Coupled Level Set And Volume Of Fluid Research Articles

Experimental and Computational Investigation of Flow Boiling in a 52 μm Hydraulic Diameter Microchannel Evaporator With Inlet Restrictions and Heat Spreading

Abstract Microchannel flow boiling presents an effective thermal management strategy for high heat flux (>1 kW/cm2) devices. Fundamental mechanisms of microchannel flow boiling behaviors are difficult to determine due to macroscopic limitations of experimental hardware. In addition, flow stabilizing features of microchannel evaporators such as inlet restrictions and heat spreading further complicate fluid flow and heat transfer dynamics. Computational models, when utilized with experiments, can provide a more detailed understanding of behaviors which cannot be determined experimentally. The present study developed a computational model for flow boiling heat transfer in a 52 μm silicon microchannel evaporator designed to cool a laser diode bar, with inlet restrictions and a nonuniform heating profile at the channel level. A conjugate heat transfer model along with a coupled level set and volume of fluid (CLSVOF) model was created in ansysfluent and compared with experimental flow boiling data to gain further insights into the performance of a realistic microdevice. Heat spreading in the channel outside of the heater footprint was observed due to the high thermal conductivity of the silicon substrate. The inlet orifices impacted local flow patterns by creating a large pressure drop and forming a recirculation zone immediately downstream. This behavior resulted in pressure recovery zones and regions of separated flow boiling behavior. Bubbly, slug, and churn flows were seen to be dominant flow regimes. The heat transfer coefficient was found to be dependent on heat flux and flow regime, and more weakly on mass flux and outlet vapor quality.

Numerical simulation of macroscopic viscoelastic melt filling and mesoscopic spherulite growth

Abstract In this work, a non-isothermal viscoelastic computational framework is proposed for macroscopic polymer melt filling and mesoscopic spherulite growth. Firstly, the macroscopic viscoelastic governing equation is solved by coupled level set immersed boundary and finite-volume (LS-IB-FV) method. The melt-air interface is captured by the coupled level-set and volume-of-fluid (CLSVOF) method. And the mesoscopic crystallization behavior is predicted by the phase field model. Then, the numerical simulation for melt filling process is compared with experimental one to validate the coupled method. And it is simulated that the melt filling stage in a complex annular cavity with 17 small solid discs for the semi-crystalline polymer of isotactic polystyrene, and it is studied that the impacts of three different injection velocities on the flow modes, temperature distribution and solidified layers. Finally, in the regions of solidified layers, the growth of spherulites is simulated with/without melt flows at two different points. Numerical results show that the injection velocities can affect the flow modes and temperature distribution significantly. The morphology of polymer spherulite that is consistent with the experimental result can be observed clearly. With flow fields, the spherulites grow faster and densely towards the upstream direction.

Numerical investigation on the effects of wave suppression baffles in vehicle-integrated water tanks

The danger of liquid sloshing in pump-driven water tanks has significantly increased due to the growing need to integrate a water tank into new energy vehicles. The best approach to reduce the negative effects of liquid sloshing is to add baffles to the integrated water tank. The addition of baffles to integrated water tanks to reduce liquid sloshing is investigated in this study using the discontinuous mesh approach and the coupled level set and volume of fluid (CLSVOF) method. Comparative experiments and simulations are used to confirm the reliability of the method. In this study, the length ratio, distance to initial free surface, and angle of the added baffle are taken into consideration. The free surface height, magnitude velocity, turbulence energy, and flow field are used to assess the impact of the baffle on the suppression of liquid sloshing. The addition of baffles can improve the liquid sloshing phenomenon caused by the pump excitation conditions in the integrated water tank, increase the volume suction of liquid, inhibit the height of the wave and reduce the liquid flow rate in the tank. Also, at the depth where the baffle has the most obvious suppression effect, the deeper the baffle, the lower the height of the free surface in the tank and the lower the average magnitude velocity in the tank cross-section. The baffle reduces the height of the free surface in the tank to 6.39 mm, and the magnitude of maximum average velocity in the tank cross-section is reduced to 0.12 m/s.

