Interface Tracking Method Research Articles

An interface tracking method with triangle edge cuts

This paper introduces a volume-conserving interface tracking algorithm on unstructured triangle meshes. We propose to discretize the interface via triangle edge cuts which represent the intersections between the interface and the triangle mesh edges using a compact 6 numbers per triangle. This enables an efficient implicit representation of the sub-triangle polygonal material regions without explicitly storing connectivity information. Moreover, we propose an efficient advection algorithm for this interface representation that is based on geometric queries and does not require an optimization process. This advection algorithm is extended via an area correction step that enforces volume-conservation of the materials. We demonstrate the efficacy of our method on a variety of advection problems on a triangle mesh and compare its performance to existing interface tracking methods including VOF and MOF.

Self-adaptive and time divide-and-conquer physics-informed neural networks for two-phase flow simulations using interface tracking methods

Physics-informed neural networks (PINNs) are emerging as a promising artificial intelligence approach for solving complex two-phase flow simulations. A critical challenge in these simulations is an accurate representation of the gas–liquid interface using interface tracking methods. While numerous studies in conventional computational fluid dynamics (CFD) have addressed this issue, there remains a notable absence of research within the context of PINNs-based two-phase flow simulations. Therefore, this study aims to develop a robust and generic PINNs for two-phase flow by incorporating the governing equations with three advanced interface tracking methods—specifically, the Volume of Fluid, Level Set, and Phase-Field method—into an improved PINN framework that has been previously proposed and validated. To further enhance the performance of the PINNs in simulating two-phase flow, the phase field constraints, residual connection and the time divide-and-conquer strategies are employed for restricting neural network training within the scope of physical laws. This self-adaptive and time divide-and-conquer (AT) PINNs is then optimized by minimizing both the residual and loss terms of partial differential equation. By incorporating the three different interface tracking methods, it efficiently handles high-order derivative terms and captures the phase interface. The case of single rising bubble in two-phase flow is simulated to validate the robustness and accuracy of the AT PINNs. The simulation's accuracy is evaluated by comparing its performance in terms of velocity, pressure, phase field, center of mass, and rising velocity with that of conventional PINNs and CFD benchmarks. The results indicate that the AT PINNs coupled with these interface tracking methods offers a satisfactory performance in simulating rising bubble phenomenon.

Capture of the Morphology Transfer Process in a High-Momentum Centrally Aerated Bubble Column with a Hybrid Multifield Two-Fluid Model

The role of pool scrubbing in attenuating radioactivity release after severe accidents has been explored extensively. It is known that scrubbing efficiency is largely determined by the hydrodynamic phenomenology in pools, which is still insufficiently understood. Aerosol gas forms large globules at the nozzle exit, which subsequently break up into a swarm of stable bubbles, where the change of bubble size can reach more than two orders depending on the injection rate. Furthermore, with the increase of flow rates, the injection regime changes from globule to jet characterized by a continuous gas structure. The flow field in the pool can be divided into two zones, injection and rise (swarm), according to the gas-liquid interface morphology. In different zones, scrubbing is governed by different mechanisms such as inertial impact, diffusion, and gravity, whereby bubble rise velocity is one major influential parameter. So far, numerical analysis of pool scrubbing is routinely based on system codes, which rely on empirical correlations for the determination of hydrodynamic parameters as well as scrubbing zones. More recently, owing to the increasing availability of computational resources, knowledge is improved through three-dimensional computational fluid dynamics simulations. Nevertheless, morphology and regime change still present a challenge for both two-fluid and interface-tracking models. Because of the limitation of closures, the conventional two-fluid model (TFM) is generally effective for bubble size smaller than cell size while interface-tracking (capturing) methods demand dozens of cells per bubble size. Combining the two kinds of approaches into one simulation is not straightforward. The present work aims to present a hybrid multifield TFM with extensions for capturing the transfer between different morphologies and for considering the effect of mesh resolution in momentum exchange. The developments are validated by simulating the complex hydrodynamic process in a pool-scrubbing column, which operates in the globule regime with an injection Weber number between 103 and 105. By comparison with experimental data, the results are shown to be promising, which provides a versatile framework for investigation of particle scrubbing in the future. The most attractive feature of the model is that compared to one-fluid interface-tracking models, it reliably predicts the bubble rise velocity. Furthermore, it is able to capture the lateral gas distribution without the need of applying a population balance model since most large bubbles are resolved.

