Theoretical calculation of wind (Or water) turbine considering kinetic and potential energy to exceed the Betz limit
Résumé
The Betz limit sets a theoretical upper limit for the energy efficiency of turbines. The energy efficiency of turbines, expressed as a maximum power coefficient of 16/27.
Betz's theory is precise and is based on the calculation of kinetic energy. However, if the potential energy is taken into account the theoretical energy efficiency of a turbine can be higher. Fast wind turbines recover the kinetic energy of the wind in an optimal way. A large amount of potential energy is created without being recovered. The notion of potential energy is fundamental, it is not possible to recover energy, if we do not create a constraint.
This article examines this potential energy and the possibility for a wind turbine to transform it into kinetic energy. The Betz theory has been defined from the model of fast moving turbines. This theory has been generalized to slow and fast moving turbines and it has been defined as a law.
The conservation of energy implies that if a variation of kinetic energy increases, the variation of potential energy decreases. In the case of slow moving turbines, the conservation of energy applies, but not for the case of fast moving turbines, however this is the reality.
This paper proposes a new formulation of the turbine power with a notion of temporal, in order to be able to verify the conservation of energy.
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