Analysis of axisymmetric boundary layers

Axisymmetric boundary layers are studied using integral analysis of the governing equations for axial flow over a circular cylinder. The analysis includes the effect of pressure gradient and focuses on the effect of transverse curvature on boundary layer parameters such as shape factor and skin-friction coefficient (C_f), defined as H = δ/θ and C_f = τ_w/(0.5pU²_e)respectively, where δis displacement thickness, θ is momentum thickness, τ_w is the shear stress at the wall, p is density and U_e is the streamwise velocity at the edge of the boundary layer. Relations are obtained relating the mean wall-normal velocity at the edge of the boundary layer (V_e) and C_f to the boundary layer and pressure gradient parameters. The analytical relations reduce to established results for planar boundary layers in the limit of infinite radius of curvature. The relations are used to obtain C_f which shows good agreement with the data reported in the literature. The analytical results are used to discuss different flow regimes of axisymmetric boundary layers in the presence of pressure gradients.