## README.md This archive contains all relevant simulation data for the following publication: > M. Heinrich, B. Voisiat, A.F. Lasagni, R. Schwarze > Numerical simulation of periodic surface structures created by direct laser interference patterning > PLOS One (2023) ### Abstract of the Publication Surface structuring using nano-second lasers can be used to enhance certain properties of a material or even to introduce new ones. One way to create these structures efficiently is direct laser interference patterning using different polarization vector orientations of the interfering beams. However, experimentally measuring the fabrication process of these structures is very challenging due to small length and time scales. Therefore, a numerical model is developed and presented for resolving the physical effects during formation the predicting the resolidified surface structures. This three-dimensional, compressible computational fluid dynamics model considers the gas, liquid, and solid material phase and includes various physical effects, such as heating due to the laser beam for both parallel and radial polarization vector orientations, melting, solidification, and evaporation, Marangoni convection, and volumetric expansion. The numerical results reveal a very good qualitatively and quantitatively agreement with experimental reference data. Resolidified surface structures match both in overall shape as well as crater diameter and height, respectively. Furthermore, this model gives valuable insight on different quantities during the formation of these surface structures, such as velocity and temperature. In future, this model can be used to predict surface structures based on various process input parameters. ### Structure of the Archive The archive is structured as follows: - The raw data of all simulations is stored in the folder `1_Simulations`. This folder itself contains one folder for each simulation case with the following nomencalture: - `_Fluence_Jcm2`, where - `Laser_Orientation` denotes the laser polarisation orientation and can be either `Parallel` or `Radial` - `Laser Fluence` stands for the laser fluence in Joule / cm² depending on the case, either `2.1`, `2.9`, or `4.2` for parallel polarisation orientation, and `2.4`, `3.5`, `4.8`, or `6.3` for radial polarisation orientation. - Since all simulations were performed with `OpenFOAM`, the folder structure for each case is identical to a typical `OpenFOAM` simulation case: - `0` stores all initial and boundary conditions of the case - `` holds all field variables for a given time step - `constant` stores all information regaring the mesh in `constant/polyMesh` as well as material properties for gas/liquid, phase transfer and turbulent properties. - `system` finally contains all settings for the numerical model, such as discretization schemes (`fvSchemes`), solver settings (`fvSolution`), laser heat source and solidification/melting source (`fvOptions`), and time stepping settings (`controlDict`). - The extracted data from all simulations is stored in the folder `2_extracted_data` with the same nomenclature as in `1_Simulations`. This includes surfaces in VTK format for different time steps of the fields common velocity of gas and liquid phase, common temperature of gas and liquid phase, liquid phase fraction, and solid phase fraction: - Cut-plane through `(0 0 0)` in x normal direction - Cut-plane through `(0 0 0)` in y normal direction - Iso-surfaces of the liquid surface field at `alpha.liquid = 0.5` - The folder `3_Figures` contains raw data of figures in the given publication. The subsequent folder is named according to the figure number and its content in the publication, specifically: - `Figure_12_Structure_Height`: Data of structure height of the simulation with radial polarisation orientation for both simulation and experiment, the latter extracted from: > Bogdan V., Zwahr C., Lasagni A.F. > Growth of regular micro-pillar arrays on steel by polarization-controlled laser interference patterning > Aplied Surface Science, Vol. 471, 2019, pp. 1065--1071 ### General Information The simulations were performed with [OpenFOAM v2206](http://www.openfoam.com). The solver is based on `compressibleInterIsoFoam` and extended for: - volumetric laser heat source with parallel or radial polarisation orientation - phase transfer due to evaporation of liquid phase including volumetric expansion - melting and solidification of solid phase - Marangoni convection The source code of the solver is not publicly available. However, the individual numerical models for all simulations are presented in detail in the previously mentioned publication and all relevant numerical settings can be found in this archive. In order to postprocess the raw data, it is not necessary to install `OpenFOAM`. The data can easily be accessed and visualized using the free post-processing software `ParaView`. > ***Note:*** Since the computational mesh is the same for each simulation, it is only stored once in the case `1_Simulations/Parallel_Fluence_2.1Jcm2`. For each other case, a symbolic link is used to reference to the `constant/polyMesh` folder inside of `Parallel_Fluence_2.1Jcm2`. ### Nomenclature The field variables solved with OpenFOAM throughout the simulations are as follows: Variable | Description | Unit -------- | -------- | -------- `U` | Common velocity field of gas and liquid phase | m/s `T` | Common temperature field of gas and liquid phase | K `p_rgh` | Common pressure field of gas and liquid phase | Pa `rho` | Common density field of gas and liquid phase | kg/m³ `massSource` | Mass evaporation source for pressure equation | kg/(m³ s) `alpha.liquid` | Gas-liquid phase fraction | - `alpha.liquid.solid` | Liquid-solid phase fraction | -