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Research Papers: Flows in Complex Systems

Application of Realizability and Shock Unsteadiness to kε Simulations of Under-Expanded Axisymmetric Supersonic Free Jets

[+] Author and Article Information
Babak Emami1

Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, M5S 3G8, Canadabemami@mie.utoronto.ca

Markus Bussmann

Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, M5S 3G8, Canadabussmann@mie.utoronto.ca

Honghi Tran

Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, ON, M5S 3E5, Canadahonghi.tran@utoronto.ca

1

Corresponding author.

J. Fluids Eng 132(4), 041104 (Apr 15, 2010) (7 pages) doi:10.1115/1.4001341 History: Received June 26, 2009; Revised February 12, 2010; Published April 15, 2010; Online April 15, 2010

An explicit cell-centered finite volume solver coupled to a kε turbulence model corrected for structural compressibility fails to satisfactorily predict the behavior of under-expanded supersonic jets exhausting into still air, because the model does not properly account for the turbulence/shock wave interaction. Two approaches are examined: imposing a realizability constraint and taking into account shock unsteadiness effects. Although both corrections yield better agreement with experimental data of under-expanded jets, the realizability constraint yields better results than the shock unsteadiness correction.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 8

Calculations of the under-expanded jet of Panda and Seasholtz (32) with Thivet’s realizability constraint

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Figure 7

Calculation of the under-expanded jet of Norum and Seiner (35) with Thivet’s realizability constraint, and the Sinha-2005 correction, r/D=0.25

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Figure 6

Distribution of the eddy viscosity along the jet centerline, calculated with the compressibility-corrected model, Thivet’s realizability constraint, and the Sinha-2005 correction

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Figure 5

Mach number contours corresponding (from top to bottom) to calculations with the compressibility-corrected model, Thivet’s realizability constraint, and the Sinha-2005 correction

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Figure 4

Calculations of normalized pressure (top) and Mach number (bottom) with the Sinha-2005 shock unsteadiness correction

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Figure 3

Calculations of normalized pressure (top) and Mach number (bottom) with Thivet and Durbin realizability constraints

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Figure 2

Normalized pressure (top) and Mach number (bottom) along the centerline of an under-expanded jet, as a function of mesh size, calculated by the compressibility-corrected model

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Figure 1

The decaying shock-cell structure: flow visualization of an under-expanded jet with an exit Mach number of 2.53 and Pe/P∞=3.12

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