An Edge-based Interface Tracking (EBIT) method for multiphase flows with phase change

In this paper, the Edge-Based Interface Tracking (EBIT) method is extended to simulate multiphase flows with phase change. As a novel Front-Tracking method, the EBIT method binds interfacial markers to the Eulerian grid to achieve automatic parallelization. To include phase change effects, the energy equation for each phase is solved, with the temperature boundary condition at the interface sharply imposed. When using collocated grids, the cell-centered velocity is approximately projected. This will lead to unphysical oscillations in the presence of phase change, as the velocity will be discontinuous across the interface. It is demonstrated that this issue can be addressed by using the ghost fluid method, in which the ghost velocity is set according to the jump condition, thereby removing the discontinuity. A series of benchmark tests are performed to validate the present method. It is shown that the numerical results agree very well with the theoretical solutions and the experimental results.

An edge-based interface tracking (EBIT) method for multiphase-flow simulation with surface tension

We present a novel Front-Tracking method, the Edge-Based Interface Tracking (EBIT) method for multiphase flow simulations. In the EBIT method, the markers are located on the grid edges and the interface can be reconstructed without storing the connectivity of the markers. This feature makes the process of marker addition or removal easier than in the traditional Front-Tracking method. The EBIT method also allows almost automatic parallelization due to the lack of explicit connectivity.In a previous journal article we have presented the kinematic part of the EBIT method, that includes the algorithms for piecewise linear reconstruction and advection of the interface. Here, we complete the presentation of the EBIT method and combine the kinematic algorithm with a Navier–Stokes solver. A circle fit is now implemented to improve the accuracy of mass conservation in the reconstruction phase. Furthermore, to identify the reference phase and to distinguish ambiguous topological configurations, we introduce a new feature: the Color Vertex. For the coupling with the Navier–Stokes equations, we first calculate volume fractions from the position of the markers and the Color Vertex, then viscosity and density fields from the computed volume fractions and finally surface tension stresses with the Height-Function method. In addition, an automatic topology change algorithm is implemented into the EBIT method, making it possible the simulation of more complex flows. The two-dimensional version of the EBIT method has been implemented in the free Basilisk platform, and validated with seven standard test cases: stagnation flow, translation with uniform velocity, single vortex, Zalesak's disk, capillary wave, Rayleigh-Taylor instability and rising bubble. The results are compared with those obtained with the Volume-of-Fluid (VOF) method already implemented in Basilisk.

CFD simulation of the inundation effect for saturated propane vapor condensation on the surface of a horizontal tube using the volume of fluid method

The inundation of the lower tubes in a tube bundle with condensate formed on the upper tubes is among the major causes of reduced condensation rate. Experimental methods can hardly be used to get detailed information on the inundation effect, since each factor that controls the condensation process should be considered individually. However, CFD modelling using direct interface-tracking methods is an effective tool for analyzing such processes. This paper reports the results of simulation of the saturated propane vapor condensation on the surface of a horizontal tube using the Volume of Fluid method with the modified Lee model. The study presents, for the first time, the characteristics of saturated vapor condensation including the effect of inundation predicted using a 3D model. The interphase surface and the distribution of instantaneous heat transfer coefficients over the surface of the inundated pipe are presented. It has been shown that increasing the temperature of the condensate flow can substantially affect the distribution of the heat transfer rate over the tube surface due to the formation of a thermal entrance region. These results may become a starting point for modelling condensation in a tube bundle that enjoys current interest in practice.

An interface tracking, finite volume code for modeling axisymmetric implosion of a rotating liquid metal liner with free surface

