Three-dimensional Multiphase Flow Research Articles

Industrial dry spinning processes: algorithmic for a two-phase fiber model in airflows

The dry spinning of fibers can be described by three-dimensional multi-phase flow models that contain key effects like solvent evaporation and fiber-air interaction. Since the direct numerical simulation of the three-dimensional models is in general not possible, dimensionally reduced models are deduced. We recently developed a one-two-dimensional fiber model and presented a problem-tailored numerical solution strategy in Wieland et al. (J Comput Phys 384:326–348, 2019). However, in view of industrial setups with multiple fibers spun simultaneously the numerical schemes must be accelerated to achieve feasible simulation times. The bottleneck builds the computation of the radial concentration and temperature profiles as well as their cross-sectionally averaged values. In this paper we address this issue and develop efficient numerical algorithms.

Optimizing pink-beam fast X-ray microtomography for multiphase flow in 3D porous media.

A fast pink-beam X-ray microtomography methodology was developed at the GSECARS 13-BMD beamline at the Advanced Photon Source to study multiphase flow in porous media. The white beam X-ray distribution of the Advanced Photon Source is modified using a 1-mm copper filter and the beam is reflected off a platinum mirror angled at 1.5 mrad, resulting in a pink beam with X-ray intensities predominately in the range of 40-60 keV. Bubble formation in the wetting phase and wettability alteration of the solid phase from x-ray exposure can be a problem with high flux and high energy beams, but the suggested pink-beam configuration mitigates these effects. With a 14-second acquisition time for capturing a complete dataset, the evolving fluid-fronts of nonequilibrium three-dimensional multiphase flow can be studied in real-time and the images contain adequate image contrast and quality to measure important multiphase quantities such as contact angles and interfacial areas. LAY DESCRIPTION: Understanding how fluids are transported through porous materials is pertinent to many important societal processes in the environment (e.g. groundwater flow for drinking water) and industry (e.g. drying of industrial materials such as pulp and paper). To develop accurate models and theories of this fluid transportation, experiments need to track fluids in 3-dimensions quickly. This is difficult to do as most materials are opaque and therefore cameras cannot capture fluid movement directly. But, with the help of x-rays, scientists can track fluids in 3D using an imaging technique called x-ray microtomography (μCT). Standard μCT takes about 15 minutes for one image which can produce blurry images if fluids are flowing quickly through the material. We present a technique, fast μCT, which uses a larger spectrum of x-rays than the standard technique and acquires a 3D image in 14 seconds. With the large amount of x-rays utilized in this technique, bubbles can start to form in the fluids from x-ray exposure. We optimized the utilized x-ray spectrum to limit bubble formation while still achieving a rapid 3D image acquisition that has adequate image quality and contrast. With this technique, scientists can study fluid transport in 3D porous materials in near real-time for the improvement of models used to ensure public and environmental health.

A mass-conserved multiphase lattice Boltzmann method based on high-order difference**Project supported by the National Natural Science Foundation of China (Grant Nos. 11862003 and 81860635), the Key Project of the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2017GXNSFDA198038), the Project of Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2018GXNSFAA281302), the Project for Promotion

The Z–S–C multiphase lattice Boltzmann model [Zheng, Shu, and Chew (ZSC), J. Comput. Phys. 218, 353 (2006)] is favored due to its good stability, high efficiency, and large density ratio. However, in terms of mass conservation, this model is not satisfactory during the simulation computations. In this paper, a mass correction is introduced into the ZSC model to make up the mass leakage, while a high-order difference is used to calculate the gradient of the order parameter to improve the accuracy. To verify the improved model, several three-dimensional multiphase flow simulations are carried out, including a bubble in a stationary flow, the merging of two bubbles, and the bubble rising under buoyancy. The numerical simulations show that the results from the present model are in good agreement with those from previous experiments and simulations. The present model not only retains the good properties of the original ZSC model, but also achieves the mass conservation and higher accuracy.

