C.P. No. 893

MINISTRY OF AVIATION

AERONAUTICAL RESEARCH COUNCIL

CURRENT PAPERS

The Performance of Conical Convergent-Divergent Nozzles of Area

Ratio 2.44 and 2.14 in External How BY

G. T. Goleswtxhy

J. 6. Roberts and C. Ovew

LONDON. HER MAJESTY’S STATIONERY OFFiCE

1966

. SIX SHILLINGS NET

U.D.C. NC. 62%225.1:533.691.18

C.P. Nc.a93* 0

The performance of conical convergent-divergent nozzles of area ratios 2.44 and 2.14 in external flow

- by -

G. T. Gcleswcrthy, J. B. Roberts and C. Overy

Two model internal-expanslcn propelling nozzles wrth conical diver-

gence of IO0 semi-angle, area ratios 2.44 and 2.14 (design pressure ratios

15 and 12), parallel afterbodies and thin annular bases, have been tested

in external flow ever the range of Mach NC. 0.7 to 2.25. Measurements

have been made of nozzle base pressure, and thrust effxiencles derived

with reference to both ambient and base pressure levels.

It is found that, in supersonic external flow, with complete expan-

sion of nozzle internal flow to ambient pressure, the value of base pres-

sure ratio 1s independent of nozzle design pressure ratio, provided the

bas?e thickness is unchanged. For a given overall operating pressure

ratio, again with constant base thickness, the effect of decreasing nozzle

design pressure ratio 1s to raise base pressure ratio. In subsonx

external flow, for a given overall operating pressure ratio, base pres-

sure ratlo can be Independent of nozzle design pressure ratio.

- --_-__ . . . . . . . . . . .,“A-.-ll-l.---. -_-

*Rcplc~os N.G.T.E. M-372 - iLR.C.26 494

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CONTFNTS

110 Introduction

2.0 Test equipment

3.0 Instrumentztlon and air suppIles

4.0 Model oper2tlng conditions

5.0 Model performance

::: Base pressure Internal pressures

5.3 Thrust effxclency

6.0 Conoluslon

Acknowledgement

References

Detachable abstract cards

A? PENDIX

Title

Symbols and deflnltlons

M

4

4

4

5

5

: 7

7

7

8

9

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ILLUSTRATIONS

Fig. No.

1

2

3

4

5

6

7

a

9

10

11

12

13

14

15

16

17

Title

Model propelling nozzle test rig

Model propelling nozzle - D.P.R.12

Interns1 arrangement of model nozzle

Bese pressure ratio - D.P.R.15

Base prossure ratlo - D.P.R.12

Base prsssure coefflclent - D.P.R.15

Beoe prcssure cocfficlent - D.P.R.12

Effect of D.P.R. on base pressure ratio - I '

Effect of D.P.R. on bese pressure retlo - II

Internal pressure dxatrlbutlon - D.P.R.15

Internal pressure distribution - D.P.R.12

External thrust efficxncy - D.P.R.15

External thrust efficiency - D.?.R.12

Intern&l thrust efflclency - D.P.R.15

Internal thrust efflclency - D.P.R.12

Base drag term - D.D.R.15

Base drag term - D.P.R.12

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1 .o Introduotlon

In Reference 1 are described tests of an axrsymmetric model internal-expansion propelling nozzle with area ratio 2.9 (design pressure rat10 20). The present work is concerned with two similar models with design pressure ratios of 12 and 15. These also have been tested in externtil flow over the range of l&h No. 0.7 to 2.25.

2.0 Test equipment

A description of the external flow rig usod for these tests v:ili be found in Reference 1. Figure 1 illustrates the rig layout. It had two alternative working sections: a transonic giving external Xach numbers from 0.7 to 1.5, and a supersonic covering the range between 1.5 and 2.4. Test models were carried on a long parallel hollow sting, which could be arranged to pass through the throat of either external flow nozzle.

The two models, shown in Figures 2 and 3, utilised the same conical inlet and outlet sections as the model of Reference 1, new throat sections being fitted. Throat diameters were 2.180 and 2.327 in., giving ratios of plane outlet area/geometric throat area equal to 2.440 and 2.145 res- pectively. Approach and divergent semi-angles were IO', and the radius of curvature of the throat transition was made equal to the throat radius in either case. As with the previous model, the afterbody continued parallel up to the outlet plane, forming an annular base 0.050 in. wide.

