AIM 89-2560 Internal Mass Addition Flow Simulation W. Xiao and W. Xinping Northwestern Polytechnical Univ. Xian, CHINA

AI AA/ASM E/SAE/ASEE 25th Joint Propulsion Conference

Monterey, CA / July 10-12, 1989

~

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AIM-89-2580

I2TEWAL MASS ADDITION FZOW SIMULATION

Tim+ Vu Xinping"

Northwestern Polytechnioal TJniversity

'Xian, F.R. China

Abstract

Tu0 dimensional, in te rna l mass addition flow

is simulated theore t ica l ly with a computer pro-

gram developed by the authors. To ver i fy the

oalculated results, a s e t of experimental r i g is

designed and tes ted.

gether with the experimental da ta , possesses a

same tendency with some exis t ing results.

Theoretical predict icn, tc-

Introduction

The phenomencnna ex is t ing i n the working

prooess of Sol id Rocket Rotors (SRM), such as osc i l l a t ion combustion, erosive burning, a r e deeply

re la ted t o the in te rna l flow of a combustion cham

b ~ .

the desigo of motors and in accurately predioting

t h e i r performances. a f i e l d has been conducted theore t ica l ly and ex-

perimentally.

Researches are ala0 important i n improving v

Row the invest igat ion on such

Generally, most of the f lowfield in a SIO! chamher is

One. A s fundamental researches, the chamber f l o w

is usually t rea ted as two-dimensional, gas-phase

and ncn-reacting one i n numerical simulations.

Such an assumption is also adopted i n present paper as Sabnis c 1 I and Salvetat L 2 I have done.

Because of the presence of high temperature, high

3D two-phase and chemioally react ing

+ Qraduate Student

*Professor, Aerospace hg inee r ing

copyright @J Amerioan Ins tx tu te of Aeronautios

and hstronautics, Inc., 1989. A l l r i p h t s reserved.

pressure burning products i n a chamber, i t is nearly impossible t o measure

chamber f l o w f ie lds . Existing experimental

s tud ies a re mainly based cn cold flow simulations.

Yamada etc . , Dunlap etc . and Traineau etc . have

designed different types of experimental rig f o r

cold f l o w simulation respectively.

of t h e i r work, an improved experimental r i g is

demonstrated i n present paper.

d i r eo t ly the SRI?

On the base

Wumerical simulation is conducted f o r 2D. so le ly injeotion-induced mass addition flow and

experimental ver i f ica t ion is performed t o check

the oalculated resu l t s .

Qoverning Equations And Numerical Algorithm

Ocverning Esuatlons and Bovmdarg Conditions

steady-state, incompressible and a x i s w e t r i o

in t e rna l flow is governed by following dimension-

l e s s Favier-Stokes equations and continuity equs-

t i cnr

where ut v are two veloci ty components i n x- and

y- d i rec t ions respectively! Re is Reynolds number

based on port diameter and referenoe velocity.

The computational domain, shown i n Fig. 1, is an

azisymmetric plene of a pipe with its radius 0.05 and i t s length 1.0 i n ncn-dimensionness. The as-

ampt ian cf uniform in jec t ion is adopted.

ca l simulation is emphasized on so le ly inJect ion

-induced flow i n a tube with one end closed.

putat icnal boundary conditions are a l so i l l u s t r a -

ted i n Fig. 1. A simplied pressure correction

method is used, with which the r e l a t ive value of pressure is dominant.

Xmeri-

Corn-

An arh i t re ry pressure

1

d i s t r ibu t ion can be presumed at the beginning of

i t e r a t i o n s and has no e f feo t on f i n a l computational

resu l t s .

MAC Grid System And F i n i t e Differen00 Equations

Points f o r primitive variables u, v, p ape

defined at d i f f e ren t positions.

sure a re located at center of each elementary

control oell; the u- and v- ve loc i t i e s a re stored

f o r mid-points of y- and x- wise l i nks connecting

g r id nodes respectively (Fig. 2a). The governing

equations a re f i n i t e l y differenced at f u l l y stag- gered con tml c e l l s (Fig. 2b).

