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Blades of propellers and wind generators are designed on the basis of aerodynamic principles described mathematically more than a century ago. However, engineers long ago realized that these formulas are not always applicable, and introduced correction factors based on empirical observations. Specialists from the USA proposed a new, more accurate physical model of the movement of air flows around the rotor, which takes into account even the most extreme conditions.
The fluid momentum theory was developed at the end of the 19th century and allows engineers to calculate the maximum amount of energy that a rotor of a given design and configuration can produce, or how much energy must be produced to produce the required amount of thrust.
However, this the theory almost immediately broke down in practice, since it could not predict not only the amount, but also the direction of changes in the axial force at high speeds of rotation or at other angles of the blades. Therefore, when developing rotors, engineers had to enter correction coefficients into mathematical formulas, based on experiments and personal experience.
A team of scientists from the Massachusetts Institute of Technology analyzed the interaction of air flow and turbines using a detailed computer model of aerodynamics, MIT News reports. Finding discrepancies with the original theory, they made corrections by applying the fundamental equations created to predict the thrust of three-dimensional wings. After that, the corrected theory was tested on a fluid dynamics model and in a wind tunnel.
The new theory can be applied to determine the forces, jet speeds, and power of a rotor, both when it receives energy from the air flow, as in the case of a wind turbine, and when it gives energy to the flow, as in the case of an airplane or ship propeller. For wind farm operators, the model offers a simpler and faster way to optimize the many parameters that they have to take into account in order for the wind turbine to work at maximum efficiency.
In addition, the formula changes the former limit of values, that is, it states that wind generators can receive slightly more wind energy than before.
«Now that we have a new theory, the Betz limit, which had been a rule of thumb for hundreds of years, has changed, — said Michael Howland, one of the researchers. — And it can be applied practically now.
For 15 years, Japan has been using vertical coaxial counter-rotating turbines that produce energy even in light winds. Recently, one of the Hawaiian islands decided to test this solution.