"Face of a Flame," we called this image when it ran on the cover of the December 1994 Research/Penn State and on the poster for the 1995 Graduate Research Exhibition. Then we got to thinking. Who took this fiery portrait, and how? (Not to mention, Why?)

In coffee cups and cars' engines, turbulence is a good thing.

For one, "It allows the engine to be small enough to fit inside your car," quips chemical engineer Lance Collins.

Easiest to see in smoke, clouds, or the swirls of milk poured into coffee and stirred, turbulence is that characteristic pattern -- large swoops and swirls that break off into smaller and smaller curlicues -- that occurs when one substance flows quickly through or past or into another. Outside a car, it causes friction and drag; under the hood is another story.

As Collins explains, in a chemical reaction like combustion "you're typically wanting to mix -- and turbulence is the most efficient way to mix anything. The rate of reaction can be orders of magnitude faster than it would be without turbulence.

"If you were to fill this room with a combustible mixture," he continues, gesturing with a smile toward the concrete walls of his office, "it would take millenia to get a reaction. If you ignited it, it would go bang!"

As the spark heats the molecules next to it, they begin to jostle and bump into their neighbors, which hit into their neighbors, and the reaction begins. "You get a wave," Collins says. "In effect, the reaction is only occurring in that two-dimensional wave. Combustion looks very much like a hot region and a cold region separated by a sheet of flame."

A sheet that gets increasingly "bent and contorted and twisted," Collins notes, as the reaction proceeds.

Through a numerical simulation, he and his graduate students, Mark Ulitsky and Ajit Dandekar, have taken a snapshot of this wrinkled sheet of turbulent flame. Starting with a flat 96-by-96-by-96 grid, they solved the mathematical equations describing fluid flow for each point, taking into consideration the molecular properties of the fuel. The computations, which took some two weeks to solve on IBM workstations, compare well with flame experiments being done across campus by Penn State mechanical engineer Dom Santavicca. Using a laser imaging system to see inside an actual flame, Santavicca "exactly creates the physical analogue of what we simulate," says Collins, "a flame in a box.

"He has easily the most careful measurements of the effect of molecular properties on flame propagation," Collins adds, "but potentially, we have more information than his experiment. It's like running the experiment with extremely high precision -- precision limited only by the number of points you use.

"Now, the experiment is the reality, and it's much harder to do -- I don't want to imply that one is better than the other. And he keeps pushing the experimental limits. It's only a matter of time before he can do experimentally what we can do numerically.

"So we're slowly closing in on seeing what's actually going on inside a flame. We're merging at what I think is the precise representation."

With their calculations backed up by hard experimental data, Collins and his graduate students can turn to the next problem: transforming their numerical simulation of a flame in a box into a true mathematical model able to describe combustion in any geometry, from a car engine to a gas turbine.

Already, they've seen through one of turbulence's tricks. To explain, Collins holds up the now-familiar devil's-eye-red flame-in-a-box image. "If you look at the picture," he says, "you'll see there are big folds, but superimposed upon them are intermediate wrinkles and fine-scale features. That's important. Your eye will gravitate to the big folds, but the fine-scale wrinkles can produce more surface area -- and the rate of a reaction is essentially proportional to the surface area.

"And that's the challenge. Standard, classical models account for large-scale turbulence, because in almost every other sense -- drag on an airplane wing, for example -- that's the dominant scale. The large-scale eddies generally are the most important since they carry the most kinetic energy.

"But reacting flows are unique. Because they're trying to mix, the fine-scale features become more important.

"When I teach about this in my undergraduate classes," Collins adds, "I say, suppose you have a cup of coffee and you pour milk in. One thing you could do is sit there and wait the five-day period until it homogenizes. But you don't. You stir. Now, if turbulence was only one size, you'd contort and wrap the milk around the inside of the cup" -- your coffee would look like vanilla-fudge twirl ice cream. "But you don't. When you stir, you don't just generate vortices on the cup scale, they break down into smaller and smaller scales until diffusion kicks in and takes it the rest of the way."

The same, according to Ulitsky and Dandekar's sheet-of-flame image, will be true in a hot engine. Notes Collins, "I never would have expected that. What's interesting with turbulence is, we do the simulations and pore over the data, and our hypotheses are right about 25 percent of the time. It's very clear why before they had all this information, people couldn't make much progress understanding combustion. Turbulence fools you a lot. But when your assumptions were wrong is when you've probably learned something."

Lance R. Collins, Ph.D., is assistant professor of chemical engineering in the College of Engineering, 118B Fenske Building, University Park, PA 16802; 814-863-7113. Ajit Dandekar and Mark Ulitsky are graduate students in chemical engineering. Their work is funded by the National Science Foundation and a Dow Chemical Young Minority Investigator Award; Ulitsky holds a National Science Foundation Graduate Research Fellowship.