Theoretical performance estimation of shrouded-twin-rotor wind turbines using the actuator disk theory

Wind energy is anticipated to play a vital role to fulfill the worldwide energy requirements, whereas existing bare wind turbines can convert only a fraction of flow energy into electricity. To bridge the gap between the escalating demand and the generation capability, we propose a shrouded-twin-rotor turbine design, whose power coefficient exceeds the Betz-Joukowsky limit. We analyze the flow through the wind turbine assembly, using the actuator disk theory, and estimate the power output for a pair of rotor-loading coefficients. We find the existence of two regimes in which the proposed design performs better than the single-rotor configuration: (a) a turbine-turbine mode where both rotors work as turbines and (b) a turbine-fan mode where one rotor is a turbine while the other is a fan- an idea proposed by Betz (A. Betz, Wind-Energie und ihre Ausnutzung durch Windmühlen, Vandenhoeck, 1926). Both modes enable achieving maximum power for multiple combinations of the loading coefficient pair. Moreover, power output depends solely on a single parameter, defined using the area weighted sum of the loading coefficients. We derive the optimum performance criterion and present the effects of the shroud geometry, back pressure, and flow-efficiency parameters on the power output and the performance envelope.