DOI /j.cnki.cjhd SST-DES SST-URANS,, , shear stress transport, SST detached-eddy simulation,

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1 DOI0.6076/.cnki.chd SST-DES SST-URANS,, 0040, shear stress transport, SSTdetached-eddy simulation, DES SST SST-DES SST-URANS Re = 3900 SST-DES SST-RANS U66. A Numerical study of 3D flow past a circular cylinder at subcritical Reynolds number using SST-DES and SST-URANS ZHAO Wei-wen, WAN De-cheng (State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 0040, China) Abstract: The SST-DES is a hybrid RANS/LES model which employs Reynolds-Averaged Navies-Stokes (RANS) in the regions near boundary layers, and Large-Eddy Simulation (LES) in the separated regions. Numerical simulations of flow past a * : (05--6 ) : ( )() (030)(973 )(03CB03603) : (990),,,. :, [email protected] Received: July 6, 05 (Revised December 6, 05) Proect supported by foundations: Supported by the National Natural Science Foundation of China (53795, and 43009), the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning (030) and the Maor State Basic Research Development Plan of China (973 Program, 03CB03603) Biography: ZHAO Wei-wen (990 ), Male, Ph. D. Candidate. Corresponding author: WAN De-cheng, [email protected]

2 A 06 circular cylinder at subcritical Reynolds number ( Re = 3900) with both SST-DES and SST-URANS turbulence model have been carried out in current study. The mean pressure distribution on cylinder, vortex shedding patterns and mean velocity profile downstream of the cylinder are extensively studied and analyzed. Comparing with the experimental results, SST-DES shows better results than SST-URANS in subcritical Reynolds number cylinder flows. Key words: circular cylinder; flow separation; detached-eddy simulation; subcritical Reynolds number Reynolds-averaged Navier-Stokes, RANS Navier-Stokes RANS URANS direct numerical simulation, DNSlarge eddy simulation, LES RANS/LES RANS/LES RANS LES RANS LES detached-eddy simulation, DES RANS/LES 997 Spalart [] Spalart-AllmarasSA [] SA-DES DES97DES97 RANS d % d % SA d RANS LES LES LES modeled stress depletion, MSD Spalart [3] d % SA DESdelayed DES, DDES MSD Menter [4] sheared stress transport SST [5] DES MSD grid-induced separation, GIS OpenFOAM SST-DES SST-URANS Re D = 3900 SST-DES. SST SST Menter [5] SST k - ε k -ω k -ω k - ε k -ω k -ω OpenFOAM SST Menter [5] [6,7] Ω S OpenFOAM k ω k ( uk ) * k + = G% β kω + ( ν + αkνt) () t x x x ω t ( u ω) + = γs βω + x ω ( ν + αωνt) + ( F ) CD x x G % G % = G c k, * min(, β ω) G F 4 kω () = ν ts (3) F = tanh(arg ) (4a) k 500ν 4α k ω arg = min max,, * * βωy y ω CDkω y (4b)

3 SST-DES SST-URANS 3 = max(,0 ) CDk ω = α ω * CD 0 kω CDkω k ω x ω x F 0 k - ε k -ω F φ = Fφ + ( F) φ (5) F DES L t = max ( FS ), CDESΔ (0) * L = k /( β ω) t Δ= 3 ΔxΔyΔz C DES DES 0.6 F s F F F φ α β γ ν k ω ak t = (6) max( aω, bsf ) S invariant measure of the strain rate S =, S i S i S i u u i = + x x i F (7) F = tanh(arg ) (8a) k 500ν arg = max, * β ωy y ω (8b) y. Re D = 3900 [8-0] [0-3] L z =πd Kravchenko [3] x y z 5D< x< 30D 5D< y < 5D π D/ < z < πd/ 5D O N z = 30 Δ= 0.005D α k α k α ω α ω SST Table. Coefficients of the SST turbulence model * β β γ γ β a b c / SST-DES SST DES [4] k F DES k ( uk ) * k + = G% β kωfdes + ( ν + αkνt) t x x x (9) FDES. OpenFOAM Rhie [4] TVD PIMPLEPISO [3] SIMPLE PISO Navier-Stokes PIMPLE PISO

4 A 06 U min / U SST-DES L rec / D SST-URANS St 0. 0.5 z = 0 SST-DES Norberg SST-URANS Fig. Global and local mesh for circular cylinder Fig.

