Volume Of Fluid Simulations Research Articles

Numerical Investigation on Two-Phase Flow Pressure Drop in Cathode Channels of Proton Exchange Membrane Fuel Cells

As liquid water is produced by electrochemical reactions in a proton exchange membrane (PEM) fuel cell, liquid–gas two-phase flow forms within the porous structure of the electrodes and gas channels (GCs), resulting in complex gas pressure drop within GCs. This study investigates the two-phase flow pressure drop in a GC connected with a fibrous gas diffusion layer (GDL) using volume of fluid simulations. Fibrous GDLs are stochastically reconstructed to give a rather realistic liquid water breakthrough, and the effect of GDL straight and curved carbon fibers is studied. The results show that droplet breakthrough position and breakthrough size are dependent on the carbon fiber shape, resulting in further distinct pressure drop in GCs. It is also found that the two-phase flow pressure drop has no close correlation with the water content within the GC but a strong relationship with the liquid flow types. Specifically, the cross-section liquid area variation along the gas flow direction is found to be proportional to the pressure drop variation. This study aims to provide the information required for an accurate two-phase flow pressure drop prediction model.

Capturing thin structures in VOF simulations with two-plane reconstruction

A novel interface reconstruction strategy for volume of fluid (VOF) methods is introduced that represents the liquid-gas interface as two planes that co-exist within a single computational cell. In comparison to the piecewise linear interface calculation (PLIC), this new algorithm greatly improves the accuracy of the reconstruction, in particular when dealing with thin structures such as films. The placement of the two planes requires the solution of a non-linear optimization problem in six dimensions, which has the potential to be overly expensive. An efficient solution to this optimization problem is presented here that exploits two key ideas: an algorithm for extracting multiple plane orientations from transported surface data, and an efficient and mass-conserving distance-finding algorithm that accounts for two planes with arbitrary orientation. Additionally, a simple and robust strategy is presented to accurately represent the surface tension forces produced at the interface of subgrid-thickness films. The performance of this new VOF reconstruction is demonstrated on several test cases that illustrate the capability to handle arbitrarily thin films.

Segment-based Eulerian-Lagrangian transition method for flat nozzle spray atomization simulation

This paper presents a novel segment-based Eulerian-Lagrangian transition method for predicting the primary and secondary breakup behavior of a flat nozzle spray. It combines the Volume of Fluid (VOF) method for simulating liquid sheet disintegration and primary breakup with the Discrete Phase Model (DPM) method for secondary breakup. The VOF simulation predicts the varying thickness and local velocity characteristics of the liquid sheet from the center region to the edge region near the nozzle exit. Meanwhile, the proposed segment-based linear stability analysis in this study is capable of predicting the initial droplet variation resulting from primary breakup, considering the varying behavior of the liquid sheet from different regions. The simulation results match reasonably well with experimental data at both macroscopic and microscopic levels, effectively predicting the overall spray structure, mass flow rate, and droplet size variations across different regions with good accuracy. Both experimental and numerical data show that the Sauter mean diameter (SMD) values differ between the center and edge regions, with the edge region displaying larger droplets than the center region. This indicates that the segment-based approach is crucial for successfully predicting the spatial distributions of droplet size characteristics.

Dewetting of a corner film wrapping a wall-mounted cylinder

In this study, we investigate the stability of a film that is attached to a corner between a cylinder and a substrate, using a combination of theoretical and numerical approaches. Notably, we place our focus on flat and thin films where the contact line is almost perpendicular to the cylinder wall whereas a small angle forms between the contact line and the substrate, and the film size is smaller than the cylinder radius. The film stability, which depends on the film size and the wall wettability, is first predicted by a standard linear stability analysis (LSA) within the long-wave theoretical framework. We find that the film size plays the most important role in controlling the film stability. Specifically, the thicker the film is, the less sensitive it becomes to the large-wavenumber perturbation. The wall wettability mainly impacts the growth rates of perturbations and slightly influences the marginal stability and postinstability patterns of wrapping films. We compare the LSA predictions with numerical results obtained from a disjoining pressure model (DPM) and volume-of-fluid (VOF) simulations, which provide more insights into the film breakup process. At the early stage there is a strong agreement between the LSA predictions and the DPM results. Notably, as the perturbation grows, thin film regions connecting two neighbouring satellite droplets form which may eventually lead to a stable or temporary secondary droplet, an aspect which the LSA is incapable of capturing. In addition, the VOF simulations suggest that beyond a critical film size, merging between two neighbouring drops becomes involved during the breakup stage. Therefore, the LSA predictions are able to provide only an upper limit on the final number of satellite droplets.

