Rotorcraft Aerodynamics Group

Rotor Free-Wake Modeling using a Relaxation Technique

Dr. Ashish Bagai and Dr. Gordon Leishman

Introduction

A pseudo-implicit predictor-corrector relaxation algorithm with five-point central differencing in space has been developed for the numerical solution of the non-linear partial differential equations that govern the helicopter rotor free- wake problem. The scheme has been used to predict the locations of the vortices trailed by the rotor blades in hover and forward flight, and to predict the rotor induced velocity field. The work has been directed toward the development of a more robust and versatile free-wake scheme that can be used on a routine basis and incorporated into comprehensive rotor analyses.

Numerical convergence, stability, and accuracy characteristics of the methodology are discussed in detail in the available publications. The pseudo- implicit numerical scheme is compared with more conventional explicit-type free-wake algorithms such as those currently used in CAMRAD and 2GCHAS to demonstrate the enhanced stability and convergence trends of the new scheme. The method is shown to approach a grid-independent wake solution for increasing discretization resolutions, and converges to a unique solution. The use of typical artificial tuning parameters, such as adjustable core radii, has also been eliminated from the formulation, resulting in a scheme that is significantly more robust and versatile than existing methods. The method is also extended to investigate the flow field structures of tandem, side-by-side and coaxial rotor configurations.

The method has been applied to examine rotor wake geometries for a wide variety of geometric rotor configurations and flight conditions, including variations in advance ratio, rotor thrust, number of blades and rotor shaft angles. Comparisons between predictions and experiment are made in the published papers for wake geometries, wake boundaries, rotor induced inflow distributions and flow field velocities, to help validate the predictive capabilities of the new method. The overall agreement between the predictions and experiment are demonstrated to be good.

Predicted wake geometries

Predicted wake geometry for a 4-bladed rotor at several advance ratios

References

Bagai, A., Leishman, J.G., "Rotor Free-Wake Modeling using a Relaxation Technique - Including Comparisons with Experimental Data," Journal of the American Helicopter Society, Vol. 40, No. 2, April 1995.

Bagai, A., Leishman, J.G., "Free-Wake Analysis of Tandem, Tilt-Rotor and Coaxial Rotor Configurations," Presented at the 51st Annual Forum of the American Helicopter Society, Fort Worth, TX, May 9-11, 1995.

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Ashish Bagai

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