Turns out turbulence isn’t just something to concern anxious fliers clasping onto their seats at 30,000 feet.
Apart from jiggling your plane around, turbulence also affects how cars drive, the stability of tall buildings and the amount of energy that can be produced by wind turbines.
While the experience of turbulence is all around us, the mathematics behind this bumpy phenomenon remains a mystery. So much so it’s one of seven Millennium Prize Problems posed by the Clay Mathematics Institute. These problems challenge the field of mathematics to solve some of the “deepest, most difficult problems” of classical physics.
Understanding turbulence is of crucial importance for engineers around the world. And that’s just what a team from Imperial College London, headed by Peter Vincent, Reader and EPSRC Fellow, has set out to do using highly accurate flow simulations on GPU-accelerated supercomputers.
The Physics Behind Turbulence
Turbulent flows are chaotic, containing millions of small vortices — spinning regions of the flow — that interact in incredibly complicated ways.
When designing stable buildings and optimal vehicles, engineers can often ignore the smallest-scale chaotic motions and instead focus on averages of pressure and velocity.
But it turns out that even these average properties are extremely difficult to predict accurately since their behavior is linked to chaotic small-scale motions. This means engineers generally resort to using approximate models.
To improve the accuracy of turbulent flow calculations, Vincent and his team ran thousands of turbulent flow simulations, each requiring billions of calculations to complete, over a period of 12 months. To power these, the team made use of two of Europe’s fastest supercomputers — Piz Daint at CSCS and Wilkes-2 from the University of Cambridge.
These NVIDIA GPU-accelerated systems enabled the team to identify for the first time so-called “eigenmode” solutions of averaged turbulent flow in a channel. This provides fundamental insights into the flow physics, which can be used to develop improved approximate models for use in industry.
“From these calculations, we’ve been able to shed new light on the physics that governs averaged properties of turbulent flow,” explained Vincent. “In particular, they show that the governing equations cannot possess certain symmetries, which are often assumed by existing models.”
With a deeper understanding of the physics behind turbulence, engineers can design the next generation of airplanes, wind turbines, submarines and many other objects to be more stable and secure.
“With the mainstream emergence of unsteady turbulence modeling for wind energy applications, the need for improved models is vital,” stated David Standingford, co-founder and director of Zenotech and an expert in mathematics and fluid dynamics. “The current work from Imperial College London addresses fundamental questions that will enable better industrial simulations in the future.”
Photo credit: Thomas Angus, Imperial College London