Adaptive Grid Sequencing and Interpolation Schemes for Helicopter Rotor Wake Analyses

Numerical acceleration schemes have been developed to improve the computational efe ciency of free-vortex analysesofhelicopter rotor wakes. Two general methodologieswere formulated based on adaptivegrid sequencing and velocity e eld interpolation schemes. Both approaches considerably reduce the number of induced velocity evaluations in free-vortex schemes but without signie cant loss in predictive accuracy of the wake geometry. The methods have been implemented and evaluated for a rotor wake analysis based on a pseudoimplicit predictor ‐ corrector(PIPC)relaxationalgorithm.Theaccelerationschemeswerefoundtoproduceuptoanorderofmagnitude decrease in execution times. Both methods are generic in formulation and application and may be adapted for use in other free-vortex methodologies. A third method that specie cally exploits the pseudoimplicitness of the PIPC scheme has also been developed, resulting in further increases in computational efe ciency. Nomenclature Nb = number of rotor blades NCP = total number of wake collocation points NE = number of Biot ‐Savart induced velocity evaluations N‡ = number of free collocation points per vortex e lament NA = number of discrete azimuthal locations n = number of rotor revolutions of free-vortex wake rj;k = collocation point position vector, m Vind = induced velocity vector, ms i1 V1 = freestream velocity vector, ms i1 1‡ = vortex e lament discretization resolution, deg 1A = azimuthal discretization resolution, deg ‡k = kth collocation point along vortex e lament π = advance ratio Ab = blade azimuthal location, deg A j = jth discretized azimuth location on rotor A = rotor rotational frequency, rad s i1