A discrete free vortex method of analysis for inviscid axisymmetric flows around parachute canopies

Abstract

A discrete vortex method is developed for modelling inviscid, incompressible, axisymmetric flows at high Reynolds numbers around parachute canopies. In this model the canopy surface is represented by a lattice of panels, each one of which contains a bound vortex ring. The free shear layer which carries high vorticity fluid from the upstream surface boundary layer, is simulated by a sheet of discrete free vortex rings. The shedding location and the strength of each newly-created vortex ring, together with the time step for model calculations are determined as functions of the undisturbed stream velocity and canopy shape. A standing eddy on the downstream body surface, ensures that near the canopy hemline the Kutta condition is maintained. The wake developed behind the canopy is found to be characterised by vortex ring clusters, shed at nearly periodic intervals. Calculated results for differential pressure distributions and the resulting axial forces. in both steady and unsteady flows, are obtained from the model and are in good agreement with established experimental data. The model could be used in conjunction with a material strength model for the prediction of aerodynamic loads during the canopy inflation phase.