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RESEARCH PAPERS: Model Development

Compressibility and Variable Density Effects in Turbulent Boundary layers

[+] Author and Article Information
Kunlun Liu1

Department of Mechanical Engineering, Iowa State University, Ames, IA, 50011liukl@umn.edu

Richard H. Pletcher

Department of Mechanical Engineering, Iowa State University, Ames, IA, 50011

1

Present address: Department of Biomedical Engineering, University of Minnesota. Minneapolis, MN 55455.

J. Heat Transfer 129(4), 441-448 (Nov 17, 2006) (8 pages) doi:10.1115/1.2709971 History: Received April 06, 2006; Revised November 17, 2006

Two compressible turbulent boundary layers have been calculated by using direct numerical simulation. One case is a subsonic turbulent boundary layer with constant wall temperature for which the wall temperature is 1.58 times the freestream temperature and the other is a supersonic adiabatic turbulent boundary layer subjected to a supersonic freestream with a Mach number 1.8. The purpose of this study is to test the strong Reynolds analogy (SRA), the Van Driest transformation, and the applicability of Morkovin’s hypothesis. For the first case, the influence of the variable density effects will be addressed. For the second case, the role of the density fluctuations, the turbulent Mach number, and dilatation on the compressibility will be investigated. The results show that the Van Driest transformation and the SRA are satisfied for both of the flows. Use of local properties enable the statistical curves to collapse toward the corresponding incompressible curves. These facts reveal that both the compressibility and variable density effects satisfy the similarity laws. A study about the differences between the compressibility effects and the variable density effects associated with heat transfer is performed. In addition, the difference between the Favre average and Reynolds average is measured, and the SGS terms of the Favre-filtered Navier-Stokes equations are calculated and analyzed.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Comparison of the mean streamwise velocity profiles

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Figure 2

Comparison of the velocity rms profiles

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Figure 3

Comparison of mean streamwise velocity with experimental results reported by (20)

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Figure 4

Comparison of rms profiles normalized using local properties with the DNS results reported by (21)

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Figure 5

The plots of −u′v′¯∕Uτ,local versus Y+

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Figure 6

Plot of the mean density, ρ¯∕ρe, and the rms of density, ρ′2¯∕ρe as functions of Y+

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Figure 7

The mean and rms of dilatation of velocities versus Y+, i.e., θ¯δd∕uτ and θ′2¯δd∕uτ, where δd is the displacement thickness

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Figure 8

Turbulent Mach number Mat as functions of y+

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Figure 9

Turbulent Prandtl number Prt as functions of Y+ and the test of strong Reynolds analogy as express by Eq. 7

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Figure 10

Comparison of (u1̃−u1¯)∕uτ

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Figure 11

The components of τ11. The solid line is τ11, the dashed line is the τ11t, the dashed-dotted line is τ11c, and the dashed-double-dotted line is τ11F. The square samples are τ22, the triangle samples are τ22t, the right triangular samples are τ22c, and the left triangular samples are τ22F.

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Figure 12

Comparison of γ and π versus Y+, where the solid line is γ for the case 1, the dashed-dotted line is γ for the case 2, the dashed line is π for the case 1, the dashed-double-dotted line if π for the case 2

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