The effect of a solid boundary on the propagation of thermodynamic disturbances in a rarefied gas

Abstract

We study the effect of a rigid boundary on the propagation of thermodynamic disturbances in a gas under non-continuum conditions. We consider a semi-infinite setup confined by an infinite planar wall and introduce initial gas disturbances in the form of density and temperature inhomogeneities. The problem is formulated for arbitrary small-amplitude perturbations and analyzed in the entire range of gas rarefaction rates, governed by the Knudsen (Kn) number. Our results describe the system relaxation to equilibrium, with specific emphasis on the effect of the solid surface. Analytical solutions are obtained in the free-molecular and near-continuum (based on the Navier–Stokes–Fourier and regularized 13 moment equations) regimes and compared with direct simulation Monte Carlo results. The impact of the solid wall is highlighted by comparing between diffuse (adiabatic or isothermal) and specular boundary reflections. Focusing on a case of an initial temperature disturbance, the results indicate that the system relaxation time shortens with increasing Kn. The isothermal boundary consistently reverberates the weakest acoustic disturbance, as the energy carried by the impinging wave is partially absorbed by the surface. The specular and adiabatic wall systems exhibit identical responses in the continuum limit while departing with increasing Kn due to higher-order moment effects. The unsteady normal force exerted by the gas on the surface is quantified and analyzed.