{"product_id":"quantifying-non-equilibrium-in-hypersonic-flows-using-entropy-generation-1288331428","title":"Quantifying Non-Equilibrium in Hypersonic Flows Using Entropy Generation","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 1288331428\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Carr, Ryan W\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e New\u003c\/p\u003e\u003cp\u003eThe 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.\u003c\/p\u003e","brand":"Mia Karts","offers":[{"title":"Default Title","offer_id":67950700036384,"sku":"NEW1288331428","price":21.06,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0980\/7426\/3840\/files\/71OYbQ_EsoL.jpg?v=1792819040","url":"https:\/\/miakarts.com\/products\/quantifying-non-equilibrium-in-hypersonic-flows-using-entropy-generation-1288331428","provider":"Miakarts Books","version":"1.0","type":"link"}