Coupled Level Set Research Articles

Coupling level-set with volume-of-fluid for interface computation of incompressible gas-liquid flows

In this study, a solver coupling the level-set and volume-of-fluid methods is developed for interface computation of incompressible two-phase flows on the OpenFOAM platform. It corrects the surface tension, density, and viscosity of the fluids with the level-set function synchronously. To examine the effect of density and viscosity corrections, an intermediate solver that only corrects the surface tension force is also developed. Two test cases, that is, a bubble rising freely in stagnant water and a drop impacting on a liquid surface, are performed to validate and compare the capabilities of the new solvers. It is found that the coupling solver which corrects all the fluids’ properties mentioned above has the best prediction accuracy, especially for Rayleigh jet issues. With the application of this solver, the mechanism for the bubble entrainment in drop impact on a liquid pool is explained.

A finite volume coupled level set and volume of fluid method with a mass conservation step for simulating two‐phase flows

AbstractThis article presents a finite volume method for simulating two‐phase flows using a level set approach coupled with volume of fluid method capable of simulating sharp fluid interfaces. The efficiency of the method is a result of the fact that the interface is calculated in order to satisfy mass conservation with no explicit interface reconstruction step and the mass fluxes across cell‐faces are corrected to respect the recovered volume fraction. The mass‐conservation correction step proposed here, is utilized using an iterative algorithm which solves a reaction‐diffusion equation for the mass correction of the level set. The re‐sharpened volume fraction is used for the new volumetric fluxes at each cell which are calculated through the proposed algorithm that guarantees that they satisfy mass conservation. The algorithm is not limited in representing the interface with the 0.5‐contour and is applicable for arbitrary polyhedral cells. Good accuracy and mass conservation are achieved when compared to other conservative approaches.

Bouncing modes and heat transfer of a dielectric droplet in the presence of an external electric field

A numerical investigation of droplet bouncing and heat transfer over a heated surface in the presence of an external electric field has been reported. The coupled set of governing equations including the electrostatic and incompressible Navier-Stokes equations, have been implemented in the finite-volume framework of OpenFOAM®. The coupled level set and volume of fluid (CLSVOF) approach has been used to capture the droplet interface. The influence of the electric field over the droplet dynamics and bouncing modes are systematically studied. Different bouncing modes are observed and they have been mapped with respect to the electric capillary number, CaE and Weber number, We. Two new modes have been identified at CaE=0.1. The Coulombic attraction at the solid-liquid contact line extends the total contact time of the droplet. The local electric field distribution depends on the droplet’s local curvature. The stronger distribution of electrostatic pressure near the tip of the droplet induces a stretching behavior. The stretched droplet, extended contact time and enhanced fluid circulation increase the heat transfer. This work provides a deeper understanding of droplet impact, bouncing dynamics and related heat transfer characteristics influenced by an external electric field.

Study of the secondary droplet breakup mechanism and regime map of Newtonian and power law fluids at high liquid–gas density ratio

This work reports the numerical investigation of the secondary breakup of non-Newtonian droplets at different Weber Weg and Ohnesorge Ohl numbers. As part of this work, an in-house coupled level set volume of fluid solver is developed based on OpenFOAM libraries. It uses improved curvature calculation techniques like smoothening and the closest point search method. Flow is assumed to be axisymmetric. Approximately 95 different cases were simulated to investigate the effect of Weg and Ohl numbers on secondary breakup for Newtonian, shear-thinning, and shear-thickening fluids. Ohl varies from 10−3 to 101, and, correspondingly, Weg varies from 101 to 103. The non-Newtonian rheology is modeled as a power-law fluid, and the power-law index n ranged from 0.2–1.8. The present work describes the flow field near the droplet and the effects of non-Newtonian parameters and viscosity on the flow field. The various aspects of droplet dynamics like droplet deformation ratio y, deformation rate ẏ, and coefficient of pressure Cp are studied and compared with the internal flow theory. A generalized relation for critical Weber number Weg,cr is proposed for both Newtonian and non-Newtonian fluids and is shown in a phase diagram plot to map the different regimes of secondary droplet breakup.

