DNS Scrutiny of the zeta-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(W)/U(b) = 0.75, intermediate-type with U(W)/U(b) = 1.215, and Couette-type with U(W)/U(b) = 1.5 (U(W) and U(b) are the wall and the bulk velocity), were compared with the pure Poiseuille U(W)/U(b) = 0, at a bulk Reynolds number equal to 4,800 corresponding to Re(tau) = 288. The DNS results were used to scrutinize the capabilities of zeta-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 zeta-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 zeta-f model can reasonably reproduce the phenomenology of these flows in terms of velocity and turbulent kinetic energy profiles and budgets.