We present Integrated System Model-hydrodynamics (ISM-hydro)—an interface tracking, finite volume code for modeling a shaped implosion of a rotating, initially cylindrical, fluid shell (liner) with a free surface. The code is a novel implementation of the mixed Lagrangian–Eulerian approach, applied to a compressible fluid in an axisymmetric geometry described by cylindrical coordinates (r, ϕ, z). In ISM-hydro, a structured quadrilateral mesh follows fluid elements in the r-direction (radially Lagrangian) and is fixed in the z-direction (axially Eulerian). This approach accurately captures the motion of the liner's free surface, making it an interface tracking method. Using this mesh, we derive a finite volume discretization of the axisymmetric Euler equations for a rotating compressible fluid that has an exact balance of kinetic energy. An extensive comparison between ISM-hydro and the open-source software OpenFOAM is presented; results for different test cases show very good agreement in simulated implosion trajectories and flow fields. ISM-hydro is the purely hydrodynamic component of the Integrated System Model (ISM), a framework developed at General Fusion (GF) for comprehensive predictive modeling of GF's magnetized target fusion (MTF) scheme, where an imploding rotating liquid metal liner compresses a magnetized plasma target to fusion conditions. Among advantages of the code is its speed: a full implosion simulation with a coarse mesh takes on the order of one minute on a single core while preserving high accuracy. This makes ISM-hydro a valuable tool for the design optimization of GF's MTF machines.

Thermal boundary layer modelling for heat flux prediction of bubbles at saturation: A priori analysis based on fully-resolved simulations

This study presents and investigates uni-directional thermal sub-layer enhancement techniques within the context of an interface tracking method for simulating bubbly flows at saturation. Current discretisation methods on structured and fixed Cartesian grids tend to spread the bubbles' interface region, creating a trade-off between the freely moving nature of the bubble to the detriment of accurately capturing the discontinuous aspect of the interface and variations of properties and fluxes crossing it. Although robust techniques have been described in the literature to ensure energy conservation, less research has been undertaken to develop a methodology to retrieve the non-linear behaviour of quantities in the interface vicinity at a reasonable computational cost. In this study, the discretised bubble surface is used as a basis for addressing several quasi-static radial sub-problems that are bounded by an interfacial constant saturation temperature and a CFD temperature field value. A first approach, based on an analytical solution fitted at each time step using underlying Eulerian field values, has been developed to incorporate near-interface physics. This includes the tangential effect, incoming fluid velocity, and local mean curvature (first order surface approximation). A semi-analytical approach needs to meet certain assumptions to be valid. This is due to its derivation from a simplified plane boundary-layer development or from a spherical diffusion problem which limits its applicability range. Therefore, a second approach based on a uni-directional sub-resolution fed carefully by interpolated velocity and tangential source terms demonstrates promising results as it aligns with the principal variations of the solution. Both methodologies have been applied onto DNS data of a steady rising bubble configuration at low and moderate Reynolds {3.6;62.5} and Prandtl {1;2.5;5} numbers with a constant interfacial temperature after an extensive analysis of the advection-diffusion terms hierarchy. The key aspects to maximise the effectiveness of the sub-resolution method have been clearly identified and discussed. The Sub-resolution shows better applicability to our case study on moderately large thermal layers. The newly predicted interfacial temperature gradient and temperature profile could be re-employed for Eulerian fluxes correction.

Direct Numerical Simulation of Atomization Characteristics of ECN Spray-G Injector: In-Nozzle Fluid Flow and Breakup Processes

AbstractIn order to sustain applications dealing with various liquid fuels in internal combustion engine (ICE), it is essential to make available prediction methodologies that allow an early evaluation of the potential usefulness of such fuels in terms of favourable mixture preparation process already in realistic configurations. Since the air-mixture formation and subsequent processes are predominantly governed by the fuel injection, a DNS based numerical investigation coupled with VOF as an interface tracking method is carried out in this paper to gain better insight on the fuel injection from an industrial injector "Spray G" configuration. Chosen from Engine Combustion Network (ECN), this is a gasoline direct injector (GDI) featuring 8-holes orifices and operating with high injection pressure (200 bar). Under consideration of the required computational cost associated with DNS, only the 1/8 of the nozzle geometry including one orifice is used. The numerical simulation is accomplished for the quasi-steady injection condition with nozzle needle fully opened. The obtained results are first validated with available experimental data for nozzle mass flow rate and spray spread angle showing a good agreement. Then, a detailed numerical analysis is provided for the in/near nozzle flow evolution especially for flow turbulence, primary and secondary atomization. Furthermore, droplet statistics in terms of droplet shape, and droplet size-velocity distribution together with a breakup regime map are reported. Finally, a 2-D data curation technique is proposed to extract the droplet statistics along selected planes and evaluated by direct comparison with three-dimensional droplet data, which may allow handling of the DNS data in more feasible and economical way especially for time series data with higher frequency. The comprehensive DNS data generated by this DNS-VOF approach enable not only to carry out detailed numerical analysis of in- and near-nozzle physical phenomena for which experimental data are still scarce, but also to provide a hint of more reliable injector boundary conditions useful for lower order spray injection method based on Lagrangian particle tracking.

