Quantifying Non-Equilibrium in Hypersonic Flows Using Entropy Generation

<p>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 may 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 for benchmark comparison. Solutions were obtained for hypersonic flow over two axi-symmetric 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 solutions fail 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.</p><p>This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact and remains as true to the original work as possible. Therefore you will see the original copyright references library stamps (as most of these works have been housed in our most important libraries around the world) and other notations in the work.</p><p>This work is in the public domain in the United States of America and possibly other nations. Within the United States you may freely copy and distribute this work as no entity (individual or corporate) has a copyright on the body of the work.</p><p>As a reproduction of a historical artifact this work may contain missing or blurred pages poor pictures errant marks etc. Scholars believe and we concur that this work is important enough to be preserved reproduced and made generally available to the public. We appreciate your support of the preservation process and thank you for being an important part of keeping this knowledge alive and relevant.</p>