Volume of Fluid simulation of air–water co-current and Counter-current flow with variable density turbulence formulation

Co-current and counter-current air–water flows are studied by Volume of Fluid (VOF) simulation, with emphasis on turbulence modelling near the interface. The relevance of constant density (ρ-con) and variable density (ρ-var) formulations of the turbulence transport equations in two classical two-equation turbulence models, k−ϵ RNG and k−ω SST models, is discussed. The Reynolds Stress Tensor (RST) model approach is also investigated and literature results with the two-fluid model are included for comparison. Our results with VOF show that the widely used constant density formulation underestimates the turbulence dissipation without capturing the turbulence jump across the interface, which also affects the interface liquid height, the velocity profiles of both phases and the pressure drop along the domain. In contrast, the variable density formulation significantly improves the results by increasing the turbulence dissipation at the interface. Although the best solutions have been obtained using the RST model, the ρ-var and k−ϵ RNG gave quite good agreement with experimental data. Despite the narrowness of the domains, three-dimensional simulations have been in better agreement than the two-dimensional ones. Both the VOF results obtained with either the RST and the ρ-var turbulence formulations were found to be superior to those reported with the TF model using damping corrections specifically calibrated for the tests. This study demonstrates that VOF simulation combined with ρ-var two equations turbulence models is a suitable method for modelling large-scale interface segregated flows.

Droplet Injection for Multiphase Rainfall Simulations on Dynamically Refined Mesh for Effective Interface Capturing

This paper presents a volume of fluid (VOF) model for multiphase rainfall simulation that injects rain droplets as a continuous phase alongside the adaptive mesh refinement (AMR) method to resolve air-water interfaces. An approach based on multi-level domains and a pseudo-random algorithm is proposed to determine injection locations in a random and non-intrusive manner with the least bias. Face zones instead of faces are adopted as constituent elements for droplet injection to prevent droplet fragmentation due to a change of face IDs caused by AMR. Correspondingly, a new multi-level address system is introduced to establish the correspondence among subdomains at different levels. The model is applied to multiphase flow VOF simulation for parametric 2-D and 3-D rainfall analysis. The results are verified by the data reported in the literature. It demonstrates that the model can efficiently simulate realistic rainfall phenomena, capture the droplet interface, and preserve droplet injection uniformity.

Understanding the role of perforations on the local hydrodynamics of gas–liquid flows through structured packings

Structured packings are widely used to perform gas–liquid separation processes as they provide a large mass-transfer area and low-pressure drop. The overall performance of these packings is governed by the local liquid distribution/gas–liquid interfacial area. The local liquid distribution is substantially influenced by the arrangement and geometrical features of the structured packing. While the influence of arrangement and few geometrical features on the local liquid distribution has recently been investigated using the structure-resolved simulations, the perforations on the structured packings are usually ignored. In the present work, we have performed structure-resolved gas–liquid flow simulations, using the Volume-of-Fluid (VOF) method implemented in the open-source C++ library OpenFOAM, in a periodic domain of Mellapak.250 with and without resolving the perforations. We show that the presence of perforations results in flow separation as well as droplet formation leading to an increase in the liquid holdup, interfacial and wetted areas, irrespective of the fluid properties and wetting conditions (specified using static contact angle ‘θw’) considered in this work. We also show that at an inclination angle ‘β’ of 45° from horizontal, the location of the perforations governs the local liquid distribution and the resulting flow metrics. However, at a β of 90°, the number of perforations governs the local liquid distribution, irrespective of their location. Further, we also show that the predictions of structure-resolved VOF simulations, with perforations resolved, are in a relatively better agreement with the correlations in the literature at small values of θw in terms of liquid holdup and interfacial area.

