients w e r e obtained by Lt. R. M.Houston (Ref. 1) and F i t . Lt. I. Singh (Ref. 2), using a m a s s t r a n s f e r method involving napthalene. The investigation of mean heat t r a n s f e r coefficients by convection i s dealt with in t h i s r e p o r t .

Conduit Design

The rocket m o t o r casing was manufactured from a p e r s p e x tube 4 . 5 " i n t e r n a l d i a m e t e r and 1 8 " long. P e r s p e x grain m o d e l s of any conduit design could be slid into t h i s tube and s e c u r e d f i r m l y in the r e q u i r e d axial position r e l a t i v e to the nozzle. To obtain a highly disturbed flow pattern at the nozzle, a seven-pointed s t a r shape conduit with a low value of conduit c r o s s - s e c t i o n to throat a r e a r a t i o was chosen.

Using Stone (Ref. 3) a s a guide, a seven point s t a r conduit was designed with the following c h a r a c t e r i s t i c s :

-(a) P r o g r e s s i v i t y r a t i o

final propellant surface - i n initial propellant surface

(b) Loading fraction

propellant c r o s s section _ r» 7S m o t o r c r o s s section

which when used in conjunction with a nozzle of 1.98" throat d i a m e t e r , r e s u l t e d in a conduit c r o s s section to throat a r e a r a t i o of 1.3, a s recommended by R . P . E . , Westcott.

The conduit model featured perspex flanges at each end and another midway along i t s length. The s t a r shape was made from 1/16" thick perspex sheet, each point being folded s e p a r a t e l y to the required r a d i u s and then bonded to

other points and to the locating flanges. The com.plete model was 16" long (Fig. 10), Nozzle Design

The nozzle shape was produced to R . P . E . Westcott r e c o m m e n d a t i o n s , the converging face being a cone of half angle of 60 turned into the throat by an a r c of a c i r c l e whose r a d i u s was equal to the throat r a d i u s . The throat a r e a was a p p r o x i m a t e l y 0.77 of the conduit a r e a , thus giving a throat d i a m e t e r of 1.98". The diverging face, when incorporated for the flow visualisation studies and for the m a s s t r a n s f e r investigations, had an included angle of 30 .

2. Mean Heat T r a n s f e r Determination Apparatus

The principle of the method used was constant flow c a l o r i m e t r y . The surface of a copper nozzle was heated by a flow of hot w a t e r and cooled by a i r flow through the n o z z l e . Rates of heat t r a n s f e r w e r e derived from m e a s u r e m e n t s of flow and t e m p e r a t u r e drop of the w a t e r . Nozzle surface t e m p e r a t u r e s were a l s o m e a s u r e d and hence the heat t r a n s f e r coefficients calculated,

The a p p a r a t u s i s shown d i a g r a m m a t i c a l l y in F i g . 3 . The w a t e r in the main tank (which was well insulated to r e d u c e heat leakage to a minimum) was heated by four 2.KW. i m m e r s i o n h e a t e r s , one of which was controlled by a V a r i a c , so that the w a t e r t e m p e r a t u r e at inlet to the nozzle could be maintained r e a s o n a b l y constant. The w a t e r was pumped round the s y s t e m by m e a n s of an e l e c t r l c a U y driven centrifugal pump and the water volume flow r a t e determined from a visual reading flowmeter.

The airflow was supplied from an Allis C h a l m e r s c o m p r e s s o r , the a i r being drawn through the conduit and nozzle and thence through a m e t e r i n g orifice. The installation was on the suction side of the com.pressor for the following r e a s o n s :

-(a) The danger of velocity and t e m p e r a t u r e tratification of the a i r flow was t h e r e b y considerably reduced,

(b) M e a s u r e m e n t of a i r flow total t e m p e r a t u r e ( i . e . ambient a i r t e m p e r a t u r e ) was simplified,

(c) The r i g components ( e . g . perspex m o d e l s , e t c . ) were not subjected to m o r e than 15 lb. livr p r e s s u r e ,

(d) Control of flow down to v e r y low values could be achieved by altering the c o m p r e s s o r suction butterfly valves without introducing turbulence into the working section.

