Adaptive downstream tensorial eddy viscosity for hybrid large‐eddy simulations‐Reynolds‐averaged‐Navier–Stokes simulations

Abstract

An adaptive method is developed to improve the accuracy of eddy‐viscosity Reynolds‐averaged‐Navier–Stokes (RANS) model in hybrid large‐eddy simulations (LES)‐RANS simulations by using available upstream LES results. The method first gets the tensorial eddy viscosity from the upstream LES solution at the LES‐RANS interface and then uses that information to improve the downstream RANS model by invoking the weak‐equilibrium assumption. The proposed method was evaluated via two test problems—flow in a channel and over a periodic hill. Results obtained show the proposed approach to increase the accuracy and stability of hybrid LES‐RANS simulations. Since the modification of the downstream RANS model is based on the tensorial eddy viscosity from the upstream LES solution, the method is adaptive to the problem being studied.

Hybrid large‐eddy simulation with adaptive downstream anisotropic eddy viscosity model

“…At the LES‐to‐RANS interface, in addition to mean flow variables such as density, velocity, and pressure, the effective eddy viscosity is also needed. Several methods have been developed to obtain the eddy viscosity by using the LES solution at the LES‐to‐RANS interface 4 . One method directly averages all quantities in the LES solution that are needed to calculate the eddy viscosity such as the turbulent kinetic energy and its dissipation rate 18–21 .…”

“…Still another first applies the stiffest RANS momentum equation at the interface with the mean flow variables obtained from the LES solution and then solves for the eddy viscosity 24,25 . Since the eddy viscosity of most flows of engineering interest is tensorial, which the LES solution is able to capture, and the eddy‐viscosity model used in the downstream RANS region is typically scalar, the mean velocity profile from the LES region cannot be sustained in the RANS region—although it is perfectly transferred from the LES region to the RANS region at the LES‐to‐RANS interface 4 . As a result, numerical oscillations take place about the LES‐to‐RANS interface.…”

“…Other methods such as using forcing functions to dampen oscillations reduce the accuracy of hybrid LES‐RANS methods 19 . Zhang and Shih 4 took a different approach to reduce the mismatch between LES and RANS regions. Recognizing oscillations resulted because of inadequacies of the scalar eddy viscosity models used in the downstream RANS region, they used the upstream LES solution to modify the downstream RANS model to one with a tensorial eddy viscosity.…”

“…By using their method, they showed that oscillations are essentially eliminated and that the size of the upstream LES region could be significantly decreased, which greatly enhances computational efficiency since LES is much more resource intensive than RANS. However, the tensorial eddy‐viscosity model developed in Reference 4 requires the determination of the dominant eddy‐viscosity element by using the velocity gradient, which is related to the choice of the coordinate system. For attached flows, if the direction of the main flow is aligned with a coordinate direction, then the dominant element is easy to find.…”

“…If not aligned, then the dominant element can be difficult to identify. Thus, the tensorial eddy‐viscosity model developed in Reference 4 may be impractical for turbulent flows with complicated mean flow features. The objective of this article is to present a method to overcome the shortcoming of the method developed in Reference 4 so that it can be applied to complicated turbulent flows.…”