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Stephen Pope accepted the challenge of unraveling the behavior of turbulent combustion, for which he develops computational models.
Beatrice Jin/Frank DiMeo
Beatrice Jin/Frank DiMeo

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Pope’s work is important for electrical power generation; aircraft engines; internal combustion engines for cars, trucks, and ships; furnaces; and subsequently sustainable energy.
Beatrice Jin
Beatrice Jin

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Pope pioneered the use of statistical models, for example, the PDF (probability density function) method, which provides a statistical description of the distribution of combustion properties.
Frank DiMeo
Frank DiMeo

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Pope’s lab tested the success of PDF methods in modeling turbulent jet flames, which has implications for building smaller, lighter engines for aircrafts.
Frank DiMeo
Frank DiMeo

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“…Two things that I really enjoy about Cornell. One is the ease in which you can interact with people in other departments…” says Pope.
Frank DiMeo
Frank DiMeo

Turbulent Combustion

by Alexandra Chang

Stephen B. Pope, Mechanical and Aerospace Engineering, is still chipping away at his longtime passion, which happens also to be a continuation of his PhD project. He works on developing computational models that describe how turbulent combustion behaves in engines—a notoriously difficult challenge. “It will be a decade or two before we really satisfactorily solve all of the problems,” says Pope.

Pope’s work is relevant to gas turbines for electrical power generation; aircraft engines; internal combustion engines for cars, trucks, and ships; and furnaces. Inside a combustion chamber, an unsteady three-dimensional flow occurs, known as turbulent flow. This turbulence, plus the chemistry of various fuels combusting, makes for very complex phenomena.

Modeling and Combustion Technologies

Working on turbulent combustion is especially important given our current energy state. The vast majority of energy is dependent on burning fuels. Though many researchers, scientists, and industry experts are making progress in developing renewable and sustainable energy, it’s crucial to simultaneously develop new combustion technologies that better address our current fuel supply. That said, the engineers who build combustion equipment need a way to test how it will behave in various scenarios. Instead of actually building the expensive equipment and then testing it, engineers look to computational modeling. This stage is when people like Pope come in.

Since Pope’s graduate research, he’s made significant contributions to this field of study. He pioneered the use of statistical models known as the PDF (probability density function) method. The PDF method is able to provide a statistical description of the distribution of combustion properties such as the velocity of the fluid, temperature, and concentration of chemical species—of which there can be on the order of hundreds.

The computational and statistical models are always developed in conjunction with laboratory data. Researchers are able to apply models to data to see if they work. When the models fail, the researchers then figure out what ingredients are missing and what could lead to the success of a model.

For example, Pope and his lab spent time testing the success of PDF methods in modeling turbulent jet flames. When one increases the jet velocity of a turbulent flame, there comes a point at which the flame will blow off. A pilot flame can delay the blow-off, but if velocity is cranked high enough, even a piloted flame will extinguish.

Studying such flame blow-off is important because engineers want to build smaller, lighter engines for aircraft. Combustion chambers need to be as small as possible, which means the fluid is not allowed to remain in the chamber for long, making flame blow-off more likely. Previous models were unable to account for the flame’s extinction and re-ignition. Using data from such flames, Pope and his colleagues were able to develop a highly accurate model of these phenomena.

Pope has also developed a tool called ISAT (in situ adaptive tabulation) that enhances the computational performance of PDF models. It takes characteristics of some underlying equations relevant to combustion chemistry and increases the speed at which a computer can perform chemical calculations.

ISAT works by building a table with information about the changes in particle composition as the computation is taking place. “Rather than having to integrate these very expensive differential equations, you just look up the result in the table that ISAT provides,” says Pope. “We typically speed things up by a factor of 1,000. That’s huge and has been a major advance that we’ve made.”

“Rather than having to integrate these very expensive differential equations, you just look up the result in the table that ISAT provides,” says Pope. “We typically speed things up by a factor of 1,000. That’s huge and has been a major advance that we’ve made.”

The models and methods that Pope and his colleagues have developed make their way to industry through partners such as ANSYS and CD Adapco, who are the market leaders in supplying simulation software to companies such as General Electric, General Motors, and Exxon.

The Challenge of Simulating Turbulent Combustion

Despite the many advances, many problems still need to be solved, says Pope, before we can simulate the turbulent combustion in engines to the required detail and accuracy. His lab is currently looking at experiments performed at Yale University and at the Sandia National Labs, the leading place for combustion experiments.

In these studies, two jets face each other. One blows out a fuel/air mixture and the other blows out hot combustion products. The two streams collide to create a turbulent mixing region, and under the right conditions, produce a flame. Researchers have observed that the flame properties change as you change the composition of the hot combustion, says Pope. This finding is relevant to internal combustion engines, such as car engines. Now, Pope’s lab is performing computations to see how well their models work under this particular combustion situation.

Working to solve combustion problems at Cornell has been particularly beneficial to Pope as well as to the field as a whole, says Pope. “There are two things that I really enjoy about Cornell. One is the ease in which you can interact with people in other departments, and we have extremely good people,” he says. “The second thing is that it’s an environment where you are encouraged to do good work, but there isn’t one mold for what constitutes good work. You’re allowed the freedom to have different forms of scholarship.”

Pope has collaborated with colleagues across departments, including Computer Science, Mathematics, and Operations Research and Engineering. Though he certainly hadn’t thought he’d be working on computational modeling of turbulent combustion in his high school years, he says that once he started his PhD project, he was “totally motivated to keep working at it.”