Two-dimensional scattering of sound at noncontinuum conditions

We study the propagation and wall scattering of two-dimensional thermodynamic disturbances in a gas at noncontinuum conditions. Initial system perturbations are modeled as arbitrary (local) small-amplitude density or temperature inhomogeneities, prescribed in the vicinity of an impermeable specular or diffuse (isothermal) wall. The problem is analyzed in the free-molecular and ideal-flow limits, complemented by direct simulation Monte Carlo (DSMC) calculations at arbitrary rarefaction rates. Closed-form results are obtained for the collisionless and ideal-flow gas responses to impulse excitation, followed by comparisons between DSMC and limit-case predictions for the case of Gaussian perturbations. While the acoustic signal is subject only to a geometric two-dimensional decay and carries to large distances in the inviscid limit, it decays rapidly at high rarefaction rates due to the mechanism of molecular dispersion. Different from the identical gas responses to local compression and heating in the inviscid regime, qualitative differences are highlighted and analyzed in the free-molecular limit. The results additionally indicate lower pressure levels in an isothermal- compared with a specular-wall system, due to the exchange of gas-surface energy taking place in the former. Finally, the acoustic force acting on the solid surface is examined. Apart from an early-time repelling impact, peculiar late-time attraction is found in the case of gas heating excitation at high Knudsen numbers.