Multiphase modelling of the transient flow for Sn-15Pb and 357.0 alloys in semi-solid die casting process

Abstract The transient flow behavior of the semi-solid slurries for Sn-15Pb and 357.0 alloys during die casting process is investigated by experimental and numerical methods. A model for the transient-state three-dimensional multiphase flow based on the kinetic theory of granular flow is developed. This model is applied to investigate the distribution of solid concentration, flow state, pressure variation of the semi-solid slurry in the die casting process. The three important aspects of the multiphase flow, flow regime, particle-particle interaction and particle-liquid interaction, are interpreted according to the characteristic of the system. The model is verified by partial filling and in-situ observation experiments. Then it is applied for the phase segregation study of an elbow cavity encountered in practice. Results indicate that the 3D multiphase model can depict the flow characteristics of the semi-solid slurry very well. The inner arc side of the elbow cavity is easier to have liquid phase segregation than the outer arc side for the lower velocity gradients of the solid and liquid phases.

A modified monotonicity-preserving high-order scheme with application to computation of multi-phase flows

The monotonicity preserving (MP) polynomial-based reconstruction scheme with Runge-Kutta time stepping by Suresh and Huynh (1997) has been applied extensively in computational fluid dynamics for solving hyperbolic partial differential equations and other convection-dominated problems. However, despite of its algorithmic simplicity in achieving a desired high-order of accuracy, the MP scheme is shown to lose the accuracy and robustness for a long-term computation of flows containing complex smooth structures interspersed with discontinuities. In this paper, the original MP scheme is first reviewed with a focus on the potential causes that lead to its failure. We then propose an improved MP scheme that can overcome the weakness in the MP scheme. The proposed MP scheme is constructed so that it can bypass smooth extrema without loss of accuracy while preserving monotonicity and properly reducing the order of accuracy near discontinuities. Various challenging scalar advection test cases are considered to demonstrate the performance of the presented method. Numerical results reveal that it achieves the highly accurate solutions in smooth parts of the flow and yields a significant improvement in accuracy and shape-preserving property. Moreover, the successful application to several classes of two- and three-dimensional unsteady multi-phase flows highlights the potential of the present method for resolving both sharp and complex interface deformations.

A guideline for appropriate application of vertically-integrated modeling approaches for geologic carbon storage modeling

Mathematical modeling is an essential tool for answering questions related to geologic carbon storage (GCS). The choice of modeling approach depends on the type of questions being asked. In this paper we discuss a series of approaches with a hierarchical complexity including vertically-integrated single-phase flow approaches, vertically-integrated multi-phase flow approaches (with and without vertical equilibrium assumption), three-dimensional multi-phase flow approaches, and fully-coupled multi-phase flow approaches that couple flow with geochemistry and/or geomechanics. Three spatial scales are used to categorize the questions to be addressed by modeling: regional scale (encompasses CO2 plume extent and majority of area of pressure impact of one or more injection operations), site scale (includes the CO2 plume extent and some of the area impacted by the pressure increase of a single injection site), and well scale (the immediate vicinity of an injection well). A set of guidelines is developed to help modelers choose the most appropriate modeling approach, and show when simpler modeling approaches may be the better choice. Vertically-integrated single-phase flow models are the most appropriate choice at both the site and regional scales, if the pressure impact outside of the CO2 plume is of interest. Vertically-integrated multi-phase flow models should be chosen at the regional scale, if the locations of CO2 plumes are of interest, and at the site scale if vertical segregation of CO2 and brine is fast or vertical heterogeneity in properties can be presented by distinct, continuous layers. Three-dimensional multi-phase flow models are the appropriate choice at the well and site scales for cases with significant vertical flow components of CO2 and brine. Fully-coupled multi-phase flow models should only be chosen if pore-space alteration through geochemistry or geomechanics feeds back to fluid flow.

