On Modelling Periodic Motion with Turbulence Closures

Abstract

In periodic flows near walls transport effects may be considerably larger than in a steady turbulent boundary layer. The question explored in this contribution is, therefore, whether providing separate transport equations for each of the Reynolds stresses consequently leads to a better modelling of a periodic flow's evolution than an eddy viscosity scheme whose constitutive equation is inherently linked to the generation and dissipation terms being in balance (local equilibrium). Our conclusion is that, while a stress-transport scheme is indeed better equipped to reproduce the phenomena, it does not consistently out-perform the EVM over the range of flows studied. In some cases it is suggested that more attention must be paid to modelling diffusive transport in order to secure the benefits of second-moment closure. To illustrate sensitivity to diffusive transport, two different diffusion models are tested, one of which leads to different effective transport coefficients in each stress component.