DNS scrutiny of the ζ-f elliptic-relaxation eddy-viscosity model in channel flows with a moving wall

In this paper we present a Direct Numerical Simulations (DNS) of channel flow with stationary and moving walls. Three cases, Poiseuille-type with U /U = 0.75, intermediate-type with U/U = 1.215, and Couette-type with U/U = 1.5 (U and U are the wall and the bulk velocity), were compared with the pure Poiseuille U/U = 0, at a bulk Reynolds number equal to 4,800 corresponding to Re $-{\uptau} =288$ . The DNS results were used to scrutinize the capabilities of ζ-f eddy viscosity model (based on the elliptic relaxation concept) in reproducing the near-wall turbulence in non conventional flows where the shear stress structures are strongly different with respect to the cases used for models calibration. The ζ-f model (also in its basic formulation) demonstrated to have good prospects to reproduce the main phenomenology of such class of flows due to its built-in capabilities to account separately for the different (and opposite) near wall effects on turbulence: the damping due to viscosity and pressure reflection. The results of the computations demonstrated that standard ζ-f model can reasonably reproduce the phenomenology of these flows in terms of velocity and turbulent kinetic energy profiles and budgets. © 2011 Springer Science+Business Media B.V.