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Research Papers: Fundamental Issues and Canonical Flows

# Review: Adapting Scalar Turbulence Closure Models for Rotation and Curvature

[+] Author and Article Information
Paul Durbin

Department of Aerospace Engineering,  Iowa State University, Ames, IA 50011 e-mail: durbin@iastate.edu

J. Fluids Eng 133(6), 061205 (Jun 16, 2011) (8 pages) doi:10.1115/1.4004150 History: Received December 13, 2010; Revised April 22, 2011; Published June 16, 2011; Online June 16, 2011

## Abstract

Scalar, eddy viscosity models are widely used for predicting engineering turbulent flows. System rotation, or streamline curvature, can enhance or reduce the intensity of turbulence. Methods to incorporate the effects of rotation and streamline curvature consist of introducing parametric variation of model coefficients, such that either the growth rate of turbulent energy is altered; or such that the equilibrium solution bifurcates from healthy to decaying solution branches. For general use, parameters must be developed in coordinate invariant forms. Effects of rotation and of curvature can be unified by introducing the convective derivative of the rate of strain eigenvectors as their measure.

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## Figures

Figure 1

Evolution of k with time for ○ , Ro=-1/2;,Ro=0;Δ,Ro=-1;♦,Ro=-3/2;∇,Ro=1/2. The symbols are from DNS, the curves from rapid distortion theory. From Ref. [4].

Figure 2

Turbulent kinetic energy and mean flow for rotating channel; curves for three rotation rates. From Ref. [5]

Figure 3
Figure 4

Turbulent kinetic energy in rotating homogeneous shear by 2-equation model with 21

Figure 5

Mean velocity in channel with bulk rotation numbers Rob=2ΩF/Ub=0.2 and 0.5. Symbols are DNS data of Ref. [5]; models are from Refs. [19] and [22]

Figure 6

Bifurcation diagram. Two examples: chaindash curve is the SSG solution, solid is from Ref. [22]. ℜ=η2/η1=1+CrRo. The vertical line at ℜ=1 is the non-rotating case.

Figure 7

Turbulent kinetic energy and mean velocity in a U-duct, in the middle of the bend. Dashed lines are the original SST model; chain-dashed lines invoke a curvature correction.

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