Computation of 3D Viscous Annular Cascade Flows_1988_AVCO

7/28/2019 Computation of 3D Viscous Annular Cascade Flows_1988_AVCO

1/10

I IM-88-3092I Computation of 3D Viscous Annular Cascade FlowsD. Choi and C. J . KnightAVCO RESEARCH LABORATORY, INC.a Subsidiaryof Textron Inc.2385 Revere Beach ParkwayEverett, MA~

A IAAIASMEISAEIASEE 24th JOINTPROPULSION CONFEREWEJ ULY 11-13, 1988/Boston, MassachusettsFo r permission to copy or re ublish, contact the American Institute of Aemnautlcs and Astronaut ics370 L'P lant Promenade, S.W., Washinpton, D.C. 20024


2/10

,

COMPUTATION OF 30 V I S C O US ANNULAR CASCADE FLOWS0. Choi* and C.J . K night**

A V C O Research Laboratory, Inc.a Subs id iary o f Textron Inc.2385 Revere Beach ParkwayEveret t , MA 02149

AbstractA visc ous cascade code has been developed fo r30 annular cascades. This code solves the "thi n-lay er" Navier-Stokes equations w it h a two-equationturbu lence model i n cur v i l in ea r coord inates us inga time asymptotic method for steady state solu-t i ons . It employs s ca lar i mp l i c i t approximatefac tor iz at io n i n time and a f i n i te volume formula -t i o n w i th second order upwind d i f fe ren cing i nspace. Two turb ule nc e model equations are in te -grated to the wa l l w i thout us ing a wa l l func t iontreatmen t. This code has been val ida ted by con-s id er ing exper imenta l s tud ies o n vane cascadegeometries .

I n t roduct i onfl ow phenomena i n advanced gas tu rb in e enginesare qui te complex, gene ral ly inv olv ing shocks aswell as complex 30 v o r t i c a l f l ow i n a h i g h l ytur bu le nt environment. C urrent design methodolo-gie s do no t have adequate means t o pr ed ic t second-ary f low loss, e x i t angle d i s t r i bu t i on , and 30sur face heat t rans fer e f fects . Each o f these i sstrongly inf luenced by various types of v o r t i cesar is in g i n cascade passages (horseshoe, t i p.

e t c . ) . The need to improve pr ed ic tive techniqueshas motivated purs u i t o f a mul t iyear e f fo r t a t ourorgan iza t ion to deve lop 30 viscous codes fo rsteady trans onic cascade f lows. This i s based onasymptotic t ime in teg rat io n us ing sca ldr im pl ic i tfac tor i z at io n to ach ieve computationa l e f f i c ie nc yand good vectorizationE ar l ie r work addressed a lgor i thm opt imizat ionand phys ical model ing issues i n the co ntext ofl inear cascades(1 e 2 ) inc lud ing deta i led compari -son t o experiment. Robust. ef fi c ie nt means ofimplementing two-equation turbule nce mode ling wasdef ined w i th sub layer res o lut io n down to y+ - 1 .This has shown promise i n pre di cti ng laminar-turbu le nt boundary layer t ra ns i t io n , ( l ) a keycons iderat ion i n turbomachinery. E xcel lent per-formance of t he re s u l ti n g HCAS30 code was achievedon c ur vi l i ne ar sheared H-gr ids w ith a second orderupwind di f fe re nc ing formulat ion. Convergence i n600-800 timesteps was achieved using the h ig hl yre f i ned g r i ds requ i red f o r accura te i n teg ra t i on to

the wa l l . F u l l y imp l i c i t tr eatment o f boundarycond i ti ons and dua l t imes tep se lec t i on c r i t e r i awere key fac tors i n th a t accompl ishment.

