Unifying Formalism for Coarse-Grained Approaches to Turbulence Closures: the Dynamic k-ω Model

This work represents an advancement in the development of a new class of turbulence closures conceived by Cimarelli et al. [1]. This new class of closures is based on the theoretical framework provided by the temporally filtered Navier-Stokes equations. This framework represents a unifying formalism for coarse-grained approaches to turbulence ranging from the statistical to the scale-resolving ones and provides exact equations relating turbulent stresses at different levels of coarsening. These equations have been introduced in Cimarelli et al. [1] to derive a new class of closures based on the dynamic computation of the model coefficient cµ appearing in the definition of eddy viscosity. Here, an extension of this class of dynamic RANS model is presented by deriving a new formulation based on the k − ω model including an alternative version where the non-physical decay of free-stream turbulence reproduced by the transport equations of k and ω is solved in a elegant way. A simulation campaign is performed and the analysis of the results reveals interesting features. Among others, the new dynamic k − ω model demonstrates strong robustness to the coarsening of the temporal resolution and successfully captures complex flow phenomena, including laminar-to-turbulent transition and the sensitivity of boundary-layer separation and reattachment dynamics to free-stream turbulence levels prescribed at the boundaries.