Coupled Level Set Research Articles

Crown behavior and bubble entrainment during a drop impact on a liquid film

Physical and mathematical models are established to simulate a single liquid drop impinging onto a liquid film using the coupled level set and volume of fluid method. The crown liquid sheet after impact is obtained, which coincides well with the experimental results in literatures. Influence of Weber number, Reynolds number and the dimensionless film thickness on the crown diameter and height is discussed quantitatively. Results indicate that the crown diameter is independent of the two non-dimensional numbers, while it can be increased by reducing the dimensionless film thickness. The crown height increases with the increasing of Weber number, but Reynolds number has small effect on it. Mechanism of the jet formation process is revealed by analyzing pressure distribution and velocity field in the liquid. It is found that both pressure difference in the neck region and velocity discontinuity can greatly affect the jet formation. Besides, the bubble entrainment phenomenon during a liquid drop impact on a liquid film is successfully captured with this numerical method. It is found that the increase in both impact Weber number and the drop diameter contributes to the emerging of bubble rings.

Comparison of the VOF and CLSVOF Methods in Interface Capturing of a Rising Bubble

The VOF (Volume of Fluids) and CLSVOF (Coupled Level Set and VOF) methods are both methodologies in capturing the interface of two phase fluids. Despite some comparison on the rising velocity and interface capturing for certain simple cases of bubbles at certain times of the simulation, no full comparison of the interface capturing for cases of breakups and coalescence along with the stage by stage interface comparison has been completed. In this paper, the shape and deformation of buoyancy driven spherical bubble rising in a 2D channel is numerically investigated. The VOF and CLSVOF models have been used in the numerical simulation and the results were compared both qualitatively and numerically for both models. This specific bubble size and case was chosen since it involves breaking up, coalescence and deformation which is essential in examining the ability of accurate interface capturing of different methodologies. The results show the effectiveness and faster mesh convergence of the CLSVOF method; however higher computational time is required for this method. The results show that while the VOF method required a finer mesh to capture the bubble accurately, the CLSVOF has effect on the shape of the bubble, and significant effects on the velocity field and wake pressure.

Analysis of liquid sheet and jet flow mechanism after droplet impinging onto liquid film

Physical and mathematical models are established to simulate the phenomenon of single droplet impinging onto flat liquid film by using the coupled level set and volume of fluid method, and influences of viscosity and surface tension on the morphology of the crown liquid sheet are discussed. Besides, the mechanism of jet flow in the neck region is revealed and the theory of kinematic discontinuity proposed by Yarin and Weiss is verified by analyzing the distributions of pressure and velocity after impingement. The research result shows that the effect of surface tension on the crown morphology is far stronger than that of viscosity. Generation of jet flow is due to the higher pressure difference, the effect of which becomes weak with impact evolution and the jet flow is developed into the crown gradually with the help of radial flow in the liquid film.

Simulation of Three-dimensional Complex Flows in Injection Molding Using Immersed Boundary Method

In this paper, an immersed boundary method (IBM) has been developed to simulate three-dimensional (3D) complex flows in the injection molding process, in which the irregular boundary of mould is treated by a level set function. The melt front (melt-air interface) is captured and treated using the coupled level set and volume of fluid (CLSVOF) method. The finite volume method on the nonstaggered meshes is implemented to solve the governing equations, and the melt filling process is simulated in a rectangular mould with both thick- and thin-wall sections. The numerical result shows good agreement with the available data. Finally, the melt filling processes in three different moulds, i.e., ring-shaped channels with concentric, eccentric and thin cylindrical insets, are investigated respectively. It is found that the so-called “race-tracking effect” and air traps phenomena could be observed successfully, which demonstrates the applicability of IBM to complex flows in injection molding.

Hybrid model of lattice Boltzmann and CLSVOF methods for immiscible two-fluid flow

For the development of two-fluid flow simulation with simple and high phase volume conservation, a hybrid model of lattice Boltzmann method (LBM) and coupled level set volume of fluid (CLSVOF) method is proposed. It is confirmed that finite-difference-based CLSVOF is compatible with LBM which shows similar behaviour to those by other simulation methods, and the weakly-compressibility of LBM induces the loss of phase volume. To reduce this volume error, the density distribution correction treatment is implemented in the system. This improved model is validated in cases of immiscible two-fluid flow; an oscillating droplet, a sessile droplet on various wettability surfaces, a droplet flowing through a porous medium, and T-shape channel flow. It is found that incompressible flow fields are well-represented by our improved model. For the case where the compressibility affects largely on the flow, the tendency of the flow is depicted better by unimproved model.

