Free Surface Lattice Boltzmann Method Research Articles

Volume of fluid based modeling of thermocapillary flow applied to a free surface lattice Boltzmann method

Thermocapillary flow, also termed as thermal Marangoni convection, is an important material transport mechanism in many technical processes. Thus, it has to be considered in the corresponding simulations. In this work, a novel numerical model for the implementation of thermocapillary flow into a volume of fluid based free surface lattice Boltzmann method is presented. It is based on the idea of discretizing the surface normal vector in accordance to the discretization scheme of the velocity space. This approach is used to interpolate the temperature at the surface and to calculate the local surface gradients.The result is a simple and efficient numerical model, which is able to calculate the Marangoni stress along a liquid surface with sufficient accuracy and without the need to explicitly reconstruct the interface. We show that the Marangoni stress can readily be incorporated into a free surface lattice Boltzmann model by adjusting the boundary condition at the surface. In doing so, no additional forcing scheme has to be applied.In order to verify the presented model, it is tested using several simulation setups. As the lattice Boltzmann method is particularly suitable for complex geometries, a special attention is paid to the behavior at curved surfaces. Additionally, a simple test case for thermocapillary flow that can be regarded as a modified version of the Couette flow problem, is presented.

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.

Analysis and comparison of boundary condition variants in the free‐surface lattice Boltzmann method

AbstractThe accuracy of the free‐surface lattice Boltzmann method (FSLBM) depends significantly on the boundary condition employed at the free interface. Ideally, the chosen boundary condition balances the forces exerted by the liquid and gas pressure. Different variants of the same boundary condition are possible, depending on the number and choice of the particle distribution functions (PDFs) to which it is applied. This study analyzes and compares four variants, in which (i) the boundary condition is applied to all PDFs oriented in the opposite direction of the free interface's normal vector, including or (ii) excluding the central PDF. While these variants overwrite existing information, the boundary condition can also be applied (iii) to only missing PDFs without dropping available data or (iv) to only missing PDFs but at least three PDFs as suggested in the literature. It is shown that neither variant generally balances the forces exerted by the liquid and gas pressure at the free surface. The four variants' accuracy was compared in five different numerical experiments covering various applications. These include a standing gravity wave, a rectangular and cylindrical dam break, a rising Taylor bubble, and a droplet impacting a thin pool of liquid. Overall, variant (iii) was substantially more accurate than the other variants in the numerical experiments performed in this study.

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.

Comparison of Free Surface and Conservative Allen-Cahn Phase Field Lattice Boltzmann Method

Comparison of Free Surface and Conservative Allen-Cahn Phase Field Lattice Boltzmann Method

Multiple-relaxation-time lattice Boltzmann method for three dimensional free-surface flows with multi-bubble model

Flow with bubbles is a commonly occurring phenomenon in nature and industrial applications. This study provides a multi-bubble model for the free surface lattice Boltzmann method (FSLBM) which can be used to simulate fluid flow with bubbles as well as their splitting and merging processes. FSLBM neglects the flow of gas and considers only the gas pressure, and thus simplifies the gas-liquid two-phase flow to a single-phase free surface. The compression of the bubble will influence its pressure and lead to movement, splitting, or merging processes within the bubble flow. The multi-bubble model considers the evolution of bubble's pressure by enhancing the model for free surface which simulates the behavior of gas-liquid interface inside the liquid. The Smagorinsky subgrid-scale model (SGS) and the more advanced multiple-relaxation-time (MRT) collision model is used for high Reynolds number. In this study, a bubble algorithm to handle the bubble splitting and merging without incurring significant computational costs is provided. The verification and analysis of this model are given by a comparison between both analytical solution and an experiment. Therefore, the multi-bubble as an extension of FSLBM can be used to solve a wider range of two-phase flow problems more efficiently, such as bubble formation, metal foaming process, and development in chemical reactors.

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.

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.

