A Ffowcs Williams - Hawkings Solver for Lattice-Boltzmann Based Computational Aeroacoustics
16th AIAA/CEAS Aeroacoustics Conference
This paper presents the development of an efficient far-field noise prediction code using the near-field results from a Lattice-Boltzmann flow solver as input to an acoustic analogy solver. Two formulations, based on the Ffowcs Williams-Hawkings equation, are implemented to efficiently perform far-field prediction from large input data sets. For configuration where the noise source is moving through a fluid at rest (such as aircraft certification), the efficient and well-validated formulation
... dated formulation 1A is implemented. For windtunnel configurations where both the source and observer are stationary in a uniform flow, a formulation based on the Garrick Triangle, and referred to as GT, is used to increase the computational efficiency. Numerical simulations and far-field prediction are performed for three representative validation cases: a three-dimensional monopole source, a tandem cylinder flow, and a fan noise case. Comparisons of the results from the far-field solver show excellent agreement with the theoretical predictions and the available experimental data. of the small amplitude acoustic fluctuations from the near-field source region to the far-field microphones within the computational domain. A classical approach to overcome this difficulty is through the use of integral methods: first, computational fluid dynamic (CFD) simulations are performed to capture all the potential noise sources in the near-field (i.e., sound generation mechanism); then an acoustic analogy method is used to propagate this near-field information to the far-field (i.e., sound propagation mechanism). This paper presents the development and implementation of an efficient far-field noise prediction code relying on Lattice Boltzmann method (LBM) for the CFD simulation, and on the Ffowcs Williams-Hawkings (FW-H) equation 1 for the acoustic analogy method. The CFD/CAA code PowerFLOW 4.2 based on the Lattice Boltzmann method is used in this study. LBM simulations have been used extensively for aerodynamics and flow prediction over a wide range of problems, from simplified geometries 2, 3 to fully detailed ground vehicles 4, 5 and aerospace applications. 6, 7 Coupled with turbulence modeling, the LBM scheme has been shown to accurately resolve the large-scale unsteady flow structures and the turbulent wall pressure fluctuations due to separated and reattached flows. 8, 9 These structures and pressure disturbances are key components of the near-field sound sources, which, through the acoustic analogy method, will be the main contributors to the far-field noise. Details of the LBM code, including the fundamental Lattice Boltzmann equations, numerical scheme, wall boundary conditions, and turbulence modeling, can be found in Refs. 10-13. For real-world applications such as landing gear noise and train certification, the CFD input to the acoustic analogy method is expected to be large, requiring numerically efficient methods for the far-field noise prediction capability. The implemented FW-H solver was developed to efficiently handle these large data sets for arbitrary moving noise sources, both in a fluid at rest (e.g., aircraft fly-over or train passby configuration) and in a uniform flow (e.g., wind-tunnel testing or wind-turbine noise). For the former case (referred to as moving-source), the time-domain FW-H formulation developed by Farassat known as formulation 1A 14, 15 is an efficient and concise method well-suited for numerical computation. For the most general form of the latter case, an extension of Formulation 1A based on the convective form of FW-H equation was developed to predict far-field sound radiation of an arbitrary moving source in uniformly moving media. 16 In the present work, only the typical wind-tunnel testing is considered, where both the source and observer are stationary in a uniform flow. For this particular case (referred to as wind-tunnel), a formulation based on the Garrick Triangle 17, 18 is used to increase the computational efficiency. Details on the different formulations and the numerical implementation are presented in section II. Validation of the coupling between the CFD and the acoustic analogy method is shown for a three-dimensional monopole source in section III. Results for tandem cylinder noise (representative of the wind-tunnel capability) are then presented in section IV, including comparison with the measured radiated noise from experiments. Finally, preliminary results for fan noise (representative of the moving-source capability) are discussed in section V.