The vortex theme may seem esoteric. But their impact is making headlines, as seen in a recent outbreak of tornadoes, swirling vortices that killed at least 80 people in eight US states in December 2021. Scientists do not yet fully understand the dynamics of vortices today, chaotic but coherent patterns are common in nature, also illustrated by hurricanes, vortices in an air or water flow, drag, fuel combustion and more.
Supercomputer simulations are helping scientists dig deeper into the mysterious properties of vortices and turbulence, according to recent studies by scientists at Texas Tech University. A potential application of their research could help improve fuel efficiency in cars, develop energy-saving aircraft designs, and more.
Her vortex research was published in January 2022 Annual review of fluid mechanics. “A finding from the study is that we find that two vertebrae of opposite sign reconnect where they come together and connect to form two new vertebrae, leaving some remaining unconnected parts as threads that undergo further sequential reconnections.” said the study’s lead author, Jie Yao, a postdoctoral researcher in the Department of Mechanical Engineering at Texas Tech.
“We contend that vortex reconnection is the essence behind most turbulence cascades, fluid mixing and aerodynamic noise generation,” said study co-author Fazle Hussain, President’s Endowed Professor of Engineering, Science and Medicine and senior adviser to the President . Texas Tech University. Hussain is Yao’s advisor and professor in the departments of mechanical engineering, physics, chemical engineering, petroleum engineering, internal medicine, and cell physiology and molecular biophysics.
Hussain gave an example of the reconnection of vortices in the two contrails of an airplane. Under suitable atmospheric conditions, the rolling twin wake vortices recombine into vortex rings and thence into turbulence.
“When vortices rejoin, they create two large structures plus many small structures,” Hussain said. “Initially, you see some smoke in lab visualizations. But when the two vortices are pulled and move apart, they pull these threads that eventually unravel. These details only came out through numerical simulations using supercomputers.”
Supercomputers solve vortex equations
For the review study, XSEDE, the National Science Foundation (NSF)-funded Extreme Science and Engineering Discovery Environment, gave Yao and Hussain supercomputer access to the Stampede2 system at the Texas Advanced Computing Center. In addition, they took advantage of XSEDE’s Extended Collaborative Support Services (ECSS) program, which provides researchers with expertise to make the most of the granted supercomputer time.
“Through XSEDE ECSS, Manu Shantaram from the San Diego Supercomputer Center helped us analyze our code. We had a good connection and discussion with him, and he did a good job of profiling the code and checking for issues, which improved its performance,” Yao said.
“We have benefited greatly from XSEDE projects and even more from TACC, whose people have helped us with technical issues and problem solving,” added Yao. “And TACC gives us more than just access to Stampede2. TACC has also given us access to the Frontera and Lonestar5 systems in addition to the new Lonestar6.”
Yao and Hussain have harnessed significant supercomputing power from XSEDE, TACC, and their local cluster at Texas Tech University’s High Performance Computing Center (HPCC). It basically involves solving the Navier-Stokes equations that describe the fluid motion of air, water and more. Their direct numerical simulations have yielded highly time- and space-resolved, accurate distributions of measures such as velocity, eddy strength or fluid rotation, enstrophy – a term that refers to the energy dissipation of an eddy, helicity, temperature, and scalar concentration.
The growth of peak vortices and enstrophy both address a very fundamental mathematical question relevant to a million dollar question being asked by the Clay Mathematics Institute, which has the money to correctly solve one of several Millennium Prize promised problems.
The question has to do with the formation of a finite time singularity (FTS) of the Navier-Stokes equations, which can be stated as the question of whether, given an initial instant and smooth velocity field of finite kinetic energy, a singularity of the field appears within a finite time under evolution, which is governed by the incompressible Navier-Stokes equations.
“Direct numerical simulation (DNS) with supercomputers was also used to study the possible formation of an FTS,” Yao said. DNS computer simulations are used in computational fluid dynamics to solve Navier-Stokes equations without using a model, a computationally intensive method. He noted that simulations cannot provide conclusive evidence for the existence of an FTS, as the length scale of the phenomenon inevitably decreases to less than the computational grid resolution.
“In particular, we found that the maximum vorticity growth during the collision of slender vortices rings is much smaller than predicted by theory – ruling out the possible formation of a finite singularity for this configuration during the approach phase and the subsequent introduction of an appropriate scaling analysis near the singular.” Timing could be a way to address this challenging issue, but little progress has been made in that direction so far,” Yao said.
