| The conventional form of the Burnett equations, developed in 1939, has been shown in recent years to predict the behavior of monatomic gases in the continuum transition flow regime better than the Navier-Stokes equations. An inherent part of the conventional Burnett equations is an inviscid, isentropic approximation for the material derivative present in both the viscous stress and heat conduction expressions of the original Burnett equation of 1935. While the inviscid, isentropic substitution maintains the order of accuracy of the Burnett expressions, other representations of the material derivative may further improve the accuracy of the second order constitutive equations. In addition, a frame-indifferent and a modified second order set of constitutive equations have been proposed by Woods.; Alternate forms for the Burnett and Woods viscous stress and heat flux are investigated herein using the exact material derivative definition, an inviscid, isentropic substitution, and an improved approximation for the material derivatives based on the Navier-Stokes equations. A rigorous stability examination details the effects of the augmented terms required to allow the use of these higher order constitutive equations with time dependent numerical methods. Comprehensive numerical tests are conducted using three model problems (monatomic shock structure, hypersonic flow about a 2-D circular body, and hypersonic leading edge problem) to examine the behavior of these higher order constitutive equations for translational nonequilibrium, rarefied compressive flow and rarefied shear flow.; Of the nine different forms of higher order constitutive equations examined, the Conventional Burnett equations feature a robustness and accuracy that the eight other forms of the Burnett and Woods constitutive equations lack. Unphysical behavior, unnecessary complexity and negative entropy production limit the applicability of the other forms of the Burnett and Woods equations examined. |