Numerical simulation and experimental investigation of bubble behaviour during pool boiling in the coiled wire

Under the computational fluid dynamics (CFD) framework, an interface tracking method has been used to perform several multiple simulations of coiled wire boiling in a pool. This study includes simulations of the boiling regime, including the Critical Heat Flux (CHF), ranging from nucleate boiling to film boiling. The purpose of this research was to investigate using coiled wire to increase the rate of heat transfer under constant heat flux conditions. The range of the applied heat flux is 130–1075 kW/m2. This research delves into the formation of bubble shapes, bubble diameter, and bubble departure frequency. The vapour bubble grows in size as the heat flux increases; with a heat flux of q'' = 600 kW/m2, it reaches its maximum measured diameter of about 9 mm. Additionally, the heat transfer coefficients and wall temperature distribution were determined using the simulation findings. The heat flux was gradually increased in the critical heat flux investigation until burnout of the coiled wire was observed and a bubble layer formed. This led to the conclusion that q'' = 1075 kW/m2 represents the CHF for this particular geometry. It was observed that the CHF conditions occur in the coil portion, which emphasises the importance of considering the critical heat flux more carefully while designing this geometry.

Flow and Heat Transfer in Two-Phase Flow Immiscible Droplets in Microchannels

ABSTRACT The enhancement of heat transfer in microchannels without phase change is a significant area of study, primarily driven by the internal fluid recirculation in two-phase flows. This investigation focuses on a circular microchannel, 100 μm in diameter, where mineral oil droplets are introduced into a water flow. The study utilizes the conservative level set method for precise interface tracking and liquid film thickness measurement. This research introduces a modified Nusselt number, specifically tailored to describe the heat transfer characteristics of multiphase flows. The study delves into the effects of varying droplet sizes, from small spheres to a slug. The findings indicate that the most significant heat transfer enhancement occurs with droplets whose volume closely matches that of a sphere fitting within the channel. Moreover, the investigation explores the impact of parameters like inlet velocity, primary-phase slug length, and contact angle. Notably, higher inlet velocities lead to improved heat transfer, resulting in a substantial increase in the Nusselt number compared to single-phase flows. The study underscores the delicate balance between recirculation intensity and droplet heat capacity concerning slug length, as excessive variations can harm thermal performance. It also highlights the pivotal role of surface wettability, showing improved thermal performance on hydrophobic surfaces.

Numerical investigation of ultrasound focusing and bubble collapse

Ultrasound focusing and microbubble collapse are numerically investigated using a level-set interface tracking method for two-phase flows with multiple interfaces. The computations for ultrasound propagating through a spherical lens demonstrate the ultrasound refraction and pressure intensification at the rear of the lens. The focusing of the initial negative pressure wave through the lens induces a converging flow and the focusing of the subsequent positive pressure wave further intensifies the pressure at the lens. Computations are extended to bubble oscillations near the focusing lens and compared with the no-lens case. The lens not only amplifies the bubble expansion and contraction rates significantly but also generates a larger pressure gradient across the bubble. This ultrasound focusing effect contributes to the asymmetric collapse of the bubble and the formation of a liquid jet that penetrates the bubble. The effects of lens size, initial bubble radius and bubble-lens distance on bubble expansion and liquid jet are further investigated.

An extended model for the direct numerical simulation of droplet evaporation. Influence of the Marangoni convection on Leidenfrost droplet

In this paper, we propose an extended model for the numerical simulation of evaporating droplets within the framework of interface capturing or interface tracking methods. Most existing works make several limiting assumptions that need to be overcome for a more accurate description of the evaporation of droplets. In particular, the variations of several physical variables with local temperature and mass fraction fields must be accounted for in order to perform more realistic computations. While taking into account the variations of some of these physical properties, as viscosity, seems rather obvious, variations of other variables, as density and surface tension, involve additional source terms in the fundamental equations for which a suitable discretization must be developed. The paper presents a numerical strategy to account for such an extended model along with several original test-cases allowing to demonstrate both the accuracy of the proposed numerical schemes and the strong interest in developing such an extended model for the simulation of droplet evaporation. In particular, the impact of thermo-capillary convection will be highlighted on the vapor film thickness between a superheated wall and a static Leidenfrost droplet levitating above this wall.

