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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
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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Refer to the sketches in Fig. 8.13. Consider a wind, upstream speed u, passing through the rotor of a turbine, with n blades each of length R turning at angular velocity 2. Assume that this 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 tip-speed ratio 2 = (2nR/nd). (iii) If wind tunnel tests on certain model turbines show that maximum power extraction occurs when approximately d R/2, show that the maximum power coefficient occurs at à =6 for a 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 your analysis?
Transcribed Image Text:Refer to the sketches in Fig. 8.13. Consider a wind, upstream speed u, passing through the rotor of a turbine, with n blades each of length R turning at angular velocity 2. Assume that this 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 tip-speed ratio 2 = (2nR/nd). (iii) If wind tunnel tests on certain model turbines show that maximum power extraction occurs when approximately d R/2, show that the maximum power coefficient occurs at à =6 for a 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 your analysis?
(a) Rotation (b) Disturbed airstream Undisturbed airstream (c) Fig. 8.13 Turbine 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.
Transcribed Image Text:(a) Rotation (b) Disturbed airstream Undisturbed airstream (c) Fig. 8.13 Turbine 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.
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