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Computing multi-mode shock-induced compressible turbulent mixing at late times

Published online by Cambridge University Press:  19 August 2015

T. Oggian ,
D. Drikakis ,
D. L. Youngs  and
R. J. R. Williams
T. Oggian
Affiliation:
Cranfield University, Cranfield, Bedfordshire MK43 0AL, UK
D. Drikakis*
Affiliation:
Faculty of Engineering, University of Strathclyde, Glasgow G1 1XW, UK
D. L. Youngs
Affiliation:
AWE, Aldermaston, Reading, Berkshire RG7 4PR, UK
R. J. R. Williams
Affiliation:
AWE, Aldermaston, Reading, Berkshire RG7 4PR, UK
*
†Email address for correspondence: dimitris.drikakis@strath.ac.uk
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Abstract

Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late-time behaviour of a single-shocked Richtmyer–Meshkov instability (RMI) and the associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that the RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field, the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible–incompressible solver that removes the low-Mach-number limitations of the compressible solvers, thus allowing numerical simulations of late-time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

JFM classification

Compressible Flows: Shock waves Turbulent Flows: Turbulence simulation Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 779 , 25 September 2015 , pp. 411 - 431
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© Crown Owned Copyright. Published by Cambridge University Press 2015 

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