Points f o r pres-

Incompressible '-s equations a re i n e l l i p t i c

form with convective and d i f fus ive terms. Second

-order cent ra l f i n i t e differencing scheme should

be adopted f o r d i f fus ive terms and a kind of mix-

ing differencing scheme is used f o r convective

terms with an upwind f ac to r . of the f a c t o r must he chosen t o insure the nu-

merical s t a b i l i t y and t o av0i.d excessive a r t i f i c i a l

viscosity. The f i n a l pa t te rns of f i n i t e difference

f o r the s e t of par t ia l d i f fe renc ta l equations ape

formed by in tegra t ing Fqs. ( 1 ) and (2 ) over an elementary c e l l and a s e t of nonlinear algebraic

equations are derived:

An appropriate value

asu;.j = a.u,,,i + a.u+ + a,u,.;.,

+v;.j = + a,v3,.j + a,vt.j., + a.u+, + - (P~. ,~ - PLj )/AX (4 )

+ a*vvi.jw - (Pi.,+, - Pj,) )/dY (5) where the coefficient *;are functions of oonvec-

t i v e and d i f fus ive mass f luxes across the c e l l and

must be of pos i t ive value t o insure the s t a b i l i t y

and convereence of numerical procedure.

Pressure Correction

Determination of pressure d is t r ibu t ion is

dominant i n solution of incompressible 7's equa-

t i ons and severa l Pressure-correction methods have

been developed. The e : ; s e n t i d steps o f the pres-

sure-correction method employed I 3 1 are described

as followst

A. Yractionation of pressure

p ~ p* + P'

where p i s ,?&curate pressure;

pressure value i n i t e r a t ions ;

( 4 ) p* is a s t a r t i n g

p' i s a correction

value of pressure. 5. Relation of correction

value of pressure with velocity divergency

AU b V v (7)

PI= -E( - +- + - ) ay Y

where6 is an empirioal constant within 0 - 1 and

is determined by t e s t computations.

Experimental Work

The theore t ica l prediction is ver i f ied by corn-

paring with present experimental data as well as with ex is t ing computational r e s u l t s and with Yama-

da's t 41 experimental da ta i n odder to check the

computer code.

of a chamber and a nozzle (Fie. 3 ) . case i s a cy l indr ica l porous tube with one end

closed and another end is connected with a suhmer-

ged nozzle, whose e x i t is conjucted with the draw-

ing pipe of a vacuum pump. While the pump is woking, some ai r is dram out of the ohamher

t i irowh nozzle and the chamher possesses a oertain

vacuum. sure is exhausted in to the chamber t h m w h porous

w a l l of the tube under the action of pressure d i f -

ference.

injeotion.

at x/L = 0.1, 0.3, 0.5, 0.7, L is the leneth o f

cy l indr ica l tube and x is the distance aww;\y from

the head end.

The experimental device cons is t s

The chamber

Enviimnmental air at atomcspheric pres-

Thus the flow is so le ly induced by air

Four measuring s t a t ions a re d is t r ibu ted

Five-Aperture probe is used t o measure the

flowfield.

produced by probe rod and increasing the measuring

accuracy and sens i t i v i ty of the probe head, a prohe

i s employed with a 3mm diameter rod and a Sphere -shaped head.

For the sake of reducing disturbance

Pesul t s And niscussion

7eyno lds number i n aotual chamber flow is Tho experimental mea- about at the l eve l of 10'

surement i s performed at ne = 0.24 X 10"

computational simulation is f o r f l o w at Re = 0.2X

ICfConparisons between numerical r e s u l t s and

experimental data :.ZQ ,iven helcw.

and

Fit'. 4 shows t i e p ro f i l e s o f dimensionless

ax ia l velocity a t di f fe ren t cross-section f o r com-

putational and experimental r e s u l t s respectively.

