Matthias Markl

Simulating fast electron beam melting with a parallel thermal free surface lattice Boltzmann method

This paper introduces a three dimensional (3D) thermal lattice Boltzmann method for the simulation of electron beam melting processes. The multi-distribution approach incorporates a state-of-the-art volume of fluid free surface method to handle the complex interaction between gas, liquid, and solid phases. The paper provides a detailed explanation of the modeling of the electron beam gun properties, such as the absorption rate and the energy dissipation. Additionally, an algorithm for the construction of a realistic powder bed is discussed. Special emphasis is placed to a parallel, optimized implementation due to the high computational costs of 3D simulations. Finally, a thorough validation of the heat equation and the solid-liquid phase transition demonstrates the capability of the approach to considerably improve the electron beam melting process.

Numerical investigations on hatching process strategies for powder-bed-based additive manufacturing using an electron beam

This paper investigates in hatching process strategies for additive manufacturing using an electron beam by numerical simulations. The underlying physical model and the corresponding three-dimensional thermal free-surface lattice Boltzmann method of the simulation software are briefly presented. The simulation software has already been validated on the basis of experiments up to 1.2kW beam power by hatching a cuboid with a basic process strategy, whereby the results are classified into porous, good, and uneven, depending on their relative density and top surface smoothness. In this paper, we study the limitations of this basic process strategy in terms of higher beam powers and scan velocities to exploit the future potential of high power electron beam guns up to 10kW. Subsequently, we introduce modified process strategies, which circumvent these restrictions, to build the part as fast as possible under the restriction of a fully dense part with a smooth top surface. These process strategies are suitable to reduce the build time and costs, maximize the beam power usage, and therefore use the potential of high power electron beam guns.

Electron Beam Absorption Algorithms for Electron Beam Melting Processes Simulated by a Three-Dimensional Thermal Free Surface Lattice Boltzmann Method in a Distributed and Parallel Environment☆

Abstract This paper introduces two electron beam absorption algorithms for a three–dimensional thermal free surface lattice Boltzmann method simulating electron beam melting processes. The algorithms use a state-of-the-art volume of fluid free surface method of the lattice Boltzmann multi–distribution approach to handle the interaction between the electron beam and the material. Modeling the electron beam gun properties, such as absorption and energy dissipation, is explained in detail. Special emphasis is given to an implementation in a distributed and parallel environment due to the high computational costs of three–dimensional simulations. Finally, a thorough validation for the beam absorption behavior against the analytical solution is proceeded and a concluding example in a powder bed shows the capability of the approach to simulate and support understanding the electron beam melting process.

Validation experiments for LBM simulations of electron beam melting

This paper validates three-dimensional (3D) simulation results of electron beam melting (EBM) processes by comparing experimental and numerical data. The physical setup is presented which is discretized by a 3D thermal lattice Boltzmann method (LBM). An experimental process window is used for the validation depending on the line energy injected into the metal powder bed and the scan velocity of the electron beam. In the process window, the EBM products are classified into the categories, porous, good and swelling, depending on the quality of the surface. The same parameter sets are used to generate a numerical process window. A comparison of numerical and experimental process windows shows a good agreement. This validates the EBM model and justifies simulations for future improvements of the EBM processes. In particular, numerical simulations can be used to explain future process window scenarios and find the best parameter set for a good surface quality and dense products.

Predictive Simulation of Process Windows for Powder Bed Fusion Additive Manufacturing: Influence of the Powder Bulk Density

The resulting properties of parts fabricated by powder bed fusion additive manufacturing processes are determined by their porosity, local composition, and microstructure. The objective of this work is to examine the influence of the stochastic powder bed on the process window for dense parts by means of numerical simulation. The investigations demonstrate the unique capability of simulating macroscopic domains in the range of millimeters with a mesoscopic approach, which resolves the powder bed and the hydrodynamics of the melt pool. A simulated process window reveals the influence of the stochastic powder layer. The numerical results are verified with an experimental process window for selective electron beam-melted Ti-6Al-4V. Furthermore, the influence of the powder bulk density is investigated numerically. The simulations predict an increase in porosity and surface roughness for samples produced with lower powder bulk densities. Due to its higher probability for unfavorable powder arrangements, the process stability is also decreased. This shrinks the actual parameter range in a process window for producing dense parts.

Free surface Neumann boundary condition for the advection-diffusion lattice Boltzmann method

The main objective of this paper is the derivation and validation of a free surface Neumann boundary condition for the advection-diffusion lattice Boltzmann method. Most literature boundary conditions are applied on straight walls and sometimes on curved geometries or fixed free surfaces, but dynamic free surfaces, especially with fluid motion in normal direction, are hardly addressed. A Chapman-Enskog Expansion is the basis for the derivation of the advection-diffusion equation using the advection-diffusion lattice Boltzmann method and the BGK collision operator. For this numerical scheme, a free surface Neumann boundary condition with no flux in normal direction to the free surface is derived. Finally, the boundary condition is validated in different static and dynamic test scenarios, including a detailed view on the conservation of the diffusive scalar, the normal and tangential flux components to the free surface and the accuracy. The validation scenarios reveal the superiority of the new approach to the compared literature schemes, especially for arbitrary fluid motion.

A Python extension for the massively parallel multiphysics simulation framework waLBerla

We present a Python extension to the massively parallel HPC simulation toolkit waLBerla. waLBerla is a framework for stencil based algorithms operating on block-structured grids, with the main application field being fluid simulations in complex geometries using the lattice Boltzmann method. Careful performance engineering results in excellent node performance and good scalability to over 400,000 cores. To increase the usability and flexibility of the framework, a Python interface was developed. Python extensions are used at all stages of the simulation pipeline: they simplify and automate scenario setup, evaluation, and plotting. We show how our Python interface outperforms the existing text-file-based configuration mechanism, providing features like automatic nondimensionalization of physical quantities and handling of complex parameter dependencies. Furthermore, Python is used to process and evaluate results while the simulation is running, leading to smaller output files and the possibility to adjust parameters dependent on the current simulation state. C++ data structures are exported such that a seamless interfacing to other numerical Python libraries is possible. The expressive power of Python and the performance of C++ make development of efficient code with low time effort possible.

Development of Single-Crystal Ni-Base Superalloys Based on Multi-criteria Numerical Optimization and Efficient Use of Refractory Elements

The development of new Ni-base superalloys with a complex composition consisting of eight or more alloying elements is a challenging task. The experimental state-of-the-art development cycle is based on the adaption of already existing compositions. Although new alloy compositions with potentially improved material properties are expected to be similar to already known superalloys, this procedure impedes efficiently finding these compositions in the large multi-dimensional design-space of all alloying elements. Modern alloy development combines numerical optimization methods with experimental validation to guide the development towards promising compositions. In this work, an improved numerical multi-criteria optimization tool using CALPHAD calculations and semi-empirical models for alloy development is presented. The model improvements to its predecessor are described and the successful application for the development of rhenium-free single-crystal Ni-base superalloys ERBO/13 and ERBO/15 is revisited. The optimization tool is described and the designed alloys are discussed regarding phase stability. Finally, a possible phase stability model extending the optimization tool and improving the alloy composition predictions is presented.