Three-dimensional multiphase flow modeling of membrane humidifier for PEM fuel cell application

Purpose In this paper, a single module of cross-flow membrane humidifier is evaluated as a three-dimensional multiphase model. The purpose of this paper is to analyze the effect of volume flow rate, dry temperature, dew point wet temperature and porosity of gas diffusion layer on the humidifier performance.Design/methodology/approach In this study, one set of coupled equations are continuity, momentum, species and energy conservation is considered. The numerical code is benchmarked by the comparison of numerical results with experimental data of Hwang et al.Findings The results reveal that the transfer rate of water vapor and dew point approach temperature (DPAT) increase by increasing the volume flow rate. Also, it is found that the water recovery ratio (WRR) and relative humidity (RH) decrease with increasing volume flow rate. In addition, all mixed results decrease with increasing dry side temperature especially at high volume flow rates and this trend in high volume flow rates is more sensible. Although the transfer rate of water vapor and DPAT increases with increasing the wet inlet temperature, WRR and RH reduce. Increasing dew point temperature effect is more sensible at the wet side is compared with the dry side. The humidification performance will be enhanced with increasing diffusion layer porosity by increasing the wet inlet dew point temperature, but has no meaningful effect on other operating parameters. The pressure drop along humidifier gas channels increases with rising flow rate, consequently, the required power of membrane humidifier will enhance.Originality/value According to previous studies, the three-dimensional numerical multiphase model of cross-flow membrane humidifier has not been developed.

Fragmentation of cavitation bubble in ultrasound field under small pressure amplitude.

In the present study, dynamic behavior and fragmentation mechanism of acoustic cavitation bubbles are investigated under relatively small pressure amplitudes of ultrasonic wave through a three-dimensional compressive multiphase flow simulation and experimental observations. It is found that the oscillating bubble takes a non-spherical shape soon after occurring the Rayleigh collapse following the sound pressure distribution around the bubble. Then, the amplitude of non-spherical deformation is enhanced during small high-frequent oscillations after the Rayleigh collapse due to the fluid inertial effect. Finally, the oscillating bubble is fragmented into two smaller ones with the Laplace pressure gradient becoming the final trigger of bubble fragmentation. Besides, the results reveal that the temperature of bubble surface is varied when the non-spherical bubble deformation is large, while during spherical bubble oscillations the surface temperature remains almost unchanged.

Adaptive Cartesian cut-cell sharp interface method (aC3SIM) for three-dimensional multi-phase flows

A sharp interface method has been developed for treating interfacial discontinuities in compressible multi-phase fluids on three-dimensional Cartesian cut-cell grids. The evolution of the interfacial discontinuities in the Cartesian grid is captured by the level-set method. The intersections between interfacial fronts and Cartesian grids are interpolated using level-set function values at the vertices of Cartesian grids. Triangular surfaces are then constructed on the interfacial fronts. A novel cell merge method is used for complex topological changes. Jump conditions across discontinuous interfaces are enforced by reconstruction of interfacial flow variables using a constrained least-squares method. The inviscid flux across internal faces of the same fluid is calculated by the local Lax–Friedrichs flux. Manufactured solutions for interfaces are suggested for validation of the reconstruction method. Laplace’s law test results show that the present method drastically reduces the parasite currents compared to conventional interface treatment methods. Bubble rise problems also show the validity and accuracy of the proposed sharp interface method for immiscible two-phase fluids.

Three-dimensional modeling of coalescence of bubbles using Lattice Boltzmann model

The original Lattice Boltzmann method (LBM) based binary color model is modified to simulate three-dimensional buoyant multiphase flow. An effective force term is included during collision step in D3Q19 LBM to account for buoyancy force due to density contrast between fluid components. Buoyancy is not directly simulated as an effect of pressure gradients in the flow but was introduced from an analytical understanding of buoyancy effects due to density difference between the two phases. We are presenting results from three-dimensional numerical simulations to demonstrate the ability of the proposed approach to accurately predict the behavior of a single and multiple bubbles in a buoyant multiphase flow system. The effect of parameters such as grid size, viscosity ratio, surface tension, and interfacial thickness on the model accuracy are presented in this article. The shape and terminal velocity of bubbles in various flow regimes, characterized by the non-dimensional numbers (Eo, Mo, Re), are compared against experimental data and analytical model. The 3-D simulation results of Co-axial and oblique coalescence of a pair of bubbles from LBM simulations were found to be in good agreement with the experimental data.