To d e t e r m i n e the heat t r a n s f e r from, the surface of the nozzle t o the a i r , hot w a t e r at approximately 85 C. was circulated through the passageways in the n o z z l e . The t e m p e r a t u r e drop of the w a t e r flowing through the nozzle was d e te rmi n e d by m e a n s of a c h r o m e l - c o n s t a n t a n differential thermocouple

connected to a galvanom.eter. The actual w a t e r t e m p e r a t u r e s at inlet and outlet to the nozzle w e r e m e a s u r e d with m e r e u r y - i n - g l a s s thermiometers (range 55-105 C. X 0.2 C ), t h e s e t h e r m o m e t e r s all having an N . P . L . certificate. The nozzle surface t e m p e r a t u r e was obtained from the mean reading of six copper-constantan t h e r m o c o a x i a l therm.ocouples embedded in the wall of the nozzle.

T e s t s w e r e c a r r i e d out over a r a n g e of a i r flows from 500 lb. / h r . to approximately 3200 l b . / h r . ( i . e . choking conditions in nozzle), using (a) the s t a r - s h a p e d conduit configuration, and (b) the cigarette-burning shaped

configuration. In addition, the distance of the conduit to the nozzle e n t r y face was v a r i e d from z e r o to 0.75".

3 ' Nozzle Construction

The nozzle was manufactured from solid copper b a r , copper being chosen for i t s excellent thernaal c h a r a c t e r i s t i c s . The production of the passageways

p r e s e n t e d sonae p r o b l e m s , ideally a s p i r a l form was envisaged, but due to the nozzle profile it seemed that to produce this form would be too costly. The finalised form was a s e r i e s of concentric grooves 0.125" wide by 0.1875" deep. A slot was cut in each separating wall between the grooves to allow the water to flow from, one groove to the next, each groove being suitably blanked off to form a continuous passageway approxim.ately 6 5 " long. Six copperconstantan t h e r m o -coaxial therm.ocouples of 0.02" d i a m e t e r w e r e embedded in the nozzle surface at random positions, the nozzle surface being of the o r d e r of 0.062" thick. The outside of the grooves was then sealed off by m e a n s of copper s t r i p s soldered on to the top of the separating w a l l s . The nozzle was sandwiched between two 0.625" thick ebonite flanges, and the intervening space filled with powdered a s b e s t o s to reduce all heat l o s s e s , other than the heat lost to the a i r flow, to a minimum (Fig. 11).

The m a x i m u m w a t e r flow r a t e through the passageways was 1625 c c . / m l n . a1 a p r e s s u r e of 30 p . s. i. g. The weight of the copper nozzle was 1.26 l b . , and the calculated t e m p e r a t u r e d r o p a c r o s s the wall was of the o r d e r of 0.05 C, maximum..

4. Tem.perature M e a s u r e m e n t

Calibration of the Chromel-Constantan Differential Thermocouple

Since the t e m p e r a t u r e drop of the w a t e r flowing through the nozzle was always s m a l l , it was e s s e n t i a l that the m e a s u r e m e n t of v a r i o u s t e m p e r a t u r e s r e q u i r e d from the a p p a r a t u s should be a c c u r a t e l y obtained. All t e m p e r a t u r e m e a s u r i n g i n s t r u m e n t s w e r e t h e r e f o r e carefully calibrated.

In the case of the chromel-constantan differential thermocouple, the ends of the thermocouple w e r e placed in s e p a r a t e oil baths ( t h e r m o s flasks) each containing an e l e c t r i c a l l y d r i v e n s t i r r e r , a snaall heating element, and an N . P . L . calibrated m e r c u r y - i n - g l a s s t h e r m o m e t e r (range 55-105 C. x 0.2 C ), The ends of the leads w e r e connected via a cold junction to a spot galvanometer. Oil was heated to about 85-90 C. and poured into the oil baths; one oil bath had a sm^all quantity of cold oil added until the t e m p e r a t u r e difference betwen the two baths was about 4 C , By m e a n s of r h e o s t a t s and a m m e t e r s , incorporated in the heating coil c i r c u i t s , it was possible to maintain a constant t e m p e r a t u r e difference between the two oil b a t h s . The galvanometer deflection was calibrated against a Beckmann differential t h e r m o m e t e r (range 6 C x 0.01 C ), and a suitable calibration curve was produced,

