Laminar flow of viscous fluid around elliptical contours under angle of attack

TL;DR

This paper analyzes laminar flow around elliptical cylinders at an angle of attack, deriving shear stress, separation points, circulation, and lift and resistance coefficients, with validation against experimental and numerical data.

Contribution

It provides a complete analytical solution for velocity, pressure, and force coefficients for elliptical cylinders in laminar flow, incorporating angle of attack effects.

Findings

Shear stress and separation points are determined analytically.

Lift and resistance coefficients depend on angle of attack and ellipse axes ratio.

Theoretical results align well with experimental and numerical data.

Abstract

The planar problem of a viscous laminar flow around elliptical cylinders under angle of attack is considered. From the solution of the laminar boundary layer equations using the Loytsyansky local similarity method, the shear stress at the ellipse boundary and the separation point is found. From the separation points velocities equality, the circulation is found. A complete solution to the problem of the velocity and pressure field outside the boundary layer is also constructed. The coefficients of lift and resistance are found depending on the angle of attack and the ellipse axes ratio. The theoretical results are compared with the available experimental data and direct numerical solutions of the Navier-Stokes equations.