A Novel Multipolar Expansion for Acoustic Footprint Reduced Order Modeling
Giorgio PALMA, Stefano MELONI, Christophe BOGEY, Lorenzo, BURGHIGNOLI, Caterina POGGI, Jacopo SERAFINI
Abstract. High-fidelity computational aeroacoustic simulations are often too computationally expensive for rapid evaluation of aircraft noise, especially when assessing full-system acoustic footprints during operations. This work introduces a physics-informed multipolar-expansion methodology that generates equivalent acoustic sources capable of accurately reproducing complex pressure fields in both near- and far-field regions at a fraction of the computational cost. The method employs expansions from monopoles to higher-order terms for noise modeling and prediction, using spherical harmonics as a complete basis of the Helmholtz equation. Acoustic moments coefficients are identified through linear regression analysis of pressure data obtained from numerical or experimental sampling, enabling the accurate reconstruction of the acoustic field once the coefficients are determined. The methodology is assessed using two representative aeroacoustic problems: a helicopter rotor operating in Blade–Vortex Interaction conditions and a subsonic jet at Mach 0.9 with varying nozzle temperatures. The results show excellent agreement with reference data, maintaining amplitude accuracy up to the far field while drastically reducing computational time. The proposed reduced-order model demonstrates strong robustness and generalizability, offering a fast and physically grounded tool for aerodynamic optimization, real-time control, and digital-twin frameworks, enabling efficient and scalable noise prediction in complex aeroacoustic environments.
Keywords
Aeroacoustics, Reduced Order Modeling, Jet Noise, BVI, Equivalent Sources
Published online 7/20/2026, 6 pages
Copyright © 2026 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Giorgio PALMA, Stefano MELONI, Christophe BOGEY, Lorenzo, BURGHIGNOLI, Caterina POGGI, Jacopo SERAFINI, A Novel Multipolar Expansion for Acoustic Footprint Reduced Order Modeling, Materials Research Proceedings, Vol. 69, pp 287-292, 2026
DOI: https://doi.org/10.21741/9781644904251-51
The article was published as article 51 of the book CEAS – AIDAA Conference 2025
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] A. Filippone, “Aircraft noise prediction,” Progress in Aerospace Sciences, vol. 68, pp. 27-63, 2014 https://doi.org/10.1016/j.paerosci.2014.02.001
[2] M. Gennaretti, G. Bernardini, J. Serafini, A. Anobile, and S. Hartjes, “Helicopter noise footprint prediction in unsteady maneuvers,” International Journal of Aeroacoustics, vol. 16, no. 3, pp. 165-180, 2017. https://doi.org/10.1177/1475472X17709927
[3] B. Aflalo, D. Ferrari, et al., “Metamodeling techniques applied to aircraft noise prediction,” Blucher Mechanical Engineering Proceedings, vol. 1, no. 1, pp. 5018-5033, 2012. https://doi.org/10.5151/meceng-wccm2012-20194
[4] C. Poggi, M. Rossetti, J. Serafini, G. Bernardini, M. Gennaretti, and U. Iemma, “Neural network meta-modelling for an efficient prediction of propeller array acoustic signature,” Aerospace Science and Technology, vol. 130, p. 107910, 2022. https://doi.org/10.1016/j.ast.2022.107910
[5] G. Palma, L. Burghignoli, C. Poggi, and J. Serafini, “Multipolar expansion for aircraft noise equivalent sources,” Aerospace Science and Technology, vol. 155, 2024. https://doi.org/10.1016/j.ast.2024.109629
[6] E. G. Williams, “Chapter 6 – spherical waves,” in Fourier Acoustics (E. G. Williams, ed.), pp. 183-234, London: Academic Press, 1999. https://doi.org/10.1016/B978-012753960-7/50006-1
[7] B. G. van der Wall, “2nd hhc aeroacoustic rotor test (hart ii)-part i: Test documentation,” tech. rep., US Army AFDD, NASA Langley, DLR, ONERA and DNW, 2003.
[8] B. G. van der Wall, C. L. Burley, Y. Yu, H. Richard, K. Pengel, and P. Beaumier, “The hart ii test – measurement of helicopter rotor wakes,” Aerospace Science and Technology, vol. 8, no. 4, p. 273-284, 2004. https://doi.org/10.1016/j.ast.2004.01.001
[9] B. G. van der Wall and C. L. Burley, “2nd hhc aeroacoustic rotor test (hart ii)-part ii: representative results,” tech. rep., US Army AFDD, NASA Langley, DLR, ONERA and DNW, 2005.
[10] M. Gennaretti, G. Bernardini, J. Serafini, and G. Romani, “Rotorcraft comprehensive code assessment for blade-vortex interaction conditions,” Aerospace Science and Technology, vol. 80, pp. 232-246, 2018. https://doi.org/10.1016/j.ast.2018.07.013
[11] C. Bogey, O. Marsden, and C. Bailly, “Large-eddy simulation of the flow and acoustic fields of a reynolds number 105 subsonic jet with tripped exit boundary layers,” Physics of Fluids, vol. 23, p. 035104, 2011. https://doi.org/10.1063/1.3555634
[12] C. Bogey, O. Marsden, and C. Bailly, “Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based reynolds number of 105,” Journal of Fluid Mechanics, vol. 701, p. 352-385, 2012. https://doi.org/10.1017/jfm.2012.162
[13] S. Meloni, R. Camussi, and C. Bogey, “An analysis of the effect of the jet initial conditions on the wavelet separated near-field acoustic pressure,” Theoretical and Computational Fluid Dynamics, vol. 39, no. 1, p. 5, 2025. https://doi.org/10.1007/s00162-024-00727-9
[14] G. Palma, S. Meloni, R. Camussi, U. Iemma, and C. Bogey, “Data-driven multiobjective optimization of wave-packets for near-field subsonic jet noise,” AIAA Journal, vol. 61, no. 5, pp. 2179-2188, 2023. https://doi.org/10.2514/1.J062261
[15] G. Palma, S. Meloni, R. Camussi, U. Iemma, and C. Bogey, “Subsonic jet noise prediction in near and far field with optimized wave-packet approach,” AIAA Journal, vol. 62, no. 11, pp. 4144-4152, 2024. https://doi.org/10.2514/1.J064232