Stratification in Main Supply Tank

To check on the effect of t e m p e r a t u r e drift a r i s i n g from stratification of the w a t e r in the heating tank, a t e m p e r a t u r e drift indicator was made. This

consisted of a 0.25" b o r e copper tube approximately 6 1 " long, made into a coil of 3.75" d i a m e t e r and having 5 t u r n s , the whole weighing 1.25 lb. , sensibly the s a m e a s the copper nozzle. Two constantan w i r e s w e r e soldered one at each end of the coil, and the ends of the q i r e s w e r e connected to a spot galvanometer via a cold junction. The coil was well insulated with m i n e r a l wool inside an aluminium container 6" x 6" x 3 " in s i z e , and was placed in the supply line between the pump and the nozzle. The sensitivity of the galvanometer was such that one c e n t i m e t r e deflection on the scale was equivalent to 0.6 C . It was found, for the range of t e s t s covered, that the instrument was quite sensitive to sudden changes in t e m p e r a t u r e , and no significant changes in t e m p e r a t u r e s due to stratification were observed once steady state conditions had been achieved,

5. Heat Leakage

It was n e c e s s a r y to d e t e r m i n e the amount of heat leakage from the nozzle, other than that through the nozzle s u r f a c e . To obtain this factor, the conduit and m o t o r c a s e w e r e removed from the nozzle, and the nozzle surface completely insulated from the a t m o s p h e r e with cotton wool. Hot w a t e r at the n o r m a l

working t e m p e r a t u r e was circulated through the nozzle passageways, s t a r t i n g at the m a x i m u m w a t e r flow r a t e and gradually reducing the flow r a t e in stages to the minimum likely to be used. Values of heat leakage were determined at each of these s t a g e s after steady state conditions had been established. These values have been plotted in graphical form (Graph 3),

6, T r e a t m e n t of Results Air Flow M e a s u r e m e n t

1. The a i r m a s s flow r a t e s were m e a s u r e d using B r i t i s h Standard orifice plates with D and D / 2 p r e s s u r e tappings. Using Ref. 4, it was calculated that two

orifice plates would be sufficient to cover the range of flows from 300 to 3600 lb. /hr The m a s s flow equations a r e :

-(a) 3.8" dia. orifice plate

W = 0.825 e ^ l ^ ^

(b) 1.9" d i a , o r i f i c e p l a t e

jP.Ah

W = 0.186 e ^ rj, I b . / s e c . a w h e r e P = p r e s s u r e u p s t r e a m of o r i f i c e " h g . a b s . A h = d i f f e r e n t i a l h e a d a c r o s s o r i f i c e p l a t e " w a t e r gauge T = t e m p e r a t u r e of a i r u p s t r e a m of o r i f i c e K. e = e x p a n s i o n coefficient S i n c e t h e t o t a l t e m p e r a t u r e of t h e a i r flow w a s a t m o s p h e r i c t e m p e r a t u r e , r e a d i n g s w e r e t a k e n f r o m a m e r c u r y - i n - g l a s s t h e r m o m e t e r ( r a n g e -5 t o 55 C . !x 0.2 C ) p l a c e d a t t h e conduit e n t r a n c e . 2 . W a t e r V o l u m e F l o w R a t e "wao V c c / s e c . = f l o w m e t e r r e a d i n g X V ^ « Wmax ^ P,^^ 60 = f l o w m e t e r r e a d i n g x 37.88, p ws w h e r e V = w a t e r v o l u m e flow r a t e at full s c a l e m e t e r r e a d i n g at 20 C ^maix = 2273 c c / m i n . p = w a t e r d e n s i t y at 20 C . W 8 0 = 0.998 g r m / c c . p = w a t e r d e n s i t y at T ( G r a p h 2) w a '' W2 T = w a t e r o u t l e t t e m p e r a t u r e f r o m n o z z l e C . W 2 V a l u e s of w a t e r d e n s i t y o v e r r a n g e of t e m p e r a t u r e s w e r e obtained f r o m K a y e and L a b y ( R e f . 5 ) , 3 . T h e v a l u e s of a b s o l u t e v i s c o s i t y of a i r , and t h e r m a l c o n d u c t i v i t y of a i r w e r e o b t a i n e d f r o m K a y s and London (Ref. 6 ) .

