Coupled Level Set And Volume Of Fluid Research Articles

Density-Scaled Balanced Continuum Surface Force Model with a Level Set Based Curvature Interpolation Technique

We examine the recently-proposed density-scaled balanced continuum surface force (CSF) model with a level set-based curvature interpolation technique. The density-scaled balanced CSF model is combined with a numerical framework which is based on the coupled level set and volume-of-fluid (CLSVOF) method, the tangent of hyperbola for interface capturing/weighted line interface calculation (THINC/WLIC) scheme, the constrained interpolation profile conservative semi-Langrangian with rational function (CIP-CSLR) and the volume/surface integrated average-based multi-moment method (VSIAM3). The present CSF model is examined for various bench mark problems such as drop–drop collisions and drop splashing. Comparisons of the present model results with experimental observations and those from the other CSF models show that the present CSF model can minimize spurious current and capture complicated fluid phenomena with minimizing floatsam.

Numerical investigation on the influence of surface tension and viscous force on the bubble dynamics with a CLSVOF method

We numerically investigated the rising of bubbles in a quiescent liquid layer. The numerical simulation is performed by solving the incompressible, multiphase Navier-Stokes equations via computational code in axisymmetric coordinates using a Coupled level-set and volume-of-fluid (CLSVOF) method. The numerical results show that the CLSVOF method with a novel algebraic relation between F and ∅ for axisymmetric two-phase flows not only can predict the bubble surface accurately, but also overcome the deficiency in preserving volume conservation. The effects of the Reynolds number Re and the Bond number Bo on the bubble deformation and its motion are investigated. The results show that with the increasing of Re (10 < Re < 150), the bubble shape transfers from oblate ellipsoidal cap to toroidal when Bo = 116. With the increasing of Bo (10 < Bo < 700), the bubble shape transfers from oblate ellipsoidal to toroidal when Re = 30. Although the toroidal bubble shapes are reached in these two cases, the transition modes are different. For the case Bo = 116, the bubble front is pierced by an upward jet from the rear of the bubble. While for the case Re = 30, the rear of the bubble is pierced by a downward jet from the front part.

Numerical simulation of axisymmetric drop formation using a coupled level set and volume of fluid method

Numerical simulations have been carried out to examine the axisymmetric formation of drops of Newtonian liquid injected from a vertical orifice under constant flow conditions into the ambient air. The numerical simulation was performed by solving axisymmetric Navier–Stokes equations with a coupled level-set and volume-of-fluid (CLSVOF) method. In this work, the dynamics of the formation of drops are investigated over a range of the Ohnesorge number Oh=0.01,0.023 and 0.13, and the Bond number Bo=0.33,0.5 and 2.205, as the Weber number We increases. The different responses of drop formation such as period-1 dripping with (P1S) or without satellite drops (P1), complex dripping (CD) and jetting (J) are discussed. The different responses of drop formation were identified quantitatively from the time history of growing length of drop at the orifice. The transition of different responses is shown on the map which exhibits the variation of limiting length of drop at breakup or the volume of the detached primary drop with We while keeping Oh and Bo fixed. The numerical investigation of liquid jet formation in terms of the evolution of growing length of jet under different computational grid sizes was discussed. It is proposed that the almost stable liquid jet formation can be found as the mesh size decreases. The accuracy of the present computed results is assessed by comparisons with the previous investigations. Furthermore, it is shown that at high Bo=2.205, low Oh=0.023 and We=0.0177, the system exhibits period-2 with satellite drop (P2S) response which was not reported before in literature.

Numerical simulation of melt filling process in complex mold cavity with insets using IB-CLSVOF method

A coupled level-set and volume-of-fluid (CLSVOF) method is proposed for tracking interface of incompressible two-phase flows, where the VOF advection is carried out only, and a zero level-set (LS) formula and LS reinitialization equation are employed to reestablish the signed distanced field near the interface, which can program easily. Meanwhile, a mass-correction scheme based on the interface curvature is used to conserve the liquid mass correctly. Firstly, the performance of the CLSVOF method is evaluated through two- and three-dimensional deformation field tests. Then, the CLSVOF method is adopted to simulate the rising bubble and droplet falling problems. Finally, a shape LS function is used to describe and treat the irregular surface (immersed boundary) of mold cavity. With the aid of the shape function, the coupled immersed boundary (IB) and CLSVOF (IB-CLSVOF) method is applied to the melt filling process in the complex mold cavity with insets. The numerical results show that the proposed IB-CLSVOF method has the capability to cope with complex interface variations accurately. And also, the numerical results demonstrate that IB-CLSVOF method is able to successfully depict the phenomena of race-tracking, air entrapment and weldline development, which are very helpful for determining processing conditions and designing mold cavities.

