Indian-origin student cracks century-old math puzzle, advancing wind turbine research

Divya Tyagi, an aerospace engineering graduate student at Pennsylvania State University, has made a groundbreaking mathematical discovery by refining a 100-year-old problem in aerodynamics.

Her innovative approach simplifies a complex equation initially formulated by British aerodynamicist Hermann Glauert, paving the way for improved wind turbine efficiency.

Glauert’s original research focused on maximising the power coefficient - a measure of how efficiently wind energy is converted into electricity. However, his work did not account for total force and moment coefficients acting on the rotor or the structural impact of wind pressure on turbine blades.

Building on this foundation, Tyagi introduced a mathematical addendum that optimises the ideal flow conditions needed to maximise turbine power output. Her work, published on Penn State University’s official website, has opened new avenues in wind energy research.

"I developed an extension of Glauert’s problem to determine the optimal aerodynamic performance of a wind turbine by identifying ideal flow conditions for peak power generation," Tyagi explained.

Tyagi’s adviser, Professor Sven Schmitz, highlighted that her approach, based on the calculus of variations, offers a simpler yet powerful framework for constrained optimisation. This allows researchers to analyse new aspects of wind turbine mechanics with greater ease.

"Glauert’s original work did not account for the total aerodynamic load on the rotor. Understanding these forces is crucial because wind turbines must resist downwind thrust forces and bending moments, just like a person pushing against pressure on their palm," Schmitz noted.

Her refined solution is expected to influence next-generation wind turbines, leading to more efficient and resilient designs. Schmitz believes her findings will soon be incorporated into academic curricula worldwide, benefiting students and researchers alike.

Tyagi’s perseverance in tackling the problem sets her apart. Professor Schmitz revealed that three students before her had attempted to solve it but were unable to make progress.

"Divya was the fourth student I challenged with this problem, and the only one who took it on. Her work is truly impressive," he said.

Having completed her bachelor’s degree in aeronautical engineering, Tyagi is now pursuing her master’s degree with a focus on computational fluid dynamics (CFD). She is currently engaged in cutting-edge research funded by the US Navy, aimed at improving helicopter flight simulations and aviation safety.