laserbeamFoam solvers

Overview

Presented here is a growing suite of solvers that describe laser-substrate interaction. This repository begins with the laserbeamFoam solver. Additional solvers are being added incrementally.

Currently, this repository contains two solvers:

laserbeamFoam

A volume-of-fluid (VOF) solver for studying high energy density laser-based advanced manufacturing processes and laser-substrate interactions. This implementation treats the metallic substrate and shielding gas phase as in-compressible. The solver fully captures the metallic substrate's fusion/melting state transition. For the vapourisation of the substrate, the explicit volumetric dilation due to the vapourisation state transition is neglected; instead, a phenomenological recoil pressure term is used to capture the contribution to the momentum and energy fields due to vaporisation events. laserbeamFoam also captures surface tension effects, the temperature dependence of surface tension (Marangoni) effects, latent heat effects due to melting/fusion (and vapourisation), buoyancy effects due to the thermal expansion of the phases using a Boussinesq approximation, and momentum damping due to solidification. A ray-tracing algorithm is implemented that permits the incident Gaussian laser beam to be discretised into several 'Rays' based on the computational grid resolution. The 'Rays' of this incident laser beam are then tracked through the domain through their multiple reflections, with the energy deposited by each ray determined through the Fresnel equations. The solver approach is extended from the adiabatic two-phase interFoam code developed by OpenCFD Ltd. to include non-isothermal state transition physics and ray-tracing heat source application.

multiComponentlaserbeamFoam

An extension of the laserbeamfoam solver to multi-component metallic substrates. This solver can simulate M-Component metallic substrates in the presence of gas-phases. Diffusion is treated through a Fickian diffusion model with the diffusivity specified through 'diffusion pairs', and the interface compression is again specified pair-wise. The miscible phases in the simulation should have diffusivity specified between them, and immiscible phase pairs should have an interface compression term specified between them (typically 1).

Target applications for the solvers included in this repository include:

• Dissimilar Laser Welding
• Dissimilar Laser Drilling
• Dissimilar Laser Powder Bed Fusion
• Dissimilar Selective Laser Melting

Installation

The current version of the code utilises the OpenFOAM-10 libraries. A branch that compiles against the older OpenFOAM-6 libraries is provided. The code has been developed and tested using an Ubuntu installation but should work on any operating system capable of installing OpenFOAM. To install the laserbeamFoam solvers, first, install and load OpenFOAM-10, then clone and build the laserbeamFoam library:

git clone https://github.com/micmog/laserbeamFoam.git laserbeamFoam
./Allwmake -j

where the -j option uses all CPU cores available for building.

The installation can be tested using the tutorial cases described below.

Optional: Installation of the LIGGGHTS® Discrete Element Model Solver

Some of the tutorial cases use a discrete element method (DEM) solver called LIGGGHTS to simulate the creation of a powder bed, e.g. see this powder bed fusion tutorial. For these cases, if available, the liggghts executable will be used in the case pre-processing process.

On Linux, LIGGGHTS® can be installed with

# Install required dependencies
sudo apt update
sudo apt install -y build-essential cmake gfortran git \
  libfftw3-dev libjpeg-dev libpng-dev libvtk6-dev \
  libopenmpi-dev openmpi-bin
  
# Clone the LIGGGHTS repository
git clone https://github.com/CFDEMproject/LIGGGHTS-PUBLIC.git
cd LIGGGHTS-PUBLIC/src

# Compile
make auto

# The `liggghts` executable should now be available in this directory

While on macOS, LIGGGHTS® can be installed with

# Install required dependencies using Homebrew
brew install cmake gcc openmpi vtk
  
# Clone the LIGGGHTS repository
git clone https://github.com/CFDEMproject/LIGGGHTS-PUBLIC.git

# Compile
# You may need to update the vtk version in the cmake command to the version
# installed on your system (i.e., replace 9.4.2_1 with another version)
cd LIGGGHTS-PUBLIC
mkdir build
cd build
cmake ../src -DCMAKE_C_COMPILER=mpicc -DCMAKE_CXX_COMPILER=mpicxx -DVTK_DIR=/opt/homebrew/Cellar/vtk/9.4.2_1/lib/cmake/vtk-9.4
make

# The `liggghts` executable should now be available in this directory

For convenience, you can add add liggghts to your PATH (e.g. in ~/.bashrc):

export PATH="~/LIGGGHTS-PUBLIC/build:$PATH"

where the location should be updated to match the location on your system.

Tutorial Cases

The tutorial cases can be run with the included Allrun scripts, i.e.

./Allrun

The Allrun script prepares the mesh and fields, and runs the solver. Typically the following steps are performed:

# Create the 0 directory
cp -r initial 0

# Create the mesh
blockMesh

# Set the initial fields
setFields

# Run the solver in serial
laserbeamFoam

# Or run the solver in parallel, e.g. on 6 cores
#decomposePar
#mpirun -np 6 laserbeamFoam -parallel &> log.laserbeamFoam

Cases can be cleaned and reset using the included Allclean scripts, i.e.

./Allclean

2D Plate

In these cases, the penetration rate of an incident laser source is investigated based on the angle of incidence of the laser beam. Two cases are presented where the beam is perpendicular to the substrate or 45 degrees to the initial plate normal.

3D Plate

In this case, the two-dimensional 45-degree example is extended to three dimensions.

2D Circular Particles

In this example, a series of circular metallic regions are seeded on top of a planar substrate. The laser heat source traverses the domain and melts these regions, and their topology evolves accordingly.

2D Laser-Powder Bed Fusion

In this example, a two-dimensional domain is seeded with many small powder particles with a complex size distribution, representative of that observed in the L-PBF manufacturing process. The laser heat source traverses the domain, and some particles melt and re-solidify in the heat source's wake.

