Identifying equivalent sound sources from aeroacoustic simulations using a numerical phased array

Abstract

PostprintThis is the accepted version of a paper published in Journal of Sound and Vibration. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination.Citation for the original published paper (version of record):Pignier, N., O'Reilly, C J., Boij, S. (2017) Identifying equivalent sound sources from aeroacoustic simulations using a numerical phased array. Journal of Sound and Vibration AbstractAn application of phased array methods to numerical data is presented, aimed at identifying equivalent flow sound sources from aeroacoustic simulations. Based on phased array data extracted from compressible flow simulations, sound source strengths are computed on a set of points in the source region using phased array techniques assuming monopole propagation. Two phased array techniques are used to compute the source strengths: an approach using a Moore-Penrose pseudo-inverse and a beamforming approach using dual linear programming (dual-LP) deconvolution. The first approach gives a model of correlated sources for the acoustic field generated from the flow expressed in a matrix of cross-and auto-power spectral values, whereas the second approach results in a model of uncorrelated sources expressed in a vector of auto-power spectral values. The accuracy of the equivalent source model is estimated by computing the acoustic spectrum at a far-field observer. The approach is tested first on an analytical case with known point sources. It is then applied to the example of the flow around a submerged air inlet. The far-field spectra obtained from the source models for two different flow conditions are in good agreement with the spectra obtained with a Ffowcs Williams-Hawkings integral, showing the accuracy of the source model from the observer's standpoint. Various configurations for the phased array and for the sources are used. The dual-LP beamforming approach shows better robustness to changes in the number of probes and sources than the pseudo-inverse approach. The good results obtained with this simulation case demonstrate the potential of the phased array approach as a modelling tool for aeroacoustic simulations.

Multi-Approach Study of Nose Landing Gear Noise

“…The acoustic data extracted from the flow computations was propagated to the simulated microphone arrays and processed using several beamforming approaches [33]. In this paper only results obtained with an adapted version of Linear Programming Deconvolution (LPD) [73], called dual-LPD [56], are presented. This method is essentially an alternative version of solving the inverse problem considered in deconvolution methods such as DAMAS [74], but using linear programming.…”

“…A detailed explanation about the computational setup and simulations is out of the scope of this paper. More information about the computational setup and the propagation analysis can be found in [33][34][35]56].…”

Analysis of nose landing gear noise comparing numerical computations, prediction models and flyover and wind-tunnel measurements

“…The acoustic data extracted from the flow computations was propagated to simulated microphone arrays and processed using several beamforming approaches [27]. In this paper only results obtained with an adapted version of Linear Programming Deconvolution (LPD) [63], called dual-LPD [47], are presented. This method is essentially an alternative version of solving the inverse problem considered in deconvolution methods such [27].…”

“…A detailed explanation about the computational setup and simulations is out of the scope of this paper. More information about the computational setup and the propagation analysis can be found in [27][28][29]47].…”

The Moore–Penrose inverse: a hundred years on a frontline of physics research

“…Further papers demonstrating applications of the Moore-Penrose matrix inverse within the scope of theoretical physics include, among other, articles: Beylkin et al (2008), where the formulae for the inverse of modified matrices were exploited in a Green's function iteration algorithm introduced to solve the timeindependent, multiparticle Schrödinger equation, He et al (2012), which introduced phase-entanglement and phase-squeezing criteria for two bosonic fields that are robust against a number of fluctuations using the inverse to normalize the particle number operator, Huang and Li (2020), where formulae for the resistance distance and Kirchhoff index of a linear hexagonal (cylinder) chain were derived by means of the inverses of Laplacian matrices, Kametaka et al (2015), where the inverse of singular discrete Laplacian was used to solve difference equations to estimate a maximal deviation of a carbon atom from the steady state in C60 fullerene buckyball, Kirkland (2015) dealing with a quantum state transfer in a quantum walk on a graph, with the inverse used to derive expressions for the first and second partial derivatives of the fidelity of the transfer with respect to a weight of an edge, Kougioumtzoglou et al (2017), where an inverse based frequency response function was introduced to generalize frequency domain random vibration solution methodologies to account for linear and nonlinear structural systems with singular matrices, Lian et al (2019), where the inverse was exploited for calculating charge density distribution through Hartree potential to disclose the physical mechanism of electrostatic potential anomaly in 2D Janus transition metal dichalcogenides, McCartin (2009) reexpressing the Rayleigh-Schrödinger perturbation theory procedure in terms of the inverse, Meister et al (2014), where the inverse was used to formulate an optimal control algorithm with a control subspace defined by a superposition of arbitrary waveforms, Pignier et al (2017), where a model of an aeroacoustic sound source was created based on compressible flow simulations, with the inverse used to compute the sound source strengths, Ranjan and Zhang (2013) exploring the geometry of complex networks in terms of an Euclidean embedding represented by the inverse of its graph Laplacian, Yang et al (2018), where the inverse was used to solve an equilibrium equation originating in an empirical mode decomposition method combining the static and dynamic information for structural damage detection, and Yang et al (2020), where an expression for the inverse of Laplacian matrices of two connected weighted graphs was established and utilized to derive a recursion formula for the resistance distance.…”