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In 1975, it was estimated that 7.5 million Americans lived in areas where aircraft noise exceeded 65 decibels – equal to having a TV set playing loudly in the background 24-hours a day. The Airport Noise and Capacity Act of 1990 set down what became known as “Stage 3” regulations that required more than 7,500 jet airliners to be modified with quieter engines or to be retired from the fleet by December 31, 1999. The direct result of Stage 3 regulations saw the number of people affected by jet noise reduced to about 600,000 according to the Federal Aviation Administration. Currently, the International Civil Aviation Organization, in conjunction with aviation regulatory agencies in the United States and the European Union, are working to address noise and environmental issues from jet aircraft. The results of these meetings will establish noise reduction and emission guidelines for future Stage 4 regulations. Two sources of noise from jet engines can be identified – one mechanical due to rotating components moving at high speeds, the other due to aerodynamical effects. The latter is also called aeroacoustic noise, which is the whistle that one hears when a high-pressure valve is opened, or the noise that the air makes when a car window is opened while moving at high speed on the highway. While the aviation community successfully reduced noise emissions emanating from a jet engine’s fan and turbine section, reduction of noise caused by the mechanical components has nearly reached its limit. New methods to quiet an engine are being pursued actively by the jet engine manufacturers, NASA, and the academic community. Scientists George S. Constantinescu and Sanjiva K. Lele of the Center for Turbulence Research (CTR) are continuing work on a computational model for predicting jet exhaust behavior using the NAS Facility’s high-end computing resources. Their goal is to reduce the intensity of acoustic noise sources in a jet’s exhaust that in turn will reduce engine noise. Investigating Sound Attenuation Through Numerical Computations Before researchers can offer solutions for reducing the sound emanating from a jet’s exhaust, they must first understand the mechanisms that are responsible for noise generation. To accomplish this, researchers calculated the spatial and temporal distribution of the acoustic sources, a task that is “practically impossible to perform using experimental measurements,” says Lele. These acoustic sources emanate from the interactions of the turbulent eddies in the flow of the jet. The flow of fluids is characterized by a non-dimensional number, called the Reynolds number, which is the ratio of the inertia forces over the viscous forces. When the velocity of a fluid flow is small, the viscous forces are large compared to the inertia forces, thus the Reynolds number is small. A fluid flow in this regime can be observed to be regular and is characterized as laminar (or smooth). At high speeds, the Reynolds number is large and the observed fluid flow consists of eddying motions that are chaotic. The fluid flow in this regime is called turbulent. As the Reynolds number increases, the range of the size of the eddies also increases. Two simulation methods that are actively being pursued by NAS and CTR scientists are the Direct Numerical Simulation (DNS) technique and the Large Eddy Simulation (LES) technique. In DNS all the scales of motion are resolved, which limits the simulations to moderate/low Reynolds numbers. Using LES, the energy containing large eddies are resolved and the effects of small eddies on the large eddies are modeled, which enable high Reynolds number simulations. To determine where and how exhaust noise is generated, the acoustic group at CTR, led by professors Lele and Parviz Moin of Stanford University, have used both LES and DNS techniques to simulate noise generation from turbulent flows. Constantinescu and Lele have been employing the LEStechnique to accurately simulate turbulent eddies in jet exhaust. Future use of DNS for high-speed jets will be ideal, but, in the foreseeable future, will be limited to moderate Reynolds numbers. Working with Moin and Lele in 1999, Jonathan B. Freund, currently a professor at the University of Illinois Urbana-Champaign, used DNS calculations to develop an understanding of the sound generation in exhaust jets. In his simulations, Freund was only able to simulate jet exhaust turbulence at a Reynolds number of 3,600 by using 25 million gridpoints – a very expensive simulation. DNS simulations at Reynolds numbers close to one million, which correspond to the actual operating conditions of jet engines, will be out of reach for supercomputers in the foreseeable future. Constantinescu and Lele’s computational modeling may be seen as an extension of Freund’s work for high-speed (high Reynolds numbers) jets. In Constantinescu and Lele’s computational model, they omitted the jet engine’s exhaust nozzle. This was done primarily because modeling the nozzle would be too expensive. To compensate, the researchers imposed a velocity profile into the calculations similar to that measured at the jet’s nozzle. In addition, most of the noise is produced at the end of the exhaust flow – away from the nozzle, where the exhaust transitions from laminar, or smooth flow, into a turbulent flow. “Because we are using a subgrid scale model we want to show that the model’s contribution to the noise generation is very small and doesn’t contaminate the sound field,” Constantinescu says. “The purpose of doing these calculations is not to calculate the aerodynamic field. What we really want to do is capture the sound that is emitted by a propulsive jet. In order to do that, we must employ a very accurate numerical method. “Sound is emitted through very small pressure fluctuations, which are two orders of magnitude less than the pressure fluctuations associated with the jet turbulence. If the goal is only to compute the average velocity field and the mean quantities that characterize turbulence in the jet, it can be accomplished using a second-order method. But for aero-acoustic applications, we really need a very accurate method. In our case, we chose to employ a six-order accurate method based on Padé schemes in the streamwise and radial directions, and Fast Fourier Transform methods in the azimuthal direction,” Constantinescu explains. The higher fidelity of the six-order accurate method more efficiently represents the jet’s turbulent eddies with a minimum