An eddy viscosity PANS model for non-zonal continuous hybrid RANS/LES simulations

Abstract

The extremely stringent requirement of fully resolving turbulence in Direct Numerical Simulation (DNS) of fluid flows has forced researchers and engineers to rely heavily on averaged methods like the Reynolds’ Averaged Navier-Stokes (RANS) for common engineering applications. The process of averaging in RANS results in the full spectrum of turbulent scales being fully modeled instead of resolved as in DNS. This comes at a cost of lower accuracy and reliability, which could have adverse effects on the design or research at hand. With the current computer technology barely keeping up with Moore’s law, it is expected that we are decades away from having enough computing power to make DNS a feasible option outside purely academic settings. The huge gap between RANS and DNS has led to the development of hybrid models that offer the benefits of both extremes, by allowing part of turbulence to be exactly resolved, thus reducing the inaccuracies associated with the smaller modeling part. Partially Averaged Navier-Stokes (PANS) bridges between RANS and DNS, providing the adequate balance between modeled and resolved quantities. In this study, a new PANS model based on the one-equation transport of the unresolved turbulent eddy viscosity νtu is proposed. This is, to the author’s knowledge, the first PANS model in which the resolution level is controlled by the ratio of unresolved-to-total turbulent eddy viscosity fνt . In addition, fνt is both a spatially and temporally varying quantity derived directly from the integration of the energy density spectrum. This gives the proposed model a more physically sound formulation, compared to the empiricism and ad-hoc shielding usually used in hybrid models. Two validation test cases are investigated, with the first involving shear flow between a moving and stationary fluid i.e., the backward-facing step, and the external aerodynamic flow over a simplified car body, i.e., the Ahmed body. Both cases are simulated using the proposed model, Improved Delayed Detached Eddy Simulation (IDDES), and Wall Modeled Large Eddy Simulation (WMLES). The latter two models are also scale-resolving methods used for comparison in the current study. Validation of the results are performed against data from well established experimental setups. The proposed PANS model shows higher accuracy in predicting the average velocity profiles, as well as the turbulent stresses in the backward-facing step compared to IDDES and WMLES. In addition, PANS is able to release more structures than the other models for the same grid density, showing that strong shielding is not always an advantage. For external aerodynamics applications, i.e., the Ahmed Body, PANS shows better drag predictions with levels of turbulent stresses comparable to IDDES. With the given grid of this case, PANS is able to automatically adjust the level of resolution to cover upstream locations with a fully modeled formulation, and switch to a more resolving one on the slant and downstream the body. Overall, the proposed PANS model shows promising results in this preliminary study.