Published February 28, 2024 | Version v1

Theoretical calculation of wind (Or water) turbine considering kinetic and potential energy to exceed the Betz limit

  • 1. association eXeco
  • 2. UNICAEN, M2C
  • 3. UNICAEN, ABTE

Description

The Betz limit sets a theoretical upper limit for the energy efficiency of turbines with a maximum power coefficient of 16/27. Betz's theory is precise and 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 and it is not possible to recover energy, if we do not create a stress.
We examine 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.
The paper proposes a new formulation of the turbine power  with a transfer of temporal energy, in order to be able to verify the conservation of energy.

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