Development of a finite state coaxial rotor dynamic inflow model
Kong, Yong Boon
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Accurate modeling of rotor inflow dynamics in flight simulations is crucial for rotorcraft performance and handling qualities evaluations. Both Pitt-Peters and Peters-He inflow models are used to predict induced inflow distribution of a single rotor configuration. For coaxial rotor system, most published work focus on performance related studies (both experimental and numerical simulations), which are not compatible for use in real-time rotor inflow simulations. A novel approach to formulate a coaxial rotor inflow model from first principles by superposition of upper and lower rotor pressure potentials is explored in this thesis. By representing both rotors' pressure and downwash in terms of harmonic and radial expansion terms, a finite state coaxial rotor inflow model known as the Pressure Potential Superposition Inflow Model (PPSIM) is developed. Steady hover inflow predictions from PPSIM match well with results obtained from GT-Hybrid and the Viscous Vortex Particle Method (VVPM), but differences in inflow distributions are observed in steady forward flight. This is attributed to wake contractions/distortions and other real flow effects which PPSIM does not account for. In order to identify and incorporate real flow effects into coaxial rotor PPSIM, VVPM induced inflow results are used for system identification. The influence coefficient matrix or L-matrix is extracted from VVPM steady-state change in pressure coefficients and inflow states using the least-square-fit method. The extracted L-matrix is then compared against the original PPSIM L-matrix for calculating correction to each element in the L-matrix. Inflow states from the L-matrix corrected PPSIM show good correlations with VVPM inflow data, capturing wake contractions/distortions, wake diffusion and swirl effects in its new L-matrix. It is also found that these correction terms are insensitive to different upper and lower rotor thrust loading conditions. A second order curve-fitted correlations between elements in the L-matrix correction terms and rotor wake skew functions are found to simplify its implementation into the original coaxial rotor PPSIM L-matrix. While corrections to PPSIM L-matrix improves its steady-state inflow state correlations with VVPM data, it increases phase differences between the two models when comparing their frequency responses. To address this issue, elements in the off-diagonal apparent mass matrix (M-matrix) blocks are modified. A system identification tool, CIFER is used to minimize the cost function between L-matrix corrected PPSIM and VVPM frequency response data over 0.35~5.0 rad/s, which is sufficient for flight dynamics analysis. Average cost functions corresponding to the original PPSIM, L-matrix corrected PPSIM and the newly improved PPSIM (L-matrix corrections and modifications to off-diagonal M-matrix blocks) are compared for hover and various advance ratios. In each comparison, the improved PPSIM has the lowest average magnitude and phase cost functions; indicating that it has the best match with VVPM frequency response data. The improved coaxial rotor PPSIM correctly captures complex rotor-to-rotor aerodynamic coupling effects in its inflow equation and can be easily implemented for computer simulations. Furthermore, since the corrections and modifications are applied to the L- and M-matrices, respectively, its state-space structure is preserved. This means that the improved PPSIM can also be used for eigenvalue analysis as well as control law development in coaxial rotor aeromechanics problems.