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MATTERS OF REFLECTION
by J. William Bell, NCSA Access magazine editor

The three-pronged attack has always been a staple of military planning-- sometimes ending in victory, sometimes in disaster. The Soviet Union used the tactic to great effect in Europe at the close of World War II. George Custer and his men, on the other hand, didn't fare so well on the plains of Montana in 1876.

For an international group of aerospace engineers using NCSA computing resources, there's no Little Bighorn in sight. The team is making a successful attack on Mach reflections, unusual high-speed airflows that are a bane to airplane designers. They have found that lasers can diminish or eradicate these confounding events when they crop up in the inlets at the front of supersonic engines.

Two members of the team, Hong Yan of Rutgers University and Dmitry Khotyanovsky of the Russian Academy of Science's Institute of Theoretical and Applied Mechanics (ITAM), are running calculations on NCSA's Platinum cluster. Though they are modeling identical systems, Yan and Khotyanovsky use different codes to get the job done. The University of Illinois at Urbana-Champaign's Gregory Elliott represents the third prong in the team's battle plan and conducts experiments on the system in a wind tunnel.

"It is critical to make sure that our final results are not a numerical artifact caused by the influence of…errors present in any [particular] shock- capturing scheme," Khotyanovsky says. "The cross comparison of our results gives us confidence."

Take the good, fight the bad

Air traveling through an engine at many times the rate of sound doesn't mix readily with fuel injected into the engine, resulting in unburned fuel and inefficient combustion. To combat this situation, designers typically place an inlet in front of the engine. "The inlet creates shock waves, which lower the air's speed and allow for good mixing with the fuel. Otherwise, it blows past too fast," explains Yan. She is a research assistant professor in Rutgers' mechanical and aerospace engineering department.

When shock waves intersect, what are known as regular reflections typically form. These reflections result in minimal energy loss and thus have little detrimental impact on engine performance. Under very turbulent conditions caused by extreme acceleration or unusual maneuvering, however, shock wave intersections can instead form Mach reflections. These reflections decrease total air pressure and degrade engine performance.

Using a laser pulse or other source of heat, engineers have found that they can turn Mach reflections into regular reflections as they form. At the spot of the temperature increase, the air expands and a subsonic region develops. This change deflects one of the shock waves responsible for the Mach reflection, which eliminates, or at least momentarily reduces the size of, the Mach reflection.

Small scale, big impact

Yan and Khotyanovsky are modeling tiny versions of such a system. Air moves at Mach 3.45 between two wedges pitched 22 degrees off the top and bottom of the simulated domain. The entire domain is less than six inches across. Despite the small size and the fact that an inlet would only have one wedge and the flat aircraft body instead of two wedges, the simulation represents with great fidelity what would occur inside a real engine inlet.

"This is a common and widely used model for experiments on shock wave reflection," Khotyanovsky says. It allows the team to discount the effects of the boundary layer, a viscid airflow that runs along the body of the aircraft and weakens the resulting shock waves. Introducing the boundary layer into the simulations would "greatly complicate the problem," he says, without much of an upside.

Whether the simulation is run by Yan, who uses the commercial GASPex software, or by Khotyanovsky, who uses a code developed by ITAM's Alexey Kudryavtsev, the simulations begin by calculating the initial flow. The domain is separated into millions of cells of varying sizes, placing smaller cells in the areas of the domain that are most relevant. GASPex automatically groups cells that will be calculated on the same computer processor depending on the amount of memory and number of processors available for the calculations. The Euler equations, which determine the motion of the flow, are solved for each cell over and over until a Mach reflection appears and the flow reaches a steady state.

Energy equal to that of a 10-nanosecond, 215-millijoule laser pulse is then introduced into the system, raising the temperature of the targeted area to 8,000 Kelvin for a matter of microseconds. The flow is recalculated, and the team can watch the laser pulse's impact.

Meanwhile, Greg Elliott recreates the entire system in a miniature wind tunnel. "The simulations are [looking at a system] exactly the same size of the wind-tunnel experiment," Yan says. The air blasts through the system at the same speed, and the laser pulse is of the same power and duration, too.

Though the goal is simple comparison and confirmation, as Khotyanovsky explained previously, there are other benefits to combining experiment and simulation.

"The different approaches verify one another, and both allow us to understand the system's fluid dynamics," says Elliott, an associate professor of aerospace engineering at the University of Illinois. "With the combination, though, we can also see what's the best use of our resources. Some changes to the wind tunnel model can be made in a matter of seconds to probe for an optimal solution. The flow field can then be computed, which may take a much longer time, to obtain details of the flow so that the reason for changes in the flow characteristics can be better understood."

Cleaning up, moving on

The team has completed a series of simulations using both GASPex and the ITAM code. The correlation of the results from the two codes is very tight, according to the team. The team has also tested GASPex at two different levels of detail, running some simulations with 1.5 million cells and others with a more taxing 5 million cells. These simulations, which required as many as 64 processors on NCSA's Platinum cluster, also had very similar outcomes.

In every case, the laser pulse caused the detrimental Mach reflection to change into its more innocuous cousin. Details of these results were published in the journal Shock Waves in 2003.

To date, however, results from the experiments don't quite match up. Instead of being eradicated, the Mach reflection in the wind tunnel is only reduced to 30 percent of its original size. While this decrease is still a testament to the ability of the laser to influence and improve a supersonic inlet's aerodynamics, it is also a discrepancy that the team would like to overcome. The most likely cause of the inconsistency is additional turbulence created by the wind tunnel itself.

"In the wind tunnel, there is additional turbulence in the supersonic free stream [the moving air that creates the flow and shock waves around the wedges] that is not present in a perfectly clean flow. In the simulations, they can obtain a free stream without the effects of turbulence," Elliott says. In the future he hopes to be able to run the experiments in a tunnel that generates less unintended turbulence. This "quieter" tunnel will allow for an improved comparison between the experiments and computations.

The simulations will move forward in the coming months as well. Yan and Khotyanovsky plan to embellish their fundamental models. Among other things, they will move the location of the laser's thermal spot and introduce multiple spots--and, of course, study the impact those alterations have on the Mach reflections.

But even without these additional efforts, the work is considered a success. "These are the first such simulations of their kind," according to Doyle Knight, another Rutgers professor who studies aerodynamics using NCSA resources. "They've shown how you can do this--how you can take a Mach reflection when it appears and flip it back into a regular reflection using a laser pulse."