code development ef fo rt : annular turbi ne i n l e tThis paper covers on e aspect o f th e cont inu ing

guide vanes wit h adiaba tic wal ls . using shearedH-gr ids s tacked i n the rad ia l d i re ct io n . We havenot yet addressed heat t rans fer i n annu lar cas -cades, though th i s has been done fo r l i ne a rcascades wi th good re su lts .( 2)mixed topology 0-H g r id fo rmula tion and on r a d i a land axial compressor rotors, w i l l be reportedseparate ly i n the near fu ture .organized as fo l lows.F i r s t the means o f e xtendin g the HCAS30 formu-la t ion to annu lar cascades w i l l be sumnarized,employing f u l l 30 metr ics as requ i red fo r genera la i r f o i l geometr ies an4 contoured endwal ls . C arte-si an ve lo c ity components a re r etai ne d as dependentvar iab les to s imp l i f y code convers ion and mainta in

st rong cons ervation law form. Th i s requ i res ca te -f u l s e l e c t i o n of the ve loc i ty t rans format ionmatr ix under ly ing the sca lar impl ic i t scheme, sotha t pe r io d i c i ty can be s t ra igh t forward ly imposedi n the pitchwis e di re ct i on . The new annular cas-cade code i s known as ANCAS30.

Other work. o n a

The paper i s

A cen t ra l cons ide ra ti on f o r a 30 viscous codei s i t s run c os t. We u ti l i z e a mini-supercomputer,t he A l l i a n t FX/E with four computing elements and80 MBytes of high speed memory. A b r i e f i n tr o du c -t i o n i s given t o techniques used t o take advantageof i t s concurrency and vector iz at ion features . A tthe current le ve l o f optimiz at ion, the code takes3 ~ 1 0 . ~PU sec per t imestep per gr id po in t . Thati s comparable t o performance on the I B M 3090. Thecos t of a rep res entat ive annular cascade case i saround $1000 on ou r machine, a very nominal fi gu ref o r a 30 v iscous s imulat ion o f a complex transonicf l o w f i e l d .The code has been applied t o 30 viscous f lowsof a subsonic annul ar cascade of tur bi ne vanesstu die d experime ntally hy Goldman e t a1.(3) and at ranson ic annu lar turb ine s tator s tud ied exper i -men tall y by Gardner e t on the Energy E f f i -c ie nt Engine geometry. Comparisons wi th ex pe ri -ment i l lu s tr a te the accuracy of the code and i t spo ten t i a l u se as a v ia ble aerodynamic design to o l .

Governins EauationsThe conservation law form of the compressible

30 Navier-Stokes equations wi th con tinu ity andenergy equations can be wr i t ten i n C artes ian coor-d inates as the vector re la t ions h ip-; + - + - + - = oF aG aHax ay a z

where ( i n transposed form)"P r incip al Research S ci en t is t , Member A l A ADi re cto r. E ngine Technology. Member A I A A*-Copyright 1988 by the American I ns t i t u te o fAeronautics and As tronautics, Inc . A l l RightsReserved.


3/10

aF aG a Hau + J (- +- -) = 0a t a6 an ag

Only a per fec t gas i s considered. i n which casethe s ta t ic pressure and to ta l energy per un i tvolume are

The adiabatic index, 1 . i s assumed t o be co nstant.

components a re most simply defined i n C artes iantensor notat ion . L inear fo rms fo r an i s o t rop icmedium w i l l be employed--

The shear stress tensor and heat f lux vector

au. au. auT..= " ( -1 t - 3 ) e k -k 6 . .i j a x . a x . axk 1~3 1aTq. = I( -1 ax i

( 4 1

where ( X I . x2. x3) = (x ,y.z) . etc. , II and L a rethe two coe f f i c ie nts o f v isc os i ty . and c i s th ethermal cond uc tiv ity . Since an eddy v is co s ityformu latio n has been adopted, these re la tio nsapply to turbu lent f low as well wi th su i tab lein te rp re ta t i on o f ", A. and I( _with laminar v iscos i ty g iven by Suther land 's lawand eddy viscosity by a Kolmogorov relationship.It i s assumed th at the second co ef f i c ie nt o fv i s cos i t y , A = -U i n ou r p resen t code t o a l l ows i mpl i f i ca t ion of the v iscous terms. D i la tat io nef fec ts have minor s ig n i f i ca nce f o r transon icf low. A lso . x = IIL/Pr + ,T/PrT where con-s ta nt P ra nd tl numbers ar e assumed: P r - 0.72 and

