LATTICE BOLTZMANN PSEUDO-POTENTIAL MODELLING OF MULTIPHASE DROPLET PHENOMENA

The multiphase modeling of a droplet in a multiphase system is considered becoming a fundamental problem in fluid dynamics. A complex understanding of droplet behavior is critical to reveal a deeper insight into a more complex multiphase system. Droplet behavior studies are necessary to obtain a better understanding of solving multiphase problems in both the science and industrial aspect. The droplet behavior is characterized by a non-dimensional number such as the Eötvös number. In this study, numerical simulation was performed using the Lattice Boltzmann method. Parametric studies of Eötvös number was done. The parametric study of the Eo number is obtained using LBM. Based on the results obtained, it is concluded that the gravitational force influences the downwards rate of the droplet. Furthermore, the shape of the droplet during falling was depended on the Eo number as well. The higher Eo number means higher gravitational force, hence the velocity of the droplet is increasing as well as the reaction force of surface tension. This study is beneficial to give a deeper explanation of multiphase phenomena as well as contribute to the modeling of multiphase phenomena using an alternative numerical method of LBM.

Liquid-Liquid Flow Pattern Prediction Using Relevant Dimensionless Parameter Groups

Accurate predictions of flow patterns in liquid-liquid flow are critical to the successful design and operation of industrial and geo-energy systems where two liquids are jointly transported. Unfortunately, there is no unified flow pattern map, because all published maps are based on limited ranges of dimensional parameters. Dimensional analysis was performed on oil-water horizontal flows, to obtain some relevant dimensionless parameter groups (DPG) for constructing flow pattern maps (FPM). The following combinations of DPG were used: (i) the ratio of mixture Reynolds number to Eötvös number versus water fraction, (ii) the ratio of Weber number to Eötvös number versus water fraction, (iii) the mixture Froude number versus water fraction, (iv) the water Froude number versus oil Froude number, (v) the ratio of gravity force to viscous force versus water fraction. From twelve published experimental studies, 2696 data points were gathered and analysed covering a variety of flow patterns including stratified, stratified mixed, dispersed oil in water, dispersed water in oil, annular and slug flows. Based on the performed analysis, it was found that flow patterns could occupy more than one isolated region on the DPG-based flow pattern map. None of the combinations of DPG can mark out all the considered flow patterns, however, some combinations of DPG are particularly suitable for marking out the regions associated with some flow patterns.

Numerical study of single bubble rising dynamics using the phase field lattice Boltzmann method

In this paper, the rising dynamics of a two-dimensional single bubble in the duct is systematically studied by using an improved phase field lattice Boltzmann (LB) multiphase model. This model enables to handle multiphase flows with mass conservation and high density ratio, up to the order of [Formula: see text], which are unavailable in the LB community. The model is first validated by simulating bubble rising problem with the density ratio of 1000 and numerical solutions for bubble shape and position agree well with the previous literature data. Then, it is used to study single bubble rising through a quiescent liquid. The dynamic behavior of the bubble and rising velocity are shown, and the influences of several important physical quantities, including the Eotvos number, Reynolds number, density ratio, viscosity ratio, bubble size and initial bubble shape, are investigated in detail. The numerical results show that the bubble undergoes a great deformation with the increase of the Eotvos number or Reynolds number, and even could break up into multiple satellite bubbles at a sufficiently large value of Eotvos number or Reynolds number. Several classic terminal bubble shapes are also successfully produced in the system. The terminal rising velocity of bubble at equilibrium shows to present an initial increase with the Eotvos number and finally decreases with it, while increasing the Reynolds number could enhance the bubble rising velocity. Both the density ratio and viscosity ratio have less influence on the terminal shape of the bubble, while a greater influence on the rising velocity is reported for the density ratio smaller than 20 and it seems to be independent of the viscosity ratio. At last, we discuss the effects of the bubble size and initial bubble shape. It is found that bubble size has little influence on terminal bubble shape, but decreasing the bubble size can improve the bubble terminal velocity. On the other hand, both the deformation and terminal velocity of the bubble are found to no longer change much with its initial shape.

