Grid dependence of k-ε model for oscillatory boundary layers

The low Reynolds number k-ε model is used in some commercial hydrodynamic models to determine boundary layer properties. Such models have been found to produce grid-dependent solutions. A reliable engineering estimate of fundamental boundary layer properties is of utmost importance for practicing engineers. Here, the effect of grid spacing in four different versions of the low Reynolds number k-ε model is studied using direct numerical simulation data of a one-dimensional sinusoidal oscillatory boundary layer. A detailed comparison is made for cross-stream velocities, turbulent kinetic energy, bottom shear stress, friction factor and phase difference. For the present data, the limiting value of the distance to the first grid point from the wall is expressed in terms of Stokes layer thickness. It is observed that, in order to predict the boundary layer properties with reasonable accuracy, the first grid point should be placed at a distance of about 0.02 times the Stokes layer thickness from the wall. The results of the present study may be useful for practicing engineers and researchers in their choice of appropriate grid spacing for low Reynolds number k-ε models.