Penn Undergraduate Solves Century-Old Wind Energy Problem
Haley Zaremba

It’s a turbulent time for wind energy. The sector is virtually paralyzed in the United States due to what seems to be Donald Trump’s personal vendetta against wind turbines, and the offshore wind industry is facing catastrophic delays and soaring costs thanks to inflation, high interest rates, and supply chain problems. 

But it’s not all doom and gloom for the wind industry – a mathematical breakthrough thanks to a Penn State engineering student may have just paved the way for a new generation of more efficient wind turbines. Amazingly, Divya Tyagi refined and improved a century-old math problem determining the optimal aerodynamic performance of a wind turbine in her undergraduate thesis for Schreyer Honors College. 

“Tyagi's work expands research in aerodynamics, unlocking new possibilities in wind turbine design that Hermann Glauert, a British aerodynamicist and the original author, did not consider,” Tech Xplore reported this week. 

"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," said Tyagi, who is now a graduate student pursuing her master's degree in aerospace engineering.

Glauert’s problem, published in 1935, provides a mathematical formula to determine blade element momentum by “considering the effects of blade design ie. shape, section, twist, etc. Blade element theory models the rotor as a set of isolated two-dimensional blade elements to which we can then apply 2-dimensional aerodynamic theory individually and then perform an integration to find thrust and torque.”

But Tyagi found that there are additional critical elements that Glauert did not consider. Namely, he failed to take into account the total force and moment coefficients impacting the rotor’s movements, or the ways in which turbine blades bend in the wind. 

"If you have your arms spread out and someone presses on your palm, you have to resist that movement," Tyagi’s adviser Sven Schmitz told Tech Xplore. "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."

Glauert’s problem is not the only math equation standing between the current wind power industry and optimal wind turbine design. In fact, the Millennium Prize is currently offering $1 million to anyone who can solve the Navier–Stokes Equation, first formulated in the 19th century. The unsolved mathematical model of fluid dynamics would allow us to reliably predict how air currents, breeze, and turbulence interact, revolutionizing atmospherically-reliant technologies such as wind power. 

Establishing a better understanding of the intricacies of wind and weather through mathematical modeling, the better we can design wind turbines and wind farms for more efficient and therefore cheaper wind energy. But the models currently used in the sector lack the sophistication necessary to capture all of these real-world elements accurately. When a 2022 study applied more complicated atmospheric conditions (such as reduced wind at high altitudes) to their model than the more simplistic ones that are typically used, researchers found that the power output of some turbines dropped by as much as 30%. 

Improving the efficiency of wind energy technologies would be a critical step toward meeting global climate goals. The globally recognized Net Zero Emissions by 2050 Scenario calls for 7900TWh of wind electricity generation worldwide in 2030. According to the International Energy Agency, this would require an increase in average annual wind power capacity additions to almost 250GW globally.

Tyagi says that her breakthrough is a step in the right direction. "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. "A 1% improvement in power coefficient could notably increase a turbine's energy output, potentially powering an entire neighborhood."

By Haley Zaremba for Oilprice.com

Haley Zaremba is a writer and journalist based in Mexico City. She has extensive experience writing and editing environmental features, travel pieces, local news in the Bay Area, and music/culture reviews.

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