Ashish Bagai

FREE-VORTEX FILAMENT METHODS FOR THE ANALYSIS OF HELICOPTER ROTOR WAKES

The theoretical basis and the numerical implementation of free-vortex filament methods are reviewed for application to the prediction and analysis of helicopter rotor wakes. The governing equations for the problem are described, with a discussion of finite difference approximations to these equations and various numerical solution techniques. Both relaxation and time-marching wake solution techniques are reviewed. It is emphasized how the careful consideration of stability and convergence (grid-independent behavior) are important to ensure a physically correct wake solution. The implementation of viscous diffusion and filament straining effects are also discussed. The need for boundary condition corrections to compensate for the inevitable wake truncation are described. Algorithms to accelerate the wake solution using velocity field interpolation are shown to reduce computational costs without a loss of accuracy. Several challenging examples of the application of free-vortex filament methods to helicopter rotor problems are shown, including multirotor configurations, flight near the ground, maneuvering flight conditions, and descending flight through the vortex ring state

Flow visualization of compressible vortex structures using density gradient techniques

Mathematical results are derived for the schlieren and shadowgraph contrast variation due to the refraction of light rays passing through two-dimensional compressible vortices with viscous cores. Both standard and small-disturbance solutions are obtained. It is shown that schlieren and shadowgraph produce substantially different contrast profiles. Further, the shadowgraph contrast variation is shown to be very sensitive to the vortex velocity profile and is also dependent on the location of the peak peripheral velocity (viscous core radius). The computed results are compared to actual contrast measurements made for rotor tip vortices using the shadowgraph flow visualization technique. The work helps to clarify the relationships between the observed contrast and the structure of vortical structures in density gradient based flow visualization experiments.

Accelerated, High Resolution Free-Vortex Wakes For Rotor Aeroacoustic Analysis

Numerical acceleration algorithms have been developed to improve the computational efficiency of rotor free-vortex wake analyses. Two general methodologies were formulated: an adaptive grid sequencing algorithm, and a velocity field interpolation algorithm. The methods were found to produce up to an order of magnitude decrease in execution time, but without significant loss in predictive accuracy. Examples are shown for very high fidelity wake geometries required for rotor aeroacoustic analyses. t/jj jth rotor discretized azimuth location Ot kth collocation point along vortex filament fl Rotor rotational frequency, rad/s