A foundational step towards understanding and improving the transition between URANS and LES in hybrid URANS-LES methodology

Abstract

Appropriate transition between URANS and LES plays an integral role in the performance of hybrid URANS-LES techniques. However, dynamics of the transition region (also known as the Gray Area) have not yet been well understood, despite several efforts to mitigate negative impacts of inappropriate modeling of this region such as deviation from law-of-the-wall (also referred to as log-layer mismatch (LLM)) in turbulent attached boundary layers. The current paper centers on Scale Adaptive Simulation (SAS) hybrid URANS-LES methods and aims to address some shortcomings of the SAS methodology while providing new insights into the dynamics of the Gray Area. More specifically, necessary requirements, including the length scale, grid design and underlying RANS model to appropriately model essential dynamics of the Gray Area and, thus, mitigating the log-layer mismatch, are presented, which could be used for broader framework of hybrid URANS/LES and probably wall-modeled LES approaches.SAS methods traditionally have difficulty transitioning from URANS to LES without a sufficiently unstable base flow. Here we introduce an improved triggering mechanism based on departure-from-equilibrium dynamics formulated for the SAS method, primarily to enable the model to transition from URANS to scale resolving mode in attached/mildly separated flows, a well-known deficiency of the classical SAS formulations. The improved triggering mechanism considers deviations from equilibrium through a vortex stretching term in the dynamical equation for turbulent dissipation rate. The present study demonstrates that the length scale obtained for the gray area using straightforward blending of URANS and LES regions results in inaccurate transition dynamics. Therefore, we introduce a transport equation for the length scale of energy-containing eddies that allows an appropriate transition of length scale from URANS to LES mode. The modified framework uses the k−ɛ−ζ−f model as the underlying RANS model and is shown to trigger a transition from URANS to LES in stable attached stationary turbulent channel flow and mitigate the log-layer mismatch problem to a great extent. When applied to flows that feature boundary layer separation (flow over a periodic hill and flow over the wall-mounted hump), the current hybrid framework delivers results in agreement with existing experimental data and comparable to high fidelity LES calculations.