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Abstract(s)
According to the centenary Betz-Joukowsky law, the power extracted from a wind turbine inopen flow cannot exceed 16/27 of the wind transported kinetic energy rate. This limit is usuallyinterpreted as an absolute theoretical upper bound for the power coefficient of all wind turbines,but it was derived in the special case of incompressible fluids. Following the same steps of Betzclassical derivation, we model the turbine as an actuator disk in a one dimensional fluid flowbut consider the general case of a compressible reversible fluid, such as air. In doing so, we areobliged to use not only the laws of mechanics but also and explicitly the laws of thermodynamics.We show that the power coefficient depends on the inlet wind Mach numberM0,andthatitsmaximum value exceeds the Betz-Joukowsky limit. We have developed a series expansion forthe maximum power coefficient in powers of the Mach number M0that unifies all the cases (compressible and incompressible) in the same simple expression: 𝜂max= 16∕27 + 8∕243M20.
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Keywords
Betz law Thermodynamics Wind turbines
Citation
TAVARES, José Maria; PATRÍCIO, Pedro – Maximum thermodynamic power coefficient of a wind turbine. Wind Energy. ISSN 1099-1824. Vol. 23, N.º 4 (2020), pp. 1077-1084