Beyond Navier-Stokes: Burnett equations for flows in the continuum-transition regime

In hypersonic flows about space vehicles in low earth orbits or flows in mi crochannels of microelectromechanical devices, the local Knudsen number lie s in the continuum-transition regime. Navier-Stokes equations are not adequ ate to model these flows since they are based on small deviation from local thermodynamic equilibrium. To model these flows, a number of extended hydr odynamics or generalized hydrodynamics models have been proposed over the p ast fifty years, along with the direct simulation Monte Carlo (DSMC) approa ch. One of these models is the Burnett equations which are obtained from th e Chapman-Enskog expansion of the Boltzmann equation [with Knudsen number ( Kn) as a small parameter] to O(Kn(2)). With the currently available computi ng power, it has been possible in recent years to numerically solve the Bur nett equations. However, attempts at solving the Burnett equations have unc overed many physical and numerical difficulties with the Burnett model. As a result, several improvements to the conventional Burnett equations have b een proposed in recent years to address both the physical and numerical iss ues; two of the most well known are the "augmented Burnett equations" and t he "BGK-Burnett equations." This paper traces the history of the Burnett mo del and describes some of the recent developments. The relationship between the Burnett equations and the Grad's 13 moment equations is elucidated by employing the Maxwell-Truesdell-Green iteration. Numerical solutions are pr ovided to assess the accuracy and applicability of Burnett equations for mo deling flows in the continuum-transition regime. The important issue of sur face boundary conditions is addressed. Computations are compared with the a vailable experimental data, Navier-Stokes calculations, Burnett solutions o f other investigators, and DSMC solutions as much as possible. (C) 2001 Ame rican Institute of Physics.