Ryan W. Carr

Date of Award

3-2007

Document Type

Thesis

Degree Name

Master of Science in Aeronautical Engineering

Department

Department of Aeronautics and Astronautics

First Advisor

Richard Branam, PhD

Abstract

The constitutive relations traditionally used for finding shear stress and heat flux in a fluid become invalid in non-equilibrium flow. Their derivation from kinetic theory only demonstrates they are valid only for small deviations from equilibrium. Because it is fundamentally linked to non-equilibrium, entropy generation is used to investigate the limits of the continuum constitutive relations. However, the continuum equations are inherently limited to near equilibrium conditions due to the constitutive relations; thus kinetic theory must be used as a basis for comparison. Direct Simulation Monte Carlo (DSMC), a particle method alternative to continuum methods, is based on kinetic theory and is used to develop a flow solution free from equilibrium assumptions. Solutions were obtained for hypersonic flow over two axisymmetric geometries using both a continuum solver and DSMC. Formulations for entropy generation are presented for each method, and the two solutions are compared. The continuum solver fails to capture regions of non-equilibrium as evidenced by thicker shocks in the DSMC solution. To extend the useful range of the continuum constitutive relations, the Lennard-Jones model is offered as an alternative to Sutherland's Law for calculating viscosity and thermal conductivity. The two are compared, and parameters offering a good fit for these flows are suggested for the Lennard-Jones model.

AFIT Designator

AFIT-GAE-ENY-07-M07

DTIC Accession Number

ADA468381

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