Finite State Inflow Flow Model for Coaxial Rotor Configuration

Abstract

An analytical coaxial rotor inflow model has been developed from potential flow theory using the pressure potential superposition approach. The coaxial rotor pressure potential superposition inflow model (PPSIM) is formulated in statespace form with structure similar to the Peters–He model, except that additional off-diagonal blocks are included in the apparent mass (M-matrix) and influence coefficient matrices (L-matrix). These off-diagonal blocks take into account mutual interference effects present in a coaxial rotor system by relating the rotor's inflows due to other rotor's pressure loadings. Induced inflow distributions on both upper and lower rotors are computed using PPSIM for comparison against predictions from high-fidelity models such as GT-Hybrid and the viscous vortex particle method (VVPM). Good agreement between PPSIM-induced inflow results and GT-hybrid as well as VVPM data has been shown for hover flight condition. At low advance ratio, there are differences in fore-to-aft inflow states between PPSIM and the high-fidelity models. This is because PPSIM assumed rigid, skewed cylindrical wake geometries for both upper and lower rotors during forward flight. But in GT-Hybrid and VVPM, wake structures are allowed to move freely in space and are mainly affected by rotor-induced velocities at low advance ratios. Owing to the close proximity between upper and lower rotors, mutual interference-induced velocities significantly distorted the rotors' wake geometries. The rigid rotor wake geometry assumptions in PPSIM and the distortion captured in higher fidelity models are the reasons behind differences in rotor-induced inflows. At higher advance ratios, wake distortion effects are less prominent since free-stream inflows are significantly larger than rotorinduced velocities. Hence, smaller differences between PPSIM inflow states and those extracted from GT-Hybrid as well as VVPM are observed at high advance ratios.