Formulation of a new set of simplified conventional burnett equations for computation of rarefied hypersonic flows

Wenwen Zhao, Weifang Chen, Ramesh K. Agarwal

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

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.

Original languageEnglish
Title of host publicationAIAA AVIATION 2014 -7th AIAA Theoretical Fluid Mechanics Conference
PublisherAmerican Institute of Aeronautics and Astronautics Inc.
ISBN (Print)9781624102936
DOIs
StatePublished - 2014
EventAIAA AVIATION 2014 -7th AIAA Theoretical Fluid Mechanics Conference 2014 - Atlanta, GA, United States
Duration: Jun 16 2014Jun 20 2014

Publication series

NameAIAA AVIATION 2014 -7th AIAA Theoretical Fluid Mechanics Conference

Conference

ConferenceAIAA AVIATION 2014 -7th AIAA Theoretical Fluid Mechanics Conference 2014
Country/TerritoryUnited States
CityAtlanta, GA
Period06/16/1406/20/14

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