4 4 A 06 U min / U SST-DES L rec / D SST-URANS St z = 0 SST-DES Norberg SST-URANS Fig. Global and local mesh for circular cylinder Fig. Pressure coefficient distribution around cylinder surface C d Table. Coefficients for flow past a cylinder C pb St L / D U / rec min U ([3]) 0.990± ± ±0.005 [9].33± ±0.0 [8] PIV [0] ± LES [0] ± SST-DES SST-URANS D / U 78 T = 390 D/ U Beaudan [] Kravchenco [3] 7 C C St d pb 3 SST-DES SST-URANS SST-URANS SST-DES 4 U V SST-DES x/ D=.06 U Kravchenko [3] LES Parnaudeau [0] PIV LES [5] LES Lourenco [8] PIV V Lourenco

5 SST-DES SST-URANS 5 [8] y = 0 5 Lourenco [8] 4 5 SST-DES Parnaudeau [0] PIV SST-URANS 3. 6 Hunt [6] Q Q - criterion Q ( Ω S ) Q= () 3 U U Fig.3 Velocity and pressure contour normalized with U or U Ω S SST-DES SST- URANS SST-DES Kravchenko [3] LES Wissink [7] DNS 4 Fig.4 Mean stream-wise velocity at three locations in the near wake

6 A 06 5 Fig.5 Mean cross-flow velocity at three locations in the near wake 7 ωdu / = 0.5-0.0 6 Fig.

6 6 A 06 5 Fig.5 Mean cross-flow velocity at three locations in the near wake 7 ωdu / = Fig.7 Karman vortex street in the downstream flow, shown by 6 contours of D/ U from 0.5 to 0.0 ω 6 Q = 0 Fig.6 Isosurface of instantaneous vorticity in the wake, Q = 0 7 z = 0 SST-DES SST-URANS SST-DES SST-URANS SST-DES SST-URANS

7 SST-DES SST-URANS 7 OpenFOAM SST-DES SST-URANS Re D = 3900 () C d C pb St U / U min SST-DES SST-URANS St () SST-DES SST-URANS SST-DES SST-URANS (3) SST- URANS SST-DES 53795, 54303, CB03603 : [] SPALART P, JOU W, STRELETS M, et al. Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach[j]. Advances in DNS/LES, 997, (): 4-8. [] SPALART P R, ALLMARAS S R. A one-equation turbulence model for aerodynamic flows[j]. Recherche Aerospatiale, 994, (): 5-. [3] SPALART P R, DECK S, SHUR M L, et al. A new version of detached-eddy simulation, resistant to ambiguous grid densities[j]. Theoretical and Computational Fluid Dynamics, 006, 0(3): [4] MENTER F R, KUNTZ M, LANGTRY R. Ten years of industrial experience with the SST turbulence model[j]. Turbulence, Heat and Mass Transfer, 003, 4(): [5] MENTER F R. Two-equation eddy-viscosity turbulence models for engineering applications[j]. AIAA Journal, 994, 3(8): [6] MENTER F, ESCH T. Elements of industrial heat transfer predictions[c]. 6th Brazilian Congress of Mechanical Engineering (COBEM), Uberlandia, Brazil, 00. [7] HELLSTEN A. Some improvements in Menter s k - omega SST turbulence model[c]. 9th AIAA, Fluid Dynamics Conference, Albuquerque, USA, 998. [8] LOURENCO L, SHIH C. Characteristics of the plane turbulent near wake of a circular cylinder[j]. A Particle Image Velocimetry Study, 993. [9] ONG L, WALLACE J. The velocity field of the turbulent very near wake of a circular cylinder[j]. Experiments in Fluids, 996, 0(6): [0] PARNAUDEAU P, CARLIER J, HEITZ D, et al. Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900[J]. Physics of Fluids, 008, 0(8): [] BEAUDAN P, MOIN P. Numerical experiments on the flow past a circular cylinder at sub-critical Reynolds number[r]. Technical Report TF-6, Stanford University, USA, 994. [] BREUER M. Large eddy simulation of the subcritical flow past a circular cylinder: Numerical and modeling aspects[j]. International Journal for Numerical Methods in Fluids, 998, 8(9): [3] KRAVCHENKO A G, MOIN P. Numerical studies of flow over a circular cylinder at Re D = 3900 [J]. Physics of Fluids, 000, (): [4] RHIE C M, CHOW W L. Numerical study of the turbulent flow past an airfoil with trailing edge separation[j]. AIAA Journal, 983, (): [5],,. [J]. :, 03(): ZHOU Qiang, CAO Shu-yang, ZHOU Zhi-yong. Numerical studies of wake characteristics on a circular cylinder at sub-critical Reynolds number[j]. Journal of

8 8 A 06 Tongi University: Natural Science, 03(): [6] HUNT J C R, WRAY A A, MOIN P. Eddies, streams, and convergence zones in turbulent flows[r]. Center for Turbulence Research Report CTR-S88, Stanford University, USA, 988. [7] WISSINK J G, RODI W. Numerical study of the near wake of a circular cylinder[j]. International Journal of Heat and Fluid Flow, 008, 9(4):

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