Scale-resolving simulations of turbulent flows with coherent structures: Toward cut-off dependent data-driven closure modeling

Complex turbulent flows with large-scale instabilities and coherent structures pose challenges to both traditional and data-driven Reynolds-averaged Navier–Stokes methods. The difficulty arises due to the strong flow-dependence (the non-universality) of the unsteady coherent structures, which translates to poor generalizability of data-driven models. It is well-accepted that the dynamically active coherent structures reside in the larger scales, while the smaller scales of turbulence exhibit more “universal” (generalizable) characteristics. In such flows, it is prudent to separate the treatment of the flow-dependent aspects from the universal features of the turbulence field. Scale resolving simulations (SRS), such as the partially averaged Navier–Stokes (PANS) method, seek to resolve the flow-dependent coherent scales of motion and model only the universal stochastic features. Such an approach requires the development of scale-sensitive turbulence closures that not only allow for generalizability but also exhibit appropriate dependence on the cut-off length scale. The objectives of this work are to (i) establish the physical characteristics of cut-off dependent closures in stochastic turbulence; (ii) develop a procedure for subfilter stress neural network development at different cut-offs using high-fidelity data; and (iii) examine the optimal approach for the incorporation of the unsteady features in the network for consistent a posteriori use. The scale-dependent closure physics analysis is performed in the context of the PANS approach, but the technique can be extended to other SRS methods. The benchmark “flow past periodic hills” case is considered for proof of concept. The appropriate self-similarity parameters for incorporating unsteady features are identified. The study demonstrates that when the subfilter data are suitably normalized, the machine learning based SRS model is indeed insensitive to the cut-off scale.