The Math Behind the Future of Energy Savings

Illinois Institute of Technology Assistant Professor of Mechanical and Aerospace Engineering Scott T. M. Dawson has received funding from the United States Department of Energy Early Career Research Program for his project that aims to use advances in mathematical methods for predicting and approximating coherent features within fluid flows. This can help optimize designs in a range of applications including aircraft, boats, HVAC ducts, wind turbines, and more, leading to energy savings.

“Despite the fact that we now have a lot more computational power than we used to, we’re still somewhat limited in the types of problems that we can very accurately simulate,” says Dawson.

He plans to test his methods for a range of applications where flow is complex or chaotic, which tend to be more difficult to simulate because they have highly unsteady and turbulent dynamics. Examples include rectangular ducts, where the corners lead to complex flow, and advanced surfaces that move when a fluid flows over them, tending to offer beneficial features such as reduced drag but also making simulations more complex.

“These problems were chosen because they provide a good test of the methods that we’re developing and also because they’re related to problems of engineering importance,” he says.

In particular, for problems that are multiscale, meaning that they have important features that occur on both large- and small-length scales, you typically need an extremely high number of points in a simulation, which translates to lots of time and computational power for problems such as simulating the air flow over an entire airplane.

The current method for doing this is to use a very general equation with lots of terms corresponding to various flow features, but not every term considered in the equation ends up showing up in the solution.

Dawson recognized that if you could find a way to predict which features would appear in the final solution, you could cut a number of terms out of the equation, making it faster and easier to solve.

This has been tried by using measured data to construct those terms, but that can lead to noisy or inaccurate solutions. Dawson is hoping to get the best of both worlds by using his novel methodology.

“The idea is we can do some preliminary calculations that are cheaper to do on a simplified version of the problem that gives us a starting point for what these functions would be,” says Dawson.

Dawson says he’s hopeful that for certain types of problems, this method could improve calculation speed and efficiency by an order of magnitude.

“There’s always a trade off. The more complex or the larger the scale of a system, the more approximations you need to make in order to run a simulation that is computationally feasible,” says Dawson. “My hope is that we’ll be able to develop methods that don’t have to make as much of an extreme trade off, that can get us better resolution with a feasible amount of computational power.”

Dawson says he’s excited for the opportunity. His project was funded through the Office of Advanced Scientific Computing Research. 

“I think that the program gives recipients the opportunity to really spend a good amount of time and resources on working on difficult problems that advance cutting-edge knowledge and methods,” he says.

Image: (Left to right) Ahmed El-Nadi (Ph.D. MAE Candidate), Min-Lin Tsai (Ph.D. MAE Candidate), and Assistant Professor Scott Dawson.

Disclaimer: “Research reported in this publication was supported by the U.S. Department of Energy under Award Number DE-SC0025597. This content is solely the responsibility of the authors and does not necessarily represent the official views of the U.S. Department of Energy.”

Scott Dawson, “Adaptive Multiscale Modeling Using Pseudospectral Wavepackets,” U.S. Department of Energy; Award Number DE-SC0025597.