Entropy in self-similar shock profiles

Margolin, Len G.; Reisner, Jon Michael; Jordan, Pedro M.

doi:10.1016/j.ijnonlinmec.2017.07.003

Title: Entropy in self-similar shock profiles

Journal Article · Sun Jul 16 00:00:00 EDT 2017 · International Journal of Non-Linear Mechanics

DOI:https://doi.org/10.1016/j.ijnonlinmec.2017.07.003· OSTI ID:1372792

^[1]; Reisner, Jon Michael ^[1]; Jordan, Pedro M. ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
U.S. Naval Research Lab., Stennis Space Center, MS (United States)

In this paper, we study the structure of a gaseous shock, and in particular the distribution of entropy within, in both a thermodynamics and a statistical mechanics context. The problem of shock structure has a long and distinguished history that we review. We employ the Navier–Stokes equations to construct a self–similar version of Becker’s solution for a shock assuming a particular (physically plausible) Prandtl number; that solution reproduces the well–known result of Morduchow & Libby that features a maximum of the equilibrium entropy inside the shock profile. We then construct an entropy profile, based on gas kinetic theory, that is smooth and monotonically increasing. The extension of equilibrium thermodynamics to irreversible processes is based in part on the assumption of local thermodynamic equilibrium. We show that this assumption is not valid except for the weakest shocks. Finally, we conclude by hypothesizing a thermodynamic nonequilibrium entropy and demonstrating that it closely estimates the gas kinetic nonequilibrium entropy within a shock.

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Research Organization:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1372792

Alternate ID(s):: OSTI ID: 1702343

Report Number(s):: LA-UR-15-26684

Journal Information:: International Journal of Non-Linear Mechanics, Vol. 95; ISSN 0020-7462

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 13 works

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References (17)

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Cited By (3)

Entropy growth and entropy production rate in binary mixture shock waves Madjarević, Damir; Simić, Srboljub Physical Review E, Vol. 100, Issue 2 https://doi.org/10.1103/physreve.100.023119	journal	August 2019
Scale matters Margolin, L. G. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 376, Issue 2118 https://doi.org/10.1098/rsta.2017.0235	journal	March 2018
Scale Matters Goldsmith, Marc Mechanical Engineering, Vol. 133, Issue 04 https://doi.org/10.1115/1.2011-apr-5	journal	April 2011

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