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Title: The stability of the contact interface of cylindrical and spherical shock tubes

Abstract

The stability of the contact interface for radial shock tubes is investigated as a model for explosive dispersal. The advection upstream splitting method with velocity and pressure diffusion (AUSM+-up) is used to solve for the radial base flow. To explore the stability of the resulting contact interface, perturbed governing equations are derived assuming harmonic modes in the transverse directions. The perturbed harmonic flow is solved by assuming an initial disturbance and using a perturbed version of AUSM+-up derived in this paper. The intensity of the perturbation near the contact interface is computed and compared to theoretical results obtained by others. Despite the simplifying assumptions of the theoretical analysis, very good agreement is confirmed. Not only can the magnitude of the instability be predicted during the initial expansion, but also remarkably the agreement between the numerical and theoretical results can be maintained through the collision between the secondary shock and the contact interface. Since the theoretical results only depend upon the time evolution of the base flow, the stability of various modes could be quickly studied without explicitly solving a system of partial differential equations for the perturbed flow.

Authors:
ORCiD logo [1];  [1]
  1. Univ. of Florida, Gainesville, FL (United States)
Publication Date:
Research Org.:
Univ. of Florida, Gainesville, FL (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1540193
Alternate Identifier(s):
OSTI ID: 1440386
Grant/Contract Number:  
NA0002378
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physics of Fluids
Additional Journal Information:
Journal Volume: 30; Journal Issue: 6; Journal ID: ISSN 1070-6631
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING

Citation Formats

Crittenden, Paul E., and Balachandar, S. The stability of the contact interface of cylindrical and spherical shock tubes. United States: N. p., 2018. Web. doi:10.1063/1.5026583.
Crittenden, Paul E., & Balachandar, S. The stability of the contact interface of cylindrical and spherical shock tubes. United States. https://doi.org/10.1063/1.5026583
Crittenden, Paul E., and Balachandar, S. Tue . "The stability of the contact interface of cylindrical and spherical shock tubes". United States. https://doi.org/10.1063/1.5026583. https://www.osti.gov/servlets/purl/1540193.
@article{osti_1540193,
title = {The stability of the contact interface of cylindrical and spherical shock tubes},
author = {Crittenden, Paul E. and Balachandar, S.},
abstractNote = {The stability of the contact interface for radial shock tubes is investigated as a model for explosive dispersal. The advection upstream splitting method with velocity and pressure diffusion (AUSM+-up) is used to solve for the radial base flow. To explore the stability of the resulting contact interface, perturbed governing equations are derived assuming harmonic modes in the transverse directions. The perturbed harmonic flow is solved by assuming an initial disturbance and using a perturbed version of AUSM+-up derived in this paper. The intensity of the perturbation near the contact interface is computed and compared to theoretical results obtained by others. Despite the simplifying assumptions of the theoretical analysis, very good agreement is confirmed. Not only can the magnitude of the instability be predicted during the initial expansion, but also remarkably the agreement between the numerical and theoretical results can be maintained through the collision between the secondary shock and the contact interface. Since the theoretical results only depend upon the time evolution of the base flow, the stability of various modes could be quickly studied without explicitly solving a system of partial differential equations for the perturbed flow.},
doi = {10.1063/1.5026583},
url = {https://www.osti.gov/biblio/1540193}, journal = {Physics of Fluids},
issn = {1070-6631},
number = 6,
volume = 30,
place = {United States},
year = {2018},
month = {6}
}

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Works referenced in this record:

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    Temperature determination in a shock tube using hydroxyl radical A-X band emission
    journal, February 2019