An Algebraic Hybrid RANS-LES Model with Application to Turbulent Heat Transfer

Abstract

An algebraic hybrid RANS-LES model is proposed. The RANS mode employs a modified mixing-length approach near walls. Instead of using the magnitude of the resolved strain-rate tensor, the advanced spatial operator used by the WALE subgrid-scale model is embedded into the formulation due to its better scaling properties for the turbulent/eddy-viscosity. The LES mode incorporates the well-known WALE model to resolve flow in the rest of the domain. Similar to the robust, well-calibrated, low-cost, algebraic hybrid RANS-LES model (HYB0) which combines simple mixing length-type RANS near wall with Smagorinsky model in the off-wall region, the same turbulent length-scale adaptation approach for the RANS-LES interface is utilized for proper interaction between the modes. In addition to correct near-wall behaviour, the use of the advanced WALE differential operator should theoretically ensure smooth transition at the interface, detection of turbulent structures inside the eddies and better prediction of the log-layer velocity profile. Turbulent Rayleigh-Bénard problem is studied using both models to examine and to compare their performances without the Boussinesq approximation. It is found that HYB0 is slightly dissipative compared to mHYB0 and predicts fewer interactions among thermal plumes. However, HYB0 has interestingly better near-wall behavior. No interface issues are observed with the usage of the WALE operator. Further applications are required to characterize the behavior of the both models.