Thus. )r = vL + "T

P r T = 0.9.Since the hub and shroud are surfaces ofrevolut ion and the f low must be periodic upstream

and downstream of the a i r f o i l s i n a typ i ca l tur -bi ne cascade geometry. the go verning equations ar etransformed t o boundary-conforming g ene raliz ed co-ordinates. This i s cu rre ntly based on a shearedH-gr id . w i th ca re fu l con t ro l o f t r ansve rse g r i dsmoothness and s pe c if ic at io n of th e nonnal d i s -ta nc e o f th e f i r s t c e l l c e n te r o f f w a l l s . Bytransforming only the independent var iables(x.y.2) t o the computational coordinates ( ~ , ~ , c ) ,the strong conservation law form can be main-ta ined --

whereF = ( C X F t 6 G + CzH) /JYG = ( n x F + n G t nZH)/JY

W( 5 )

fo r a time-independent gr id , where trans formatio nmetric coefficients can be computed by

and the transformation J acobian, J. i s th e d e t e r-minant of Eq. ( 6 ) . No te th a t momentum equ atio nsare w r i t te n i n C artes ian ve loc i ty components .Viscous terms i n Ea. 1 5 ) are incoroorated v ia aspec ial form of the thi n la yer approximation, asnoted i n Ref. 1 .C oakley's q w turbulence model was selectedla rge l y due to i t s numeri ca l compat ib i l i t w i thasymptotic t ime integ rat i on procedures.(5r A sreported i n Ref, 2, the heat t rans fer ca lc u la t ioni n a 30 l in ea r cascade case w i th th is turbu lencemodel has been ve ry enc ourag ing. The dependentv a r iab les a re d i r ec t l y re l a ted to the tu rbu len tk i ne t ic energy, k. and d iss ipat ion ra te , C . v iaq = fi and o = c / k ; they def ine a turbu le ntvel oc ity sc ale and inverse t ime scale, respec-

v i s c o s i t ynear-wall damping function.t i v e l y . In terms of these variables, the eddy v= pC,Qq2/o where C = 0.09 and Q i s a

Q = 1 - exp (-epqd / y ) ( 7 )n Lwhere o = 0.0065 and dn i s def ined us ing aBuleev length scale i n terms of the normal dis-tance t o the nearest a i r f o i l and endwall sur faces

The conse rva t ion l aw f o rm o f the q model i nCartes ian tensor notat ion i s as fo l lows:a a,(Pa +- (Puiq) =axi

where we d e f i n e d = ( u i , j + uj,j)ui; and flo wdi la ta t i o n has been dropped i n both the turbu lencesource terms and the s t ra in ra te invar iant ( d ) sneg l i g i b l e f o r tr ansoni c f low. a f te r p re l imina rystudy. Turbulenc e co nstan ts used ar e th e same as v

2


4/10

i n th e o r ig i na l p u b l i ~ a t i o n : ( ~ )0.4050. Cz = 0.92. P rq = 1, and Pr = 1.3 whereC, and 0 are defined above.on D i s be l i ev ed t o be one reason tha t q w can bemade re la t iv e l y ins ens i t ive to t imestep se lec-., tio n. These re la tio ns assume the same basic formas Eq. (6) i n curv i l in ea r coord inates . w i th addedsource terms. The s tra in rate inv ar ia nt i s s i m -pl i f ied through the th in layer approx imat ion ,using normal derivat ives.I n o rder to keep the ca pab i l i ty t o emulate thelaminar t o turbul enc e t ra ns it io n phenomenon whichus ual ly occurs on gas- turbine engine blades, theseq-u turbulence equations are integrated to thewa l l , without using any form of wa l l fun ct ion,with res olu t ion down t o about yt = 1. However.much more in ve s tig ati on should be done before t h i sturbulenc e model can be used as a re li a b le to o lfo r pre d ic t ing t ra ns i t io n phenomena accurate ly .

