"Evil and baffling things happened in the transonic zone which began at about .7 Mach. Wind tunnels choked out at such velocities. Pilots who approached the speed of sound in dives reported that the controls would lock or 'freeze' or even alter their normal function.”

"The Right Stuff,” by Tom Wolfe, describing Chuck Yeager’s first supersonic flight in 1947

The aerodynamic disturbances in pressure and airflow caused by shock waves play a dangerous role in ultra-high-speed flight. “If your shock induces a very serious separation, then the engine can stop working,” said Chaoqun Liu, mathematics professor and director of the Center for Numerical Simulation and Modeling at The University of Texas at Arlington. “If there’s no air inside the engine, you lose power and you’re going to crash.”

It’s a problem that Liu is familiar with. Having worked for more than two decades for NASA and the Air Force on issues related to turbulence and aircraft design, he has had ample opportunity to consider the problem of how to stabilize jets at supersonic speeds.

As the Air Force begins to design aircraft destined to travel at hypersonic speeds (from Mach 2 to approximately Mach 8, or up to 5,280 miles per hour) they have recruited Liu and others to perform fundamental research aimed at understanding and controlling the nature of shock waves. Through a grant from the Air Force Office of Scientific Research (AFOSR), Liu is using the Ranger supercomputer at the Texas Advanced Computing Center, as well as high-performance computers at the Army High Performance Computing Center, to explore and manage these interactions for next-generation aircraft.

All solid objects traveling through a fluid (in this case, air) acquire a boundary layer around them where resistance occurs, leading to turbulence and swirling eddies. A shockwave interacting with the boundary layer can cause an adverse reaction known as separation, which affects the performance of key aircraft and engine components.

“We try to understand the mechanisms involved in the shock and boundary-layer interaction, and also figure out how they can be controlled,” Liu explained. “This interaction is very important for high speed vehicles and engines because whenever the boundary layer encounters shock, it will generate noise, drag, intense localized heating, especially at high supersonic and hypersonic Mach numbers, and create the danger of a high speed crash.”

Modeling Shock

There is little room for inefficiencies in frame design on supersonic aircraft, so accurate and reliable prediction tools are necessary for forecasting shock/boundary-layer interactions. These predictions are only possible through direct numerical simulation and large eddy simulation on the emerging class of petascale supercomputers — systems capable of reaching performance in excess of one quadrillion floating point operations per second.

“There are common features between low- and high-speed flight, but there are also big differences,” Liu said. “High speed simulations include shock waves, which are discontinuities that have challenged mathematical theory.” Until recently, many researchers thought it was impossible to simultaneously simulate shock and turbulence with high fidelity, because of shock’s discontinuous nature.

Liu set out to prove them wrong.

He developed a new mathematical framework capable of representing shock/boundary-layer interactions at super- and hypersonic speeds. Using approximately 370,000 computing hours on Ranger since April 2008 (from the 5 percent allocation awarded to researchers at Texas Higher Education institutions), Liu has shown that his framework is able to capture the discontinuity faced by high-speed turbulence while maintaining extreme accuracy.

[A paper describing this framework will be published in the International Journal of Computer Mathematics in 2009 (citation 4 below).]

The mathematics he described goes beyond aerospace engineering. “This scheme is very important, not just for the Air Force, but also for nuclear weapons, because they involve shock and sound waves, for finding cancer, and modeling porous media flow, where you have fluids, sands, and stone,” Liu explained. “All of these functions are discontinuous and this numerical scheme will be good for any such phenomenon. I think it’s a breakthrough.”

Though not yet accepted by the mathematics community, his algorithm for discontinuous flows has been generating excitement among his community of users, including NASA and the Air Force, who were eager to test it themselves and apply its insights to their problems.

Fins for Faster Flight

With a method of modeling high-speed fluid flows at his disposal, Liu turned his attention to the still-theoretical, but more concrete task of testing design solutions that can reduce the drag, noise and danger associated with shock/boundary-layer interactions. Fundamental scientific research, like Liu's, is crucial to the Air Force’s goals because a design can only be intelligently improved once the physical mechanics are understood.

