A consistent and conservative volume distribution algorithm and its applications to multiphase flows using Phase-Field models

A VOSET method combined with IDEAL algorithm for 3D two-phase flows with large density and viscosity ratio

A multiphase MPS method for bubbly flows with complex interfaces

A simplified method is proposed to implement a wetting boundary condition on curved surfaces within the conservative phase-field lattice-Boltzmann (LB) simulation framework. It combines the idea of Huang et al. [“An alternative method to implement contact angle boundary condition and its application in hybrid lattice-Boltzmann finite-difference simulations of two-phase flows with immersed surfaces,” Eur. Phys. J. E 41, 17 (2018)] to find the order parameter on the other side of the wall with the conservative Allen–Cahn equation (CACE) for interface evolution solved by the LB equations. It inherits the advantage of the original method using the Cahn–Hilliard equation to avoid complicated interpolations under different geometries. By using the CACE, the boundary condition for the chemical potential is circumvented (making it more simplified), and the overshooting of the order parameter is also greatly suppressed, enabling it to simulate two-phase flows with solid objects of various shapes and wettabilities at large density and viscosity ratios. Several two-dimensional, axisymmetric, and three-dimensional problems, including some previously studied by experiments, were simulated and the capability of the proposed method is demonstrated through its good agreement with theoretical predictions and/or experimental observations.

In today’s world, concern is growing about the future of energy. Despite very ambitious international climate goals by 2050, global energy-related carbon dioxide (CO2) emissions keep increasing. In order to tackle this problem, hydrogen (H2) might become a significant part of the solution since it is a way to produce, store, move and use energy in a clean way. However, more than 95% of the actual hydrogen production is made of grey hydrogen, e.g. H2 produced from fossil fuels, which leads to high CO2 emissions [1]. One way to decarbonise this energy vector is to use renewable energies (solar panels, wind turbines, etc.) to produce green hydrogen via water electrolysis.Among the various technologies available to perform water electrolysis, alkaline water electrolysis (AWE) is the most mature one. In general, AWE consists of two planar electrodes separated by a certain distance and operating in a liquid alkaline electrolyte solution (e.g. KOH, potassium hydroxide). Recent studies show that it is possible to significantly increase the performance of such electrolysers by substituting the traditional gap-cell design by a zero-gap cell [2,3]. To do so 3D electrodes such as foams and 3D-printed structures are used, leading to an increase of the surface area and as a result, to a higher hydrogen production rate. These 3D electrodes are incorporated between the planar current distributors at either side of a membrane or diaphragm, reducing the interelectrode distance to the thickness of the separator. In the case of traditional cells, the hydrogen bubbles will tend to evolve only from the surface of the 2D current distributor plates, while for zero-gap cells gases evolve inside the porous structure. The process can be improved even more by forcing the electrolyte flow, favouring bubble removal. Finally, a bi-layer configuration with a catalyst layer presenting high specific surface area near the separator along with a porous transport layer (PTL) allows for a very high hydrogen production in the catalyst and an easy evacuation of the bubbles through the PTL.Recent experimental results in our group validate the enhanced performance of a bi-layer foam configuration where a fine foam acts as the catalyst layer and a coarser one as the PTL. In order to have a better understanding of the electrolyte flow behaviour inside these 3D electrodes, Computational Fluid Dynamics (CFD) was used as a tool to simulate the single-phase flow numerically. The purpose of this is to determine optimal flow parameters in order to favour hydrogen bubble removal while benefiting from the high surface area of the 3D electrodes. Up to now, it appears that this kind of analysis has rarely been addressed in the literature [4].In our specific case, the foams used as the catalyst and the PTL have characteristic pore sizes of 450 µm and 3000 µm, respectively. In order to obtain an accurate geometric representation, the foams were scanned using high-resolution micro-CT (computed tomography). A computational mesh was then obtained by reconstructing the highly detailed scanned data. The incompressible Navier-Stokes equations for the single-phase flow were solved using the Finite Element Method (FEM) implemented in MigFlow software [5]. In Figure 1 we present results from a simulation with the PTL width being three times the width of the catalyst layer, and the inlet velocity 1 m/s. It appears that the electrolyte velocity in the direction perpendicular to the flow is the highest in the area close to the interface between the catalyst and the PTL, meaning that this configuration would help extracting hydrogen bubbles off the catalyst layer, towards the coarser porous region.It is important to note that the results obtained in this case were not considering the gas phase. We are currently working on the development of a multiphase pore-resolved model to see whether the assumption of optimal bubble removal is confirmed for multiphase flow. To this end, a Eulerian-Eulerian two-fluid model must be implemented for the liquid electrolyte and the gaseous bubbles. One key aspect is to correctly define closure relations for the interfacial exchange terms that appear in the momentum equations. Hydrogen bubble formation, growth and escape from the porous electrodes might also be considered. This work is a first step towards the modeling of the whole alkaline water electrolysis process through 3D porous electrodes. Figure 1

