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I ConJerence onCoqmtingC $&ms andAm&, ZCCCSA-2012

Unsteady Collnpu~~&onf Over-Exp&iadpdFlo

Abstracts

a Convergent Divergent Nozzleh h u l B.V', Swapnesl R#, Thanusha IW.T';and ~ . ~ . ~ h a n ~

Pm pn ko n Division, Natianal Aerospace LaboratoriesJ Bangalore(COUNCILOF %X lWW I C AND INDUSTREALmEAW&NDIA)',"' Student Member, ~e mn au ti& ,& ieb of India, 13B, IndmprasthaEstate, New D e b

Scientist, ropulsion Divisio~, &@~I Aerospace h r a t o r I e s , BeIw?Bmgalo-56Qo.37.res.in, Phone: +9 1-80-25051605,Frtx: 4-91-80-25222494

The classical one-dimensional inviscid theory does notreveal the complex flow features in an over-expanded nozzleaccurately. The code Fluent has been used to simulate thetransient flow passing through a 2-D Convergent-Divergent (CD)nozzle (AJAt=l.7, %=3.03', Symmetric about centerline) fornozzle pressure ratios (NPR) corresponding to overexpandedflow. The transient RANS equation with Shear Stress Transportk -o (SSTKW) turbulence model has been simulated. Bothinviscid and viscous flows have been simulated. Both the firstorder and second order upwind scheme has been used for 1111 theconsewation equations. The invisdd solutions predicted steadyresults for both first and second order simulations after a certaintime. There is no significant unsteadiness in the first orderviscous solutions too. Shock structure is also symmetric in thefirst order viscous predictions for all NPRs. However, secondorder viscous predictions captured unsteadiness, lambda shock,aftershock and flow separation @Sf3and RSS) depending uponNPRs. The lambda shock becomes asymmetric after a certaintime for NPRtl.41. The flow unsteadiness is significant withasymmetric lambda shock. The shock oscillates with theasymmetry. The number of aftershock increases and the size ofMach stem reduces with increase in NPR The computedsolutions di ier from the simple theory as far as shock location,shock structure, normal shock strength and aftershocks areconcerned. However, the 2'* order viscous predicted results(shock structure, shock location, size of normal shock,aftershock, and asymmetric lambda shocks) are close to theexperiments in most of the cases.NomenclatureA =Nozzle areaM = Local Mach numberP, Po= Static, Total pressureT, To= Static, Total temperatureV= Velocitya = Half nozzle wall angleCp = Specific heat at constant pressureAx, At= grid size, Time step respectively

t, e, s = throat, exit, shock respectively

AcronymNPR =Nozzle Pressure Ratio (PA)FSS = Free Shock SeparationRSS = Restricted Shock Separation

1. INTRODUCTIONThe one-dimensional inviscid isentropic flow in a CDnozzle is a classical text-book problem, which has differentflow regimes depending upon NPR. The inviscid theorypredicts a simple shock structure consisting of a normalshock followed by a smooth recovery to exit pressure in thedivergence part of a choked nozzle for NPRs corresponding tothe over-expanded flow regime. But, in reality, multi-dimensionality and viscous effects like wall boundary layerand flow separation drastically alter the flow in a CD nozzle.Stable separation (with a passive porous cavity) could improvethe thrust efficiency of off-design Nozzle [I]. Viscous effectsthicken the boundary layer before the shock and the base ofthe shock also becomes thick or bifurcate the shock in theform of lambda shape depending upon the nature andthickness of boundary layer [2].So, the shock contains normal

bifurcate as lambda shock. The first leg of the la(known as incident shock) turns he flow away fiwhile the second leg (knownback the flow to the original direction. The coMach stem, incident shock and reflected shocktriple point. At higher NPR,

the reflected shock is still supersonic.the slip stream and shear layer behinincreasing for a short distance, hence,a certain distance with expansion wave. Thethe flow becomes subsonic behind the Mach

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Ma& R& College ofEn-P and Technolorn

stream known as a h h o c k to match the ambient(NPM),he separation is not the

Two different patterns of flow separation may occur innozzle (Free shock separation and Restrictedseparation). In free shock separation (FSS), the flowfiom the wall and separationcontinues till the exit ofnozzle. However, in restricted shock separation(RSS), theflow reattaches to the wall and becomes supersonicthe downstream of the reattachment point [8-111. The peakof wall static pressure is associated with reattachment of[12].(Two different vorhcal regions have been found during

tion from wall, whereas the second vortex spreads in the

The CFL criterion for stability should be 5 . The CFLis given by ,nS-ri.;V x At 1 )

