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Physics of Fluids / Volume 16 / Issue 3 / ARTICLES

Phys. Fluids 16, 530 (2004); http://dx.doi.org/10.1063/1.1637604 (16 pages)

Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2.25

S. Pirozzoli1, F. Grasso1, and T. B. Gatski2

1Dipartimento di Meccanica ed Aeronautica, Università di Roma “La Sapienza,” via Eudossiana 18, 00184 Roma, Italy
2Computational Modeling & Simulation Branch, NASA Langley Research Center, Hampton, Virginia 23681

(Received 4 November 2002; accepted 15 October 2003; published online 13 January 2004)

A spatially developing supersonic adiabatic flat plate boundary layer flow (at M∞ = 2.25 and Reθ ≈ 4000) is analyzed by means of direct numerical simulation. The numerical algorithm is based on a mixed weighted essentially nonoscillatory compact-difference method for the three-dimensional Navier–Stokes equations. The main objectives are to assess the validity of Morkovin’s hypothesis and Reynolds analogies, and to analyze the controlling mechanisms for turbulence production, dissipation, and transport. The results show that the essential dynamics of the investigated turbulent supersonic boundary layer flow closely resembles the incompressible pattern. The Van Driest transformed mean velocity obeys the incompressible law-of-the-wall, and the mean static temperature field exhibits a quadratic dependency upon the mean velocity, as predicted by the Crocco–Busemann relation. The total temperature has been found not to be precisely uniform, and total temperature fluctuations are found to be non-negligible. Consistently, the turbulent Prandtl number is not unity, and it varies between 0.7 and 0.8 in the outer part of the boundary layer. Nonetheless, a modified strong Reynolds analogy is still verified. In agreement with the low Mach number results, the streamwise velocity component and the temperature are only weakly anti-correlated. The turbulent kinetic energy budget also shows similarities with the incompressible case provided all terms of the equation are properly scaled; indeed, the leading compressibility contributions are negligible throughout the boundary layer. © 2004 American Institute of Physics.

© 2004 American Institute of Physics

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KEYWORDS and PACS

Keywords

boundary layer turbulence, numerical analysis, fluctuations, flow visualisation, supersonic flow, flow simulation, Mach number, Navier-Stokes equations

PACS

  • 47.27.nb

    Boundary layer turbulence

  • 47.40.Ki

    Supersonic and hypersonic flows

  • 47.11.-j

    Computational methods in fluid dynamics

  • 47.10.-g

    General theory in fluid dynamics

  • 47.80.-v

    Instrumentation and measurement methods in fluid dynamics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.1637604

PUBLICATION DATA

ISSN

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

Publisher

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

For access to fully linked references, you need to log in.
    S. Pirozzoli, F. Grasso, and A. D'Andrea, "Interaction of a shock wave with two counter-rotating vortices: Shock dynamics and sound production," Phys. Fluids 13, 3460 (2001)PHFLE6000013000011003460000001.


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