Coupled Level Set Research Articles

Dynamics of an Evaporating Drop Migrating in a Poiseuille Flow

Abstract The evaporation of a liquid drop of initial diameter (Ddrop) migrating in a tube of diameter (D0) is investigated using the coupled level set and volume of fluid method focusing on determining the heat and mass transfer coefficients for a deforming drop. A robust phase change model is developed using an embedded boundary method under a finite difference framework to handle vaporizing flows. The model is extensively validated through simulations of benchmark problems such as arbitrary evaporation of a static drop and reproduction of psychrometric data. The results show that the Sherwood number and the Nusselt number reach a steady value after an initial transient period for the drop subjected to Hagen-Poiseuille flow. A parametric study is conducted to investigate the effect of drop deformation on the rate of evaporation. It is observed that Stefan flow due to evaporation has a negligible impact on the drop deformation dynamics. We also observed that, for different values of Ddrop/D0, the Sherwood number follows a linear correlation with Re1/2Sc1/3.

Coupled material point and level set methods for simulating soils interacting with rigid objects with complex geometry

The material point method (MPM) is often used to simulate soils that interact with (nearly) rigid objects, such as structures, machines, or rocks. Yet MPM simulations of such problems are quite challenging when the objects have complex shapes. In this paper, we propose an efficient approach for incorporating geometrically complex rigid objects into MPM modeling. The proposed approach leverages the level set method, which can efficiently delineate arbitrary surface geometry, to represent the boundary of a discrete object. For coupling the level set object with the MPM domain, a robust algorithm is developed on the basis of contact mechanics. Through numerical examples of varied complexity, we verify the proposed approach and demonstrate its ability to efficiently simulate challenging problems wherein soils interact with complex rigid objects such as debris-resisting baffles, a vehicle wheel, and basal terrain.

An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change

An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change

An investigation on the impact of two vertically aligned drops on a liquid surface

The dynamics of two vertically coalescing drops and a pool of the same liquid have been investigated using a Coupled Level Set and Volume of Fluid (CLSVOF) method. Such a configuration enables us to study the dynamic interaction of an arbitrary-shaped liquid conglomerate, formed owing to drop–drop coalescence, with a pool. Similar to drop–pool and drop–drop interactions, partial coalescence is observed when a conglomerate interacts with a pool. The presence of the pool below the father drop is found to influence the coalescence characteristic of the two drops. At the same time, the movement of the capillary waves resulting from the interaction of two drops governs the coalescence dynamics of the conglomerate with the pool. As liquid interfaces interact and generate capillary waves at multiple locations, complex trajectories of capillary waves are observed, which play a crucial role in determining the pinch-off characteristics of the satellite during conglomerate–pool interaction. We examine the effect of the ratio of the diameters of the lower/father drop to the upper/mother drop (Dr) on the coalescence dynamics while maintaining the size of the mother drop constant. The variation in the coalescence dynamics due to change in Dr is quantified in terms of the residence time (τr), pinch-off time (τp) and the satellite diameter to conglomerate diameter ratio (Ds/Dc). The coalescence dynamics of the conglomerate is then compared with that of an equivalent spherical drop of the same volume and also with that of a drop initialized with the same shape as that of the conglomerate. Finally, the regions of complete and partial coalescence for the conglomerate–pool interactions are demarcated on the Weber number–diameter ratio (We−Dr) space.

Experimental and numerical study of liquid film by jet impingement: Based on contact angle model

Liquid film by jet impingement is widely applied in aerospace, steel quenching, ink-jet printing, and cleaning. In this paper, simulations with the modified contact angle model were used to describe the characteristics of the liquid film. Based on the Hoffman's law and the Tanner's correlation, the contact angle model was constructed and further nested within the Coupled Level Set and Volume of Fluid model. The model determined the movement direction of contact line according to the inner product of the normal vector at the phase interface and the lateral velocity in the cell and then outputted the value of the contact angle. Results showed that the advancing and the receding contact angles of droplet were inappropriate for the simulation of the liquid film. The size of the liquid film obtained by the static contact angle largely depended on the selection of contact angle values. Instead, the modified contact angle model provided an accurate prediction on the morphology and the size of the liquid film.