3.0 Instrumentation and air supplies

Ho thrust measuring equipment was fitted in this test rig, and model interns1 gross thrust was derived from:-

(1) Knowledge of discharge coefficrent (C,). This was taken to be 0.991 when choked, as for the model of Reference 1 with geometrically similar throat f.

(ii) Calculated stream thrust at the throat plane.

(iii) Measurement of pressures along the divergent portion of the nozzle.

(iv) Measurement of base pressure.

(VI Computed allowance for friction.

The expression for gross thrust efficiency* was derived in Reference 2:-

Ae/Ag

-5-

taking y = 1.4,

where CI = veouum stream thrust effrcxncy at the throat, taken to be 1.003 when choked as m Referencss 1 and 4 for srmiler throat geometry.

In accordance wrth the argument presented in Reference 2, no correctron for “real air” effects has been applied.

Pressure instrumentatron on the models accordingly consisted of:-

(i) A rake of 7 pitot tubes 1 mm o.d. et entry, spaced on an equal- area basis.

(ii) Nine or eight statrc t’appmgs spirally posItroned down the divergent section, each 0.020 in. drameter.

(iii) Two tapprngs spaced 90' apart rn the base annulus.

(iv) Two statlo tauprngs on the external surface.

External flow lines were frtted with wall pressure tappings, and these were consrdered to be more relrable m assessment of external Maoh number than the model afterbody tappings.

Arr supply temperature to both model and both the working sections wre maintained wrthin the range 25 to 35’C at all times, and no further attentron was paid to temperature measurement. Air dryness was measured by an R,A.E.-Bedford pattern frost-point hygrometer, and held at better than -2O’C throughout.

Supply pressure was at a level of 5 atmospheres, and throttled independently as requrrcd for model and external flow lines.

4.0 Node1 oporotrng condltrons

The following values of external Each number were chosonz-

(1) Supersonic line: bl,= 1.5, 1.75, 2.0, 2.25

(ii) Transonic line: Mm= 0.7, 0.9, 1.1, 1.3, 1.5

At each Mach number the model was tosted over a representative band of exhaust pressure ratlo (E.P.R.) between the limrts 2 and 20.

5.0 Model performance

5.1 Base oressure

As explarncd m Reference 1, the outer boundary layer at the end of the afterbody In these tests was somewhat thicker than would be repre- sentative of a typlcel flrght installntron. For this reason, base pressures m practrce would tend to be rnthor lower than those measured here.

-6-

Two ways of presenting the base pressure information have been

used. 'b Figures 4 and 5 give the ratio p =

E.P.R. +

a3 i -l A.P.R. ' urhlle Figures 6

and 7 show the base pressure coefficient, in both cases as functions of

E.P.R. and &.,a PO It will be observed that the value of p, drops fairly

sharply at oonditions of ion S.P.R. snd low !&,, implying a quite large change in A.P.R. for a small variation in E.P.R. This same type of pattern was noted in Reference 1. In the present models (especially

% that with D.P.R.12)fth~s fall in p is more limited in extent than was 00

the case v,ith D.P.R.20, and with f'urtner increase of E.P.R. (above 4) the base pressure ratio now rises again quite steeply. The higher Mach number curves lie close together in a band rising with E.P.R.

7hen completely expanded to ambient pressure (E.P.R. = D.P.R.) in 'b

supersonic external flow, both models give similar values of --* PLC

The

additional evidence of Reference 1 suggests that for this condition, and with constant base thickness, the base pressure ratio is independent of D.P.R., the appropriate values for all three models lying in the band 0.62 to 0.68 according to external Mach number. This implies that all pressures within the base flow system can remain similar, although the nozzle outlet Vach nurrber is changing. Such a conclusion is in line with theoretical work on backward-facing steps (e.g. Reference 5), which Indicates that, provldlng all other quantltres are maintained constalit, variation of approach stream L!acn number within similar limits has little effect on base pressure.

Information from References 1 and 3 has been inoorporated in Figures 8 and 5, illustrating the behaviour of a number of conical convergent-divergent nozzles with the same divergence angle >+hen immersed in subsonic and supersonic external flow. All models had parallel after-bodies of the same outside diameter, and variation of D.P.R. was achieved in tno ways: in Reference 1 and the present work, by varying throat diameter and keeping base thickness fixed; in Reference 3 by fixing the throat diameter and varying base thickness.