Numerical study on flow and heat transfer characteristics of two oil droplets impinging the wall simultaneously under the influence of micro-bubble

In the process of oil-gas micro lubrication, affected by high pressure, temperature and other factors, part of the air in the transportation pipeline will be mixed into the oil liquid or part of the gas will be released in the oil liquid. Hollow oil droplets containing bubbles are easy to form at the nozzle. Micro-bubbles have an important influence on the morphological evolution and heat transfer characteristics of synchronous oil droplets impinging the oil film. Based on the coupled level set volume fraction (CLSVOF) method, the numerical simulation of the synchronous oil droplet impinging the oil film is carried out, the effects of different bubble distribution forms on the heat transfer characteristics of the two oil droplets synchronously impinging the oil film jet are investigated, and the formation mechanism of the central film jet in the impingement process is discussed, The influence of different bubble distribution forms on the cooling and heat dissipation effect in the impingement region is analyzed. The results show that there is a film jet at the gap between the two droplets in the process of synchronous impinge. The asymmetric distribution of hollow oil droplets will lead to the deflection of the central film jet. The synchronous impinge behavior improves the flow characteristics of the fluid in the impingement area, enhances the convective heat transfer efficiency between the high-temperature and low-temperature fluids, and has the effect of improving the heat flux in the region. The heat flux in the impingement spreading region of oil droplet containing bubbles is relatively low and the distribution uniformity is poor. The simultaneous impinge behavior under different bubble distribution modes has different degrees of negative effects on the cooling effect of the wall of the impingement area. During the impinge process, the cooling and heat dissipation efficiencies of solid oil droplet and oil droplet containing bubbles on the inner wall of the domain will reverse halfway.

Numerical analysis of shock interaction with a spherical bubble

Two-dimensional and three-dimensional computational fluid dynamics studies of a spherical bubble impacted by a supersonic shock wave (Mach 1.25) have been performed to fully understand the complex process involved in shock–bubble interaction (SBI). The unsteady Reynolds-averaged Navier–Stokes computational approach with a coupled level set and volume of fluid method has been employed in the present study. The predicted velocities of refracted wave, transmitted wave, upstream interface, downstream interface, jet, and vortex ring agree very well with the relevant available experimental data. The predicted non-dimensional bubble and vortex velocities are also in much better agreement with the experiment data than values computed from a simple model of shock-induced Rayleigh–Taylor instability (the Richtmyer–Meshkov instability). Comprehensive flow visualization has been presented and analyzed to elucidate the SBI process from the beginning of bubble compression (continuous reflection and refraction of the acoustic wave fronts as well as the location of the incident, refracted and transmitted waves at the bubble compression stage) up to the formation of vortex rings as well as the production and distribution of vorticity. Furthermore, it is demonstrated that turbulence is generated with some small flow structures formed and more intensive mixing, i.e., turbulent mixing of helium with air starts to develop at the later stage of SBI.

Numerical simulation of primary atomization process of liquid jet in subsonic crossflow

Studies of primary atomization of liquid transverse jets in subsonic crossflow consider surface waves as the main cause of jet fragmentation. The characteristics of surface waves during jet fragmentation have been initially analyzed, but there is a lack of understanding of the mechanism of surface wave generation and development. This paper investigates the primary atomization of liquid transverse jets in subsonic crossflow based on the numerical method of Large Eddy Simulation (LES) with the coupled level set and volume of fluid method (CLSVOF) interface tracking, combined with adaptive mesh encryption techniques, where the liquid phase medium is water. This paper focuses on the fine structure of the primary atomization of the jet column, including the evolution of the jet column and the process of shedding the surface of the jet column, to clarify the physical process of primary fragmentation of the jet. The near-field flow structure and gas–liquid interaction are also analyzed to investigate the mechanism of primary atomization of liquid transverse jets and the mechanism of surface wave generation and development in subsonic flows. The results show that the shear action of gas and liquid leads to the generation of Kelvin–Helmholtz (KH) unstable wave, and KH surface wave dominates the surface breaking of jet column. The extrusion of gas and liquid results in the unstable fluctuation of Rayleigh–Taylor (RT), and the RT surface wave dominates the jet column, and finally the cylindrical fracture occurs. The development trend of RT surface wave is to increase the wavelength along the jet direction. When the wavelength of the RT surface wave develops from 0.12 mm to 1.2 mm, the jet column will be columnar broken at the trough of the last RT wave.

