Volume Of Fluid Model Research Articles

Numerical analysis of roll waves in chutes

Uniform flow will become unstable when the channel slope is very steep. When this happens, the free surface will form a series of roll waves. This paper, using the Fluent software and applying the volume of fluid model to simulate free surface flow and the k – ε turbulence model, analyzes conditions for roll wave formation in free surface flow with the aim of predicting their occurrence in chutes. This study describes how the type of cross-section of the chutes influences the formation of roll waves. Hydraulic characteristics of the flow in the physical model of the flood control structure for Azad Dam spillway, which consists of a side spillway, chute, and flip, are three-dimensionally simulated. Numerical predictions were compared against the experimental data and results show that there is a good agreement between numerical and experimental results. Results indicate that an increase in side slope tends towards flow stability and the slower formation of rolling waves. Also, the rolling waves are expected to be generated for sections of the chute when the difference between the maximum dynamic pressure and the minimum dynamic pressure in those sections is above 9,000 Pa.

Droplet characteristics and behaviors in a high-speed disperser

In order to intensify the gas absorption process, a high-speed disperser with a rotor 219mm in external diameter was designed to disperse the continuous liquid into droplets. The effects of rotational speed, radial distance, and inlet flow rate on droplet size and velocity were measured by using a high-speed camera in the air-water system. Results showed that the mean droplet diameter decreased with increasing rotational speed and decreasing radial distance or inlet flow rate. On the other hand, the droplet resultant velocity increased with increasing rotational speed or decreasing radial distance, but was hardly affected by the inlet flow rate. The Rosin–Rammler (R–R) distribution and three-parameter volume-based maximum entropy formalism (MEF) appropriately represented the droplet size distribution. Models for droplet motion in the rotor and cavity zones were successfully established to calculate the droplet velocity. The commercial code Fluent was adopted to simulate droplet characteristics and behaviors. The volume of fluid (VOF) model and the Euler–Euler multiphase model were implemented to predict the droplet size and velocity fields for gas and liquid, respectively. A comparison of simulated and experimental results indicated that the VOF model predicted the droplet size reasonably well, and the Euler–Euler multiphase model provided good estimates of the droplet velocity.

Simulation on the infiltration with insufficience of molten Cu into W micro-channel

The effect of wettability between Cu and W on the flow behavior was simulated at the given condition of insufficience of molten Cu in this investigation. A single channel geometrical model of the W skeleton was established, the flow process of immiscible hydrogen and molten Cu in micro-channel was simulated based on VOF (Volume of Fluid) model by using Fluent Version 6.1, and the effect of wettability and infiltration time on the flow behavior in the W channel and at the flow front of molten Cu was analyzed as well. The results show that the flow front of molten Cu presents a convex shape under the insufficience of molten Cu condition, and progressively becomes more sharpened with infiltration time and the decreased contact angle, and, thus, results in the separation of molten Cu from W surface and the formation of pores, along with the poor performance of CuW alloy. The simulated results are in good agreement with experimental results.

Implications of Adjustable Fountain Wave in Pin Through Hole Soldering Process

This paper presents the implications of the adjustable fountain wave soldering process during pin through hole (PTH) component assembly process. The PTH vertical fill was carried out experimentally by using a newly developed adjustable fountain wave soldering machine (\({0^{\circ}}\) conveyor angle). A similar printed circuit board and components were assembled by using a conventional wave soldering machine (\({6^{\circ}}\) conveyor angle). This paper focuses on vertical filling by using both wave soldering methods. A non-destructive X-ray computed tomography scanning machine was employed to inspect the vertical fill of each PTH. The percentage of the vertical fill for two different wave soldering machines was analyzed. The PTH filling phenomenon during wave soldering was also discussed. FLUENT software was utilized to simulate the PTH vertical filling of adjustable fountain wave soldering. The volume of fluid model tracked the flow front of the molten solder. The simulation and experimental results showed a nearly identical solder filling profile. The void of the PTH vertical filling was also visualized under an X-ray CT scanning machine.