Base pressure ratio ~1 subsonx external flow 1s apparently unaf- fected by all geometric variables, as shown in Figure 8, so long as the

'b E.P.R. 1s below the critical value at which p turns sharply downwards

00 ( see Figures 4 and 5). In supersonic external flow (Figure 9) two effects can be distinguished for any fixed E.P.R. First, as D.P.R. is reduced with constant base thickness, the outlet flow becomes increas-

% ingly under-expanded, and - rises. PC0

Secondly, for constant internal

expansion (or D.P.R.), increase of base thickness lowers the value of 'b F- M

-7-

Apparently, for the tests reported in Reference 3, these opposing effects have more or less cancelled out, and the results show very little influ- ence 0f D.P.R.-

5.2 Internal pressures

Typical pressure distributions are shown in Figures 10 and 11 for each model over a range of A.P.R. These were obtained in the transonic working section, where model entry conditions were such that a turbulent internal boundary layor would be expected. The separation pressure pat- terns correspond to this state. In the supersonic working section, very few instances of internal separation were encountered during these tests.

5.3' Thus t efficiency

Figures 12 and 13 give the nozzle thrust efficiency based on E.P.R. for each model, according to the rslation in Section 3.0. Con- stant values of the friction correction term have been applied to each nozzle, namely 0.60 and 0.55 per cent for D.P.R.15 and 12 respectively. These values were obtained from the curves presented in Reference 4, taking the design-point operating conditions.

The same allowance for friction was made in the case of effi- ciency based on A.P.R., shown in Figures 14 and 15. Design-point effi- ciency levels came out as 0.995 and 0.9945 for D.P.R.15 and 12 respec- tively. It is thought thnt these values are about 0.5 per cent too high, and accuracy better than this would not be claimed for pressure plotting methods.

Finally, in Figures 16 and 17 is ~howm tho quantity 011, represent- ing the deduction from nF(RpR) which is required to include the drag force on the annular base, according to the method of Reference 1.

6.0 Conclusion

The present work has extended that of Reference 1 to cover a family of three conical convergent-divergent model propelling nozzles with similar internal form, the same base thickness, and design pree- 8ure ratios of 20, 15 and 12.

When completely expanded to ambient pressure in supersonic external flow, all three nozzles produce similar values of base pressure

pb rat10 - , ( ) PO0 in the band 0.62 to 0.68 according to external Mach number.

Also with supersonio extornal flow, but at constant exhaust pressure

( pt‘;

rat1o PO4 the value of base pressure ratlo for these nozzles rises with

decrease in deoign pressure ratio, that is as the outlet flow becomes increasingly under-expanded. In subsonic external flow with repre- sentative exhaust pressure ratios, the base pressure ratio is effec- tively independent of nozzle design prossure ratio.

ACKNOWLSDGEPXRT

The authors are Indebted to UIiss Irl. Faiers and Xiss V. Searle for their assistance in this programme of tests.

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&. Author(s)

1 G. T. Golesworthy Al. V. Herbert

2 R. J. Herd G. T. Golesworthy

3 J. B. Roberts G. T. Golesworthy

4 M. V. Herbert D. L. Martlew

5 J. F. Nash

Title. etc.

The performance of a conical convergent-divergent nozzle with area ratio 2.9 in external flow. A.R.C. C.P. ~0.891 November, 1963

The performance of e centrebody propelling nozzle with a parallel shroud in external flow - Pert I. A.R.C. C.P. No.841 November, 1963

iin experimental investigation of the influence of base bleed on the base drag of v&riors propelling nozzle configurations. A.R.C. C.P. ~0.892 Februaqj, 1964

The design-point performance of model internal-expansion propelling nozzles with area. ratios up to 4. t.R.C. R. & M.3477 December, 1963

yin analysis of two-dimensional turbulent base flow, including the effect of the approachzag boundary layer. a.R.C. R. Re M.3344 July, 1962

A’