Where supercomputers have helped make progress, Yao said, is in providing results that have created more accurate and realistic representations of the vortices addressed in the review.
“We mainly reviewed recent advances in vortex reconnection in classical viscous flows, including the physical mechanism, its relationship to the turbulence cascade, finite singularity formation, helicity dynamics, and aeroacoustic noise generation,” Yao said.
In a previous study, Yao and Hussain looked at two key mechanisms of turbulent flow, the turbulence cascade and eddy reconnection. “We also claim and demonstrate that reconnection is one of the dominant pathways for energy to cascade to the finest turbulence scales before being converted to heat by the dissipation process,” Yao said.
A challenge in studying vortex reconnection in viscous flow is that reconnection is never complete. It leaves the unconnected parts as threads that can have rich dynamics (including mixing and turbulence cascade).
avalanche of vortices
For example, they recently completed computer simulations of reconnection at moderate Reynolds numbers, which represent the ratio of inertial to viscous forces, with higher values corresponding to more turbulent flow. The simulations show that the threads can undergo a cascade of secondary reconnections.
As the Reynolds number increases, the dynamics become even more complicated.
“The collision of the vortex tubes leads to an instantaneous generation of multi-filament dipoles. These dipoles then undergo an enormous number of reconnections, causing an avalanche of large vortices in a turbulent cloud,” Yao said.
“Avalanche,” a term used by Yao and Hussain to explain the cascade in different flow situations, “is very important,” Hussain added. “We have shown through computer simulation that vortices reconnect from one to two until suddenly we have many vortices.”
“Imagine vortices of fuel and oxygen,” Hussain said. “And suddenly fuel and oxygen are next to each other, their vortices reconnecting. You could have a more complete burn and burn less fuel. It can be a big breakthrough.”
He also pointed out that fuel-powered vehicles such as cars, submarines, airplanes and missiles must overcome the aerodynamic drag of the environment.
“It turns out that in US civil aviation alone, improving drag by one percent could save $3 billion is phenomenal,” Hussain said.
Yao and Hussain also investigated skin friction drag reduction from wall turbulence at supersonic speeds in a paper published in November 2021 in the American Physical Society’s journal Physical Review Fluids.
“Drag control in wall turbulence is another important research area in our group,” said Yao, where successful control of wall turbulence requires a thorough understanding of the underlying physics.
“From our point of view, turbulence is a collection of many vortices of different magnitudes,” Hussain said. According to Yao, a major advance in wall turbulence research over the past few decades has been the discovery, understanding, and documentation of organized “coherent structures” such as vortices and their important role in near-wall dynamics. Vortices basically form a self-sustaining generation cycle of wall turbulence.
“In general, disrupting any phase of this self-perpetuating cycle could result in suppression of downflow vortex formation and hence reduction in drag – reducing fuel consumption and pollution. Most importantly, we find that the large-scale and very large-scale motions become dominant at high Reynolds numbers, we have proposed large-scale opposing wall-jet propulsion spanwise control techniques and composite control techniques,” Yao said.
Allocations were made by XSEDE on Stampede2 for vortex and turbulence research. And the team received a separate grant for the Lonestar5 system from TACC and from Texas Tech University HPCC.
Yao and Hussain continue their pipe flow research on TACC’s NSF-funded Frontera supercomputer, the world’s fastest academic supercomputer. The main goal of her work at Frontera is the simulation of turbulent pipe flow at relatively high Reynolds numbers.
About half of the energy expended in moving fluids through pipes, or by vehicles through air and water, is dissipated by turbulence near walls. “Therefore, a clearer understanding of the related flow physics has a direct and significant impact, and a better knowledge of these issues will be essential to find scientific methods to control the flow phenomena such as drag and heat and mass transfer,” Yao said.
“Although it is an esoteric subject,” Hussain said, “we cannot live without turbulence. The damage from tornadoes and hurricanes is real. And there are examples of mixing, entrainment, combustion, drag – all of these phenomena require detailed knowledge, as we do now with pipe flows. Supercomputers are not yet large enough to simulate realistic turbulence, such as that found at the wing tip of a flying jet at Reynolds numbers of 10 million or more. It requires tremendous computational resources, and we’re only just beginning to scratch the surface.”