Algorithm

Initially the solver loads the mesh, reads in fields and boundary conditions, reads certain mesh information into arrays (for the heat source application), 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 discretized 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 solution of hyperbolic convective transport equations with defined bounds (0 and 1 for α1). Once the updated phase field is obtained, the program enters the pressure–velocity loop, in which p and u are corrected in an alternating fashion. In this loop T is also solved for, such that he buoyancy predictions are correct for the U and p fields. The process of correcting the pressure and velocity fields in sequence is known as pressure implicit with splitting of operators (PISO). In the OpenFOAM environment, PISO is repeated for multiple iterations at each time step. This process is referred to as 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:

• beamWeldFoam Simulation Algorithm Summary:
  • Initialize simulation data and mesh
  • WHILE t<t_end DO
  • 1. Update delta_t for stability
  • 1. Phase equation sub-cycle
  • 1. Update interface location for heat source application
  • 1. Update fluid properties
  • 1. PISO Loop
       • 1. Form u equation
       • 1. Energy Transport Loop
            • 1. Solve T equation
            • 1. Update fluid fraction field
            • 1. Re-evaluate source terms due to latent heat
       • 1. PISO
       • 1. Obtain and correct face fluxes
       • 1. Solve p-Poisson equation
       • 1. Correct u
  • 1. Write Fields

Two sample tutorial cases, i.e. Gallium Meliing, and Sen and Davies cases are in strong agreement with experimental and analytical data available in the literature and serve as the validation cases for the implementation in beamWeldFoam.

License

OpenFoam, and by extension the beamWeldFoam 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 of continued free use, within the terms of the GPL.

Acknowledgements

The work was generously supported by the Engineering and Physical Sciences Research Council (EPSRC) under the ‘‘Cobalt-free Hard-facing for Reactor Systems’’ grant EP/T016728/1, and Science Foundation Ireland (SFI), co-funded under European Regional Development Fund and by I-Form industry partners, grant 16/RC/3872.

Citing This Work

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

Thomas F. Flint, Gowthaman Parivendhan, Alojz Ivankovic, Michael C. Smith, Philip Cardiff, beamWeldFoam: Numerical simulation of high energy density fusion and vapourisation-inducing processes, SoftwareX, Volume 18, 2022, 101065, ISSN 2352-7110, https://doi.org/10.1016/j.softx.2022.101065

References

• Kay Wittig and Petr A Nikrityuk 2012 IOP Conf. Ser.: Mater. Sci. Eng. 27 012054
• Sen, A., & Davis, S. (1982). Steady thermocapillary flows in two-dimensional slots. Journal of Fluid Mechanics, 121, 163-186. doi:10.1017/S0022112082001840
• Sabina L. Campanelli, Giuseppe Casalino, Michelangelo Mortello, Andrea Angelastro, Antonio Domenico Ludovico, Microstructural Characteristics and Mechanical Properties of Ti6Al4V Alloy Fiber Laser Welds