Coupled Level Set And Volume-of-fluid Method Research Articles

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.

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.

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.

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.

Numerical simulation for liquid sloshing with baffle by the CLSVOF/IB method

The liquid sloshing problem in a partially filled rectangular tank is numerically investigated by a Coupled Level Set and Volume Of Fluid (CLSVOF) method. In the present CLSVOF method, the Level Set (LS) equation needs to be solved to advect the LS function for calculating interface curvature; the re-distancing equation is also taken into account for the LS function being maintained as a distance function. For capturing the interface, the Tangent of Hyperbola for INterface Capturing (THINC) scheme with Weighted Linear Interface Calculation (WLIC) is implemented to advect the Volume of Fluid (VOF) function. To preserve mass conservation, the interface reconstruction procedure needs to be carried out on the basis of the connection between LS and VOF functions. Rectangular and prismatic tanks are used to validate the accuracy and mass conservation of the present CLSVOF method. Then, further simulations of the problem of partially filled liquid sloshing with baffle considered are conducted by combining the CLSVOF method and the Immersed Boundary (IB) method. Finally, the influence of different baffle lengths on the slapping pressure and free-surface is discussed.

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.

Effect of Eccentric Distance on Successive Dual-droplet Impacting a Super-hydrophobic Tube

Droplet impact is a common but significant phenomenon in industry. The CLSVOF (coupled level set and volume-of-fluid) method is used to numerically study the successive dual-droplet impacting a super-hydrophobic tube. For the impact velocity of 1.0 m/s, the effect of the eccentric distance on dynamic characteristics is analysed, the corresponding eccentric distances are 0.5, 1.0 and 2.0, respectively. In addition, the break-up during rebound is analysed with velocity field and pressure nephogram. Results show that, the eccentric distance hinders the spread during the initial period of spreading. With the increase in eccentric distance, more liquid gathers at the eccentric side and the liquid film might rebound easily without break-up under the same impact velocity. The break-up during rebound mainly depends on the local airflow and pressure difference. The high-pressure zone near the solid-liquid interface moves towards the eccentric side with the increase in eccentric distance.

Numerical study of a laser generated cavitation bubble based on FVM and CLSVOF method

Based on the open source software OpenFOAM, the finite volume method (FVM) is applied for discretization of the Navier-Stokes equation. A coupled level set and volume of fluid (CLSVOF) method is established to track the movement of the gas-liquid interface, for improving the accuracy of the simulation of interface curvature and surface tension force. The spherical collapse of a laser generated bubble in water is modeled with the consideration of viscosity, compressibility of both the gas and the liquid, and the surface tension of the liquid. The variations of the bubble radius during collapse predicted by the CLSVOF method are compared with the Gilmore model, the VOF method, which are more consistent with the experimental results. The velocity and the pressure around the bubble are also investigated. And the shock waves emitted by the bubble during the process are illustrated.

Numerical study on dynamic behaviors of the coalescence between the advancing liquid meniscus and multi-droplets in a microchannel using CLSVOF method

The coalescence between the advancing liquid meniscus and multiple droplets is usually encountered in the liquid filling process and photothermal effect based microdevices. To shed light on how the coalescence between the advancing liquid meniscus and multiple droplets affects the liquid meniscus advancement, its dynamic behaviors are numerically investigated using the coupled level set and volume-of-fluid (CLSVOF) method along with the continuum surface force (CSF) model in this study. Particular attention is paid to the dynamic interfacial phenomena during the coalescence process. The effect of the droplet and its volume distributions is also investigated. The simulation results show that the coalescence between the advancing liquid meniscus and each droplet is able to instantly accelerate the original liquid flow as a result of the induced concave meniscus with large curvature. As compared to the coalescence with a single droplet, the fluctuation and deformation of the interface is stronger in the case of simultaneous coalescence with multiple droplets, which can further lower the average liquid pressure and thus show more significant advancement of the liquid flow. The velocity increment ratio is the largest when four droplets simultaneously coalesce with the advancing liquid meniscus. It is shown that the coalescence with large droplet can result in large velocity increment ratio because more surface energy is supplied. Large length of the advancing liquid segment before its coalescence with the droplets can weaken the advancing effect. It is also found that the overall variation trend of the simulation results is in agreement with that of the experimental results.