T h e o r y

If hot w a t e r i s c i r c u l a t e d a r o u n d t h e c o p p e r n o z z l e when a i r i s p a s s i n g t h r o u g h t h e n o z z l e , t h e n t h e h e a t l o s t by the w a t e r can be e q u a t e d t o the h e a t gained b y the a i r . H e n c e t h e m e a n v a l u e of t h e h e a t t r a n s f e r of t h e n o z z l e b y c o n v e c t i o n c a n b e d e t e r m i n e d . H e a t t r a n s f e r r e d = ( p . V . C AT) g r m . c a l . / s e c . p w ° q" = h A (T - T ) C H U / h r . ^ o s s a 7- ( P . V . C .AT) x 7.938 „ • • h = p W .-.TTTT/U **2 o ° A ( T - T ) C H U / h r . ft C . s s a

2 where A = surface a r e a of nozzle = 0.1241 ft

s

C = specific heat of w a t e r at T g r m . c a l . / g r m . C (Graph 2) . P W W 2 ^ ' «

w = density of w a t e r at T g r m . / c c . (Graph 2)

W 2

T . = w a t e r outlet t e m p e r a t u r e from nozzle C.

W 2

T = m e a n surface t e m p e r a t u r e of nozzle C. T = a i r t e m p e r a t u r e C.

7.938 = conversion factor to convert g r m . c a l . / s e c . to C H U / h r . Values of C w e r e obtained from r e f e r e n c e 5 .

Pw

Heat leakage h to s u r r o u n d i n g s , o v e r the range of flows covered in the t e s t s , was obtained from (Graph 3).

. ' . h = iï - ïï^ C H U / h r . ft^ C ° . o L

Now the Nusselt No. Nu = "^ ° T K

where D = nozzle throat d i a m e t e r = 0.165 ft.

K = t h e r m a l conductivity of a i r C H U / h r . ft. C .

W •'^T 4

The Reynolds No. Re = - ^ x 3600 = 2.76 x 10 W/jj where W = a i r m a s s flow r a t e l b . / s e c .

D ^ = nozzle throat d i a m e t e r = 0.165 ft. 2 A „ = nozzle throat a r e a = 0.0215 ft .

ft = absolute v i s c o s i t y of a i r 1 b . / h r . ft. C .

The r e s u l t s of the t e s t c a r r i e d out have been plotted in the form of Nu against Re and a r e shown (Graph 1). A value of 0.71 was taken for the P r a n d t l No. and hence the following r e l a t i o n s h i p s w e r e derived from the plotted r e s u l t s .

F o r the case of the s t a r - s h a p e d charge : Nu = 0.1976 Re'-'^' P r " ' ^ ^ ^ and the case of the c i g a r e t t e burning c h a r g e

Nu = 0.7013 Re''^'' Pr''^'' 7. Flow Visualisation

To be able to a s s e s s the v a r i a t i o n s of nozzle heat t r a n s f e r coefficient in r e l a t i o n to the a i r flow p a t t e r n , it was considered d e s i r a b l e to be able to visualise and study this p a t t e r n ,

A three dimensional water flow visualisation r i g was constructed (Fig. 6), and basically consisted of models of rocket components made of perspex, identical in size to those used in the heat transfer apparatus. Water was

pumped by means of a small centrifugal pump through the models and recirculated back to the storage tank. Flow and p r e s s u r e control were achieved by suitable valves and a British Standard orifice plate was used to determine the water m a s s flow r a t e . The flow t r a c e r s used were polystyrene pellets of the order of 0.3 - 0.5 m m . diameter and having a density close to that of water.

