Study of transonic separated flows with zonal-des based on weakly non-linear turbulence model

Transcription

1 Study of transonc separated flows wth zonal-des based on weakly non-lnear turbulence model Xao Z.X, Fu S., Chen H.X, Zhang Y.F and Huang J.B. Department of Engneerng Mechancs, Tsnghua Unversty, Bejng, PRC Symposum on hybrd RANS/LES methods Stockholm, Sweden July 4-5, 25

2 Table of content Introducton Weakly nonlnear turbulence model and zonal-des method Numercal methods Results and dscusson Concluson July 4-5, 25 Hybrd Symposum, Stockholm 2

3 Introducton and objectve 3-D separaton flow loss of lft, ncrease n drag and amplfcaton of unsteady fluctuatons n pressure flow-feld; 2-D separaton flows are domnated by adverse pressure gradent, flow reversal etc.; 3-D separaton flows can be senstve to the confguraton, angle of attack, Reynolds number, and so on Our man purposes Investgatng the performance of weekly non-lnear RANS models and valdate our code for separated flows wth nterference between components of the arcraft; Constructng RANS/LES hybrd method and nvestgate the advantage; Comparng the performance of orgnal DES and zonal-des methods. July 4-5, 25 Hybrd Symposum, Stockholm 3

4 Development of RANS/LES methods The most attractve features of RANS/LES methods Combnng the best advantage of RANS wth that of LES Predctng the unsteady, geometry-dependent separated flows n a LES mode and the small scale moton usng a standard turbulence model (the best choce s the low-re one) near the wall for hgh Reynolds flows wth boundary layer; Many knds of hybrd RANS/LES methods Detached Eddy Smulaton on S-A model (Spalart, et al, 997); Hybrd stress tensor (Spezale, 998); DES on Menter s Shear-Stress Transport model (Strelets, 2); Hybrd on k-ω and a one-equaton SGS-model (Davdson, 2); Zonal hybrd wth blendng functon (Baurle et al., 23); Zonal-DES on M-SST model (Menter, 23); DES (especally on S-A) s one of the most wdely used hybrd methods. July 4-5, 25 Hybrd Symposum, Stockholm 4

5 Choce of turbulence models To construct the hybrd RANS/LES methods ratonally, we generally hope that the RANS turbulence model can be ntegrated to the wall (no need of wall-dumpng functon and low-re number correcton). S-A model K-ω famly models Wlcox k-ω model Menter s k-ω shear-stress transport (M-SST) K-ω model wth weakly nonlnear eddy-vscosty formulaton named as WD+ model It was found that weakly nonlnear eddy-vscosty formulatons mprove the performance of turbulence models for flows n the presence of adverse pressure gradents, partcularly n shockwave/boundary- layer nteractons July 4-5, 25 Hybrd Symposum, Stockholm 5

6 Wlcox/WD+/M-SST models Wlcox s k-ω model WD + model ncludng 3-D effect where ρ k k * + ρ uk j ( µ + σ kµ t) = τ jsj β ρkω t x j x j ρω ω 2 + ρujω ( µ + σ ωµ t) = Pω βρω t x j x j S% S S S 2 2 = 2 j j 3 kk M-SST model ρk k * + ρ uk j ( µ + σ kµ t) = τ jsj β ρkω t x j x j ρω ω ρσ ( ) 2 ω k ω + ρu 2 ( ) 2 jω µ + σ ωµ t = Pω βρω + F t x j x j ω xj xj S j s the local stran rate µ µ µ tw, t,wd+ ρk = ω ρk = mn ; ω ρk ρa k 2 2 ( Ω + S% ) ρa k t,m-sst = mn ; ω ΩF2 /2 July 4-5, 25 Hybrd Symposum, Stockholm 6

7 DES method on WD+ model Reynolds-stress tensor: In the Smagornsky closure: τ = uu ' ' j j = 2 S and = C 2S S S = C S % C s s a constant and s the grd scale τ ν ν j Sma j Sma s j j 3 kk s To construct DES-type methods based on two-equaton models, a length scale L t s ntroduced for the dsspatve terms n the turbulence knetc energy equaton. ( ρk ) k * + ρ uk j ( µ + σ kµ t) = Pk β ρkωfdes t x j x j /2 ( FSST ) Lt k FDES = max ; L t = * F CDES β ω SST can be taken as, F and F 2. When the turbulence producton s balanced wth the dsspatve term P =ρν S = D =ρk 3/2 / L, k t j k t * L = C, k = β ( C ) 2 S, t DES DES j t 3 ( β ) 2 ( DES ) ν = C S% S% 2 /2 /2 * 2 July 4-5, 25 Hybrd Symposum, Stockholm 7

8 Roe scheme 3-D compressble solver usng Flux-Dfference-Splttngtype Roe scheme (MUSCL and van Albada lmter) wth Radspel-Swanson entropy fx ncludng the hgh rato of vscous grds near the wall n a cell-centered fntevolume formulaton; L R R L F = FI ( q ) + FI ( q ) A% nv ( q q ) For λ,2,3 For λ 4,5 symmetrc flux λ n λ n λ numercal dsspaton when % δ n n = 2 2 λ + % δ n β + ( β ) δ n n 2δ λ λ < % % when = λ n λ 2 n + δ% 2δ% 2 when when λ λ n λ n δ% < δ% j ω k % δ = δσ max σ, σ + σ σ ω β max max σ, σ =, κ j k σ σ July 4-5, 25 Hybrd Symposum, Stockholm 8

