Models for Solidification and Splashing in Laser Percussion Drilling

Smith, Warren R.

doi:10.1137/s003613990037234x

Cited by 24 publications

(27 citation statements)

References 9 publications

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“…Nevertheless, the lumped-parameter approach remains a useful element in the multiscale vascular modelling for retaining the computational tractability, as demonstrated by a number of recent works 30,49,51,67,87,88,101…”

Section: Earlier Concepts In Coronary Modellingmentioning

confidence: 99%

The Multi-Scale Modelling of Coronary Blood Flow

Lee

Smith

2012

Ann Biomed Eng

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Coronary flow is governed by a number of determinants including network anatomy, systemic afterload and the mechanical interaction with the myocardium throughout the cardiac cycle. The range of spatial scales and multi-physics nature of coronary perfusion highlights a need for a multiscale framework that captures the relevant details at each level of the network. The goal of this review is to provide a compact and accessible introduction to the methodology and current state of the art application of the modelling frameworks that have been used to study the coronary circulation. We begin with a brief description of the seminal experimental observations that have motivated the development of mechanistic frameworks for understanding how myocardial mechanics influences coronary flow. These concepts are then linked to an overview of the lumped parameter models employed to test these hypotheses. We then outline the full and reduced-order (3D and 1D) continuum mechanics models based on the Navier–Stokes equations and highlight, with examples, their application regimes. At the smaller spatial scales the case for the importance of addressing the microcirculation is presented, with an emphasis on the poroelastic approach that is well-suited to bridge an existing gap in the development of an integrated whole heart model. Finally, the recent accomplishments of the wave intensity analysis and related approaches are presented and the clinical outlook for coronary flow modelling discussed.

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Section: Earlier Concepts In Coronary Modellingmentioning

confidence: 99%

The Multi-Scale Modelling of Coronary Blood Flow

Lee

Smith

2012

Ann Biomed Eng

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“…However, the mass fraction removed by evaporation is typically less than a tenth of the total mass removed. 20,21 Also the cavity grows mainly in the z direction compared to the r direction, as shown in Fig. 1͑a͒ ͑i.e., along the direction of laser beam propagation͒ during laser drilling.…”

Section: Mass and Energy Balances In The Liquid Metal Layermentioning

confidence: 93%

Two-dimensional model for melting and vaporization during optical trepanning

Zeng

Latham

Kar

2005

Journal of Applied Physics

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Annular laser beams provide a drilling mechanism that can be referred to as optical trepanning. In this paper an analytical two-dimensional model is developed for optical trepanning. The analysis accounts for conduction in the solid, vaporization, and convection due to the melt flow caused by an assist gas. Based on the model, the influences of pulse duration, laser-pulse length, pulse repetition rate, intensity profiles, and beam radius are investigated to examine their effects on the recast layer thickness, hole depth, and taper. Deeper cavity depth, thicker recast layer, and larger taper are obtained with the increase in the laser intensity. By using different types of intensity profiles, the nature of the hole taper can be modified, i.e., convergent or divergent holes can be produced. The effects of the inner radius of annular beams are more significant than other laser parameters. An increase in the inner radius reduces the hole taper and produces thinner recast layer and deeper cavity depth.

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“…A wind, suitably provoked around the beam, pushes the melted material downwards. For its industrial interest, this phenomenon is widely considered in the specialized literature, see [13][14][15][16][26][27][28]32,33], while information specific to the cut of aluminum are for instance in [30]. A phenomenological description of the whole process can be summarized as follows.…”

Section: A Laser Beam Cutting a Metal Platementioning

confidence: 99%

Nonlocal systems of balance laws in several space dimensions with applications to laser technology

Colombo

Marcellini

2015

Journal of Differential Equations

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For a class of systems of nonlinear and nonlocal balance laws in several space dimensions, we prove the local in time existence of solutions and their continuous dependence on the initial datum. The choice of this class is motivated by a new model devoted to the description of a metal plate being cut by a laser beam. Using realistic parameters, solutions to this model obtained through numerical integrations meet qualitative properties of real cuts. Moreover, the class of equations considered comprises a model describing the dynamics of solid particles along a conveyor belt.

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Models for Solidification and Splashing in Laser Percussion Drilling

Cited by 24 publications

References 9 publications

The Multi-Scale Modelling of Coronary Blood Flow

The Multi-Scale Modelling of Coronary Blood Flow

Two-dimensional model for melting and vaporization during optical trepanning

Nonlocal systems of balance laws in several space dimensions with applications to laser technology

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