1drr -

tions because of their wide range of applications. The61. Jnvestigation 1161 contains detailed

rstanding the complex flow structure in a CD nozzle.2.COMPUTATIONAL ETAILS

The computational domain for the CD nozzle has beenhas been used to generate geometry and grid

in the CD nozzle (Ae/At=1.7, ac=3.030,etric about centerline) for different NPRs. Both first and

e second order inviscid simulations have been made afterwith k t wber schemes. Rowever,simulated with second order upwind

schemes twice (1. initialized with inlet conditions, 2.initialized with first order converged solutions). Boundarylayer grid has been generated to capture the boundary layereffect. Based on the previous experience, SSTKW turbulencemodel has been chosen for the simulation. The inlet boundaryconditions consisted of total pressure, ~~=3.5x10 ' / m ~ndtotal temperature, To=300K. The exit static pressure wasvaried to obtain different NPRs (NPR=1.20, 1.25, 1.32, 1.41,1.65, 1.92, 2.03 and 2.36). For stability of the unsteadysimulation, the time step At has been taken as 2.0 e-06 basedon the CFL criterion. The grid size for the flow domain is 143x 41. h1.?!li RqL3. RESULTS AND DISCUSSION I-' 'b3h'r ~ 1 ' T L j d .MUnsteadiness has not been found in the invlscidpredictions for all NPRs. In addition, the predicted invisciusolutions are close to 1-D inviscid theory in regard of shocklocation and shock structure(one n m a l shock followed bysmooth recovery of pressure) for lower NPRs. For higherNPRs, the theoreticalarea ratio (MAt) t the shock location ishigher than the exit area ratio (i.e. Shock location is outsidethe Nozzle). But, inviscid solutionpredicted shock at the exititself for higher NPRs to match static pressure specified at theoutlet boundary condition. The locationsof shock for inviscidpredictions are compared with the theoreticalvalues inTablel. The second order predictions are better than the fMorder as shown in Tablel. iG-yv~l

The flow becomes steady after a certain time(approximately 4-5111s) in case of viscous prediction with 1storder upwind discretization.The 1 order viscous solution isdifferent fiom the inviscid solutions in regard of shockstructure and shock location. Symmetric lambda shock nearthe wall, Mach stem in the central region and flow separationdownstream of the shock have been observed for NPR21.32 inIS' order viscous predictions; However, the 2nd order upwinddiscretized solutions looked to be transient in nature even after1Oms for NPR21A1. The converged solutions predictedlambda shock near the wall, Mach stem in the central region,flow separation and after shock in the divergent part of thenozzle. The lambda shock is symmetric for lower NPRs.However, it becomes asymmetric for NPR21Al. Boundarylayer shock interaction converts the normal shock into twooblique shocks (incident and reflected shock) in boundarylayer region. The flow compresses through the incident shockand turn the flow away from the wall. Because of the turningof flow towards the center, the flow separates and the effectivearea of the flow reduces fiom the geometric area. Thereflected shock tries to turn the flow towards original flowdirection. The flow behind the reflected shock is stillsupersonic for a small region just above the shear layer. Thewhole flow behind the lambda shock is divided into tworegion separated by slip stream as shown in Fig. 1schematically. The sonic line disappears after short distancefrom the main shock which indicates that the slip line becomessupersonic. This supersonic flow again experiences a shock

depending upon the exit pressure. This shock is known asaB.eSb& The sepmated Bow is .leaWhed WS) or lowexNPRs. However, it becomes FSS at the larger leg of the

