A generally applicable hybrid unsteady Reynolds-averaged Navier–Stokes closure scaled by turbulent structures

Abstract

This work demonstrates a strategy for hybrid turbulence modeling that relies on parameters identifying flow structures to regulate the model's level of scale resolution, independent of the computational grid and user input. The approach can be classified as second-generation unsteady Reynolds-averaged Navier–Stokes (URANS), where it is assumed that increased scale resolution inside rapidly deformed turbulence regions can consistently reduce modeling error compared to basic URANS closures. The methodology selects flow structures by evaluating the second invariant of the velocity gradient tensor in the resolved field. The functions used for this purpose are similar to techniques applied in topology studies to identify coherent structures. The proposed formulation extends a baseline nonlinear eddy-viscosity URANS model and achieves completeness by means of a differential Lagrangian operator that approximates a locally computed average. The model addresses the lack of general applicability deriving from globally filtering at small scales by reverting to the baseline URANS in flow locations with low acceleration, in which the URANS solution achieves best accuracy. Three flow test cases are presented, demonstrating substantial accuracy enhancement over the baseline URANS on the same grid sizes. Results obtained with this new closure demonstrate robust applicability to internal flows, showing large-eddy simulation (LES)-like statistics on coarse RANS computational grids. The observed increase in computational cost compared to the baseline URANS is only 3% to 24%, which represents almost two orders of magnitude reduction from LES.