Researchers at the University of Illinois Urbana-Champaign have unlocked new insights into the turbulent behavior of hypersonic flows by using advanced 3D simulations.
Leveraging supercomputing power and custom-built software, they discovered unexpected instabilities and flow breaks around cone-shaped models at Mach 16, disturbances never seen before in previous 2D or experimental studies. These findings could significantly impact the design of future hypersonic vehicles by helping engineers understand how extreme speeds interact with surface geometries in new ways.
Hypersonic Flows and New Discoveries
At hypersonic speeds, air behaves in complex ways as it interacts with a vehicle’s surface, forming features like boundary layers and shock waves. For the first time, researchers in the Department of Aerospace Engineering at the Grainger College of Engineering, University of Illinois Urbana-Champaign, have observed new disturbances in these interactions using fully 3D simulations.
Running high-resolution 3D simulations at hypersonic speeds requires immense computational power, making such work costly and challenging. Two key resources made this study possible: access to Frontera, a leadership-class supercomputer funded by the National Science Foundation at the Texas Advanced Computing Center, and specialized software developed over the years by several of Professor Deborah Levin’s former graduate students. Levin led the study alongside her Ph.D. student, Irmak Taylan Karpuzcu.
A New Look at Flow Instabilities
“Transitioning flows are 3D and unsteady in nature, regardless of the flow geometry. Experiments were conducted in 3D in the early 2000s didn’t provide enough data to determine any 3D effects or unsteadiness because there weren’t enough sensors all around the cone-shaped model. It wasn’t wrong. It was just all that was possible then,” said Karpuzcu. “We have those data to compare, but having the full picture now in 3D, it’s different. Normally, you would expect the flow around the cone to be concentric ribbons, but we noticed breaks in the flow within shock layers both in the single and double cone shapes.”
Surprising Breaks at Mach 16
Karpuzcu said they observed the breaks near the tip of the cone, and with a shock wave near where the air molecules were closer together making them more viscous at Mach 16.
“As you increase the Mach number, the shock gets closer to the surface and promotes these instabilities. It would be too expensive to run the simulation at every speed, but we did run it at Mach 6 and did not see the break in the flow.”
Karpuzcu said the cone geometry represents a simplified version of many hypersonic vehicles and understanding how the flow affects surface properties can help lead to design considerations.
Unexpected Findings in 3D
“Our group’s in-house software made it efficient to run the simulation in parallel processors, so it’s much faster. There were already data from experiments under high-speed conditions so we had some intuition about how the simulations would look, but in 3D we found breaks that we didn’t expect to see.”
He said the most difficult part of the work for him was in analyzing why the break in the flow was happening.
“The flow should be going in all directions, but uniformly. We needed to justify what we were seeing. Our literature review indicated that a linear stability analysis based on triple-deck theory can be applied to this flow. After analyzing the complex formulations and connecting them to our case, we developed a code to numerically simulate the problem again. Running the 3D direct simulation Monte Carlo simulation is hard, but then we set up a second computer program to make sure everything works and is within the limits for our flow conditions. When we did that, we saw the break in two big chunks in 180-degree periodicity around the cone.”
The Power of Monte Carlo Simulations
Karpuzcu said the beauty of the direct simulation Monte Carlo is that it tracks each air molecule in the flow and captures the shocks.
“When you use other methods to calculate fluid dynamics, it’s all deterministic. When we introduce a particle to the flow field, there is a probability of that particle colliding with other particles or any solid surfaces that’s calculated on physics-based formulas, but the output is a roll of the dice. The Monte Carlo method does random, repetitive attempts. It’s more extensive than classical computational fluid dynamics methods and we’re tracking billions of particles. This makes sure there are enough particles within the flow field and collisions are captured properly.”
Reference: “Loss of axial symmetry in hypersonic flows over conical shapes” by Irmak T. Karpuzcu and Deborah A. Levin, 7 March 2025, Physical Review Fluids.
DOI: 10.1103/PhysRevFluids.10.033901
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