Using blade element momentum methods with gradient-based design optimization

Blade element momentum methods are widely used for initial aerodynamic analysis of propellers and wind turbines. A wide variety correction exist, but common to all variations, a pair residuals converged ensure compatibility between the two theories. This paper shows how rearrange sequence calculations reducing single residual. yields significant advantage that convergence can be guaranteed machine precision. Both these considerations particularly important gradient-based optimization where atypical inputs may explored, tight is necessary accurate derivative computation. On moderate-sized example problem we show over an order magnitude increase in speed, with no changes physics. done by using residual form, providing numerically exact gradients algorithmic differentiation adjoint, leveraging sparsity Jacobian graph coloring techniques. Finally, demonstrate revised formulation cases when inflow exists one directions (e.g., hovering rotor or parked rotor). These new allow robust applications, avoiding occasional numerical difficulties exist standard formulation.