C \ = 0.045 +Making C1 dependent

Numerical MethodA sca la r imp l i c i t app roximate f a c to r i z a t i onalg ori thm has been used in the code with a c e l l -based formulat ion.( l ) To maintain high perform-ance character i s t i cs o f the im pl ic i t method,bounda ry cond i t i ons a re t rea ted fu l l y imp l i c i t l y .This i s es se ntia l to achieve a ra te of convergencei n f in e g r i d v iscous reg ions comparable t o tha t o fthe inv is c i d core reg ions . Im pl ic i t boundarytreatment i s part icu lar ly important w i th two-equation turbulence modeling when very fine gridspacing i s requ i red near the nons l ip wa l l .For the exp l ic i t procedure (eva luat ion o fresiduals), second order upwinding i s used with ace l l -based fo rmulat ion. The d is s i pat io n funct ionfo r t hi s scheme i s evaluated based on nonconserva-t i ve var iab les and cha rac ter i s t i c increments g ivenby Roe-averaging(6) a t c e l l faces. Fo r the im-p l i c i t procedure. f i r s t order upwinding (s olv i ng aser ies o f sca l ar t r id iagona l l in ea r systems) i s

used. T his may a ff e c t convergence r a te somewhat.but the computat ional cos t per t imestep i s r e-l ieved . When accu rate steady s tate so luti on s arethe only concern. th is im pl ic i t procedure can bemore e f f i c i en t , i n te rms o f CPU time, than asecond-order upwinding im pl ic i t procedure. Morede ta il s of the numerical method were repo rted i no ur e a r l i e r p a p e r . (l )

-

Boundarv TreatmentS tagna tion temperature, entropy. and fl owangle are s peci f ie d a t in f low. and the hub s t a t i cp ressu re i s f i x ed a t ou tf low . Rad ia l v a r i a t i on o fthe pressure a t the out f low p lane i s der ived f romthe s imple rad ia l equ i l ib r ium equat ion . withs ta ti c pres sure on the hub chosen t o match experi-mental condit ions, and other var iab les are extrap-o la ted f rom the in ter io r .I n o rder t o mainta in good conse rvation withthe a lgor ithm, the gr id i s const ructed to havec e l l faces which l i e on so l id sur faces and a longthe p er io di c bo undaries upstream and downstream ofthe vane cascade. F or s ol id boundaries on thea i r fo i l surfaces and endwall s . nons l ip cond i t ionsfo r vel oc iti es (u=v=wlO). zero normal pressurede riv at i ve (dp/dn=O). and an adia batic c ond it ionare imposed.v

Since the Cartes ian ve loc i t ies are used asdependent variables, the following orthonormal.t rans format ion i s in t roduced t o apply correctperiodic boundary condit ion.

where q v a r i e s i n the c i r cumfe ren t i a l p i t chw ised i re c t i on and vn i s a ve lo c it y component normalt o sur face of constant 1. v t and vs areve lo c ity components normal t o vn which are al soor thogona l to each other . Th is set o f ve l oc i t ieswith density and pressure are periodic from onep i t c h to the nex t. It i s n ote d t h a t t h i s o r th o -normal transformation i s a l so used i n the ex p l i c i tprocedure t o get proper damping func tion . and i nthe imp l i c i t procedure to decouple the eauat ions .Optimization on Supercomputer

Very high ef fi c ie nc y of th e code has beenobta ined by care fu l ly s t ructur ing the code on amini-supercomputer A l l ia nt F X / 8 with four comput-in g elements i n our Lab. T his computer system haspar a l l e l i sm cap abi l i ty , w i th hardware-supportedconcurrency on multiple computing elements andv e c t o r i z a t i o n i n each computing element. As i swell-known, it i s s t ra i g ht fo r wa r d t o u t i l i z e c on-currency and vector izat ion fo r the exp l ic i t proce-dure because residual evaluations can be donewithout any data dependencies.s t r u c t u r i n g i s requ i red f o r the imp l i c i t p rocedurewhere banded Gaussian eliminations. requiring re-cu rsi ve processes, are involved. There are threedo-loops i n each o f the three approximate factor i -z atio n sweeps i n a three-dimens ional problem. Oneof these three do-loops i s a recurs ive procedure.Thus, we app ly the con currency on the outermostdo- loop and vecto r i ra t ion i n innermost loop whi lekeep ing the recurs ive do- loop i n the midd le . Th isk ind o f st ru ctur i ng can a lso be app l ied to o thermult i-proces sor computers. This opt imized vers ionof the code takes about 3.0~10-4 second CP U timeper each t ime step and g r i d po int. which i s compa-rab le t o the re su l ts on today s la rge-sca le super -computers.(7)it procedure takes only about 30 percent of theto ta l computing time.