9 LU-SGS-τTS method A modfed mplct Lower-Upper Symmetrc-Gauss- Sedel method wth pseudo tme sub-teraton tme steppng s appled to acheve a hgher accuracy n tme ; ( ) (L+ D)D (D+ U) Q = 3Q 4 Q + Q /2 tr m m n n m, j, k, j, k, j, k, j, k L α( ) = A +, j, k B +, j, k C + + +, j, k A, j, k B, j, k C + +, j, k+ U α( ) = + + D [.5 α χσ σ σ ) 2αθ] = + ( I A B C The computng practces show that the rate of convergence wth the pseudo tme level s very fast, and only a few sub-teratons are needed. July 4-5, 25 Hybrd Symposum, Stockholm 9

10 Others methods The equatons of turbulence model are decoupled wth the mean equatons usng Lower-Upper Symmetrc- Gauss-Sedel method mplct tme steppng; Unform tme steppng s appled to capture the unsteady propertes n the separaton flow; Implct resdual smoothng s employed to accelerate the convergence; For the wng/fuselage model, the parallel mplementaton s done usng the Message-Passng-Interface model; Ghost cells method s appled to deal wth all knds of boundary condtons. July 4-5, 25 Hybrd Symposum, Stockholm

11 Consdered flows ONERA-M6 wng shock-wave/boundary-layer nteracton flow NASA TN D-72 wng-fuselage model wng/body nterference transonc flow July 4-5, 25 Hybrd Symposum, Stockholm

12 M6-wng: grds and surface flow M =.8447, α=5.6, Re=.7 6 The man features nteractons of shock-wave/boundary-layer the separaton nduced by the strong shock July 4-5, 25 Hybrd Symposum, Stockholm 2

13 M6-wng: coeffcents and hstory x/2b= 2% x/2b= 44% x/2b= 65% Cl SST WD x/c.6.8 x/2b= 8%.2.4 x/c x/c.6.8 x/2b= 9%.2.4 x/c x/c.6.8 x/2b= 96% Exp SST Roe wth R-S WD+.2.4 x/c.6.8 Iteraton Iteraton July 4-5, 25 Hybrd Symposum, Stockholm 3 Max&Mean Resduals

14 Grds around TN D-72 July 4-5, 25 Hybrd Symposum, Stockholm 4

15 RANS s results wth dfferent grds HPR -.5 2z/B= 6% -.5 2z/B=25% -.5 2z/B= 4% -.5 2z/B= 6% -.5 2z/B=75% x/c x/c x/c z/B= 95% x/c x/c Exp.5M 2.M.2.4 x/c.6.8 July 4-5, 25 Hybrd Symposum, Stockholm 5

16 Temporal-averaged pressure coeffcents by the orgnal-des -.5 2z/B=6% -.5 2z/B=25% -.5 2z/B=4% -.5 2z/B=6% -.5 2z/B=95% x/c x/c x/c z/B=75% x/c x/c x/c.6.8 July 4-5, 25 Hybrd Symposum, Stockholm 6

17 Unsteady vortex by the orgnal DES July 4-5, 25 Hybrd Symposum, Stockholm 7

18 Unsteady vortex by the orgnal DES For local fne grds, the swtch from RANS to DES can take place somewhere nsde the boundary layer and produce a premature (grd-nduced) separaton and vortex breakdown. 2x/B=.875 July 4-5, 25 Hybrd Symposum, Stockholm 8

19 Temporal-averaged Vortces 2x/B=2.26 2x/B=2.4 2x/B=2.67 July 4-5, 25 Hybrd Symposum, Stockholm 9

20 Results wth RANS and zonal-des HPR -.5 2z/B=6% -.5 2z/B=25% -.5 2z/B=4% x/c x/c x/c z/B=6% -.5 2z/B=75% -.5 2z/B=95% x/c x/c Exp RANS zonal-des.2.4 x/c.6.8 July 4-5, 25 Hybrd Symposum, Stockholm 2

21 Trace-lnes at secton 2x/B=2.67 July 4-5, 25 Hybrd Symposum, Stockholm 2

22 Unsteady vortex by zonal-des July 4-5, 25 Hybrd Symposum, Stockholm 22

23 Concluson Weakly non-lnear k-ω WD+ model can predct the transonc shock-wave and boundary-layer nteracton flow very well comparng wth another wde-used and successful M-SST model; RANS model can predct the nterference between the wng and fuselage very well wth both Grds A and B; July 4-5, 25 Hybrd Symposum, Stockholm 23

24 Concluson (contnued) Orgnal DES predct the vortex prematurely and swtch RANS to DES advance result n the local grds; Zonal-DES method can mprove the results of pressure over the wng and predct more detal change of vortex structures n both stream-wse and span-wse drecton and unsteady vortex sheddng; Zonal-DES predct the poston of start pont a bt upstream than that of RANS when vortex breakdown s undergong. July 4-5, 25 Hybrd Symposum, Stockholm 24

25 THANKS! July 4-5, 25 Hybrd Symposum, Stockholm 25