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### 1. Introduction

The low-Re k-e model has the undesirable feature of requiring very high numerical resolution near the wall because of the steep gradient of the dissipation rate EP, for which an equation is solved. Also, the models have been found to perform rather poorly in adverse-pressure-gradient boundary layers; and the damping functions are not always well-behaved in separated flows.

Hence, in order to save mesh points and improve convergence rates, and also to introduce the fairly well-established length scale (L) distribution very near the wall, one alternative is the use a two- layer k-e model ( see for example Elhadidy [1980] and Rodi [1991] ).

The two-layer k-e model uses the high-Re k-e model only away from the wall in the fully-turbulent region, and the near-wall viscosity- affected layer is resolved with a one-equation model involving a length-scale prescription.

PHOENICS has been equipped with the two-layer model of Rodi [1991] which employs the one-equation model of Norris and Reynolds [1975] in the near-wall region.

### 2. Description of the model

In the near-wall layer, the two-layer k-e model fixes the dissipation rate EP, which appears in the KE equation, to:

EP = CD * KE**1.5 * FTWO / LM (2.1)

with CD = 0.1643,

FTWO = 1. + 5.3/REYN (2.2)

REY = KE**0.5*YN/ENUL (2.3)

and YN is the minimum distance to the nearest wall.

The turbulent kinematic viscosity in the near-wall layer is calculated from:

ENUT = CMU * KE**0.5 * FMU * LM (2.4)

where CMU=0.5478,

FMU = ( 1. - EXP ( -0.0198 * REYN ) ) (2.5)

LM = AK * YN (2.6)

and von Karman's constant AK = 0.41. The one-equation model is matched with the high-Re k-e model at those locations where REYN= 350.

### 3. Activation of the model

The two-layer KE-EP model is selected by TURMOD(KEMODL-2L) which is equivalent to the following PIL commands:

TURMOD(KEMODL);IENUTA=8;DISWAL

The DISWAL command activates the solution of a scalar variable LTLS, from which is deduced the minimum distance to the nearest wall YN. Subsequent WALL and CONPOR commands will set COVAL statements for the appropriate velocities, LTLS and the turbulent kinetic energy.

No COVAL is required for EP as the near-wall value is fixed according to eqn (2.1) via modification of the standard source terms for EP. Where needed, COVALs for wall PATCHes should take the form described below in Section 3.4.4 for the LAM-Bremhorst KE-EP turbulence model.

When STORE(FMU,FTWO,REYN) appears in the Q1 file, the damping functions defined by eqns (2.2) and (2.5), and the Reynolds number (2.3), may be printed in the RESULT file or viewed via PHOTON and AUTOPLOT.

The FORTRAN coding sequences for the two-layer model may be found in Group 1, Section 1 of GREX, Group 13 of GREX and the files GXTURB. FOR and GXPROP.FOR. Examples which demonstrate the use of the two- layer model may be found in the advanced-turbulence-models user library.

### 4. Sources of further information

M.A.Elhadidy,'Applications of a low-Reynolds-number turbulence model and wall functions for steady and unsteady heat-transfer computations', PhD Thesis, University of London, (1980).

L.H.Norris and W.C.Reynolds,'Turbulent channel flow with a moving wavy boundary', Rept. No. FM-10, Stanford University, Mech. Eng. Dept., USA, (1975).

W.Rodi, 'Experience with two-layer models combining the k-e model with a one-equation model near the wall', AIAA-91-0216, 29th Aerospaces Sciences Meeting, January 7-10, Reno, Nevada, USA, (1991)

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