Direct numerical simulation of noise production and propagation remains prohibitively expensive for engineering problems due to resolution requirements. Consequently, hybrid approaches are adopted, which consist of predicting near-field flow quantities via a suitable computational fluid dynamics simulation, and far-field sound radiation by aero-acoustic integral methods, or acoustic analogy formulations. It is critical that the complex flow physics associated with sound generation in the near field is accurately captured by the computational fluid dynamics simulation. Therefore, it is necessary to use a high-order numerical scheme with very low dispersion/dissipation errors. Also, the most significant airframe noise sources are landing gear and high-lift components, such as slats and flaps. The geometric complexity of these components calls for use of numerical methods that can perform well on unstructured grids. The high-order Vincent-Castonguay-Jameson-Huynh (VCJH) schemes recently developed by the principal investigator and colleagues at Stanford University with National Science Foundation funding satisfy both of the aforementioned requirements. In the present work, a state-of-the-art computational framework will be developed for performing aero-acoustics simulations by integrating advanced sub-grid scale (SGS) models for large-eddy simulations (LES) of turbulent flow, and a new Ffowcs Williams-Hawkings (FWH) acoustic analogy formulation for sound propagation, with a graphical processing unit (GPU) enabled high-order VCJH flow solver for unstructured grids. The resulting software will enable the principal investigator and colleagues to undertake high-fidelity large scale aero-acoustics simulations over complex configurations at an affordable cost. The ability to perform such simulations will greatly facilitate design of new aircraft with reduced noise signatures.

The future growth of commercial air transportation (currently predicted to triple by the year 2030) may be severely limited by its adverse environmental impacts (both emissions and noise). Noise regulations have become, and will continue to become, increasingly stringent, and noise reduction is now a major consideration in the design of transport aircraft. Although computer simulations currently play a major role in airplane design, their ability to predict noise, and in particular airframe noise (which is the largest component of noise during landing) remains very limited. The principal investigator and his colleagues aim to combine new mathematical and computational techniques to advance the state-of-the-art in noise prediction, and thereby enable design of new, quieter aircraft, with the ultimate target of restricting their noise footprint to within airport perimeters. A successful outcome is significant to the United States economy because commercial aircraft continue to be the largest single export sector.

Project Report

Intellectual Merit and Broader Impact This project has succeeded in developing the ability to simulate turbulent flows over complex geometry using high-order accurate schemes on unstructured meshes. Such an ability is of paramount importance to the future of aerospace design, as it is widely recognized that high-order numerical methods are key to achieving greater accuracy in very large-scale CFD simulations. In particular, the high-order Flux Reconstruction (FR) methods pioneered in the Aerospace Computing Lab and advanced thanks to this grant, are provably and demonstrably an ideal basis for turbulent flow simulation, having excellent wave propagation and stability properties as well as low computational cost relative to conventional methods. Although time did not permit the development of an aeroacoustics solver as intended, we are confident that the technology developed can be easily extended to aeroacoustics in the near future. Other notable achievements include the development of turbulence models based on a new set of innovative filters designed for high-order discontinuous discretizations. Use of the models with a high-order scheme improved accuracy in coarsely resolved turbulent flow simulations compared to using the scheme alone. Extension of the turbulence models to unstructured grids began during this project and is the subject of ongoing research. When completed, this work will enable significantly improved predictions of turbulent flows over complex geometry. The release of the open-source code HiFiLES is a major milestone, giving researchers across the world and in many different disciplines access to cutting-edge numerical technology. We believe that it will stimulate wider interest in high-order numerical methods and open the door to future collaborations. It is at an early developmental stage and is intended for research purposes, but in future it may be a template for the next generation of commercial software packages. The move to high-order accurate methods would advance the state of the art in industrial CFD and benefit many areas of engineering, from designing the next generation of quieter, more fuel-efficient commercial aircraft and jet engines to more energy-efficient automobiles and trucks. These in turn would be an important step towards reducing environmental impacts of the transportation sector. The improved methods can also contribute significantly in other scientific disciplines such as astrophysics or weather prediction. Our program is also supporting the development of STEM skills in minority groups. David Williams is African American, Manuel Lopez is Hispanic and three new Hispanic students have joined the Aerospace Computing Lab during the last two years. David has succeeded in defending his PhD thesis and now works in research and development at Boeing Commercial Airplanes.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Leland M. Jameson
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Stanford University
Palo Alto
United States
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