Theoretical And Experimental Studies Of Swirling FlowsIn Diverging Streamtubes

Abstract

Analytical and experimental methods are used to study the presence of vortex breakdown states appearing on slender vortices in slightly diverging streamtubes. Asymptotic methods are used to obtain analytical solutions of the steady and axisymmetric Euler equations for near-critical rotating flows. Multiple flow states which describe either a small perturbation of the base rotating flow or a larger-amplitude disturbance may appear. The stability of the various flow states around the critical swirl is also studied. It is found that, for swirling flows below the critical value, the slightly perturbed states are linearly stable whereas the large-disturbance states are unstable to a certain mode of disturbance. The analysis suggests the transition to vortex breakdown as the swirl level is increased. To demonstrate the applicability of these relations, LDV measurements were made of the leading-edge vortices that develop over a delta wing with a 67.6° sweep back angle. The measured axial and azimuthal velocity profiles are utilized in the formulae for equilibrium and stability and a relation is established to predict the presence of the vortex breakdown phenomenon in leading-edge vortices. It is demonstrated that the location of vortex breakdown along the wing chord can be predicted from flow measurements at a lower angle of attack where no breakdown exists.