Numerical study of bubbles rising and merging during convective boiling in micro-channels

A three dimensional numerical study on bubble growth and merger in a micro-channel with diameter of 0.64 mm has been conducted. The working fluid is R134a and the wall material is steel. The inlet Reynolds number is set at 549 in order to keep the flow in laminar regime. Two different heat fluxes (14 and 28kWm2) are supplied to the wall to heat up the fluid. The coupled level set and volume of fluid (CLSVOF) method is used to capture the distorted two-phase interface. An evaporation model is also implemented through UDF (User defined function). The combination of these two methods has successfully eliminated spurious velocities which is a common problem in two phase flow simulation. The boiling and merger processes are well-predicted by the simulation. It is found that the whole process can be divided into three sub-stages: sliding, merger, and post-merger. The dynamics and heat transfer are found to be different in these stages. The evaporation rate is much higher in the first two stages due to the thermal boundary layer effects.

Numerical simulation on weld line development of injection molding in mold cavity with inserts

A gas-liquid two-phase model for a viscoelastic fluid is proposed and used to simulate and predict the behavior of melt welding in injection molding process, in which the extended pom-pom (XPP) model and cross-WLF viscosity model combined with Tait state equation are used to describe the constitutive relationship and viscosity change of the viscoelastic melt in this paper, respectively. Meanwhile, the coupled level-set and volume-of-fluid (CLSVOF) method is employed to capture the melt front, and the immersed boundary method is applied to the simulation of the polymer melt flows with the aid of a shaped level-set function to describe and treat the irregular mold cavities. A finite volume method on non-staggered grid is used to solve the mass, momentum, and energy conservation equations. Firstly, the benchmark problem of the single shear flow is simulated to verify the validity of the CLSVOF method. Then, the non-isothermal filling process of the viscoelastic fluid based on the XPP model in a mold with square inset is simulated, and the behavior of the weld line devolopment in the filling process is shown and compared with the experimental result. Finally, it is to simulate the evolution processes of the melt front interface and weld line in a mold with the circular notched inset; and the linear stress-optical rule is adopted to calculate the flow-induced birefringence. Numerical results show that the numerical model proposed in this paper can be employed to simulate the non-isothermal filling process in complex mold cavity and to capture the weld line automatically. Because of the complexity of polymer melt flows, the flow-induced stress increases quickly near the weld line region and then decreases gradually until reaching the mold cavity wall. The maximum value of the flow-induced stress appears at some point after the insert. The distributions of physical quantities, such as pressure and temperature in the mold, are given during the mold filling process. Moreover, it is also discussed the influence of melt and mold temperatures on the solidified layer thickness. The higher the melt or mold temperature, the thinner the solidified layer is. Thus, raising the melt or the mold temperature will improve or remove the weld line in melt filling process.

Numerical simulation of wave slamming on 3D offshore platform deck using a coupled Level-Set and Volume-of-Fluid method for overset grid system

The numerical simulation of wave slamming on a 3D platform deck was investigated using a coupled Level-Set and Volume-of-Fluid (CLSVOF) method for overset grid system incorporated into the Finite-Analytic Navier-Stokes (FANS) method. The predicted slamming impact forces were compared with the corresponding experimental data. The comparisons showed that the CLSVOF method is capable of accurately predicting the slamming impact and capturing the violent free surface flow including wave slamming, wave inundation and wave recession. Moreover, the capability of the present CLSVOF method for overset grid system is a prominent feature to handle the prediction of wave slamming on offshore structure.

