A new approach for the calculation of the cut-off resolution parameter in bridging methods for turbulent flow simulation

The bridging HRL (hybrid RANS/LES) method is being increasingly used to solve complex and high-Reynolds number industrial flows. The increase in popularity is equally due to the conceptual simplicity and the potential ability to affect cut-off at an optimal length scale depending upon the problem on hand. In the bridging-type of HRL methods, the ratios of resolved-to-total kinetic energy and dissipation serve to partition the flow field into resolved and computational fields for reduced-order computations. Modeled transport equations for unresolved kinetic energy and dissipation equations are solved. In this paper, we develop an additional model transport equation to determine the resolved turbulent kinetic energy equation which enables an accurate and computational means of specifying the resolution control parameter for optimal computations. The proposed approach obviates the need for expensive averaging operations currently employed to compute the partition between resolved and modeled fields. This development will expedite the bridging HRL computations for flows with transient boundaries and moving geometries. The development is in the context of Partially-Averaged Navier-Stokes (PANS) model, but the conclusions are broadly applicable to other bridging HRL approaches. The advantage of the new approach is demonstrated for the flow past a square cylinder.