Prediction of vortex breakdown in leading edge vortices above slender delta wings

Abstract

This paper applies a recent theory on the axisymmetric vortex breakdown process to experimental flow profiles of leading edge vortices above slender delta wings at high angles of attack. Using several simplifying assumptions about the nature of the vortex generation process and its swirl ratio dependence on angle of attack, the necessary conditions for the breakdown of the vortices are calculated. The computations show good agreement with the available experimental data and, thus, provide an efficient method to accurately predict the burst locations as function of angle of attack along a delta wing. Specifically, this can be predicted out of a single set of measurements at a lower angle of attack where no sign of breakdown yet exists. In addition, the calculation of the swirl ratio based on the ratio of the maximum circumferential speed over the maximum axial speed, at the breakdown conditions reveals that it is almost independent of both the angle of attack and location along the wing chord, having an average value of 0.58. This swirl ratio may, therefore, serve as a simple universal criterion for the appearance of breakdown along leading edge vortices above slender wings with sharp edges. Nomenclature