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Turbulence structure behind the shock in canonical shock–vortical turbulence interaction

Published online by Cambridge University Press:  01 September 2014

Jaiyoung Ryu  and
Daniel Livescu
Jaiyoung Ryu
Affiliation:
CCS-2, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Daniel Livescu*
Affiliation:
CCS-2, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
*
†Email address for correspondence: livescu@lanl.gov
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Abstract

The interaction between vortical isotropic turbulence (IT) and a normal shock wave is studied using direct numerical simulation (DNS) and linear interaction analysis (LIA). In previous studies, agreement between the simulation results and the LIA predictions has been limited and, thus, the significance of LIA has been underestimated. In this paper, we present high-resolution simulations which accurately solve all flow scales (including the shock-wave structure) and extensively cover the parameter space (the shock Mach number, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}M_s$, ranges from 1.1 to 2.2 and the Taylor Reynolds number, ${\mathit{Re}}_{\lambda }$, ranges from 10 to 45). The results show, for the first time, that the turbulence quantities from DNS converge to the LIA solutions as the turbulent Mach number, $M_t$, becomes small, even at low upstream Reynolds numbers. The classical LIA formulae are extended to compute the complete post-shock flow fields using an IT database. The solutions, consistent with the DNS results, show that the shock wave significantly changes the topology of the turbulent structures, with a symmetrization of the third invariant of the velocity gradient tensor and ($M_s$-mediated) of the probability density function (PDF) of the longitudinal velocity derivatives, and an $M_s$-dependent increase in the correlation between strain and rotation.

JFM classification

Turbulent Flows: Compressible turbulence Compressible Flows: Shock waves Turbulent Flows: Turbulence simulation
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , R1
Copyright
© 2014 Cambridge University Press 

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Footnotes

‡

Present address: Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA.

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