Investigations of the Atomization Characteristics and Mechanisms of Liquid Jets in Supersonic Crossflow

In the combustion chamber of scramjets, fuel jets interact with supersonic airflow in the form of a liquid jet in crossflow (LJIC). It is difficult to achieve adequate jet–crossflow mixing and the efficient combustion of fuel in an instant. Large eddy simulation (LES), the coupled level-set and volume of fluid (CLSVOF) method, and an adaptive mesh refinement (AMR) framework are used to simulate supersonic LJICs in this article. This way, LJIC atomization characteristics and mechanisms can be further explored and analyzed in detail. It is found that the surface waves of the liquid column exist in a two-dimensional form, including vertical and spanwise directions. Column breakup occurs when all the spanwise surface waves between adjacent vertical surface waves break up. Bow shock waves, composed of multiple connected arcuate shock waves, are dynamic and will change with the evolution of the liquid column. The vortex ring movement of supersonic LJICs, whose trends in the vertical and spanwise directions are different, is relatively complex, which is due to the complex and time-dependent shape of liquid columns.

A coupled level-set and volume-of-fluid (CLSVOF) method for prediction of microgravity flow boiling with low inlet subcooling on the international space station

The present study is part of a series of NASA-supported investigations of flow boiling of n-perfluorohexane (n-PFH, C6F14) under microgravity on the International Space Station (ISS). The fluid physics and heat transfer characteristics of flow boiling with low inlet subcooling are explored using the Flow Boiling and Condensation Experiment (FBCE) (which is actual name of the test facility), the largest endeavor in microgravity two-phase research conducted to date. Experimental data are collected from the FBCE's Flow Boiling Module (FBM), which features a rectangular channel with 5.0-mm x 2.5-mm cross-section and 114.6-mm heated length. Results for three flow rates are used to explore the effects of mass velocity on flow structure and heat transfer characteristics in the absence of the body force. A Computational Fluid Dynamics (CFD) model is constructed to predict the measured FBM results. The CFD model employs the Coupled Level-Set and Volume-of-Fluid (CLSVOF) method, which is modified with improved interface capture and additional force terms in the momentum equation to determine the bubble dynamics more accurately. Validity of the CFD model is assessed in two ways, by comparing predictions against video-captured interfacial behavior and heat transfer data. The CFD model shows good ability to capture detailed evolution of the interfacial structure both across and along the flow channel, including bubble nucleation, growth, departure, and coalescence, as well as axial development of dominant flow patterns. Details of the flow structure are examined via axial development of both flow velocity and void fraction profiles. Similarly, heat transfer results are presented in terms of streamwise variations of both wall temperature and fluid temperature, which are also predicted accurately with the CFD model. Overall, this study proves the CFD model is an effective method for both design and performance assessment of flow boiling subsystems in space vehicles.

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.

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.

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.

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.

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.

Numerical study of instability mechanism in the air-core vortex formation process

Air-core vortices are a ubiquitous phenomenon in the intakes of hydropower stations. Due to the transient and instability of two-phase vorticial flow, the prediction of air-core vortex formation is challenging, and understanding of the instability mechanism remains elusive. In this study, the large eddy simulation (LES) method and a coupled level-set and volume-of-fluid (CLSVOF) method are performed to study air-core vortex formation in a benchmark reservoir with a horizontal intake pipe. The process of air-core vortex formation can be classified into an inception stage, an instability stage, and a stability stage. In the instability stage, the surface vortex repeatedly goes through the process of inception, enhancement, attenuation, and extinction. The movement of the counterrotating secondary vortices and water surface level fluctuation plays a negative role in air-core vortex formation. The additional motion generated by the counterrotating pair drives the pair to the back wall. The main vortex undergoes attenuation due to the stretching/tilting effects induced by the secondary vortex. Water level fluctuations briefly increase the submergence depth, which in turn reduces the vertical velocity gradient and vertical vorticity, destabilizing the vortex. The perturbation of the air-core vortex by water level fluctuations is present only at the beginning of the instability stage.

Accurate Prediction of Transport Coefficients of an Evaporating Liquid Drop

Abstract Numerical simulations were carried out to study the evaporation of a drop that is released into a parallel stream of fluid at a higher temperature. A coupled level-set and volume-of-fluid (CLSVOF) interface capturing method was deployed to capture the dynamic interface between the drop liquid and the surrounding fluid. Modified forms of mass, momentum, and energy equations were solved together with the species concentration equation. The pressure jump at the interface was handled by accurate estimation of the continuum surface force. The jumps in mass and energy at the interface were carefully resolved by considering appropriate source terms in the continuity and energy equations. At the interface, the procedure of velocity computation was incorporated by extending the liquid-phase velocity onto the entire domain and by calculating the Stefan flow to predict the interface velocity accurately. The calculation of the velocity using this step leads to the exact estimation of mass transfer through the interface. The model was validated against both temperature gradient-based and vapor mass concentration gradient-based evaporation test cases. Temporal histories of the average Nusselt number and Sherwood number during the lifetime of an evaporating drop were predicted in terms of the pertinent input parameters, namely, Reynolds number, Prandtl number, and Schmidt number.

