Comparison of Burnett and DSMC predictions of pressure distributions and normal stress in one-dimensional, strongly nonisothermal gases

The Burnett equations have been shown to provide improved descriptions, relative to the Navier-Stokes equations, of flow structure in high-velocity (i.e., hypersonic) gases. We examine here the accuracy of the Burnett constitutive equation for fluid stress as applied to stationary gases. Specifically, we investigate the effects of "thermal stress" (fluid stress induced by a temperature gradient), as predicted by the Burnett equation, on the pressure distributions and normal stress in a stationary, buoyancy-free, hard-sphere gas for the case of one-dimensional heat transfer. We show, using first-law principles and the Burnett equation, that thermal stress results in a reduction in normal stress in the nonisothermal gas relative to that in the equilibrium state. The normal stress, in turn, can be obtained as an eigenvalue to a second-order ordinary differential equation, representing the Burnett equation, for the pressure distribution in the gas. Simple asymptotic solutions to the Burnett equation are developed, and are used in combination with order-Kil pressure slip relations to formulate pressure boundary conditions at the heated and cooled surfaces. The approximate solutions, as well as exact numerical calculations, are compared with pressure distributions generated from the direct-simulation Monte Carlo (DSMC) method. The Burnett and DSMC predictions of pressure are in good agreement for effective Knudsen numbers (based on the temperature gradient in the gas) less than 0.1. In particular, the Burnett equations can provide a reasonable description of the Knudsen (or rarefaction) layers adjacent to the heated and cooled surfaces that bound the gas, and can also describe the variation in pressure in the bulk gas. In addition, theoretical predictions of the reduction in normal stress correspond well to DSMC-derived values. (C) 1999 American Institute of Physics. [S1070-6631(99)01507-X].