The standard k-e model is known to yield unsatisfactory predictions when applied to flow around bluff bodies as encountered for example in wind-engineering applications. The model fails to reproduce well the surface pressure distribution around a body because of the tendency to overestimate turbulent production in the impingement region on the frontal area of the body.

The result is that excessive turbulence levels are convected around the body, thereby reducing the extent of separation. This deficiency arises from the failing of the eddy-viscosity concept to represent adequately the strong irrotational straining that appears in impingement and reattachment regions.

Two variants of the k-e model have gained popularity in building aerodynamics for the improved prediction of impinging flow fields, namely:

- the Kato-Launder [1993] model (hereafter referred to as KL), and
- the so-called MMK model of Murakami, Mochida and Kondo (see Tsuchiya et al [1997]).

- The
**KL k-e model**differs from the standard model only in that the volumetric production rate of turbulence energy is calculated from the ad-hoc replacement:P

_{k}= n_{t}S W (2.1)rather than

P

_{k}= n_{t}S^{2}(2.2)where S and W are, respectively, strain and vorticity parameters defined by

S

^{2 }= (U_{i,j}+ U_{j,i})^{2 }/2 (2.3)W

^{2 }= (U_{i,j}- U_{j,i})^{2 }/2 (2.4)The excessive k levels in impingement regions are produced by S. Now, in simple shear flows the modification has little effect because W and S are essentially equal, whereas in stagnation regions W is nearly zero so that turbulence production is much reduced by the modification.

- The
**MMK k-e model**differs from the standard model in that the eddy viscosity n_{t}is computed fromn

_{t}= F_{W}C_{m}C_{d}k^{2}/e (2.5)where the multiplier F

_{W}is calculated fromF

_{W}= min (1.0, W/S ) (2.6)so that the standard model is recovered whenever W/S > 1.

The **KL modification** is selected by **TURMOD(KEKL)**, and
the **MMK model **by **TURMOD(KEMMK)**.

These commands are equivalent to TURMOD(KEMODL) plus the following PIL commands:

STORE(FOMG);FIINIT(FOMG)=1.0 IF(STORE(U1)) THEN IF(NY.GT.1) STORE(DUDY) IF(NZ.GT.1) STORE(DUDZ) ENDIF IF(STORE(V1)) THEN IF(NX.GT.1) STORE(DVDX) IF(NZ.GT.1) STORE(DVDZ) ENDIF IF(STORE(W1)) THEN IF(NX.GT.1) STORE(DWDX) IF(NY.GT.1) STORE(DWDY) ENDIF

with IENUTA=12 for the MMK model, and IENUTA=13 for the KL model.

The FORTRAN coding sequences for the computation of F_{
W}
may be found in subroutine GXOMEG.

The field values of F_{W}
are written to the PHI and RESULT file as FOMG.

The Q1 input files T307 and T308 demonstrate the use of these models, and they may be found in the advanced-turbulence-model input-file libraries.

Scientific publications describing the models and their application can be found in the following references:

G.Bosch and W.Rodi, 'Simulation of vortex shedding past a square cylinder with different turbulence mdoels', Int. J. Num.Methods in Fluids, Vol.28, 601-616, (1998).

M.Kato and B.E.Launder, 'The modelling of turbulent flow around stationary and vibrating square cylinders', 9th Symposium on Turbulent Shear Flows, Kyoto, Japan, (1993).

D.Lakehal and W.Rodi, 'Calculation of flow past a surface-mounted cube with two-layer turbulence models', J.Wind Engineeering & Industrial Aerodynamics, 67 & 68, 65-78, (1997).

S.Murakami, 'Current status and future trends in computational wind engineering', J.Wind Engineeering & Industrial Aerodynamics, 67 & 68, 3-34, (1997).

M.Tsuchiya, S.Murakami, A.Mochida, K.Kondo & Y.Ishida, 'Development of a new k-e model for flow and pressure fields around bluff body', J.Wind Engineeering & Industrial Aerodynamics, 67 & 68, 169-182, (1997).

T.Tamura, H.Kawai, S.Kawamoto, K.Nozawa, S.Sakamoto & T.Ohkuma, 'Numerical predictions of wind loading on buildings and structures', J.Wind Engineeering & Industrial Aerodynamics, 67 & 68, 671-685, (1997).

N.G.Wright & G.J.Easton, 'Comparison of several computational turbulence models with full-scale measurements of flow around a building', Wind & Structures, Vol.2, No.4, 305-323, (1999).

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