Showing papers on "Volume of fluid method published in 2009"

Drop impact onto a liquid layer of finite thickness: dynamics of the cavity evolution.

Abstract: In the present work experimental, numerical, and theoretical investigations of a normal drop impact onto a liquid film of finite thickness are presented. The dynamics of drop impact on liquid surfaces, the shape of the cavity, the formation and propagation of a capillary wave in the crater, and the residual film thickness on the rigid wall are determined and analyzed. The shape of the crater within the film and the uprising liquid sheet formed upon the impact are observed using a high-speed video system. The effects of various influencing parameters such as drop impact velocity, liquid film thickness and physical properties of the liquids, including viscosity and surface tension, on the time evolution of the crater formation are investigated. Complementary to experiments the direct numerical simulations of the phenomena are performed using an advanced free-surface capturing model based on a two-fluid formulation of the classical volume-of-fluid (VOF) model in the framework of the finite volume numerical method. In this model an additional convective term is introduced into the transport equation for phase fraction, contributing decisively to a sharper interface resolution. Furthermore, an analytical model for the penetration depth of the crater is developed accounting for the liquid inertia, viscosity, gravity, and surface tension. The model agrees well with the experiments at the early times of penetration far from the wall if the impact velocity is high. Finally, a scaling analysis of the residual film thickness on the wall is conducted demonstrating a good agreement with the numerical predictions.

CFD Simulation of Boiling Flows Using the Volume-of-Fluid Method within OpenFOAM

Abstract: This article describes the implementation and validation of a nucleate boiling model in the volume-of-fluid solver of OpenFOAM. Emphasis is put on the implementation of the contact line evaporation, which can typically not be resolved by the numerical grid, and on the conjugate heat transfer between solid and fluid. For validation, the sucking interface problem and the growth of a spherical bubble have been simulated successfully. In order to validate the contact line model and the conjugate heat transfer, the growth of a bubble from a heated steel foil has been calculated.

The dam-break problem for Herschel-Bulkley viscoplastic fluids down steep flumes

Abstract: In this paper we investigate the dam-break problem for viscoplastic (Herschel–Bulkley) fluids down a sloping flume: a fixed volume of fluid initially contained in a reservoir is released onto a slope and flows driven by gravitational forces until these forces are unable to overcome the fluid’s yield stress. Like in many earlier investigations, we use lubrication theory and matched asymptotic expansions to derive the evolution equation of the flow depth, but with a different scaling for the flow variables, which makes it possible to study the flow behavior on steep slopes. The evolution equation takes on the form of a nonlinear diffusion–convection equation. To leading order, this equation simplifies into a convection equation and reflects the balance between gravitational forces and viscous forces. After presenting analytical and numerical results, we compare theory with experimental data obtained with a long flume. We explore a fairly wide range of flume inclinations from 6° to 24°, while the initial Bingham number lies in the 0.07–0.26 range. Good agreement is found at the highest slopes, where both the front position and flow-depth profiles are properly described by theory. In contrast, at the lowest slopes, theoretical predictions substantially deviate from experimental data. Discrepancies may arise from the formation of unsheared zones or lateral levees that cause slight flow acceleration.

Numerical Study on Taylor Bubble Formation in a Micro-channel T-Junction Using VOF Method

Abstract: A volume of fluid (VOF) method is used to study the immiscible gas–liquid two-phase flow in a microchannel T-junction, through which the accurate interface of the Taylor bubble flow inside the micro-channel is captured and compared with visualization experiment of Taylor bubbles’ generation inside a T-junction microfluidic chip. The numerical results are in good agreement with the experimental measurements, which confirms the validation of our model. Then the length of gas–liquid slugs and velocity distribution inside slugs at various conditions are investigated with the superficial velocity of gas and liquid phase ranging from 0.01 to 0.90 m/s, and capillary number ranging from 6.4 ×10 − 4 to 1.7 ×10 − 2. A comprehensive description of mechanism of bubbles’ break-off is achieved and the transition capillary number from squeezing regime to shearing regime is found around 5.8 ×10 − 3. Finally the influences of fluid viscosity, surface tension of the gas–liquid interface and the velocity of both gas and liquid phases on the characteristic of the gas–liquid two-phase flow in micro-channel are also discussed in detail.