Breakup of planar liquid sheets injected at high speed in a quiescent gas environment

Using a combination of mean flow spatial linear stability and two-dimensional volume-of-fluid (VoF) simulations, the physics governing the instability of high-speed liquid sheets being injected into a quiescent gas environment is studied. It is found that the gas shear layer thickness $\delta _G$ plays an influential role, where for values $\delta _G/H\lesssim 1/8$ , the growth of sinuous and varicose modes is nearly indistinguishable. Here, $H$ is the liquid sheet thickness. With larger values of $\delta _G/H$ , a second peak develops in the lower wavenumber region of the dispersion relation, and becomes increasingly dominant. This second peak corresponds to a large-scale sinuous mode, and its critical wavelength $\lambda _{crit,sinuous}$ is found to scale as $\lambda _{crit,sinuous}/H = 14.26 (\delta _G/H)^{0.766}$ . This scaling behaviour collapses onto a single curve for various combinations of the liquid-based Reynolds ( $Re_L$ ) and Weber ( $We_L$ ) numbers, provided that $\delta _G/H > O({10^{-1}})$ . For the varicose modes, the shape of the dispersion relation does not change with variations in $\delta _G/H$ , and the liquid shear layer thickness has an almost negligible influence on the growth of instabilities. Two-dimensional VoF simulations are employed to examine the validity of the linear stability assumptions. These simulations also show that the dominant sinuous mode remains active as the process transitions into the nonlinear regime, and that this mode is ultimately responsible for fragmenting the sheet. Based on an energy budget analysis, the most influential contributors to the growth of the sinuous mode are the gas Reynolds shear stress and the lateral working of pressure on the gas side.

Analysis of dynamic acoustic resonance effects in a sonicated gas–liquid flow microreactor

In this work, we characterize acoustic resonance phenomena occurring between gas bubbles in a segmented gas-liquid flow in a microchannel irradiated with a frequency around 500kHz. A large acoustic amplitude can be reached, leading to gas-liquid interface deformation, atomization of micrometer sized droplets, and cavitation. A numerical approach combining an acoustic frequency-domain solver and a Lagrangian Surface-Evolver solver is introduced to predict the acoustic deformation of gas-liquid interfaces and the dynamic acoustic magnitude. The numerical approach and its assumptions were validated with experiments, for which a good agreement was observed. Therefore, this numerical approach allows to provide a description and an understanding of the acoustic nature of these phenomena. The acoustic pressure magnitude can reach hundreds of kPa to tens of MPa, and these values are consistent with the observation of atomization and cavitation in the experiments. Furthermore, volume of fluid simulations were performed to predict the atomization threshold, which was then related to acoustic resonance. It is found that dynamic acoustic resonance gives rise to atomization bursts at the gas bubble surface. The presented approach can be applied to more complex acoustic fields involving more complex channel geometries, vibration patterns, or two-phase flow patterns.

The role of breakup and coalescence in fine-scale bubble-induced turbulence. II. Kinematics

This second part of our research explores the kinematic aspect of fine-scale bubble-induced turbulence (BIT) to (i) present the effect of bubble breakup and coalescence and (ii) compare it against the universal kinematic fine-scale turbulence characteristics reported in the literature. To this end, we simulate a dilute bubbly system of 0.5% void fraction using two distinct numerical simulations. In the volume-of-fluid (VoF) simulation, bubbles undergo breakup and coalescence. In the immersed boundary method (IBM) simulation, however, they act as rigid spheres. We also perform a simulation of classical homogeneous isotropic turbulence (HIT). The first important outcome of this study is that BIT is radically different from HIT in terms of its kinematic fine-scale characteristics. In the vorticity-dominating regions, BIT exhibits a weak vortex stretching. This weak vortex stretching is due to (a) the intermediate strain-rate eigenvalues skewed weakly to positive and (b) the extensive strain-rate eigenvector aligning perpendicular to the vorticity vector. The BIT has, on average, not only a weak enstrophy production but also a weak strain production in strain-dominating regions. The weak strain production is due to (a) the presence of vortex stretching in highly strained fluid elements and (b) the absolute magnitude of compressive strain-rate eigenvalue being as close to the extensive strain-rate eigenvalue. Thus, none of the kinematic fine-scale HIT characteristics is noted for BIT. The second important conclusion is that bubble breakup and coalescence play little to no influence on the kinematics of fine-scale BIT as VoF and IBM simulations produce similar results.

