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Research Papers: Fundamental Issues and Canonical Flows

# Partially Averaged Navier–Stokes (PANS) Method for Turbulence Simulations: Flow Past a Circular Cylinder

[+] Author and Article Information
Sunil Lakshmipathy

Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141

Sharath S. Girimaji1

Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141girimaji@aero.tamu.edu

1

Corresponding author.

J. Fluids Eng 132(12), 121202 (Dec 22, 2010) (9 pages) doi:10.1115/1.4003154 History: Received June 03, 2010; Revised October 22, 2010; Published December 22, 2010; Online December 22, 2010

## Abstract

The objective of this study is to evaluate the capability of the partially averaged Navier–Stokes (PANS) method in a moderately high Reynolds number $(ReD 1.4×105)$ turbulent flow past a circular cylinder. PANS is a bridging closure model purported for use at any level of resolution ranging from Reynolds-averaged Navier–Stokes to direct numerical simulations. The closure model is sensitive to the length-scale cut-off via the ratios of unresolved-to-total kinetic energy $(fk)$ and unresolved-to-total dissipation $(fε)$. Several simulations are performed to study the effect of the cut-off length-scale on computed closure model results. The results from various resolutions are compared against experimental data, large eddy simulation, and detached eddy simulation solutions. The quantities examined include coefficient of drag $(Cd)$, Strouhal number $(St)$, and coefficient of pressure distribution $(Cp)$ along with the mean flow statistics and flow structures. Based on the computed results for flow past circular cylinder presented in this paper and analytical attributes of the closure model, it is reasonable to conclude that the PANS bridging method is a theoretically sound and computationally viable variable resolution approach for practical flow computations.

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## Figures

Figure 1

Geometry of the computational domain

Figure 2

Grid in the vicinity of the cylinder

Figure 3

Mean streamwise velocity along the wake centerline for various fk values

Figure 4

Mean streamwise velocity at two locations in the near wake for various fk values

Figure 5

Mean normal velocity at x/D=1.0 for various fk values

Figure 6

Instantaneous iso-z-vorticity contours: (a) fk=0.5, (b) fk=0.7, and (c) fk=1.0

Figure 7

Unresolved turbulent kinetic energy: (a) fk=0.5, (b) fk=0.7, and (c) fk=1.0

Figure 8

Unresolved eddy viscosity: (a) fk=0.5, (b) fk=0.7, and (c) fk=1.0

Figure 9

Cp distribution over the cylinder surface for various fk values

Figure 10

Time-dependent force coefficients: (a) fk=0.7 and (b) fk=0.5

Figure 11

Grid refinement study: (a) mean streamwise velocity along the wake centerline, (b) mean streamwise velocity at different locations in the near wake, (c) mean normal velocity at x/D=1.0, and (d) Cp distribution along the wake centerline

## Errata

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