New Approach To Hypersonic Calculations

The potential to travel across the country in less than an hour will depend upon an enhanced understanding of hypersonic aerodynamics.

Traveling at speeds far in excess of the speed of sound is usually reserved for ballistic missiles, re-entering space shuttles, and a small number of experimental and proposed space planes. Engineers designate various speed regions as subsonic (below the approximately 760 mph that is the speed of sound), transonic (around the speed of sound, designated Mach 1), supersonic (between Mach 1 and Mach 4), and hypersonic (above Mach 5).

The potential for ultrafast worldwide air travel has enhanced interest in studies of hypersonic airflow “Imagine flying from New York City to Los Angeles in an hour. Imagine incredibly fast unmanned aerial vehicles providing more updated and nuanced information about Earth’s atmosphere, which could help us better predict deadly storms,” said Chen, PhD, assistant professor in the Department of Mechanical and Aerospace Engineering at the University of Buffalo’s School of Engineering and Applied Sciences.

A 3D computer simulation of air flowing over a hill creating turbulence at transonic speed. The ring-like features are eddies of air. (Image source: James Chen / University at Buffalo)

Limitations of Current Methods

At subsonic speeds, calculation of forces and stresses on an object moving through the air can be calculated using the Navier-Stokes equations. At speeds above Mach 0.3, (230 mph), and into the supersonic range, compressibility and thermal effects begin to come into play—the Navier-Stokes equations can still be used, but additional factors must be included in the calculations.

“There is so much we don’t know about the airflow when you reach hypersonic speeds. For example, eddies form around the aircraft creating turbulence that affect how aircraft maneuver through the atmosphere,” said Chen in a U of B news release describing his work. .

At extremely high speeds, into the hypersonic and high hypersonic (above Mach 10) speeds, the Navier-Stokes equations no longer accurately predict the forces and stresses that fluid flow over a surface produces. At these speeds, heating and even dissociation of the air becomes a significant factor. In addition, air no longer acts as an ideal gas and the effects of the spin of air molecules must be factored into the equations in order to more accurately represent the air flow.

Chen is the corresponding author of a study published Jan. 3 in the Journal of Engineering Mathematics. The study pertains to Austrian physicist Ludwig Boltzmann’s classical kinetic theory, which uses the motion of gas molecules to explain everyday phenomena, such as temperature and pressure.

Long-Standing Problems

Chen’s work extends classical kinetic theory into high-speed aerodynamics, including hypersonic speed, which begins at 3,836 mph or roughly five times the speed of sound. The new study and others by Chen attempt to solve long-standing problems associated with high-speed aerodynamics.

 “When you go faster, the molecule is going to spin,” said Chen to Design News. “My hypotheses was that speed is going to affect the flow—and this shows up in experimental results where the Navier-Stokes analyses cannot predict flow properly, it’s nowhere close to the experiments.”

The Matter Of Turbulence

There are other considerations at hypersonic velocities. “At hypersonic speeds, the flow is moving at high Mach numbers, but there are also wings or flaps on the vehicle. At each of those junctures, you can have very strong recirculation, which leads to unsteadiness. It’s difficult to predict how bad the unsteadiness can become before the flow is no longer smooth, and becomes turbulent,” said Deborah Levin, professor in the Department of Aerospace Engineering in the College of Engineering at the University of Illinois. Her research was described in a U of I news release in 2016.

 Chen described to us the need to consider the turbulence. “The second thing is for turbulence. We all know that it is full of eddys—in order to resolve the small-scale rotational motion, we rely on vorticity. To calculate vorticity you need two points, as your flow speed goes up, in order to capture those smaller motions, your mesh needs to be finer and this increases the computational cost. In my method, I don’t need two points, I formulate the rotation for each point theoretically, allowing me to reduce the mesh by an order of magnitude,” said Chen. The mesh reduction will significantly reduce the computational resources required to simulate hypersonic flow.

Moving to Open Source

“We are moving our code to OPENFOAM. We will release it to the OPENFOAM community so it becomes open source. It is already in the package and some people have started using it, but I just haven’t made it public yet,” said Chen. “I think I can foresee my theory, once it’s more established, will be able to use an order of magnitude less of computational resources. Then we can do a full airplane for the whole analyses—including the flow phenomena and temperature and pressure and how it affects the aircraft structure. We will be able to do full analyses for all of it,” Chen told us.

Senior Editor Kevin Clemens has been writing about energy, automotive, and transportation topics for more than 30 years. He has masters degrees in Materials Engineering and Environmental Education and a doctorate degree in Mechanical Engineering, specializing in aerodynamics. He has set several world land speed records on electric motorcycles that he built in his workshop.

 

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