Math professor’s algorithms could solve the problem of ice buildup on planes

The build-up of ice on an airplane in flight can seriously impair its ability to fly and, in extreme cases, lead to catastrophe. In Dr. David Del Rey Fernández's lab, algorithms and software are being developed to understand these processes and enhance future aircraft designs to prevent negative outcomes.

Del Rey Fernández, a professor in the University of Waterloo's Department of Applied Mathematics, leads research teams at the Waterloo Institute for Sustainable Aeronautics (WISA), focusing on developing simulation software algorithms to design safer, more aerodynamic and fuel-efficient aircraft that are environmentally friendly.

Funded by the Government of Canada, through the Federal Economic Development Agency for Southern Ontario (FedDev Ontario), the WISA research team uses algorithms to solve partial differential equations, simulating aircraft flight under a range of conditions, instead of creating traditional physical models. algorithms to solve partial differential equations, simulating aircraft flight under a range of conditions, instead of creating traditional physical models.

“We live in a physical world, and we develop mathematical models to predict how the physical world works,” Del Rey Fernández explains. “With math you can push into aircraft designs that could not otherwise be considered.”

One major problem he’s trying to solve involves the buildup of ice on an aircraft’s wings and body, which happens when atmospheric water droplets are super-cooled then freeze and accumulate.

“This is hugely problematic because an aircraft’s performance depends on the shape of its wings and fuselage — both of which can be impacted by ice. Ice accretion can make it harder for a plane to take off, more likely to stall, interfere with its vital sensors and may result in aircraft failure,” Del Rey Fernández says.

Del Rey Fernández, along with Waterloo master’s student Donze Li, postdocs Dr. Sarah Nataj, and Dr. Anita Gjesteland, are addressing the challenge of ice accretion for Canadian business jet manufacturer Bombardier Inc. They aim to enhance understanding of ice formation on aircraft and strategies to mitigate it by developing software for three-dimensional ice accretion simulations.

“Computer simulation is the third pillar of science today,” Del Rey Fernández says.

For decades, aviation engineers used simple math formulas to draft preliminary aircraft designs which were used for testing scale models in wind tunnels, then refined into finished products. However, such physical experimentation is labour intensive, time consuming and expensive. Today’s engineers employ computer software to quickly and economically produce thousands of designs that are turned into select physical models that undergo tests.

"For the last several decades, state-of-the-art computer simulation software has effectively predicted ice accretion in two dimensions. Our group seeks to advance this by developing software capable of three-dimensional predictions, because an aircraft is a three-dimensional object," Del Rey Fernández explains.

“Partial differential equations are key in this process since they describe how physical systems evolve and let us predict how they will work,” he says. “Most partial differential equation models can’t be solved with a pen and paper. We approximately solve them, using computers and numerical methods.”

Such advances in computer simulation could address a range of challenges related to aircraft design.

Del Rey Fernández and Nataj are collaborating with Ansys, a company specializing in advanced simulation software for designing, testing and operating products. They aim to improve the software's ability to simulate complex interactions, like how air flows and interacts with airplane wings during flight. This work is vital for aviation, as understanding these interactions helps in designing better performing and safer aircraft.

“If a wing vibrates too wildly, it can break off,” Del Rey Fernández says. “Our work will enable Ansys to improve the efficiency of its current approaches to fluid-structure interaction by providing mathematical guarantees on solver performance. The resulting gains in efficiency will improve turnaround time of simulations, and therefore, time to market and refined designs.”

Del Rey Fernández and project leader Dr. Hans De Sterck are collaborating with Pratt & Whitney Canada, a company that designs, manufactures and services aircraft engines, to enhance the performance of its gas turbines. With the help of master’s students Andrew Gray and Adam Vieno, they're focusing on innovative approaches using machine learning and simplified modeling to speed up design processes, such as optimizing the shape of parts. These methods allow for a deeper dive into engine design possibilities, paving the way for improvements. The aim of their work is to boost the efficiency of gas turbine engines, reducing their fuel use, weight, and the emissions contributing to climate change.

While Del Rey Fernández and his team have seen encouraging early results, their projects are designed for the long haul. For example, he anticipates that completing his work for Bombardier will require three to four years of dedicated effort.

“With computer simulation you can push the envelope on design to get better performance and a better product,” he says. “And it significantly reduces the time for development and saves money.”

WISA received nearly $9.2 million from FedDev Ontario in 2023. The funding is supporting 38 Research-for-Impact projects, including $176,925 for these projects.