The structure of hypersonic shock waves using Navier-Stokes equations modified to include mass diffusion

Greenshields, C.J. and Reese, J.M.; (2007) The structure of hypersonic shock waves using Navier-Stokes equations modified to include mass diffusion. In: 2nd European Conference on Aero-Space Sciences (EUCASS). Von Karman Institute, BEL.

[thumbnail of strathprints006675]
Preview
Text (strathprints006675)
strathprints006675.pdf
Accepted Author Manuscript

Download (202kB)| Preview

    Abstract

    Howard Brenner has recently proposed modifications to the Navier-Stokes equations that relate to a diffusion of fluid volume that would be significant for flows with high density gradients. In a previous paper (Greenshields & Reese, 2007), we found these modifications gave good predictions of the viscous structure of shock waves in argon in the range Mach 1.0-12.0 (while conventional Navier-Stokes equations are known to fail above about Mach 2). However, some areas of concern with this model were a somewhat arbitrary choice of modelling coefficient, and potentially unphysical and unstable solutions. In this paper, we therefore present slightly different modifications to include molecule mass diffusion fully in the Navier-Stokes equations. These modifications are shown to be stable and produce physical solutions to the shock problem of a quality broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. The modifications primarily add a diffusion term to the mass conservation equation, so are at least as simple to solve as the Navier-Stokes equations; there are none of the numerical implementation problems of conventional extended hydrodynamics models, particularly in respect of boundary conditions. We recommend further investigation and testing on a number of different benchmark non-equilibrium flow cases.

    ORCID iDs

    Greenshields, C.J. and Reese, J.M. ORCID logoORCID: https://orcid.org/0000-0001-5188-1627;