Free-surface Lattice Boltzmann Research Articles

Lattice Boltzmann modeling of convective heat and solute transfer in additive manufacturing of multi-component alloys

Additive manufacturing (AM) is a remarkable breakthrough technology, allowing for the direct fabrication of three-dimensional components through the layer-by-layer stacking of materials. A novel free Surface lattice Boltzmann (LB) model is developed to simulate the heat and solute transfer in AM of multi-component alloys. The behavior liquid phase is described by using the free surface LB model, and the phase transitions between solid and liquid are modeled by using the LB-enthalpy method. A LB equation is directly constructed, which accounts for solute transfer in a certain multi-component alloys system. The thermodynamic information used in the calculation of phase transitions are determined by an extensive thermodynamic database. The model is validated via several benchmark examples of fluid flow and heat transfer. The characteristics of convective heat and solute transfer within various AM are investigated. Finally, the non-equilibrium convective heat transfer, phase transitions, and macroscopic segregation are discussed within the AM melt pools. The melt pool expands and convective heat transfer is enhanced by the Marangoni effect. Thus there is a consistent decrease in solute segregation. The solute segregation is more severe near the surface of the deposit layer. Additionally, the thermal convection experiences cyclic intensification attributed to the successive impact of multiple droplets in wire feeding and melting AM. This continuous impact serves to diminish the solute segregation. The results underscore the significant potential and advantages of LB method in accurately simulating the AM, which provides valuable insights for understanding the underlying mechanism of heat and solute transfer in materials and manufacturing.

A new approach to aircraft ditching analysis by coupling free surface lattice Boltzmann and immersed boundary method incorporating surface tension effects

This study primarily addresses the phenomenon of aircraft ditching. This phenomenon presentspresenting a significant challenge for numerical simulations due to its highly nonlinear and multiphase-coupled water entry impact problem involving fluid-structure interaction. Traditional numerical methods have difficulties and deficiencies in free surface evolution and accuracy. An improved iterative velocity correction scheme has been presented by coupling the single-phase free surface-lattice Boltzmann method (FS-LBM) based on the volume of fluid method with the immersed boundary (IB) method to simulate water entry impact issues. Notably, this model incorporates the effect of surface tension, enhancing its ability to accurately simulate various phenomena, such as rolling, breaking, splashing, and fusion with the free surface in gas-liquid-solid multi-physical field conditions. Through the correction of the boundary force of the interface lattice and the gas lattice and the improved scheme, the non-slip boundary is satisfied, and the particle penetration is prevented. Furthermore, several benchmark tests have been conducted to verify the rationality and feasibility of the FS-LBM-IB method in simulating aircraft ditching. A scaled model of an aircraft has been developed to investigate the dynamic response characteristics of aircraft ditching at a specific attitude angle, with the simulation results confirming the accuracy of the FS-LBM-IB method in predicting the secondary head-up of the aircraft under suction force. This research highlights the efficiency of the FS-LBM-IB method as a novel approach for simulating aircraft ditching behavior.

Comparison of free-surface and conservative Allen–Cahn phase-field lattice Boltzmann method

This study compares the free-surface lattice Boltzmann method (FSLBM) with the conservative Allen–Cahn phase-field lattice Boltzmann method (PFLBM) in their ability to model two-phase flows in which the behavior of the system is dominated by the heavy phase. Both models are introduced and their individual properties, strengths and weaknesses are thoroughly discussed. Six numerical benchmark cases were simulated with both models, including (i) a standing gravity and (ii) capillary wave, (iii) an unconfined rising gas bubble in liquid, (iv) a Taylor bubble in a cylindrical tube, and (v) the vertical and (vi) oblique impact of a drop into a pool of liquid. Comparing the simulation results with either analytical models or experimental data from the literature, four major observations were made. Firstly, the PFLBM selected was able to simulate flows purely governed by surface tension with reasonable accuracy. Secondly, the FSLBM, a sharp interface model, generally requires a lower resolution than the PFLBM, a diffuse interface model. However, in the limit case of a standing wave, this was not observed. Thirdly, in simulations of a bubble moving in a liquid, the FSLBM accurately predicted the bubble's shape and rise velocity with low computational resolution. Finally, the PFLBM's accuracy is found to be sensitive to the choice of the model's mobility parameter and interface width.

Comparison of refilling schemes in the free-surface lattice Boltzmann method

Simulating mobile liquid–gas interfaces with the free-surface lattice Boltzmann method (FSLBM) requires frequent re-initialization of fluid flow information in computational cells that convert from gas to liquid. The corresponding algorithm, here referred to as the refilling scheme, is crucial for the successful application of the FSLBM in terms of accuracy and numerical stability. This study compares five refilling schemes that extract information from the surrounding liquid and interface cells by averaging, extrapolating, or assuming one of the three different equilibrium states. Six numerical experiments were performed, covering a broad spectrum of possible scenarios. These include a standing gravity wave, a rectangular and cylindrical dam break, a Taylor bubble, a drop impact into liquid, and a bubbly plane Poiseuille flow. In some simulations, the averaging, extrapolation, and one equilibrium-based scheme were numerically unstable. Overall, the results have shown that the simplest equilibrium-based scheme should be preferred in terms of numerical stability, computational cost, accuracy, and ease of implementation.