Numerical simulation of droplet deposition onto a liquid film by VOF–MPS hybrid method

Droplet entrainment and deposition are a couple of significant mechanisms for the heat transfer in annular two-phase flows existing in some heat exchange systems. The basic physics include the peeling of droplets from the liquid film due to high friction with the gas phase and the collision of droplets with the liquid film or deposition into the liquid film. Droplet deposition particularly plays a crucial role in the course of film dryout events which might have a vital importance for particular systems. In this study, a new numerical method (named as VOF–MPS hybrid method) based on the moving particle semi-implicit (MPS) method was developed to analyze the droplet deposition onto a stagnant thin liquid film. That proposed method combines the volume of fluid (VOF) solver of the open-source CFD code OpenFOAM with the MPS method. VOF–MPS technique introduces the surface tension force calculation of VOF model into the MPS method. MPS method formerly employed the continuum surface force (CSF) approach based on the particles. Three-dimensional (3D) VOF–MPS simulation with the novel surface tension modeling addition to the MPS-based modeling provides a smoother liquid–gas interface on the crown formed after the impact. Droplet deposition experiments were also carried out for the validation and comparison of two models. VOF–MPS method could predict the crown parameters such as crown thickness relatively better than the MPS method employing the CSF. However, the instabilities formed at the tip of the crown, observed in the experiments, could not be resolved with both methods.

Volume of Fluid Model of Open Channel Contraction

In the present paper, the effect of channel contraction has been studied using FLUENT. Contracted channels having three different contraction ratios (0.77, 0.61, and 0.44) have been investigated. The effect of channel contraction on the vertical profiles of longitudinal mean velocity, turbulence intensity, turbulent kinetic energy (TKE) and turbulent dissipation rate in comparison to the open channel case is explored. The velocity profile of the contracted channel with contraction ratio 0.44 is compared with experimental data obtained from laboratory flume experiment. The mean longitudinal velocity, turbulence intensity, TKE and turbulent dissipation rate increases with the decrease in contraction ratio and vice versa.

A novel optimization approach to convective heat transfer enhancement for solar receiver

Convective heat transfer enhancement for solar receiver is considered as a variational problem in this paper. A predictive optimization method based on the minimum heat transfer entropy generation (MHEG) principle is developed for ideal gas in turbulent flow. A set of Euler–Lagrange equations is derived by the calculus of variations. By employing a porous media model and multiphase Volume of Fluid (VOF) model in the variational problem, the optimization constrained by the mechanical energy loss is performed to achieve a physically feasible geometry configuration to improve the performance of the convective heat transfer in a solar receiver. To validate and demonstrate the method, turbulent convection heat transfer process in a two-dimensional rectangular channel with fixed heat flux boundaries is optimized. The computation results show that higher air temperature at the outlet and lower wall temperature can be obtained, which may lead to the use of cheaper materials with lower heat-resistance for the exchanger. The present work shows that combining the calculus of variations with porous media and multiphase VOF model may be helpful for the design of efficient convective solar receiver.

Effect of T-Shaped Micro-Channel Structure Dimension on Formation of Micro-Liquid-Columns Formed by Vertical-Shear-Flow

Effects of T-shaped micro-channel structure sizes on the formation of micro-liquid column formed by vertical-shear-flow were studied. The method of CFD based on VOF (Volume of Fluid) model was used in the computation. H2O and C5H3 were used as continuous-phase and as dispersed-phase. Interface-tracking method was used to get data of the two phases. The size parameters include crossing angle (∠β), width ratio of vertical channel and main channel (W2/W1), depth ratio of vertical channel and main channel (D2/D1), depth-width ratio of main channel (D1/W1). The above parameters affect the forming time of micro-liquid columns, the order of importance is D2/D1,∠β, D1/W1, W2/W1; And for the length, the order is∠β, D2/D1, D1/W1, W2/W1. For the shortest forming time, the optimized parameters of ∠β, D2/D1, D1/W1 and W2/W1 are 90°, 1.00, 1.00 and 1.60. To get the shortest micro-liquid columns, the optimized parameters of ∠β, D2/D1, D1/W1 and W2/W1 are 60°, 1.00, 1.00 and 1.60.

