Three-dimensional boundary layer flow approaching a circular cylinder normal to a semi-infinite flat plate

Abstract

The three-dimensional laminar and turbulent boundary layer flows past a flat plate with a cylinder normally attached to itself have been numerically analysed. A finite difference method was used for the solutions to the governing partial differential equations. The numerical scheme is an extension of Crank-Nicolson``s implicit one to the case of three-dimensional flow by introducing the zone of dependence principle which is important in three-dimensional boundary layer calculation. A stable numerical scheme was developed to predict the three-dimensional separation line at which the conventional numerical scheme is very unstable. Mixing length model and k-$\varepsilon$ model were used to express the turbulent shear stresses, -$\overline{eu``v``}$ and -$\overline{ev``w``}$. Predicted velocity profiles were favorably compared with experimental data reported by previous workers. The method of solution used was found to be stable and good in its convergency.