• Proceedings of the KSME Conference
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• 2002.08a
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• pp.763-766
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• 2002

A BEM is highly efficient method in the sense of economic computation. However, boundary integration is not easy for the complex and moving surface e.g. in a rotating blade. Thus, Kirchhoff surface is designed in an effort to overcome the difficulty resulting from complex boundary conditions. A Kirchhoff surface is a fictitious surface which envelopes acoustic sources of main concern. Acoustic sources may be distributed on each Kirchhoff surface element depending on its acoustic characteristics. In this study, an axial fan is assumed to have loading noise as a dominant source. Dipole sources can be computed based on the FW-H equation. Acoustic field is then computed by changing Kirchhoff surface on which near-field is implemented, to analyze the effect of Kirchhoff surface on it.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.772-777
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• 2002

A BEM is highly efficient method in the sense of economic computation. However, boundary integration is not easy for the complex and moving surface e.g. in a rotating blade. Thus, Kirchhoff surface is designed in an effort to overcome the difficulty resulting from complex boundary conditions. A Kirchhoff surface is a fictitious surface which envelopes acoustic sources of main concern. Acoustic sources may be distributed on each Kirchhoff surface element depending on its acoustic characteristics. In this study, an axial fan is assumed to have loading noise as a dominant source. Dipole sources can be computed based on the FW-H equation. Acoustic field is then computed by changing Kirchhoff surfaces on which near-field is implemented, to analyze the effect of Kirchhoff surface on it.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.701-713
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• 2003

The BEM is a highly efficient method in the sense of economical computation. However, boundary integration is not easy for the complex geometry and moving surface, e.g. a rotating blade. Thus, Kirchhoff surface is designed in an effort to overcome the difficulty resulting from complex boundary conditions. A Kirchhoff surface is a fictitious surface which envelopes acoustic sources of main concern. Acoustic sources may be distributed on each Kirchhoff surface element according to their acoustic characteristics. In this study, an axial fan is assumed to have unsteady loading noise as a dominant source. Dipole sources can be modeled to solve the FW-H equation. Acoustic field is then computed by determining Kirchhoff surface on which near-field is implemented, to analyze the effect of Kirchhoff surface on it. The optimal shape and the location of Kirchhoff surface are discussed by comparing with experimental data acquired in an anechoic chamber.

• Journal of KSNVE
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• v.6 no.5
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• pp.607-616
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• 1996

A combined computational fluid dynamics(CFD)-Kirchhoff method is presented for predicting high-speed impulsive noise generated by a hovering blade. Two types of Kirchhoff integral formula are used; one for the classical linear Kirchhoff formulation and the other for the nonlinear Kirchhoff formulation. An Euler finite difference solver is solved first to obtain the flow field close to the blade, and then this flow field is used as an input to a Kirchhoff formulation to predict the acoustic far-field. These formulas are used at Mach numbers of 0.90 and 0.95 to investigate the effectiveness of the linear and nonlinear Kirchhoff formulas for delocalized flow. During these calculiations, the retarded time equation is also carefully examined, in particular, for the cases of the control surface located outside of the sonic cylinder, where multiple roots are obtained. Predicted results of acoustic far-field pressure with the linear Kirchhoff formulation agree well with experimental data when the control surface is at the certain location(R=1.46), but the correlation is getting worse before or after this specific location of the control surface due to the delocalized nonlinear aerodynamic flow field. Calculations based on the nonlinear Kirchhoff equation using a linear sonic cylinder as a control surface show a reasonable agreement with experimental data in negative amplitudes for both tip Mach numbers of 0.90 and 0.95, except some computational integration problems over a shock. This concliudes that a nonlinear formulation is necessary if the control surface is close to the blade and the flow is delocalized.

• The Journal of the Acoustical Society of Korea
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• v.28 no.3
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• pp.174-186
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• 2009

When we apply a propagation model to the ocean with boundaries, we can calculate reflected wave using reflection coefficient suggested by Rayleigh assuming the boundaries are flat. But boundaries in ocean such as sea surface and sea bottom have an irregular rough surface. To calculate the reflection loss for an irregular boundary, it is needed to compute the coherent reflection coefficient based on an experimental formula or scattering theory. In this article, we derive the coherent reflection coefficients for a fluid-fluid interface using perturbation theory, Kirchhoff approximation and small-slope approximation respectively. Based on each formula, we can calculate coherent reflection coefficients for a rough sea surface or sea bottom, and then compare them to the Rayleigh reflection coefficient to analyze the reflection loss for a random rough surface. In general, the coherent reflection coefficient based on small-slope approximation has a wide valid region. Comparing it with the coherent reflection coefficients derived from the Kirchhoff approximation and perturbation theory, we discuss a valid region of them.

