Modeling the Aerodynamic Interaction Among Closely Spaced Coplanar Propellers

Abstract

This work presents a low-order framework to predict aerodynamic interaction and the associated tonal loading noise in closely spaced co-rotating propellers under forward-flight conditions. The modeling approach moves beyond acoustic-interference-based methods by explicitly accounting for rotor–rotor aerodynamic coupling. The wake of each propeller is modeled as a system of de-singularized rigid helical tip vortices, which induce velocity via the Biot–Savart law, both on the generating rotor and on neighboring disks. The formulation relies solely on isolated-propeller forces, computed using blade-element momentum theory. The induced velocity field is used to reconstruct the unsteady inflow and blade loading, with unsteady effects incorporated through a Sears-function-based correction. Comparisons against LB-VLES simulations of three side-by-side propellers show that the model accurately predicts the spatial distribution and phase of the unsteady thrust, with peak locations within approximately 10 deg and amplitude errors of about 30%. The resulting loading is coupled to a rotating-dipole acoustic formulation. At the blade-passing frequency (BPF), the predicted far-field directivity agrees within 1-4 dB in most directions. The model captures both the aerodynamic source modulation and the resulting constructive and destructive interference patterns in the tonal acoustic field. Owing to its low computational cost, the proposed model enables rapid assessment of installation effects in early design stages, including variations in propeller spacing and relative phase angle.