New theory could improve the design and operation of wind farms

The blades of propellers and wind turbines are designed based on aerodynamics principles that were first described mathematically more than a century ago. But engineers have long realized that these formulas don’t work in every situation. To compensate, they have added ad hoc “correction factors” based on empirical observations.

Now, for the first time, engineers at MIT have developed a comprehensive, physics-based model that accurately represents the airflow around rotors even under extreme conditions, such as when the blades are operating at high forces and speeds, or are angled in certain directions. The model could improve the way rotors themselves are designed, but also the way wind farms are laid out and operated.

The new findings are described in the journal Nature Communications, in an open-access paper by MIT postdoc Jaime Liew, doctoral student Kirby Heck, and Michael Howland, the Esther and Harold E. Edgerton Assistant Professor of Civil and Environmental Engineering.

“We’ve developed a new theory for the aerodynamics of rotors,” Howland says. This theory can be used to determine the forces, flow velocities, and power of a rotor, whether that rotor is extracting energy from the airflow, as in a wind turbine, or applying energy to the flow, as in a ship or airplane propeller. “The theory works in both directions,” he adds.

Because the new understanding is a fundamental mathematical model, some of its implications could potentially be applied right away. For example, operators of wind farms must constantly adjust a variety of parameters, including the orientation of each turbine as well as its rotation speed and the angle of its blades, in order to maximize power output while maintaining safety margins. The new model can provide a simple, speedy way of optimizing those factors in real time.

“This is what we’re so excited about, is that it has immediate and direct potential for impact across the value chain of wind power,” Howland says.

Modeling the momentum

Known as momentum theory, the previous model of how rotors interact with their fluid environment—air, water, or otherwise—was initially developed late in the 19th century. With this theory, engineers can start with a given rotor design and configuration, and determine the maximum amount of power that can be derived from that rotor—or, conversely, if it’s a propeller, how much power is needed to generate a given amount of propulsive force.

Momentum theory equations “are the first thing you would read about in a wind energy textbook, and are the first thing that I talk about in my classes when I teach about wind power,” Howland says. From that theory, physicist Albert Betz calculated in 1920 the maximum amount of energy that could theoretically be extracted from wind. Known as the Betz limit, this amount is 59.3% of the kinetic energy of the incoming wind.

But just a few years later, others found that the momentum theory broke down “in a pretty dramatic way” at higher forces that correspond to faster blade rotation speeds or different blade angles, Howland says. It fails to predict not only the amount, but even the direction of changes in thrust force at higher rotation speeds or different blade angles: Whereas the theory said the force should start going down above a certain rotation speed or blade angle, experiments show the opposite—that the force continues to increase. “So, it’s not just quantitatively wrong, it’s qualitatively wrong,” Howland says.

This story is republished courtesy of MIT News (web.mit.edu/newsoffice/), a popular site that covers news about MIT research, innovation and teaching.