Computational solution of acoustic radiation problems by Kussmaul's boundary element method

This study focuses on a numerical investigation of an initial stable jet through the air-sealed electrocentrifugal spinning process, which is known as a viable method for the mass production of nanofibers. A liquid jet undergoing electric and centrifugal forces, as well as other forces, first travels in a stable trajectory and then goes through an unstable curled path to the collector. In numerical modeling, hydrodynamic equations have been solved using the perturbation method-and the boundary integral method has been implemented to efficiently solve the electric potential equation. Hydrodynamic equations have been coupled with the electric field using stress boundary conditions at the fluid-fluid interface. Perturbation equations were discretized by a second order finite difference method, and the Newton method was implemented to solve the discretized non-linear system. Also, the boundary element method was utilized to solve electrostatic equations. In the theoretical study, the fluid was described as a leaky dielectric with charges only on the surface of the jet traveling in dielectric air. The effect of the electric field induced around the nozzle tip on the jet instability and trajectory deviation was also experimentally studied through plate-plate geometry as well as point-plate geometry. It was numerically found that the centrifugal force prevails on electric force by increasing the rotational speed. Therefore, the alteration of the applied voltage does not significantly affect the jet thinning profile or the jet trajectory. Published by AIP Publishing. https://doi

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“…30 He proposed a correction formula for a Gaussian quadrature over a triangular element to eliminate the singularity of the integrand, Eq. (17),…”

Section: Numerical Solutionmentioning

confidence: 99%

Numerical and experimental study on the steady cone-jet mode of electro-centrifugal spinning

et al. 2018

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“…The integral in (3.44) is evaluated through dividing the integral with respect to the generator direction into two parts at p and transforming the integral through changing the power of the variable in line with a method described in references [25] and [40]. The resulting regular integral on both parts is computed via the quadrature rule supplied to the routine.…”

Section: Axisymmetric Three-dimensional Problemsmentioning

confidence: 99%

“…The integral in (3.45) is evaluated by using the result that if the surface of integration in (3.45) is extended to enclose a three-dimensional volume then the integral vanishes (see [40]). As each panel is a truncated right circular cone shell a 45…”

Section: Axisymmetric Three-dimensional Problemsmentioning

confidence: 99%

The Boundary Element Method in Acoustics

Kirkup¹

2000

Journal of Computational Acoustics

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“…Due to the complexity of the regularization technique few numerical implementations have been reported. Kirkup and Henwood (1992) used this method to compute solutions of some acoustic radiation problems.…”

Section: Kussmaulmentioning

confidence: 99%

A Comprehensive Review of Boundary Integral Formulations of Acoustic Scattering Problems

Zaman

2000

SQU Journal for Science

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This is a review presenting an overview of the developments in boundary integral formulations of the acoustic scattering problems. Generally, the problem is formulated in one of two ways viz. Green’s representation formula, and the Layer-theoretic formulation utilizing either a simple-layer or a double-layer potential. The review presents and expounds the major contributions in this area over the last four decades. The need for a robust and improved formulation of the exterior scattering problem (Neumann or Dirichlet) arose due to the fact that the classical formulation failed to yield a unique solution at (acoustic) wave-numbers which correspond to eigenvalues (eigenfrequencies) of the corresponding interior scattering problem. Moreover, this correlation becomes more pronounced as the wave-numbers become larger i.e. as the (acoustic) frequency increases. The robust integral formulations which are discussed here yield Fredholms integral equations of the second kind which are more amenable to computation than the first kind. However, the integral equation involves a hypersingular kernel which creates ill-conditioning in the final matrix representation. This is circumvented by a regularisation technique. An extensive useful list of references is also presented here for researchers in this area.

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Computational solution of acoustic radiation problems by Kussmaul's boundary element method

Cited by 12 publications

References 11 publications

Numerical and experimental study on the steady cone-jet mode of electro-centrifugal spinning

Numerical and experimental study on the steady cone-jet mode of electro-centrifugal spinning

The Boundary Element Method in Acoustics

A Comprehensive Review of Boundary Integral Formulations of Acoustic Scattering Problems

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