A high-accuracy framework for phase-field fracture interface reconstructions with application to Stokes fluid-filled fracture surrounded by an elastic medium

This work considers a Stokes flow in a deformable fracture interacting with a linear elastic medium. To this end, we employ a phase-field model to approximate the crack dynamics. Phase-field methods belong to interface-capturing approaches in which the interface is only given by a smeared zone. For multi-domain problems, the accuracy of the coupling conditions is, however, of utmost importance. Here, interface-tracking methods are preferred, since the interface is resolved on mesh edges up to discretisation errors, but it does not depend on the length scale parameter of some smeared zone. The key objective of this work is to construct a robust framework that computes first a crack path via the phase-field method (interface-capturing) and then does an interface-tracking reconstruction. We then discuss several approaches to reconstruct the Eulerian description of the open crack domain. This includes unfitted approaches where a level-set of the crack interface is constructed and an approach where the geometry is re-meshed. Using this reconstructed domain, we can compute the fluid–structure interaction problem between the fluid in the crack and the interacting solid. With the explicit mesh reconstruction of the two domains, we can then use an interface-tracking Arbitrary-Lagrangian–Eulerian (ALE) discretisation approach for the resulting fluid–structure interaction (FSI) problem. Our algorithmic procedure is realised in one final numerical algorithm and one implementation. We substantiate our approach using several numerical examples based on Sneddon’s benchmark and corresponding extensions to Stokes fluid-filled regimes.

Breakup of thin liquid films with viscous interfaces

Thin liquid films are ubiquitous in nature and have many practical applications. From biological films to the curtain coating process, thin films are present in both large and small scales. Despite their importance, understanding the stability of these films remains a significant challenge due to the fluid–fluid interface that is free to deform, affected by interfacial tension and complex rheological behavior. Instabilities in thin films are often caused by van der Waals attractions, which can lead to the rupture of the layer. To investigate the rupture dynamics, numerical methods are commonly used, such as asymptotic derivations of the lubrication theory or interface tracking methods. In this paper, we present a computational study of the breakup dynamics of a stationary thin liquid sheet bounded by a passive gas with a viscous interface, using the arbitrary Lagrangian–Eulerian method and the Boussinesq–Scriven constitutive law to model the rheological behavior. Our results demonstrate that the stability of thin liquid films is influenced by both surface rheology and disjoining effects and that the viscous character of the interface can delay sheet breakup, leading to more stable films.

A contact line force model for the simulation of drop impacts on solid surfaces using volume of fluid methods

Characterizing the contact line dynamics on solid walls is often a crucial problem encountered in the simulation of complex interfacial unsteady flows, such as drop impacts on solid surfaces. In this work, a new model is proposed to reproduce the contact line dynamics in a simple but effective way, based on introducing in the momentum equation a force term proportional to the deviation of the calculated contact angle from the value predicted by a dynamic model that takes into account wettability hysteresis. The model has been implemented in a volume of fluid (VOF) method and is applied to the simulation of drop impacts leading to deposition outcomes, although it could be extended to other interface tracking methods and is also applicable to more complex drop impacts involving fingering and splashing. Numerous tests have been performed to evaluate the accuracy and robustness of the proposed model over a wide range of Reynolds and Weber numbers. The results substantially improve those obtained by imposing only the contact angle as a boundary condition at the contact line, and satisfactorily predict a variety of experimental results from the literature for very different impact and wettability conditions.

Application of Motion Interface Tracking CVOFLS Method to Zalesak Disk Problem

The interface curvature calculation is not accurate in VOF method and the interface mass is not conserved in Level Set method, A new interface tracking method CVOFLS is proposed (Coupled Volume of Fluid and Level Set method). This method combines the advantages of VOF and Level Set, The VOF and Level Set functions are simultaneously solved according to the fluid velocity, The interface obtained by the VOF function is used to correct the fluid quality, The Level Set function is used to calculate the interface norma, The Level Set function reinitialization process is omitted, Thus, the deficiencies of the two methods are overcome effectively. An example of interface tracking numerical simulation shows that, this method can guarantee high precision of free interface tracking and good mass conservation, and it can improve the calculation efficiency.