As can been seen f r o m Pig. 4, t ha t f l o w s i n a mass

2

addition tube a re accelerated along axial direc-

t ion , ve loc i t i e s being l a rge r at downstream than

those a t upstream; and t h e i r p ro f i l e s becoming

more ‘ f u l l - toward downstream. The veloci ty pro-

f i l e s f o r both computational and experimental

r e s u l t s possess same tendency, especial ly at up-

stream. The reason for t h i s is tha t , as the flow

speeds up t o w a r d the aft end of t he port and loca l

Reynolds numberbecomeslarger and la rger , which

r e s u l t s i n the diminition of the e f f ec t of w a l l

f r i c t i o n on the flow out of the sublayer and tends

t o be uniform veloci ty pmf i l e s . For the prof i le

at x/L = 0.7 i n Pig. 4, it can he seen tha t there

e x i s t s a s l i g h t l y l a rge r difference between ,calcu-

l a t ed rsrult, and experimental data. The l a t e r

d i s t r ibu t ion appears decreasing tendency i n the

a rea near r/R = 0.7. blocked i n the v i c in i ty of submerged p a r t s of a nozzle, i ts s t a t i o pressure goes up and i t s speed

slows down. This reglbn i s , loc&ed near the l i p ,

of nozzle i n l e t ssotion. Plow veloci ty enhances

w a i n within the i n l e t area with the decrease of

r/R .

-v

This is because the flow is

Fig. 5 and Fig. 6 show the simulated u- and - v- veloci ty prof i les and .experimental d a t a at

x/L = 0.5 seen f r o m Fig. 5 t ha t theore t ica l resu l t s have a

same tendency with experimental da ta end with

those of Sabnis, Culick[ 53 and Yamada, but mani-

fest t o be ‘thinner’ than the l a t e r s . The reason

f o r t h i s might be tha t the assumption of laminar

f l o w is adopted. Fig. 6 gives out the good agree-

ment between present r e s u l t s and those o f Salvetat

and 2ul ick i n v- veloci t ies .

and the results of others’. It can be

Conclusion And Future Work

Two-dimentional, so le ly injection-induced flow

is numenioally simulated by a computer code deve-

loped by the authors. An improved experimental r i g

is designed and tes ted which i s avai lable i n ex-

perimental invest igat ion i n SXM chamber flowfields.

Theoretical prediction, t 0 , p t t e r with experimental

da t a show t h a t for a injection-induced f lowfield,

flows speed up t o w a r d down strean: and beoome more

‘ f u l l ’ ; submerged par t of a nozzle con af fec t the

f lowfield of its v ic in i ty area obviously. ~~ -.”’

To simulate f f i tual flow i n a SRl! chamber, a

30 turbulent computer code should Be developed

which can deal with the s i tua t ions of f lowfield

with complicated geometrical boundaries.

pr i l iminary experiment+ invest igat ion, an tou-

ched-means of measuring device i s used, but en op t i ca l measuring device, such as L’D, is expected

t o be adopted t o improving the accuracy o f experi-

mental data.

A s a

Acknowledgement

The authors a re gra te fu l for Yr. L i So and

N r . Cui Xianbin f o r t h e i r help i n experimental

work.

References

1. Sahnis, J.S. etc., Aw-85-1625. 2. s a lve t a t , R., ~ ~ , - 8 4 - 1 3 7 5 .

3 . Wang LichenE, Chen Xixiu, Journal of Aerodyna- mics, Vol. 5, NO. 1, 1987.

4. Yamada, K. e t c , AIM-75-1201. 5. Culick, P.E.C., AIM J., Vol. 4, No. 8, 1966.

Fig. 1 , Computational plane and boundary

oonditions

Fig. 2 Computational gr id system

3

Fig. 3 Wer imenta l device f o r mass

addition f low

Fig. 4 Development of u- velocity

along x- direct ion

Y v

J - " 0 .a .4 . 6 .8 1.0 -IJ

Fig. 5 Comparison of u- veloci ty prof i les

A