The blades of propellers and wind turbines are designed based on aerodynamic principles that were first described mathematically more than a century ago. However, 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 today 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 says.
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.
The existing model, known as momentum theory, was developed in the late 19th century and forms the basis for understanding how rotors interact with their fluid environment. However, this theory breaks down under higher forces, and misalignment between the rotor and airflow, and fails to accurately predict thrust force changes at higher rotation speeds.
Howland and his team used detailed computational modeling to analyze the interaction of airflow and turbines, leading to the development of their new “unified momentum model.” This model accounts for factors like pressure changes behind the rotor and three-dimensional aspects of airflow, addressing the limitations of the previous theory.
The new model has significant implications for wind energy. It refines the calculation of the Betz limit, suggesting the possibility of extracting slightly more power from wind than previously thought. More importantly, it provides a way to maximize power from misaligned turbines, a common occurrence in wind farms.
This breakthrough has immediate practical applications. Wind farm operators can use the model to optimize turbine control and improve overall energy output without needing to modify existing hardware. The model’s ability to accurately predict power output based on factors like wind angle eliminates the need for empirical corrections, providing a more precise and efficient way to manage wind farms.
The applications extend beyond wind energy. The model’s principles can be applied to propellers in aircraft and ships, as well as hydrokinetic turbines used in tidal or river power generation. Howland and his team have made their unified momentum model available to the public as both a set of mathematical formulas and an open-source software package on GitHub. This accessibility aims to accelerate the development and deployment of wind energy solutions, contributing to a more sustainable future.
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