Piston driven converging shock waves in a stiffened gas
Abstract
We present that the problem of a onedimensional (1D) cylindrically or spherically symmetric shock wave converging into an inviscid, ideal gas was first investigated by Guderley[Starke kugelige und zylinrische verdichtungsstosse in der nahe des kugelmitterpunktes bzw. Der zylinderachse,” Luftfahrtforschung 19, 302 (1942)]. In the time since, many authors have discussed the practical notion of how Guderleylike flows might be generated. One candidate is a constant velocity, converging “cylindrical or spherical piston,” giving rise to a converging shock wave in the spirit of its classical, planar counterpart. A limitation of preexisting analyses along these lines is the restriction to flows in materials described by an ideal gas equation of state (EOS) constitutive law. This choice is of course necessary for the direct comparison with the classical Guderley solution, which also features an ideal gas EOS. However, the ideal gas EOS is limited in its utility in describing a wide variety of physical phenomena and, in particular, the shock compression of solid materials. This work is thus intended to provide an extension of previous work to a nonideal EOS. The stiff gas EOS is chosen as a logical starting point due to not only its close resemblance to the ideal gas lawmore »
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1570638
 Report Number(s):
 LAUR1830293
Journal ID: ISSN 10706631; TRN: US2100241
 Grant/Contract Number:
 89233218CNA000001
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physics of Fluids
 Additional Journal Information:
 Journal Volume: 31; Journal Issue: 8; 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
Citation Formats
Ramsey, Scott D., and Baty, Roy S. Piston driven converging shock waves in a stiffened gas. United States: N. p., 2019.
Web. doi:10.1063/1.5109097.
Ramsey, Scott D., & Baty, Roy S. Piston driven converging shock waves in a stiffened gas. United States. doi:10.1063/1.5109097.
Ramsey, Scott D., and Baty, Roy S. Wed .
"Piston driven converging shock waves in a stiffened gas". United States. doi:10.1063/1.5109097. https://www.osti.gov/servlets/purl/1570638.
@article{osti_1570638,
title = {Piston driven converging shock waves in a stiffened gas},
author = {Ramsey, Scott D. and Baty, Roy S.},
abstractNote = {We present that the problem of a onedimensional (1D) cylindrically or spherically symmetric shock wave converging into an inviscid, ideal gas was first investigated by Guderley[Starke kugelige und zylinrische verdichtungsstosse in der nahe des kugelmitterpunktes bzw. Der zylinderachse,” Luftfahrtforschung 19, 302 (1942)]. In the time since, many authors have discussed the practical notion of how Guderleylike flows might be generated. One candidate is a constant velocity, converging “cylindrical or spherical piston,” giving rise to a converging shock wave in the spirit of its classical, planar counterpart. A limitation of preexisting analyses along these lines is the restriction to flows in materials described by an ideal gas equation of state (EOS) constitutive law. This choice is of course necessary for the direct comparison with the classical Guderley solution, which also features an ideal gas EOS. However, the ideal gas EOS is limited in its utility in describing a wide variety of physical phenomena and, in particular, the shock compression of solid materials. This work is thus intended to provide an extension of previous work to a nonideal EOS. The stiff gas EOS is chosen as a logical starting point due to not only its close resemblance to the ideal gas law but also its relevance to the shock compression of various liquid and solid materials. Using this choice of EOS, the solution of a 1D planar piston problem is constructed and subsequently used as the lowest order term in a quasiselfsimilar series expansion intended to capture both curvilinear and nonideal EOS effects. The solution associated with this procedure provides correction terms to the 1D planar solution so that the expected accelerating shock trajectory and nontrivially varying state variable profiles can be obtained. This solution is further examined in the limit as the converging shock wave approaches the 1D curvilinear origin. Lastly, given the stiff gas EOS is not otherwise expected to admit a Guderleylike solution when coupled to the inviscid Euler equations, this work thus provides the semianalytical limiting behavior of a flow that cannot be otherwise captured using selfsimilar analysis.},
doi = {10.1063/1.5109097},
journal = {Physics of Fluids},
number = 8,
volume = 31,
place = {United States},
year = {2019},
month = {8}
}
Web of Science
Works referenced in this record:
On the question of universality of imploding shock waves
journal, August 2008
 Hornung, H. G.; Pullin, D. I.; Ponchaut, N. F.
