Divya Tyagi Cracks Century-Old Math Problem; Discovers Hack to Maximize Power Like Never Before

Divya Tyagi, a graduate student in aerospace engineering at Penn State, has transformed a century-old math problem to optimize wind turbine flow, ultimately improving their energy output. Inspired by her adviser, Dr. Sven Schmitz, Divya revisited British aerodynamicist Hermann Glauert’s complex rotor disk solution and discovered gaps in it. “When I thought about the Glauert problem, I thought steps were missing and it was very complicated,” says Schmitz, who was impressed by Divya’s dedication to the challenge.

Divya spent countless hours on the problem, using the calculus of variations—a method for constrained optimization—to derive a new solution. “I created an addendum to Glauert’s problem which determines the optimal aerodynamic performance of a wind turbine,” she explains. While Glauert’s work focused solely on the maximum power coefficient, Divya’s approach considers total force and moment coefficients on the rotor, addressing how blades bend under wind pressure.

Schmitz emphasizes that understanding these additional factors is critical for wind turbine design, noting, “If you have your arms spread out and someone presses on your palm, you have to resist that movement.” He believes Divya’s findings will influence the next generation of turbine design and efficiency. A mere 1 percent improvement in power coefficient can lead to significant energy production increases, enough to power a neighborhood.

Divya’s exceptional work has earned her the Anthony E. Wolk Award for the best thesis in aerospace engineering among her peers. Now pursuing her master’s degree and focusing on computational fluid dynamics, she hopes her research will continue to enhance turbine designs and contribute to renewable energy advancements. Currently, she’s studying airflow around helicopter rotors, a project supported by the U.S. Navy, aimed at improving flight simulations and pilot safety. Reflecting on her dedication, Divya recalls, “I would spend about 10 to 15 hours a week between the problem, writing the thesis, and on research,” expressing pride in her accomplishments.

Re-reported from the article originally published in Wind Energy Science (WES).

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Suparna Rao, Staff Reporter