The light source used for general viewing was 3 KW line filament tungsten lamp; an adjustable slit on the side of the lamp running parallel to the filament cppcentrated the light into the required beam. The lighting source could be

fl^pved bodily so that various c r o s s - s e c t i o n s of the flow conditions could be studied. The s t a r - s h a p e d conduit model was specifically designed with seven points so that by passing a beam of light directly a c r o s s the diameter of the model it was possible to view, simultaneously the flow patterns issuing from a peak of the s t a r - s h a p e , and also the flow patterns issuing midway between two peaks. To provide permanent r e c o r d s of the flow p a t t e r n s , photographs were taken by Houston (Ref. 1) using (a) a 120 mm. plate camera loaded with Royal x Pan film with an exposure time of 1/25 sec. at f 4.5, and (b) a 35 m m . camera using HP3 film, exposure time 1/25 s e c . at f 2.8. Full illumination from the 3 KW tungsten lamp was used. The flow patterns in F i g s . 7 - 9 clearly indicate the unsteady and recirculating flow issuing from the peaks of the star-shaped conduit. 8. Surface T e m p e r a t u r e Measurement

The final stage of the investigation was to determine the adiabatic wall

temperature distribution along the surface of the nozzle under ambient conditions, and to a l e s s e r degree the static pressure.distribution. F o r this work the nozzle was made from solid perspex b a r , the convergent section only being used. Seven static p r e s s u r e tappings were drilled normal to the surface of the nozzle, and at equal spacings along the nozzle surface in a horizontal plane. Diametrically opposite were installed seven chromel-constantan thermocouples made from 0.005" diameter wire: these were embedded in the surface of the nozzle by laying them in grooves 0.008" deep and sealing with perspex cement; the whole surface was then repolished to renaove i r r e g u l a r i t i e s (Fig. 11).

Provision was made for rotating the conduit in relation to the p r e s s u r e and t e m p e r a t u r e tappings, by placing 0.1875" diameter steel ball bearings in the grooves machined in the end flanges of the conduit model, formerly used for the friction rings in the flow visualisation apparatus. A degree m a r k e r was fitted to the outer flange of the perspex motor c a s e , so that the conduit could be moved to any given position in relation to the tappings in the nozzle. The conduit model was the same as that used in previous t e s t s , and the profile of the perspex nozzle was made to the same speicifications as the other nozzles used in these investigations. The nozzle and conduit model were connected to the same a i r supply a s was used for the heat transfer apparatus (Fig. 2).

T e s t s were carried out at choking conditions in the nozzle, with the s t a r -shaped conduit in position, and with it removed. At first, t e s t s were carried out taking p r e s s u r e s and t e m p e r a t u r e s for complete rotation of the conduit, but r e s u l t s showed that it was only n e c e s s a r y to c a r r y out further t e s t s at two

positions: (a) when the peak of the s t a r was in line with the tappings, and (b) when the peak was not in line ( i . e . a rotation of 25.7 ). The star-shaped conduit was also moved in stages from being in contact with the nozzle entry face to 0.75" from the nozzle face; no significant variation in readings was noted.

T^ - T P* - P t s t Results were plotted graphically in the form of — and ——

t t where T = total temperature K

T = nozzle surface temperature K P = total p r e s s u r e "Hg.abs.

P = nozzle static p r e s s u r e " H g . a b s . Instrumentation

All p r e s s u r e s were measured from 40" m e r c u r y manometers; the surface thermocouples were connected differentially with a chromelconstantan t h e r m o -couple sited in the a i r s t r e a m at entrance to the motor casing. The entry a i r t e m p e r a t u r e was measured independently with a chromel-constantan thermocouple and also with an N . P . L . calibrated t h e r m o m e t e r (range -5 to 55 C. x 0.2 C . ) . A potentiometer was used to m e a s u r e the e . m . f ' s generated by the thermocouples. Air flow m e a s u r e m e n t s were carried out a s described e a r l i e r in this r e p o r t . 9. Discussion

Much of the puboished heat t r a n s f e r data for rocket nozzles s e e m s to be confined to liquid propellant rocket engines, where there is relatively smooth a x i s y m m e t r i c flow from the combustion chamber to the nozzle. With the solid propellant engine, the geometry of the charge markedly influences the flow conditions at entry to the nozzle, with the result that a solid propellant charge having excellent burning c h a r a c t e r i s t i c s may have to have its conduit shape modified to prevent s e r i o u s erosion of the convergent face of the nozzle.

