Theoretical and experimental investigation of vortex breakdown in diverging streamtubes

The structure and instability of incompressible inviscid and viscous swirling flow in a diverging streamtube and its relation to the onset of vortex breakdown are studied. Flows of this type have technological applications ranging from the design of combustion chambers in gas turbine systems to the control of leading-edge vortices over slender wings of airplanes. The study is based on an analytical investigation of the axisymmetric Euler equations and complemented by experiments performed on a 67° swept back delta wing.; Asymptotic expansions, in terms of streamtube divergence, are constructed for swirling flows in a finite-length domain. As the swirl level is increased to the critical swirl, the regular asymptotic expansion becomes misordered, implying that large amplitude disturbances may be induced by a small but finite amount of flow divergence. This leads to an alternate set of expansions for studying the interactions of these types of near-critical swirling flows. It is found that a small but finite streamtube divergence breaks the transcritical bifurcation of flow states to a straight tube into two branches of solutions. These branches fold at limit swirl levels near the critical swirl with a finite gap separating them. This means that no near-columnar axisymmetric state can exist in a finite range of incoming swirl around the critical swirl level; the flow must develop large disturbances in this swirl range. Beyond this range, two steady states may exist under the same inlet/outlet conditions. However, when the streamtube divergence is further increased this special behavior uniformly changes and only a single branch of states with no fold exits.; The stability of these steady state non-columnar solutions around the critical swirl is also investigated. This analysis indicates that the critical swirl is a point of exchange of stability and that the large-amplitude states are unstable and not physically realizable flow states. Therefore, a transition process takes place leading to the evolution of large-amplitude disturbances that may form axisymmetric vortex breakdown states. These results extend the recent theory of Wang and Rusak [88, 89] for the axisymmetric breakdown in high Reynolds number flows in a straight tube to the case of a diverging tube.; Experimental measurements, using LDV, were made of the axial and azimuthal velocity components of leading-edge vortices that develop over a delta wing with a 67° sweep angle. This information is used in the steady state and stability analyses to demonstrate the applicability of this analysis in characterizing the susceptibility of these slender vortices to breakdown.