LBfoam: An open-source software package for the simulation of foaming using the Lattice Boltzmann Method

This paper presents a 2D/3D Free Surface Lattice Boltzmann Method simulation package called LBfoam for the simulation of foaming processes. The model incorporates the essential physics of foaming phenomena: gas diffusion into nucleated bubbles, bubble dynamics and coalescence, surface tension, the stabilizing disjoining pressure between bubbles, and Newtonian and non-Newtonian rheological models. The software can simulate the growth and interaction of bubbles, and predict final foam structures. The implementation is based on the Palabos library (in C++), which enables large-scale parallel simulations. The software is freely available under the GNU Affero General Public License version 3. Program summaryProgram title:LBfoamCPC Library link to program files:https://doi.org/10.17632/zgxfx6xk4t.1Developer’s repository link:https://github.com/mehdiataei/LBfoamCode Ocean capsule:https://codeocean.com/capsule/8471850Licensing provisions: Affero General Public License (AGPL) v3Programming language: C++Nature of problem: Foaming is a process by which nucleated gas bubbles expand in liquid media such as a molten polymer or a liquid metal to create a cellular structure, which has many applications in industries such as automotive, aerospace, furniture and packaging. This comprehensive simulation model for foaming allows industry to determine optimum foaming conditions more quickly and more accurately, while providing a platform for researchers to study phenomena observed in foaming.Solution method: LBfoam implements a 2D/3D Free Surface Lattice Boltzmann Method (FSLBM) solver that can simulate various foaming phenomena. The model couples the Navier–Stokes and the advection–diffusion equations, and incorporates all essential aspects of foaming such as the growth and interaction of bubbles. All routines are written in C++ and are parallelized using the Message Passing Interface (MPI) library.

A numerical model coupling bubble flow, light transfer, cell motion and growth kinetics for real timescale microalgae cultivation and its applications in flat plate photobioreactors

A comprehensive numerical model based on volume-of-fluid (VOF) is established in this paper for the simulation of multiphysical process of the microalgae cultivation in photobioreactors (PBRs). The comprehensive numerical model is composed of the following four models: (1) a free-surface lattice Boltzmann model for VOF simulations of bubble flow, (2) a discrete ordinate model for collimated light transfer, (3) a Lagrangian model for cell motion, and (4) a kinetic model for microalgae growth. A temporal extrapolation scheme is proposed first to extend the simulation in small time steps into the real timescale. The growths of microalgae in a two-dimensional flat plat PBR are then simulated by the model. The effects of the gas hold-up, bubble distribution, light intensity and light/dark history on the growth of microalgae are further studied in detail. The result showed that the average growth rate can be adopted for the whole PBR. The non-uniform distribution of bubbles attenuates the positive effects of bubbles on increasing light intensity inside the PBRs. Meanwhile, the simulation with the average flow field without fluctuations can lead to non-uniform distributions of cells and errors in prediction the microalgae growth due to the centrifugal effects. The residence time distribution (RTD) of cells in the PBR is almost uniform under the condition studied, and the simulation results with RTD are close to the results with cell tracking. Finally, an improved structure of flat plat PBRs with horizontal deflectors is proposed. The results demonstrated that the inserted deflectors can increase the gas hold-ups and the uniformity of gas distributions. These effects lead to higher light intensity in the PBR, which increases the growth rate of the microalgae.

Three-Dimensional Numerical Method for Simulating Large-Scale Free Water Surface by Massive Parallel Computing on a GPU

Water wave dynamics and its engineering application have always been a key issue in the field of hydraulics, and effective and efficient numerical methods need to be proposed to perform three-dimensional (3-D) simulation of large-scale water fluctuation in engineering practice. A single-phase free-surface lattice Boltzmann method (SPFS-LB method) is coupled with a large-eddy simulation approach for simulating large-scale free water surface flows, and the simulation is accelerated on a GPU (graphic processing unit). The coupling model is used to simulate the evolution process of dam-break wave after complete and partial dam-break. The formation mechanism of horizontal and vertical vortices in water after partial dam-break and the advance and evolution process of dam-break flow on non-contour riverbed are analyzed. The method has been verified to be reasonable and can obtain a more accurate time curve of water level fluctuation. Applying this method to practical arch dams, discharge coefficients consistent with empirical formulas can be obtained by comparison and analysis, and the surface flow phenomena (such as tongue diffusion, surface fragmentation, and surface fusion) can be well simulated by this method. In addition, based on the key technology of parallel computing on a GPU, the implementation of the SPFS-LB model on a GPU unit achieves tens of millions of lattice updates per second, which is over fifty times higher than that on a single CPU chip. It is proved that the proposed method for large-scale water fluctuations can be used to study practical engineering problems. The mathematical model method realizes the efficient and accurate simulation of practical physical problems.

