Tham khảo tài liệu 'fundamental and advanced topics in wind power part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 2 Wind Turbines Theory - The Betz Equation and Optimal Rotor Tip Speed Ratio Magdi Ragheb1 and Adam M. Ragheb2 department of Nuclear Plasma and Radiological Engineering department of Aerospace Engineering University of Illinois at Urbana-Champaign 216 Talbot Laboratory USA 1. Introduction The fundamental theory of design and operation of wind turbines is derived based on a first principles approach using conservation of mass and conservation of energy in a wind stream. A detailed derivation of the Betz Equation and the Betz Criterion or Betz Limit is presented and its subtleties insights as well as the pitfalls in its derivation and application are discussed. This fundamental equation was first introduced by the German engineer Albert Betz in 1919 and published in his book Wind Energie und ihre Ausnutzung durch Windmuhlen or Wind Energy and its Extraction through Wind Mills in 1926. The theory that is developed applies to both horizontal and vertical axis wind turbines. The power coefficient of a wind turbine is defined and is related to the Betz Limit. A description of the optimal rotor tip speed ratio of a wind turbine is also presented. This is compared with a description based on Schmitz whirlpool ratios accounting for the different losses and efficiencies encountered in the operation of wind energy conversion systems. The theoretical and a corrected graph of the different wind turbine operational regimes and configurations relating the power coefficient to the rotor tip speed ratio are shown. The general common principles underlying wind hydroelectric and thermal energy conversion are discussed. 2. Betz equation and criterion performance coefficient Cp The Betz Equation is analogous to the Carnot cycle efficiency in thermodynamics suggesting that a heat engine cannot extract all the energy from a given source of energy and must reject part of its heat input back to the environment. Whereas the Carnot cycle efficiency can be expressed in terms of the Kelvin .
