Divya Tyagi, an aerospace engineering graduate student of Indian origin at Pennsylvania State University, has made a groundbreaking discovery by refining a century-old mathematical problem. Her innovative approach simplifies the complex calculations, making them more practical for further exploration.
The problem, originally formulated by British aerodynamicist Hermann Glauert, has been a key component of aerodynamics research for decades. By building on Glauert’s work, Tyagi has introduced a fresh perspective that could revolutionize wind turbine design, as highlighted by Penn State University’s official website.
“I developed an extension to Glauert’s work that determines the optimal aerodynamic conditions for a wind turbine, ensuring maximum power output,” explained Tyagi.
Her adviser and co-author, Sven Schmitz, noted that Glauert’s initial research primarily focused on maximizing power conversion efficiency. However, it did not take into account the total force and moment coefficients on the rotor, nor did it address how wind pressure causes turbine blades to bend under stress.
“Imagine extending your arms while someone pushes against your palm—you must resist that force. This concept, known as downwind thrust force and root bending moment, is crucial for wind turbines, yet Glauert’s work did not account for it,” said Schmitz, who is part of the Institute of Energy and the Environment.
Tyagi’s breakthrough, which employs the calculus of variations, introduces a structured optimization framework that simplifies these calculations. This advancement allows researchers to explore previously unconsidered aspects of wind turbine efficiency with greater ease.
“This discovery could shape the next generation of wind turbines. Divya’s elegant solution is likely to be incorporated into university curricula worldwide,” Schmitz remarked.
He commended Tyagi’s perseverance in tackling the challenge. “When I analyzed Glauert’s problem, I felt that something was missing—it seemed overly complicated. Divya was the fourth student I assigned to study it, and the only one who took it on. Her work is truly remarkable,” he added.
Tyagi, who holds a bachelor’s degree in aeronautical engineering, is now pursuing her master’s degree while conducting cutting-edge research in computational fluid dynamics (CFD). Currently, she is working on a project funded by the US Navy, focusing on improving helicopter flight simulations and advancing aviation safety.