of artificial or numerical viscosity. Solving The Singularity Problem The LES method allows Constantinescu and Lele to accurately capture the distribution of acoustic sources and radiated sound waves in the jet near field. These waves are a direct result of the sound emitted by the acoustic sources in the jet. However, before successfully performing these simulations, an accurate treatment of the jet centerline had to be developed. When the researchers attempted to perform LES at high Reynolds numbers on relatively coarse meshes compared to DNS, they ran into convergence problems, which caused the code to diverge. The origin of the problem is a difficulty encountered by almost all numerical methods used to solve the governing equations in cylindrical coordinates – the flow equations are discretized in cylindrical coordinates, which is the natural coordinate system chosen to simulate flows that are nearly axisymmetric (the jet axis, or the centerline, plays this role in the jet simulations). However, in the cylindrical coordinate system, the governing flow equations are multi-valued at the centerline (known as the singularity problem). A special mathematical treatment had to be used on the centerline and in its vicinity. Although Constantinescu and Lele tried to employ several methods previously proposed by other researchers to solve the singularity problem, they were not entirely satisfied with the results. “Many people have tried different approaches to deal with coordinate singularity, and what George and I have done is develop a rather nice way of dealing with the coordinate singularity in the context of high-order numerical methods,” Lele says. “We are dealing with a flow that has a nearly circular symmetry, at least in an average sense. When a jet comes out of a circular nozzle, it has that statistical symmetry, but the eddies in the instantaneous flow are three-dimensional.” To resolve the singularity problem, the researchers developed a more accurate algorithm to solve the governing flow equations at the centerline. In this method, a new set of equations, valid at the centerline, was derived using the most general series expansions of the flow variables near the centerline. This maintains the same order of accuracy of the solution at the centerline as in the rest of the computational domain. Running a parallel code on the NAS Facility’s Origin 2800 computers, employing 32 processors, Constantinescu and Lele can now run LES simulations at much higher Reynolds numbers (100,000) on coarser grids using only four million gridpoints. This has enabled the scientists to more accurately estimate the amount of sound generated by high-speed engine exhaust jets. Continuing Research Using the data provided by Constantinescu and Lele’s simulations, engineers will be able to introduce disturbances with a specific frequency spectrum into the exhaust, thereby attenuating the intensity of the noise. This will result in a significant reduction of the sound radiated by the jets. Finding ways to force the jet to attenuate noise will be a challenging task. Constantinescu predicts it will take at least two more years of research to arrive at a point where scientists can physically control noise at Reynolds numbers corresponding to actual operating conditions. A parallel effort will be directed toward developing LES subgrid models that are suitable for noise calculations in high speed flows. These models should not introduce spurious noise that can destroy the directly simulated noise field from LES. As computer modeling capabilities expand during the next few years, an additional goal of the researchers will be to simulate the presence of the jet nozzle . This will allow a more complete understanding of the flow physics and enable researchers to propose more efficient ways of controlling the noise. More Information About LES Research papers describing the Large Eddy Simulation techniques employed by Constantinescu and Lele can be viewed at the Center for Turbulence Research website: http://ctr.stanford.edu/publications.html Information about the research within the NASA Advanced Supercomputing Division can be found at: www.nas.nasa.gov About the Researchers: George S. Constantinescu received his master of science degree in environmental engineering at the Civil Engineering Institute, Bucharest, Romania, and his doctorate from the Iowa Institute of Hydraulic Research (University of Iowa). He served as a postdoctoral associate in both the Department of Mechanical and Aerospace Engineering at Arizona State University and at the Center of Turbulence Research, Stanford University. Constantinescu has recently moved to Stanford’s Center for Integrated Turbulence Simulations where he works on numerical simulations of gas turbine engines. Sanjiva K. Lele is an associate professor with joint appointments in the Departments of Aeronautics and Astronautics and Mechanical Engineering at Stanford University. He received his bachelor of science degree from the Indian Institute of Technology, Kanpur, India, and his doctorate from Cornell University, both in Mechanical Engineering. Lele worked at NASA Ames from 1986 to 1990, then he joined the staff at Stanford. He has received the Francois N. Frenkiel award from the American Physical Society, Division of Fluid Dynamics, and the National Science Foundation’s Presidential Young Investigator award. Last year he received best paper awards from both the American Society of Mechanical Engineers and the American Institute of Aeronautics and Astronautics. Center For Turbulence Research The Center for Turbulence Research (CTR) is a joint NASA/Stanford University center that sponsors the work of post-doctoral fellows studying turbulence research. This includes studies of turbulence modeling, combustion modeling, turbulence control, aero-acoustics and, in general, research on flows where turbulence plays a dominant role. The center has a facility at Stanford and one at Ames Research Center (ARC). Co-located in the same building at ARC are civil service scientists from the Physics Simulation and Modeling Office of the NAS Division who collaborate with CTR post-doctoral fellows and visitors. By Nicholas A. Veronico Editor, Gridpoints Magazine NASA Advanced Supercomputing (NAS) Division NASA Ames Research Center ---------- Supercomputing Online wishes to thank both Nicholas A. Veronico and NASA’s NAS division for allowing us to bring this story to our readers. It would also like to thank NAS’s Jill Dunbar for her assistance. ----------