On the accuracy of partially averaged Navier–Stokes resolution estimates

Partially Averaged Navier–Stokes computations can employ three different approaches for specifying the ratio of
modelled-to-total turbulence kinetic energy fk. Use can be made of either a constant, a spatially- or a spatially and temporally-varying value. This work compares different estimates for fk found in literature and evaluates them for two test-cases: a circular cylinder at Re=3900 and a turbulent channel flow at Re=395. Additionally, the estimates are compared to the a posteriori computed ratio of modelled-to-total turbulence kinetic energy() hfk obtained from the PANS flow solution. The trends observed for the estimates are similar, although the magnitude varies significantly. All spatially varying fk approaches reduce the PANS model to a DES-like model, thereby entangling modelling and discretisation errors. At the same time, f˜k shows that the behaviour of these estimates is incorrect: fk becomes too large near the wall of the object and in the far field. It is observed that f˜k is always lower than the set value, when using fk fixed in space and time. Finally, it is clear that the estimates, applied to internal, boundary layer, flows yield too high values for fk. In order to minimise errors and increase the reliability of industrial CFD results, the approach with a constant fk is still preferable, assuming suitably fine grids are used.