High-lift trapezoidal test wing configuration Multiple solutions at same flight condition due to changes in predicted location of smooth-body separation.

High-lift trapezoidal test wing configuration: Multiple solutions at same flight condition due to changes in predicted location of smooth-body separation.

Jaguar maneuvers the problematic multiple solutions phenomena

To better understand complex aerodynamics systems, designers rely on computationally intensive simulations to provide one single, desired answer that comports with or predicts reality. But engineers beware: What happens when these numerical simulations provide more than one answer?

Such was the challenge facing the world’s leading airline manufacturer during its runs on the Cray XK6 Jaguar supercomputer at the Oak Ridge Leadership Computing Facility (OLCF).

Through the US Department of Energy’s (DOE’s) ASCR Leadership Computing Challenge, via the OLCF’s HPC Industrial Partnerships Program, Boeing used the Jaguar supercomputer, aiming to establish more reliable computational methods for estimating high-lift (takeoff/landing) characteristics for its commercial transport aircraft.

Designing high-lift configurations is a big focus in the aeronautics industry, but designs involve compromises. The faster a plane goes, the easier it can take off. But going faster on the runway means expending more fuel—and finding that delicate balance comes down to details so small and precise that simulations are highly desirable to augment physical tests. It’s important because even the smallest adjustments can mean big efficiency gains for companies as large and expansive as Boeing.

“By all accounts things were off to a great start,” said Boeing engineer Dmitry Kamenetskiy. “That was, until we found something rather surprising.”

While performing one of their high-lift trapezoidal test wing configuration simulations, the Boeing researchers unexpectedly came across not one, not two, but three distinct solutions, all for the exact same flight condition. If the model is telling you all three solutions are correct, the obvious question arises: Which one is the right one?

Understanding Airflow

In general, analyzing airflow can be done in two ways: physically, for example, by means of wind tunnel experiments, or numerically via computational fluid dynamics (CFD) simulations on large computers.

The ability to analyze airflow around aircraft components allows designers to pinpoint troublesome areas where drag is affecting lift and controllability. Even the slightest change in any one design parameter such as component placement (including size and shape), Mach number, the level of turbulence, angle of attack (the angle of the wing in relation to airflow), and side-slip (flying horizontally in relation to the flight path), can have a drastic effect on drag. Not only do the configurations of these factors have significant effects on fuel efficiency, but also, and more importantly, they affect flight stability and maneuverability.

Specifically, Boeing wanted to study areas where smooth-body separation occurs, or the point at which viscous airflow becomes detached from the aircraft’s surfaces, causing vortices, or eddies, another major factor creating drag.

Although physical testing in wind tunnels has traditionally been used to study airflow, it’s a costly and time-consuming process and often cannot provide the detail needed to fully understand its effects. In contrast, modeling and simulating with high-performance computing (HPC) allows design engineers to explore and analyze airflow in unprecedented detail.

However, explained Boeing’s principal investigator John Bussoletti, “The computational requirements needed to optimize today’s wing designs are incredibly demanding, both in terms of memory and compute cycles. We need large numbers of solutions over a broad flight envelope in a short period of time to allow assessment of configuration characteristics to guide our design decisions.”

It was those computational demands that prompted Boeing to seek out the HPC resources at the OLCF in the first place—and fortunately for the researchers, they were already running on Jaguar, then the most powerful system in the world, when the real problems began.

Navigating the Unknown

In aerodynamic analysis, engineers commonly use an approach called the continuation method. In this approach, the airflow around the wing goes through a series of perturbations, typically starting from a low angle of attack—with a steady-state solution where airflow is stabilized around the wing—and increasing the angle with each iteration up to the point of stall, or vice versa, going from post-stall to low angles. This allows designers to observe how airflow changes around the wing during changes in the aircraft’s elevation and how long it takes for the flow to stabilize to a steady-state solution after each change.

But when the order is reversed, something interesting happens—hysteresis.

Hysteresis occurs when multiple flow patterns are generated for the same angle of attack under the same flow conditions. Simply put, that’s because air travels around an aircraft’s wings differently on the way up than it does on the way down—hence, multiple solutions for a given set of design parameters.

At the time of Boeing’s first encounter with numerical hysteresis and the multiple solutions dilemma at the OLCF, very little in terms of scientific literature existed on the subject. This meant that finding an explanation for the problem required the team to venture into some largely uncharted territory. But not one to back down from a challenge, the Boeing team began looking for new methods for understanding the phenomena.

