Differential 2. order shear stress model

A three dimensional turbulent flow field in unbaffled tank with turbine stirrer or 6-paddle stirrer was numerically simulated by the method of finite volume elements [80], whereas in the case of free surface the vortex profile was also determined using iterative techniques. The prediction of the velocity and turbulence fields in the whole tank and the stirrer power was compared with literature data and their own results. Of the two simulation techniques used, turbulent eddy-viscosity/zc-e turbulence model and the DS model (differential 2. order shear stress), only the latter produced satisfactory results. In particular it proved that fluctuating Coriolis forces have to be taken into account by source terms in the transport equation for the Reynolds shear stress. 

In order to determine the three dimensionless shear stresses and dimensionless first normal stress differences, which are functions of the shear rate and relaxation times, that contribute to Eqs. 90 and 91 we utilised a model due to Larson [63], who showed that a differential approximation to Eq. 5 is given by. 

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