An Eddy-Resolving Reynolds Stress Transport Model for Unsteady Flow Computations

Abstract

The present work deals with the development of an instability-sensitive turbulence model on the Second-Moment Closure level and its application to flow configurations of increasing complexity featured by boundary layer separation. The model scheme adopted, functioning as a ‘sub-scale’ model in the Unsteady RANS framework, represents a differential near-wall Reynolds stress model formulated in conjunction with the scale-supplying equation governing the homogeneous part of the inverse turbulent time scale ω h (ω h = e h / k ). The latter equation was straightforwardly obtained from the model equation describing the dynamics of the homogeneous part e h (e h = e − 0.5ν ∂ 2 k / ( ∂ x j ∂ x j ), Jakirlic and Hanjalic, 2002) of the total viscous dissipation rate e by applying the derivation rules to the expression for ω h . The model capability to account for the vortex length and time scales variability was enabled through a selective enhancement of the production of the dissipation rate in line with the SAS proposal (Scale-Adaptive Simulation, Menter and Egorov, 2010) pertinent particularly to the highly unsteady separated shear layer region. The predictive performances of the proposed model (solved in conjunction with the Jakirlic and Hanjalic’s Reynolds stress model equation) were tested by computing the fully-developed channel flow at different Reynolds numbers, backward-facing step flow, periodic flow over a smoothly contoured 2-D hill in a range of Reynolds numbers and flow in a 3D-diffuser.