An Inviscid model for predicting unsteady forces in doubly connected domains

Abstract

Inviscid analytical-numerical model for predicting unsteady forces on two aerofoil configurations is developed and validated with the past literature. First the unsteady inviscid, incompressible and irrotational, except the logarithmic singularities at vortex points, flow field around the doubly connected domain is evaluated using a conformal mapping method. A discrete vortex shedding mechanism is incorporated to model the free shear layers of the real fluid flow. The complex potential associated with uniform flow and the vortex motion is obtained using elliptic functions and the modified Green’s function respectively. The strengths of the vortices are evaluated using Kutta condition which keeps the regularity of the flow field. Circulation development around the aerofoils is quantified by utilizing Kelvin’s circulation theorem. The unsteady forces are obtained using the unsteady version of the Blasius equation. Both trapezoidal rule and finite difference method are incorporated to solve the unsteady Blasius equation. The developed inviscid model is applied to various aerofoil configurations to predict the unsteady forces on the aerofoils. The results obtained were validated to the past relevant literature. Results showed a good agreement with the past literature.