Blade Element Momentum (BEM) for propellers and turbines: part 2 blade element (plus momentum)
Deriving thrust and torque from the blade element perspective. Equating with momentum theory to solve for the axial and tangential induction factors. Showing how to solve more efficiently with a 1D residual. Overview of the implementation for computing across the whole rotor. Non-dimensionalization.
For more detail see the following two references:
Ning, A., “Using Blade Element Momentum Methods with Gradient-Based Design Optimization,” Structural and Multidisciplinary Optimization, Vol. 64, No. 2, pp. 994–1014, May 2021. doi:10.1007/s00158-021-02883-6
Ning, A., “A Simple Solution Method for the Blade Element Momentum Equations with Guaranteed Convergence,” Wind Energy, Vol. 17, No. 9, pp. 1327–1345, Sep. 2014. doi:10.1002/we.1636