“From our side, we don’t design these aircraft, we try to understand the physical processes,” Liu said. “The Air Force may find that something is useful, but we need to understand why and how. They can do tests, but they just tell you it could be the case. But with numerical simulation, we get very detailed data and graphics and movies that tell you the ‘why’ and ‘how ‘of the mechanics.”

Liu’s specific avenue of research for AFOSR explores the effect of micro-vortex generators (MVGs) on flight — small fins that sit on aircraft wings and inlets, which the Air Force believes might hold the secret to stabilizing flows past high-speed aircraft. But why these fins work, and how they can be optimized to impart the greatest advantage, remains a mystery.

“The shape of the vortex generator is used to control the shock and the boundary layer,” Liu said. “We use these MVGs to reduce the extent of flow separation, and if we reduce the separation, we can potentially reduce drag and noise.”

In the second year of a three-year project for AFOSR, Liu — working with experimentalist Frank Lu, director of the Aerodynamics Research Center at UT-Arlington — is testing various shapes and types of MVGs, both virtually on Ranger, and in a supersonic wind tunnel in Arlington. Their research will explore the fundamental physics of supersonic turbulence, and determine how shocks can be effectively managed by MVGs.

“Such a synergistic approach enables the computational code to be validated and then used to provide comprehensive data to understand the complex interaction,” Lu said. “Liu's work is novel in providing a very high level of accuracy and in further developing large eddy simulations. His work adds to the tools needed for understanding complex flowfields.”

Both physical and simulated experiments are necessary to fully understand the dynamics of shock/boundary-layer interactions, but increasingly, it is the virtual trials, on supercomputers like Ranger, that have the greatest benefit for aircraft design and testing.

“Wind tunnel simulations can only provide limited capabilities in revealing the time-dependent process, whereas computational simulations with millions of grid points over hundreds of thousands of time-steps can provide high spatial and temporal resolution. That is to say, they can provide a lot more information than experiments,” Liu said. “But the experimental work is necessary to check if our simulations are correct. They complement each other.”

Having developed a new class of algorithms for discontinuous functions and tested various MVG designs at lower-speeds, Liu is moving into the final phase of his research, where high-speed, high-fidelity shock/boundary-layer scenarios will be simulated, producing a novel understanding of hypersonic turbulence.

“That’s why the Air Force supports us,” Liu said. “Because we’re developing something completely new.”

The results of Liu’s fundamental research may still be decades away, but when you hear about (or step into) a future aircraft, flying at speeds of Mach 8 and above, and see the small fins on its wings, remember that those fins were put there by computational scientists like Liu and systems like Ranger.

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Publications:

1. Ping Lu and Maria Oliveira, and Chaoqun Liu, High Order Compact Scheme for Boundary Points, Journal of Computer Mathematics, to appear

2. Maria Oliveira, Jianzhong Su, Peng Xie, and Chaoqun Liu, Truncation Error, Dissipation and Dispersion Terms of 5th Order WENO and of WCS for 1D Conservation Law, Journal of Computer Mathematics, to appear

3. Ping Lu, Maria Oliveira, and Chaoqun Liu, High Order Compact Schemes for Dirichlet Boundary Points, J. of Neural, Parallel & Scientific Computation, Vol 16, Number 2, ISSN 1061 5369, P273-282, June 2008

4. Maria Oliveira, Ping Lu, Xiaobing Liu and Chaoqun Liu, A New Shock/Discontinuity Detector, Journal of Computer Mathematics, to appear.

Aaron Dubrow
Texas Advanced Computing Center
Science and Technology Writer
March 25, 2009

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The Ranger supercomputer is funded through the National Science Foundation (NSF) Office of Cyberinfrastructure “Path to Petascale” program. The system is a collaboration among the Texas Advanced Computing Center (TACC), The University of Texas at Austin’s Institute for Computational Engineering and Science (ICES), Sun Microsystems, Advanced Micro Devices, Arizona State University, and Cornell University. The Ranger and Lonestar supercomputers, and the Spur HPC visualization resource, are key systems of the NSF TeraGrid (www teragrid.org), a nationwide network of academic HPC centers, sponsored by the NSF Office of Cyberinfrastructure, which provides scientists and researchers access to large-scale computing, networking, data-analysis and visualization resources and expertise.