Fluids -- liquids and gases -- are such an integral part of our everyday lives that we often don't even give them a second thought. However, for engineers, the behavior of fluids bears great importance. Fluid flow affects everything from the miles per gallon we get in our car, to how well a golf ball flies through the air.
Now a key breakthrough in understanding of fluid modeling has been achieved. For years the key equation in the world of fluid mechanics was the Prandtl equation, developed by Ludwig Prandtl, which described how air and water flowed over objects. Despite its brilliance in 1904 when it was conceived, it had serious limitations -- it only worked for steady flow, such as a car traveling at low speeds, and it only applied to idealized 2 dimensional problems. For decades researchers tried to improve the equation to little avail.
Solutions obtained often diverged greatly from real world mechanics. For example, the air flow around a car making a hairpin turn, would often fall off, unable to keep up -- something the Prandtl equation could not explain.
This was a sizable problem as optimizing fuel flow is extremely important to many applications. One perfect example is Speedo's quest for the perfect swimsuit, which was showcased in its new designs which made their official mark on the Beijing Olympics. Another example is in car aerodynamics. Cars are sculpted to try to make airflow less unsteady. In an optimal scenario air would just glide across the car's surface and reform into a steady stream. In the real world air flows off the car in a turbulent stream akin to a boat wake, and separates from the surface as it passes over the car. By minimizing these effects, fuel economy can be improved.
However, nothing could explain exactly how these unsteady-state behaviors worked -- until now. MIT's George Haller, a visiting professor in the Department of Mechanical Engineering, developed a theory which applies to 3 dimensional unsteady state flows. This was confirmed with the help of Thomas Peacock, the Atlantic Richfield Career Development Associate Professor in the same department, who led experimental efforts to validate the results.
The new work -- if it survives the extensive peer review that is to come -- will likely go down as the greatest scientific advance of the decade. The research has already survived a strenuous initial round of peer review. Papers on the theory and experiments will be published in the Journal of Fluid Mechanics and in the September issue of Physics of Fluids, respectively.
Professor Haller's quest began when in 2004 he devised an equation for unsteady state in two dimensions. Having remedied half the shortcomings of Prandtl's equation, he set to work trying to extend the equation into three dimensions. Four years later, his dream has finally been achieved. Assisting Professor Haller in his research and coauthoring the paper were Amit Surana, now at United Technologies; MIT student Oliver Grunberg; and Gustaaf Jacobs, now on the faculty at San Diego State University.
Professor Peacock says the experimental verification is equally important, though, stating, "While we fully trust George's new mathematical results, the engineering community is usually skeptical until they also see experimental results."
Professor Haller concurs, stating, "While giving a beautiful validation of the 2D theory, Tom's work also gives strong experimental backing to our new 3D theory."
The experimental work was coauthored by Haller, Jacobs, Matthew Weldon, and Moneer Helu.
Having reached a solution, scientists can now begin to use it to optimize their systems. The equation will forever change the face of advanced fluid dynamics and will have a profound impact on many industries, including the aerospace and automotive industries. Professor Peacock states, "This is the tip of the iceberg, but we've shown that this theory works."
The research received initial funding from MIT's Ferry Fund. It is now funded by the Air Force Office of Scientific Research and the National Science Foundation.