More careful

it i s a lso noted that the impl ic -

R esults and DiscussionsTWO se ts o f te s t cases were computed to assessperformance o f the ANCAS3D code. One i s f o r a

NASA subsonic ann ular vane stu die d experi mentallyby G o ld mn e t a 1 . wEnergy E ff ic ie n t Engine (3) annular vane withan S-shaped t i p- s i de endwal l . (4)The o the r i s f o r the NASA

3


5/10

Subsonic Vane CaseANCAS3D has been appl ie d t o th e subsonics tato r cascade s tudied expe rimental ly a t NASALewis. The deta il ed cascade geometry and eXP eri-mental configuration can be found i n Ref. 3. Theuntwisted vanes, of constant pr o f i le f rom hub tot i p , had a height of 38.10 mn and an axial chordof 38.23 mn. The stacking axis of the vane waslocated at the center o f the t ra i l ing- edge

c i r c l e .the mean radius based on axial chord were 1.0 and0.93. re spe ct ive ly . The s tator hub-t ip rad iusra t i o was 0.85 and the t i p diameter was 508 mn.The vane aspect ra t i o and the s o l i d i ty a t

A to ta l number of 171,696 co mputational g ri dpo in ts a re used (NX=73. NY=42, and NR=56; the y a renumbers o f g r i d po ints i n the ax ia l , c i rcumfer -en t i a l , and rad ia l d i rec t i ons , r e spect i v e l y . )F i gu re 1 shows th e 73x42 H -g ri d system f o r ablade -to- blade plane and the 73x56 gr id s ystem fo ra meridional plane f o r the NASA turbin e s tator .Ax ia l gr id d is t r ibu t ion s are chosen to g ive enoughgr id po ints t o proper ly descr ibe the shape o f theb lunt lead ing and t ra i l i n g edges .f i r s t gr id spac ing i s 4 . 1 ~ 1 0 -the maximum grid spacing i s about 5 percent ofc i r cumfe ren t i a l p i t ch . In the r -d i rect io n . drmini s 3 . 8~1 0 - 3mn and drmax i s 1.9 mn. Convergedresults were achieved with 800 timesteps even withth is h igh ly re f ined gr id fo r good v iscous sub layerreso lu t i on .

dymin for themn and dymax fo r

The s ta t ic pressure pro f i le s on the b ladesurfa ces ar e shown i n F igu re 2 for three spanwiselocat ions . A s shown i n these fig ure s, computa-t ional results compare very wel l with correspond-in g measurements. S ince pressure var ia tio ns onthe blade surfaces are mainly inviscid phenomena,these results show that the code can handleinv i s c id e f f ec t s accu ra te l y . F u l l viscous effectso f the f lows can be found i n the loss pred i ct ionand the f low ang le var ia t ion at ex i t p lane.The to ta l pressure lo ss pre d ict ions a t about29 pe rcen t of the chord le ngth downstream from thetr a i l i n g edge are shown i n F igu re 3wi th theexperimental data measured a t 33 perce nt chorddownstream. These ar e averaged based on mass fluxa long the c i r cumfe ren t i a l d i r e c t i on a t a g i venrad i a l l o ca t i on . Th i s t o ta l p ressure loss pred ic-t i o n agrees very we l l wi th the experiment excepta t about 10 perc ent of the span near the hub,which i s one of passage vortex centers. Thecomputational results behave somewhat similarly.bu t not as c le a rl y as the measurements.The vane e ff i ci en cy contours based on kin e t icenergy are compared i n F igure 4.passage vortex lo cat ions ar e we l l pred icte d by the

q w turbulence model. F i gu re 5 shows the flowang le v a r i a t i o n ve rsus the rad ia l d i rec t i on a ta f tenn ixed f low cond i t ions . def ined a t each rad i a ll o ca t i on bdirec tion.!8*9) The agreement wi th the experimenti s w ith in the accuracy of the measurement, 1 .2 . .

Note that the

averaging a long the c i rcumferen t ia l

Transonic NASA 3 Vane CaseThe case considered involves transonic f lowthrough a vane i n a s ingle- stage wi th 0.35

re ac tion . The de tai le d cascade geometry andexperimental co ndit ions can be found i n Ref. 4The Reynolds number based on e x i t fre e s treamcond i t ion and vane a x ia l chord length i s about1.3~106and des ign e x i t f l ow ang le i s ID.4O.corresponding t o f low turn in g o f some 80".

