A time-domain Kirchhoff formula for the convective acoustic wave equation

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

doi:10.1098/rspa.2015.0689

Cited by 9 publications

(7 citation statements)

References 25 publications

(54 reference statements)

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“…Equation (2.12) is the integral solution to the acoustic analogy that considers the convection effect of oncoming flows. Similar processes in deriving the solution were also employed in several previous aeroacoustic studies (Najafi-Yazdi et al 2011;Ghorbaniasl, Siozos-Rousoulis & Lacor 2016;Zhong & Zhang 2017). For rotor noise, a remaining difficulty is considering the influences of unsteady motions in estimating the retarded time and |∂g/∂τ |.…”

Section: Formulations For Rotor Noise Computationmentioning

confidence: 99%

An investigation of rotor aeroacoustics with unsteady motions and uncertainty factors

et al. 2023

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The aeroacoustic characteristics of flying vehicles with pitch-fixed rotors differ from traditional helicopters with pitch-controlled rotor blades. Accurate predictions of rotor noise are still challenging because many uncertainty factors and unsteadinesses exist. This work investigates the aeroacoustic effects of rotational speed deviation, rotation speed fluctuation, blade vibration and blade geometric asymmetry. The analysis is based on the efficient computation of rotor noise under different working conditions. The mean aerodynamic variables are computed using the blade element moment theory, while small-amplitude fluctuations are introduced to account for the unsteadiness and uncertainty factors. It is shown that periodic rotation speed fluctuations and blade vibrations can produce significant extra tones. By contrast, if the fluctuations and vibrations are random, the noise level in a wide frequency range is increased. The intriguing result reminds us of the need to revisit the rotor broadband noise sources commonly attributed to turbulent flows. The influences are observer angle dependent, and the extra noise production is more significant in the upstream and downstream directions. The asymmetric blade geometry can cause extra tonal noise at the harmonics of the blade shaft frequency. The noise features of dual rotors are also investigated. Usually, the noise is sensitive to the initial phase difference and rotation directions due to the interference effect. However, the noise features are vastly altered if there are slight differences in the rotation speeds. Although the influences of some factors on rotor noise were already known, the present study provides a more comprehensive analysis of the problem. The results also highlight the need to consider these practical factors for accurate noise prediction of multi-rotor flying vehicles.

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Section: Formulations For Rotor Noise Computationmentioning

confidence: 99%

An investigation of rotor aeroacoustics with unsteady motions and uncertainty factors

et al. 2023

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“…It is known that the effects of mean flow incidence on a rotating source is equivalent to an unsteady acoustic source. 42 Also, from the linear acoustic theories, by converting the convective wave equation to a simple wave equation, it has been shown that there is some influence of uniform flow on overall noise levels. 42,43 From Figure 35, we can identify and confirm that some broadband contributions arise from the wake effects in the lower frequencies, but we cannot explicitly quantify this source.…”

Section: Near-field Acousticsmentioning

confidence: 99%

Simulations of multi-rotor interaction noise at hovering & forward flight conditions

Afari

Mankbadi

2023

International Journal of Aeroacoustics

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A high-fidelity simulation of two in-line counter-rotating propellers in hover, and in forward flight conditions are performed. Near field flow and acoustic properties were resolved using Hybrid LES-Unsteady RANS. Far-field sound predictions were performed using Ffowcs-Williams-Hawkings formulation. The two-propeller results in hovering are compared with that of the single propeller. This enabled us to identify the aerodynamic changes resulting from the proximity of the two propellers to each other and to understand the mechanisms causing the changes in the radiated sound. We then considered the forward flight case and compared it with the corresponding hovering case. This enabled us to identify the aerodynamic changes resulting from the incoming stream. By examining the near acoustic field, the far-field spectra, the Spectral Proper Orthogonal Decomposition, and by conducting periodic averaging, we were able to identify the sources of the changes to the observed tonal and broadband noise.

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“…The fluid momentum equation (33) is converted to the Maxwell's equations by defining the 'fluid electric field', E ! , and the 'fluid magnetic field', B !…”

Section: The Electromagnetic Analogymentioning

confidence: 99%

“…A comprehensive treatment of the subject can be found in literature. [32][33][34] Of particular interest to this paper are the Kirchhoff acoustic velocity formulations, KV1 and KV1A, presented in literature. 34 The derivation of these results is based on Farassat's formulation 1 and 1 A solutions of equation 158for acoustic pressure.…”

Section: Dunnmentioning

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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A time-domain Kirchhoff formula for the convective acoustic wave equation

Cited by 9 publications

References 25 publications

An investigation of rotor aeroacoustics with unsteady motions and uncertainty factors

An investigation of rotor aeroacoustics with unsteady motions and uncertainty factors

Simulations of multi-rotor interaction noise at hovering & forward flight conditions

The acoustic analogy in four dimensions

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