The experimental method in this report suggests a practical and relatively straightforward way of examining the effect of different conduit shapes on the mean convective heat t r a n s f e r coefficients of a nozzle. While the test r i g does not simulate combustion, it does have the advantage that the effective diameter of the conduit r e m a i n s constant throughout the t e s t , so that investigations can be c a r r i e d out at the worst flow conditions, (i. e. commencement of burning in the actual case when the velocity of the g a s e s a r e at their peak) for a s long a s is felt n e c e s s a r y .

F o r turbulent flow conditions Wimpress (Ref. 7) suggests a relationship of Nu_^ = 0.023 Re ' P r ' , (where D is the effective d i a m e t e r of the flow channel), which is the generally accepted formula for fully developed turbulent flow in pipes with length/diameter ratios > 4.0. Entry conditions to a nozzle have an

important effect on the boundary layer conditions, and in the case of the s t a r -shaped conduit used in these investigations, the r e s u l t s (Graph 1) suggest a mixture of laminar and turbulent boundary layer. The relationship obtained Nu= 0.1976 Re P r ' i s s i m i l a r to that of Winding and Cheney (Ref. 8)

for tubes in c r o s s flow.

It was found that the variation of the distance between the conduit and the nozzle entry face ( i . e . 0 - 0.75") had no significant effect on the mean heat t r a n s f e r coefficient.

The disturbed conditions at entry to the nozzle are clearly shown in F i g s . 7 - 9 obtained from the flow visualisation apparatus. The main flow out of the conduit appears to maintain its s t a r - s h a p e (Fig. 7) but the secondary flow outside of this region is a combination of two vortex systems (Fig. 9), giving strong r e v e r s e fluid flow and causing a vigorous scouring action on the nozzle surface. This action must, in the case of actual combustion, lead to high local heat t r a n s f e r coefficients and, ultimately, erosion of the nozzle. Houston (Ref. 1) found that these high local heat transfer coefficients occurred opposite the s t a r outer points, a s was expected and also between the s t a r points closer to the nozzle throat. They a r e probably caused by the turbulent interaction of the vortex p a i r s . Work c a r r i e d out by Singh (Ref. 2) using the m a s s t r a n s f e r technique for determining local heat t r a n s f e r coefficients, shows good agreement with the mean values obtained with the star-shaped conduit.

A calculation was c a r r i e d out using the dimensions of the test nozzle to determine the mean heat transfer coefficients in a laminar boundary with constant fluid p r o p e r t i e s and a constant surface t e m p e r a t u r e . The method used was that outlined by Smith and Spalding (Ref. 9). The r e s u l t s a r e shown plotted on Graph 1 and in tabular form.

10. Conclusions

The constant flow calorimetry apparatus described in this r e p o r t , together with the flow visualisation apparatus and the m a s s transfer technique, can provide valuable information on the variation of the mean and local heat transfer coefficients of nozzles due to the variation of the conduit shapes of solid propellant c h a r g e s .

Repeatability was an essential feature of this work, and the number of t e s t s c a r r i e d out with such small scatter gives considerable confidence in the r e s u l t s obtained.

It i s felt that further work should be carried out with this type of apparatus, using different conduit shapes and different nozzle profiles, as it is not possible to determine accurately these heat transfer coefficients from theoretical

References

Houston, R . M . Nozzle heat t r a n s f e r predictions from sublimation m e a s u r e m e n t s on a model of a solid fuel rocket. College of Aeronautics T h e s i s , June, 1960.

Singh, U. Nozzle heat t r a n s f e r predictions from sublimation m e a s u r e m e n t s on a model of a solid fuel rocket. College of Aeronautics T h e s i s , June, 1961.

Stone, M. W. A practical mathematical approach to grain design. J e t Propulsion, v o l . 2 8 , 1959, pp 236-244.

Flow m e a s u r e m e n t .

British Standards Institution, B.S.1042, 1943, Kaye, G , W . C . , Physical and Chemical Constants. 1948. Laby, T . H , Longmans Green & Co.

Kays, W . M . , Compact heat exchangers,

London, A , L , The National P r e s s , Palo Alto, California. W i m p r e s s , R.N. Internal ballistics of solid fuel rockets.

