Sensitized-RANS Modelling of Turbulence: Resolving Turbulence Unsteadiness by a (Near-Wall) Reynolds Stress Model

Abstract

A turbulence model designed and calibrated in the steady RANS (Reynolds-Averaged Navier-Stokes) framework has usually been straightforwardly applied to an unsteady calculation. It mostly ended up in a steady velocity field in the case of confined wall-bounded flows; a somewhat better outcome is to be expected in globally unstable flows, such as bluff body configurations. However, only a weakly unsteady mean flow can be returned with the level of unsteadiness being by far lower compared to a referent database. The latter outcome motivated the present work dealing with an appropriate extension of a near-wall Second-Moment Closure (SMC) RANS model towards an instability-sensitive formulation. Accordingly, a Sensitized-RANS (SRANS) model based on a differential, near-wall Reynolds stress model of turbulence, capable of resolving the turbulence fluctuations to an extent corresponding to the model’s self-balancing between resolved and modelled (unresolved) contributions to the turbulence kinetic energy, is formulated and applied to several attached and separated wall-bounded configurations—channel and duct flows, external and internal flows separating from sharp-edged and continuous curved surfaces. In most cases considered the fluctuating velocity field was obtained started from the steady RANS results. The model proposed does not comprise any parameter depending explicitly on the grid spacing. An additional term in the corresponding length scale-determining equation providing a selective assessment of its production, modelled in terms of the von Karman length scale (formulated in terms of the second derivative of the velocity field) in line with the SAS (Scale-Adaptive Simulation) proposal (Menter and Egorov, Flow Turbul Combust 85:113–138, (2010) [14]), represents here the key parameter.