Measurement Investigation of Complex Eddy Viscosity Model in Non-Equilibrium Wavy Wall Turbulence with TRPIV

Abstract

The spatial flow fields of turbulent boundary layer over a wavy wall were measured by TRPIV at three different Reynolds numbers in a water channel, the mean streamwise and wall-normal velocities near the wall were calculated from the time series of instantaneous spatial 2D-2C flow fields of turbulent boundary layer, and the periodic distributions of the streamwise and wall-normal velocity in streamwise direction influenced by the wavy wall were found. The spatial distributions of Reynolds stress and mean velocity strain rate were obtained by ensemble average. Using the spatial cross-correlation technique, the spatial phase relationship in streamwise direction between mean velocity strain rate and Reynolds stress was investigated. It is found that there exist spatial phase differences between Reynolds stress components and mean velocity strain rate components, the phase differences increase gradually after decrease gradually from zero away from the wavy wall in wall-normal direction and reach a minimum at 0.4~0.5 times the wavelength of wavy wall, and in a certain range the effect of the Reynolds number on the phase differences is very small. The reasonability of the complex eddy viscosity model is confirmed by these experimental evidences in order to forecast non-equilibrium turbulence accurately.