Indian-Origin Student Divya Tyagi Solves 100-Year-Old Math Problem at Penn State, Boosting Wind Turbine Efficiency

In a remarkable scientific achievement, Divya Tyagi, an aerospace engineering graduate student at Penn State University, has redefined a century-old mathematical formula, paving the way for more efficient wind turbine designs. Her elegant solution, which refines British aerodynamicist Hermann Glauert’s classic rotor disk model, promises to significantly enhance power output by optimizing turbine flow conditions.

Encouraged by her advisor, Dr. Sven Schmitz, a Boeing/A.D. Welliver Professor in the Department of Aerospace Engineering, Tyagi tackled the long-standing Glauert problem with a fresh perspective. Schmitz, who co-authored the study, had assigned the problem to three previous students—none of whom managed to solve it.

“When I thought about the Glauert problem, I felt steps were missing, and it was very complicated,” Schmitz explained. “Divya was the fourth student I challenged, and she was the only one who took it on. Her work is truly impressive.”

Using the calculus of variations—a mathematical technique for constrained optimization—Tyagi developed an amendment to Glauert’s model. Her solution identifies the ideal aerodynamic conditions for wind turbines, maximizing power output by accounting for the rotor’s total force and moment coefficients—factors that Glauert had overlooked.

“Glauert’s original work only addressed the maximum attainable power coefficient, which measures how effectively a turbine converts wind into electricity,” Schmitz explained. “However, he didn’t consider the total load on the rotor or how the blades bend under wind pressure.”

Schmitz compared the concept to holding out one’s arms against a force. “If you have your arms spread out and someone presses on your palm, you have to resist that movement. We call that the downwind thrust force and the root bending moment, which wind turbines must also withstand.”

Tyagi’s refined model offers a more comprehensive understanding of turbine dynamics, which could drive significant improvements in wind energy production. Even a modest 1% increase in power coefficient could substantially boost the energy output of large turbines, potentially powering entire neighborhoods.

“Improving the power coefficient of a large wind turbine by just 1 percent has significant impacts on its energy production,” Tyagi said. “That translates to the other coefficients we derived relations for, making turbines far more efficient.”

Tyagi’s groundbreaking research has earned her the prestigious Anthony E. Wolk Award for the best aerospace engineering thesis among her peers. Now pursuing her master’s degree, she is focusing on computational fluid dynamics simulations, aiming to see her findings applied to next-generation wind turbine technology.

Schmitz believes Tyagi’s solution will soon be a fixture in academic settings. “I think her elegant solution will find its way into classrooms across the country and around the world,” he said.

With Tyagi’s contribution, the renewable energy sector stands to benefit from more efficient turbine designs, potentially accelerating the transition to sustainable power solutions.