Aerospace Engineering and Design

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Photo: Charbel Farhat Charbel Farhat, University of Colorado, Boulder.


Access to the Terascale system leads to more accurate flutter predictions for the F-16.

"The Angel of Death is abroad in the land, only you can't always hear the flutter of its wings," said Winston Churchill in the fall of 1944. He was talking about the infamous V-2 rocket, some 500 of which rained death and terror on British civilians during the last eight months of World War II.

As the world's first supersonic weapon, the V-2 fell from the sky silently, giving virtually no warning of impending destruction. It had no wings to flutter, only tail-fin stabilizers, and although Churchill was speaking metaphorically, he referred unknowingly to a major obstacle that confronted the German technologists.

Flutter as a phenomenon of flight engineering means a vibration that can amplify into structural damage. As a matter of "what if" history, it undoubtedly saved lives and may have altered the war's outcome. Because of flutter, about 70 early V-2 flights crashed or veered off course as the rocket arrived at supersonic speed. By September 1944, when the Germans overcame the problem and began firing V-2s at London and other targets, Hitler's secret weapon was too late and too inaccurate to seriously hinder the Allied advance.

"The V-2 is where panel flutter was discovered," says Charbel Farhat, professor of aerospace engineering sciences at the University of Colorado, Boulder. "The rocket structure was a thin container, and it was flexible, at least at the scale of forces encountered in transonic flight." As the V-2 went from subsonic to supersonic speed, its metal skin shook apart.

Flutter still challenges designers of high-performance aircraft. As recently as September 1997, wing flutter — partly the result of faulty structural maintenance — caused an F-117A Nighthawk, the first operational "stealth" plane, to lose most of one wing and crash at an air show. "Flutter can be catastrophic and must be avoided at all cost," says Farhat, who directs the University of Colorado's Center for Aerospace Structures, an interdisciplinary center focusing on aircraft structural technology.

For about 10 years, Farhat has worked to develop more sophisticated computational methods for predicting the "flutter envelope" of high-performance aircraft and to encourage wider use of these methods in industry. Through a collaborative program with Edwards Air Force Base, he's been trying out his methods on the F-16 fighter.

"We do blind tests," explains Farhat. "We develop the simulation technology and try it on the aircraft. Then they fly it to get actual flight data, and we see how we're doing." In the spring of 2001, "friendly user" time on the prototype Terascale Computing System allowed him to improve the resolution of the F-16 model and achieve his best results to date.

Model Neuromuscular Junction

Mach contours and streamlines for an aeroelastic simulation at Mach 0.9.
Color indicates local variation in Mach number (increasing from blue to red) at the surface of the aircraft.

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The Flutter Envelope

Although most of us have experienced in-flight turbulence, we may not — for good reason — be looking out the window to see the wings shimmy as the plane encounters a turbulent patch. Made of flexible material, aluminum or composite, modern high-speed aircraft experience stress in the range of 40,000 pounds per square inch. When these structures vibrate, the engineering question is whether the air will absorb the vibration or amplify it into flutter. The answer depends, says Farhat, on three things — speed, altitude, and stiffness and mass of the structure.

To calibrate these interactions, the design process aims at accurately predicting the plane's flutter envelope — a curve that plots speed versus altitude. "At a given altitude," says Farhat, "it tells you the speed not to exceed, even if the engines can do it, because any perturbation is going to be amplified. You want that speed to be relatively high, so flutter won't bother you. It's often the determining factor in the design of wings and tail surfaces."

Obviously, the plane's mission is crucial in flutter analysis. "If I've built the engine to deliver Mach 2 performance," says Farhat, "and analysis tells me that at 30,000 feet the flutter speed is Mach 0.7, then I have to go back to structural design." For supersonic fighters especially, because their mission requires aggressive, high-speed maneuvers, flutter is a sensitive factor.

Even for supersonic fighters, however, relatively uncomplicated analytical techniques — that can be solved with "linear" mathematics — give reliable flutter predictions at subsonic and supersonic speeds. "These linear methods simplify many things," says Farhat. "They break down to a simple equation that can be solved on your PC in almost real time. You have a linear structure and a linear fluid, and you can predict the flutter envelope even before you fly the aircraft."

The problem comes in the transition from subsonic to supersonic flow, what's called the transonic regime — from about Mach 0.85 to almost Mach 1. By definition, transonic flow begins at the speed where a wing first hits supersonic shock. Linear methods can't reliably predict flutter in this transitional regime, and the aircraft industry for many years has relied on wind-tunnel testing.

