Turbulent Momentum Transport. Modeling of the

In the RANS-approach, turbulence or turbulent momentum transport models are required to calculate the Reynolds-stresses. This can be done starting from additional transport equations, the so-called Reynolds-stress models. Alternatively, the Reynolds-stresses can be modeled in terms of the mean values of the variables and the turbulent kinetic energy, the so-called turbulent viscosity based models. In either way, the turbulence dissipation rate has to be calculated also, as it contains essential information on the overall decay time of the velocity fluctuations. In what follows, the more popular models based on the turbulent viscosity are focused on. A detailed description of the Reynolds-stress models is given in Annex 12.5.l.A which can be downloaded from the Wiley web-page. 

Turbulent viscosity based models start from the Boussinesq hypothesis [1877] relating the Reynolds stresses to the mean velocity gradients, the turbulent kinetic energy and the turbulent viscosity ix.  

Using (12.5.1-1), the Reynolds-averaged momentum equation for statistically stationary flow, (12.5-6), reduces to  

The isotropic stress term, 2pkSiJ3, is combined with the mean pressure to form a modified or effective mean pressure. The effective viscosity jueffis the sum of the molecular and turbulent viscosities  

The calculation of the six components of the Reynolds stress tensor, that is, six second-order moments of the micro-PDF, f v,yf), is reduced to the calculation of k and the modeling of the turbulent viscosity pf As seen from (12.5.1-2), is a function of a limited number of second-order moments of the micro-PDF. Turbulent viscosity based closure models for the Reynolds-stresses can be used at relatively low computational effort. In the two-equation model approach, the turbulent viscosity is expressed in terms of the turbulent kinetic energy, k, and the turbulence dissipation rate, s, according to  

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Turbulent Momentum Transport. Modeling of the Reynolds-Stresses... 

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