Validity of Stokes' hypothesis for near-continuum hypersonic flows

Abstract

The alternative interpretation of Stokes' hypothesis provided by Buresti [Acta Mech. 226, 3555–3559 (2015)] is investigated by an analysis of a near-continuum, hypersonic flow of oxygen over a double cone obtained from a large-scale direct simulation Monte Carlo computation. We show that for molecular oxygen, which has comparable bulk and shear viscosity coefficients, the difference between mechanical and thermodynamic pressure is negligible throughout most of the flow. This result justifies neglecting viscous stresses in the normal stress tensor associated with fluid particle dilatation, as is often done in continuum descriptions of compressible flows. The violation of the revisited Stokes' hypothesis was only observed in highly nonequilibrium regions of the flow (shocks and strong expansions) and wherever non-continuum effects become significant. For nonequilibrium flows of gases with large bulk viscosity relative to their shear viscosity, the revisited Stokes' assumption may still breakdown and requires further investigation.