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Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number

Published online by Cambridge University Press:  02 March 2011

L. DUAN ,
I. BEEKMAN  and
M. P. MARTÍN
L. DUAN
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA
I. BEEKMAN
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA
M. P. MARTÍN*
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA
*
†Email address for correspondence: pmartin@umiacs.umd.edu
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Abstract

In this paper, we perform direct numerical simulations (DNS) of turbulent boundary layers with nominal free-stream Mach number ranging from 0.3 to 12. The main objective is to assess the scalings with respect to the mean and turbulence behaviours as well as the possible breakdown of the weak compressibility hypothesis for turbulent boundary layers at high Mach numbers (M > 5). We find that many of the scaling relations, such as the van Driest transformation for mean velocity, Walz's relation, Morkovin's scaling and the strong Reynolds analogy, which are derived based on the weak compressibility hypothesis, remain valid for the range of free-stream Mach numbers considered. The explicit dilatation terms such as pressure dilatation and dilatational dissipation remain small for the present Mach number range, and the pressure–strain correlation and the anisotropy of the Reynolds stress tensor are insensitive to the free-stream Mach number. The possible effects of intrinsic compressibility are reflected by the increase in the fluctuations of thermodynamic quantities (p′rms/pw, ρ′rms/ρ, T′rms/T) and turbulence Mach numbers (Mt, M′rms), the existence of shocklets, the modification of turbulence structures (near-wall streaks and large-scale motions) and the variation in the onset of intermittency.

JFM classification

Turbulent Flows: Compressible turbulence Aerodynamics: High-speed flow Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 672 , 10 April 2011 , pp. 245 - 267
Copyright
Copyright © Cambridge University Press 2011

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