1950. McGraw Hill Book Co. Inc. Winding, C. C. , Mass and heat t r a n s f e r in tube banks.

Cheney, A , J . Ind. and Engg. Chem. vol.40, 1948, pp 1087-1093. Smith, A . G . , Heat t r a n s f e r in laminar boundary layer with constant Spalding, D . B . fluid p r o p e r t i e s and constant wall t e m p e r a t u r e .

Roy. Aero. Soc. v o l . 6 2 , 1958, pp 60-66.

E c k e r t , E . R . G . Die Berechnung des Warmeubergangs in den laminaren Grenzschicht u m s t r o m t e r Korper.

Z . Ver. dtsch. Ing. Forschungsheft, 4 . 6 , 1942.

Mangier, W. Zusammenhang zwischen ebenen und rotations symmetrische n Grenzschichten in kompressiblen Flussigkeiten.

Notation to Appendix 1 A nunaber defined in equation (1) B number defined in equation (1)

c c h a r a c t e r i s t i c length of body, i . e . throat d i a m e t e r of nozzle. A "heat flux t h i c k n e s s " defined by h = k/ A

h mean heat t r a n s f e r coefficient ra

h heat t r a n s f e r coefficient

k t h e r m a l conductivity of the fluid Nu Nusselt No. (hc/k) (local) Nu Nusselt No. (h c/k) (mean)

m m

V kinematic viscosity of the fluid

Re Reynolds No. (U c/v)

U approach o r r e f e r e n c e velocity, i . e . velocity at the throat of nozzle

U m a i n s t r e a m velocity at a point on the surface, i . e . velocity at X

X distance along surface of nozzle y distance n o r m a l to surface

APPENDIX 1

Theoretical Calculation of the Heat Transfer Coefficients for Laminar Flow through the Nozzle Configuration used in the Experimental Work

Numerous approximate methods a r e available to calculate heat transfer In

a laminar boundary layer with constant fluid properties and constant wall

t e m p e r a t u r e . The simplest of all the methods appears to be that of Smith and Spalding (Ref. 9) whose simple quadratures give r e s u l t s identical with those of Eckert (Ref, 10),

Therefore, the theoretical calculations using dimensions of the experimental nozzle, and the velocity profile from (Graph 5) were carried out by the method of Smith and Spalding. Their equations in a simple form a r e

:-x / c „ B-1 and

(^)J¥

(1) (2) c

the values of A and B for P r = 0,70 a r e : A = 11.68, B = 2.87.

The above mentioned equations a r e valid only for two dimensional flow. To obtain r e s u l t s for the nozzle, all the dimensions were converted to the

corresponding two dimensional units by the use of the following Mangier's transformations (Ref, 11). X X dx y = ('"/c) y

-1 h-

2 C A = C/c) A h = i^/r) h U = U

The mean heat transfe/ coefficient was obtained by :

-.dx h m fer coef

i_h.r.<

7

o r

V*^ / lUc

/(T)AI^-F--UJ

dx

The above integrations w e r e c a r r i e d out by the use of Simpson's Rule.

Values of local heat t r a n s f e r coefficients for equal intervals of x / c were obtained from (Graph 6).

The mean heat t r a n s f e r coefficient obtained using the experimental nozzle dim.ensions is : -o r Nu m

I ke = 0.395

Nu m 0.395 Re 0.5 for P r = 0.70

MEASURED SURFACE WISE

DIMENSIONS NOT SHOWN ON DIAGRAM ab • 0-8877*

bg • 0 7 6 B 7 * Id . O 4937"

