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Physics of Fluids / Volume 21 / Issue 12 / ARTICLES / Compressible Flows

Phys. Fluids 21, 126101 (2009); http://dx.doi.org/10.1063/1.3275856 (12 pages)

Direct numerical simulation of canonical shock/turbulence interaction

Johan Larsson and Sanjiva K. Lele

Center for Turbulence Research, Stanford University, 488 Escondido Mall, Stanford, California 94305-3035, USA

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(Received 13 January 2009; accepted 10 November 2009; published online 28 December 2009)

A set of direct numerical simulations of isotropic turbulence passing through a nominally normal shock wave is presented. Upstream of the shock, the microscale Reynolds number is 40, the mean Mach number is 1.3–6.0, and the turbulence Mach number is 0.16–0.38. It is shown that the Kolmogorov scale decreases during the shock interaction, which implies that the grid resolution needed to resolve the viscous dissipation is finer than that used in previous studies. This leads to some qualitative differences with previous work, e.g., a rapid increase in the streamwise vorticity variance behind the shock and large anisotropy of the postshock Reynolds stresses. The instantaneous structure of the shock/turbulence interaction is examined using averages conditioned on the instantaneous shock strength. For locally strong compressions, the flow is characterized by overcompression, followed by an expansion. At points where the shock is locally weak, the profiles differ qualitatively depending on the strength of the incoming turbulence relative to the strength of the shock, as measured by the turbulence and mean Mach numbers, respectively. In the wrinkled shock regime, these profiles are discontinuous and the shock has a simple topology. In the broken shock regime, the weak interaction profiles are smooth without any discontinuity.

© 2009 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. NUMERICAL METHOD
    1. Inflow turbulence
    2. Outflow boundary condition
    3. Grid sensitivity
  3. SINGLE-POINT STATISTICS
    1. Mean profiles
    2. Reynolds stresses
    3. Vorticity variances
    4. Length scales
  4. INSTANTANEOUS RESULTS
    1. The “wrinkled” and “broken” shock regimes
    2. Conditionally averaged profiles
  5. SUMMARY AND CONCLUSIONS

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KEYWORDS and PACS

Keywords

flow simulation, Mach number, shock waves, turbulence, vortices

PACS

  • 47.40.Nm

    Shock wave interactions and shock effects

  • 47.32.-y

    Vortex dynamics; rotating fluids

  • 47.27.-i

    Turbulent flows

  • 47.11.-j

    Computational methods in fluid dynamics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3275856

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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    References

    G. P. Zank, Y. Zhou, W. H. Matthaeus, and W. K. M. Rice, “The interaction of turbulence with shock waves: A basic model,” Phys. Fluids 14, 3766 (2002)PHFLE6000014000011003766000001.

    J. R. Ristorcelli and G. A. Blaisdell, “Consistent initial conditions for the DNS of compressible turbulence,” Phys. Fluids 9, 4 (1997)PHFLE6000009000001000004000001.

    S. K. Lele, “Shock-jump relations in a turbulent flow,” Phys. Fluids A 4, 2900 (1992)PFADEB000004000012002900000001.


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