Analytical solution for sound radiated from the rotating point source in uniform subsonic axial flow

Mao, Yijun; Xu, Chunxiao; Qi, Datong

doi:10.1016/j.apacoust.2014.12.012

Cited by 11 publications

(8 citation statements)

References 12 publications

(28 reference statements)

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“…This can be explained by an acoustic monopole source in transverse axis. A comparison with the results of monopole source in the origin point 100,101 shows that the effects of displacement of an axisymmetric monopole source in the positive radial direction decrease the acoustic pressure amplitude, according to an observation point in the near and far field zones around the source object. On the other hand, for non-axisymmetric cases of azimuthal order n≠0, we observe that the distribution of the sound amplitude in the upper and lower regions has values more intense than the upstream and downstream pressure fields.…”

Section: Numerical Results and Discussionmentioning

confidence: 91%

A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

Barhoumi

Bessrour

2020

International Journal of Aeroacoustics

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This paper presents a new numerical analysis approach based on an improved Modal Boundary Element Method (MBEM) formulation for axisymmetric acoustic radiation and propagation problems in a uniform mean flow of arbitrary direction. It is based on the homogeneous Modal Convected Helmholtz Equation (MCHE) and its convected Green’s kernel using a Fourier transform method. In order to simplify the flow terms, a general modal boundary integral solution is formulated explicitly according to two new operators such as the particular and convected kernels. Through the use of modified operators, the improved MBEM approach with flow takes a convective form of the general MBEM approach and has a similar form of the nonflow MBEM formulation. The reference and reduced Helmholtz Integral Equations (HIEs) are implicitly taken into account a new nonreflecting Sommerfeld condition to solve far field axisymmetric regions in a uniform mean flow. For isolating the singular integrations, the modal convected Green’s kernel and its modified normal derivative are performed partly analytically in terms of Laplace coefficients and partly numerically in terms of Fourier coefficients. These coefficients are computed by recursion schemes and Gauss-Legendre quadrature standard formulae. Specifically, standard forms of the free term and its convected angle resulting from the singular integrals can be expressed only in terms of real angles in meridian plane. To demonstrate the application of the improved MBEM formulation, three exterior acoustic case studies are considered. These verification cases are based on new analytic formulations for axisymmetric acoustic sources, such as axisymmetric monopole, axial and radial dipole sources in the presence of an arbitrary uniform mean flow. Directivity plots obtained using the proposed technique are compared with the analytical results.

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Section: Numerical Results and Discussionmentioning

confidence: 91%

A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

Barhoumi

Bessrour

2020

International Journal of Aeroacoustics

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“…It can be seen from equation (10) that when the vibration frequency of the sound source, propagation environment, and distance from the equivalent source surface to the sound source surface are constant, the equivalent source intensity density is only related to the discrete unit area of the equivalent source surface and the source intensity at the geometric center.…”

Section: Theory Of Esdimmentioning

confidence: 99%

“…The Hermit interpolation function not only restricts the function value of the discrete data point but also restricts the derivative at the node so that the constructed polynomial can better approximate the function P(). From equation (10), the coordinates of N discrete source strength density values Q (r Ei ) and their geometric centers r Ei (x i , y i ) (i = 1, 2, . .…”

Section: Theory Of Esdimmentioning

confidence: 99%

“…The main idea of ESM is that the sound field generated by a source is replaced by a set of monopole sources distributed on a surface at a certain distance from the surface of the radiating structure, and the source intensity of the equivalent source can be obtained by matching the normal vibration velocity of the surface of the source. Compare with other methods, such as the analytical method [9][10][11], finite element method [12][13][14], boundary element method [15][16][17], and ESM [18][19][20][21] are more suitable for reconstructing the radiated sound field of arbitrarily shaped sources and can require less computational effort and avoid complex interpolation operations and singular integration processing. Many scholars have conducted a series of studies on ESM to improve the resolution of sound sources and the accuracy of sound field reconstruction.…”

Section: Introductionmentioning

confidence: 99%

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Application of equivalent source intensity density interpolation in near-field acoustic holography

Gao

Yang

et al. 2023

Meas. Sci. Technol.

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The spatial resolution of near-field acoustic holography based on the equivalent source method (ESM) is closely related to the number of measurement points, the higher the number of measurement points, the higher the resolution. However, the number of measurement points in the actual measurement cannot be increased infinitely. To solve the contradiction between the resolution and the number of measurement points, this paper proposes an equivalent source density interpolation method (ESDIM). First, the equivalent source intensity is obtained using the sound pressure measured by the array element and the Green function, and the equivalent source intensity density is obtained based on the equivalent source intensity and grid area. Second, the Hermite interpolation function was used to obtain the interpolated equivalent source intensity density. However, as the number of interpolated grids increased, the resolution, computation, and running time of ESDIM increased, and the number of subdivided grids per unit grid was 9-25 in this study. Finally, the sound field was reconstructed based on the obtained interpolated equivalent source intensity and Green transfer function, and the reconstruction accuracies of ESDIM and ESM were compared and analyzed. The simulation and experimental data processing results showed that the resolution of the equivalent source intensity density interpolation method was higher than that of the equivalent source method.

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“…On the other hand, the Lorentz or Prandtl-Glauert transformation [33,34] is an alternative method to analyze sound propagation in uniform mean flow. Investigations have indicated that a moving background flow with high Mach numbers has a significant effect on sound generation and propagation [28,[30][31][32]35], implying that the classic exponent law of radiated acoustic power [1][2][3] is only valid approximately for low-Mach-number flows and should be corrected at high Mach numbers. In a quiescent acoustic medium, acoustic power can be computed once the distribution of the acoustic pressure is known on a closed far-field surface with an enough distance between sources and observers.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for sound radiated from the rotating point source in uniform subsonic axial flow

Cited by 11 publications

References 12 publications

A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

Application of equivalent source intensity density interpolation in near-field acoustic holography

Vector Aeroacoustics for Uniform Mean Flow: Acoustic Velocity and Vortical Velocity

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