A f3

A,

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APPENDIX

Symbols and definitions

isentroprc throat area

geometric throat area

geometric plane outlet area

CD

Tt model entry total temperature

v isentropic velocity

"F

dischnrgc cocfflclent = actual am mass flow A*

lsfntroplc azr mass flow for the same throat arse

=q

free-stream Mach number

model entry tote1 prosoure

model base pressure

model internal wall pressure

free-streem static prossure

pressure rat.10 (see A.P.R. and R.D.R.)

model throat Reynolds number (based on throat dicmeter and sonx condrtrons)

measured gauge thrust at grvsn pressure ratio R

gross thrust offiorency gauge thrust of an isentropic nozzle, passing the same flow, at the same pressure ratlo R, and fully expanded

P vacuum stream thrust effxioncy at the throat

friction corroctlon term

A.P.R. applied pressure ratlo =

E.P.R.

D.P.R.

exhaust pressure ratlo =

design pressure ratio

model entry tots1 pressure Pt =- model base pressure Pll

model ontry total prossure Pt free-stream stat10 pressure = r;-,

D 76923/l/125875 Klc IO/66 II & TXL

FIGJ

MODEL PROPELLING NOZZLE TEST RIG.

FIG. 2

‘_

.

. . I ,‘

\.

INLEi PIT&T RAKE CONNECTING TUB&

IN STING PASSAGE

STATIC TAPPINGS

BASE TAPPING IN DIVERGENT WALL

MODEL PROPELLING NOZZLE

SnlnNNV

NOIlVlN3Wl~lSNI

(3NlddVl M3d 3NO) SnlnNNV NOl1VlN3b’4nntllSNI 01 f)NlddVl

31~~15 wotlj 38ni SE)NlddVl 3llVlS lVNt131X3 \

I ,,OIS E

1

I-- ,050 0

I I AQM39VSSVd 3NllS 01

SN01133NNO~ 3QfU

‘-1

38nL 3N US cm0

3NVtl lOlId 131NI

3enl

L)NIlS ti3NNI

NO11335 1311nO NOl133S LVOtlt-tl NO11335 13lNI

FIG.4

-

-

-

-

-

-

-

-

m

”

m

Q

c-4

BASE PRESSURE RATIO- D.P. R. IS

0-b

‘b - P..

0.4

0.2

0

‘75 LINETESTS

2 4 6 8 IO I2 14 lb I8 20

EXHAUST PRESSURE RATIO 5

40

-FIG.6

e 0 0

9 .8

L 0

n8= ’ 8 k.n 0

w

I n

i -a- 0

BASE PRESSURE COEFFICIENT- D.PR. 15

FIG.7

- a p: Y

--I-

BASE PRESSURE COEFFICIENT-D.l? R.12

FIG.8

REF ILPRSENT TESTS

IO I2 14 16 I0 20

DESIGN PRESSURE RATIO

EFFECT OF D.F? R. ON BASE PRESSURE RATIO-1

FIG. 9

I.0

% - P..

06

04

02

A REF 3

0 REF I& PRESENT TESTS

VARYING BASE THICKNESS b ,-L-m ----a-

E P RIIS

E.P R.12

IO 12 14 16 18 20

DESIGN PRESSURE RATIO

0 REF IL PRESENT TESTS

IO I2 I4 I6 18 20

DESIGN PRESSURE RATIO

‘b - PO.

) E.PR.20

) E P R-16

04

07

EFFECT OF D.l?R. ON BASE PRESSURE RATIO-n:

;; w 0 ; 0 0

3tMlSS3t4d lt’lO1 3tUlSS3tld 311VlS 1lVM I

FIG. IO

INTERNAL PRESSURE DISTRIBUTION- D.PR. IS

FIG. II

? 0 0” 0” 0

0

3dfISS3tJd lVlO1 I

3UIFEZWd 311VlS 7lVM

INTERNAL PRESSURE DISTRIBUTION-D.P R. I2

-h-m-

:

m-h -4

-I- I 0.9c 4----

3 ,

F(E.P.R)

..a . 085

NOZZLE RUNS FULL

FILLED SYMBOLS DENOTE SUPERSONIC

LINE TESTS

/

2 ” 4 6 8 IO 12 14 16 I.9 20 22 y:”

