2D Navier-Stokes equations - Shock Wave Reflections

The unsteady flow of the 2D shock "wedge" reflection for a perfect gas with variable viscosity and conductivity was simulated using the Navier-Stokes equations and the Sutherland model. For an initial Mach number of 4.5, inital temperature 300 K, pressure 2000 Pa, and specific heat ratio 1.4 the different shock reflection regimes for a varying wedge angle were analysed. While keeping the Mach number constant and increasing the wedge angle (or equivalently the angle of incidence for the rotated problem) from zero the flow configuration changes from a vNR to a SMR to a TMR to a DMR to a RR or respectively the von Neuman, single Mach, Transitionary Mach, Double Mach, and regular reflections. These are the basic types of shock reflections. Yet, note that in the most recent literature, there are many other subtypes.

For each of the transition regions, the invicsid Euler equations and the Navier-Stokes equations were compared for slip and no slip boundary conditions.

• thetawvsMs_PG_transition.pdf: Inviscid Perfect Gas Transition Regimes, (a different example using three shock theory)

*2nd order van Albada limited Clawpack, x = [-0.006,0.03], y = [0,0.015], 4 levels of Refinement, 144x36 cells on the first level, last time, t = 1e-5 seconds, refinefactors = 2, 2, 2, 4

General Results : Mach 4.5, "Wedge" angle 9 - 30 degrees

DMR-RR Transition: DmrRr

TMR-DMR Transition: TmrDmr

SMR-TMR Transition: SmrTmr

vNR-SMR Transition: VnrSmr

Basic Shock Reflection Theory

• RR: Regular Reflection
• DMR: Double Mach Reflection
• TMR: Transitionary Mach Reflection
• SMR: Single Mach Reflection
• vNR: von Neumann Reflection

-- JackZiegler^? - 30 Jul 2008