On the total enthalpy behavior inside a shock wave

Abstract

The total enthalpy behavior inside a shock wave in a dilute monatomic gas has been numerically studied for various values of Mach and Prandtl numbers with the continuum (the Navier-Stokes-Fourier equations) and kinetic (the Shakhov model and the direct simulation Monte Carlo method) approaches. A significant difference between the results by the continuum and kinetic approaches has been observed for the internal shock wave structure. In a wide range of the free-stream Mach numbers, the continuum approach predicts qualitatively similar behavior of total enthalpy distributions that can be of a concave, constant, or convex shape depending on the Prandtl number. The more sophisticated kinetic approach predicts a more complicated form of total enthalpy profiles: e.g., an inflection point for Mach numbers around two and Prandtl numbers close to unity. The evolution of the total enthalpy in the shock is determined by the balance of heat conduction and mechanical work of normal viscous stress - processes that are predicted inaccurately by using the Navier-Stokes-Fourier equations at high Mach numbers.