Estimating bubble interfacial heat transfer coefficient in pool boiling

Interfacial heat transfer coefficient (IHTC) is one the most deterministic factors of nucleate boiling characteristics in pool boiling. IHTC and bubble dynamics have a reciprocal effect on each other, which makes accurate estimations of IHTC even more challenging, but important for nucleate boiling studies. In this study, by considering interfacial heat resistance, micro-layer heat transfer and conjugate heat transfer, a comprehensive model that is capable of simulating phase change phenomena and IHTC has been developed and a modified form of Volume of Fluid method (VOF) is used to simulate pool boiling phenomena. In this study, three major challenges in simulating bubble dynamics and related phase change heat transfer using a VOF method have been successfully addressed to achieve more accurate simulations. First, spurious currents resulting from approximating curvature in VOF and interface diffusion have been minimized by introducing curvature smoothing and employing a simplified coupled level set volume of fluid method (S-CLSVOF). Second, simulation instability due to the concentration of source terms on the interface has been addressed by smearing source terms around the interface. Third, micro-layer thickness, which is noticeably smaller than computational cells, has been calculated based on a linear depletable micro-layer method. Effects of three-phase contact line were adopted by introducing a dynamic contact angle model and temperature variation inside the heater. The model shows great agreement with available experimental and numerical results in nucleate boiling of water and R113 in terms of bubble growth and departure rate, frequency and temperature distribution, and micro-layer thickness. The new model developed in this study simulates IHTC in two water cases and its relationship to interfacial relative velocity.

Comparison of interface capturing methods for the simulation of two-phase flow in a unified low-Mach framework

This paper proposes a comparison of four popular interface capturing methods : the volume of fluid (VOF), the standard level set (SLS), the accurate conservative level set (ACLS) and the coupled level set and volume of fluid (CLSVOF). All methods are embedded into a unified low-Mach framework based on a Cartesian-grid finite-volume discretization. This framework includes a sharp transport of the interface, a well-balanced surface tension discretization and a consistent mass and momentum transport which allows capillary-driven simulations with high density ratio. The comparison relies on shared metrics for geometrical accuracy, mass and momentum conservation which exposes the weakness and strengths of each method. Finally, the versatility and capabilities of the proposed solver are demonstrated on the simulation of a 3D head-on collision of two water droplets. Overall, all methods manage to retrieve reasonable results for all test cases presented. VOF, CLSVOF and ACLS tend to artificially create little structures while SLS suffers from conservation issues in the mesh resolution limit. This study leads us to the conclusion that CLSVOF is the most promising method for two-phase flow simulations in our specific framework because of its inherent conservation properties and topology accuracy.

Correction: Kim, H.; Park, S. Coupled Level-Set and Volume of Fluid (CLSVOF) Solver for Air Lubrication Method of a Flat Plate. J. Mar. Sci. Eng. 2021, 9, 231

The authors would like to make a correction to their published paper [...]