Algorithm

Initially, the solver loads the mesh, reads in fields and boundary conditions, and selects the turbulence model (if specified). The main solver loop is then initiated. First, the time step is dynamically modified to ensure numerical stability. Next, the two-phase fluid mixture properties and turbulence quantities are updated. The discretised phase-fraction equation is then solved for a user-defined number of subtime steps (typically 3) using the multidimensional universal limiter with explicit solution solver MULES. This solver is included in the OpenFOAM library and performs conservative solutions of hyperbolic convective transport equations with defined bounds (0 and 1 for $α_1$). Once the updated phase field is obtained, the program enters the pressure–velocity loop, where p and u are corrected alternatingly. $T$ is also solved in this loop so that the buoyancy predictions are correct for the $U$ and $p$ fields. Correcting the pressure and velocity fields in the sequence is known as pressure implicit with the splitting of operators (PISO). In the OpenFOAM environment, PISO is repeated for multiple iterations at each time step. This process is called the merged PISO- semi-implicit method for pressure-linked equations (SIMPLE) or the pressure-velocity loop (PIMPLE) process, where SIMPLE is an iterative pressure–velocity solution algorithm. PIMPLE continues for a user-specified number of iterations.

The main solver loop iterates until program termination. A summary of the simulation algorithm is presented below:

• laserbeamFoam Simulation Algorithm Summary:

  • Initialise simulation data and mesh

  • WHILE $t < t_{\text{end}}$ DO

    1. Update $\Delta t$ for stability

    2. Phase equation sub-cycle

    3. Update interface location for the heat source application

    4. Update fluid properties

    5. Ray-tracing for Heat Source application at the surface

    6. PISO Loop

       1. Form $U$ equation

       2. Energy Transport Loop

          1. Solve $T$ equation
          2. Update fluid fraction field
          3. Re-evaluate source terms due to latent heat

       3. PISO

          1. Obtain and correct face fluxes
          2. Solve $p$ Poisson equation
          3. Correct $U$

    7. Write fields

There are no constraints on how the computational domain is discretised.

Visualising the rays in ParaView

laserbeamFoam writes the individual ray beams to VTK/rays_<TIME_INDEX>.vtk, where <TIME_INDEX> is the time-step index, i.e. 1, 2, 3, etc. ParaView recognises that these files are in a sequence, so they can all be loaded together: File -> Open... -> Select rays_..vtk. As the VTK files do not store time-step information, by default, ParaView assumes the time-step size for the rays is 1 s; however, you can use the ParaView “Temporal Shift Scale” filter on the rays object to sync the ray time with the OpenFOAM model time, where the OpenFOAM time-step value (e.g. 1e-5) is used as the Scale.

License

OpenFOAM, and by extension, the laserbeamFoam application, is licensed free and open source only under the GNU General Public Licence version 3. One reason for OpenFOAM’s popularity is that its users are granted the freedom to modify and redistribute the software and have a right to continued free use within the terms of the GPL.

Acknowledgements

Tom Flint and Joe Robson thank the EPSRC for financial support through the associated programme grant LightFORM (EP/R001715/1). Joe Robson thanks the Royal Academy of Engineering/DSTL for funding through the RAEng/DSTL Chair in Alloys for Extreme Environments.

Philip Cardiff and Gowthaman Parivendhan authors gratefully acknowledge financial support from I-Form, funded by Science Foundation Ireland (SFI) Grant Numbers 16/RC/3872 and 21/RC/10295 P2, co-funded under the European Regional Development Fund and by I-Form industry partners. In addition, Philip Cardiff received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 101088740), and acknowledges financial support from the Irish Research Council through the Laureate programme, grant number IRCLA/2017/45, and Bekaert, through the Bekaert University Technology Centre (UTC) at University College Dublin www.ucd.ie/bekaert.

Citing This Work

If you use laserbeamFoam in your work. Please use the following to cite our work:

laserbeamFoam: Laser ray-tracing and thermally induced state transition
simulation toolkit. TF Flint, JD Robson, G Parivendhan, P Cardiff - SoftwareX,
2023 - https://doi.org/10.1016/j.softx.2022.101299

References

Flint, T. F., Robson, J. D., Parivendhan, G., & Cardiff, P. (2023). laserbeamFoam: Laser ray-tracing and thermally induced state transition simulation toolkit. SoftwareX, 21, 101299.

Flint, T. F., Parivendhan, G., Ivankovic, A., Smith, M. C., & Cardiff, P. (2022). beamWeldFoam: Numerical simulation of high energy density fusion and vapourisation-inducing processes. SoftwareX, 18, 101065.

Flint, T. F., et al. A fundamental analysis of factors affecting chemical homogeneity in the laser powder bed fusion process. International Journal of Heat and Mass Transfer 194 (2022): 122985.

Flint, T. F., T. Dutilleul, and W. Kyffin. A fundamental investigation into the role of beam focal point, and beam divergence, on thermo-capillary stability and evolution in electron beam welding applications. International Journal of Heat and Mass Transfer 212 (2023): 124262.

Parivendhan, G., Cardiff, P., Flint, T., Tuković, Ž., Obeidi, M., Brabazon, D., Ivanković, A. (2023) A numerical study of processing parameters and their effect on the melt-track profile in Laser Powder Bed Fusion processes, Additive Manufacturing, 67, 10.1016/j.addma.2023.103482.

Disclaimer

This offering is not approved or endorsed by OpenCFD Limited, producer and distributor of the OpenFOAM software via www.openfoam.com, and owner of the OPENFOAM® and OpenCFD® trade marks.

Acknowledgement

OPENFOAM® is a registered trademark of OpenCFD Limited, producer and distributor of the OpenFOAM software via www.openfoam.com.