Numerical simulation of unsteady aerodynamic heating phenomena due to shock wave reflections with vibrational equilibrium

In the present study thin-layer Navier-Stokes equations have been solved in order to investigate unsteady aerodynamic heating phenomena induced by the shock impingement on a ramp surface with emphasis on high temperature effects. Especially the effect of energy transfer between translational energy and vibrational energy is investigated carefully. The major objectives are focused on the role of the vibrational energy on unsteady aerodynamic heating phenomena. Two-dimensional thin-layered Navier-Stokes equations are solved.For inviscid terms a Harten and Yee's TVD scheme is used and for viscous terms a conventional central difference is used. For boundary conditions non-slip conditions are applied for the ramp surface and zero derivatives along freestream are assumed at incoming and downstream boundaries. Also zero physical derivatives normal to incoming flow are imposed and a constant wall temperature condition is assumed. For the high temperature effects vibrational energy is considered as the internal energy of gas molecules. Vibrational equilibrium condition is assumed, that is, T = T_v everywhere. Calculations have been conducted under the conditions of incident Mach number M_s = 3.0 and ramp angle = 35° by changing initial temperatures from 300K to 2000K. Quite significant changes of aerodynamic heating phenomenon with initial temperature are observed. Also the results are compared with those without vibrational equilibrium. The results suggest that the vibrational energy has a quite important role in unsteady aerodynamic heating phenomenon at high temperatures.