The Reynolds-Averaged Navier-Stokes (RANS) equations are the most widely used approach for modeling turbulent flows. But because turbulence is still an unsolved problem in classical physics, the RANS equations cannot provide exact solutions to turbulent flows. However, there are basic principles derived from simplified flows that can be calculated to within an acceptable threshold of accuracy that very closely reflect reality. In turn, those idealized flow situations can be adapted to design more developed models that can accurately describe realistic turbulent flows of greater complexity. The closer the solutions converge into the threshold, the more confident engineers are about the reliability of the solution.

“In the numerical modeling, we are using a much wider variety of the continuation processes, mostly to facilitate the reliable solution of the steady-state equations,” Kamenetskiy said. “What we found, and quite unexpectedly, is that numerical modeling at the scale possible on Jaguar can result in many more—and, formally, totally valid—flows which have never been observed in practice. Furthermore, we have discovered them at flow conditions where multiple solutions have never been detected in the wind tunnel tests.

“It’s important to note, however, that these are just the solutions we were able to find. There is of course a possibility that there are other solutions that were not found.

“A pessimistic view is that multiple solutions may be endemic to all flows involving smooth-body separation, and that CFD would be an unreliable tool for such flows as, basically, a new type of the modeling-related uncertainty is introduced: discrete and spurious in its nature,” he said. “On the other hand, a more optimistic view is that it is possible that some of the solutions could be dismissed if they change drastically with certain grid refinements or small perturbations.”

Bussoletti concluded, “We discovered that, at least under some conditions, multiple solutions will persist with different kinds of grids, different solvers, and different turbulence models. So they aren’t solely due to a particular discretization approach, a particular solution methodology, or a particular turbulence model. But they do help to explain why attempts to use RANS modeling to capture maximum lift in a CFD model may succeed in some cases and fail in others.”

Onward and Upward

For Boeing, the accomplishments made at the OLCF—a DOE Office of Science User Facility located at DOE’s Oak Ridge National Laboratory—reinforced that numerical modeling and simulation at large scales can offer a significant return on investment. The new insights Boeing gained from using Jaguar presented a strong case for the firm to increase its own in-house capabilities.

“Using Jaguar, we demonstrated the ability to run our code analyzing a takeoff configuration in as little as 2 hours,” Bussoletti said. “When fully validated, such a capability could allow us to make radical changes to our [low-speed] wing design process.”

And, Kamenetskiy added, “Using the OLCF resources, we were able to decrease our turnaround time by a factor of 20 or more. Jobs that took almost 40 hours on our in-house systems took only 1 to 2 hours on Jaguar.

“Access to Jaguar was an eye opener for our management as to what is possible. We were able to make a much stronger case for bringing new hardware into the company once we could demonstrate that these tools can reduce the cycle time from more than a day to a few hours. As a result, Boeing has systematically upgraded its internal HPC capabilities twentyfold in terms of the number of cores and the acceleration of processor clock speed.

“That has had a powerful effect on our productivity,” he said. “With those improved capabilities we’ll be able to design new vehicles so much faster. The design cycle time will come down by orders of magnitude.”

Despite the team being unable to exactly carry out its intended research for the high-lift configuration, investigations into the multiple solutions phenomenon did yield tremendous insights on multiple fronts—and not just for Boeing.

The team’s findings were presented to the entire flight community at the prestigious 51st American Institute for Aeronautics and Astronautics (AIAA) Aerospace Sciences Meeting and were recently published in the AIAA journal.

“Just being able to identify the issue is a major form of success,” Bussoletti said. “Now that we know how to identify them, the next step is understanding how to control the solution process to select the ‘correct’ solution.

“The CFD community should be aware of the phenomenon because it is bound to arise in many flows of practical interest,” he added. “With the compute power available today, greater emphasis should be placed on obtaining reliable, converged solutions. But as far as completely solving the multiple solutions problem, we still have many questions left unanswered.”

Related publication:

Dmitry Kamenetskiy, et al., “Numerical Evidence of Multiple Solutions for the Reynolds-Averaged Navier-Stokes Equations.” American Institute for Aeronautics and Astronautics 52, no. 8. (2014), doi:10.2514/1.J052676.

Oak Ridge National Laboratory is supported by the US Department of Energy’s Office of Science. The single largest supporter of basic research in the physical sciences in the United States, the Office of Science is working to address some of the most pressing challenges of our time. For more information, please visit science.energy.gov.