0 0.05 0.10 0.15 0.20 0,25 0.30 0.35 0.40 0.45 0.50 0.55 0,60 0.625 0 0.0418 0.0845 0,1316 0.1797 0.2319 0.2916 0.3620 0.4370 0.5190 0,6116 0,7276 0,8840 1.0 0.10 0,105 0.115 0.130 0.145 0.163 0.190 0.230 0,281 0,352 0 , 4 5 0 0,590 0,825 1,0 0 0.00070 0.0015 0,00248 0,00371 0.00451 0.00566 0,00737 0,010 0,0143 0,0214 0,0333 0,0550 0,0762 0 0.00818 0.0175 0.290 0.0433 0.0527 0.0661 0.0861 0.1168 0.1670 0.250 0.390 0,642 0.890 oc 6,312 8.536 10.10 11.04 9.616 7.74 5.817 4,431 3.340 2.470 1.773 1.114 0.890 oc 0,3981 0.3423 0.3147 0.3010 0.3225 0.3594 0.4146 0.4751 0,5472 0.6361 0.7514 0.9434 1.06 oc 0,4405 0,355 0.323 0.297 0.3025 0.317 0.342 0.351 0.379 0,399 0,431 0.478 0.53 x / c I = / , (U/U)^'®"^ d ( ! ) N u / j R e he k

Iff

0 9 8 u .^ E o: UJ

I

0 9 6 0-95 6 0 \ / " * — • . 7 0 8 0 TEMPERATURE C 9 0 ' ^ U O. I 0 0 3 |Ü < I 0 0 2 ^. < UJ I y lOOI ö UJ a I oo

GRAPH. 2.

5 lO 15 2 0 25 WATER MASS FLOWRATE g r m / s e c .

A . I H R . SETTLING TIME FOR EACH POINT. B. lO MINS *' Il II II II

( N O T E h^ SHOULD BE CONSTANT, HOWEVER VARIATION IS VERY S M A L L " )

GRAPH. 3a. HEAT LEAKAGE, v WATEP MASS

FLOWRATE, NOZZLE FACE INSULATED. NO

AIRFLOW.

o ' U a 4 0 z rM *-^ u. 5 20 ' " , /^ ' • ••

y

. — . — . — o s K) 15 20 25

WATER MASS FLOWRATE. grm/sec. -«- STAR SHAPED CONDUIT

- + - CIGARETTE BURNING CHARGE. — HEAT LEAKAGE.

GRAPH, 3b. HEAT FLOWRATE v WATER MASS

FLOWRATE. FULL RANGE OF AIRFLOW.

O S 0 4 0 3 0 2

I

T

C:;

(INLET) • — NO CHARGE BEFORE N O Z Z L E .

CHARGE BEFORE NOZZLE.

+• PEAK OF STAR IN LINE WITH THERMOCOUPLES." O . — PEAK OF STAR NOT IN LINE WITH

NOZZLE CHOKED.

• ^ ^ - ^

2 3 4 5 TEMPERATURE PLANES.

(THROAT)

GRAPH. 4. VARIATION OF ^ i ^ - ï ^ ALONG

NOZZLE SURFACE.

a

I or 0 5 0 4 0 3 0 2 ( ^ I N L E T ) (THROAT^ R- P

GRAPH. 5. VARIATION O F Izl ALONG N O Z Z L E

Pt

SURFACE.

4J 0 6 O S 0 4 O 3 0 2 0 1 X / /

J

f

y

/ ^

>.-r:r:

0 5 0 - 4 O 3 O 0 2 0 4 O 6 0-8 1 0 U'/U

GRAPHS. 6.

m

^^^^^ffTT 1-. J.

II

•1:1 .

1

I * * •! , , j 1 A .

1

— r

1

^ 1

1

*fP r^ •

li 1

II

FIG. 2. RIG FOR DETERMINING THE ADIABATIC WALL T E M P E R A T U R E DISTRIBUTION

wATEW nan cónnoL V W U / E S

VWTER FLOW METER /o v,

W THERMOMETER • THERMOCOUPLE

-e2«E5_Iw„T^2,*Tw

Ta

n.

V//////I/////V/

CIRCULATING

CONDUIT / WATER PUMP

'TANK

0 0 0

o

o

^ ®

HEATERS t PUMP CONTROL BWEL

NtVtIAC

NOZZLE SURFACE THERMOCOUPLES

SWITCH T, METERINC ORIFICE

P.4h

AIR FLOW

AIR CONTROL vm.VE

TO EXHAUSTER

WATin MLtT

PASSACtVIAYS FPU HOT WATER CIRCULATION

EBONin FUW.e^

_ POWOERED AOBtSTOt LACCINC

- C O P P I R CONSTANTAN THtHMOCOUPLCt

WATER OJTLIT

COCIfR NOIILC

I

t t