Modeling of capillary-driven flows in axisymmetric geometries

We present an analytical approach, as well as computer simulations based on the free surface lattice-Boltzmann (FSLB) method, in order to model capillary-driven infiltration of liquids into porous structures. The analytical method is an extension of the Lucas-Washburn (LW) equation and applies to axisymmetric geometries with a circular cross-section. The treatment of irregular capillaries is achieved by a discretization procedure in which the original geometry is divided into small cylinders. In order to validate the derived analytical equation, we perform FSLB simulations in test geometries which show a good agreement.

LBM-LES Simulation of the Transient Asymmetric Flow and Free Surface Fluctuations under Steady Operating Conditions of Slab Continuous Casting Process

Transient flow structures in a continuous casting mold can strongly influence the slag entrainment in liquid steel and the bubbles capture in the initial solidified shell, both of which are associated with the quality of the final product. This paper presents a numerical study of the turbulent flow with a top free surface in the continuous casting mold at a meso-scale level by a three-dimensional combined approach of Free Surface Lattice Boltzmann Method and Large Eddy Simulation (FSLBM-LES). The validity of the model is verified by the good agreement between the calculated results and the measurements from various water experiments in terms of the flow velocity and free surface profile. The mathematical model is then used to reveal the transient and spatiotemporal asymmetric characteristics associated with the transient flow field and the free surface fluctuation, although the steady state operation is considered during the continuous casting process. The results show that the locations of the jets of liquid steel from the two out ports of the Submerged Entry Nozzle (SEN) always fluctuate alternatively within a certain range, and periodically deviate from the design angle of the SEN within the same time period. The oscillating behavior of the jets promotes the asymmetric flow patterns and multi-scale vortices at both sides of the SEN. By introducing the Q-criterion in the results analysis, the formation, development, and shedding of the coherent structure (CS) of the turbulent flow are quantitatively characterized. The interaction between the transient flow patterns and the fluctuations of the top free surface as well as the evolution of the transient profile and velocities of the free surface are also demonstrated. The results obtained from the current study suggest that the FSLBM-LES model offers a promising way to study the complex flows and related transfer phenomena in the continuous casting process.

Curvature estimation from a volume-of-fluid indicator function for the simulation of surface tension and wetting with a free-surface lattice Boltzmann method.

The free surface lattice Boltzmann method (FSLBM) is a combination of the hydrodynamic lattice Boltzmann method with a volume-of-fluid (VOF) interface capturing technique for the simulation of incompressible free surface flows. Capillary effects are modeled by extracting the curvature of the interface from the VOF indicator function and imposing a pressure jump at the free boundary. However, obtaining accurate curvature estimates from a VOF description can introduce significant errors. This article reports numerical results for three different surface tension models in standard test cases and compares the according errors in the velocity field (spurious currents). Furthermore, the FSLBM is shown to be suited to simulate wetting effects at solid boundaries. To this end, a new method is developed to represent wetting boundary conditions in a least-squares curvature reconstruction technique. The main limitations of the current FSLBM are analyzed and are found to be caused by its simplified advection scheme. Possible improvements are suggested.

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.

An Improved Single-Phase Free-Surface Lattice Boltzmann Model with Surface Tension and Wall Adhesion

Free-surface model with surface tension and wall adhesion(wetting) is a very efficient technique to simulate two-phase flows with high density and viscosity ratios, such as etching and casting processes. In this paper, a conservative surface tension and wall adhesion model based on lattice Boltzmann single-phase free-surface method is proposed. The effectiveness of the model is demonstrated by simulating the flows induced by wall adhesion and surface tension, and filling processes in a 2D cavity.

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

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.

MODELING OF IRRIGATION CHANNELS — A COMPARATIVE STUDY

A free surface Lattice Boltzmann (LB) model – based on a two-fluid system – is considered to simulate the flow of water in an irrigation canal. We compare the behavior of our numerical simulations with simple experiments and theoretical results obtained from the Saint-Venant equation, the partial differential equation commonly used to describe water flow in irrigation canals. The case study we consider are (1) the height of water along the canal in a stationary regime and (2) a draining experiment. The comparisons show that the two-fluid LB approach captures correctly the draining speed and the qualitative water profile.

A free-surface lattice Boltzmann method for modelling the filling of expanding cavities by Bingham fluids

The filling process of viscoplastic metal alloys and plastics in expanding cavities is modelled using the lattice Boltzmann method in two and three dimensions. These models combine the regularized Bingham model for viscoplastic fluids with a free-interface algorithm. The latter is based on a modified immiscible lattice Boltzmann model in which one species is the fluid and the other one is considered to be a vacuum. The boundary conditions at the curved liquid-vacuum interface are met without any geometrical front reconstruction from a first-order Chapman-Enskog expansion. The numerical results obtained with these models are found in good agreement with available theoretical and numerical analysis.