Nonlinear Large Angle Solutions of the Blade Element Momentum Theory Propeller Equations

Stephen Whitmore, Utah State University
S. R. Merrill

Originally published by AIAA in AIAA Journal of Aircraft.

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Propeller Blade Element Momentum theory is a first-order method commonly used to analyze propeller performance. Blade Element theory discretizes the rotor and analyzes aerodynamic forces acting on each element, and requires only a rudimentary description of the blade geometry. Blade Element theory alone lacks the ability of predicting the propeller-induced inflow velocity needed to complete the flow field description. The flow model is completed using concepts from momentum theory, which assumes a single continuous axi-symmetric flow through rotor disk. The traditional method used to solve the Blade Element Momentum equations assumes a small local angle-of-attack at all sections along the blade, and that local induced drag negligibly reduces the local propeller thrust coefficient. These assumptions, while allowing a closed form solution to be obtained, are known to be inaccurate at high advance ratios and along the inner half-span of the blade. An alternative non-linear, numerical solution method that avoids these inaccurate simplifying assumptions is presented. Solution methods are compared for multiple pitch angles and advance ratios. Solutions are compared to thrust and power coefficient data collected from wind tunnel tests of small radio-control aircraft propellers. The non-linear theory corrections better represent measured propeller performance, especially at high advance ratios.