A New Adaptive Turbulence Model for Unsteady Flow Fields in Rotating Machinery

In order to predict unsteady ¯ow ®elds one can use the Reynolds Averaged Navier-Stokes Equations (RANS) with a statistical turbulence model or Large Eddy Simulation (LES) in conjunction with a subgrid-scale model.Since the ¯ow ®eld in rotating machinery, internal combustion engines etc., is often strongly three-dimensional and unsteady, the calculation with LES and RANS are similar in terms of cpu-time providing the grid resolutions are similar.The turbulence models used with RANS have been designed in order to capture all the turbulence eects since a steady state calculation cannot resolve any ¯uctuation.If one wants to perform an unsteady calculation, then a fraction of the turbulent ¯uctuations is already resolved by the numerical scheme, depending on the temporal and spatial resolution, and therefore the turbulence model must only model the unresolved part of the turbulence.The standard turbulence models used today cannot be used for such simulations, since they model always the whole turbulence spectrum.On the other hand, the subgrid-scale models for LES model only a fraction of the turbulent spectrum, but they fail to model the turbulence in the limit of high cell Reynolds numbers (Speziale, 1998).A new adaptive turbulence model based on the popular two-equation models will be proposed which can be used for all cell Reynolds numbers in the unsteady case.It has the property that it reduces to a Direct Numerical Simulation (DNS) if the temporal and spatial resolution of the ¯ow ®eld is in the order of the Kolmogorov micro scale.If one does not resolve ¯uctuations (steady state) then the model reduces to a standard two-equation model.In between these two extremes it automatically adapts itself to the resolved turbulent ¯uctuations.