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3.4.2 The Chen-Kim modified KE-EP turbulence model

Contents

  1. Introduction
  2. Description of the model
  3. Activation of the model
  4. Sources of further information

(a) Introduction

PHOENICS provides the standard high-Reynolds-number form of the two- equation eddy-viscosity KE-EP turbulence model. This model employs a single time scale (KE/EP) to characterize the various dynamic processes occurring in turbulent flows. Accordingly, the source, sink and transport terms contained in the closed set of model equations are held to proceed at rates proportional to EP/KE.

Turbulence, however, comprises fluctuating motions with a spectrum of time scales, and a single-scale approach is unlikely to be adequate under all circumstances because different turbulence interactions are associated with different parts of the spectrum.

In order to remedy this deficiency in the standard model, Chen and Kim (hereafter referred to as CK) [1987] proposed a modification which improves the dynamic response of the EP equation by introducing an additional time scale (KE/PK), where PK is the volumetric production rate of KE.

In addition, several of the standard-model coefficients are adjusted so that the model maintains good agreement with experimental data on classical turbulent shear layers. Because of its success for a number of separated-flow calculations, the CK modification is provided as an option in PHOENICS.

The CK modification involves dividing the EP production term into two parts, the first of which is the same as for the standard model but with a smaller multiplying coefficient, and the second of which allows the 'turbulence distortion ratio' (PK/EP) to exert an influence on the production rate of EP.

According to the authors the extra source term represents the energy transfer rate from large-scale to small-scale turbulence controlled by the production-range time scale and the dissipation- range timescale.

The net effect is to increase EP (and thereby decrease KE) when the mean strain is strong (PK/EP>1), and to decrease EP when the mean strain is weak (PK/EP < 1). This feature may be expected to offer advantages in separated flows and also in other flows where the turbulence is removed from local equilibrium.

Chen ( see Monson et al [1990] ) extended the model to perform low- Reynolds-number simulations of bounded flows by introducing the low- Reynolds-number KE-EP extension of Lam and Bremhorst [1981]. This extension is provided for in PHOENICS by allowing the CK modification to be used in combination with the Lam-Bremhorst extension.

(b) Description of the model

The CK modified KE-EP model differs from the standard high-Reynolds- form of the KE-EP model in that: (a) the following model constants take different values:

PRT(KE)=0.75 ; PRT(EP)=1.15 ; C1E=1.15 ; C2E=1.9 (2.1)

and (b) an extra timescale KE/PK is included in the EP-equation via the following additional source term per unit volume:

S,EP = RHO*F1*C3E*PK**2/KE (2.2)

where C3E=0.25, PK is the volumetric production rate of KE, and F1 is the Lam-Bremhorst [1981] damping function which tends to unity at high turbulence Reynolds numbers.

(c) Activation of the model

The CK modification to the KE-EP model is selected by TURMOD(KECHEN) which is equivalent TURMOD(KEMODL) plus the following PIL commands:

IENUTA=2;PRT(KE)=0.75;PRT(EP)=1.15 PATCH(KECHEN,PHASEM,1,NX,1,NY,1,NZ,1,1) COVAL(KECHEN,EP,FIXFLU,GRND4)

The FORTRAN coding sequences for the CK modification may be found in Group 1, Section 1 of GREX and also in Group 13 of GREX.

The low-Reynolds-number extension to this model can be selected by TURMOD(KECHEN-LOWRE), which invokes the Lam-Bremhorst extension to the KE-EP. This extension requires that the minimum distance to the nearest wall be calculated for each cell in the flow field.

The PIL command TURMOD(KECHEN-LOWRE) is equivalent to TURMOD(KEMODL) plus IENUTA=4 and DISWAL.

The TURMOD statement activates the PIL command DISWAL which activates the solution of a differential equation for a generalised turbulence-length scale LTLS, from which the wall distance is then deduced. For further information the user is referred to the help entry DISWAL, Section 3.4.4 on the Lam-Bremhorst KE-EP model, and Section 3.1.2 on the LVEL model.

Q1's which demonstrate the use of the model may be found in the advanced-turbulence-model input-file library.

(d) Sources of further information

Y.S.Chen and S.W.Kim, 'Computation of turbulent flows using an extended k-e turbulence closure model', NASA CR-179204, (1987).

D.J.Monson, H.L.Seegmiller, P.K.McConnaughey and Y.S.Chen, 'Comparison of experiment with calculations using curvature- corrected zero and two-equation turbulence models for a two- dimensional U-duct', AIAA 90-1484, (1990).

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