A hybrid moment of fluid–level set framework for simulating primary atomization

This paper presents a hybrid moment of fluid–level set (HyMOFLS) method of liquid/gas interface reconstruction for the application to simulate primary atomization of liquid fuel. This method combines the moment of fluid (MOF) method and the level set framework in the coupled level set volume of fluid (CLSVOF) method. In this hybrid method, the MOF and CLSVOF methods are used to reconstruct the interface in the under-resolved and the resolved regions of the flow, respectively. An interface surface resolution metric called interface resolution quality (IRQ) is introduced to identify and classify these two flow regions in the computational domain. Such a strategy classifies/tags each computational cell with MOF or CLSVOF method based on a threshold value for the IRQ. The MOF method uses liquid volume fraction as well as centroids of liquid and gas phases for the interface reconstruction. The CLSVOF method uses the level set for describing the interface and liquid volume fraction for conserving the mass. The phase centroids in the HyMOFLS method are computed and transported on-the-fly during the cell tagging process. The transport of the liquid volume fraction, level set, and the phase centroids are performed using a directionally split algorithm. This algorithm is coupled with the Navier-Stokes equations solver that uses ghost fluid method as well as consistent mass and momentum flux computation for the momentum equation. Various numerical tests that exhaustively assess the capabilities, accuracy, and computational time consumption of the HyMOFLS method under multiple flow conditions and configurations are presented. The results from these tests suggest that this hybrid framework is capable of well capturing the liquid/gas interface belonging to thin and under-resolved structures that are often encountered in simulations of turbulent atomization of liquids. Following these tests, a detailed parametric study on the threshold value of IRQ is presented to test its effect on the accuracy of interface reconstruction. Finally, this hybrid framework is employed to simulate turbulent jet injection and pre-filming planar Airblast atomization cases of engineering applications. The proposed HyMOFLS method is found to achieve a good balance between the accuracy and the computational cost of reconstructing the liquid/gas interface for complex and turbulent atomization configurations.

Eulerian–Eulerian multiphase models for simulating collapse of submarine sediment column with rheological characteristics in air–water flow

Submarine massive sediment movement, which may devastate submarine infrastructure and cause huge waves threatening the coastal areas, combined with the air–water interface is a significant issue of the multiphase flows in the areas of ocean engineering and geoscience. Currently, simulating rheology-based sediment flows is still a challenge because of the complex intergranular dynamics and its coupling with computational fluid dynamics. In particular, air–water–sediment multiphase models that can simulate such rheology-based flows while also taking into account the accurate capture of the air–water interface have not been developed yet. Coupling with the coupled level set method and volume of fluid method in the air–water two-phase flow, this study develops two new Eulerian–Eulerian multiphase models for simulating the rheology-based sediment flows. The difference between the two developed models is that how to model the drag force of the particle–fluid interactions. To demonstrate their capabilities, the two developed models are employed to simulate the gravitational collapse of submarine sediment column in air–water flow with loose-packing case and dense-packing case. The results of collapse process, induced air–water interface fluctuation, and contractancy/diltancy behavior are all agree well with those in previous experiments and simulations. In addition, comparing the results of two developed models, it can be concluded that different modeling methods of the drag force not only directly affect the water–sediment interactions, but also indirectly influence the air–water interface fluctuations and the intergranular stresses remarkably.

Numerical investigation on the influence of different physical factors on the interface evolution in 3D RTI using CLSVOF method

The three-dimensional (3D) Rayleigh–Taylor instability (RTI) problem is numerically investigated using the coupled level set and volume of fluid (CLSVOF) method. The CLSVOF method combines the level set and volume of fluid methods to ensure good mass conservation performance, enabling the curvature of the interface captured by numerical simulations to be accurately calculated. A classical single-mode RTI (with only one “mushroom” generated under the initial setting) is adopted for numerical verification, and the shape of the interface and the penetration depth with respect to time are determined. Based on this initial two-dimensional single-mode RTI problem, the influence of factors such as the surface tension, density ratio, Reynolds number, and viscosity ratio on the 3D effects caused by the velocity gradient on both sides of the interface are thoroughly analyzed. This analysis allows us to obtain the basic laws governing the influence of different physical factors on the 3D effects of the RTI.