Phase-locked confocal micro-PIV measurement for 3D flow structure of transient droplet formation mechanism in T-shaped microjunction

This paper aims to develop a phase-locked multicolor confocal micro-particle image velocimetry (PIV) technique to investigate the flow mechanism of microdroplet formation at a micro T-shaped micro junction. The object to be measured is a three-dimensional (3D) periodic multiphase flow with random disturbances, and this method is a solution for the 3D flow measurement of this complicated phenomenon. The phase-locking technique is needed to reconstruct the 3D flow field from the two-dimensional (2D) confocal micro-PIV measurement data. We successfully obtained each temporal phase of the periodic phenomenon noninvasively by detecting the passage of a droplet from the transmitted light of an optical proximity sensor. Then, the phase-locking technique also enabled us to select the same conditions of formation frequency, size, and translational velocity of droplets to minimize instability in the droplet formation phenomenon. The multicolor system can measure the dynamic behavior of each phase of a multiphase flow separately and simultaneously. As a result, the 3D flow structure of droplet formation was successfully reconstructed and investigated with high spatial and temporal resolution.

A generic algorithm for three-dimensional multiphase flows on unstructured meshes

Binary fluid flows distinguished by high-density ratio are of practical importance to many of the engineering applications. Numerical simulations of such flows having sharp discontinuities across the interface is a challenging task and may lead to the generation of spurious velocities if proper care is not taken during discretization. In this regard, we present a consistent and balanced–force algorithm for binary fluid flows with very large density ratios using algebraic volume of fluid technique over three-dimensional hybrid unstructured meshes using a collocated framework. The algorithm emphasizes on the proper force balancing needed at the discrete level and also on the importance of consistent numerical treatment of similar terms across the equations. The efficacy of the formulation is demonstrated through extensive numerical experiments involving strong surface tension and/or gravitational forces. The results clearly indicate the importance of enforcing discrete balance of forces and ensuring consistent treatment of mass and momentum for robust and accurate simulations of multiphase flows.

A hybrid interface tracking – level set technique for multiphase flow with soluble surfactant

A formulation for soluble surfactant transport in multiphase flows recently presented by Muradoglu and Tryggvason (JCP 274 (2014) 737–757) [17] is adapted to the context of the Level Contour Reconstruction Method, LCRM, (Shin et al. IJNMF 60 (2009) 753–778, [8]) which is a hybrid method that combines the advantages of the Front-tracking and Level Set methods. Particularly close attention is paid to the formulation and numerical implementation of the surface gradients of surfactant concentration and surface tension. Various benchmark tests are performed to demonstrate the accuracy of different elements of the algorithm. To verify surfactant mass conservation, values for surfactant diffusion along the interface are compared with the exact solution for the problem of uniform expansion of a sphere. The numerical implementation of the discontinuous boundary condition for the source term in the bulk concentration is compared with the approximate solution. Surface tension forces are tested for Marangoni drop translation. Our numerical results for drop deformation in simple shear are compared with experiments and results from previous simulations. All benchmarking tests compare well with existing data thus providing confidence that the adapted LCRM formulation for surfactant advection and diffusion is accurate and effective in three-dimensional multiphase flows with a structured mesh. We also demonstrate that this approach applies easily to massively parallel simulations.

