带有剪切应力输运性质的k-ε两方程湍流模型构造与应用
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摘要
由于传统的壁面衰减函数峰值并不考虑雷诺数的变化,因此仅能在特定的雷诺数下还原边界层的近壁衰减效应。为了改善这个缺陷,一个结合不同湍流雷诺数的因子被引入壁面衰减函数,从而使其峰值对雷诺数的变化能够合理感知。另外,基于DNS数据,将Bradshaw假设中的常数进行了重新标定,引入平滑的湍涡黏性系数切换函数,最终形成了一个带有剪切应力输运性质的k-ε两方程湍流模型。通过平板、翼型、二维鼓包以及翼身组合体进行了校验,结果显示新模型的精度较高,具有一定的工程实用价值。
The wall damping effect only can be recovered at the specific Reynolds number in traditional turbulence model due to the lack of considering the Reynolds effect.In order to overcome this drawback,a factor containing different turbulent Reynolds numbers is introduced into the wall damping function.In addition,the Bradshaw assumption is recalibrated by the DNSdata set,and then a smooth changing function is built to blended the two turbulent eddy viscosity coefficients.The two-equation turbulence model based on the recalibrated Bradshaw assumption can be converted to a shear-stress transport model.The new model is validated by a fullydeveloped turbulent flat plate,an airfoil with separated bubble,a two-dimension bump,and a wing-body with shock/wave boundary interaction,and the results are in good agreement with the experimental data.
The wall damping effect only can be recovered at the specific Reynolds number in traditional turbulence model due to the lack of considering the Reynolds effect.In order to overcome this drawback,a factor containing different turbulent Reynolds numbers is introduced into the wall damping function.In addition,the Bradshaw assumption is recalibrated by the DNSdata set,and then a smooth changing function is built to blended the two turbulent eddy viscosity coefficients.The two-equation turbulence model based on the recalibrated Bradshaw assumption can be converted to a shear-stress transport model.The new model is validated by a fullydeveloped turbulent flat plate,an airfoil with separated bubble,a two-dimension bump,and a wing-body with shock/wave boundary interaction,and the results are in good agreement with the experimental data.
引文
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[2] BALDWIN B S,BARTH T J.A one-equation turbulence transport model for high Reynolds number wall-bounded flows[M].National Aeronautics and Space Administration,Ames Research Center,1990.
[3] MENTER F R.Eddy viscosity transport equations and their relation to the k-epsilon model[J].Journal of Fluids Engineering-Transactions of the ASME.1997,119(4):876-884.
[4] RAHMAN M M,SIIKONEN T,AGARWAL R K.Improved low-Reynolds-number one-equation turbulence model[J].AIAA Journal,2011,49(4):735-747.
[5] SPALART P R,ALLMARAS S R.A one-equation turbulence model for aerodynamic flows[C]//30th Aerospace Sciences Meeting and Exhibit,Aerospace Sciences Meetings.Reno,NV,U.S.A.,1992.Doi:10.2514/6.1992-439
[6] MENTER F R.Zonal two equation k-cl,turbulence models for aerodynamic flows[R].AlAA 93-2906.Reston:AIAA,1993.
[7] COAKLEY T. Turbulence modeling methods for the compressible Navier-Stokes equations[C]//16th Fluid and Plasmadynamics Conference,1983:1693.
[8] BRADSHAW P,FERRISS D H,ATWELL N P.Calculation of boundary-layer development using the turbulent energy equation[J].J Fluid Mech,1967,28(3):593-616.
[9] ELKHOURY M.Effect of Cε1on the performance of the menter one-equation model of turbulence[J].Journal of Aircraft,2008,45(2):733-736.
[10]FARES E,SCHRODER W.A general one-equation turbulence model for free shear and wall-bounded flows[J].Flow Turbulence and Combustion,2004,73(3-4):187-215.
[11]NAGANO Y,PEI C Q,HATTORI H.A new low-Reynoldsnumber one-equation model of turbulence[J].Flow Turbulence and Combustion,2000,63(1):135-151.
[12]SHE Z X,CHEN X, WU Y,et al.New perspective in statistical modeling of wall-bounded turbulence[J].Acta Mech Sinica,2010,26:847-861.
[13]JONES W P,LAUNDER B E.The prediction of laminarization with a two-equation model of turbulence[J].International Journal of Heat Mass Transfer,1972(15):301-314.
[14]PATEL V C,RODI W,SCHEUERER G.Turbulence models for near-wall and low Reynolds number flows-A review[J].AIAA Journal,1985,23(9):1308-1319.
[15]RODI W, MANSOUR N N.Low Reynolds number k-εmodelling with the aid of direct simulation data[J].J Fluid Mech,1993,250:509-529.
[16]ZHANG Y,BAI J Q,XU J L,et al.An improved lowReynolds-number k-εmodel for aerodynamic flows[J].International Journal of Nonlinear Sciences and Numerical Simulation,2016,17(2):99-112.
[17]ABID R.Evaluation of two-equation turbulence models for predicting transitional flows[J].Int J Eng Sci,1990,31:831-840.
[18]YANG Z,SHIH T H.New time scale based k-epsilon model for near-wall turbulence[J].AIAA Journal,1993,31:1191-1198.
[19]LAUNDER B E,SHARMA B I.Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc[J].Letters in Heat and Mass Transfer,1974,1(2):131-138.Doi:10.1016/0094-4548(74)90150-7
[20]文晓庆,柳阳威,方乐,等.提高k-ωSST模型对翼型失速特性的模拟能力[J].北京航空航天大学学报,2013,39(8):1127-1132.WEN X Q,LIU Y W,FANG L,et al.Improving the capability of k-ωSST turbulent model for predicting stall characteristics of airfoil[J].J Beijing Univ Aeronaut Astronaut,2013,39(8):1127-1132.(in Chinese)
[21]ZHANG Y,BAI J Q,XU J L,et al.A one-equation turbulence model for recirculating flows[J].Science China Physics,Mechanics&Astronomy,2016,59:664701.
[22] WIEGHARDT K,TILLMAN W.On the turbulent friction layer for rising pressure,NASA/TM 1314[R].Hanover,Maryland, United States:NASA Center for Aerospace Information,1951.
[23] WILD J.Experimental investigation of Mach-and Reynoldsnumber dependencies of the stall behavior of 2-element and 3-element high-lift wing sections[C]//50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition,2012:108.
[24]COLES D,WADOCK A J.Flying-hot-wire study of flow past an NACA4412airfoil at maximum lift[J].AIAA Journal,1979,17:321-328.
[25]ANDERS S,SELLERS III W,WASHBURN A.Active flow control activities at NASA Langley[C]//2nd AIAA Flow Control Conference,2004:2623.
[26]LAFLIN K R,KLAUSMEYER S M,ZICKUHR T,et al.Data summary from second AIAA computational fluid dynamics drag prediction workshop[J].Journal of Aircraft,2005,42(5):1165-1178.