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Title: Converging Shock Flows for a Mie-Grüneisen Equation of State

Abstract

Previous work has shown that the one-dimensional (1D) inviscid compressible flow (Euler) equations admit a wide variety of scale-invariant solutions (including the famous Noh, Sedov, and Guderley shock solutions) when the included equation of state (EOS) closure model assumes a certain scale-invariant form. However, this scale-invariant EOS class does not include even simple models used for shock compression of crystalline solids, including many broadly applicable representations of Mie-Grüneisen EOS. Intuitively, this incompatibility naturally arises from the presence of multiple dimensional scales in the Mie-Grüneisen EOS, which are otherwise absent from scale-invariant models that feature only dimensionless parameters (such as the adiabatic index in the ideal gas EOS). The current work extends previous efforts intended to rectify this inconsistency, by using a scale-invariant EOS model to approximate a Mie-Grüneisen EOS form. To this end, the adiabatic bulk modulus for the Mie-Grüneisen EOS is constructed, and its key features are used to motivate the selection of a scale-invariant approximation form. Here, the remaining surrogate model parameters are selected through enforcement of the Rankine-Hugoniot jump conditions for an infinitely strong shock in a Mie-Grüneisen material. Finally, the approximate EOS is used in conjunction with the 1D inviscid Euler equations to calculate a semi-analyticalmore » Guderley-like imploding shock solution in a metal sphere and to determine if and when the solution may be valid for the underlying Mie-Grüneisen EOS.« less

Authors:
 [1];  [1];  [2];  [3];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Univ. of California, Los Angeles, CA (United States). Dept. of Mathematics
  3. Univ. of Washington, Seattle, WA (United States). Dept. of Physics
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1481137
Report Number(s):
LA-UR-17-30971
Journal ID: ISSN 1070-6631
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Fluids
Additional Journal Information:
Journal Volume: 30; Journal Issue: 4; Journal ID: ISSN 1070-6631
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING

Citation Formats

Ramsey, Scott D., Schmidt, Emma Marie, Boyd, Zachary M., Lilieholm, Jennifer Flora, and Baty, Roy S. Converging Shock Flows for a Mie-Grüneisen Equation of State. United States: N. p., 2018. Web. doi:10.1063/1.5018323.
Ramsey, Scott D., Schmidt, Emma Marie, Boyd, Zachary M., Lilieholm, Jennifer Flora, & Baty, Roy S. Converging Shock Flows for a Mie-Grüneisen Equation of State. United States. doi:10.1063/1.5018323.
Ramsey, Scott D., Schmidt, Emma Marie, Boyd, Zachary M., Lilieholm, Jennifer Flora, and Baty, Roy S. Mon . "Converging Shock Flows for a Mie-Grüneisen Equation of State". United States. doi:10.1063/1.5018323. https://www.osti.gov/servlets/purl/1481137.
@article{osti_1481137,
title = {Converging Shock Flows for a Mie-Grüneisen Equation of State},
author = {Ramsey, Scott D. and Schmidt, Emma Marie and Boyd, Zachary M. and Lilieholm, Jennifer Flora and Baty, Roy S.},
abstractNote = {Previous work has shown that the one-dimensional (1D) inviscid compressible flow (Euler) equations admit a wide variety of scale-invariant solutions (including the famous Noh, Sedov, and Guderley shock solutions) when the included equation of state (EOS) closure model assumes a certain scale-invariant form. However, this scale-invariant EOS class does not include even simple models used for shock compression of crystalline solids, including many broadly applicable representations of Mie-Grüneisen EOS. Intuitively, this incompatibility naturally arises from the presence of multiple dimensional scales in the Mie-Grüneisen EOS, which are otherwise absent from scale-invariant models that feature only dimensionless parameters (such as the adiabatic index in the ideal gas EOS). The current work extends previous efforts intended to rectify this inconsistency, by using a scale-invariant EOS model to approximate a Mie-Grüneisen EOS form. To this end, the adiabatic bulk modulus for the Mie-Grüneisen EOS is constructed, and its key features are used to motivate the selection of a scale-invariant approximation form. Here, the remaining surrogate model parameters are selected through enforcement of the Rankine-Hugoniot jump conditions for an infinitely strong shock in a Mie-Grüneisen material. Finally, the approximate EOS is used in conjunction with the 1D inviscid Euler equations to calculate a semi-analytical Guderley-like imploding shock solution in a metal sphere and to determine if and when the solution may be valid for the underlying Mie-Grüneisen EOS.},
doi = {10.1063/1.5018323},
journal = {Physics of Fluids},
number = 4,
volume = 30,
place = {United States},
year = {2018},
month = {4}
}

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