Parametric study of passive flow enhancement on a magnus VAWT blade using response surface methodology and direct-forcing immersed boundary method

Abstract

The Magnus vertical axis wind turbine harnesses the principle of the Magnus effect in conjunction with a vertical axis orientation. This mechanism is based on the lift and drag produced by rotating cylinders to propel the rotor and generate power. The proposed method involved installing a flat plate near each rotating cylinder to generate a higher unidirectional torque. As the configuration of the plate affects both the flow pattern and the forces exerted on the blade, the current study aims to identify an optimal blade configuration consisting of a rotating cylinder and a flat plate. A numerical model of the direct-forcing immersed boundary method was used to simulate the flow past a single blade using the static rotor simulation approach, and the Box–Behnken design for the response surface methodology (RSM) was applied to find an optimized flat plate arrangement that would produce the highest mean torque coefficient (CT¯). Three design parameters were examined, specifically the length of the plate (L/D), the gap between the plate and the cylinder (g/D), and the plate's shift angle with respect to the cylinder axis (β). The Reynolds number was 5000, and the cylinder spin ratio (α) was 3. The optimum configuration to achieve a maximum CT¯ was identified at L/D=0.53, g/D=0.1, and β=0°. Validating this optimal CT¯ yielded a value of 0.290, indicating an increase in torque of almost 70% compared to the central design. Furthermore, this value corresponds closely to the predicted result obtained through the RSM optimization method. Considering the flow analysis at various positions, it is crucial to emphasize a critical scenario where the potential for countertorque emerges due to excessive drag at ψ=0° and ψ=315°.