Two-particle method for liquid–solid two-phase mixed flow

Liquid–solid two-phase flows are a very important class of multiphase flow problems widely existing in industry and nature. This paper establishes a two-phase model for liquid–solid two-phase flows considering multiphase states of granular media. The volume fraction is defined by the solid phase, determining the material properties of the two phases, and momentum is exchanged between the phases by drag and pressure gradient forces. On this basis, a two-particle method for simulating the liquid–solid two-phase flow is proposed by coupling smoothed particle hydrodynamics with smoothed discrete particle hydrodynamics. The coupling framework for the two-particle method is constructed, and the coupling between the algorithms is realized through interphase momentum exchange, volume fraction constraint, and field variable sharing. The liquid phase density changes are divided into two types. One is caused by weak compressibility, and the other is caused by changes in the solid phase volume fraction. The former is used to calculate the liquid-phase flow field, and the latter is used to calculate the two-phase coupling to solve the problem of sudden bulk density changes in the liquid phase caused by changes in particle volume fractions. The two-particle method maintains the dual advantages of the particle method for free interface tracking and material point tracking for particles. The new method is validated using a series of fundamental test cases, and comparison with experimental results shows that the new method is suitable for resolving liquid–solid two-phase flow problems and has significant practical value for future simulations of mudflow motions, coastal breakwaters, and landslide surges.

Interaction between a rising bubble and a stationary droplet immersed in a liquid pool using a ternary conservative phase-field lattice Boltzmann method.

When a stationary bubble and a stationary droplet immersed in a liquid pool are brought into contact, they form a bubble-droplet aggregate. Its equilibrium morphology and stability largely depend on the combination of different components' surface tensions, known as the "spreading factor." In this study, we look at the interaction between a rising bubble and a stationary droplet to better understand the dynamics of coalescence and rising and morphological changes for the bubble-droplet aggregate. A systematic study is conducted on the interaction processes with various bubble sizes and spreading factors in two dimensions. The current simulation framework consists of the ternary conservative phase-field lattice Boltzmann method (LBM) for interface tracking and the velocity-pressure LBM for hydrodynamics, which is validated by benchmark cases such as the liquid lens and parasitic currents around a static droplet with several popular surface tension formulations. We further test our LBM for the morphology changes of two droplets initially in contact with various spreading factors and depict the final morphologies in a phase diagram. The separated, partially engulfed, and completely engulfed morphologies can be replicated by systematically altering the sign of the spreading factors. The rising bubble and stationary droplet interaction are simulated based on the final morphologies obtained under stationary conditions by imposing an imaginary buoyancy force on the rising bubble. The results indicate that the bubble-droplet aggregate with double emulsion morphology can minimize the distortion of the bubble-droplet aggregate and achieve a greater terminal velocity than the aggregate with partially engulfed morphology.

Investigation Into Hybridization of the Two-Fluid Model and Phase-Field Model for Multi-Scale Two-Phase Flow Simulations

Abstract To simulate heterogeneous bubbly flows, a hybrid method has been developed in several studies by combining the two-fluid model and the interface tracking method. Since this original hybrid method is based on the one-pressure modeling, which is a common approach for the two-fluid model, unphysical flow would occur in the flow where the surface tension is dominant. To resolve this inherent weakness of one-pressure modeling, we proposed a new formulation of the hybrid method in this study. The proposed hybrid method includes no pressure term in the dispersed phase because we regarded the dispersed phase as a group of discrete particles. The phase-field method is employed as the interface-tracking method. The proposed hybrid method was validated in several numerical simulations. Using the static bubble problem, we confirmed that in the proposed hybrid method simulation, there is no unphysical flow that is observed in the original hybrid method. In the bubble plume problem, we compared the bubble plume behavior and the time-averaged void fraction of the simulation results with those of previously reported experiments and found good agreement between them. From these validations, we confirmed that the proposed hybrid method was applicable to heterogeneous bubbly flow simulation, and it avoided the weakness which the original hybrid method has.