DNS Scrutiny of the ζ-f Elliptic-Relaxation Eddy-Viscosity Model in Channel Flows with a Moving Wall

Abstract

In this paper we present a Direct Numerical Simulations (DNS) of channel flow with stationary and moving walls. Three cases, Poiseuille-type with UW/Ub = 0.75, intermediate-type with UW/Ub = 1.215, and Couette-type with UW/Ub = 1.5 (UW and Ub are the wall and the bulk velocity), were compared with the pure Poiseuille UW/Ub = 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.