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Grétar Tryggvason
Worcester Polytechnic Institute
Bernard Bunner


B. Bunner and G. Tryggvason. Direct Numerical Simulations of Three-Dimensional Bubbly Flows. Phys. Fluids, 11 (1999), 1967-1969.

B. Bunner and G. Tryggvason. An Examination of the Flow Induced by Buoyant Bubbles. Journal of Visualization. 2 (1999), 153-158.

Dancing Bubbles: Simulating Multiphase Flows

H ow do the complex interactions among bubbles rising in a boiling liquid affect the efficiency of a power plant? Although scientists and engineers have long known that the details of what happens around bubbles can have a decisive impact on the much larger overall flow, they have lacked a good understanding of the small-scale dynamics necessary for accurate predictions. Now, detailed simulations of bubbly flows that researcher Grétar Tryggvason of Worcester Polytechnic Institute is running on NPACI supercomputers are revealing the surprising secrets of dancing bubbles. Benefits could range from more efficient power plants to better modeling of many industrial processes.

Figure 1. Simulation of Ellipsoidal Bubbles Showing Streaming
Frame from a direct numerical simulation of 27 flattened or ellipsoidal bubbles (corresponding to lower surface tension) that have risen many diameters and are streaming, with many bubbles following each other up. The void fraction is 6% and bubbles have an average rise Reynolds number of 20, modeling bubbles in a liquid like oil. Vorticity contours and streamlines are shown for a plane through the middle of the computational domain (clearest bubbles lie this side of plane).

Multiphase flows containing mixtures of liquids, gases, and solids abound in both nature and many technologically important processes. Rainfall, ocean spray, the combustion of sprayed fuels, and boiling liquids are just a few of the cases that researchers would like to understand better. And such research is not just an academic exercise--these flows have great practical importance. Better understanding of multiphase flows could improve processes ranging from heat transfer and atomization to suspensions, droplet impact, and solidification; new engine designs that improve combustion could reduce emissions and increase mileage.

Because of their great practical importance, scientists and engineers have long constructed models to predict these multiphase flows. But all such models must still rely on approximate, empirically-derived coefficients because they cannot resolve the fine scales where the details of the interactions between bubbles take place. And while it is the overall, integral characteristics of such flows that have the greatest practical significance, they are strongly influenced by the evolution of the smallest scales in the flow, including the dynamics of bubbles.

"You simply cannot leave out the small scale dynamics of bubbles if you want to understand and predict the overall characteristics of multiphase flows, such as heat transfer in a boiling liquid," says Grétar Tryggvason, professor and head of the Department of Mechanical Engineering at Worcester Polytechnic Institute, whose simulations are among the first to successfully model the dynamics of bubbly flows.

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To learn more about the dynamics of bubbles rising in a liquid and how they interact, researchers traditionally carry out experiments. But the motions of bubbles take place on short spatial scales and rapid time scales. An even bigger problem is that the bubbles at the edge tend to hide the interior bubbles, so that despite advances in technology, experimentalists continue to have difficulties in getting a clear look at detailed bubble interactions, the intricate dances of rising bubbles.

To address these difficulties, Tryggvason and his former student, Bernard Bunner, both formerly of the University of Michigan (Bunner is now at DaimlerChrysler), have run direct numerical simulations (DNS) on NPACI supercomputers to model the complex motions of large numbers of bubbles interacting as they rise through a liquid. What makes these simulations so realistic is that they solve the Navier-Stokes equations--the full equations of motion--for the fluid movements, including all the physical mechanisms of viscosity, inertia, and surface tension.

The researchers have applied similar methods to a number of situations including atomization, suspensions, droplet impact, and solidification, but their work on bubbly flows is the furthest along. They started by modeling just one bubble, and have since simulated up to 216 bubbles.

"Real world flows are extremely complex, and DNS cannot simulate the complete system for cases like combustion in a car engine or boiling liquids in a boiler. But with advances in computational methods and the growing power of supercomputers, the realistic DNS simulations we can now run are giving us fundamentally new insights into the key mechanisms at the small scales of multiphase flows," Tryggvason says. And what the researchers are learning through these simulations about the "elementary" processes in bubbly flows is laying the groundwork for improved models of many important, real-world multiphase flows.

Figure 2. Detail of Interacting Ellipsoidal Bubbles
Detail of interacting ellipsoidal bubbles showing the bubbles along with vorticity contours and streamlines in a plane through the middle of the computational domain.
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Figure 3. Simulation of Spherical Bubbles
Frame from a direct numerical simulation of 27 nearly spherical bubbles (corresponding to greater surface tension). The void fraction is 6% and the bubbles have an average rise Reynolds number of 20. Vorticity contours and streamlines are shown for a plane through the middle of the computational domain (clearest bubbles lie this side of plane).