Computation of three-dimensional multiphase flow dynamics by Fully-Coupled Immersed Flow (FCIF) solver

This work presents a Fully-Coupled Immersed Flow (FCIF) solver for the three-dimensional simulation of fluid–fluid interaction by coupling two distinct flow solvers using an Immersed Boundary (IB) method. The FCIF solver captures dynamic interactions between two fluids with disparate flow properties, while retaining the desirable simplicity of non-boundary-conforming grids. For illustration, we couple an IB-based unsteady Reynolds Averaged Navier Stokes (uRANS) simulator with a depth-integrated (long-wave) solver for the application of slug development with turbulent gas and laminar liquid. We perform a series of validations including turbulent/laminar flows over prescribed wavy boundaries and freely-evolving viscous fluids. These confirm the effectiveness and accuracy of both one-way and two-way coupling in the FCIF solver. Finally, we present a simulation example of the evolution from a stratified turbulent/laminar flow through the initiation of a slug that nearly bridges the channel. The results show both the interfacial wave dynamics excited by the turbulent gas forcing and the influence of the liquid on the gas turbulence. These results demonstrate that the FCIF solver effectively captures the essential physics of gas–liquid interaction and can serve as a useful tool for the mechanistic study of slug generation in two-phase gas/liquid flows in channels and pipes.

A solver for massively parallel direct numerical simulation of three-dimensional multiphase flows

We present a new solver for massively parallel simulations of fully three-dimensional multiphase flows. The solver runs on a variety of computer architectures from laptops to supercomputers and on 65536 threads or more (limited only by the availability to us of more threads). The code is wholly written by the authors in Fortran 2003 and uses a domain decomposition strategy for parallelization with MPI. The fluid interface solver is based on a parallel implementation of the LCRM hybrid Front Tracking/Level Set method designed to handle highly deforming interfaces with complex topology changes. We discuss the implementation of this interface method and its particular suitability to distributed processing where all operations are carried out locally on distributed subdomains. We have developed parallel GMRES and Multigrid iterative solvers suited to the linear systems arising from the implicit solution of the fluid velocities and pressure in the presence of strong density and viscosity discontinuities across fluid phases. Particular attention is drawn to the details and performance of the parallel Multigrid solver. The code includes modules for flow interaction with immersed solid objects, contact line dynamics, species and thermal transport with phase change. Here, however, we focus on the simulation of the canonical problem of drop splash onto a liquid film and report on the parallel performance of the code on varying numbers of threads. The 3D simulations were run on mesh resolutions up to $1024^3$ with results at the higher resolutions showing the fine details and features of droplet ejection, crown formation and rim instability observed under similar experimental conditions. Keywords:

A two-way FSI analysis of multiphase flow in hydrodynamic journal bearing with cavitation

This work deals with a study of a three-dimensional CFD analysis and multi-phase flow phenomena for hydrodynamic journal bearing with integrated cavitation. The simulations are carried out considering the realistic bearing deformations by two-way fluid–structure interactions (FSI) along with cavitation using ANSYS®Workbench software. The design optimization module is used to generate the optimized solution of the attitude angle and eccentricity for the combination of operating speed and load. Bearings with and without cavitation are investigated. A drop in maximum pressure value is observed when cavitation is considered in the bearing. The rise in oil vapor distribution is noted with an increase in shaft speed which lowers the magnitude of the pressure build up in the bearing. The bearing deformations are analyzed numerically and found increasing with an increase in shaft speed. The experimental data obtained for pressure distribution showed good agreement with numerical data along with a considerable reduction in computation time.

