Formulation of a New Set of Simplified Conventional Burnett Equations for Computation of Rarefied Hypersonic Flows

Abstract

Abstract For computation of rarefied flows in continuum-transition regime with Knudsen number Kn of O(1), Burnett equations have been proposed about a century ago as a set of extended hydrodynamics equations (EHE) that represent the second-order departure from thermodynamic equilibrium in the Chapman–Enskog expansion of Boltzmann equation; the first order terms in the expansion result in the Navier–Stokes equations. Over the years, a number of variations of original Burnett equations have been proposed in the literature known as the Conventional Burnett equations, the Augmented Burnett equations and the BGK–Burnett equations. In this paper, another simpler set of Burnett equations is proposed by order of magnitude analysis in the limit of high Mach numbers for hypersonic flow applications. These equations, designated as ‘Simplified Conventional Burnett (SCB)’ equations are stable under small perturbations and do not violate the second law of thermodynamics. An implicit numerical solver is developed for the solution of SCB equations. The SCB equations are applied to compute the hypersonic flow past 2D and 3D blunt bodies for Kn in continuum and continuum-transition regime. The SCB solutions are compared with the Navier–Stokes and DSMC solutions. It is shown that the SCB equations can be employed to compute the hypersonic flow past bodies in continuum-transition regime with much less computational effort because of their simplicity compared to Conventional and Augmented Burnett equations.