Simpified theory of wind turbine noise

Abstract

The noise is expected to be accounted for by the forces exerted on the air by the blades and pillar; the idealized design is presumed sufficiently optimal that the power is maximum and the generated sound is minimal for that power generation. Betz’s law applies, and the steady torque exerted on the air by the turbine has a relation to the net drag force (in the direction of incoming flow) exerted on the turbine blade system. The forces associated with the torque create an acoustic pressure field that is even in the coordinate along the turbine axis. The forces associated with the drag create a field that is odd in this coordinate. These two contributions can constructively reinforce or interfere, so the various pure tone contributions at multiples of the blade passage frequency can have nodes in the polar plot of radiated far‐field intensity. The locations of these are explained with the use of Betz’s law. At moderate to higher frequencies, interest is typically in finite‐frequency bands, which contain a large number of discrete tones. To predict the noise within such bands, sums that appear in the basic Gutin theory are replaced by integrals, and appropriate smoothing techniques are applied.