Understanding Turbulence In The Fast Lane at Mach 10 And Beyond

Although NASA’s X-43A and other hypersonic airplanes use air-breathing engines and fly much like 747s, there’s a big difference between ripping air at Mach 10 (around 7,000 mph) and cruising through it at 350 mph.

These differences are even more pronounced when hypersonic aircraft sip rarified air at 100,000 feet, while commercial airliners gulp the much thicker stuff at 30,000. Aero-thermodynamic heating is a very big deal at Mach 10. The critical point comes where air changes from flowing smoothly across a surface < laminar flow < to when it becomes chaotic < turbulent flow. Aero-thermodynamic heating largely determines the engine size, weight, choice of materials and overall size in hypersonic airplanes. So engineers would like to have a much better understanding of what triggers turbulence and how they can control it at hypersonic speeds. Air goes from laminar to turbulent at what engineers call the “boundary layer.” They understand how this happens at slower speeds, but they’re still grappling with which factors influence it at hypersonic speeds. University of Arizona Associate Professor Anatoli Tumin, of Aerospace and Mechanical Engineering (AME), is among those studying the problem and has developed a model that predicts the surface roughness effects on the transition from laminar to turbulent flow at hypersonic speeds. His theory has a lot to do with partial differential equations, Navier-Stokes equations and other brain-taxing mathematics that Tumin and Applied Math Ph.D. student Eric Forgoston have grappled with during the past couple of years. “In principle, the theory tells us what the optimal perturbations are that will lead to turbulent flow,” Tumin said. “Now we can explore different geometries for roughness elements to see which are best. We can explore how to space them and where we should position them.” The researchers will soon run a supercomputer simulation to compare their theory with what actually happens when air flows across a roughened surface at hypersonic speeds. Currently, these simulations guzzle tens of hours of supercomputing time. But if Tumin’s theory is correct, engineers will soon get the same results from their office laptops. Tumin is working with Research Assistant Professor Simone Zuccher, of UA AME, to develop a software package that will allow designers to do this laptop-style analysis. The software will help them predict when and where the transitions from laminar to turbulent flow occur in engines and on surfaces operating at hypersonic speeds. “We developed our theory and arrived at what is called the ’transient growth mechanism,’” Tumin said. “The airflow is stable, but there are some tiny disturbances within it that can grow downstream. We can generate these downstream, streamwise vortices (spiraling flows) by using the correct amount of roughness in the right places. We can do this at an engine inlet, for instance, in order to trip the boundary layer and to have stable engine performance.” “If we can understand the laminar-turbulent transition mechanism, we can predict the transition point accurately,” Tumin said. “This is important for heat protection, where you want laminar flow. Otherwise, you need to add a lot of weight for thermal insulation because you have to assume turbulent flow at the surface when you do your design calculations. Similarly, engine designers would like to have a quick transition to turbulence to have a turbulent flow at an engine inlet.” Ultimately, better understanding the transition to turbulence at hypersonic speeds will allow designers to build lighter, faster, more efficient airplanes capable of traveling at even higher speeds of Mach 15 or more. Contact Information: Anatoli Tumin
Associate Professor
Aerospace and Mechanical Engineering
tumin@email.arizona.edu