Analytical and numerical investigation of whirl flutter

Abstract

The increasing integration of electrification into aircraft design has introduced new challenges in aeroelastic stability, particularly for unconventional configurations such as NASA's X-57 Maxwell. This thesis investigates whirl flutter behavior, an aeroelastic instability caused by the interaction between gyroscopic moments from rotating propellers and the elastic properties of the airframe. The phenomenon has historically led to catastrophic failures, most notably in the Lockheed L-188 Electra. Growing concerns regarding sustainability, carbon reduction, and the use of renewable energy have brought innovative solutions to the field of aviation. In this context, the widespread adoption of Distributed Electric Propulsion (DEP) has made wing-integrated distributed thrust systems an inevitable component of next-generation electric aircraft designs. As DEP systems require explicit consideration of the whirl flutter phenomenon in the design process and the demonstration of compliance with certification requirements, this phenomenon has once again gained critical importance. This study presents a comprehensive analytical and numerical framework to analyze whirl flutter phenomena in propeller-driven aircraft. The research builds upon the foundational work of Wilmer H. Reed and Houbolt, who developed analytical models for propeller precession instability. The numerical analysis tool (MSC Nastran), commonly used for complex designs and integrated aircraft models, is implemented with an aerodynamic approach based on Reed and Houbolt theory. The analytical and numerical models employed in this thesis have been adapted and extended for both conventional and modern aircraft configurations. The thesis begins by reviewing the historical and theoretical background of the subject, including the Lockheed Electra cases and experimental studies conducted by NASA Langley. Special emphasis is placed on the assumptions used to mathematically model the physical problem, the Houbolt Reed aerodynamic model applied in both numerical and analytical solutions, and the validation procedures supported by experimental data. These analyses form the foundation of the modeling approaches developed throughout the thesis. Using different methods analytical models and numerical models the findings from NASA research group's whirl flutter experiments were reproduced and validated. Two dynamic models were developed: Model I: Analytical calculation of whirl flutter of a rigid-bladed propeller elastically mounted in pitch and yaw directions. Model II: Numerical calculation (MSC Nastran) of whirl flutter of a rigid-bladed propeller elastically mounted in pitch and yaw directions. In the analytical solution model, the quasi-steady aerodynamic theory developed by Houbolt and Reed was implemented using symbolic programming techniques in MATLAB, and the equations of motion were derived. Within the scope of the parametric studies, the effects of propeller pivot location, mass distribution, stiffness ratios, and damping coefficients on the onset of flutter were analyzed. In the numerical solution model, the Fortran code developed by MSC Nastran to obtain propeller aerodynamic derivatives based on Houbolt–Reed theory was utilized. The aerodynamic derivatives computed using the MATLAB code developed for the analytical model were compared with those obtained from MSC Nastran's Fortran code implementation and validated using experimental data published from NASA's research group. The validation studies were carried out using historical experimental data from Bennett and Bland (1961), comparing six different configurations. Results from the proposed analytical models showed closer agreement with experimental flutter boundaries than existing literature estimates, demonstrating the accuracy and robustness of the modeling approach. This work not only contributes to the theoretical understanding of whirl flutter but also addresses regulatory demands. In particular, NATO STANAG 4671, paragraph USAR.629, mandates the analysis of whirl mode instabilities for all propeller-driven unmanned aircraft. The models and solution methodology developed in this thesis are fully compatible with such certification requirements. In conclusion, this study offers a validated and adaptable toolset for early-stage aeroelastic assessment of propeller-driven aircraft. The outcomes are directly applicable to emerging electric aircraft technologies and support the continued evolution of safe and sustainable aviation.