A Penn State engineering student has refined a century-old math problem paving the way for more efficient wind turbine designs.
A young student has revamped a century-old math problem and unlocked a simple, yet elegant solution to optimize wind turbine flow conditions and enhance power output.Divya Tyagi, an aerospace engineering graduate student at Penn State, Pennsylvania, created an amendment to British aerodynamicist Hermann Glauert’s optimum rotor disk solution, after her adviser, Sven Schmitz, PhD, encouraged her to take a deeper look.
“When I thought about the Glauert problem, I thought steps were missing and it was very complicated,” Schmitz, a Boeing/A.D. Welliver Professor in the Department of Aerospace Engineering and co-author of the study, reveals adding that he was sure there was a better approach.Divya Tyagi, right, a Penn State engineering graduate student, shows her work on a century-old math problem to Sven Schmitz, a College of Engineering faculty member and Tyagi’s adviser.Credit: Kevin Sliman“That’s when Divya came in,” he continues. “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.”The student took on the challenge and dedicated hours to the problem before eventually developing a solution based on the calculus of variations, a mathematical method for constrained optimization.Improving wind turbine efficiency by revisiting the math problem“I created an addendum to Glauert’s problem which determines the optimal aerodynamic performance of a wind turbine by solving for the ideal flow conditions for a turbine in order to maximize its power output,” Tyagi says.Schmitz emphasizes that Glauert’s original work focused only on the maximum attainable power coefficient, which measures how efficiently a turbine converts wind into electricity. Yet, Glauert failed to consider the total force and moment coefficients on the rotor—the spinning unit with attached blades—or 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 explains. “We call that the downwind thrust force and the root bending moment, and wind turbines must withstand that, too.”“You need to understand how large the total load is, which Glauert did not do,” the professor continues, highlighting that he expects Divya’s method to shape the next generation of wind turbines, driving advancements in design and efficiency.“As for Divya’s elegant solution, I think it will find its way into the classrooms, across the country, and around the world,” the professor adds. “Improving the power coefficient of a large wind turbine by just 1 percent has significant impacts on the energy production of a turbine, and that translates towards the other coefficients that we derived relations for,” the student says. “A 1 percent improvement in power coefficient could notably increase a turbine’s energy output, potentially powering an entire neighborhood.”Future goals and plansMeanwhile, Divya whose work has earned her the Anthony E. Wolk Award for the best aerospace engineering thesis among her peers, believes her findings could contribute to more efficient turbine designs and further advancements in renewable energy.Now pursuing her master’s degree and studying computational fluid dynamics simulations, the student hopes to see her research integrated into advanced wind turbine solutions.Wind turbines supply renewable energy to microgrids across Alaska.Credit: Chris Pike, the Alaska Center for Energy and Power, University of Alaska FairbanksNow studying airflow around a helicopter rotor, in research backed by the U.S. Navy, Divya aims to improve flight simulation and pilot safety by better understanding these dynamic interactions.“I would spend about 10 to 15 hours a week between the problem, writing the thesis and on research,” Divya recalls in a press release, adding that the challenge was very math intensive. “But I feel really proud now, seeing all the work I’ve done.” The study has been published in the journal Wind Energy Science .
Energy &Amp Environment Maths Physics Power Research Rotors Science Turbine Wind Wind Turbine
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