Contributions to the Measurement and Analysis of Helicopter Blade Tip Vortices
Leishman, John G
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The physical structure and the evolution of helicopter blade tip vortices, particularly the effect of the filament strain and flow rotation effects on the turbulent structure, were investigated through model-scale hovering rotor experiments as well as by developing a mathematical model from the Navier-Stokes (N--S) equations. The flow properties were measured using a high-resolution, three-component Laser Doppler Velocimetry (LDV) system. Images of the tip vortices were also obtained using laser sheet flow visualization. A strain field on the tip vortices was introduced by placing a solid boundary downstream of the rotor. As the vortices approached this boundary, they were convected radially outwards enabling measurements to be obtained in a known strain field. Comparing these measurements with vortex measurements in free-air provided considerable insight into the interdependence of strain and diffusion and their impact on the evolution of rotor tip vortices. The measurements also served to validate a mathematical model developed to predict the core growth of the tip vortices, which included the effects of both filament strain and diffusion. The measurements also laid the groundwork for the development of a comprehensive engineering tip vortex core growth model, which combined the effects of vortex filament strain and Reynolds number effects. Laser sheet flow visualization of the vortex core structure indicated the presence of three distinct regions --- an inner laminar region, an intermediate transition region and an outer turbulent region. Analysis of the velocity profiles measured across the vortex core at various wake ages further supported this hypothesis. The effects of flow rotation on the turbulence present inside the vortex core was quantified based on a Richardson number concept. This results in a laminar flow structure until a particular distance from the vortex center that correlated with the location where the Richardson number fell below a threshold value Based on these observations an eddy viscosity intermittency function was developed, which modeled the flow transition within the three regions of the core. This function was incorporated into a comprehensive tip vortex model formulated in terms of vortex Reynolds number. The empirical constants used in the present model were obtained from the present measurements, as well as several other sources. The dependence of the results on vortex Reynolds number ensured that the model successfully predicted the core growth of tip vortices for both sub-scale as well as full-scale rotors.