 Acta Mechanica, Vol. 201, Issue 14
On the Existence of SelfSimilar Converging Shocks in NonIdeal 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
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
Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux
journal, September 1987
 Noh, W. F.
 Journal of Computational Physics, Vol. 72, Issue 1
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
Second‐type self‐similar solutions to the strong explosion problem
journal, April 1993
 Waxman, Eli; Shvarts, Dov
 Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 4
A selfsimilar isochoric implosion for fast ignition
journal, August 2007
 Clark, D. S.; Tabak, M.
 Nuclear Fusion, Vol. 47, Issue 9
On the motion of piston in a polytropic gas
journal, January 1977
 Kozmanov, M. Iu.
 Journal of Applied Mathematics and Mechanics, Vol. 41, Issue 6
Converging shock flows for a MieGrüneisen equation of state
journal, April 2018
 Ramsey, Scott D.; Schmidt, Emma M.; Boyd, Zachary M.
 Physics of Fluids, Vol. 30, Issue 4
Doubledetonation supernovae of subChandrasekhar mass white dwarfs
journal, October 2007
 Fink, M.; Hillebrandt, W.; Röpke, F. K.
 Astronomy & Astrophysics, Vol. 476, Issue 3
Solutions of the Noh problem for various equations of state using LIE groups
journal, January 2000
 Axford, Roy A.
 Laser and Particle Beams, Vol. 18, Issue 1
Convergence of Strong Shock in a Van der Waals Gas
journal, January 2006
 Arora, Rajan; Sharma, V. D.
 SIAM Journal on Applied Mathematics, Vol. 66, Issue 5
The converging shock wave from a spherical or cylindrical piston
journal, July 1982
 Dyke, Milton Van; Guttmann, A. J.
 Journal of Fluid Mechanics, Vol. 120
Symmetries of the gas dynamics equations using the differential form method
journal, November 2017
 Ramsey, Scott D.; Baty, Roy S.
 Journal of Mathematical Physics, Vol. 58, Issue 11
The Riemann problem for fluid flow of real materials
journal, January 1989
 Menikoff, Ralph; Plohr, Bradley J.
 Reviews of Modern Physics, Vol. 61, Issue 1
Initial Behavior of a Spherical Blast
journal, November 1952
 McFadden, J. A.
 Journal of Applied Physics, Vol. 23, Issue 11
A simplified analysis of spherical and cylindrical blast waves
journal, August 1961
 Friedman, Manfred P.
 Journal of Fluid Mechanics, Vol. 11, Issue 1
SelfSimilar Solutions for Converging Shocks and Collapsing Cavities
journal, April 1981
 Lazarus, Roger B.
 SIAM Journal on Numerical Analysis, Vol. 18, Issue 2
An analytic description of converging shock waves
journal, January 1998
 Chisnell, R. F.
 Journal of Fluid Mechanics, Vol. 354
Verification Assessment of Piston Boundary Conditions for Lagrangian Simulation of the Guderley Problem
journal, September 2017
 Ramsey, Scott D.; Lilieholm, Jennifer F.
 Journal of Verification, Validation and Uncertainty Quantification, Vol. 2, Issue 3
Analysis of selfsimilar problems of imploding shock waves by the method of characteristics
journal, January 1983
 Nakamura, Y.
 Physics of Fluids, Vol. 26, Issue 5
Works referencing / citing this record:
On the NobleAbel stiffenedgas equation of state
journal, November 2019
 Radulescu, M. I.
 Physics of Fluids, Vol. 31, Issue 11
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