CFD MODELING OF PNEUMATIC OIL BARRIER

Pneumatic oil barriers (so called “bubble oil boom (BOB)”) are based on the rise of air bubbles which are injected from the submerged parallel line spargers (McClimans et al., 2012). Local outward flows are formed when the bubbles and entrained water reach the sea surface, and thereby could counterbalance the opposing sea current to retain the spilled oil. It could function alone or work together with a traditional oil boom to improve the recovery effectiveness. A multiphase Computational Fluid Dynamic model, which couples volume of fluid (VOF) and discrete phase model (DPM) approach together with an enhanced k-epsilon model, is developed. Trajectories of bubbles are computed in the Lagrangian frame of reference, exchanging momentum and turbulent energy with water and oil slick, represented in the Eulerian frame of reference. The interface between atmosphere, water and oil slick is captured by the VOF model. The model is applied to meso-scale experiments in McClimans et al. (2012) for validation. The validated numerical model can provide improved basis for the further design of BOB system.

Simulation of gas absorption into string-of-beads liquid flow with chemical reaction

This study is an attempt to investigate the chemical absorption of CO2 in aqueous monoethanolamine (MEA) solution in a wetted-wire column consisting of one wire. Computational fluid dynamics method along with volume of fluid model was employed for modeling of two-phase flow, mass transfer and chemical reaction inside the column. The modeling results were compared with available experimental data and very good agreement was achieved. The simulation results showed that the diameter and intervals of liquid beads increases by increasing the gas and liquid flow rates. The beads velocity increases by increasing the liquid flow rate and decreasing mass fraction of MEA in the liquid phase. Also, mass transfer resistance in the liquid phase reduces by formation of the beads. It was concluded that the developed model is capable to predict the effect of operating and physical parameters on the investigated chemical absorption process.

Ascent modes of jets and plumes in a stationary fluid of contrasting viscosity

Using multi-phase numerical experiments based on the Volume of fluid (VOF) methods we show the ascent behavior of a fluid injected into another immiscible fluid with higher viscosity. Our VOF models reveal that the injected fluid forms jets characterized by a large head trailing to a slender tail, which do not break up, but ascend in two principal modes, Mode 1: continuous and Mode 2: pulsating. In Mode 1, their heads grow continuously either by volume expansion, forming balloon-shaped geometry (Mode 1a) or by curling, forming mushroom-shaped geometry (Mode 1b). In contrast, Mode 2 jets ascend in pulses, forming multiple heads, leading to pinched-off geometry. In this study we show the viscosity ratio (R) between the injecting and the ambient fluids as a crucial parameter in controlling the ascent modes, and provide an estimate of critical R for the Mode 1–2 transition under varying fluid injection rates (non-dimensionalized as Reynolds number, Re). From the entrainment velocity field we explain that the transition of continuous to pulsating process results from the flow convergence at several locations along the upwelling direction. We have also discussed the effects of buoyancy on the ascent modes in case of plumes.

Contribution of Trapped Air, Deck Superelevation, and Nearby Structures to Bridge Deck Failure during a Tsunami

Failure of the Utatsu concrete girder highway bridge in Minamisanriku, Miyagi Prefecture during the 2011 Great East Japan Tsunami was puzzling because the bridge decks were not pushed off their piers but rather were flipped off the landward side of the bridge piers after being deeply submerged by the surging tsunami. To determine what caused this to happen, two simulations were conducted. The first was a large-scale Delft shallow-water simulation (beginning with published tsunami source free surface deviation) to determine the behavior of the tsunami (time series of flow depth and speed) at the bridge site. The second was a small-scale two-dimensional (2D) (profile view) software volume-of-fluid (VOF) simulation of flow over the bridge deck, with boundary conditions taken from the Delft model. The VOF model then allowed calculation of lift force, drag force, and overturning moment on the bridge deck. Results show that factors contributing to failure included the presence of a seawall near the bridge, inclination (superelevation) of the deck upward toward the ocean, sediment entrained in the water, and air trapped between girders.

