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Multiphase Flow
When crude oil is pumped from the ground, it enters a pipeline as a mixture of liquid oil and some water. As the liquid moves along the pipeline, the pressure falls and hydrocarbon gases (e.g., methane) originally dissolved in the oil come out of solution, much like opening a soft drink. The fluid being pumped then becomes a mixture of gas and liquid, which behaves 
very differently from liquid alone. This is one of the many headaches that multiphase flows (i.e., flows in which gases, liquids, and, in other cases, solids are mixed together) present to the engineer.
Farther down the line in the oil refinery, another important instance of multiphase flow arises in the “cracking” process, in which the long chains of hydrocarbons that constitute crude oil are broken down into products such as gasoline, kerosene, naptha, and household heating oil. Cracking is accomplished by mixing oil vapor with catalyst powder at very high temperatures. Any gain in the efficiency of thecracking process would have a tremendous impact in terms of reduced pollution and enhanced productivity.
Oil refining is just one of many examples of the many ways in which multiphase flows affect technology and, ultimately, our lives. Others include agriculture (e.g., the flow of grains in a silo), food processing, combustion, and power generation.
In all these instances, the particles or bubbles traveling along with the fluid complicate fluid dynamics considerably—they exert drag on the flow, change the density of the medium, affect its compressibility, and introduce all sorts of complex flow structures in their paths.
Current understanding of these complex phenomena is not well enough developed to permit the reliable design of optimized industrial systems. In the absence of a robust theory, it is also difficult to rely on experiment: if one runs tests on a small-scale version of a plant, there is no way to know how the full-scale system would behave.
In principle, since the laws of mechanics are known, the equations describing each particle or bubble together with the motion of the surrounding fluid could be solved—an approach called Direct Numerical Simulation. In practice, the amount of computational firepower necessary to tackle even relatively small practical problems in this way is far beyond what is feasible not only now but in the foreseeable future. Hence a “shortcut” must be found, and this is a problem that has plagued the field for decades.
Professor Andrea Prosperetti has spent the better part of the past 20 years working on such “reduced” approaches to multiphase flow, and his stature at the front of the field is a tribute to his tenacity. The challenge is to devise a formulation in which the complex details of the actual flow (e.g., what each particle does) are lumped together in an average description of the system. Many such approaches have been attempted over the years, mostly with disappointing results. As long as the fluid contains only a few particles or bubbles, our intuition is sufficient to develop a satisfactory formulation, but when their density increases, one is at a loss to capture the unexpected effects that arise. Prof. Prosperetti’s approach consists in trying to gain a physical understanding of what happens in these situations by means of Direct Numerical Simulation. He makes the point that while, as mentioned before, it is impossible to simulate large realistic systems, much can be learned by looking at small assemblies of, for example, 500 particles. The task of building a “reduced” formulation for multiphase flow is therefore to take the computer output of the DNS simulation, develop average laws that describe those results, and finally come up with equations that govern this “reduced” system. This is in some sense the reverse of what is normally done: usually one starts with the equations and ends up with numbers by solving the equations on a computer. Needless to say, this reversal of roles makes things rather complicated and that ultimate “high-tech” tool—mathematics—has to be relied upon very heavily to carry out the job.