US innovative student unlocks key to optimising wind turbine output

A young aerospace engineering student at the US Penn State has cracked a century-old math problem, unlocking a groundbreaking solution to optimise wind turbine performance. 

Interesting Engineering unveils in a new article that Divya Tyagi, a graduate student at Penn State University in Pennsylvania, tackled the challenge of revising British aerodynamicist Hermann Glauert's optimum rotor disk solution. Her adviser, Sven Schmitz, PhD, encouraged her to dig deeper into the issue, which ultimately led to her breakthrough.

“When I thought about the Glauert problem, I thought steps were missing and it was very complicated,” said Schmitz, a Boeing/A.D. Welliver Professor in the Department of Aerospace Engineering and co-author of the study. “I was sure there was a better approach.”

Schmitz, who had already challenged several students to solve the problem, praised Tyagi for taking on the task. “She was the fourth student I challenged with looking at it, and she was the only one who took it on. Her work is truly impressive.”

Tyagi devoted countless hours to the problem, eventually developing a solution based on the calculus of variations—a mathematical method used for constrained optimization. Her amendment to Glauert’s problem identifies the optimal aerodynamic performance of wind turbines, determining the ideal flow conditions that maximize power output.

“I developed an addendum to Glauert’s problem that determines the optimal aerodynamic performance of a wind turbine by solving for the ideal flow conditions to maximize its power output,” Tyagi explained.

Schmitz noted that while Glauert’s original work focused only on the maximum achievable power coefficient, a measure of how efficiently a turbine converts wind into electricity, it overlooked key factors such as the total force and moment coefficients on the rotor. These include the impact of wind pressure on the blades, which can cause bending.

“If you have your arms outstretched and someone presses on your palm, you have to resist that pressure,” Schmitz clarified. “We refer to that as the downwind thrust force and the root bending moment, and wind turbines need to withstand that as well.”

Schmitz further emphasized that understanding the full extent of the load on a wind turbine rotor is crucial—an aspect that Glauert failed to address. He believes that Divya’s approach will significantly influence future wind turbine designs, driving advancements in both design and efficiency.

“Divya’s elegant solution, I believe, will eventually make its way into classrooms nationwide and globally,” Schmitz predicted.

Tyagi highlighted the impact of even minor improvements in wind turbine performance. “Improving the power coefficient of a large wind turbine by just 1 percent can have a substantial effect on its energy production,” she said. “This improvement translates to the other coefficients we developed relations for. A 1 percent increase in the power coefficient could significantly boost a turbine’s energy output, potentially powering an entire neighborhood.”

In recognition of her work, Divya received the Anthony E. Wolk Award for the best aerospace engineering thesis among her peers. She hopes her findings will contribute to more efficient turbine designs and propel further advancements in renewable energy.

Currently working toward her master’s degree with a focus on computational fluid dynamics simulations, Tyagi is eager to see her research integrated into advanced wind turbine solutions.

In addition to her wind turbine research, Tyagi is now studying airflow around helicopter rotors with support from the U.S. Navy. Her goal is to improve flight simulation and enhance pilot safety by deepening understanding of these dynamic interactions.

Reflecting on the journey, Divya said, “I would spend about 10 to 15 hours a week working on the problem, writing the thesis, and conducting research. It was highly math-intensive, but I feel really proud now, seeing all the work I’ve done.”

By Naila Huseynova