Numerical simulation of coalescence phenomena of oil-in-water emulsions permeating through straight membrane pore

Abstract We numerically investigated the demulsification phenomena of oil-in-water (O/W) emulsions using a membrane coalescence process. We simulated the permeation of O/W emulsions through a membrane with a single straight pore using our numerical framework based on the coupled level set and volume-of-fluid (CLSVOF) method. With a low droplet volume fraction, small droplets, and a large pore size, the oil droplets frequently passed through the membrane without attaching to its surface. After the steady coalescence of the droplets on the membrane surface at the permeation side, large oil droplets could be obtained. With a higher droplet volume fraction, larger oil droplets, and smaller membrane pores, the oil droplets easily blocked the membrane pores and were thus forced away by the permeating flow, which yielded relatively small oil droplets. Our numerical work revealed the fundamental dynamics of the coalescence of oil droplets in an O/W emulsion using a simple membrane model.

Characteristics of the Cross-Sectional Vorticity of the Natural Spawning Grounds of Schizothorax prenanti and a Vague-Set Similarity Model for Ecological Restoration.

Schizothorax prenanti is an endemic fish in the mountain rivers of southwestern China with unique protection value. To further explore the vortex motion of hydraulic habitats, which is closely related to the fish breeding process, the cross-sectional vorticity was used to evaluate the hydraulic conditions of the natural spawning habitat of S. prenanti. A coupled level-set and volume-of-fluid (CLSVOF) three-dimensional (3D) model was applied to simulate the hydraulic habitat of the Weimen reach, a typical natural spawning ground for S. prenanti in the upper Yangtze River. The model was used in conjunction with the Wilcoxon rank sum test to distinguish the distributions of vertical vorticity in spawning and non-spawning reaches. Statistical analysis revealed that the cross-sectional vorticity in spawning reaches was significantly greater than in non-spawning reaches, with likely biological significance in the spawning process. The range of cross-sectional mean values of vorticity was 0.17 s-1–0.35 s-1 in areas with concentrated fish sperm and eggs; the minimum value was 0.17 s-1, and the majority of values were greater than 0.26 s-1. Based on this study, a vague-set similarity model was used to assess the effectiveness of ecological restoration by evaluating the similarity of the cross-sectional vorticity of the natural spawning reach and rehabilitated spawning reach after implementing ecological restoration measures. The outcome might provide a theoretical basis for the recovery of damaged S. prenanti spawning grounds and act as an important complement for the assessment of recovery effectiveness and as a useful reference for the coordination of ecological water use with the demands of hydraulic and hydropower engineering.

Numerical simulation of 3D sloshing flow in partially filled LNG tank using a coupled level-set and volume-of-fluid method

The motion induced 3D sloshing flow in partially filled LNG tank was investigated using a new coupled Level-Set and Volume-of-Fluid (CLSVOF) method incorporated into Finite-Analytic Navier–Stokes (FANS) method. In addition to accurately simulating the sloshing pattern inside LNG tank, impact pressures acting upon tank wall were also predicted by the CLSVOF method. Furthermore, the predicted impact pressures were compared with the corresponding experimental data and another numerical data by the pure level set method with global mass conservation scheme. The comparisons showed the CLSVOF method is capable of predicting the accurate sloshing induced impact and capturing the violent sloshing flow including wave breaking, jet formation, gas entrapping and liquid-gas interactions. The CLSVOF method also demonstrated the prominent feature in local and stable mass conservation.

A coupled level-set and volume-of-fluid simulation for splashing of single droplet impact on an inclined liquid film

A coupled level set and volume of fluid (CLSVOF) method is utilized to simulate the droplet evolution, during splashing after impacting on an inclined liquid film, and the bubble entrainment by the droplet impacting of the liquid. The influence of impact angles of bubble entrainment, the processes of splashing pressure field and velocity field after impingement are studied and discussed. Compared with the results obtained by experiment, the validity of CLSVOF method is verifiled by simulating the droplet splashing on an inclined liquid film. Results indicate that the mechanisms of front and back splashing are different. The front splashing is caused by pressure difference in the neck region, and the back splashing is produced by radial flow in the liquid film. It is also found that along with the impact angle moving towards the large angle direction, the bubble entrainment number shows a reducing trend.

Numerical Simulation of Two-dimensional Forced Convective Film Boiling Flow over a Horizontal Flat Surface

In this numerical study, a Coupled Level Set and Volume of Fluid (CLSVOF) interface capturing method with multi-directional advection algorithm is used to investigate the flow and heat transfer characteristics of a two-dimensional, incompressible, laminar, forced convective saturated film boiling over an isothermal horizontal flat plate. In this study, the effects of wall superheats and liquid free stream velocities are considered for water and refrigerant R-134a. In the numerical simulation of forced convection saturated film boiling flows, the wall shear stress and the heat transfer coefficient results are evaluated with Cess and Sparrow1 correlations developed based on the boundary layer approximations. The numerical results show good agreement with the correlations developed based on the boundary layer theory. Both heat transfer coefficient and wall shear stress are strongly dependent on the wall superheats and inflow free stream velocities.

