A Penn State aerospace engineering student, Divya Tyagi, has refined a century-old mathematics problem into a simpler, more elegant form, making it easier to use and explore. Her solution is likely to expand existing research in aerodynamics, unlocking new possibilities in wind turbine design that the original author, Hermann Glauert, did not consider.
Tyagi, a graduate student pursuing her master’s degree in aerospace engineering, completed this work as a Penn State undergraduate. Her research was published in Wind Energy 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 maximise its power output,” said Tyagi. Her adviser, Sven Schmitz, a professor in the Department of Aerospace Engineering and co-author of the paper, said Glauert’s original work focused exclusively on the maximum attainable power coefficient, which measures how efficiently a turbine converts wind energy into electricity. However, Glauert did not account for the total force and moment coefficients acting on the rotor, or how turbine blades bend under wind pressure. “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,” said Schmitz.
He said the simplicity of Tyagi’s addendum based on calculus of variations, a mathematical method used for constrained optimisation problems, will allow people to explore new facets 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 said. “As for Divya’s elegant solution, I think it will find its way into the classrooms, across the country and around the world.”
Tyagi said she sees her work as a step toward improving wind energy production and reducing costs. “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 said.