Dynamics of bubbles detached from non-circular orifices: Confinement effect of orifice boundary

In practice, gas usually escapes from non-circular orifices due to machining accuracy, plugging, and other reasons, especially gas leakage in the natural environment. Compared to circular orifices, the bubble behavior and dynamics of non-circular orifices have rarely been investigated. This paper presents three-dimensional imaging system results to obtain comprehensive information on bubble dynamics generated from five elliptical orifices with equal cross-sectional areas and different aspect ratios. Computational fluid dynamics studies using the coupled level set and volume of fluid methods were adopted to assist in the flow field analysis. Experimental data were analyzed statistically to study the effects of orifice wall structure on bubble flow pattern, size, trajectory, and other dynamic parameters. The results show that the equivalent bubble diameter increases with increasing orifice aspect ratio, as does the randomness of the bubble flow field, while the bubble flow pattern complexity increases. A force analysis as the bubble is generated is also conducted. The wall structure of the orifice affects the bubble migration effect to some extent. The work presented in this article provides valuable fundamental information for a range of heater and desalination applications in chemical engineering, wastewater treatment, and immersion leakage identification.

Simulation-based study of low-Reynolds-number flow around a ventilated cavity

Ventilated cavitating flows are investigated via direct numerical simulations, using a coupled level set and volume of fluid method to capture the interface between the air and water phases. A ventilated disk cavitator is used to create the cavity and is modelled by a sharp-interface immersed boundary method. The simulation data provide a comprehensive description of the two-phase flow and the air leakage and vortex shedding processes in the cavitating flow. The mean velocity of the air phase suggests the existence of three characteristic flow structures, namely the shear layer (SL), recirculating area (RA) and jet layer (JL). The turbulent kinetic energy (TKE) is concentrated in the JL in the closure region, and streamwise turbulent fluctuations dominate transverse fluctuations in both SL and JL. Budget analyses of the TKE show that the production term causes the TKE to increase in the SL due to the high velocity gradients, and decrease in the JL due to streamwise stretching effects. Air leakage and vortex shedding occur periodically in the closure region, and the one-to-one correspondence between these two processes is confirmed by the velocity and volume fluid spectra results, and the autocorrelation function of the air volume fraction. Moreover, the coherent flow structures are analysed using the spectral proper orthogonal decomposition method. We identify several fine coherent structures, including $SL_{KH}$ induced by the Kelvin–Helmholtz instability, $SL_{out}$ associated with large-scale vortex shedding, $SL_{in}$ associated with small-scale vortex shedding, and $SL_{r}$ associated with upstream turbulent convection. The present study complements previous research by providing detailed descriptions of the turbulent motions associated with the violent mixing of air and water, and the complex interactions between different characteristic structures in cavitating flows.

Insights into the bubble formation dynamics in converging shape microchannels using CLSVOF method

Abstract Bubble formation in a square microchannel having a converging shape merging junction has been studied using the Coupled Level-Set and Volume-of-Fluid (CLSVOF) method. The influence of variations in merging junction angles, fluid properties, and operating conditions on the bubble length and pressure drop has been analyzed. The results show a direct relationship between surface tension, gas-liquid flow ratio, and the inverse relation of continuous phase viscosity with the bubble length. Moreover, opposite variations of these parameters are observed for pressure drop. This work reveals a discerning influence of the angle variations of merging junction on the interplay between inertial, viscous, and surface tension forces in the bubble formation mechanism. We envisage that this numerical work will be of significant interest for the process intensification in various industries that deal with gas-liquid microfluidic systems.

Numerical investigation of multi rising bubbles using a Coupled Level Set and Volume Of Fluid (CLSVOF) method

A Coupled Level Set and Volume Of Fluid (CLSVOF) method is presented in this article for simulating the multi-bubble rising problem. This method can accurately conserve mass and capture gas/liquid moving interface to understated bubbles’ evolution in detail. In addition to capturing bubbles’ evolution, the present CLSVOF method is also combined with the projection method of flow field solver, which can provide two-phase flow field solutions. Comparisons with reference solutions have also been carried out for the single-bubble rising case. It is shown that the results obtained using the present method agree well with reference solutions, even where there are fewer grid points. The mass conservation performance is compared with the numerical result of the level set method. The present two-phase flow model is further adopted to study the high density ratio on bubbles’ dynamic and kinematic characteristics.

