Unlocking the Secrets of the Vortex Rings: Paving the Way for Efficient Nuclear Fusion

Researchers at the University of Michigan have developed a model to better understand the formation of vortex rings, which could aid in the efficient compression of fuel for nuclear fusion and also in the mixing of post-shock fluids. This model is beneficial not only to fusion researchers, but also to engineers designing supersonic jet engines and physicists studying supernovae.

Engineers could gain better control over the behavior of vortices in power generation and other applications with a mathematical model that links these vortices with more pedestrian types, such as smoke rings.

Gaining more insight into the formation of vortex rings, which are ring-shaped vortex disturbances, could help nuclear fusion scientists compress fuel more effectively. This would potentially take us one step closer to exploiting nuclear fusion as a viable energy source.

The model developed by the University of Michigan researchers could aid in the design of the fuel pod, minimizing the energy lost as it tries to trigger the reaction that makes stars shine. In addition, the model could help other engineers dealing with the mixing of fluids after a shock wave passes, such as those designing supersonic jet engines, as well as physicists trying to understand supernovae.

These vortex rings move outward from the collapsing star, populating the universe with materials that will eventually become nebulae, planets, and even new stars, and inward during fusion implosions, disrupting the stability of the fuel of burning fusion and reducing the efficiency of the reaction, said Michael Wadas, a mechanical engineering doctoral candidate at UM and a correspondent author of the study.

A 3D simulation showing a vortex ring forming at the leading edge of a jet, generated by a shock wave passing through an interface between two different fluids. Credit: Michael Wadas, Laboratory of Scientific Computing and Flow Physics, University of Michigan.

Our research, which elucidates how such vortex rings form, can help scientists understand some of the most extreme events in the universe and bring humanity one step closer to harnessing the power of nuclear fusion as an energy source, he said.

Nuclear fusion pushes atoms together until they fuse. This process releases many times more energy than the splitting of atoms, or fission, that powers today’s nuclear power plants. Researchers can create this reaction, merging forms of hydrogen into helium, but currently much of the energy used in the process is wasted.

Part of the problem is that the fuel cannot be compressed well. The instabilities cause jets to form that penetrate the hot spot, and fuel squirts out between them. Wadas likened it to trying to squeeze an orange with your hands, as the juice oozes between your fingers.

The vortex rings that form at the leading edge of these jets, the researchers showed, are mathematically similar to the smoke rings, the vortices behind jellyfish and the[{” attribute=””>plasma rings that fly off the surface of a supernova.

Perhaps the most famous approach to fusion is a spherical array of lasers all pointing toward a spherical capsule of fuel. This is how experiments are set up at the National Ignition Facility, which has repeatedly broken records for energy output in recent years.

This graphic shows what happens when a shockwave passes through the interface between two different fluids. The top half of the image shows the starting situation. The top section, in dark teal, shows the vorticity of the fluid, or what parts are engaging in these swirling flows (none at the start). The second layer shows the density of the fluid. The navy blue is less dense, while the yellow and green are the same densitythey just sit on opposite sides of the shockwave. The denser fluid protrudes into the less dense fluid, and the initial interface between the two fluids is marked by the dotted line. From that starting point, the shockwave passes through. A jet pushes into the denser fluid, with a vortex ring running ahead of it, traveling in the opposite direction of the shockwave. The swirling flows are shown in light teal in the vorticity panel, while the edges of the vortices are shown in orange. Credit: Michael Wadas, Scientific Computing and Flow Physics Laboratory, University of Michigan.

The energy from the lasers vaporizes the layer of material around the fuela nearly perfect, lab-grown shell of diamond in the latest record-setter in December 2022. When that shell vaporizes, it drives the fuel inward as the carbon atoms fly outward. This generates a shockwave, which pushes the fuel so hard that the hydrogen fuses.

While the spherical fuel pellets are some of the most perfectly round objects humans have ever made, each has a deliberate flaw: a fill tube, where the fuel enters. Like a straw stuck in that crushed orange, this is the most likely place for a vortex-ring-led jet to form when the compression starts, the researchers explained.

Fusion experiments happen so fast that we really only have to delay the formation of the jet for a few nanoseconds, said Eric Johnsen, an associate professor of mechanical engineering at U-M, who supervised the study.

The study brought together the fluid mechanics expertise of Wadas and Johnsen as well as the nuclear and plasma physics knowledge in the lab of Carolyn Kuranz, an associate professor of nuclear engineering and radiological sciences.

In high-energy-density physics, many studies point out these structures, but havent clearly identified them as vortex rings, said Wadas.

Knowing about the deep body of research into the structures seen in fusion experiments and astrophysical observations, Wadas and Johnsen were able to draw on and extend that existing knowledge rather than trying to describe them as completely new features.

Johnsen is particularly interested in the possibility that vortex rings could help drive the mixing between heavy elements and lighter elements when stars explode, as some mixing process must have occurred to produce the composition of planets like Earth.

The model can also help researchers understand the limits of the energy that a vortex ring can carry, and how much fluid can be pushed before the flow becomes turbulent and harder to model as a result. In ongoing work, the team is validating the vortex ring model with experiments.

Reference: Saturation of Vortex Rings Ejected from Shock-Accelerated Interfaces by Michael J. Wadas, Loc H. Khieu, Griffin S. Cearley, Heath J. LeFevre, Carolyn C. Kuranz and Eric Johnsen, 12 May 2023, Physical Review Letters.
DOI: 10.1103/PhysRevLett.130.194001

The research is funded by Lawrence Livermore National Laboratory and the Department of Energy, with computational resources provided by the Extreme Science and Engineering Discovery Environment through the National Science Foundation and the Oak Ridge Leadership Computing Facility.