Mechanism of multiphase coupling transport evolution of free sink vortex

In the evolution of confluence sink vortex with a free surface, there exists some physical processes , such as multiphase coupling, mass transfer, and intensive energy exchange. Here, the transport mechanism of multiphase coupling is a complex dynamic problem with highly nonlinear characteristics. The mechanical modeling and numerical solution of multiphase viscous coupled transport are facing a significant challenge. To address the above problem, a method of modeling and solving multiphase coupling transport of the free sink vortex is proposed. Based on the coupled level set and volume-of-fluid (CLSVOF) method, a multiphase coupling transport model of the free sink vortex is set up with a continuous surface tension model and a realizable (<i>k</i>-<i>ε</i>) turbulence model. By using an effective volumetric correction scheme, the high-speed rotating flow is calculated, and the mass conservation of flow field and the velocity field without divergence are ensured. Then, an interphase coupling solution approach accurately traces the multiphase fluid distribution and multiphase interface. The multiphase coupling interface and cross-scale vortex cluster transport laws are obtained according to the multi-characteristic physical variables. The interaction mechanism between the multiphase coupling transport process and the pressure pulsation characteristics is revealed. The results show that the multiphase coupling transport is the critical state of the fluid medium transition. The vortex microclusters are subjected to different spatiotemporal disturbance modes and form the layered threaded waveforms at the interface. With the increase of the nozzle sizes, the multiphase coupling process is strengthened, and the coupling energy shock causes nonlinear pressure pulsation. This study can offer valuable references to the researches of the vortex transport mechanism, cross-scale solution of vortex cluster, and flow pattern tracking.

An interface-resolved phase-change model based on velocity decomposition

An interface-resolved phase-change model is proposed in the interface-capturing framework based on the coupled level-set and volume of fluid (CLSVOF) method. A velocity decomposition method is employed to ensure the numerical stability and accuracy of interface propagation. Specifically, the velocity u is decomposed into the potential part u˜ associated with the phase change and the remaining rotational part u¯. The potential velocity u˜ is computed by solving a Poisson equation. A modified momentum equation is derived to solve the rotational-part velocity u¯, which is divergence-free. The momentum equation is solved using the Computational Air-Sea Tank (CAS-Tank) developed previously by Yang et al. [1]. To evolve the interface and ensure the mass conservation, a continuous interfacial velocity uΓ is constructed by adding the velocity uˆ associated with the volume change of liquid (or gas) to u¯, where uˆ is computed by solving a Poisson equation with constant coefficient. The proposed method is verified in the context of the two-dimensional (2D) droplet with constant evaporation rate, one-dimensional (1D) Stefan and sucking problems, 2D droplet evaporation at saturation temperature, 2D droplet evaporation below saturation temperature, and a three-dimensional (3D) evaporating droplet falling under the gravity. The results show that the proposed method is accurate and stable. The numerical method is also validated by simulating an evaporating droplet falling under the gravity and the numerical results are found to be in agreement with the results in the literature. The interaction of two evaporating droplets is also simulated in a 3D domain to show the capability of the proposed method in solving 3D problems.

A coupled level set and volume of fluid method for three dimensional unstructured polyhedral meshes for boiling flows

For the numerical modelling of boiling flows with accurate interface dynamics, a new coupled level set and volume of fluid (CLSVOF) method for three-dimensional unstructured polyhedral meshes has been presented in this paper. An unsplit multidirectional method is used for advecting volume fraction. In this method, the cell vertex velocities interpolated from the cell centres are used to create the flux polyhedron. A total variational diminishing (TVD) scheme is used for the advection of level set function. The level set field is geometrically reinitialized after every time step. The present CLSVOF method is tested against several two as well as three-dimensional advection test cases for both structured and unstructured polyhedral meshes to determine its accuracy and performance. In terms of advection test cases, the suggested method shows good agreement with results of previous studies that used interface reconstruction techniques of higher order. The proposed method is then used to simulate two as well as three-dimensional saturated film boiling over a flat planar surface for both unstructured polyhedral and structured meshes. The obtained results are in accordance with the results available in literature. The present CLSVOF method is also demonstrated for saturated film boiling on a horizontal cylinder in both two and three dimensions. In comparison to the earlier numerical studies, the present results are in good accordance with the available semi-empirical correlations. • A CLSVOF method is developed for boiling flows on 3D unstructured polyhedral meshes. • The proposed boiling flow solver can be used for any complex geometries. • The solver is validated for two-phase flows with and without phase change. • For boiling flows, the present results agree well with semi-empirical correlations.

