Analytical Linearization Of Rotor Simulation In Ground Effect Using A Coupled Panel And Viscous Vortex Particle Method In State-Space Form

Abstract

This study extends previous work on the state-space formulation and analytical linearization of viscous vortex particle methods by incorporating ground effect into rotary-wing simulations. The aerodynamic solver couples a panel method for modeling blade surfaces and near-wake dynamics with a Viscous Vortex Particle Method (VVPM) for capturing the far-wake. Ground effect is modeled using the method of images. The combined formulation is expressed as a system of Ordinary Differential Equations (ODEs), resulting in a Non-Linear Time-Periodic (NLTP) system in first-order form. Two linearization techniques are applied to this NLTP system: a conventional finite-difference approach and an analytical linearization scheme extended to include ground influence. Harmonic decomposition is then used to convert the Linear Time-Periodic (LTP) model into a higher-order Linear Time-Invariant (LTI) system, enabling the development of a reduced-order linear model suitable for real-time analysis and control. The simulation model is implemented in MATLAB® and applied to a utility-scale helicopter rotor blade. Validation is performed against experimental and high-fidelity numerical results for In-Ground-Effect (IGE) conditions. The linearized models are shown to closely replicate the nonlinear system dynamics across time and frequency domains. Furthermore, the analytical linearization offers a substantial computational advantage over finite-difference methods, with an efficiency gain on the order of O(n2). This simulation model enables accurate and efficient modeling of aerodynamic effects in rotary-wing applications, including ground effect interactions.