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TECHNICAL PAPERS

Partially Averaged Navier-Stokes Method for Turbulence: Fixed Point Analysis and Comparison With Unsteady Partially Averaged Navier-Stokes

[+] Author and Article Information
Sharath S. Girimaji, Ravi Srinivasan

Aerospace Engineering, Texas A&M University, College Station, TX 77843

Eunhwan Jeong

 Korea Aerospace Research Institute, 45 Eoeun-Dong, Youscong-gu, Daejeon 305-333, Korea

J. Appl. Mech 73(3), 422-429 (Nov 08, 2005) (8 pages) doi:10.1115/1.2173677 History: Received December 08, 2003; Revised November 08, 2005

Hybrid/bridging models that combine the advantages of Reynolds averaged Navier Stokes (RANS) method and large-eddy simulations are being increasingly used for simulating turbulent flows with large-scale unsteadiness. The objective is to obtain accurate estimates of important large-scale fluctuations at a reasonable cost. In order to be effective, these bridging methods must posses the correct “energetics”: that is, the right balance between production (P) and dissipation (ε). If the model production-to-dissipation ratio (Pε) is inconsistent with turbulence physics at that cutoff, the computations will be unsuccessful. In this paper, we perform fixed-point analyses of two bridging models—partially-averaged Navier Stokes (PANS) and unsteady RANS (URANS)—to examine the behavior of production-to-dissipation ratio. It is shown that the URANS-(Pε) ratio is too high rendering it incapable of resolving much of the fluctuations. On the other hand, the PANS-(Pε) ratio allows the model to vary smoothly from RANS to DNS depending upon the values of its resolution control parameters.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Evolution of P∕ε for various fk. Steady forcing.

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Figure 2

Evolution of b12 for various fk. Steady forcing.

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Figure 3

Evolution of (P∕ε) for various ω (unsteady forcing). fk=0.4.

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Figure 4

Evolution of b12 for various ω (unsteady forcing). fk=0.4.

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Figure 5

Evolution of (P∕ε) for various fk (unsteady forcing). ω=0.2.

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Figure 6

Evolution of b12 for various fk (unsteady forcing). ω=0.2.

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Figure 7

Evolution of running average of (P∕ε) for various fk. ω=0.2.

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Figure 8

Evolution of running average of b12 for various fk. ω=0.2.

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Figure 9

Vorticity contours from PANS simulations (of flow past square cylinder) of various fk values. fk=1 case corresponds to URANS.

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Figure 10

Eddy-viscosity contours from PANS simulations (of flow past square cylinder) of various fk values. fk=1 case corresponds to URANS.

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Figure 11

DES calculations of a flow past backward facing step. Midplane vorticity contours and isovorticity surfaces.

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Figure 12

URANS calculations of a flow past backward facing step. Midplane vorticity contours and isovorticity surfaces.

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Figure 13

PANS calculations of a flow past backward facing step. Midplane vorticity contours and isovorticity surfaces.

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