Numerical simulation of the settling behaviour of particles in thixotropic fluids

A numerical study on the settling behaviour of particles in shear‑thinning thixotropic fluids has been conducted. The numerical scheme was based on the volume of fluid model, with the solid particle being likened to a fluid with very high viscosity. The validity of this model was confirmed through comparisons of the flow field surrounding a sphere settling in a Newtonian fluid with the analytical results of Stokes. The rheology model for the fluid was time‑dependent, utilising a scalar parameter that represents the integrity of a “structural network,” which determines its shear thinning and thixotropic characteristics. The results of this study show that the flow field surrounding the settling sphere is highly localised, with distinct regions of disturbed/undisturbed fluids. The extension of these regions depends on the relaxation time of the fluid, as well as its shear thinning characteristics, and reflects the drag force experienced by the sphere. As the sphere settles, a region of sheared fluid that has significantly lower values of viscosity is formed above the sphere. This region slowly recovers in structure in time. As a result, a sphere that falls in a partially recovered domain (e.g., due to the shearing motion of an earlier sphere) tends to attain a greater velocity than the terminal velocity value. This was found to be true even in cases where the “resting time” of the fluid was nearly twice the relaxation time of the fluid. The results of this study could provide a framework for future analysis on the time‑dependent settling behaviour of particles in thixotropic shear‑thinning fluids.

CFD study of distillation sieve tray flow regimes using the droplet size distribution technique

A good understanding on the characteristics of sieve tray flow regimes is one of the keys to achieve an efficient distillation operation. A 3-D computational fluid dynamics (CFD) model based on the volume-of-fluid (VOF) and the large eddy simulation (LES) has been developed to simulate the complex flow phenomena in a sieve tray. The analysis of droplet size distribution (DSD), which was made possible by the use of VOF model, was then carried out to characterize the prevailing flow regime. The obtained results are in good agreement with the experimental data available in the literature in terms of the prediction of clear liquid height. The results obtained from the DSD analysis reveal that the sphere equivalent droplet diameter, ddrop,eq, is inversely proportional to the gas superficial velocity, and is directly proportional to the liquid volumetric flow rate, QLo. Approaching the froth-to-spray transition regime, ddrop,eq was found to range from 0.008m to 0.0114m. These findings may serve as valuable information in assisting tray designers and process engineers to decide on ranges of operating conditions which allows the attainment of high efficiency distillation operation, and also providing some insights into future development of sieve tray technology.

Phase Change and Heat Transfer Numerical Analysis during Solidification on an Encapsulated Phase Change Material

In this investigation the coupled phase change and heat transfer in a spherical capsule partially filled with sodium nitrate is numerically investigated during the solidification process. The finite volume method is used to compute energy and linear momentum equations along with the enthalpy-porosity method to track the melting front. The volume of fluid model is used to track the transient behavior of the PCM-Air interface. A spherical capsule under the gravitational field with inner radius, Ri, is initially filled by a determined volume of solid NaNO3, the remaining internal volume is completed with air. For time t>0, a constant temperature boundary condition Tw, which is lower than the solidification temperature of the PCM, is imposed at the outer surface of the shell. Transient melt fraction and temperature distributions within the spherical capsule are analyzed for different parameters such as Grashof, Stefan and Prandtl numbers in order to present an elaborate discussion of the thermal performance of the system. The results showed that the total solidification time decreases up to 25% when the temperature difference between the PCM melting point and the outer wall changed from 5 to 15°C.

Numerical study of two-phase flow patterns in the gas channel of PEM fuel cells with tapered flow field design

In this study the air–water two-phase flow in a tapered channel of a PEMFC was numerically simulated using the volume of fluid (VOF) method. In particular, a 3D mathematical model of the fuel cell flow channel was used to obtain a reliable evaluation of the fuel cell performance for different taper angles and different temperatures and to calculate the total amount of water produced. This information was then used as boundary conditions to simulate the two-phase flow in the cell channel through a 2D VOF model. Typical operating conditions were assigned and the numerical mesh was constructed to represent the real fuel cell configuration. The results show that tapering the channel downstream enhances the water removal due to increased airflow velocity. In the rectangular channel no film formation is noted with a marked predominance of slug flow. In contrast, as the taper angle is increased the predominant two-phase flow pattern is film flow. Finally many contact angles have been used to simulate the effect of the hydrophobicity of a GDL surface on the motion of the water. As the hydrophobicity of a GDL surface is decreased the presence of film is more evident even for less tapered channels.

