Interface methods for grey-area mitigation in turbulence-resolving hybrid RANS-LES

Highlights: • Commutation terms at RANS-LES interfaces improve the accuracy in embedded LES. • Turbulent fluctuations are achieved with a commutation term in the momentum equation. • Commutation terms in the k- and ω-equations rapidly change the turbulent viscosity. • Almost no grey area is given in plane mixing layer with the use of commutation terms. • The discretization scheme is essential for accurate predictions of plane mixing layer. A grey area mitigation method is proposed for hybrid RANS-LES modeling. The proposed methodology is evaluated using a hybrid RANS-LES method based on a Low-Reynolds-Number $k-\omega$ model applied to channel flow, boundary layer flow and a spatially developing mixing layer flow. Emphasis is put on the use of commutation terms at the RANS-LES interfaces in the transport equations for the turbulent kinetic energy, the specific dissipation rate and the momentum equation in order to rapidly reduce the turbulent viscosity across a RANS-to-LES interface and to stimulate the development of resolved turbulent fluctuations. The proposed methodologies are applied at both wall-normal (and inlet) and wall-parallel RANS-LES interfaces. The proposed methodology gives a rapid reduction of the turbulent viscosity at the wall-normal RANS-LES interface from its RANS level to its LES level. Moreover, the proposed methodology contributes to a substantially more rapid establishment of the turbulence-resolving LES flow downstream of the wall-normal RANS-LES interface than if no grey-area mitigation method is applied. However, the proposed methodology has a weaker effect at wall-parallel RANS-LES interfaces, due to a stronger entrainment of LES contents into the near-wall RANS region, than at the wall-normal RANS-LES interfaces. Good agreement with experimental data is obtained with the proposed interface method for the evaluated flow cases. The most obvious grey area mitigation effect is given in the simulated mixing layer flow. Turbulent velocity fluctuations are efficiently established with the commutation term in the momentum equation at the RANS-LES interface in this flow as well as a rapid reduction of the turbulent viscosity due to the commutation terms in the k and ω equations, which gives an almost negligible delay in the development of the resolved turbulence.