An efficient phase-field-based multiple-relaxation-time lattice Boltzmann model for three-dimensional multiphase flows

In this paper, an efficient phase-field-based lattice Boltzmann (LB) model with multiple-relaxation-time (MRT) collision operator is developed for the simulation of three-dimensional multiphase flows. This model is an extension of our previous two-dimensional model (Liang et al., 2014) to the three dimensions using the D3Q7 (seven discrete velocities in three dimensions) lattice for the Cahn–Hilliard equation and the D3Q15 lattice for the Navier–Stokes equations. Due to the less lattice-velocity directions used, the computational efficiency can be significantly improved in the study of three-dimensional multiphase flows, and simultaneously the present model can recover the Cahn–Hilliard equation and the Navier–Stokes equations correctly through the Chapman–Enskog procedure. We compare the present MRT model with its single-relaxation-time version and the previous LB model by using two benchmark interface-tracking problems, and numerical results show that the present MRT model can achieve a significant improvement in the accuracy and stability of the interface capturing. The developed model can also be able to deal with multiphase fluids with high viscosity ratio, which is demonstrated by the simulation of the layered Poiseuille flow and Rayleigh–Taylor instability at various viscosity ratios. The numerical results are found to be in good agreement with the analytical solutions or some available results. In addition, it is also found that the instability induces a more complex structure of the interface at a low viscosity.

Three-dimensional multiphase flow computational fluid dynamics models for proton exchange membrane fuel cell: A theoretical development

A review of published three-dimensional, computational fluid dynamics models for proton exchange membrane fuel cells that accounts for multiphase flow is presented. The models can be categorized as models for transport phenomena, geometry or operating condition effects, and thermal effects. The influences of heat and water management on the fuel cell performance have been repeatedly addressed, and these still remain two central issues in proton exchange membrane fuel cell technology. The strengths and weaknesses of the models, the modelling assumptions, and the model validation are discussed. The salient numerical features of the models are examined, and an overview of the most commonly used computational fluid dynamic codes for the numerical modelling of proton exchange membrane fuel cells is given. Comprehensive three-dimensional multiphase flow computational fluid dynamic models accounting for the major transport phenomena inside a complete cell have been developed. However, it has been noted that more research is required to develop models that include among other things, the detailed composition and structure of the catalyst layers, the effects of water droplets movement in the gas flow channels, the consideration of phase change in both the anode and the cathode sides of the fuel cell, and dissolved water transport.

A computational study on gas–liquid flow in a lime slurry pond equipped with a rotary jet mixing system

The flue-gas desulfurization model was studied through computational fluid dynamics software. The oxidation air was asymmetrically pumped into the slurry pond. A rotary jet mixing system was established at the bottom center of the pond to agitate the lime slurry. The Navier–Stokes equation as the control equation, the standard k–ε turbulence model, sliding grids structure, and three-dimensional Eulerian multiphase flow of lime slurry were used for the numerical simulation. The independence of the meshes and the time step was verified. The distribution of the concentration of oxidation air and influents on the velocity of flow was analyzed with five angular velocities (0.01, 0.10, 0.20, 0.50, and 1 rad/s) for the rotary jet mixing. The simulation results showed that the angular velocity has a great influence on the velocity of the slurry and the distribution of the oxidation air.

Multiphase flow analysis of hydrodynamic journal bearing using CFD coupled Fluid Structure Interaction considering cavitation

In this study, a fully three-dimensional CFD analysis and multi-phase flow phenomena, has been successfully implemented for simulation of hydrodynamic journal bearing considering the realistic deformations of the bearing with Fluid Structure Interactions (FSI) along with cavitation. Mixture model is used to model cavitation in the bearing and parametric modelling is used for modifying the flow domain due to deformation. Both systems are coupled and design optimization based on multi objective genetic algorithm (MOGA), is used to obtain optimized solution of the attitude angle and eccentricity for the combination of operating speed and load. In the study of bearings with and without effects of cavitation, it is observed that maximum pressure values drop when cavitation is considered in the bearing. Also there is decrease in maximum pressure when elastic deformation in the bearing is considered. The oil vapour distribution goes on increasing with the increase in shaft speed, thus lowering the magnitude of the pressure build up in the bearing. Multiphase study of bearings with cavitation hence becomes extremely important in case of bearings operating with higher speeds. The experimental data obtained showed very good agreements with numerical results and considerable reduction in computation time is observed.