Three Dimensional Numerical Simulation of Melt Filling Process in Mold Cavity with Insets

This paper presents a level set function, named shape function, to describe and treat the irregular surface of mold cavity. With the aid of the shape function, the continuity, momentum and energy equations can be extended for solving two-phase flows with an immersed solid surface. The governing equations are solved by using the finite volume solver with the coupled level set and volume of fluid (CLSVOF) method to track the polymer melt front. As case studies, the melt filling processes are simulated in mold cavities with cylindrical insets. The numerical results show that the mathematical model can successfully depict the phenomenon of race-tracking and fountain, which are very helpful for determining processing conditions and designing mold cavities.

Towards High-fidelity Multi-scale Simulation of Spray Atomization

Abstract Liquid jet atomization is an important process in internal combustion engine. This paper presents a multi-scale approach coupling a Eulerian interface-tracking method and a Lagrangian particle tracking method to simulate liquid atomization processes. This method aims to capture the complete spray atomization process, particularly primary and second breakup, paving the way for high-fidelity simulation of spray atomization in the dense spray zone and spray combustion in the dilute spray zone. The Eulerian method is based on the Coupled Level-Set and Volume-of-Fluid (CLSVOF) for interface tracking, which can accurately simulate the primary breakup process. For the coupling approach, the Eulerian method only describes large droplet and ligament structures, while small-scale droplet structures are removed from the resolved Eulerian description and transformed into Lagrangian point-source droplets. The Lagrangian method is thus used to track small droplets and their further secondary breakup and collision. In this study, two-dimensional simulation of liquid jet atomization is performed. We will analyse Lagrangian-droplet formation and motion due to the coupling and the atomization characteristics using the multi-scale approach.

Numerical simulation of Taylor bubble formation in a microchannel with a converging shape mixing junction

The bubble formation in a square microchannel with a converging shape mixing junction has been simulated under Taylor flow using two different interface capturing methods implemented in ANSYS FLUENT (ANSYS Inc., USA): Volume of Fluid (VOF) method, and coupled Level Set and VOF (CLSVOF) method. Compared with VOF method, CLSVOF method can yield a more accurate gas–liquid interface especially at the rupture stage of the emerging bubble and the obtained bubbles are more consistent with the experimental results. The effect of the contact angle (θ), surface tensions (σ) and liquid viscosity (μL) on the Taylor bubble details (i.e., length, volume and shape) has been investigated systematically. For the highest surface tension (σ=0.09N/m) and the highest liquid viscosity (μL=9.83mPas) investigated, the bubble length decreases substantially with an increase of the contact angle as a result of the combined effect caused by the bubble end shape change from convex to concave and the volume decrease of the liquid film surrounding the bubble body. However, the bubble volume is almost constant regardless of the contact angle, which is mainly caused by the difference in bubble shapes. Both the contact angle and the liquid viscosity have an appreciable influence on the bubble shape whereas the influence of surface tension is minor.

A Coupled Level Set and Volume of Fluid method with multi-directional advection algorithms for two-phase flows with and without phase change

A Coupled Level Set and Volume of Fluid (CLSVOF) interface capturing method using a multi-dimensional advection algorithm for non-uniform grids has been developed for two phase flows with and without phase change for two-dimensional problems. A finite volume method with a collocated grid arrangement is used for solving the governing equations. The SIMPLE algorithm is used for velocity and pressure coupling. The piecewise linear interface calculation (PLIC) based geometrical reconstruction procedure and an Edge Matched Flux Polygon Advection (EMFPA) multi-dimensional algorithm have been implemented for the Volume of Fluid (VOF) method. For the Level Set (LS) advection equation, the convective terms are discretized using the second order accurate essentially non-oscillating (ENO) scheme. The proposed multi-dimensional advection of CLSVOF method requires interface reconstruction for the advection of VOF function and the Level Set function re-initialization only once compared to the requirement of twice interface reconstruction and Level Set re-initialization in the operator-splitting method for 2D problems. The performance of proposed CLSVOF method is evaluated for accurate mass conservation, surface tension force and interface mass transfer through various standard benchmark problems. The numerical study of two-dimensional saturated film boiling flow over a horizontal plane surface was carried out for different constant wall superheats in order to validate the implementation of boiling flow model. The present numerical results of boiling flows show better agreement with the experimental correlations.

