Refer to the sketches in Fig. 8.13. Consider a wind, upstreamspeed u, passing through the rotor of a turbine, with n bladeseach of length R turning at angular velocity 2. Assume that thismovement disturbs a length d of the airflow, which passes intime tw(i) Calculate the time t, for a blade to move to the position of aprevious blade.(ii) If maximum power is extracted when ttip-speed ratio 2 = (2nR/nd).(iii) If wind tunnel tests on certain model turbines show thatmaximum power extraction occurs when approximately d R/2,show that the maximum power coefficient occurs at à =6 fora two-bladed model, and at 1 = 3 for a four-bladed model.t, show that the(iv) What other general deductions can you make from youranalysis? (a)Rotation(b)DisturbedairstreamUndisturbedairstream(c)Fig. 8.13Turbine speed (frequency) and power capture.a Rotational frequency too slow: some wind passes unperturbed through the actuator disk.b Rotational frequency optimum; whole airstream affected.c Rotational frequency too fast: energy is dissipated in turbulent air motion and vortex shedding.

(A) Power extraction is a function of the time "tb" from one blade to move into the positiin…

movement disturbs a length d of the airflow, which passes in time tw (i) Calculate the time t, for a blade to move to the position of a previous blade. (ii) If maximum power is extracted when t, - t, show that the tip-speed ratio 1=(2TR/nd). M.

movement disturbs a length d of the airflow, which passes in time tw (i) Calculate the time t, for a blade to move to the position of a previous blade. (ii) If maximum power is extracted when t, - t, show that the tip-speed ratio 1=(2TR/nd). M.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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