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Shock interactions with heavy gaseous elliptic cylinders: Two leeward-side shock competition modes and a heuristic model for interfacial circulation deposition at early times

Ray, Jaideep and Samtaney, Ravi and Zabusky, Norman J. (2000) Shock interactions with heavy gaseous elliptic cylinders: Two leeward-side shock competition modes and a heuristic model for interfacial circulation deposition at early times. Physics of Fluids, 12 (3). pp. 707-716. ISSN 1070-6631. https://resolver.caltech.edu/CaltechAUTHORS:20170408-161231294

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Abstract

We identify two different modes, types I and II, of the interaction for planar shocks accelerating heavy prolate gaseous ellipses. These modes arise from different interactions of the incident shock (IS) and transmitted shock (TS) on the leeward side of the ellipse. A time ratio t_T/t_I(M,η,λ,γ_0,γ_b), which characterizes the mode of interaction, is derived heuristically. Here, the principal parameters governing the interaction are the Mach number of the shock (M), the ratio of the density of the ellipse to the ambient gas density, (η>1), γ_0, γ_b (the ratios of specific heats of the two gases), λ (the aspect ratio). Salient events in shock–ellipse interactions are identified and correlated with their signatures in circulation budgets and on-axis space–time pressure diagrams. The two modes yield different mechanisms of the baroclinic vorticity generation. We present a heuristic model for the net baroclinic circulation generated on the interface at the end of the early-time phase by both the IS and TS and validate the model via numerical simulations of the Euler equations. In the range 1.2⩽M⩽3.5, 1.54⩽η⩽5.04, and λ=1.5 and 3.0, our model predicts the baroclinic circulation on the interface within a band of ±10% in comparison to converged numerical simulations.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.870276DOIArticle
ORCID:
AuthorORCID
Samtaney, Ravi0000-0002-4702-6473
Additional Information:© 2000 American Institute of Physics. (Received 17 August 1998; accepted 15 November 1999) The computations were done on the T3E at the Pittsburgh Supercomputing Center and the Origin2000 at NCSA, University of Illinois, Urbana–Champaign. A portion of this work was done in Vizlab, part of which is supported by CAIP, Rutgers University. Ravi Samtaney gratefully acknowledges the support of the Data Analysis Group, NAS Division at the NASA Ames Research Center. The work was supported by DOE under grants from Dr. D. Hitchcock and Dr. F. Howes.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)UNSPECIFIED
Subject Keywords:Numerical modeling; Vortex dynamics; Heat capacity; Mach numbers; Band models
Issue or Number:3
Record Number:CaltechAUTHORS:20170408-161231294
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170408-161231294
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76146
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:22 Jun 2017 23:01
Last Modified:03 Oct 2019 16:58

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