Study of continuum higher order closure models evaluated by a statistical theory of shock structure.

摘要

New generations of vehicles flying through planetary atmospheres at high speeds and altitudes, such as the Aero-assist Orbital Transfer Vehicle, will operate in flight regimes where the atmosphere may be considered a continuum, but where the conventional continuum equations of Navier-Stokes fail to yield accurate results. These conditions may be characterized by a bow shock wave thickness that is comparable to the shock stand-off distance from the hard body. The Navier-Stokes equations fail to correctly predict shock density thickness, density asymmetry, and temperature-density separation for all but very low Mach number shock waves. This research was undertaken to develop improvements to the continuum model which will yield accurate numerical solutions within hypersonic shock waves of monatomic gases.; The Direct Simulation Monte Carlo method is used in this investigation to calculate particulate solutions for shock structure, and provide more information about the shock wave than is experimentally available. These statistical simulations have indicated a strong correlation between higher order flow variable derivatives and the viscous stress needed to improve the Navier-Stokes equations. Further, these simulations showed that the Fourier law of heat conduction used in the continuum equations is not adequate for hypersonic shock waves. Attempts at developing empirical models containing this information proved futile.; The Burnett equations, derived by Chapman-Enskog expansion procedures, model viscous stress and heat flux as functions of flow variable second derivatives and products of first derivatives. Carried to a higher order, the Super-Burnett equations model viscous stress and heat flux with third order derivatives and products of first derivatives. Previous investigations have been able to solve the Burnett equations only for shock waves of Mach numbers less than 2, and have been completely unable to solve the Super-Burnett equations for any Mach number. These equations, and/or modifications to them, have now been solved for a hard sphere gas, argon, and Maxwellian gas for shock waves from Mach 1.3 to Mach 50. A numerical technique, new to shock structure analysis, has been used to obtain these solutions by allowing the equations to relax to steady-state from arbitrary initial conditions. (Abstract shortened with permission of author.)