Torque-Matched Aerodynamic Shape Optimization of HAWT Rotor

Schmitz and Blade Element Momentum (BEM) theories are integrated to a gradient based optimization algorithm to optimize the blade shape of a horizontal axis wind turbine (HAWT). The Schmitz theory is used to generate an initial blade design. BEM theory is used to calculate the forces, torque and power extracted by the turbine. The airfoil shape (NREL S809) is kept the same, so that the shape optimization comprises only the chord and the pitch angle distribution. The gradient based optimization of the blade shape is constrained to the torque-rotational speed characteristic of the generator, which is going to be a part of the experimental set-up used to validate the results of the optimization study. Hence, the objective of the optimization is the maximization of the turbines power coefficient Cp while keeping the torque matched to that of the generator. The wind velocities and the rotational speeds are limited to those achievable in the wind tunnel and by the generator, respectively. After finding the optimum blade shape with the maximum Cp within the given range of parameters, the Cp of the turbine is evaluated at wind-speeds deviating from the optimum operating condition. For this purpose, a second optimization algorithm is used to find out the correct rotational speed for a given wind-speed, which is again constrained to the generator's torque rotational speed characteristic. The design and optimization procedures are later validated by high-fidelity numerical simulations. The agreement between the design and the numerical simulations is very satisfactory.