Experimental and numerical investigation of capillary flow in SU8 and PDMS microchannels with integrated pillars

Abstract: Microfluidic channels with integrated pillars are fabricated on SU8 and PDMS substrates to understand the capillary flow. Microscope in conjunction with high-speed camera is used to capture the meniscus front movement through these channels for ethanol and isopropyl alcohol, respectively. In parallel, numerical simulations are conducted, using volume of fluid method, to predict the capillary flow through the microchannels with different pillar diameter to height ratio, ranging from 2.19 to 8.75 and pillar diameter to pitch ratio, ranging from 1.44 to 2.6. The pillar size (diameter, pitch and height) and the physical properties of the fluid (surface tension and viscosity) are found to have significant influence on the capillary phenomena in the microchannel. The meniscus displacement is non-uniform due to the presence of pillars and the non-uniformity in meniscus displacement is observed to increase with decrease in pitch to diameter ratio. The surface area to volume ratio is observed to play major roles in the velocity of the capillary meniscus of the devices. The filling speed is observed to change more dramatically under different pillar heights upto 120 μm and the change is slow with further increase in the pillar height. The details pertaining to the fluid distribution (meniscus front shapes) are obtained from the numerical results as well as from experiments. Numerical predictions for meniscus front shapes agree well with the experimental observations for both SU8 and PDMS microchannels. It is observed that the filling time obtained experimentally matches very well with the simulated filling time. The presence of pillars creates uniform meniscus front in the microchannel for both ethanol and isopropyl alcohol. Generalized plots in terms of dimensionless variables are also presented to predict the performance parameters for the design of these microfluidic devices. The flow is observed to have a very low Capillary number, which signifies the relative importance of surface tension to viscous effects in the present study.

Computational investigation of the mechanisms of particle separation and “fish-hook” phenomenon in hydrocyclones

Abstract: The motion of solid particles and the "fish-hook" phenomenon in an industrial classifying hydrocyclone of body diameter 355 mm is studied by a computational fluid dynamics model. In the model, the turbulent flow of gas and liquid is modeled using the Reynolds Stress Model, and the interface between the liquid and air core is modeled using the volume of fluid multiphase model. The outcomes are then applied in the simulation of particle flow described by the stochastic Lagrangian model. The results are analyzed in terms of velocity and force field in the cyclone. It is shown that the pressure gradient force plays an important role in particle separation, and it balances the centrifugal force on particles in the radial direction in hydrocyclones. As particle size decreases, the effect of drag force whose direction varies increases sharply. As a result, particles have an apparent fluctuating velocity. Some particles pass the locus of zero vertical velocity (LZVV) and join the upward flow and have a certain moving orbit. The moving orbit of particles in the upward flow becomes wider as their size decreases. When the size is below a critical value, the moving orbit is even beyond the LZVV. Some fine particles would recircuit between the downward and upward flows, resulting in a relatively high separation efficiency and the 'fish-hook" effect. Numerical experiments were also extended to study the effects of cyclone size and liquid viscosity. The results suggest that the mechanisms identified are valid, although they are quantitatively different. (C) 2009 American Institute of Chemical Engineers AIChE J, 56: 1703-1715, 2010

A volume‐of‐fluid method for incompressible free surface flows

Abstract: This paper proposes a hybrid volume-of-fluid (VOF) level-set method for simulating incompressible two-phase flows. Motion of the free surface is represented by a VOF algorithm that uses high resolution differencing schemes to algebraically preserve both the sharpness of interface and the boundedness of volume fraction. The VOF method is specifically based on a simple order high resolution scheme lower than that of a comparable method, but still leading to a nearly equivalent order of accuracy. Retaining the mass conservation property, the hybrid algorithm couples the proposed VOF method with a level-set distancing algorithm in an implicit manner when the normal and the curvature of the interface need to be accurate for consideration of surface tension. For practical purposes, it is developed to be efficiently and easily extensible to three-dimensional applications with a minor implementation complexity. The accuracy and convergence properties of the method are verified through a wide range of tests: advection of rigid interfaces of different shapes, a three-dimensional air bubble's rising in viscous liquids, a two-dimensional dam-break, and a three-dimensional dam-break over an obstacle mounted on the bottom of a tank. The standard advection tests show that the volume advection algorithm is comparable in accuracy with geometric interface reconstruction algorithms of higher accuracy than other interface capturing-based methods found in the literature. The numerical results for the remainder of tests show a good agreement with other numerical solutions or available experimental data. Copyright © 2009 John Wiley & Sons, Ltd.

Numerical simulation of free-surface flow using the level-set method with global mass correction

Abstract: A new numerical method that couples the incompressible Navier-Stokes equations with the global mass correction level set method for simulating fluid problems with free surfaces and interfaces is presented in this paper. The finite volume method is used to discretize NavierStokes equations with the two step projection method on a staggered grid. The free surface flow problem is solved on a fixed grid in which the free surface is captured by the zero level set. Mass conservation is improved significantly by applying a global mass correction scheme, in a novel combination with third order essentially non-oscillatory schemes and a five stage Runge-Kutta method, to advection and re-distancing of the level set function. The coupled solver is applied to simulate interface change and flow field in four benchmark test cases: (1) shear flow; (2) dam break; (3) travelling and reflection of solitary wave and (4) solitary wave over a submerged object. The computational results are in excellent agreement with theoretical predictions, experimental data and previous numerical simulations using a RANS-VOF method. The simulations reveal some interesting free surface phenomena such as the free surface vortices, air entrapment and wave deformation over a submerged object.