EXHAUST PRESSURE RATIO 5 PIW I

FILLED SYMBOLS DENOTE SUPERSONIC

LINE TESTS

.w 0.70 1

.? 2 4 8 IO I2 14 Pt

I6 18 20

;3 EXHAUST PRESSURE RATIO

P a0 G

NOZZLE RUNS FULL

k

; 0.7 0.9 A I.1

V I.25 A I 5 0 I *75

n 2.0

D 2.2 5

k

; 0.7 0.9 A I.1

V I.25 , A I 5 0 I *75

n 2.0

D 2.2 5 -I-

FI G.14

‘x\. - X’

\ X

>1

INTERNAL THRUST EFFICIENCY - D. P. R.15

FIG.15

i --

INTERNAL THRUST EFFICIENCY - D.P.R.12

FIG.16

_-----

BASE DRAG TERM - D.RR.15

0.02

x o-7 y 0’9

A I.1 FILLED

v l-25 SYMBOLS A 1.5 DENOTE

0 I - 75 SUPERSONIC LINE TWS

0 2’0

2.25

b 8 IO I2 EXHAUST PRESSURE RATIO pt

I4 lb IS 20

PO¶

A.R.C. C.P. N&S93 February, 1964 GOl~~O~, G. T.. Roberts, J. B. and Wery, C.

621-225.1: 533.691;le

THE PERF’XWXE OF CONICAL CONVF.RGENT-DIVERGENT NOZZLES OF AREA RATIOS 2& and 2.14 IN EXTERNAL FLOW

T”0 model inteti-erpanslo” propelli% nozzles With Conical diver gence of 10’ semi-wle, area ratios 2.i,4 and 2.14 (design pressure ratios 15 & 12), parallel alterbodles and thin a”“Uular bases, have bee” tested 1” external rlow over the range or Uach No. 0.7 to 2.25. lleasurements have been made Or ~~zle b&% p2p~QIIp. and theta eIflCle~les derlveh Mth ~reIWEe t0 both &lent ti base PXWY levels.

It IS round that, in 811per~0nlc external rm, ~ith cgnp1et.e expansion or nozzle interra rm to anblent pressure, the utile 0r bae plY.%XUY rat10 19 ltiW+&“t Or Mzzle design p=ssUre ratio, pmvided the base thlck”ess 1s unchanged. For a Rlre” overall operating pressure ratio.

P.T.O.

A.R.C. C.P. No.893 February, 1964

621-225.1: 533.691.18

Colesworthy, 0. T.. Roberts. J. B. ski Overy. C.

TNE PUWXWANCE OF CONICAL CONVERGKHT+IVERG NOZZLES OF AREA RATIOS 2.4J+ and 2.14 IN EITSFWL FLOW

TAO model internal-expanslo” propelling nozzles with conical direr geme of loo semi-angle, area ratios 2.44 and 2.14 (design pressure ratios 15 ati 12). parallel arterbodles ard thin a”“Uar bases. have bee” tested 1” external rlow over the range or Mach NO. 0.7 to 2.25. ?leasureme”ts have been made Or nozzle base p=‘eSSUre, and thIust errICle~1es derived with rvrerence to both ambient and base pressure levels.

P.T.O.

A.R.C. C.P. No.893 Februarg, 1964 GolesworChy. 0. T., Roberts, J. B. and Overg, C.

THE PSRFUMANCE OF CONICAL WNVERGE~-DIVERL%X~’ NOZZLES OF AREA RATIOS 2.44 and 2.14 IN EXTERNAL FLOW

Tao mcdel Internal-expansion pmpelllng nozzles with conka dlep gerce of 10’ semi-angle, area ratios 2.44 and 2.14 (design pressure ratios 15 and 12). pxallel arterbodles and thl” anrmlar bases. have bee” tested I” exte- rm over the range or Hach No. 0.7 to 2.25. neasurements hare been made or nozzle base PreSsuIp, arxi thrust err~~~encies derired with rererence to both ambient and base pressure levels.

It IS round that, in supersonic enemi rim, with cmiete expa”slo” or nozzle inter”al ri0w to Brmbient presatre. the value or base pressure ratlo Is independent or nozzle design pr-asure ratlo. provided the base thickness IS unchanged. For a Blve” uverall opwatlng pressure ratlo.

P.T.O.

/ i

C.P. No. 893

0 Crown copyrrght 1966

Prmted and pubbshed by

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C.P. No. 893

SO. Code No 23-9016-93