Laser Heat Source

If a laser heat source is present in a simulation, it can be added in this section. The default parameters are:

subsection laser parameters
  set enable               = false
  set type                 = gaussian_heat_flux_vof_interface
  set concentration factor = 2.0
  set power                = 0.0
  set absorptivity         = 0.5
  set penetration depth    = 1.0
  set beam radius          = 0.0
  set start time           = 0.0
  set end time             = 1.0
  set beam orientation     = z-
  set beam rotation angle  = 0.0
  set beam rotation axis   = 0.0, 0.0, 1.0

  subsection path
    set Function expression = 0.0; 0.0
  end

  subsection free surface radiation
    set enable                    = false
    set emissivity                = 0.6
    set Tinf                      = 0.0
    set Stefan-Boltzmann constant = 5.6703e-8
  end
end

• The enable parameter is set to true if the problem has a laser heat source term and enables its calculation.

• The type parameter is set to gaussian_heat_flux_vof_interface (default) if we assume that the laser behaves as a surface heat flux with a normal irradiation distribution. If the laser is assumed to have a uniform surface heat flux, the type can be set at uniform_heat_flux_vof_interface. In both cases, the laser model must be used in conjunction with the VOF auxiliary physic. The third available laser model is the exponential_decay and considers that the laser behaves as a volumetric source. The different models are detailed below.

• Laser concentration factor parameter indicates the definition of the beam radius. In almost all the articles, it is assumed equal to \(2.0\).

• The power parameter sets the power of the laser \([ML^2T^{-3}]\).

• The absorptivity parameter is defined as the fraction of incident radiation that is absorbed by the surface, and it is measured using diffuse reflectance spectroscopy (DRS). Generally, a constant value in the range of \(0.3\)-\(0.8\) (for welding processes with titanium) is used in the literature. However, recent studies show that it varies with powder particle size distribution and the angle of incidence that changes due to the dynamic melt pool surface [1].

• The penetration depth parameter determines the penetration depth of the laser in the simulation domain in the direction of emission.

  Attention

  The penetration depth value should be greater than \(0\) and it is only taken into account if the laser type is set to exponential_decay.

• The beam radius parameter defines the radius of the laser beam.

• The start time and end time parameters define the operation time window of the laser.

• The beam orientation parameter shows the orientation and direction of the laser beam. For instance, if a laser beam is emitted perpendicular to a plane in \(x\)-\(y\) coordinates, the orientation of the laser beam will be in the z-direction. Negative (-) or positive (+) defines the direction of the laser beam. For instance if the laser beam is emitted in the negative \(z\) direction, the value of beam orientation will be z-.

  Attention

  In two-dimensional simulations, the laser beam orientation cannot be in the z-direction.

• The beam rotation angle and beam rotation axis parameters allow to rotate the beam axis (given by beam orientation) of an angle \(\theta\) in radians around the specified rotation axis, described by its tangent vector \(\vec{t}_\text{rot}\). It is only available for the gaussian_heat_flux_vof_interface model, and the beam rotation axis is only used in 3D simulations. The rotation is performed using the matrix for rotation \(R(\vec{t}_\text{rot}, \theta)\) following:

  \[\vec{t}_\text{laser,rot} = R(\vec{t}_\text{rot}, \theta)\vec{t}_\text{laser}\]

  where \(\vec{t}_\text{laser}\) is the initial beam tangent vector, given by the beam orientation parameter, and \(\vec{t}_\text{laser}\) is the rotated one.

• In the path subsection, the laser scanning path is defined using a Function expression.

• subsection free surface radiation: In additive manufacturing simulations, radiation at the interface between the air and the metal is a significant cooling mechanism. When this interface (i.e., free surface) is resolved by the Volume of Fluid (Multiphase Flow) solver, the free surface radiation subsection defines the parameters to impose this radiation cooling following the Stefan-Boltzmann law of radiation:

  \[q_\text{rad} = \epsilon \sigma (T^4 - T_\text{inf}^4)\]

  • enable: controls if the radiation cooling is enabled. The radiation sink is modulated by the filtered phase fraction gradient norm, \(|\nabla \psi|\), in such way that the flux is applied at the interface between the fluids.

    Warning

    To apply this radiation cooling, the VOF parameter must be set to true in the Multiphysics subsection.

  • emissivity, Tinf, and Stefan-Boltzmann constant are respectively the emissivity \(\epsilon\) of the surface, the environment temperature \(T_\text{inf}\), and the Stefan-Boltzmann constant \(\sigma\).

Laser types

• When the type is set to gaussian_heat_flux_vof_interface or uniform_heat_flux_vof_interface, it must be used in conjunction with the VOF auxiliary physic.

  • The gaussian_heat_flux_vof_interface model is used to apply a gaussian heat flux only at the interface. In 3D, this heat flux is given by:

    \[q(x,y,z) = \frac{|\nabla \psi| \eta \alpha P}{\pi R^2} \exp{\left(-\eta \frac{r^2}{R^2}\right)}\]

    where \(r\) is the radial distance from the laser’s axis and \(|\nabla \psi|\) is the \(L^2\) norm of the filtered phase fraction gradient. In 2D, the pre-exponential factor accounts for the change in the receiving area (going from a disk of radius \(R\) in 3D to a line segment of length \(2R\) in 2D):

    \[q(x,y,z) = \frac{2|\nabla \psi| \sqrt{\eta\;} \alpha P}{\sqrt{\pi^3} R^2} \exp{\left(-\eta \frac{r^2}{R^2}\right)}\]

  • The uniform_heat_flux_vof_interface model is used to apply a uniform heat flux, given by the expression below, only at the interface.

    \[q(x,y,z) = \frac{|\nabla \psi| \alpha P}{\pi R^2}\]

• When the type parameter is set to exponential_decay, the exponential model from Liu et al. [2] is used to simulate the laser heat source:

  \[q(x,y,z) = \frac{\eta \alpha P}{\pi R^2 \mu} \exp{\left(-\eta \frac{r^2}{R^2}\right)} \exp{\left(- \frac{|z|}{\mu}\right)}\]

  where \(\eta\), \(\alpha\), \(P\), \(R\), \(\mu\), \(r\), and \(z\) denote the concentration factor, absorptivity, laser power, beam radius, penetration depth, radial distance from the laser focal point, and axial distance from the laser focal point, respectively.

  When the exponential_decay is used in conjunction with the VOF auxiliary physic the equation takes the following form:

  \[q(x,y,z) = \frac{\psi \eta \alpha P}{\pi R^2 \mu} \exp{\left(-\eta \frac{r^2}{R^2}\right)} \exp{\left(- \frac{|z|}{\mu}\right)}\]

  where \(\psi\) is the filtered phase fraction.

  Attention

  In this case, the heat affects the fluid initialized as fluid 1.

References

[1]

Z. Zhang et al., “3-Dimensional heat transfer modeling for laser powder-bed fusion additive manufacturing with volumetric heat sources based on varied thermal conductivity and absorptivity,” Opt. Laser Technol., vol. 109, pp. 297–312, Jan. 2019, doi: 10.1016/j.optlastec.2018.08.012.

[2]

S. Liu, H. Zhu, G. Peng, J. Yin, and X. Zeng, “Microstructure prediction of selective laser melting AlSi10Mg using finite element analysis,” Mater. Des., vol. 142, pp. 319–328, Mar. 2018, doi: 10.1016/j.matdes.2018.01.022.