4. For the Japanese wind lens turbine, the effect of the shroudis to reduce the downstream pressure, e.g., in the rotor wake, sayby ?P. Show by modifying the Betz limit, how power production canactually be greater than the Betz limit. Your power productionshould be a function of a = v4/V. Assume v4 and S4 are known. Getit as close as you can. In the process, recognize that the windspeed at the rotor plane and even in the wake region are greaterthan the measured wind speed in free stream. Consider the streamtube below. Follow the same methodology used to derive the Betzlimit.
(i). Relate all mass flows at each section to the downstreammass flow rate at section 4.
(ii). Apply conservation of mass to relate section areas toS4.
(iii). Apply conservation of linear momentum applied to andBernouli’s equation to calculate the drag force, D, across therotor plan.
(iv). Equate these expressions for Drag.
(v). Use conservation of energy to estimate power production asa function of a = v¬4 / V.
