Student refines 100-year-old math problem, expanding wind energy possibilities

A Penn State engineering pupil refined a century-old math downside into a less complicated, extra elegant kind, making it simpler to make use of and discover. Divya Tyagi’s work expands analysis in aerodynamics, unlocking new prospects in wind turbine design that Hermann Glauert, a British aerodynamicist and the unique creator, didn’t contemplate.

Tyagi, a graduate pupil pursuing her grasp’s diploma in aerospace engineering, accomplished this work as a Penn State undergraduate for her Schreyer Honors School thesis. Her analysis was published in Wind Power Science.

“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,” mentioned Tyagi, who earned her bachelor’s diploma in aerospace engineering.

Her adviser, Sven Schmitz, the Boeing/A.D. Welliver Professor within the Division of Aerospace Engineering and co-author on the paper, mentioned Glauert’s unique work targeted solely on the utmost attainable energy coefficient, which measures how effectively a turbine converts wind power into electrical energy.

Nevertheless, Glauert didn’t account for the overall drive and second coefficients appearing on the rotor—the spinning unit with connected blades—or how turbine blades bend underneath wind stress.

“If you have your arms spread out and someone presses on your palm, you have to resist that movement,” mentioned Schmitz, a college member within the Institute of Power and the Surroundings. “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.”

Schmitz mentioned the simplicity of Tyagi’s addendum based mostly on calculus of variations, a mathematical technique used for constrained optimization problemswill enable individuals to discover new aspects of wind turbine design.

“The real impact will be on the next generation of wind turbines using the new knowledge that has been unveiled,” Schmitz mentioned. “As for Divya’s elegant solution, I think it will find its way into the classrooms, across the country and around the world.”

Tyagi mentioned she sees her work as a step towards bettering wind power manufacturing and decreasing prices.

“Improving the power coefficient of a large wind turbine by just 1% has significant impacts on the energy production of a turbine, and that translates towards the other coefficients that we derived relations for,” she mentioned. “A 1% improvement in power coefficient could notably increase a turbine’s energy output, potentially powering an entire neighborhood.”

Throughout her senior yr, Tyagi received the Anthony E. Wolk Award for her thesis on the addendum to Glauert’s work. The Wolk Award is offered to a senior in aerospace engineering who has developed the most effective thesis amongst aerospace engineering college students.

Now pursuing her grasp’s diploma, Tyagi is learning computational fluid dynamics simulations, analyzing airflow round a helicopter rotor.

“The goal is to integrate that with the complex flow around a ship to see how the ship airwake interacts with a helicopter trying to land on its deck,” she mentioned.

Her U.S. Navy-supported analysis goals to enhance flight simulation and pilot security by higher understanding these dynamic interactions.

Reflecting on her undergraduate analysis, Tyagi mentioned proving her resolution on paper was difficult.

“I would spend about 10 to 15 hours a week between the problem, writing the thesis and on research. It took a long time because it was so math intensive,” she mentioned. “But I feel really proud now, seeing all the work I’ve done.”

Schmitz, who has contemplated Glauert’s downside for many years, credited Tyagi’s persistence in tackling it.

“When I thought about the Glauert problem, I thought steps were missing and it was very complicated,” Schmitz mentioned. “There had to be an easier way to do it. That’s when Divya came in. 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.”