A coupled boundary/finite element method for the computation of magnetically and electrostatically levitated droplet shapes

Song, Suping; Li, B. Q.

doi:10.1002/(sici)1097-0207(19990320)44:8<1055::aid-nme541>3.0.co;2-1

Cited by 21 publications

(25 citation statements)

References 14 publications

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“…Since the electric field inside the droplet is zero, only the potential distribution outside needs to be solved for. For this problem, the boundary integral can be obtained from the classical Green's theorem, [16] [ 18] where ⌽Ј ϭ ⌽ ϩ Er cos , ∂⍀ 2 designates the surface of the droplet, and denotes the boundary at infinity. The Green function, G, and its normal derivative are calculated by the following expressions written for a cylindrical coordinate system: [16] [19] [20] where is the geometric parameter calculated by [21] …”

Section: A Droplet Deformation Calculationsmentioning

confidence: 99%

“…[18] simplifies to a boundary integral that involves only the surface of the droplet, ∂⍀ 2 . Following the standard boundary element discretization, noticing that the potential on the surface is a constant and substituting ⌽ ϭ ⌽Ј -Er cos into the resultant equation, one obtains the final matrix form for the unknowns on the surface of the droplet,…”

Section: A Droplet Deformation Calculationsmentioning

confidence: 99%

“…The final results are expressed as a set of algebraic equations, which are then solved for the unknowns R i , K, and z c. . [17,18] B…”

Section: A Droplet Deformation Calculationsmentioning

confidence: 99%

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A mathematical model for marangoni flow and mass transfer in electrostatically positioned droplets

Huo

2005

Metall Mater Trans B

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A mathematical model is developed for the free surface deformation, full three-dimensional (3-D) Marangoni convection and solute transport phenomena in electrostatically levitated droplets under microgravity. The electric field is calculated by the boundary element method and the shape deformation by the weighted residuals method. The numerical model for the transport phenomena is developed based on the Galerkin finite-element solution of the Navier-Stokes equations, the energy balance equation, and the mass transport equation. Numerical simulations are carried out for droplet deformation by electrostatic forces and 3-D Marangoni convection in droplets heated by three different heating source arrangements. Results show that the electric forces deform a droplet into an oval shape under microgravity by pulling the droplet apart at the two poles. A two-beam heating arrangement results in an axisymmetric flow and temperature distribution in the droplet. Complex 3-D Marangoni flow structure occurs when a tetrahedral or octahedral heating arrangement is applied. The thermal transport in the droplet is conduction dominant for the cases studied. In general, the convection is stronger with higher melting point melts. The internal convection has a strong effect on the concentration distribution in the droplet. For melts with high viscosities, a significant reduction in velocity can be achieved with an appropriate laser beam arrangement, thereby permitting a diffusion-controlled condition to be developed.

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Section: A Droplet Deformation Calculationsmentioning

confidence: 99%

Section: A Droplet Deformation Calculationsmentioning

confidence: 99%

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A mathematical model for marangoni flow and mass transfer in electrostatically positioned droplets

Huo

2005

Metall Mater Trans B

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“…(3) involves the integration over the surface only and thus the boundary element method can be applied naturally to discretize the domain for a numerical solution. Following the general procedures described by Brebbia et al [13], the surface can be discretized and both E b and q can be interpolated over each of the boundary elements by use of shape functions, i.e.…”

Section: Problem Statementmentioning

confidence: 99%

“…This traditional boundary element approach should work very well if the kernel function, Kðr; r 0 Þ; is a smooth function, as demonstrated repeatedly in the traditional boundary integral solution of a wide range of engineering problems [13,14]. Unfortunately, for most practical applications involving surface thermal radiation exchanges, the kernel function is not smooth and may experience abrupt disruptions or discontinuities due to various types of geometric obstructions, which can be either the third party blocking or self-blocking of the view between point i and a point of element j: Physically, an occurrence of obstruction means that the radiation intensity emitted from surface element j is intercepted by other bodies and hence does not reach point i: This geometric effect poses a serious problem for accurately calculating the kernel functions in general.…”

Section: Problem Statementmentioning

confidence: 99%

The Galerkin boundary element solution for thermal radiation problems

Li¹,

Cui²,

Song³

2004

Engineering Analysis with Boundary Elements

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A parallel Galerkin boundary element method for surface radiation and mixed heat transfer calculations in complex 3‐D geometries

Cui

2004

Numerical Meth Engineering

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SUMMARYThis paper presents a parallel Galerkin boundary element method for the solution of surface radiation exchange problems and its coupling with the finite element method for mixed mode heat transfer computations in general 3-D geometries. The computational algorithm for surface radiation calculations is enhanced with the implementation of ideas used for 3-D computer graphics applications and with data structure management involving creating and updating various element lists optimized for numerical performance. The algorithm for detecting the internal third party blockages of thermal rays is presented, which involves a four-step procedure, i.e. the primary clip, secondary clip and adaptive integration with checking. Case studies of surface radiation and mixed heat transfer in both simple and complex 3-D geometric configurations are presented. It is found that a majority of computational time is spent on the detection of foreign element blockages and parallel computing is ideally suited for surface radiation calculations. Results show that the decrease of the CPU time approaches asymptotically to an inverse rule for parallel computing of surface radiation exchanges. For large-scale computations involving complex 3-D geometries, an iterative procedure is a preferred approach for the coupling of the Galerkin boundary and finite elements for mixed mode heat transfer calculations.

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A coupled boundary/finite element method for the computation of magnetically and electrostatically levitated droplet shapes

Cited by 21 publications

References 14 publications

A mathematical model for marangoni flow and mass transfer in electrostatically positioned droplets

A mathematical model for marangoni flow and mass transfer in electrostatically positioned droplets

The Galerkin boundary element solution for thermal radiation problems

A parallel Galerkin boundary element method for surface radiation and mixed heat transfer calculations in complex 3‐D geometries

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