Numerical simulation of the plasma–MIG process—interactions of the arcs, droplet detachment and weld pool formation

The plasma–metal inert gas (MIG) process is characterized by a variety of process parameters. Numerical simulation can be used to investigate the influence of these process parameters and thus helps to improve the properties of the weld. In this paper we discuss a procedure to describe the plasma–MIG process by coupling numerical models of the arc and the droplet detachment with a three-dimensional model for the plasma–MIG weld pool. Using the magnetohydrodynamic (MHD) arc model, the effects of process parameters on the arc pressure profile and the energy input profile on the workpiece can be analyzed. The volume-of-fluid (VoF)–MHD model of the droplet detachment describes the properties of the resulting droplet in terms of its size, temperature and speed. In the three-dimensional VoF model of the weld pool, the influences of the arc and the droplet are simplified by source terms in the mass, momentum and energy equations. Due to these simplifications in the physical complexity, the process and the seam shape can be described with reasonable computational effort.

Direct numerical simulation of wall-to liquid heat transfer in dispersed gas–liquid two-phase flow using a volume of fluid approach

In this paper a simulation model is presented for the direct numerical simulation (DNS) of wall-to-liquid heat transfer in dispersed gas–liquid two-phase flow using a volume of fluid (VOF) approach. Our model extends the VOF model developed by van Sint Annaland et al. (2005) to non-isothermal conditions. Our VOF method involves an interface reconstruction technique based on piecewise linear interface representation. The surface tension is incorporated using a three-dimensional version of the continuous surface force (CSF) model of Brackbill et al. (1992). The model is applied to predict the heat exchange rate between the liquid and a hot wall kept at a fixed temperature. It is found that, due to bubble induced agitation in the liquid phase, the heat transfer rate between the wall and the liquid is considerably enhanced especially when bubble coalescence prevails in the vicinity of the hot wall. Although this finding is obvious from an intuitive point here we present quantitative results to describe this phenomenon.

Computational Fluid Dynamics Modeling of Gas‐Liquid Two‐Phase Flow around a Spherical Particle

AbstractMicroscale studies, which can provide basic information for meso‐ and macroscale studies, are essential for the realization of flow characteristics of a packed bed. In the present study, the effects of gas velocity, liquid velocity, liquid‐solid contact angle, and liquid viscosity on the flow behavior were parametrically investigated for gas‐liquid two‐phase flow around a spherical particle, using computational fluid dynamics (CFD) methodology in combination with the volume‐of‐fluid (VOF) model. The VOF model was first validated and proved to be in good agreement with the experimental data. The simulation results show that the film thickness decreases with increasing gas velocity. This trend is more obvious with increasing operating pressure. With increasing liquid velocity, the film thickness tends to be uniform on the particle surface. The flow regime can change from film flow to transition flow to bubble flow with increasing contact angle. In addition, only at relatively high values does the liquid viscosity affect the residence time of the liquid on the particle surface.

3-D simulation of transient flow patterns in a corridor-shaped air-cushion surge chamber based on computational fluid dynamics

The 3-D characteristics of the water-air flow patterns in a corridor-shaped air-cushion surge chamber during hydraulic transients need to be considered in the shape optimization. To verify the reliability of the water-air two-phase model, namely, the volume of fluid model, the process of charging water into a closed air chamber is successfully simulated. Using the model, the 3-D flow characteristics under the load rejection and acceptance conditions within the air-cushion surge chamber of a specific hydropower station are studied. The free surface waves, the flow patterns, and the pressure changes during the surge wave process are analyzed in detail. The longitudinal flow of water in the long corridor-shaped surge chamber is similar to the open channel flow with respect to the wave propagation, reflection and superposition characteristics. The lumped parameters of the 3-D numerical simulation agree with the results of a 1-D calculation of hydraulic transients in the whole water conveying system, which validates the 3-D method. The 3-D flow structures obtained can be applied to the shape optimization of the chamber.