A semi-analytical model of the 3D boundary layer over the streamlined nose of a train

The boundary layer concept is applied to the flow around the nose of a streamlined train. In general, that flow is not axisymmetric due to the shape of the nose and the crosswind component of the relative incoming velocity. This departure from axisymmetry produces a transverse pressure gradient that is responsible for skewing an otherwise plane boundary layer. An empirical correlation, dependent on the longitudinal velocity and one unknown parameter, is used to represent the transverse velocity profile. The value of that unknown parameter is obtained from the momentum equations integrated streamwise inside the boundary layer. A visual comparison was carried out between the numerical simulations and the skin shear pattern of a scale model in a wind tunnel. The qualitative results compare well, the numerical model being able to locate the position of the main longitudinal vortices on the lee side of the train.