A practical numerical framework for free surface flows based on CLSVOF method, multi-moment methods and density-scaled CSF model: Numerical simulations of droplet splashing

We propose a practical numerical framework for free surface flows with surface tension force. The numerical framework consists of 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 the density-scaled CSF (continuum surface force) model. We also propose an efficient implementation algorithms of the density-scaled CSF model and a curvature interpolation technique, based on the level set method. The framework is validated through three benchmark problems (equilibrium drop, Rayleigh–Taylor instability and single bubble rising) and comparisons with an experiment of droplet splashing. The numerical framework can well capture free surface flows with complex interface geometries like droplet splashing. The proposed surface force algorithms, especially the level set based curvature interpolation technique, play a key role in numerical simulations of free surface flows with complex interface geometries.

A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows

A coupled level set and moment of fluid method (CLSMOF) is described for computing solutions to incompressible two-phase flows. The local piecewise linear interface reconstruction (the CLSMOF reconstruction) uses information from the level set function, volume of fluid function, and reference centroid, in order to produce a slope and an intercept for the local reconstruction. The level set function is coupled to the volume-of-fluid function and reference centroid by being maintained as the signed distance to the CLSMOF piecewise linear reconstructed interface. The nonlinear terms in the momentum equations are solved using the sharp interface approach recently developed by Raessi and Pitsch (Annual Research Brief, 2009). We have modified the algorithm of Raessi and Pitsch from a staggered grid method to a collocated grid method and we combine their treatment for the nonlinear terms with the variable density, collocated, pressure projection algorithm developed by Kwatra et al. (J. Comput. Phys. 228:4146---4161, 2009). A collocated grid method makes it convenient for using block structured adaptive mesh refinement (AMR) grids. Many 2D and 3D numerical simulations of bubbles, jets, drops, and waves on a block structured adaptive grid are presented in order to demonstrate the capabilities of our new method.

Primary breakup simulation of a liquid jet discharged by a low-pressure compound nozzle

The aim of this paper is to demonstrate the capability of a numerical approach to retrieve the involved primary breakup process in the case of a single triple disk compound injector. The present study is based on a coupling between internal flow simulations and DNS of primary breakup. The internal flow is described through RANS and LES simulations and comparisons with experimental data validate the calculation accuracy. DNS of the primary breakup is then presented (coupling level set, VOF, ghost fluid methods) and discussed by comparing the results (morphology, jet angle, perturbation wavelength) with experimental visualizations.

Large eddy simliation wave breaking over muddy seabed

The Large Eddy Simulation (LES) of the wave breaking over a muddy seabed is carried out with a Coupled Level Set and Volume Of Fluid (CLSVOF) method to capture the interfaces. The effects of the mud on the wave breaking are studied. The existence of a mud layer beneath an otherwise rigid bottom is found to have a similar effect as an increase of the water depth. As compared with the case of a simple rigid bottom, the inception of the wave breaking is evidently delayed and the breaking intensity is much reduced. The dissipation of the wave energy is shown to have very different rates before, during and after the breaking. Before and after the breaking, the mud plays an important role. During the breaking, however, the turbulence as well as the entrainment of the air also dissipate a large amount of energy.

Oblique Drop Impact on Deep and Shallow Liquid

AbstractNumerical simulations using CLSVOF (coupled level set and volume of fluid) method are performed to investigate the coalescence and splashing regimes when a spherical water drop hits on the water surface with an impingement angle. Impingement angle is the angle between the velocity vector of primary drop and the normal vector to water surface. The effect of impingement angle, impact velocity and the height of target liquid are carried out. The impingement angle is varied from 0° to 90° showing the gradual change in phenomena. The formation of ship pro like shape, liquid sheet, secondary drops and crater are seen. Crater height, crater displacement, crown height and crown angle are calculated and the change in the parameters with change in impingement angle is noted.

A new volume-of-fluid method with a constructed distance function on general structured grids

A second-order volume-of-fluid method (VOF) is presented for interface tracking and sharp interface treatment on general structured grids. Central to the new method is a second-order distance function construction scheme on a general structured grid based on the reconstructed interface. A novel technique is developed for evaluating the interface normal vector using the distance function. With the normal vector, the interface is reconstructed from the volume fraction function via a piecewise linear interface calculation (PLIC) scheme on the computational domain. Several numerical tests are conducted to demonstrate the accuracy and efficiency of the present method. In general, the new VOF method is more efficient than both the high-order level set and the coupled level set and volume-of-fluid (CLSVOF) methods. The results from the new method are better than those from the benchmark VOF method, particularly in the under-resolved regions, and are comparable to those from the CLSVOF method. Breaking waves over a submerged bump and around a wedge-shaped bow are simulated to demonstrate the application of the new method and sharp interface treatment in a two-phase flow solver on curvilinear grids. The computational results are in good agreement with the available experimental measurements.

