Development and evaluation of continuum models for translational-rotational nonequilibrium

In order to reduce space transportation costs, future spacecraft will employ fuel saving strategies including aero-maneuvering, aero-braking and air breathing propulsion. Under the rarefied conditions in which these vehicles will operate, the conventional continuum equations of gas dynamics, the Navier-Stokes equations, cease to accurately describe flow physics due to significant amounts of translational nonequilibrium. In diatomic gases such as nitrogen and oxygen rotational nonequilibrium will also be present resulting in a state of combined translational-rotational nonequilibrium. Inclusion of rotational-translational nonequilibrium effects into the continuum description of gas dynamics is necessary in order to accurately predict flow fields surrounding future transatmospheric vehicles.;It is assumed herein that continuum models for translational and rotational nonequilibrium may be developed independently and then applied to flows with combined translational-rotational nonequilibrium. The Burnett equations, obtained from the Chapman-Enskog expansion carried one order beyond Navier-Stokes (hence the only difference from Navier-Stokes is additional "higher order" terms in the constitutive relations), significantly improve computations of shock structure in monatomic gases where translational nonequilibrium alone exists. The Burnett equations are therefore assumed to model translational nonequilibrium in diatomic gases. Alternative constitutive relations which capture the essential features of the Burnett equations but are easier to implement are also presented and evaluated.;The theoretical basis of Jeans' equation for rotational energy relaxation is reviewed, and its shortcomings are outlined. A more general model is developed from recent experimental measurements of rotational quantum transition rates. These rates are used in a solution of the master equation for a stationary gas in rotational nonequilibrium, and numerous such solutions are used to create the new rotational relaxation model.;The above models are applied to the diatomic shock structure as a test case and are found to significantly improve the continuum description. The Burnett and simplified constitutive models are found to give shock thicknesses in close agreement with one another. The new rotational relaxation model based on transition rate data, in conjunction with either translational nonequilibrium model, is found to give good agreement with experimental shock thicknesses up to Mach 6 where temperatures exceeding the range of accuracy for the measured transition rates cause the model to over predict shock thickness. In a similar manner, Jeans' equation in conjunction with Lordi and Mates determinations of the rotational collision number Z...