Temporal filtering: A consistent formalism for seamless hybrid RANS–LES modeling in inhomogeneous turbulence

A consistent formalism is developed for seamless hybrid RANS–LES models in inhomogeneous, stationary flows, based on Eulerian temporal filtering. The issues of Galilean invariance of the filtering process and consistency with the Reynolds average are addressed. The similarity of the RANS and TLES equations suggests the use of the same form of model for the two limiting approaches. The inconsistency of the existing TLES models with the RANS limit leads to the choice of the opposite strategy: adapting a RANS model to the TLES limit. The method proposed to achieve this adaptation is the Temporal Partially Integrated Transport Model (TPITM), a temporal version of the spatial PITM. The applicability of the method is shown by performing channel flow simulations using transport equations for the subfilter stresses, derived from the Elliptic-Blending Reynolds-Stress RANS Model (EB-RSM). Finally, the fact that the temporal filter width can be implicitly defined by the associated spatial filter width suggests that most of the unsteady approaches used in everyday applications, such as DES, SAS, URANS, among others, can be regarded as temporally filtered approaches.