Effect of surface tension gradients on coalescence dynamics of two unequal-sized drops

Numerical simulation using the coupled level set and volume of fluid (CLSVOF) method was conducted to study the coalescence dynamics of two different-sized drops of miscible liquids. Effects of surface tension ratio, Ohnesorge number (Oh), and diameter ratio on three pinch-off regimes: first- and second-stage, and no pinch-off, are examined. Partial coalescence is characterized by its appearance, disappearance, and subsequent reappearance as the surface tension ratio decreases. A regime map of distinct coalescence outcomes is constructed for different surface tension ratios, where the critical surface tension ratio required for partial coalescence increases monotonically with an increase in Oh.

Interfacial wave of the gas-liquid two-phase flow in unsaturated reservoir pores

Unsaturated reservoir pores exist widely in porous self-lubricating materials for the continuous consumption of lubricant. The complex gas-liquid two-phase flow behavior in the pores significantly affects the self-lubricating performance. In this paper, the two-phase flow model in unsaturated pores was established based on the Couple Level Set and Volume of Fluid method. Two kinds of porous materials with significantly different wettability, stainless steel and polytetrafluoroethylene (PTFE), were concerned. The two-phase flow behaviors were investigated to reveal the flow mechanism in the unsaturated pores. The different flow behaviors caused by the wettability of materials were quantitative characterization. Results show that, the gas rises with a convex interface in the stainless steel pore, and the bubble is generated after the contact line is pinned on the edge of the pore at 35 ms. While in the PTFE pore, the gas rises with a concave interface. And the gas profile changes from concave to convex after the contact line is pinned at 32 ms. In the two pores, the gas-liquid interface fluctuates periodically. In the hydrophilic stainless steel pore, the fluctuation amplitude decreases and finally tends to be stable with the increase of time. In the hydrophobic PTFE pore, the interface has constant fluctuation amplitude for the attraction between gas and the hole wall. The fluctuation of the gas-liquid interface has an important influence on the flow state of the lubricant film. The results help to clarify the two-phase flow mechanism within unsaturated pores, and provide guidance for the self-lubrication design of the porous materials.

Numerical Study on Interfacial Structure and Mixing Characteristics in Converter Based on CLSVOF Method

The blowing flow is a key factor in molten bath stirring to affects the steel-bath interface fluctuation and chemical reaction in the top-bottom-blowing converter. The Volume of Fluid (VOF) method is widely used to capture the gas-liquid interface. However, some limitations exist in dealing with the interface curvature and normal vectors of the complex deformed slag-bath interface. The Coupled Level-Set and Volume of Fluid (CLSVOF) method uses the VOF function to achieve mass conservation and capture interface smoothly by computing the curvature and normal vector using the Level-Set function to overcome the limitations in the VOF model. In the present work, a three-dimensional (3D) transient mathematical model coupled CLSVOF method has been developed to analyze the mixing process under different injection flow rates and bottom-blowing positions. The results show that when the bottom-blowing flow rate increases from 0.252 kg/s to 0.379 kg/s, the mixing time in the molten bath gradually decreases from 74 s to 66 s. When the bottom-blowing flow rate is 0.252 kg/s, it is recommended to distribute the outer bottom-blowing position on concentric circles with Dtuy,2/D2 = 0.33.

Atomization of liquid pulsed jet in subsonic crossflow

Pulsed jet is an effective solution to improve fuel jet penetration depth and consequently increase the mixing efficiency of gas–liquid in conventional combustion chambers. This has the benefits of reducing pollutant emissions and diminishing the instability of fuel combustion. However, the atomization process of pulsed jets with small amplitude has still not been properly investigated. This paper studies such a process through Large Eddy Simulation and a Coupled Level Set and Volume of Fluid method. We investigate the atomization process in a liquid pulsed jet with a subsonic crossflow and the impact of the Strouhal number on atomization morphology and the behavior of the pulsed jet in general. Results show that, with a constant mass flow rate, the role of Rayleigh–Taylor instability is replaced by the periodic fluctuation of the jet velocity, which ends up dominating the primary process of atomization of the liquid transverse pulsed jet. This also improves atomization, in general, and the fragmentation of the jet. We also show that the Strouhal number significantly impacts the penetration depth of the jet, with high values increasing penetration by up to 12%.

