A young aerospace engineering student at Penn State has reimagined a century-old mathematical problem, unlocking a refined solution that enhances wind turbine performance. Divya Tyagi, a graduate student, has built upon the work of Hermann Glauert, a British aerodynamicist, to improve the understanding of optimal rotor disk conditions.
Encouraged by her adviser, Dr. Sven Schmitz, Divya tackled the complex problem that had puzzled researchers for years. Schmitz, a Boeing/A.D. Welliver Professor in Aerospace Engineering, had previously assigned the challenge to multiple students, but Divya was the first to crack it.
“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,” Schmitz remarked.
Divya’s breakthrough lies in her addendum to Glauert’s rotor disk model, which refines calculations for a wind turbine’s ideal flow conditions. Using the calculus of variations, a mathematical optimization technique, she developed a method that maximizes a turbine’s power output while considering forces acting on its structure.
Glauert’s original work primarily focused on the maximum attainable power coefficient—a measure of how efficiently a wind turbine converts wind energy into electricity. However, Schmitz points out that it failed to account for total force and moment coefficients on the rotor, including how the blades bend under wind pressure.
“If you have your arms spread out and someone presses on your palm, you have to resist that movement,” Schmitz explained. “We call that the downwind thrust force and the root bending moment, and wind turbines must withstand that, too.”
By addressing this gap, Divya’s model offers a more comprehensive framework for designing next-generation wind turbines that are both efficient and structurally sound.
Even a 1% increase in a turbine’s power coefficient can significantly boost energy production, potentially powering entire neighborhoods.
“Improving the power coefficient of a large wind turbine by just 1 percent has significant impacts on energy production,” Divya noted. “That translates towards the other coefficients that we derived relations for.”
Her findings could shape the future of wind energy by enabling more efficient designs that withstand aerodynamic forces while maximizing output. Schmitz is optimistic about the broader academic and industrial impact of her work.
“I think it will find its way into the classrooms, across the country, and around the world.”
For her groundbreaking research, Divya has been honored with the Anthony E. Wolk Award for the best aerospace engineering thesis among her peers. As she pursues her master’s degree, she is focusing on computational fluid dynamics simulations, aiming to integrate her findings into advanced wind turbine technology.