Numerical simulation of two droplets impacting upon a dynamic liquid film

The impact of droplets on the liquid film is widely involved in industrial and agricultural fields. In recent years, plenty of works are limited to dry walls or stationary liquid films, and the research of multi-droplet impact dynamic films is not sufficient. Based on this, this paper employs a coupled level set and volume of fluid (CLSVOF) method to numerically simulate two-droplet impingement on a dynamic liquid film. In our work, the dynamic film thickness, horizontal central distance between the droplets, droplets’ initial impact speed, and simultaneously the flow velocity of the moving film are analyzed. The evolution phenomenon and mechanism caused by the collision are analyzed in detail. We find that within a certain period of time, the droplet spacing does not affect the peripheral crown height; when the droplet spacing decreases or the initial impact velocity increases, the height of the peripheral crown increases at the beginning, and then, because the crown splashed under Rayleigh–Plateau instability, this results in the reduction of the crown height. At the same time, it is found that when the initial impact velocity increases, the angle between the upstream peripheral jet and the dynamic film becomes larger. The more obvious the horizontal movement characteristics, the more restrained the crown height; the spread length increases with the increase of the dynamic film speed, droplet spacing and the initial impact velocity. When the liquid film is thicker, more fluid enters the crown, due to the crown being unstable, the surface tension is not enough to overcome the weight of the rim at the end of the crown, resulting in droplets falling off.

Numerical investigation of hot and cold bubbles rising in water

A compressible air bubble rising in water with heat transfer is simulated. We use the coupled level set and volume of fluid method to track the interface. The solver is verified with a non-isothermal static 3D bubble. The volume change of the bubble and the pressure difference between the inside and outside of the static bubble agree well with the theoretical solutions. Hot and cold 3D air bubbles rising in water are simulated and different rising paths are observed. The mechanisms underlying the path instability are elucidated by analyzing the vortex dynamics and shape deformation. We observe the hairpin vortex with 2R mode behind the rising bubble during the zigzag motion. The oscillation frequencies of the lateral bubble motion, the vorticity accumulation on the bubble surface, the forces exerted on the bubble in X and Y directions are the same while the oscillation frequencies of the aspect ratio and forces exerted on the bubble in Z direction are twice of that of the lateral bubble motion. The temperature changes faster in the rear part of the bubble due to the intensive water motion in the bubble wake. The volume-averaged water velocity presents a linear increase with the bubble rise while the kinetic energy displays a quadratic increase.

Numerical Study of Nanosecond Pulsed Laser Impact on a Water Droplet

An integrated hydrodynamic model that involves a laser heat source, surface evaporation, and interfacial driving forces is developed to simulate the complex physical process of a nanosecond pulsed laser impacting on a water droplet. Droplet deformation tracked by the coupled level set and volume of fluid method is contrasted with the experimental results, and it is shown that the coupled model can be used to simulate the droplet expansion dynamics. From the simulation of droplet deformation, it can be found that, with increasing laser energy, the droplet becomes thinner. With the highest laser energy, the jet on the opposite side to laser impact is interpreted as the flow of high-speed fluid near the axis, which is also confirmed by the velocity field. The simulated temperature reaches or even exceeds the critical value, and the recoil pressure does not completely cover the whole hemispherical surface of the droplet. The liquid-removal depth, which represents the distance that the liquid-phase interface retreats during evaporation, is much shallower than the absorption depth. It can be concluded that propulsion is gained from the intense evaporation of the superheated layer.

