Modelled Length Scale in SAS-SST Simulation
 

Hello,
I have some issues understanding the breakup of turbulent structures into
smaller scales using the SAS-SST Model. I know, that the model uses the
von Karman length scale as an indicator for the local vortex size. So, at the beginning of the Simulation the modelled length scale is much larger than the von Karman length (in unsteady situations). Thus, the QSAS term is activated, the Eddy Viscosity is reduced which leads to a reduced damping effect and the turbulent structures are allowed to break up until the grid limit is reached.
So far so good, but what happens exactly with the modelled scale L, provided by the RANS model. In my understanding while running the simulation, the modelled length scale is also getting smaller when the Eddy Visc. is reduced by the QSAS term. This means, the modelled scale would be reduced until it matches the von karman scale (?).
So, in situations when the local vortex size is significantly larger than the grid resolution, a remaining Eddy Viscosity would exist according to
the local length scale. This leads to my assumption, that higher length scales (Lvk) result in higher remaining eddy viscosity (L/Lvk smaller).
My problem is, that in this situation the flow structures would be well resolved by the grid, so the damping of the eddyy visc. should
be very small. But as I described the progress of turbulent breakup using
the SAS model, the contrary is the case.
Could someone please explain the behaviour of the modelled length L in relation to Lvk in the progress of the Simulation and describe the reduction of the eddy visc.? And does the modelled length scale provided by the RANS model (L=sqrt(k)/(c omega)) match the
actual vortex size after the eddy visc. was reduced by the QSAS-term?


Many thanks in advance four your help