Converging Shock Flows for a MieGrüneisen Equation of State
Abstract
Previous work has shown that the onedimensional (1D) inviscid compressible flow (Euler) equations admit a wide variety of scaleinvariant solutions (including the famous Noh, Sedov, and Guderley shock solutions) when the included equation of state (EOS) closure model assumes a certain scaleinvariant form. However, this scaleinvariant EOS class does not include even simple models used for shock compression of crystalline solids, including many broadly applicable representations of MieGrüneisen EOS. Intuitively, this incompatibility naturally arises from the presence of multiple dimensional scales in the MieGrüneisen EOS, which are otherwise absent from scaleinvariant 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 scaleinvariant EOS model to approximate a MieGrüneisen EOS form. To this end, the adiabatic bulk modulus for the MieGrüneisen EOS is constructed, and its key features are used to motivate the selection of a scaleinvariant approximation form. Here, the remaining surrogate model parameters are selected through enforcement of the RankineHugoniot jump conditions for an infinitely strong shock in a MieGrüneisen material. Finally, the approximate EOS is used in conjunction with the 1D inviscid Euler equations to calculate a semianalyticalmore »
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Univ. of California, Los Angeles, CA (United States). Dept. of Mathematics
 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):
 LAUR1730971
Journal ID: ISSN 10706631
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physics of Fluids
 Additional Journal Information:
 Journal Volume: 30; Journal Issue: 4; Journal ID: ISSN 10706631
 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 MieGrüneisen 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 MieGrüneisen 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 MieGrüneisen 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 MieGrüneisen 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 onedimensional (1D) inviscid compressible flow (Euler) equations admit a wide variety of scaleinvariant solutions (including the famous Noh, Sedov, and Guderley shock solutions) when the included equation of state (EOS) closure model assumes a certain scaleinvariant form. However, this scaleinvariant EOS class does not include even simple models used for shock compression of crystalline solids, including many broadly applicable representations of MieGrüneisen EOS. Intuitively, this incompatibility naturally arises from the presence of multiple dimensional scales in the MieGrüneisen EOS, which are otherwise absent from scaleinvariant 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 scaleinvariant EOS model to approximate a MieGrüneisen EOS form. To this end, the adiabatic bulk modulus for the MieGrüneisen EOS is constructed, and its key features are used to motivate the selection of a scaleinvariant approximation form. Here, the remaining surrogate model parameters are selected through enforcement of the RankineHugoniot jump conditions for an infinitely strong shock in a MieGrüneisen material. Finally, the approximate EOS is used in conjunction with the 1D inviscid Euler equations to calculate a semianalytical Guderleylike imploding shock solution in a metal sphere and to determine if and when the solution may be valid for the underlying MieGrüneisen EOS.},
doi = {10.1063/1.5018323},
journal = {Physics of Fluids},
number = 4,
volume = 30,
place = {United States},
year = {2018},
month = {4}
}
Web of Science
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