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Research Papers: Fundamental Issues and Canonical Flows

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

[+] Author and Article Information
Eunhwan Jeong

Department of Aerospace Engineering, Texas A&M University, College Station, TX 77845

Sharath S. Girimaji1

Department of Aerospace Engineering, Texas A&M University, College Station, TX 77845girimaji@aero.tamu.edu

1

Corresponding author.

J. Fluids Eng 132(12), 121203 (Dec 29, 2010) (11 pages) doi:10.1115/1.4003153 History: Received June 03, 2010; Revised October 25, 2010; Published December 29, 2010; Online December 29, 2010

## Abstract

The partially averaged Navier–Stokes (PANS) approach is a bridging closure model intended for any level of resolution between the Reynolds averaged Navier–Stokes (RANS) method and direct numerical simulations. In this paper, the proposed closure model is validated in the flow past a square cylinder. The desired ratio of the modeled-to-resolved scales in the PANS closure is achieved by appropriately specifying two bridging parameters: the ratios of unresolved-to-total kinetic energy $(fk)$ dissipation $(fε)$. PANS calculations of different bridging parameter values are performed and the results are compared with experimental data and large-eddy simulations. The Strouhal number$(St)$, mean/root-mean-square (RMS) drag coefficient $(CD)$, RMS lift coefficient $(CL)$, mean velocity profiles, and various turbulent stresses are investigated. The results gradually improve from the RANS level of accuracy to a close agreement with the experimental results with decreasing value of the bridging parameter $fk$. Overall, the results indicate that the PANS method clearly satisfies the basic tenets of a bridging model: (i) provides a meaningful turbulence closure at any modeled-to-resolved scale ratio and (ii) yields improved accuracy with increasing resolution (decreasing modeled-to-resolved ratio).

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## Figures

Figure 1

Computational domain

Figure 2

PANS simulation settings in FLUENT

Figure 3

Time-step and grid size convergence study results. (a) Centerline streamwise mean velocity profile. (b) Streamwise mean velocity profile at different downstream stations as a function of normal distance. (c) Global turbulence statistics for different time-step sizes. (d) Global turbulence statistics for different grid sizes. In (c) and (d), symbols ○ and △ represent domain-averaged unresolved kinetic energy and unresolved dissipation rate, respectively.

Figure 4

Integrated flow parameters: PANS, LES, and experimental results

Figure 5

Streamwise mean velocity profiles along the centerline from various experiments and simulations

Figure 6

Profiles of ((u′u′)mean)1/2, ((v′v′)mean)1/2, and ((w′w′)mean)1/2 along the centerline. Legend is the same as given in Fig. 5.

Figure 7

Lateral profiles of mean velocities at various x-locations. Legend is the same as given in Fig. 5.

Figure 8

Lateral profiles of turbulent quantities at various x-locations. Legend is the same as given in Fig. 5.

Figure 9

[(a)–(c)] Instantaneous contour plots of velocity magnitude, [(d)–(f)] z-vorticity, [(g)–(i)] unresolved kinetic energy, and [(j)–(l)] unresolved eddy viscosity for various fk values

Figure 10

Instantaneous isosurfaces: [(a) and (b)] vorticity magnitude, [(c) and (d)] velocity magnitude, [(e) and (f)] z-velocity, [(g) and (h)] x-vorticity, and [(i) and (j)] y-vorticity

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