An Advanced Kinetic Description for Shock Structure under Hypersonic Conditions

The one-dimensional standing shock wave has been examined theoretically and experimentally for many years since it represents the simplest flow in which non-equilibrium effects can be observed. Naiver-Stokes simulations fail to predict accurate shock profiles as the Mach number increases. Direct Simulation Monte Carlo method is considered to be the most accurate numerical method for predicting the shock structure albeit the extensiveness of required computational resources. An alternative theoretical approach to the classical Boltzmann equation, known as Boltzmann-Curtiss equation for particles with translational and rotational degrees of freedom, is considered. The first order approximate solution to the Boltzmann-Curtiss equation yield a more general stress tensor that can account for thermal non-equilibrium. Numerical simulations of a standing shock wave of argon and nitrogen in a range of Mach numbers from 1.2 to 9, reveal that the proposed model lead to significant improvements in the density profile, normal stresses and shock thickness at non-equilibrium conditions over the solution of classical Navier-Stokes equations.