An Improved K-ω Model for High Speed Flows

Abstract:

An improved K-ω model, which allows for compressible corrections, is proposed in this paper. Numerical scheme was established utilizing the improved Total Variation Diminishing (TVD) scheme and applying implicit scheme to the negative source terms of the turbulence model. Hypersonic flat-plate boundary-layer flows and hypersonic compression ramp flows marked with separation, reattachment and shock/boundary layer interactions are then computed. Comparisons between the computational results, the experimental results and the semi-empirical formulations show that the compressible correction term of the K-ω turbulence model is a pressure-dilatation correlation. In addition, for flow with separation and without separation, calculation results of wall pressures, friction coefficients and wall heat transfer rate distributions using the improved model and established scheme agree better with the experimental results than that using the original K-ω model.

• Periodical: Advanced Materials Research (Volume 629)
• Pages: 593-600
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.629.593
• Online since: December 2012
• Authors: Jing Yuan Liu, Zeng Hui Zhao
• Keywords: Heat Transfer, Hypersonic, Numerical Simulation, Separation, Turbulence Model

References

[1] Huang P.G., Bradshaw P., and Coakley T.J., Turbulence Models for Compressible Boundary Layers [J]. AIAA. J., 1994, V32(4): 735-740.

DOI: 10.2514/3.12046

[2] Taulbee D. and VanOsdol J., Modeling Turbulent Compressible Flows: the Mass Fluctuating Velocity and Squared Density[R]. AIAA-91-0524.

DOI: 10.2514/6.1991-524

[3] Lele S.K., Compressibility Effects on Turbulence [J]. Annual Review Fluid Mechanics, 1994, V26: 211-254.

[4] Sarkar S., The Stabilizing Effect of Compressibility in Turbulent Shear Flow[J]. Journal of Fluid Mechanics, 1995, V282: 163-186.

DOI: 10.1017/s0022112095000085

[5] Wilcox D C. Reassessment of the Scale-Determining Equation for Advanced Turbulence Models[J]. AIAA. J., 1988, V26(11): 1299-1310.

DOI: 10.2514/3.10041

[6] Yee H C, Klopfer G. H, Montagne J L. High-Resolution Shock-Capturing Schemes for Inviscid and Viscous Hypersonic Flows [J]. J Comp Phys, 1990, 88: 31-61.

DOI: 10.1016/0021-9991(90)90241-r

[7] Zheng B, Lee C H. The Effects of Limiters on High Resolution Computations of Hypersonic Flows over Bodies with Complex Shapes [J]. Comm Nonlin Sci Numer Simul, 1998, 3(2): 82-87.

DOI: 10.1016/s1007-5704(98)90068-5

[8] Wilcox D C. Turbulence Modeling for CFD [M]. California: DCW Industries, Inc., 2000: 235-239.

[9] Sarkar S. The Pressure-Dilatation Correlation in Compressible Flows [J]. Physics of Fluids A, 1992, V4(12): 2674–2682.

DOI: 10.1063/1.858454

[10] Speziale C.G., Abid R., Anderson E.C., Critical Evaluation of Two-equation Models for Near-wall Turbulence [J]. AIAA J., 1992, V30(2): 324-331.

DOI: 10.2514/3.10922

[11] Liu, J. Development of High-Mach-Number Rans Turbulence Model and Numerical Simulation of Hypersonic Flows [D]. Beijing: Beihang University (2007).

[12] Barakos G., Drikakis D., Implicit Unfactored Implementation of Two-Equation Turbulence Models in Compressible Navier-Stokes Methods [J]. International Journal of Numerical Method in Fluids, 1998, V28: 73-94.

DOI: 10.1002/(sici)1097-0363(19980715)28:1<73::aid-fld700>3.0.co;2-r

[13] Menter F.R., Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications[J]. AIAA J., 1994, V32(8): 1598-1605.

DOI: 10.2514/3.12149

[14] Settles G S, Dodson L J. Hypersonic Shock/Boundary-Layer Interaction Database[R]. NASA-CR-177577, (1991).

[15] White, F. M., translated by Wei Z., Zhen S. Viscous Fluid Flow [M]. Beijing: National Mechanics Industry Press, 1982: 638.