Automatic segmentation of neonatal images using convex optimization and coupled level sets

Accurate segmentation of neonatal brain MR images remains challenging mainly due to their poor spatial resolution, inverted contrast between white matter and gray matter, and high intensity inhomogeneity. Most existing methods for neonatal brain segmentation are atlas-based and voxel-wise. Although active contour/surface models with geometric information constraint have been successfully applied to adult brain segmentation, they are not fully explored in the neonatal image segmentation. In this paper, we propose a novel neonatal image segmentation method by combining local intensity information, atlas spatial prior, and cortical thickness constraint in a single level-set framework. Besides, we also provide a robust and reliable tissue surface initialization for the proposed method by using a convex optimization technique. Thus, tissue segmentation, as well as inner and outer cortical surface reconstruction, can be obtained simultaneously. The proposed method has been tested on a large neonatal dataset, and the validation on 10 neonatal brain images (with manual segmentations) shows very promising results.

Automatic segmentation of neonatal images using convex optimization and coupled level sets

Automatic segmentation of neonatal images using convex optimization and coupled level sets

Numerical Simulation of Melt Filling and Gas Penetration in Gas Assisted Injection Molding

The governing equations of two-phase flows including gas and polymer melt are presented, which are solved using finite volume and domain extension methods with SIMPLEC technology. The melt filling and primary gas penetration in gas-assisted injection molding (GAIM) process are simulated, where the Cross-viscosity model is employed to describe the melt rheological behavior, and the CLSVOF(coupled Level Set and Volume of fluid) method is employed to capture the moving interfaces. In order to test and verify the coupled methods, melt filling in a rectangular plate with an insert is simulated, and the numerical results are in good agreement with those of the experiment. As a case study, the melt filling and gas penetration processes in a ring-shaped channel are simulated. The numerical results successfully depict some important phenomena, such as race-tracking effect, corner effect and the flow asymmetry of the gas penetration, which can deepen the understanding and studying of the GAIM process.

A robust and efficient conservative technique for simulating three-dimensional sedimentary basins dynamics

The development of new efficient numerical techniques is a key point in computational fluid dynamics, and as a consequence in geological simulations. In this paper we present a model for simulating the dynamic of three-dimensional stratified sedimentary basins. This kind of problem contains several numerical complexities such as the presence of high viscosity jumps, or the necessity of tracking multiple surfaces of interface (horizons) independently. To overcome these difficulties, we introduce a new preconditioner, that reduces significantly the amount of time required to solve the finite element linear system resulting from the Stokes problem, and a new tracking method. Using a coupled level set–volume tracking method, indeed, an unlimited number of layers can be tracked with good mass conservation properties. Finally, to prove the efficiency of these new techniques we present the results and the computation performances obtained in simulations of a realistic case with four horizons, together with a complete description of the main physical quantities involved.

Generation of secondary droplets in coalescence of a drop at a liquid–liquid interface

When a droplet of liquid 1 falls through liquid 2 to eventually hit the liquid 2–liquid 1 interface, its initial impact on the interface can produce daughter droplets of liquid 1. In some cases, a partial coalescence cascade governed by self-similar capillary-inertial dynamics is observed, where the fall of the secondary droplets in turn continues to produce further daughter droplets. Results show that inertia and interfacial surface tension forces largely govern the process of partial coalescence. The partial coalescence is suppressed by the viscous force when Ohnesorge number is below a critical value and also by gravity force when Bond number exceeds a critical value. Generation of secondary drop is observed for systems of lower Ohnesorge number for liquid 1, lower and intermediate Ohnesorge number for liquid 2 and for low and intermediate values of Bond number. Whenever the horizontal momentum in the liquid column is more than the vertical momentum, secondary drop is formed. A transition regime from partial to complete coalescence is obtained when the neck radius oscillates twice. In this regime, the main body of the column can be fitted to power-law scaling model within a specific time range. We investigated the conditions and the outcome of these coalescence events based on numerical simulations using a coupled level set and volume of fluid method (CLSVOF).

