Читать книгу Wind Energy Handbook - Michael Barton Graham - Страница 54

(This limit is also referred to as the Lanchester–Betz limit or the Betz–Joukowski limit).¹

The maximum value of C_P occurs when

that gives a value of

Hence,

(3.13)

The maximum achievable value of the power coefficient is known as the Betz limit after Albert Betz (1919), the German aerodynamicist. Frederic Lanchester (1915), a British aeronautical pioneer, worked earlier on a similar analysis and is sometimes given prior credit, and Joukowski (1920) also contributed an analysis. To date, no unducted wind turbine has been designed that is capable of exceeding the Betz limit. The limit is caused not by any deficiency in design because, as yet in our discussion, we have no design. However, because the streamtube has to expand upstream of the actuator disc, the cross‐section of the tube where the air is at the full, free‐stream velocity is smaller than the area of the disc.

The efficiency of the rotor might more properly be defined as

(3.14)

but note that C_P is not the same as this efficiency.