NY=42. and NR=42) ar e used f o r th i s case. T his i sa much coa rse r gr id compared t o the 131x66~30 ri dused i n an e ar l i e r s tudy( l ) fo r a ha l f span o f theE3 l inear cascade. I n fact , on a fu l l span bas is ,the to t a l number o f gr id po ints i s only about 25percent o f the E3 l inear cascade computation.Numerical accuracy i s degraded i n consequence.pa r t i c u l a r l y f o r s tagna ti on p ressure l o s s . A p r i -mary cons iderat ion i n th i s cho ice was unce rta intyabout in f lo w boundary cond it ion i n the experiment,which le d us t o emphasize assessment r ath er thanf u l l code va l idat ion a t th i s time. F igure 6 showsthe 73x42 H-gr id system fo r a blade-to-blade planeand the 13x42 grid system for a meridional planewi th a contoured t ip- s i de w al l . Eased on ax ia lcho rd- len gth, minimum and maximum spa cing s a re2 . 1 ~ 1 0 . ~nd 0.105 i n the Y -direc t ion. and theyare 1 .7~10-4 and 0 .085 i n the ra d ia l d i rec t ion ,respect i v e l y .

UA t o ta l number of 128,112 g r i d poi nts (NX=13.

The s ta t i c p ressu re p ro f i l e s on the vanesurfa ce, shown i n F igure 1for three spanwiselocations, compare well with the measurements.F i gu re 8 compares computed e x i t f l ow a ngle t o th eexperiment. Unfor tunate ly . the in f lo w ve l oc i typ r o f i l e was no t measured fo r the experiment. Forthe computation, a guessed in l e t ve lo c i ty pro f i lewas used: 15 percent span on the hub endwall and7.5 perc ent on the t i p endwall. based on estimatedi n F igure 8 i s b e li ev ed t o a r i s e i n l a rg e p a r tfrom not matching the unknown i n l e t co ndit io ns .Th i s p roblem i s a l so ev iden t i n the e x i t Machnumber p r o f i l e shown i n Figure 9. where the hubendwal l boundary laye r thickness i s apparentlyunderp redic ted. One reason fo r the caveat i s t h a tit i s s urpr is ing t o us tha t the endwall boundaryl a y er i s so th i ck a f te r r ap id acce le ra t i on th roughthe vane passage, ra is in g questions about theexper iment i tse l f .

Computed to ta l pressure loss contours areshown i n Fig.ire 10. These co ntour s can not bed ir e c t l y compared to the experimental data giveni n Ref . 4 because geometrica l sca l in g factors fo rthe experimental loss contours were not given i nthe repo rt ; t he l a t te r p l o t s a re obv ious l y no t t ot rue sca le . F igure 11 shows pitchwise area-averaged to ta l pressure loss pr o f i l e ve rsus ther a d i a l d i r e c ti o n .

boundary la ye r development lengths . Discrepancy W

ConclusionA new computer code f o r a nnu lar cascadegeometry, ANCAS3D. has been developed and eva luated by comparing computed results with theexperimen tal re s ul ts . As shown i n e f f i c i e n c ycontours a t the vane ex i t p lane, v iscous e f fe cthas been very wel l incorpo rated wi th C oakley'stwo-equation turbulence mdel . Accuracy andcomputat ional e f f i ci en cy of the code show i t spo ten tia l use as a v iabl e aerodynamic des ign too l . v


6/10

C urren tly, expansion of th is code to ro tat ingframe has been finished and the neu code i s beingappl ied to r oto r cases success ful ly .w i l l be reported i n the near future. This work

_I AcknowledqmentThi s rese arch was conducted under spons orshipof the Te xtron Lycoming's R esearch and DevelopmentProgram.

Cycoming management for f inancial support andpermission to present these res ults .The authors wish t o thank the Textron.

References1. Knight. C.J., and Choi. 0.. "Development of a

Vlscous Cascade Code Based on Sca la r lmp l l c i tF dr tor i zat on, 'I AIAA-87-2150, A IAA / S AE / AS WE /ASE 23r4 J oin t P ropulsion Conference. Jun.1987. San Oiego. C A.2. Choi. 0.. and K night. C.J . "Computation of 30

26th AeMSpdCe S cience Meeting, J an. 1988,Reno, NV.

