Influence of numerical and viscous dissipation on shock wave reflections in supersonic steady flows

Abstract Numerical simulations are investigated to describe precisely the shock wave reflections in supersonic steady air flow field. The main objectives are to study the influence of the wedge trailing edge corner angle, of the numerical methods and of the viscous effects on the shock wave reflections and on the hysteresis behavior. The computations are done with different MUSCL–TVD finite volume schemes and the corresponding results are compared. The flow viscosity is also taken into account and comparisons are made between inviscid and viscous flow simulations. The results display the non-negligible influence of the numerical scheme accuracy on the results, mainly on the position and height of the Mach stem, and the relatively weak influence of the flow viscosity on these parameters. Comparisons between numerical results and experimental data have also been done and a good agreement is only observed for small wedge angles mainly due to the three-dimensional effects in the experimental setup.

[1]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[2]  Hans G. Hornung,et al.  Transition to Mach reflexion of shock waves in steady and pseudosteady flow with and without relaxation , 1979, Journal of Fluid Mechanics.

[3]  E. Leclerc,et al.  Experimental investigation of the influence of downstream flow conditions on Mach stem height , 1999 .

[4]  Gabi Ben-Dor,et al.  A parametric study of Mach reflection in steady flows , 1997, Journal of Fluid Mechanics.

[5]  G. Ben-Dor.  Hysteresis phenomena in shock wave reflections in steady flows , 1999 .

[6]  Hans G. Hornung,et al.  Transition from regular to Mach reflection of shock waves Part 2. The steady-flow criterion , 1982, Journal of Fluid Mechanics.

[7]  Domenic D'Ambrosio,et al.  Numerical Instablilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon , 2001 .

[8]  Gabi Ben-Dor,et al.  Reconsideration of oblique shock wave reflections in steady flows. Part 2. Numerical investigation , 1995, Journal of Fluid Mechanics.

[9]  Y. Burtschell,et al.  Steady shock wave reflections in thermochemical nonequilibrium flows , 2001 .

[10]  Richard Sanders,et al.  Multidimensional Dissipation for Upwind Schemes , 1998 .

[11]  Domenic D'Ambrosio,et al.  Upwind methods and carbuncle phenomenon , 1998 .

[12]  G. Ben-Dor,et al.  Analytical prediction of the wave configuration size in steady flow Mach reflections , 1997 .

[13]  Richard Sanders,et al.  Regular ArticleMultidimensional Dissipation for Upwind Schemes: Stability and Applications to Gas Dynamics☆ , 1998 .

[14]  Dependence of Steady Mach Reflections on the Reflecting-Wedge Trailing-Edge Angle , 1997 .

[15]  J. Vuillon,et al.  Investigation of the hysteresis phenomena in steady shock reflection using kinetic and continuum methods , 1996 .

[16]  Mikhail S. Ivanov,et al.  Transition between regular and Mach reflections of shock waves in steady flows , 1997 .

[17]  D. J. Azevedo,et al.  Engineering approach to the prediction of shock patterns in bounded high-speed flows , 1993 .

[18]  R. Paoli,et al.  Stability of shock wave reflections in nonequilibrium steady flows and hysteresis , 2000 .

[19]  Gabi Ben-Dor,et al.  Shock wave reflection phenomena , 1992 .