Modelling laser percussion drilling

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Modelling laser percussion drilling

• Kees Verhoeven

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Overview

• The process
• Laser induced melting
• Splashing Solidification
• NumLab in this project

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Overview

• The process
• Laser induced melting
• Splashing Solidification
• NumLab in this project

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The process
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The process analysis

• Time scales
• Melting to sec.
• Splashing sec.
• Gas dynamics sec.
• One dimensional model for melting
• Shallow water equations for splashing and
  solidification
• One dimensional model for recoil pressure

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Overview

• The process
• Laser induced melting
• Splashing Solidification
• NumLab in this project

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Stefan formulation

• Heat equation in both regions
• Stefan condition
• Energy supply

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Enthalpy method

• Heat equation in enthalpy form
• Enthalpy known function of temperature

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Comparison

• Front-tracking and front-fixing methods vs.
  fixed-domain methods
• Enthalpy method can deal with mushy regions
• Enthalpy method easily extended to 2D

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Overview

• The process
• Laser induced melting
• Splashing Solidification
• NumLab in this project

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Splashing Solidification

• Dimensionless parameters
• Assumptions
• Inviscid
• Irrotational
• Leading-order effects
• Recoil pressure (splashing)
• Convection vs. diffusion (solidification)

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Solidification

• Unknowns
• Equations
• Conservation of mass
• Burgers equation
• Heat equation

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Solidification numerics
SLM Burgers
SLM Mass
Heat eq.
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Note that

• Burgers equation exhibits shocks
• Velocity has compact support, so leading edge
  shock
• This shock appears in the equation for
  conservation of mass
• Melt amasses behind leading edge shock

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Overview

• The process
• Laser induced melting
• Splashing Solidification
• NumLab in this project

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Solidification numerics
SLM Burgers
SLM Mass
Heat eq.
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Using different packages

• Sepran (FEM)
• PPPack (Splines)
• LaPack
• VTK (Visualisation)
• Own codes (Matlab, C/C)

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Example 1 Burgers mass
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Example 2 Visualisation
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Example 2 Visualisation