Question

4. For the Japanese wind lens turbine, the effect of the shroud is to reduce the downstream pressure, e.g., in the rotor wake, say by ?P. Show by modifying the Betz limit, how power production can actually be greater than the Betz limit. Your power production should be a function of a = v4/V. Assume v4 and S4 are known. Get it as close as you can. In the process, recognize that the wind speed at the rotor plane and even in the wake region are greater than the measured wind speed in free stream. Consider the stream tube below. Follow the same methodology used to derive the Betz limit.

(i). Relate all mass flows at each section to the downstream mass flow rate at section 4.

(ii). Apply conservation of mass to relate section areas to S4.

(iii). Apply conservation of linear momentum applied to and Bernouli’s equation to calculate the drag force, D, across the rotor plan.

(iv). Equate these expressions for Drag.

(v). Use conservation of energy to estimate power production as a function of a = v¬4 / V.

Answer 1