Diffusion and decay of turbulent elliptic wakes

Abstract

Three-dimensional, turbulent wakes having elliptical cross-sections were studied both experimentally and analytically for a constant-fluid-property, zero-pressure-gradient flow. An analytical solution for wake diffusion and decay was obtained from a linearized momentum equation by assuming a constant eddy viscosity in the transverse plane but variable along the wake centerline. The experimental data confirmed the prediction that elliptical wakes approach a axisymmetry far downstream. Data were obtained in wakes of 1 inch and 3 inch diameter disks having eccentricities of 1.0, 0.6 and 0.2 over a mean Reynolds number range from 2.4 x 10^4 to 7.1 x 10^4 Mean velocity and turbulent intensity data were gathered between 8 and 266 diameters downstream of the disks. Several arbitrary constants of the analysis were determined so that engineering estimates can be made from the analytical results. Unlike axisymmetric and two-dimensional geometries, elliptic wakes offer an opportunity to test eddy viscosity assumptions in one plane without adjustable factors, and this was done. However, the mean velocity profiles deviated from the predicted Gaussian shape even though approximate similarity was attained far downstream.