Analytical acoustic pressure gradient prediction for moving medium problems

Ghorbaniasl, Ghader; Huang, Zhilin; Siozos-Rousoulis, Leonidas; Lacor, Christian

doi:10.1098/rspa.2015.0342

Cited by 21 publications

(20 citation statements)

References 31 publications

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“…One method involves combining the fluid momentum equation with the formulation 1 or 1 A solution for the acoustic pressure to obtain the gradient of acoustic pressure from which an approximation to the acoustic velocity is deduced. [22][23][24] In the latter two references, the authors expanded the analysis to include predictions in a uniform background flow. On the other hand, formulations V1 and V1A 25 provide direct analytical methods for computing the acoustic velocity.…”

Section: Acoustic Velocity Predictions Via the Acoustic Analogymentioning

confidence: 99%

The acoustic analogy in four dimensions

Dunn¹

2019

International Journal of Aeroacoustics

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The classical acoustic analogy theory is incomplete in the sense that the original research on the subject focused only on the prediction of acoustic pressure. There were no provisions for predicting the three components of acoustic velocity which are needed as input for aeroacoustic scattering applications. This is because the scalar wave equations of Lighthill and Ffowcs Williams and Hawkings were derived from the fluid conservation equations by eliminating three of the four governing differential equations from which the acoustic velocity could have been obtained. Recently developed acoustic analogy methods for predicting the acoustic velocity lead to complex formulations whose numerical evaluation can be problematic when providing input for large-scale scattering problems. Their calculation can overwhelm the numerical scattering process when the incident sound has high-frequency content, such as that produced by the rotating blades of various propulsion devices. To obtain improved acoustic analogy formulations for scattering and other applications, the three discarded differential equations are returned to the analysis in this paper and the historical acoustic analogy equations are derived anew using four-dimensional tensor methods. The 4-D formulation is an application of the electromagnetic analogy (EMA), a concept based on the equivalence of Maxwell’s equations and the fluid conservation equations of mass and momentum. The scalar equations of Lighthill, Ffowcs Williams and Hawkings, Farassat, and Kirchhoff are extended to four equations – one equation for the acoustic pressure (or acoustic density) and three equations for the acoustic velocity. The 4-D tensor representation provides significant theoretical and computational simplification relative to the classical approach. For each of the original acoustic analogy results, a single, concise formulation in 4D is derived that enables the simultaneous prediction of acoustic pressure and the three components of acoustic velocity.

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Section: Acoustic Velocity Predictions Via the Acoustic Analogymentioning

confidence: 99%

The acoustic analogy in four dimensions

Dunn¹

2019

International Journal of Aeroacoustics

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“…Employing Eq. (2) and adopting a modification of the source term recently suggested by Ghorbaniasl et al [26],…”

Section: A Convective Fw-h Equation and Its Time-domain Solutionmentioning

confidence: 99%

“…To realize the more complex acoustic scattering prediction for windtunnel experiments, the convective FW-H equation [24,25], which explicitly takes into account the presence of the moving medium, should be used and the acoustic scattering boundary condition in the moving medium should be calculated as well. Recently, Ghorbaniasl et al [26] derived an analytic acoustic pressure gradient formulation in the frequency domain that accounted for the effect of a constant uniform flow with arbitrary direction. Considering that the time-domain formulation can be useful in some cases of acoustic scattering prediction (for example, the moving observer case), an analytic time-domain acoustic pressure gradient formulation that explicitly takes into account the presence of the moving medium is developed in the present paper.…”

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confidence: 99%

Analytic Time-Domain Formulation for Acoustic Pressure Gradient Prediction in a Moving Medium

Wang

Zhang

2017

AIAA Journal

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This paper presents an analytic time-domain formulation for acoustic pressure gradient prediction in a moving medium, which has significant application potential in evaluating the acoustic scattering boundary condition. Based on the convective Ffowcs Williams-Hawkings equation, a semianalytic time-domain acoustic pressure gradient formulation with a form involving the observer time differentiation outside the integrals is first developed, and then the desired analytic time-domain acoustic pressure gradient formulation is derived. Because the derived formulations are performed directly in the time domain, they are particularly applicable to the moving observer case. Simulation results for a stationary monopole source, a stationary dipole source, as well as a rotating monopole source in a moving medium demonstrate the effectiveness and accuracy of the proposed formulations for both stationary and moving sources with moving observers. Nomenclature

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“…This is possible by a solution of the convected FW-H equation. Ghorbaniasl et al have recently derived a moving-medium formulation for acoustic pressure and acoustic pressure gradient prediction, in the frequency domain [15]. Application of these formulas was shown for acoustic scattering of sources in stationary media [16] [17].…”

Section: Introductionmentioning

confidence: 99%