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Intendona1 C o ~ ~nComptuag,Chmmmdw- ' ns,&tem andAeromdim, KCCEA-2012lambda shock for NPR21.92. The l d m of elxock iss i g n i f i d y different from the inviscid themy Bhmer, "theviscous predictions are dose to the experimental,values asshown in Table 2. The l*order sdutbm wmldw a p twe heaftershock as hown inFig. 2 (Mach number plat at the Machstem for different N P b - 1 order predktion).,However, the 2& order solutions predicted one -hock forNPR=1.41, two aftershocks for NPR=1.65 a d t k eeaftershocks fm NPR=1.92 as shorn in Fig. 3 m a & numberplot at Mach stern for different MBs - 2" order upwindprediction). The number of ~ b r o c k sncreaseswith inweasein NPR. Atleast one aftershock forNPR21.41 and atleast twoaftershocks for NPR11.92 have been observed in theexperimentstoo.The 2nd rder solutions also predicted lambdashock for NFR21.25. The shock structure is symmetric for thewhole s*mulation time (2Oms) for NPRS1.32. However, itconverts to an ~ e ~ cambrfa shock 1i.e. w e side (e.g.top wall) of the tan& shock is larger than the otlm side (e.g.bottom wall)] aft& a cerfain t h e (5-15111s) for higher WRs(NPR21.41). It is very dificult to jmtify the asymmetry inlambda shock in a simuiation where geometry and boundaryconditions are symWr ic and uniform respectiveiy. But itcould be coanda effect. The experimmtal results also indicate-edF;--wm-lambda shoek f~ NPRTl.4I. Rg. 4 &ows predicted Machnumber concontoursf then o d e atm e di?Eeraimes(4rnsmdl!12ms) for NPR=1.92. It clearly shorn the conveision of.symmetric lambda shock ta i w p m e ~ cambda shock after a?'certain t h e . This t h e reduces with inaease in htPR The::pattern s f asymmetry bas been f w d to be dXaen t iq&%rent MPL.Larger kg of the lambda shockmay be either:side (i.e. topd r r r t tom waQ But the aspmetry does not,,flip within a sim-n. Ttreladxh shook has bee11 f ~ u n dobe after the conversim to aspmetry. The cize ofMach stem reduces with herease iu PJPR. The ocation ofs&ocIt- .m towards upstream with viscops prediction. Thezndorder s e 1 yW f d m shifts it upstream for NPR1!1.32.LAlso5mS .shock location b s been f ~ m do shift bwwds~qs..j+pm ith the amyersiq. tka asymmetric lambea shock.&Rg. 5 a& Pig. 6 shoy theplots d aJl shear ~ ~ e s snd wall,,pressureof t h . e ~ a t t b e ~e s ( 4msand 12nls),sshown .inF& 4 fos NPR=l.92, re@e&ivied,y. Fig. 5 clearlyindicates thesgmi5cant reductiw in wall &ear s t e s with tbs h o e k ~ h i o f a e a s e h a h e w a J 1 s h e r l r ~ ~ h b d t h eshock at boa the d s . n apdition,wall shear stresson bothd s Ohdde &3Ch ather hW O ~fm k k b Q a&pck (F,g>5+J. It &q, indbbzs the nega&ire vake.of wallrffheaqaesshroughout bebh.4 the s&k@ c i + e , p f . m

#go& (Fig-. 4 . Tbh is the m, $S a t hoth the5 ~ .PW~W, e t r i cambda d w k dmxgw the wallsh&e& W b u t i o ~ ig+ b),. 3% wall s h tress is ao, . b emw psit iye behind dm& &a-a.pectain diskme in thed w a .Elais@dkata&he of thesepm-flow& the .tog yd l . ?%.k3 k &+St3 +f ' 5 s# he Wall.- y q ~ v e r , l b o Vm4, hwe % ~ h kn@hleg shews ~eg i t i ve~va lw-wallghem ptwm behind

pressul;eisnotmin~identri both thewallsshock separated wall (bottomwall) hows s

20ms. It.clearly shows thl: s k k atterns @ymmetric

-,A . Flowwteadiness:

any signihcanf u n s e e - s s in fheu~zsteadyih m m e in cases where~ ~ e t r i i end pressure atrd'botfom wall dbnot wkcide.I

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Mla Reddv College ofEn&teering and Techmlonv13. Nasuti F. and Onotii M., " Viscous and Inviscid vortex generationduring startup of Rocket Nozzles", AIAA Joumal36(5), 809-815,199814. K. C. Muck, Jean-Paul Dussauge and S. M. Bogdonoff, "Structure of theWall Pressure Fluctuatiom in a Shock-Induced Separated TurbulentFlow", Paper AIAA 1985-0179, 198515. W. J. Baars, C. E. Tinney, J. H. Ruf, A. M. Brown and D.M. McDaniels,

" On the Unsteadiness associated with Shock-Induced Separation inOver-expanded Rocket Nozzles", 46th AIAA/ASME/SAUASEE JointPropulsion Conference and Exhibit, 2 010-672 8,201016. Zill A, "Flow separation in rectangular over-expanded supersonicnozzles", Paper AIAA 2006-17,2006

ISBN :978-81-921580-8-2