Numerical Investigation of Self-Starting Capability of Vertical-Axis Wind Turbines at Low Reynolds Numbers

Abstract

The self-starting capability of a NACA 0018 multi-bladed vertical-axis wind turbine is numerically investigated. The immersed boundary method is used to simulate the flow around a two-dimensional cross section of the wind turbine and the predictor-corrector method is used to couple the equation of motion of the turbine. A simple load model, which is linearly proportional to turbine angular velocity, is used for the load of the turbine. The angular velocity is characterized as a function of Reynolds number, density ratio, and viscous coefficient of the proposed load model. The power outputs and moment coefficients of motor-driven and flow-driven vertical-axis wind turbine are compared. For a particular Reynolds number, as the load on the flow-driven turbine is increased, the tip speed is reduced until the turbine fails to coherently rotate. The flow-driven and motor-driven moment coefficients in the computation have good agreement between each other and are qualitatively similar to the torque measured in experiments. These computations suggest that the load of a flow-driven turbine can be well-represented by the proposed load model and a motor-driven turbine can reproduce the physics of a flow-driven turbine within the range of tip-speed ratio examined. A simple model is proposed in order to analyze the starting torque. By assuming that the inertia of the blade is much larger than the fluid, the turbine can be considered stationary in the flow. The starting torque distribution of a multi-bladed turbine indicates the important orientations corresponding to maximum torque generation, at which a self-starting turbine always starts, and a stable equilibrium, where a non-self-starting turbine oscillates. These features agree with observations from the full simulations of the starting process. We further model the starting torque distribution by considering a single blade at different orientations, and construct starting torque distributions for multi-bladed turbines by linearly combining the torques at the respective positions of the blades. We show that this approximation is valid for a sufficiently low turbine solidity of about 0.5. Using this model, we find optimal starting configuration for a multi-bladed low-solidity vertical-axis wind turbine.

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