The effects of thermal conductivity and viscosity of argon on shock waves diffracting over rigid ramps

Abstract

Experiments were done with strong shocks diffracting over steel ramps immersed in argon. Numerical simulations of the experiments were done by integrating the Navier–Stokes equations with a higher-order Godunov finite difference numerical scheme using isothermal non-slip boundary conditions. Adiabatic, slip boundary conditions were also studied to simulate cavity-type diffractions. Some results from an Euler numerical scheme for an ideal gas are presented for comparison. When the ramp angle θ is small enough to cause Mach reflection MR, it is found that real gas effects delay its appearance and that the trajectory of its shock triple point is initially curved; it eventually becomes straight as the MR evolves into a self-similar system. The diffraction is a regular reflection RR in the delayed state, and this is subsequently swept away by a corner signal overtaking the RR and forcing the eruption of the Mach shock. The dynamic transition occurs at, or close to, the ideal gas detachment criterion θ_e. The passage of the corner signal is marked by large oscillations in the thickness of the viscous boundary layer. With increasing θ, the delay in the onset of MR is increased as the dynamic process slows. Once self-similarity is established the von Neumann criterion is supported. While the evidence for the von Neumann criterion is strong, it is not conclusive because of the numerical expense. The delayed transition causes some experimental data for the trajectory to be subject to a simple parallax error. The adiabatic, slip boundary condition for self-similar flow also supports the von Neumann criterion while θ < θ_e, but the trajectory angle discontinuously changes to zero at θ_e, so that θ_e is supported by the numerics, contrary to experiments.