Tip vortices--single phase and cavitating flow phenomena

Abstract

Tip vortices occur wherever a lifting surface terminates in a fluid. An understanding of tip vortices is salient to the solution of many engineering problems, including lift induced drag tip inefficiency, the overturning of small planes flown into the tip wake of larger aircraft, and marine propellor tip cavitation. The tip vortex shed by several rectangular planform wings, fitted with three different tips, was studied in a water tunnel. Four techniques were employed to examine the tip vortex: (i) Surface flow visualization to reveal the early stages of vortex rollup. (ii) Double pulsed holography of buoyant, Lagrangian particle tracers for detailed tangential and axial velocity data around the vortex core. Holograms were also a source of instantaneous core structure information. (iii) Single pulse holography of air bubbles, of uniform, measured, original size. The size of the bubbles is related to the instantaneous local static pressure. The bubbles are driven by the centripetal pressure gradient forces into the vortex core, providing a means of measuring the average and transient vortex core pressure non-intrusively. (iv) Direct observation of vortex cavitation. These measurements are useful in their own right because of the considerable technological significance of tip vortex cavitation. In addition, many single phase tip flow characteristics have cavitating flow counterparts. The present study has shown that one chord downstream of the wing trailing edge virtually all the foil bound vorticity has rolled up into the trailing vortex. Armed with this knowledge one may a priori evaluate, in the near field, the tangential velocity distribution, the core axial velocity excess, and the core mean pressure. These predictions are in agreement with the experimental measurements. Three aspects of the core flow, first observed in the present study, remain analytically inexplicable: (i) The trend towards a Reynolds number dependent, axial velocity deficit with downstream distance. (ii) The unsteady core velocity, particularly immediately downstream of the foil. (iii) The vortex kinking which is coincident with highly unsteady axial core flow. As a first approximation, cavitation inception occurs when the core pressure is reduced to the vapour pressure. The large measured fluctuating core pressure explains the occurrence of inception at core pressures somewhat above p[v] and the dependence of sigma[i] on the dissolved air content. Modifying the tip geometry profoundly affects the trailing vortex. Installation of a ring wing tip can reduce the inception index relative to that of a normal rounded tip foil by a factor of three. The reduction was caused primarily by the redistribution, in the Trefftz plane, of the shed vorticity about a line and circle. Fortuitously, this redistribution caused most of the wing bound vorticity to be shed from the ring, decreasing the tip effect lift loss over the foil body.