But wind-tunnel testing for flutter is a much more complex process than for aerodynamics. What matters in aerodynamics is shape, and a scale model can be built from nearly any material. To model flutter, the model has to reproduce the stiffness properties of the full-scale plane and vibrate in scale with reality. For this kind of wind-tunnel testing, the industry has relied for years on the experienced craft of expert structural-modeling engineers.

Even so, to build one model, test it, interpret the data, and plot five points that describe the curve of the transonic flutter envelope, says Farhat, takes at minimum a year. As computational technology improves in both hardware and software, it has begun to step forward as an alternative.

Model Neuromuscular Junction

Detailed finite-element structural model of the F-16.

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Model Neuromuscular Junction

Von Mises stress on the F-16 structure (increasing from dark blue to light blue to red) during an aeroelastic simulation.
Von Mises stress represents a criterion for the stress level at which a material may be expected to fail. From this kind of simulation, it's possible to plot the likelihood of failure for any given structural material.

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A Three-Field Formulation

While linear methods don't reliably predict flutter in the transonic regime, the continuing evolution of high-performance computing makes it feasible to turn to more sophisticated techniques. As with other "aeroelastic" instabilities — such as buffeting due to velocity fluctuations in the airflow, flutter involves the interaction between flow and structure. To realistically predict how the structure moves in time requires solving equations of motion for the structure simultaneously with those for the fluid flow, and this turns the mathematics into a complex "nonlinear" problem.

Over the last decade, Farhat's research group has developed a set of simulation programs, called AERO, that implement this more sophisticated approach through an innovative "three-field formulation." Computational fluid-dynamics problems are solved by overlaying the structure with a fine-mesh grid that gives coordinates in space at which to calculate forces. The nonlinear coupled approach requires that the fluid also be represented as a computational mesh, with exchange of energy between the air and the vibrating structure calculated at the intersections between these two grids.

Difficulties arise, however, because structural vibration necessarily changes the shape of the grid, potentially introducing serious error into the calculation unless the structure grid can simultaneously be redrawn at each microsecond time-slice of the calculation, which is impracticably cumbersome. To circumvent this problem, Farhat treats the movement of the computational mesh as a third field that interacts with the structure and the fluid. "This three-field formulation," he says, "has shed new light on the mathematics of the coupled fluid-structure problem and enabled us to develop faster algorithms."

To validate his approach, Farhat has used AERO to simulate flutter on the F-16. With modeling information provided by Lockheed-Martin, Farhat's team constructed a structural mesh with 168,799 separate elements, and a corresponding fluid mesh of 400,000 grid points. Using a 32-processor SGI Origin 2000 system, AERO simulated a clean-wing F-16 configuration — without underwing attached weapons — for one aeroelastic response, one point on the flutter envelope, in about four hours of computing time, demonstrating that AERO can be a practical simulation tool. Comparison with flight-test data showed reasonably good accuracy, within about 15 percent.

A series of runs on the prototype Terascale Computing System, however, demonstrated what can be gained with faster processing. The TCS ran AERO roughly twice as fast per processor, and using all 256 processors the overall capability increased by another factor of eight. "We were running easily an order of magnitude faster on the Terascale machine," says Farhat, "so you can imagine what a boost this was to our simulation."

The improved capability made it feasible to use a fluid mesh with 1.5 million grid points. "With the bigger machine," says Farhat, "we found we could use a finer mesh, and this improved the quality of our results." The higher resolution mesh brought agreement with flight-test data to within five percent.

Farhat notes his simulations have dealt with only one F-16 configuration, and many other configurations must be correlated with flight data, but the results are encouraging. "This shows that better computational capability can substantially improve our technology. With these kind of advances, the three-field formulation is proving itself as a mature, fast and reliable approach to model some of the critical flight conditions encountered by high-performance aircraft."

Download PDF Flutter in the Sky
from Projects in Scientific Computing 2001
Researchers Charbel Farhat, University of Colorado, Boulder
Hardware TCSini
Software AERO
Related Material
on the Web
Center for Aerospace Structures, University of Colorado at Boulder
References Charbel Farhat, "CFD-Based Prediction of the Aeroelastic Behavior of High-Performance Aircraft: Toward a Change in Culture" (2001), preprint.
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