Direct simulation of liquid–gas–solid flow with a free surface lattice Boltzmann method

ABSTRACTDirect numerical simulation of liquid–gas–solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary – in particular, if the bubble–particle aspect ratio is on the order of 10 or larger. Hence, it arises the question of both feasibility and reasonability. In this paper, we present a fully parallel, scalable method for direct numerical simulation of bubble–particle interaction at a size ratio of 1–2 orders of magnitude that makes simulations feasible on currently available super-computing resources. With the presented approach, simulations of bubbles in suspension columns consisting of more than 100,000 fully resolved particles become possible. Furthermore, we demonstrate the significance of particle-resolved simulations by comparison to previous unresolved solutions. The results indicate that fully resolved direct numerical simulation is indeed necessary to predict the flow structure of bubble–particle interaction problems correctly.

A multi-component evaporation model for beam melting processes

In additive manufacturing using laser or electron beam melting technologies, evaporation losses and changes in chemical composition are known issues when processing alloys with volatile elements. In this paper, a recently described numerical model based on a two-dimensional free surface lattice Boltzmann method is further developed to incorporate the effects of multi-component evaporation. The model takes into account the local melt pool composition during heating and fusion of metal powder. For validation, the titanium alloy Ti–6Al–4V is melted by selective electron beam melting and analysed using mass loss measurements and high-resolution microprobe imaging. Numerically determined evaporation losses and spatial distributions of aluminium compare well with experimental data. Predictions of the melt pool formation in bulk samples provide insight into the competition between the loss of volatile alloying elements from the irradiated surface and their advective redistribution within the molten region.

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.

Evaporation model for beam based additive manufacturing using free surface lattice Boltzmann methods

Evaporation plays an important role in many technical applications including beam-based additive manufacturing processes, such as selective electron beam or selective laser melting (SEBM/SLM). In this paper, we describe an evaporation model which we employ within the framework of a two-dimensional free surface lattice Boltzmann method. With this method, we solve the hydrodynamics as well as thermodynamics of the molten material taking into account the mass and energy losses due to evaporation and the recoil pressure acting on the melt pool. Validation of the numerical model is performed by measuring maximum melt depths and evaporative losses in samples of pure titanium and Ti–6Al–4V molten by an electron beam. Finally, the model is applied to create processing maps for an SEBM process. The results predict that the penetration depth of the electron beam, which is a function of the acceleration voltage, has a significant influence on evaporation effects.

Free surface lattice Boltzmann with enhanced bubble model

This paper presents an enhancement to the free surface lattice Boltzmann method (FSLBM) for the simulation of bubbly flows including rupture and breakup of bubbles. The FSLBM uses a volume of fluid approach to reduce the problem of a liquid–gas two-phase flow to a single-phase free surface simulation. In bubbly flows compression effects leading to an increase or decrease of pressure in the suspended bubbles cannot be neglected. Therefore, the free surface simulation is augmented by a bubble model that supplies the missing information by tracking the topological changes of the free surface in the flow. The new model presented here is capable of handling the effects of bubble breakup and coalesce without causing a significant computational overhead. Thus, the enhanced bubble model extends the applicability of the FSLBM to a new range of practically relevant problems, like bubble formation and development in chemical reactors or foaming processes.

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.

Verification of surface tension in the parallel free surface lattice Boltzmann method in waLBerla

The free surface lattice Boltzmann method in the parallel software framework waLBerla solves a wide range of two-phase flow scenarios efficiently by neglecting the gas flow and only taking the gas pressure into account. To obtain a good parallel efficiency, an extensive algorithm computes the curvature needed to calculate the surface tension pressure by using only a restricted set of neighboring data, reducing the communication effort. This, however, is assumed to be the main limitation of the accuracy of the surface tension computation. Nevertheless, this work shows that this method is able to simulate typical two-phase applications accurately enough. It is validated by comparing the evolution of capillary waves to analytical solution, and checking the agreement of a rising bubble’s velocity with experiments. The results show that the method differs less than 10% from theory in the micro-scale, and lies well within the confidence interval of experimental measurements.

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.