Large-eddy Simulation of Turbulent Boundary Layers with Spatially Varying Roughness

Abstract

This dissertation addresses high Reynolds number turbulent boundary layers flows with different inhomogeneous surface roughness distributions using large eddy simulations. The stretched vortex subgrid scale model for the outer flow LES is coupled with a virtual-wall model for the friction velocity with a correction accounting for local roughness effects. A semi-empirical model that describes a fully developed rough-walled turbulent boundary layer with sand-grain roughness length-scale ks = αx that varies linearly with streamwise distance is first developed, with α a dimensionless constant. For large Rex and a free-stream velocity U∞ ~ xm, a simple log-wake model of the local turbulent mean-velocity profile is used that contains a standard mean-velocity correction for the asymptotic, fully rough regime. A two parameter (α; m) family of solutions is obtained for which U∞+ (or equivalently Cf) and boundary-layer measures can be calculated. These correspond to perfectly self-similar boundary-layer growth in the streamwise direction with similarity variable z/ks where z is the wall-normal co-ordinate. Results over a range of α are discussed for cases including the zero-pressure gradient (m = 0) and sink-flow (m = -1) boundary layers. Model trends are supported by high Re wall-modeled LES. Linear streamwise growth of boundary layer measures is confirmed, while for each α, mean-velocity profiles and streamwise turbulent stresses are shown to collapse against z/(αx). Inner scaled velocity defects are shown to collapse against z/Δ, where Δ is the Rotta-Clauser parameter. The present results suggest that these flows may be interpreted as the fully-rough limit for boundary layers in the presence of small-scale, linear roughness. Next, an LES study of a flat-plate turbulent boundary layer at high Re under nonequilibrium flow conditions due to the presence of abrupt changes in surface roughness is presented. Two specific cases, smooth-rough (SR) and rough-smooth (RS) transition are examined in detail. Streamwise developing velocity and turbulent stress profiles are considered and sharp departures from equilibrium flow properties with subsequent relaxation are shown downstream. Relaxation trends are studied using integral parameters and higher-order mean flow statistics with emphasis on Reτ and ks+ dependence. Results are compared with RS experiments at matched Reτ, and show good agreement in terms of recovery rates. Finally, the case of static, impulsive wall-roughness in flows at high Re is addressed using the same LES framework. The initial perturbation from smooth-to-rough appears to dominate the flow behaviour with the length of the impulsive patch showing little effect on recovery rates at matched Reτ and ks+. The resulting trends show good agreement with low Re experiments and support the wall-modeled LES framework as a suitable method for analysing high Re flows in practical applications.