A generalized coupled level set/volume-of-fluid/ghost fluid method for detailed simulation of gas-liquid flows

A generalized coupled level set/volume-of-fluid/ghost fluid method for the detailed simulation of gas-liquid flows is proposed in this paper. The interface is captured by the coupled level set and volume-of-fluid method, where the level set method is used to compute normal vector and curvature accurately, and the volume-of-fluid method is used to conserve the global volume or mass. The ghost fluid method is also used for discretization across the interface. The novelty of the present approach lies in that a generalized formulation for the conversion between the level set function and the volume-of-fluid function is proposed in a simple and efficient manner. Three benchmarks, including Zalesak's disk, two-dimensional deformation and three-dimensional deformation, are used for validation and verification. It shows that excellent agreement is achieved, and the present method has first-order accuracy. The current method is further applied to the simulations of droplet dynamics, rising bubbles, head-on droplet collision and liquid jet breakup, demonstrating the capability to accurately capture the interface.

Laser coupling in waterjets subject to jet instabilities, laser parameters, and alignment errors.

High coupling accuracy and efficiency attract wide attention in waterjet-guided laser technology due to the requirements for high processing performance in hard-to-cut material and diamond industries. The behaviors of axisymmetric waterjets injected into the atmosphere through different types of orifices are investigated by adopting a two-phase flow k-epsilon algorithm. The water-gas interface is tracked with Coupled Level Set and Volume of Fluid method. The electric field distributions of laser radiation inside the coupling unit are modeled by wave equations and numerically solved with the full-wave Finite Element Method. The coupling efficiency of the laser beam affected by waterjet hydrodynamics is studied by considering the profiles of the waterjet shaped at transient stages, namely vena contracta, cavitation, and hydraulic flip. The growth of the cavity leads to a larger water-air interface and increases the coupling efficiency. Eventually, two types of fully developed laminar waterjets, i.e. constricted waterjets and non-constricted waterjets, are formed. Constricted waterjets that are detached from the wall throughout the nozzle are preferable to guide laser beams since they significantly increase the coupling efficiency compared to non-constricted waterjets. Furthermore, the trends of coupling efficiency affected by Numerical Aperture (NA), wavelengths, and alignments errors are analyzed to optimize the physical design of the coupling unit and develop the alignment strategies.

Numerical Study of Heat Transfer During Oblique Impact of a Cold Drop on a Heated Liquid Film

Abstract A three-dimensional study of a cold droplet impacting obliquely on a heated solid flat surface covered with a hot liquid layer has been performed. The drop Weber number, liquid film thickness, and drop impact angle are set to a range from 100 to 800, 0.1 to 0.4, and 0 deg to 60 deg, respectively. The interface evolution and thermal behavior of the drop impingement is well captured using coupled level set and volume of the fluid method (CLSVOF). The code is validated against previously published results both qualitatively and quantitatively. The results show that in the case of oblique drop impact, the crown dynamics and wall heat flux distribution exhibit an asymmetric pattern, with secondary droplets generated solely on the downstream side, as opposed to normal drop impact in which the secondary drops generated around the circumference of the crown. Based on heat flux values, two distinct region within the liquid film exist: (i) impact region around the impact point and (ii) undisturbed region far from the impact region characterized by the impact dynamics. A parametric analysis further reveals that for a moderate Weber number, asymmetric behavior increases as the drop impact angle increases, resulting in a reduction in heat transfer from the solid surface. However, for a drop impacting at an angle of 28 deg, increased asymmetry due to a increase in the Weber number results in significant cooling of the impact region. Furthermore, it is also found that a thinner liquid film promotes higher heat transfer from the solid surface, resulting in a higher wall heat flux.