Measurements i n an Annular C ascade i f CareTurbine Vanes and Comparison with Theory,"NASA Technical Paper 2018, 1982.

Engine. High-pressure Turbine Uncooled R igTechnology Report," NASA CA-165149 Oct . 1979.5. Coakley: T.J., "Turbulence Modeling Methodsfo r the C ompressible Navier-Stokes E quations,"AIAA-83-1693, 76 th F lu id and Plasmadynamics

~. Conference, July 1983.

Viscous Cascade Flows." AtAA-88-0363, A I A A

3 . Goldman. L .J . . e t al . . "Laser Anemometer

4. Gardner. W.0 . . e t a i . . "Energy E f f i c i ent

6. Roe. P.L., "Approximate Riemann S olve rs,P arameter Vec tors, and Di ffe re nc e Schemes,'J ournal of Computational Physics, Vol. 43.7. Taylor. T . D . , "F itti ng the Computer t o the8. Goldman. L.J., e t a l . . "Cold-Air Annular-

1981, Pp . 357-312.

Job ," Aerospace America. Apr. 1988, pp. 34-36Cascade Investigation o f AerodynamicP e r t o mn c e of Cooled Turbine Vanes." NASA TWX-3006. March 1974.Cascade Investigation of Aerodynamic P erform-ance of Core-Engine Cooled Turbine Vanes,"NASA TM X-3224, A pr il 1974.

9. Goldman. L . J . , e t a i . . "Cold-Air Annular-

S


7/10

73 X 42 gr idon a blade-to-blade plane

73 X 56 gr idon a mer id ional p lane

1 WF i g . 1 C o m p u t a t i o n a l G r i d f o r t h e NASA Su b s o n i c V an e

m m. a 1 1

Fig. 2 P r es s u r e D i s t r i b u t i o n s on A i r f o i l S u r fa c es f o r t h e NASA Subsonic Vane

6


8/10

'" Io EXPERIMENT 1

- 1 0 3 . 2 3 d,k> d.GS d 8 0(R - RH)ISPAN" 3 7 1 1

F i g . 3 Mass-Averaged T o t a l P r e s s u r e LossD i s t r i b u t i o n f o r t h e N A S A Subsonic Vane

, ~ , / . , , , ~ , , ' , , , , ,3.23 d . V D J .GO d . i oiff - RH)ISPAN

F i g . 5 A f t e r - M i x e d f x i t Flow A ng le U i s t r i -b u t i o n f o r t h e N A S A Subsonic Vane

COMPUTAllON,,,s

F i g . 4 E f f t c i e n c y Co n to ur s f o r t h e N A S A Subson i c Vane

7


9/10

73 X 42 gridon a blade-to-blade plane

73 X 42 gridon a mer idional plane

F i g . b Computational G r i d f o r t he N A S A E 3 VaneW

A T 11 62% OF SPAN FROM HUB

,D

\4\\67

AT 5 0%

c

0

D

D

d

\T 85.969.

\a\

F i g . 1 P r e s s u r e Distributions on A i r f o i l S u rf a ce s f o r t h e N A S A E 3 Vane

8

v


10/10

, :r----o EXIFRIMEKT

- c , 3:,, , , , , , : c 5 . j :(R - RH)/SPANI - "_ _.,

N1771

F i g . 8 Area -Ave raged E x i t F l o w A n g l eO i s t r i b u t i o n f o r t h e N A S A f 3 Vane

0 EXPERIMENT

0

0.20 0.40 0.60 0.80(R - RH)/SPAN

F i g . 9 Area-Averaged E x l t Mach NumberDistribution f o r the NASA E 3 Vane

COMPUTATION

EXPERIMENTF i g . 10 T o t a l P r e s s u r e L o s s C on t o ur s f o r t h e

N A S A E3 Vane

F i g . 1 1 A r e a- A v er a g ed T o t a l P r e s s u r e L o s sO i r t r l b u t i o n f o r N A S A E3 Vane9

Computation of 3D Viscous Annular Cascade Flows_1988_AVCO

Documents

Transcript of Computation of 3D Viscous Annular Cascade Flows_1988_AVCO