Evaluation of different interface-capturing methods for cryogenic two-phase flows under microgravity

The distribution of the gas–liquid interface is crucial to the accurate calculation of the flow and heat transfer of in-orbit cryogenic propellants, for which the surface tension force overtakes the gravitational force. As an essential oxidant, liquid oxygen has a lower surface tension coefficient and viscosity than most room-temperature fluids, causing a greater possibility of interface instability and breakage. Conventional numerical methods have seldom been assessed in terms of cryogenic two-phase flows under microgravity, and commercial software cannot provide a consistent platform for the assessment. In this study, a unified code based on OpenFOAM has been developed for evaluating four interface-capturing methods for two-phase flows, namely, the algebraic volume of fluid (VoF), geometric VoF, coupled level set and VoF (CLSVoF), and density-scaled CLSVoF with a balanced force (CLSVoF-DSB) methods. The results indicate that the CLSVoF-DSB method is most accurate in predicting the interface motion, because it uses the level set function to represent the gas and liquid phases. The gas–liquid interface predicted by the CLSVoF-DSB method is the most stable because it adopts the scaling Heaviside function to weaken the effects of spurious currents and increases the stability. The numerical algorithm of the algebraic VoF method is the most simple, so it has the highest efficiency. The geometric VoF uses the isoface to locate the gas–liquid interface in a grid cell, so it can obtain the thinnest interface. In applications of liquid oxygen, the CLSVoF-DSB method should be used if the overall accuracy is required.

Numerical study of rising Taylor bubbles driven by buoyancy and additional pressure

The Taylor bubble driven by buoyancy and additional pressure is in a non-equilibrium state, which bubble and liquid flow have an accelerated tendency of rising, and the bubble behavior is significantly different with the Taylor bubble in stagnant liquid. In order to understand the dynamic properties of such bubbles, a numerical study was conducted using the coupled level-set and volume-of-fluid (CLSVOF) method combined with the stress-blended eddy simulation (SBES) model. The research results indicated that, due to the additional pressure, the difference between the bubble pressure head and the liquid column height is larger than zero, the pressure gradient force acting on the liquid column is greater than the force of gravity, this makes the bubble have an accelerating upward trend. The bubble shape and liquid film thickness are closely related to the relative bubble velocity, the correlation between dimensionless liquid film thickness and Reynolds number of relative bubble velocity was proposed. In addition, the article analyzed the influence mechanism of bubble shape, which is determined by the stress state of the fluid surrounding the bubble. Under the additional pressure, the axial stress on the bubble top increases significantly, while the radial stress remains almost invariable, which makes the bubble shape gradually become thinner.

Performance of a coupled level-set and volume-of-fluid method combined with free surface turbulence damping boundary condition for simulating wave breaking in OpenFOAM

In the present study, an extension of the volume-of-fluid (VOF) method used in the open-source computational fluid dynamics (CFD) software OpenFOAM was developed, taking the advantages of the VOF and the level-set (LS) methods with an additional free surface turbulence damping (FSTD) boundary condition to restrict the overprediction of turbulence near the free surface. The coupled level-set and volume-of-fluid (CLSVOF) method has been developed, scripted, validated and proposed. The free surface elevation with the proposed CLSVOF method was validated in a developed numerical wave tank (NWT) against turbulence models used so far in OpenFOAM. Further, the validity of the present numerical model was evaluated for the case of plunging breaking waves against relevant experimental and numerical data. The outcome of this study demonstrates that the performance of the wave generation is improved with the proposed numerical model compared to existing turbulence models in OpenFOAM, creating a useful simulation add-on that generates long-term waves without unphysical dissipation, wave damping, and wave decay. The overprediction of turbulence created due to the significant difference in the fluid's density close to the free surface is limited by applying the FSTD boundary condition leading to a better representation of the flow field.