Numerical Study on the Improvement of Oil Return Structure in Aero-Engine Bearing Chambers

Abstract Numerical study has been carried out to improve the unreasonable oil film accumulation and oil return effect of the bearing chamber. Ramp sump and eccentricity sump offtake structures are designed and improved, and oil-gas two-phase flow calculation model based on CLSVOF (coupled level set and volume of fluid) method is proposed. Based on the grid-independent analysis and verifying the rationality of numerical data, oil-gas movement mechanism and oil return characteristics for different scavenge offtakes are calculated and analyzed. Results show that both the ramp sump and eccentricity sump offtake structures have favorable effects on improving the local oil distribution such as recirculation and stripping, etc. at low rotation speeds and alleviating the rapid decline of scavenge efficiency at high rotation speeds. Meanwhile, the air shear force is the main reason for the rapid decline of scavenge efficiency, while the design of oil return sump makes for the oil discharge from the scavenge offtake, and the deeper the sump depth is, the better.

A coupled level set and volume of fluid method on unstructured grids for the direct numerical simulations of two-phase flows including phase change

In the present study, a coupled level set and volume of fluid (CLSVOF) method is developed for two-dimensional unstructured grids to perform direct numerical simulations of two-phase flows including phase change. The volume fraction is advected using a multi-directional advection algorithm, where the flux polygons are constructed using vertex velocities and a scaling factor based on cell face velocities is used to correct the advected volume fraction. The level set field is advected using a total variational diminishing (TVD) scheme and geometrically reinitialized at the end of each time step. The performance of the proposed CLSVOF method is evaluated in detail on unstructured grids, both qualitatively and quantitatively, prior to simulation of phase change problems. A number of advection test cases and two-phase flow problems are considered for this purpose. Results obtained for film boiling over a horizontal flat plate using an unstructured grid show excellent agreement with results available in the literature. The numerical study of natural convection film boiling over a horizontal cylinder at different wall superheats shows a better agreement with semi-empirical correlations compared to other available numerical results.

Simulations of Flow Transitions in a Vertical Pipe Using Coupled Level Set and VOF Method

The level set (LS) and volume-of-fluid (VOF) methods are usually employed to simulate the two-phase flow. However every single method of them will face the mass conservative or accurate issues during the simulation. The coupled level set and volume-of-fluid (CLSVOF) method was not only able to conquer the shortages of the LS and VOF methods but also simultaneously keep the merits of both of the methods. In CLSVOF method the geometry reconstruction technology was employed to realize the coupling between LS and VOF. After the validation of single bubble rising cases, the CLSVOF method was used to simulate the complex transitional two-phase flows in a vertical pipe and the simulation results were compared to experiments.

A coupled level-set and volume-of-fluid method for simulating axi-symmetric incompressible two-phase flows

A coupled level-set and volume-of-fluid (CLSVOF) method, combining the advantages of LS method and VOF method, is presented for simulating axi-symmetric incompressible liquid–gas flow problems. In this method, the interface is implicitly captured by the LS function, and the VOF function is used as a complement to remedy the mass conservation problem aroused in the advection and re-initialization of LS function. We propose a novel explicit algebraic relation between the LS function and VOF function to achieve the coupling of the two methods. Four typical axi-symmetric liquid–gas flow problems, including an equilibrium spherical liquid drop suspending in a quiescent gas environment, a liquid drop falling under the action of gravitational force, a single spherical gas bubble rising in a container filled with quiescent liquid, and the Rayleigh–Taylor instability aroused in a cylindrical container are simulated to validate the CLSVOF method. It is shown that the calculation results obtained by the CLSVOF method agree well with the theoretical solutions and experimental results.

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 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 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 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.