Entropy Generation as a Means of Examining Continuum Breakdown

摘要

To quantify the validity and breakdown of the continuum equations of fluid flow, the concept of entropy generation is examined. This parameter is formulated utilizing statistical mechanics and kinetic theory to avoid the use of equilibrium assumptions. This analysis leads to expressions in terms of energy distribution functions. These results are applied to monatomic and diatomic molecules. A numerical procedure for computing these values using the Direct Simulation Monte Carlo Method (DSMC) is presented. Normal shock waves in argon and nitrogen were simulated at Mach numbers ranging from 1.2 to 10. Results are compared to Navier-Stokes predictions. The Navier-Stokes equations are shown to delay the onset of nonequilibrium and diminish the magnitude of nonequilibrium though the shock. Because of this, breakdown parameters based on continuum data will fail to capture the initial nonequilibrium and will not provide good measures of continuum breakdown. Error in flow variables is shown as a strong function of entropy generation, suggesting this parameter is a good indicator of continuum breakdown and onset when computed using kinetic approaches.