On the microbubble

Brown University researchers pioneer first-principles modeling of microbubble drag reduction using NCSA's Platinum and Titan Linux clusters.

by J. William Bell

Don Ho's got nothing on George Karniadakis and Martin Maxey, applied mathematics professors at Brown University. While the crooner sings of "Tiny Bubbles," Karniadakis and Maxey are going one better and immersing themselves in microbubbles. These yet-tinier bubbles, about 50 to 500 microns in size, can cut drag, reduce the amount of fuel ships use, and increase ships' range.

For 30 years, microbubble systems have been studied experimentally. Pistons push air through porous plates representing a ships hull and into tanks of moving water. Researchers have moved the locations of the plates. They've increased and decreased the number and size of the bubbles. And they've seen an incredible change in drag--a reduction of as much as 80 percent.

But they haven't been able to figure out what the optimal microbubble system looks like--where to insert bubbles, how many to insert, and how big to make them. To develop the optimal system, they must understand the fundamental physics of the water's flow around the hull and the microbubbles' impact on that flow. Traditional methods of measuring the flow details in an experimental tank are foiled when microbubbles are introduced. Optical systems can't see through the Alka-Seltzer fizz that the bubbles create.

To get around that problem, Karniadakis and Maxey are creating the first first-principle computational models of microbubbles in action. "Most of the people involved in studying microbubbles, even today, are experimentalists. We're doing the only direct numerical simulations of microbubbles in turbulent flows," says Karniadakis, who has used NCSA resources since the late 1980s.

By recently shifting his team's microbubble research to NCSA's newest Linux cluster, Karniadakis improved the state of the art by a factor of forty--jumping from models that track a mere 500 bubbles to models that track about 20,000 bubbles.

The Brown team's microbubble research is just one part of a massive program established about a year and a half ago by the Defense Advanced Research Projects Agency (DARPA). The Friction Drag Reduction program combines the efforts of 14 research teams around the country. The teams are looking for ways to reduce drag by creating models and experiments at a variety of scales--from computational models that follow the behavior of individual bubbles to mockups that are about 3 meters by 13 meters and run in the largest recirculating water tunnel in the world.

The project's broad scope will allow DARPA to develop a multi-scale modeling capability. Without such a capability, drag reduction research will remain as hit-or-miss as it was 30 years ago. By understanding the physics of the system at every level, researchers will reduce not only drag but also the inefficiencies that used to be inherent in studying drag.

"We're pushing for a whole new modeling paradigm," says Lisa Porter, DARPA's program manager on the project. "People are realizing that experimentation at the large scale is very expensive, so we need tools to narrow [those experiments] down."

A computer model of microbubble physics, for example, allows those building large-scale physical models to test a much smaller set of implementation schemes. With tools that represent the physics at many different scales working in concert, researchers can predict the behavior of any given system. That saves money and time, and it puts more fuel-efficient ships in the water.

The 20,000 or so simulated bubbles in the Brown team's studies travel in a representation of a three-dimensional channel that is about five times longer than it is tall. Previously, the team covered this space in a 128³ grid of points, which allowed them to track the flow at a Reynolds number of 9,500. The Reynolds number is a key component in fluid dynamics simulations, describing the fluid's density and the flow's velocity in relation to the fluid's viscosity. The higher the Reynolds number, the more turbulent the flow.

Each of these runs required about 100 hours on 32 Titan processors. [About how many have you done to date?]

Runs in August and September on NCSA's Titan Linux cluster, which is powered by Intel Itanium chips, will bring them closer to this goal. Those calculations will allow the team to increase the number of grid points to 512³ and view the bubbles at Reynolds numbers approaching XXXX [How high will the Reynolds number be in these runs? Are they complete will they be complete soon? We can always change this from future tense to past tense if they happen before our deadline.]. These runs will also require about 100 hours a piece, but they will run on 256 processors.

Results of this run will be showcased in the Alliance booth at the annual Supercomputing conference, SC2002, to be held in Baltimore, MD, in November.

To produce these models, the Brown team relies on a computational fluid dynamics code called NekTar, created over the years by Karniadakis using NCSA and other PACI machines. The presence of the bubbles and their influence on the flow is represented by what is known as a force-coupling method, first proposed and developed by Maxey.

The force-coupling method tracks the flow and influence of the bubbles without getting into the bubbles' surface physics. Bubbles are represented by "force envelopes", instead of solid spheres.

"We have fluid everywhere in the domain, and we impose these forces so that the fluid inside the sphere mimics and moves in the same sort of general way that the sphere would move. So away from the bubble surface, half a radius or more, you can't tell the difference," says Maxey. By imitating the sphere instead of fully representing it, the team does not have to calculate things like the slip conditions and vorticity around its edges.

This method simplifies the calculation and makes it tractable on today's supercomputers, and the level of resolution is more than sufficient for the drag reduction simulations. Other simplifications also help make the calculations possible. For example, the bubbles are currently seeded uniformly throughout the domain. The bubbles are also perfect spheres, instead of the malformed ellipses that take shape as the bubbles are influenced by the flow.

The team hopes to address these issues in future runs and thus more closely model the real-world physics. They are also developing a version of NekTar for Linux clusters that makes a hybrid of two popular parallelization schemes, MPI and OpenMP. This code allows users to efficiently harness the power of computing systems, like the newer clusters, in which data has to be passed among discrete compute nodes more often because nodes consist of fewer processors. "On older SMP (Symmetric Multi-Processor) machines, if you stayed within a node, you had very little latency," explains Karniadakis. With fewer processors in the cluster nodes, however, latency creeps in. The new version of NekTar, basically, "creates a virtual SMP," and speeds calculations.

Even the current simulations thrill DARPA, though. "The performance has been amazing," says Porter. "DARPA sets the bar very high, and I can't believe how far we have already come."

This research is supported by the Defense Advanced Research Projects Agency.

• Suchuan Dong
• George Karniadakis
• Martin Maxey
• Jin Xu