Free-Decay Heave Motion of a Spherical Buoy

We examined the heave motion of a spherical buoy during a free-decay drop test. A comprehensive approach was adopted to study the oscillations of the buoy involving experimental measurements and complementary numerical simulations. The experiments were performed in a wave tank equipped with an array of high-speed motion-capture cameras and a set of high-precision wave gauges. The simulations included three sets of calculations with varying levels of sophistication. Specifically, in one set, the volume-of-fluid (VOF) method was used to solve the incompressible, two-phase, Navier–Stokes equations on an overset grid, whereas the calculations in other sets were based on Cummins and mass-spring-damper models that are both rooted in the linear potential flow theory. Excellent agreements were observed between the experimental data and the results of VOF simulations. Although less accurate, the predictions of the two reduced-order models were found to be quite credible, too. Regarding the motion of the buoy, the obtained results indicate that, after being released from a height approximately equal to its draft at static equilibrium (which is about 60% of its radius), the buoy underwent nearly harmonic damped oscillations. The conducted analysis reveals that the draft length of the buoy has a profound effect on the frequency and attenuation rate of the oscillations. For example, compared to a spherical buoy of the same size that is half submerged at equilibrium (i.e., the draft is equal to the radius), the tested buoy oscillated with a period that was roughly 20% shorter, and its amplitude of oscillations decayed almost twice faster per period. Overall, the presented study provides additional insights into the motion response of a floating sphere that can be used for optimal buoy design for energy extraction.

Modeling and evaluation of freeform extruded filament based on numerical simulation method for direct ink writing

Direct ink writing (DIW) is an extrusion-based additive manufacturing (AM) technique. One of the required factors for printing quality in DIW is to extrude continuous and tubular freeform extruded filaments (FEF) with diameters close to the nozzle inner diameter. This paper established a simulation model of FEF with volume of fluid (VOF) method and then evaluated the FEF based on the simulation results. First, ink properties including density, surface tension coefficient, and rheological properties were determined by properties tests. Then, the model of FEF was established using VOF simulation method with the software OpenFOAM and two evaluation indicators, mean diameter and stability, were proposed to evaluate the FEF. Two inks, a cellulose ink and a Nivea Crème, were used under three levels of piston velocity to verify the method universality for different inks and variable process parameters. The prediction accuracy of the established simulation model was verified as the relative error between simulation and experimental results of diameter was less than 10.22%. In this work, it was found that (1) piston velocity needed to be set higher than a minimum value to overcome yield stress and surface tension to successfully extrude filaments; (2) mean diameter of FEF decreased while stability of FEF decreased firstly and then increased as piston velocity increased. The proposed model and evaluation indicators gave an accurate and effective framework to analyze effect of the piston velocity on FEF, characterize the ink printability, and find suitable printable windows for process parameters in DIW.

Capillary Pressure Evolution in Operating Polymer Electrolyte Fuel Cells

Capillary pressure driven transport of liquid water through the gas diffusion layer has been studied in various ex-situ, in-situ and operando setups. So far, insights into the actual capillary pressure has been limited to ex-situ experiments. Advanced image analysis tools like 3D interfacial curvature analysis, that have been developed to determine the capillary pressure in digital rock physics investigations [1], were recently applied to ex-situ X-ray tomographic microscopy (XTM) imaging experiments of the droplet release cycle in polymer electrolyte fuel cells [2]. Within this presentation, we will give insights into the water cluster formation using operando XTM imaging at a frequency of 1 Hz from liquid water emergence at the catalyst layer – gas diffusion layer interface until liquid water breakthrough and droplet formation in the gas channel of the flow field. With the help of interfacial curvature analysis as well as volume of fluid simulations [3], it was possible to obtain information about the capillary pressure evolution in the water phase [4]. We will explain the nuanced interactions of water volume and pressure evolution during the growth of the percolation network within the GDL and the droplet formation and comment on the observed distinct differences to ex-situ pressure evaluations.

