Two-equation hybrid RANS–LES models: a novel way to treat k and ω at inlets and at embedded interfaces

Abstract

ABSTRACTA novel method for prescribing k and ω at inlets and RANS–LES interfaces in embedded LES is presented and evaluated. The method is based on the proposal by Hamba to use commutation terms at RANS–LES interfaces. Commutation terms are added to the k and ω equations in the region near the inlet (i.e. the RANS–LES interface). The proposed method can also be used when prescribing inlet values for k and ω in hybrid LES–RANS. The commutation terms are added in embedded LES at the LES side of the RANS–LES interface. The influence of the extent of the region where the commutation terms are added is investigated. It is found that it is most efficient to add commutation terms in only one cell layer adjacent to the interface; in this way, tuned constants are avoided. The commutation term in the ω equation is derived from transformation of the k and ϵ equations. When the commutation terms are used in only one cell layer, the commutation term in the k equation corresponds to a negative convection term. Hence, the commutation term can be omitted and a homogeneous Neumann inlet boundary condition can be used. The commutation term in the ω equation is retained. The novel method is evaluated for channel flow (Reτ = 8000), boundary layer flow (Reθ = 11, 000) and backward-facing step flow (ReH = 28, 000). Hybrid LES–RANS is used for the first two flows and embedded LES for the backward-facing step flow.