Analysis of temperature field and convection heat transfer of oil-air two-phase flow for ball bearing with under-race lubrication

PurposeUnder-race lubrication can increase the amount of lubricating oil entering a bearing and greatly improve lubrication and cooling effects. The oil-air two-phase flow and heat transfer characteristics inside a ball bearing with under-race lubrication play a key role in lubrication and cooling performance. The purpose of this paper is to study these two characteristics, and then provide guidance for lubrication and heat dissipation of bearing with under-race lubrication.Design/methodology/approachIn this paper, a simplified three-dimension heat transfer model of ball bearing with under-race lubrication is established; the coupled level set volume of fluid method is used to track the oil-air two-phase flow, and the Palmgren method is used to calculate the heat generation. The influence of rotation speed and inlet velocity on oil volume fraction, temperature and convection heat transfer is investigated. A temperature test for under-race lubrication is carried out.FindingsBecause of the centrifugal force, lubricating oil is located more on the outer ring raceway. As the rotation speed decreases and the inlet velocity increases, the oil volume fraction increases and the temperature decreases. Furthermore, the area with high oil volume fraction has a large convection heat transfer coefficient and low temperature. The error between the simulation temperature and the test temperature is within 10%.Originality/valueThe research on the temperature field and convection heat transfer characteristics of under-race lubrication ball bearings at different rotation speeds and inlet velocities is rarely involved.

Numerical study on multiple bubbles condensation in subcooled boiling flow based on CLSVOF method

Numerical studies are performed to investigate the condensation behavior of single and multiple bubbles in subcooled boiling flow. An open-source code is developed to model the dynamic behavior of the bubbles in real-time. The Newtonian flow is considered and relative equations are solved employing a coupled Level Set (LS) and Volume of Fluid (VOF) method known as CLSVOF model according to the Pressure Implicit with Splitting of Operators (PISO) algorithm. Initially, the numerical findings were compared and verified by available experimental data. The result of a single bubble condensation revealed that the initial bubble size, the subcooling of liquid, and the velocity of the flow not only significantly affect the bubble deformation behavior, but also the rate of condensation. For multiple bubbles, the results revealed that due to interaction between bubbles, bubbles' dynamic condensation behavior is more complex compared to a single one. Due to this interaction, it is found that the rate of bubble condemnation and condensation process vary. Furthermore, the effects of the gradient velocity, gradient temperature, and gap between multiple bubbles on the rate of mass transfer through the condensation are studied. A critical gap between multiple bubbles is introduced. It is found that when (H∗=H/D≥2) for different bubble diameters, the effect of bubbles interaction can be ignored. Here H∗ is a dimensionless gap of center-to-center of bubbles.

Simulation research on hydraulic characteristics of conical X-shaped flaring gate piers in lock chamber based on CLSVOF method

3-D numerical simulation was carried out for flood discharge and energy dissipation process of conical X-shaped flaring gate piers in a hydropower project by using coupled Level Set and VOF method and RNG k-ε turbulent model. The change laws of flow pattern, water surface profile, velocities and pressures distributions in lock chamber of conical X-shaped flaring gate piers were gained. The results of numerical simulation were compared with the model test data and good agreement was found. The numerical results show that, there are differences on both of water surface profiles in lock chamber. With the increase of discharge, water surface profiles falls at the longitudinal axis and vertical diffusion of ski-jump flows are large on the downstream of flaring gate piers.

Contact angle measurements for automotive exterior water management

The simulation of fluid flow over solid surfaces is important in many applications, for example, in automotive applications where good visibility and the performance of external sensors are essential. Multiphase CFD simulation methods such as level set or coupled level set–volume of fluid typically require a validated dynamic contact angle model as a function of capillary number to accurately resolve the near wall behaviour. This paper explores an experimental approach to identify a suitable contact angle model for pure and contaminated water on glass and painted surfaces. Applying image processing methods to high-resolution digital images of droplets descending flat plate samples of the required surfaces, the dynamic advancing and receding contact angles and capillary number are determined. Cox–Voinov, de Gennes and Yokoi models are parameterised from the experimental data, and the Yokoi model is shown to be the most suited to these surface/fluid combinations where hysteresis is significant. A multiphase simulation implementing the Yokoi model demonstrates good correlation for the Bond number between simulation and experiment.Graphic abstract