A study on turbulence transportation and modification of Spalart–Allmaras model for shock-wave/turbulent boundary layer interaction flow

Abstract It is of great significance to improve the accuracy of turbulence models in shock-wave/boundary layer interaction flow. The relationship between the pressure gradient, as well as the shear layer, and the development of turbulent kinetic energy in impinging shock-wave/turbulent boundary layer interaction flow at Mach 2.25 is analyzed based on the data of direct numerical simulation (DNS). It is found that the turbulent kinetic energy is amplified by strong shear in the separation zone and the adverse pressure gradient near the separation point. The pressure gradient was non-dimensionalised with local density, velocity, and viscosity. Spalart–Allmaras (S–A) model is modified by introducing the non-dimensional pressure gradient into the production term of the eddy viscosity transportation equation. Simulation results show that the production and dissipation of eddy viscosity are strongly enhanced by the modification of S–A model. Compared with DNS and experimental data, the wall pressure and the wall skin friction coefficient as well as the velocity profile of the modified S–A model are obviously improved. Thus it can be concluded that the modification of S–A model with the pressure gradient can improve the predictive accuracy for simulating the shock-wave/turbulent boundary layer interaction.

[1]  Ali Gülhan,et al.  Investigation of the Performance of a Scramjet Inlet at Mach 6 with Boundary Layer Bleed , 2006 .

[2]  Alexander J. Smits,et al.  New Experimental Data of STBLI at DNS/LES Accessible Reynolds Numbers , 2005 .

[3]  Dong Joo Song,et al.  Modified Shear-Stress Transport Turbulence Model for Supersonic Flows , 2005 .

[4]  Soshi Kawai,et al.  Large-Eddy Simulation of an Oblique Shock Impinging on a Turbulent Boundary Layer , 2010 .

[5]  Alexander J. Smits,et al.  Analysis of shockwave/turbulent boundary layer interaction using DNS and experimental data , 2005 .

[6]  J. Dunham.  CFD VALIDATION FOR PROPULSION SYSTEM COMPONENTS , 1998 .

[7]  Gary S. Settles,et al.  Details of a Shock-Separated Turbulent Boundary Layer at a Compression Corner , 1976 .

[8]  S. Balachandar,et al.  Mechanisms for generating coherent packets of hairpin vortices in channel flow , 1999, Journal of Fluid Mechanics.

[9]  Minwei Wu,et al.  Direct numerical simulation of supersonic turbulent boundary layer over a compression ramp , 2007 .

[10]  Sergio Pirozzoli,et al.  Direct numerical simulation of impinging shock wave/turbulent boundary layer interaction at M=2.25 , 2006 .

[11]  Xian-jin Li.  A spectral interpretation for the explicit formula in the theory of prime numbers , 2010 .

[12]  Zi-Niu Wu,et al.  Review of shock wave detection method in CFD post-processing , 2013 .

[13]  Ali Gülhan,et al.  Investigation of the Flow Field of a 2D SCRAM-Jet Inlet at Mach 7 with optional Boundary Layer Bleed , 2007 .

[14]  F. A. Schraub,et al.  The structure of turbulent boundary layers , 1967, Journal of Fluid Mechanics.

[15]  Minwei Wu.  Direct numerical simulation of shockwave and turbulent boundary layer interactions , 2004 .

[16]  Nikolaus A. Adams,et al.  Direct simulation of the turbulent boundary layer along a compression ramp at M = 3 and Reθ = 1685 , 2000, Journal of Fluid Mechanics.

[17]  David S. Dolling,et al.  Fifty Years of Shock-Wave/Boundary-Layer Interaction Research: What Next? , 2001 .

[18]  Lipeng Lu,et al.  Modification of Spalart–Allmaras model with consideration of turbulence energy backscatter using velocity helicity , 2011 .

[19]  W. Rose,et al.  Wall Shear Stress Measurements in a Shock-Wave Boundary-Layer Interaction , 1978 .

[20]  Gary S. Settles,et al.  Detailed Study of Attached and Separated Compression Corner Flowfields in High Reynolds Number Supersonic Flow , 1979 .

[21]  James R. Forsythe,et al.  AN ASSESSMENT OF SEVERAL TURBULENCE MODELS FOR SUPERSONIC COMPRESSION RAMP FLOW , 1998 .

[22]  Anastasios S. Lyrintzis,et al.  The lagRST Model: a Turbulence Model for Non-Equilibrium Flows , 2012 .

[23]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[24]  Lipeng Lu,et al.  Effect of pressure gradient on coherent structures in a turbulent boundary layer , 1997 .

[25]  Z. Wang,et al.  A Modified Turbulence Model on Predicting Separated Airfoil Flow , 2002 .

[26]  J. M. Conley.  Modification of the MML turbulence model for adverse pressure gradient flows. M.S. Thesis - Akron Univ., 1993 , 1994 .

[27]  Zhaorui Li,et al.  An Optimized Low-Dissipation Monotonicity-Preserving Scheme for Numerical Simulations of High-Speed Turbulent Flows , 2013, Journal of Scientific Computing.

[28]  Parviz Moin,et al.  Direct numerical simulation of a separated turbulent boundary layer , 1998 .

[29]  D. Wilcox.  Formulation of the k-w Turbulence Model Revisited , 2008 .

[30]  Baojie Liu,et al.  Turbulence Models Assessment for Large-Scale Tip Vortices in an Axial Compressor Rotor , 2008 .