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 »
- 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 Laboratory (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. https://doi.org/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. https://doi.org/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 = {Mon Apr 02 00:00:00 EDT 2018},
month = {Mon Apr 02 00:00:00 EDT 2018}
}
Web of Science
Works referenced in this record:
Lie group invariance properties of radiation hydrodynamics equations and their associated similarity solutions
journal, January 1986
- Coggeshall, Stephen V.; Axford, Roy A.
- Physics of Fluids, Vol. 29, Issue 8
On the Existence of Self-Similar Converging Shocks in Non-Ideal Materials
journal, August 2017
- Boyd, Z. M.; Ramsey, S. D.; Baty, R. S.
- The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 70, Issue 4
Theorie des festen Zustandes einatomiger Elemente
journal, January 1912
- Grüneisen, E.
- Annalen der Physik, Vol. 344, Issue 12
The Guderley problem revisited
journal, February 2012
- Ramsey, Scott D.; Kamm, James R.; Bolstad, John H.
- International Journal of Computational Fluid Dynamics, Vol. 26, Issue 2
Zur kinetischen Theorie der einatomigen Körper
journal, January 1903
- Mie, Gustav
- Annalen der Physik, Vol. 316, Issue 8
On the Propagation and Structure of the Blast Wave, I
journal, September 1953
- Sakurai, Akira
- Journal of the Physical Society of Japan, Vol. 8, Issue 5
On the Propagation and Structure of a Blast Wave, II
journal, March 1954
- Sakurai, Akira
- Journal of the Physical Society of Japan, Vol. 9, Issue 2
Analytic solutions of hydrodynamics equations
journal, May 1991
- Coggeshall, S. V.
- Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5
A self-similar isochoric implosion for fast ignition
journal, August 2007
- Clark, D. S.; Tabak, M.
- Nuclear Fusion, Vol. 47, Issue 9
Double-detonation supernovae of sub-Chandrasekhar mass white dwarfs
journal, October 2007
- Fink, M.; Hillebrandt, W.; Röpke, F. K.
- Astronomy & Astrophysics, Vol. 476, Issue 3
Selfsimilar Spherical Compression Waves in Gas Dynamics
journal, January 1982
- Meyer-ter-Vehn, J.; Schalk, C.
- Zeitschrift für Naturforschung A, Vol. 37, Issue 8
Group‐invariant solutions and optimal systems for multidimensional hydrodynamics
journal, October 1992
- Coggeshall, S. V.; Meyer‐ter‐Vehn, J.
- Journal of Mathematical Physics, Vol. 33, Issue 10
Thermodynamic stability of the Mie–Grüneisen equation of state, and its relevance to hydrocode computations
journal, September 1991
- Segletes, Steven B.
- Journal of Applied Physics, Vol. 70, Issue 5
Self-Similar Solutions for Converging Shocks and Collapsing Cavities
journal, April 1981
- Lazarus, Roger B.
- SIAM Journal on Numerical Analysis, Vol. 18, Issue 2
Solution of the Noh problem using the universal symmetry of the gas dynamics equations
journal, July 2016
- Ramsey, S. D.; Boyd, Z. M.; Burnett, S. C.
- Shock Waves, Vol. 27, Issue 3
Empirical equations of state for solids
journal, October 1975
- Towle, Laird C.
- Applied Physics, Vol. 8, Issue 2
Scaling, self-similarity, and intermediate asymptotics
journal, May 1998
- Riley, N.
- European Journal of Mechanics - B/Fluids, Vol. 17, Issue 3
Works referencing / citing this record:
Convergence of strong shock waves in non-ideal magnetogasdynamics
journal, November 2018
- Chauhan, Antim; Arora, Rajan; Tomar, Amit
- Physics of Fluids, Vol. 30, Issue 11
Piston driven converging shock waves in a stiffened gas
journal, August 2019
- Ramsey, Scott D.; Baty, Roy S.
- Physics of Fluids, Vol. 31, Issue 8
A boundary condition for Guderley’s converging shock problem
journal, December 2019
- Ruby, J. J.; Rygg, J. R.; Gaffney, J. A.
- Physics of Fluids, Vol. 31, Issue 12