One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. Following some previous work in this area, we suggest a physically motivated regularization of the Euler equations which allows topological transitions to occur smoothly. In this model, the sharp interface is replaced by a narrow transition layer across which the fluids may mix. The model describes a flow of a binary mixture, and the internal structure of the interface is determined by both diffusion and motion. An advantage of our regularization is that it automatically yields a continuous description of surface tension, which can play an important role in topological transitions. An additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the Euler (or Navier–Stokes) and the Cahn–Hilliard equations. The model takes into account weak non–locality (dispersion) associated with an internal length scale and localized dissipation due to mixing. The non–locality introduces a dimensional surface energy; dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes. In particular, we study a non–trivial limit when both components are incompressible, the pressure is kinematic but the velocity field is non–solenoidal (quasi–incompressibility). To demonstrate the effects of quasi–incompressibility, we analyse the linear stage of spinodal decomposition in one dimension. We show that when the densities of the fluids are not perfectly matched, the evolution of the concentration field causes fluid motion even if the fluids are inviscid. In the limit of infinitely thin and well–separated interfacial layers, an appropriately scaled quasi–incompressible Euler–Cahn–Hilliard system converges to the classical sharp interface model. In order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient, we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity.

Depth-averaged systems of equations describing the motion of fluid–sediment mixtures have been widely adopted by scientists in pursuit of models that can predict the paths of dangerous overland flows of debris. As models have become increasingly sophisticated, many have been developed from a multi-phase perspective in which separate, but mutually coupled sets of equations govern the evolution of different components of the mixture. However, this creates the opportunity for the existence of pathological instabilities stemming from resonant interactions between the phases. With reference to the most popular approaches, analyses of two- and three-phase models are performed, which demonstrate that they are more often than not ill posed as initial-value problems over physically relevant parameter regimes – an issue which renders them unsuitable for scientific applications. Additionally, a general framework for detecting ill posedness in models with any number of phases is developed. This is used to show that small diffusive terms in the equations for momentum transport, which are sometimes neglected, can reliably eliminate this issue. Conditions are derived for the regularisation of models in this way, but they are typically not met by multi-phase models that feature diffusive terms.

An efficient algorithm for incompressible N-phase flows

A phase-field lattice Boltzmann model for simulating multiphase flows in porous media: Application and comparison to experiments of CO2 sequestration at pore scale

The aim of this paper is to utilize a numeri- cal model to compute bubble motion in quiescent Newto- nian and viscoelastic liquids. For our numerical method, we use a coupled level set and volume-of-fluid method with a second order treatment for the jump conditions related to surface tension. We investigate axisymmetric gas-liquid systems with large density and viscosity ratios as well as buoyancy-driven flows with complex changes in topology. We present comparisons to previous compu- tational results as well as experimental results. keyword: Level set, Volume-of-fluid, Viscoelastic, Projection method, Adaptive mesh refinement

High fidelity anisotropic adaptive variational multiscale method for multiphase flows with surface tension

Comparison of surface tension generation methods in smoothed particle hydrodynamics for dynamic systems

A multiphase lattice Boltzmann model is constructed to numerically solve the one-fluid flow equations for immiscible fluids. The method features one solver for the macroscopic pressure and momentum and another for a scalar field that captures and sharpens the interface. The surface tension is set a priori and independently of other parameters. The interface capillary tensor is embedded within the moments of the lattice Boltzmann equation so that its divergence is captured locally. The algorithm is simple and can compute flows with large density and viscosity ratios while maintaining distributed but narrow interfaces. The model is validated against analytical solutions and benchmark simulations.

Thermodynamic consistency is a key factor in heat and mass transfer simulation. A modified lattice Boltzmann pseudopotential model with the ability to simulate multiphase and multicomponent flow with a large density and viscosity ratio is proposed. Relative to a model using the exact difference method, a better thermodynamic consistency is obtained through introducing an improved external force term, a multi-relaxation-time collision operator, and a scaling coefficient k of the equation of state. The coefficient of scale k = 0.1 is preferred due to its better thermodynamic consistency, lower spurious current and a smaller surface tension. The inter-particle interaction strength has little influence over the thermodynamic consistency due to its limited contributions to the surface tension. With the model, the bubble dissolution under pressure is investigated and Henry’s law is validated.

Numerical optimisation of the pseudopotential-based lattice Boltzmann method

The temporal instability of parallel two-phase mixing layers is studied with a linear stability code by considering a composite error function base flow. The eigenfunctions of the linear problem are used to initialize the velocity and volume fraction fields for direct numerical simulations of the incompressible Navier–Stokes equations with the open-source GERRIS flow solver. We compare the growth rate of the most unstable mode from the linear stability problem and from the simulation results at moderate and large density and viscosity ratios in order to validate the code for a wide range of physical parameters. The efficiency of the adaptive mesh refinement scheme is also discussed.