A multiscale volume of fluid method with self-consistent boundary conditions derived from molecular dynamics

Molecular dynamics (MD) and volume of fluid (VOF) are powerful methods for the simulation of dynamic wetting at the nanoscale and macroscale, respectively, but the massive computational cost of MD and the sensitivity and uncertainty of boundary conditions in VOF limit their applications to other scales. In this work, we propose a multiscale simulation strategy by enhancing VOF simulations using self-consistent boundary conditions derived from MD. Specifically, the boundary conditions include a particular slip model based on the molecular kinetic theory for the three-phase contact line to account for the interfacial molecular physics, the classical Navier slip model for the remaining part of the liquid–solid interface, and a new source term supplemented to the momentum equation in VOF to replace the convectional dynamic contact angle model. Each slip model has been calibrated by the MD simulations. The simulation results demonstrate that with these new boundary conditions, the enhanced VOF simulations can provide consistent predictions with full MD simulations for the dynamic wetting of nanodroplets on both smooth and pillared surfaces, and its performance is better than those with other VOF models, especially for the pinning–depinning phenomenon. This multiscale simulation strategy is also proved to be capable of simulating dynamic wetting above the nanoscale, where the pure MD simulations are inaccessible due to the computational cost.

Dynamics of the jet wiping process via integral models

Abstract

Breakup dynamics of capillary bridges on hydrophobic stripes

The breakup dynamics of a capillary bridge on a hydrophobic stripe between two hydrophilic stripes is studied experimentally and numerically using direct numerical simulations. The capillary bridge is formed from an evaporating water droplet wetting three neighboring stripes of a chemically patterned surface. By considering the breakup process in a phase space representation, the breakup dynamics can be evaluated without the uncertainty in determining the precise breakup time. The simulations are based on the Volume-of-Fluid (VOF) method implemented in Free Surface 3D (FS3D). In order to construct physically realistic initial data for the VOF simulation, Surface Evolver is employed to calculate an initial configuration consistent with experiments. Numerical instabilities at the contact line are reduced by a novel discretization of the Navier-slip boundary condition on staggered grids. The breakup of the capillary bridge cannot be characterized by a unique scaling relationship. Instead, at different stages of the breakup process different scaling exponents apply, and the structure of the bridge undergoes a qualitative change. In the final stage of breakup, the capillary bridge forms a liquid thread that breaks up consistently with the Rayleigh-Plateau instability.

Water Distribution in Fuel Cell Gas Channels Using a Mechanistic Discrete Particle Model

Water removal and accumulation in fuel cell gas channels is a complex phenomenon which is a consequence of the strength of the capillary forces and inertial forces (1 < Re < 1000). The presence of water in the channel restricts the access of oxygen to diffuse through the gas diffusion layers to the catalyst layer. The air supplied exchanges momentum to the droplets and water clusters, causing detachment when the adhesion force is overcome.Water emerging from discrete locations as droplets interact with both the channel walls and each discrete water cluster, depending on the configuration and operating conditions. Complexity increases as multiple detachment and coalescence events occur over large channel lengths and time scales. Modelling these systems with traditional method computational fluid dynamic (CFD) methods is computationally expensive so we have developed a new mechanistic discrete particle model to handle the liquid water two-phase flow.Taking inspiration from interface resolving volume of fluid (VoF) simulations of water flow in gas channels, we use analytically equations determined by the equilibrium contact angle in different configurations on the channel wall to predict detachment times and coalescence events. We compare the prediction of water area coverage ratio and channel saturation to the VoF simulations and can also estimate dynamic pressure drop.Using this model, we are able to investigate the dynamic effects of liquid water accumulation and distribution in the channel, with often periodic detachment events arising from the formation of liquid plugs. Consequently, the model is able to investigate the effect of the channel wall wettability, from hydrophilic to hydrophobic and the impact that has on the distribution and accumulation of water in the system.We compare the speed of this model against the VoF simulations to show that this type of modelling of two-phase flow in the channel can enable higher resolution accuracy when coupled with continuum scale approaches. Furthermore, with this approach it is possible to investigate the effect of: channel dimensions, liquid water flow rate and spatial location of liquid water emergence. This should allow for designed fuel cell structures to be evaluated. Figure 1

