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# A Low-Reynolds Number Explicit Algebraic Stress Model

[+] Author and Article Information
M. M. Rahman

Department of Mechanical Engineering, Helsinki University of Technology, Laboratory of Applied Thermodynamics, Sähkömiehentie 4, FIN-02015 HUT, Finlandmizanur.rahman@hut.fi

T. Siikonen

Department of Mechanical Engineering, Helsinki University of Technology, Laboratory of Applied Thermodynamics, Sähkömiehentie 4, FIN-02015 HUT, Finland

J. Fluids Eng 128(6), 1364-1376 (Apr 07, 2006) (13 pages) doi:10.1115/1.2354527 History: Received October 04, 2005; Revised April 07, 2006

## Abstract

A low-Reynolds number extension of the explicit algebraic stress model, developed by Gatski and Speziale (GS) is proposed. The turbulence anisotropy $Πb$ and production to dissipation ratio $P∕ϵ$ are modeled that recover the established equilibrium values for the homogeneous shear flows. The devised ($Πb$, $P∕ϵ$) combined with the model coefficients prevent the occurrence of nonphysical turbulence intensities in the context of a mild departure from equilibrium, and facilitate an avoidance of numerical instabilities, involved in the original GS model. A new near-wall damping function $fμ$ in the eddy viscosity relation is introduced. To enhance dissipation in near-wall regions, the model constants $Cϵ(1,2)$ are modified and an extra positive source term is included in the dissipation equation. A realizable time scale is incorporated to remove the wall singularity. The turbulent Prandtl numbers $σ(k,ϵ)$ are modeled to provide substantial turbulent diffusion in near-wall regions. The model is validated against a few flow cases, yielding predictions in good agreement with the direct numerical simulation and experimental data.

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## Figures

Figure 1

Variation of modeled Πb with shear parameter ζ(R=1)

Figure 2

Locus of solution points for state variable P∕ϵ as a function of ζ(R=1)

Figure 3

Distribution of Cμ as a function of shear/strain parameter ζ

Figure 4

Anisotropy invariant map at different shear/strain rates

Figure 5

Variations of eddy viscosity coefficients with wall distance in channel flow

Figure 6

Mean velocity profiles of channel flow

Figure 7

Shear stress profiles of channel flow

Figure 8

Normal stress profiles in channel flow at Reτ=180

Figure 9

Normal stress profiles in channel flow at Reτ=395

Figure 10

Streamwise skin friction coefficient of boundary layer flow

Figure 11

Computational grid for contracting channel flow

Figure 12

Contracting channel flow: Reynolds normal stress and turbulent kinetic energy distributions along contraction centerline

Figure 13

Skin friction coefficients of diffuser flow: (a) along the deflected bottom wall and (b) along the straight top wall

Figure 14

Mean velocity profiles at selected locations for diffuser flow

Figure 15

Shear stress profiles at selected locations for diffuser flow

Figure 16

Normal stress profiles at selected locations for diffuser flow

Figure 17

Computational grid for U-duct flow

Figure 18

Profiles at inlet for U-duct flow

Figure 19

Velocity profiles at selected locations for U-duct flow

Figure 20

Shear stress profiles at selected locations for U-duct flow

Figure 21

Turbulence intensity profiles at selected locations for U-duct flow

Figure 22

Inner surface skin friction coefficient for U-duct flow

Figure 23

Inner surface pressure coefficient for U-duct flow

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