A Coupled Level Set Framework for Bladder Wall Segmentation With Application to MR Cystography

In this paper, we propose a coupled level set (LS) framework for segmentation of bladder wall using T(1)-weighted magnetic resonance (MR) images with clinical applications to virtual cystoscopy (i.e., MR cystography). The framework uses two collaborative LS functions and a regional adaptive clustering algorithm to delineate the bladder wall for the wall thickness measurement on a voxel-by-voxel basis. It is significantly different from most of the pre-existing bladder segmentation work in four aspects. First of all, while most previous work only segments the inner border of the wall or at most manually segments the outer border, our framework extracts both the inner and outer borders automatically except that the initial seed point is given by manual selection. Secondly, it is adaptive to T(1)-weighted images with decreased intensities in urine, as opposed to enhanced intensities in T(2)-weighted scenario and computed tomography. Thirdly, by considering the image global intensity distribution and local intensity contrast, the defined image energy function in the framework is more immune to inhomogeneity effect, motion artifacts and image noise. Finally, the bladder wall thickness is measured by the length of integral path between the two borders which mimic the electric field line between two iso-potential surfaces. The framework was tested on six datasets with comparison to the well-known Chan-Vese (C-V) LS model. Five experts blindly scored the segmented inner and outer borders of the presented framework and the C-V model. The scores demonstrated statistically the improvement in detecting the inner and outer borders.

Individual tooth segmentation from CT images using level set method with shape and intensity prior

3D visualization of teeth from CT images provides important assistance for dentists performing orthodontic surgery and treatment. However, dental CT images present several major challenges for the segmentation of tooth, which touches with adjacent teeth as well as surrounding periodontium and jaw bones. Moreover, tooth contour suffers from topological changes and splits into several branches. In this work, we focus on the segmentation of individual teeth with complete crown and root parts. To this end, we propose adaptive active contour tracking algorithms: single level set method tracking for root segmentation to handle the complex image conditions as well as the root branching problem, and coupled level set method tracking for crown segmentation in order to separate the touching teeth and create the virtual common boundaries between them. Furthermore, we improve the variational level set method in several aspects: gradient direction is introduced into the level set framework to prevent catching the surrounding object boundaries; in addition to the shape prior, intensity prior is introduced to provide adaptive shrinking or expanding forces in order to deal with the topological changes. The test results for both tooth segmentation and 3D reconstruction show that the proposed method can visualize individual teeth with high accuracy and efficiency.

A novel coupled level set and volume of fluid method for sharp interface capturing on 3D tetrahedral grids

We present a new three-dimensional hybrid level set (LS) and volume of fluid (VOF) method for free surface flow simulations on tetrahedral grids. At each time step, we evolve both the level set function and the volume fraction. The level set function is evolved by solving the level set advection equation using a second-order characteristic based finite volume method. The volume fraction advection is performed using a bounded compressive normalized variable diagram (NVD) based scheme. The interface is reconstructed based on both the level set and the volume fraction information. The novelty of the method lies in that we use an analytic method for finding the intercepts on tetrahedral grids, which makes interface reconstruction efficient and conserves volume of fluid exactly. Furthermore, the advection of volume fraction makes use of the NVD concept and switches between different high resolution differencing schemes to yield a bounded scalar field, and to preserve both smoothness and sharp definition of the interface. The method is coupled to a well validated finite volume based Navier-Stokes incompressible flow solver. The code validation shows that our method can be employed to resolve complex interface changes efficiently and accurately. In addition, the centroid and intercept data available as a by-product of the proposed interface reconstruction scheme can be used directly in near-interface sub-grid models in large eddy simulation.

A sharp surface tension modeling method for two‐phase incompressible interfacial flows

AbstractA surface tension implementation algorithm for two‐phase incompressible interfacial flows is presented in this study. The surface tension effect is treated as a jump condition at the interface and incorporated into the Navier–Stokes equation via a capillary pressure gradient. The interface is tracked by a coupled level set and volume‐of‐fluid (CLSVOF) method based on the finite‐volume formulation on a fixed Eulerian grid. It has been shown in a stationary benchmark test the spurious currents are greatly reduced and the sharp pressure jump across the interface is well preserved. Numerical instabilities caused by the sharp treatment on a fixed grid are avoided. Several dynamic tests are performed to further validate the accuracy and versatility of the present method, the results of which are in good agreement with data reported in the literature. Copyright © 2009 John Wiley & Sons, Ltd.