A Unified Momentum Model for rotor aerodynamics and wakes across operating regimes*

One-dimensional momentum theory, derived in the 19th century, is the predominant model used in engineering rotors including wind turbines, propellers, helicopters, drones, and hydrokinetic turbines. The theory represents the rotor as a porous actuator disk that imparts a thrust force on the flow, generating induced velocities and a wake. The classical theory breaks down at higher thrust coefficients and for any misalignment between inflow and rotor, which are commonly encountered in practice. Current models rely on empiricism to address these regimes. This study reports a Unified Momentum Model that predicts rotor aerodynamics and wakes across arbitrary thrust coefficients and rotor-inflow misalignments. Using conservation of mass, momentum, and energy, the limiting assumptions of the classical theory are eliminated by modeling the pressure deficit in the rotor wake, using a solution to the differential Euler equations, and by accounting for arbitrary rotor misalignment with a lifting line model. The Unified Momentum Model is validated against large eddy simulations and is also coupled with a blade element model to result in a new physics-based blade-element momentum (BEM) model without empirical corrections. Finally, the model is leveraged in applications including wind farm flow control and control co-design. The model provides a new basis for rotor modeling, design, and control tools from first-principles, rather than starting from classical theory coupled with empirical corrections.