A density-scaled continuum surface force model within a balanced force formulation

We propose a numerical framework which can simulate free surface flows with complex moving interfaces like droplet splashing as minimizing spurious currents. The numerical framework is based on the CLSVOF (coupled level set and volume-of-fluid) method, the THINC/WLIC (tangent of hyperbola for interface capturing/weighted line interface calculation) scheme, multi-moment methods (CIP-CSL and VSIAM3) and density-scaled CSF (continuum surface force) model within a balanced force formulation. In this paper, we propose a level set based algorithm of the density-scaled balanced CSF model and show that the density-scaled balanced CSF model can reduce spurious currents more than the standard balanced CSF model without using the density-scaling when the exact curvature is not given. We also show that the numerical framework can well capture the physics of droplet splashing.

Influence of the viscosity ratio on drop dynamics and breakup for a drop rising in an immiscible low-viscosity liquid

AbstractIn a low Morton number ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}M$) regime, the stability of a single drop rising in an immiscible viscous liquid is experimentally and computationally examined for varying viscosity ratio$\eta $(the viscosity of the drop divided by that of the suspending fluid) and varying Eötvös number ($\mathit{Eo}$). Three-dimensional computations, rather than three-dimensional axisymmetric computations, are necessary since non-axisymmetric unstable drop behaviour is studied. The computations are performed using the sharp-interface coupled level-set and volume-of-fluid (CLSVOF) method in order to capture the deforming drop boundary. In the lower$\eta $regimes,$\eta = 0.02 $or 0.1, and when$\mathit{Eo}$exceeds a critical threshold, it is observed that a rising drop exhibits nonlinear lateral/tilting motion. In the higher$\eta $regimes,$\eta = 0.1$, 1.94, 10 or 100, and when$\mathit{Eo}$exceeds another critical threshold, it is found that a rising drop becomes unstable and breaks up into multiple drops. The type of breakup, either ‘dumbbell’, ‘intermediate’ or ‘toroidal’, depends intimately on$\eta $and$\mathit{Eo}$.

Gas Properties on Crown Behavior and Drop Coalescence

A single drop impact on a liquid film is numerically investigated using the coupled level set and volume of fluid (CLSVOF) method. Influences of gas properties including gas density and viscosity on the crown liquid sheet behavior and the drop-film coalescence process are mainly discussed. It is found that the decrease in the liquid–gas density ratio will result in incurve of the crown, especially when the density ratio is less than 100, due to the large gas velocity difference between the crown upper and lower positions. When the liquid–gas viscosity ratio is decreased to a value of less than 0.5, both splashing occurrence and crown expansion are suppressed, caused by the combination effect of the pressure difference and the gas velocity in the drop-film-contacting neck region. The density ratio has only minor influence on the drop coalescence process. However, when the viscosity ratio is decreased, the capillary wave on the drop surface gradually disappears. It is considered that the gas eddy reduction on the drop surface should be responsible for the capillary wave disappearance during drop coalescence.

Transient analysis of a single rising bubble used for numerical validation for multiphase flow

Accurate tracking of multiphase interfaces (such as an air bubble in a fluid) is difficult yet significant to many engineering processes. Computationally, various tracking methods have been developed, including the volume of fluid (VOF), and coupled level set and volume of fluid (CLSVOF) methods. In order to accurately assess the small-scale differences between different interface capturing methods, a comprehensive experimental dataset is required for validation, including detailed information describing the interface deformation, and transient development of the stage by stage shape data. These interfacial details are better investigated from a two-dimensional (2D) rather than three-dimensional (3D) comparison, because the computational resources for determining an accurate shape can be maximized, and the interfacial complex deformation is difficult to analyze in 3D. In this paper, the fully developed shape and subsequent deformation of 2D rising bubbles have been captured experimentally and analyzed in detail using image processing. These results are then compared with the corresponding VOF and CLSVOF results, demonstrating the usefulness of the experimental dataset as a validation tool.