The Realizable k - ε Model
The realizable k - ε model (Shih et al., 1995) is a recent development that satisfies the mathematical constraints on the normal stresses. The differences between the realizable model and the other k - ε models are that the former contains a different formulation for the turbulent viscosity and that a different transport equation is used for the dissipation rate. The transport equations for the turbulent kinetic energy k and for the dissipation rate ε are
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(32.1) |
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(32.2) |
where S is a scalar value of the strain tensor. The turbulent viscosity νt is calculated from
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(32.3) |
However, Cμ is no longer a constant. It is given by
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(32.4) |
where A0 = 4.04, and As and U+ are functions of both the mean strain and rotation rates, the angular velocity of the system rotation and the turbulence field ( k and ε). This model is more accurate for predicting in the spreading rate of planar or round jets than the standard k - ε model. It is likely to provide superior performance for flows involving rotation, strong adverse pressure gradients, separation, and recirculation.
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