Volume of Fluid Computations of Gas Entrainment and Void Fraction for Plunging Liquid Jets to Aerate Wastewater

Among various mechanisms for enhancing the interfacial area between gases and liquids, a vertical liquid jet striking a still liquid is considered an effective method. This method has vast industrial and environmental applications, where a significant application of this method is to aerate industrial effluents and wastewater treatment. Despite the huge interest and experimental and numerical efforts made by the academic and scientific community in this topic, there is still a need of further study to realize improved theoretical and computational schemes to narrow the gap between the measured and the computed entrained air. The present study is a numerical attempt to highlight the air being entrained by water jet when it intrudes into a still water surface in a tank by the application of a Volume of Fluid (VOF) scheme. The VOF scheme, along with a piecewise linear interface construction (PLIC) algorithm, is useful to follow the interface of the air and water bubbly plume and thus can provide an estimate of the volume fraction for the gas and the liquid. Dimensionless scaling derived from the Fronde number and Reynolds number along with geometric similarities due to the liquid jet’s length and nozzle diameter have been incorporated to validate the experimental data on air entrainment, penetration and void fraction. The VOF simulations for void fraction and air-water mixing and air jet’s penetration into the water were found more comparable to the measured values than those obtained using empirical and Euler-Euler methods. Although, small overestimates of air entrainment rate compared to the experiments have been found, however, VOF was found effective in reducing the gap between measurements and simulations.

Pore-resolved two-phase flow in a pseudo-3D porous medium: Measurements and volume-of-fluid simulations

In the present work, high-speed imaging experiments are performed to measure the time-evolution of two-phase oil-water flow, water-saturation, oil ganglia number and size distribution in a pseudo-3D porous medium. The corresponding pore-resolved simulations are performed using the Volume-of-Fluid (VOF) method and predictions are validated using the aforementioned measurements. The experimentally-validated VOF model is used to understand the effects of water-flooding velocity and interfacial tension [i.e. Capillary number (Ca)] on the pore-scale oil recovery mechanisms. The pore-resolved VOF simulations reveal that the drainage phenomenon is dominated by Haines-jump events at low Ca values. The increase in Ca values results in the decrease in the frequency of Haines-jump events and after the transitional Ca, the drainage phenomenon is no longer governed by Haines-jump events and is governed by viscous fingering. Finally, VOF simulations are used to analyze the effect of successive step changes in the interfacial tension on the oil recovery.

Global eigenmodes of thin liquid sheets by means of Volume-of-Fluid simulations

The unsteady dynamics of planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, is numerically investigated by means of the Volume-of-Fluid (VOF) technique for supercritical regimes. The global behavior of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively small amplitude, thereby exciting sinuous modes. To gain more physical insights into the fluid system, a theoretical linear one-dimensional model is also developed. A physical interpretation of this model relates the sheet dynamics to transverse vibrations of tensional string forced by terms containing the lateral velocity and subjected to a total damping coefficient, which can assume negative values. The VOF simulation satisfactorily confirms that the velocity impulse perturbation splits into two wave fronts traveling downstream with the theoretical wave velocities. A good agreement is found in comparing the crossing times over the entire domain length of such waves with the almost constant spacing between the frequencies of the eigenvalue spectrum. Surface tension plays a stabilizing role, and for relatively high values of density ratio rρ of gaseous-to-liquid phases, the sheet becomes unstable. It is argued that the distribution of transverse velocity component of the gaseous phase represents the forcing term, which leads the system toward the instability when, for relatively high rρ, the total damping becomes negative. An analogy seems to exist between the global unstable behavior exhibited by the liquid sheet as rρ increases and the shear-induced global instability found by Tammisola et al. [Surface tension-induced global instability of planar jets and wakes,” J. Fluid Mech. 713, 632–658 (2012)] in the presence of surface tension. However, for the gravitational sheet, the surface tension is stabilizing.