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Transcript
Betz's Law
Presented by Soheil Darvishi
Intro
Intro
Albert Betz
Betz's law indicates the maximum power that can be extracted from the wind, independent of the design of a wind turbine in open flow.
1919
where did it come from?
- Conservation of mass and momentum
Where from?
What does it say?
What does it say?
- No turbine can capture more than 16/27 (59.3%) of the kinetic energy in wind.
- The factor 16/27 (0.593) is known as Betz's coefficient.
- Practical utility-scale wind turbines achieve at peak 75% to 80% of the Betz limit.
Consepts
- Betz's law applies to all Newtonian fluids, including wind.
Concepts
Let me demonstrate
OH!
proof
The Betz Limit is the maximum possible energy that may be derived by means of an infinitely thin rotor from a fluid flowing at a certain speed.
Assumptions
Proof
- The rotor does not possess a hub and is ideal, with an infinite number of blades which have no drag. Any resulting drag would only lower this idealized value.
- The flow into and out of the rotor is axial. This is a control volume analysis, and to construct a solution the control volume must contain all flow going in and out, failure to account for that flow would violate the conservation equations.
- The flow is non-compressible. Density remains constant, and there is no heat transfer.
- Uniform thrust is exerted on the disc or rotor.
Calculating power
Approach 1
1
Calculating power
Approach 2
2
from 1 and 2
from 1 and 2
Conclusion
Conclusion
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