• The Journal of the Acoustical Society of Korea
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• v.20 no.4
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• pp.81-86
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• 2001

126-kHz bistatic sea surface scattering measurements were conducted in the shallow waters off the east coasts of Korea. The range from source to receiver was altered to change the scattering angle at the grazing angles of 38％ and 52％ . Unlike bottom scattering signal, the arrival time and the amplitude of sea surface scattering signals were varied due to the fluctuation of sea surface. The measured forward scattering strengths were compared to model predictions of Kirchhoff approximation and small slope approximation. In overall, the tendency of the scattering strengths showed reasonable agreement among the experimental data, Kirchhoff approximation, and small slope approximation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.1062-1073
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• 2007

Acoustic Target Strength (TS) is a major parameter of the active sonar equation, which indicates the ratio of the radiated intensity from the source to the re-radiated intensity by a target. In developing a TS equation, it is assumed that the radiated pressure is known and the re-radiated intensity is unknown. This research provides a TS equation for polygonal plates, which is applicable to near field acoustics. In this research, Helmholtz-Kirchhoff formula is used as the primary equation for solving the re-radiated pressure field; the primary equation contains a surface (double) integral representation. The double integral representation can be reduced to a closed form, which involves only a line (single) integral representation of the boundary of the surface area by applying Stoke's theorem. Use of such line integral representations can reduce the cost of numerical calculation. Also Kirchhoff approximation is used to solve the surface values such as pressure and particle velocity. Finally, a generalized definition of Sonar Cross Section (SCS) that is applicable to near field is suggested. The TS equation for polygonal plates in near field is developed using the three prescribed statements; the redection to line integral representation, Kirchhoff approximation and a generalized definition of SCS. The equation developed in this research is applicable to near field, and therefore, no approximations are allowed except the Kirchhoff approximation. However, examinations with various types of models for reliability show that the equation has good performance in its applications. To analyze a general shape of model, a submarine type model was selected and successfully analyzed.

• 유체기계공업학회:학술대회논문집
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• 2004.12a
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• pp.89-93
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• 2004

To numerically construct the sound fields by a plenum fan mostly found in Air-Handling Unit (AHU), the Kirchhoff-BEM approach was applied to the near-field data of a turbo fan. The scattering effects were found to be significant by the plenum box structure for high-frequency components of source. The directivity petterns and sound pressure levels were also dependent upon the helmholts number which must be considered of the design stage for sound reduction program.

• Geophysics and Geophysical Exploration
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• v.1 no.1
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• pp.8-18
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• 1998

In exploration seismology, the Kirchhoff hyperbola has been successfully used to migrate reflection seismo-grams. The mathematical basis of Kirchhoff hyperbola has not been clearly defined and understood for the application of prestack or poststack migration. The travel time from the scatterer in the subsurface to the receivers (exploding reflector model) on the surface can be a kinematic approximation of Green's function when the source is excited at position of the scatterer. If we add the travel time from the source to the scatterer in the subsurface to the travel time of exploding reflector model, we can view this travel time as a kinematic approximation of the partial derivative wavefield with respect to the velocity or the density in the subsurface. The summation of reflection seismogram along the Kirchhoff hyperbola can be evaluated as an inner product between the partial derivative wavefield and the field reflection seismogram. In addition to this kinematic interpretation of Kirchhoff hyperbola, when we extend this concept to shallow refraction seismic data, the stacking of refraction data along the straight line can be interpreted as a measurement of an inner product between the first arrival waveform of the partial derivative wavefield and the field refraction data. We evaluated the Kirchhoff hyperbola and the straight line for stacking the refraction data in terms of the first arrival waveform of the partial derivative wavefield with respect to the velocity or the density in the subsurface. This evaluation provides a firm and solid basis for the conventional Kirchhoff migration and the straight line stacking of the refraction data.

• Journal of the Society of Naval Architects of Korea
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• v.42 no.5 s.143
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• pp.528-533
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• 2005

A mono-static high frequency acoustic target strength analysis scheme was developed for underwater targets, based on the far-field Kirchhoff approximation. Au adaptive triangular beam method and a concept of virtual surface were adopted for considering the effect of hidden surfaces and multiple reflections of an underwater target, respectively. A test of a simple target showed that the suggested hidden surface removal scheme is valid. Then some numerical analyses, for several underwater targets, were carried out; (1) for several simple underwater targets, like sphere, square plate, cylinder, trihedral corner reflector, and (2) for a generic submarine model, The former was exactly coincident with the theoretical results including beam patterns versus azimuth angles, and the latter suggested that multiple reflections have to be considered to estimate more accurate target strength of underwater targets.