The basic physical situation that Tryggvason and Bunner have fully modeled in 3-D consists of up to 216 bubbles rising in a liquid about the thickness of oil. Their simulations have explored variations in the void fraction occupied by the bubbles of between 2% and 24% and in the shape of the bubbles, one case being nearly spherical bubbles and the other being flattened or ellipsoidal bubbles that correspond to less viscous fluid with lower surface tension.

"Usually when we do simulations we're explaining something that's already been observed experimentally, but it's exciting that even at this early stage these simulations are really finding unanticipated behavior--they predicted something new," Tryggvason says. The most unexpected thing the researchers found is a complete reversal of lift in flattened bubbles as compared to more spherical ones. When large numbers of rising bubbles cause regions of faster and slower moving fluid, a simple fluid mechanics theory says that spherical bubbles will move in the direction of the slower moving fluid, and that's what the researchers found in their simulations.

"But as the surface tension drops and the bubbles flatten, this forces the flow to go around in a different way. The ellipsoidal bubbles become little winglets, and that changes the direction of the lift, completely reversing it so that it draws them into the faster moving fluid found in the wakes of passing bubbles. As a result, unlike spherical bubbles, flattened bubbles will sometimes stream together, following each other up in narrow columns," Tryggvason says (Figures 1 and 2).

For the case of spherical bubbles (Figure 3) what the researchers found is the more conventional results they anticipated in which the bubbles show a preferred structure with two bubbles rising side-by-side. Here are the dance-steps the bubbles follow: If one bubble is behind, following in the wake of another, it gets speeded up in the upward-moving wake, catches up, hits the top bubble, they tumble, and then both travel in horizontal alignment. "This is predicted for solid spheres, so it's not unexpected that we confirmed it in our DNS simulations," Tryggvason says. Once they're grouped horizontally, however, the spherical bubbles keep interacting--they are only stable for a while. "Although there's a theoretical model predicting horizontal rafts, our simulations show that's not the case, and the side-by-side bubble system is inherently unsteady, it keeps opening new configurations," Tryggvason says.

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Although researchers have been simulating fluid flows for decades in computational fluid dynamics, it is only very recently that direct numerical simulations have progressed to the point of offering a detailed understanding of multiphase flows. "This kind of complete simulation, where we account fully for inertial, viscous, and surface tension forces in addition to a fully deformable interface between the different phases--in this case liquid and gas--is one of the most difficult problems in computational fluid dynamics," Tryggvason says.

Tryggvason and Bunner have developed a numerical method that holds considerable promise in this area. "By combining a front-tracking technique using a moving, triangulated 2-D grid that stretches and deforms as it explicitly tracks the interface between the different phases, with a relatively conventional fixed-grid finite difference method, we are able to accurately simulate 3-D systems with many bubbles or droplets and to do this over a long time period," Tryggvason says. The longer time is important because the flow continues to evolve, so the researchers need to let the bubbles rise several tens of diameters, requiring long simulation runs.

For this work the researchers have extended a method Tryggvason developed earlier, creating a completely parallel version of the code. Bunner also wrote a multi-grid Poisson solver to solve the pressure equation using a domain decomposition method, coupled with a master-slave approach to parallelize the moving grid that marks the bubbles.

It took considerable effort for the researchers to make the parallel version reasonably efficient, and their largest simulations have been run on NPACI's IBM SP at the University of Michigan. Just as the flows themselves interact in nonlinear ways across a vast range of scales, the computer model must intensively share memory, and the researchers have found it challenging to scale the code to larger numbers of nodes due to the significant need to share memory.

In the future, Tryggvason intends to run simulations on Blue Horizon to be able to model more complex higher Reynolds number flows that will apply to a wider range of important real world problems as well as fundamentally different bubble behavior. Larger bubbles, even a single bubble, can move in very different modes than smaller bubbles, following either a spiral pattern or wobbling as they rise. "We think this is very likely to lead to fundamentally different interactions among many bubbles, and we would like to explore this," Tryggvason said. The researchers would also like to include a larger number of bubbles in their simulations, because there are more complex modes of interaction that can involve hundreds of bubbles. "As we run on larger machines like Blue Horizon," Tryggvason said, "in addition to more complex bubbly flows we also plan to extend these simulation methods to flows that include things like phase changes and mass transfer." --PT *