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TECHNICAL PAPERS

# Partially-Averaged Navier-Stokes Model for Turbulence: A Reynolds-Averaged Navier-Stokes to Direct Numerical Simulation Bridging Method

[+] Author and Article Information
Sharath S. Girimaji

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

J. Appl. Mech 73(3), 413-421 (Nov 08, 2005) (9 pages) doi:10.1115/1.2151207 History: Received February 05, 2004; Revised November 08, 2005

## Abstract

A turbulence bridging method purported for any filter-width or scale resolution—fully averaged to completely resolved—is developed. The method is given the name partially averaged Navier-Stokes (PANS) method. In PANS, the model filter width (extent of partial averaging) is controlled through two parameters: the unresolved-to-total ratios of kinetic energy $(fk)$ and dissipation $(fε)$. The PANS closure model is derived formally from the Reynolds-averaged Navier-Stokes (RANS) model equations by addressing the following question: if RANS represents the closure for fully averaged statistics, what is the corresponding closure for partially averaged statistics? The PANS equations vary smoothly from RANS equations to Navier-Stokes (direct numerical simulation) equations, depending on the values of the filter-width control parameters. Preliminary results are very encouraging.

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## Figures

Figure 1

Grid-size sensitivity study in a 2D flow past a cylinder in 2D domain. (a) Centerline velocity profile from various PANS fk=0.6 computations on different grids. The time step in all computations is 0.008s. (b) Similar plot for fk=0.8 computations. The time step in all these computations is 0.025s.

Figure 2

Time-step sensitivity study. In all the computations fk=0.6 and grid size is 95×106

Figure 3

Profiles of normal Reynolds stresses along the centerline from various calculations: fk=1.0, -∙-∙-; fk=0.7 ⋯∙; fk=0.4, —; LES, 엯; Durao expt., ▵; Lyn expt., +

Figure 4

Profiles of Coefficient of pressure distribution along the cylinder surface for various fk values: ∗, Experimental data from Achenbach for flow Reynolds number of ReD=1×105; 엯, LES data from Wang at ReD106; ▵, DES data from Travin (14) at ReD1.4×105 (data from run LS 8 corresponding to laminar separation case. For laminar separation to occur the turbulent viscosity is set to zero at the inflow boundary); —, data from PANS with fk=0.5; ⋯∙, data from PANS with fk=0.7; -∙-∙-, data from PANS with fk=1.0.

Figure 5

Vorticity structure in 3D driven cavity flow computations with various fk values

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