Modeling the impingement deformation and solidification of a hollow zirconia droplet onto a dry substrate and solidified layer

Despite the numerous research studies involving the solidification of continuous molten metal droplet impingement on dry substrates during the process of plasma spraying, the impingement between a hollow molten metal droplet and a solidified layer has, to date, not yet been thoroughly explored. A liquid shell enclosing the air cavity forms a hollow droplet. The coupled level set and volume of fluid method is used to track the air–liquid interface, and the enthalpy–porosity method is used to track the liquid–solid interface. A two-dimensional axis symmetric model is adopted to describe the impingement and solidification process. This study includes a detailed investigation of transient impact deformation and solidification. The heat transfer characteristics of the solidification of a continuous dense and hollow molten droplet impacting on a dry substrate and solidified layer are studied and compared. A thin solidified layer appears and develops between the droplet and the substrate, and the impacting droplet finally pins to the surface with mainly the liquid solidified. For a hollow droplet impact on the solidified layer, a splashed crown liquid sheet forms from the drop-solidified layer neck area. Various temperatures of the solidified layer induce a different development of the crown, spreading, and rebound counter-jet. The deterioration of local heat transfer is attributed to a strong fluctuation of the rebound counter-jet and the existence of an annular cavity (formed by the crown sheet falling back). Attention should be paid to this phenomenon in industrial applications involving droplet impact.

Freezing characters study of the sessile seawater drop on a cold substrate

Sea spray icing poses risks to vessels and offshore structures in cold ocean regions. Compared to many research works dealing with the freezing of fresh water, the freezing process of sessile seawater drop was less discussed. The coupled level set and volume of fluid method combined with the enthalpy–porosity method is used to solve the Stefan problem. A two-dimensional (2D) axis-symmetric model is adopted to describe the freezing and temperature variation process. Numerical results were verified by our experiment results. The initial geometric profile of sessile drops was characterized by the Young–Laplace equation. Various salinities within the oceanographic range (10–40 g/kg) were adopted, and results showed that the freezing time increases dramatically with increasing salinity. The influence of the contact angle and substrate temperature in the freezing process was also concentrated. All these results contributed to a better understanding of the icing mechanism on marine surfaces.

Experimental and Numerical Study of Droplet Impact on Radially Flowing Liquid Film

In this paper, a single droplet impact onto a radially flowing liquid film is investigated both experimentally and numerically. The interfacial evolution and dynamic features are studied in detail with regard to various droplet impact velocities and film flow rates. Also, the corresponding mechanisms are analyzed with the aid of numerical results using the coupled level set and volume of fluid method. Results show that the droplet impact on the radial film produces a larger crown radius in the direction perpendicular to the film flow compared with the unidirectional film. Increasing the impact velocity leads to increases in crown height and upstream radius, but it has a weak effect on the downstream radius. As for the effect of the film flow rate, its increase causes a rise in the secondary droplet number in the upstream but makes the finger jets associated with the crown splashing less developed. Besides, increasing the flow rate of the liquid film results in increases in the upstream crown height and downstream radius but decreases in the downstream crown height and upstream radius. Finally, a formula for predicting the threshold of splashing is built up based on the film flow Reynolds number and the droplet Weber number.

Numerical investigation of silted-up dam-break flow with different silted-up sediment heights

Abstract The silted-up sediment in the reservoir may have a significant influence on the propagation of dam-break flows. In this paper, a three-dimensional numerical simulation of the silted-up dam-break flow is carried out. In this paper, simulations of three-dimensional silted-up dam-break flow are carried out. A kind of Eulerian–Eulerian two-fluid model (TFM), coupled level set and volume of fluid (CLSVOF) methods, is presented. In order to calculate the motions of the air–water interface and the sediment simultaneously, kinetic particle theory (KPT) and computational fluid dynamics (CFD) are combined. The rheology-based constitutive equations of sediment are also considered to simulate scouring and deposition. In addition, a partial-slip boundary condition (BC) for the velocity of the sediment phase at stationary walls is implemented. The simulation results of the benchmark case demonstrate that the proposed model can effectively simulate the silted-up dam-break flow while taking into account multi-interface capturing problems. Subsequently, the simulations of the silted-up dam-break flow over dry are investigated numerically in a three-dimensional long channel. The simulated results reveal that, in the dam-break flows, the silted-up sediment height has a significant influence on wave propagation, dynamic pressure loads, sediment transport, and sediment deposition.