Analysis of axisymmetric boundary layers

TL;DR

This paper uses integral analysis to study axisymmetric boundary layers over a cylinder, examining how transverse curvature and pressure gradients influence boundary layer parameters and flow regimes.

Contribution

It introduces analytical relations linking boundary layer parameters and flow conditions, extending classical results to axisymmetric flows with curvature effects.

Findings

Derived relations for $C_f$ and $V_e$ that agree with existing data.

Showed curvature effects significantly influence boundary layer parameters.

Discussed flow regime transitions in axisymmetric boundary layers.

Abstract

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 ($H$) and skin-friction coefficient ($C_f$), defined as $H = \delta^*/\theta$ and $C_f = \tau_w/(0.5\rho U_e^2)$ respectively, where $\delta^*$ is displacement thickness, $\theta$ is momentum thickness, $\tau_w$ is the shear stress at the wall, $\rho$ 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.