Experimental Observation of Bubbles Released in Horizontal Water Flow

To investigate the characteristics of the bubble which is exposed to the liquid cross flow, the method of ventilation was adopted and air was injected into the water flow. A water tunnel was used to provide uniform water flow with variable velocity magnitude. A high speed camera was used to record instantaneous bubble images. An image-processing code was developed to identify bubble profile and to calculate bubble parameters. The effects of water flow velocity and the flow rate of the injected air were considered. The results indicate that bubble size decreases as the water velocity increases; meanwhile, ellipsoidal bubble shape is transformed into rounded shape. The variation in the air flow rate leads to a slight change of bubble size as well the bubble shape. The bubble velocity fluctuates with the movement of the bubble, and the fluctuations are intensified as the water velocity decreases. As the balance between the forces exerted on the bubble is reached, an approximately linear relationship between the bubble velocity and the water flow velocity is proven. For a given bubble equivalent diameter, the bubble terminal velocity with the liquid cross flow is higher than that associated with stagnant water. For small Eötvös number, the consistency of the bubble aspect ratio in the cross flow and the stagnant water is manifested; however, large Eötvös number obtained here is beyond the range associated with the stagnant water, and the existing relationship is extended.

Eulerian–Eulerian Modeling of Convective Heat Transfer Enhancement in Upward Vertical Channel Flows by Gas Injection

Two-phase bubbly flows by gas injection had been shown to enhance convective heat transfer in channel flows as compared with that of single-phase flows. The present work explores the effect of gas phase distribution such as inlet air volume fraction and bubble size on the convective heat transfer in upward vertical channel flows numerically. A two-dimensional (2D) channel flow of 10 cm wide × 100 cm high at 0.2 and 1.0 m/s inlet water and air superficial velocities in churn-turbulent flow regime, respectively, is simulated. Numerical simulations are performed using the commercial computational fluid dynamics (CFD) code ANSYS fluent. The bubble size is characterized by the Eötvös number. The inlet air volume fraction is fixed at 10%, whereas the Eötvös number is maintained at 1.0 to perform parametric studies, respectively, in order to investigate the effect of gas phase distribution on average Nusselt number of the two-phase flows. All simulations are compared with a single-phase flow condition. To enhance heat transfer, it is determined that the optimum Eötvös number for the channel with a 10% inlet air volume fraction has an Eötvös number of 0.2, which is equivalent to a bubble diameter of 1.219 mm. Likewise, it is determined that the optimum volume fraction peaks at 30% inlet air volume fraction using an Eötvös number of 1.0.

Numerical Simulation of Bubble Free Rise after Sudden Contraction Using the Front-Tracking Method

Based on the front-tracking method (FTM), the movement of a single bubble that rose freely in a transverse ridged tube was simulated to analyze the influence of a contractive channel on the movement of bubbles. The influence of a symmetric contractive channel on the shape, speed, and trajectory of the bubbles was analyzed by contrasting the movement with bubbles in a noncontractive channel. As the research indicates, the bubbles became more flat when they move close to the contractive section of the channel, and the bubbles become less flat when passing through the contractive section. This effect becomes more obvious with an increase in the contractive degree of the channel. The symmetric contractive channel can make the bubbles first decelerate and later accelerate, and this effect is deeply affected by Reynolds number (Re) and Eötvös number (Eo).

Lattice Boltzmann Simulation of Multiple Bubbles Motion under Gravity

The motion of multiple bubbles under gravity in two dimensions is numerically studied through the lattice Boltzmann method for the Eotvos number ranging from 1 to 12. Two kinds of initial arrangement are taken into account: vertical and horizontal arrangement. In both cases the effects of Eotvos number on the bubble coalescence and rising velocity are investigated. For the vertical arrangement, it has been found that the coalescence pattern is similar. The first coalescence always takes place between the two uppermost bubbles. And the last coalescence always takes place between the coalesced bubble and the bottommost bubble. For four bubbles in a horizontal arrangement, the outermost bubbles travel into the wake of the middle bubbles in all cases, which allows the bubbles to coalesce. The coalescence pattern is more complex for the case of eight bubbles, which strongly depends on the Eotvos number.

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

In 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 $\mathit{Eo}$.

A Look on Fang Number

In this study, a look on Fang number (Fa) is presented. The Fa was introduced recently in 2013 by Professor Xiande Fang to provide great facilitation in describing flow boiling heat transfer coefficients. It is defined as the product of two terms. The first term is the ratio of buoyancy force to gravitational force, which has effects on bubble departure. The second term is the ratio of surface tension force to inertial force, which affects bubble formation. As a result, Fa is associated with the formation and departure of bubbles. The Fa will be expressed by using a combination of the Eötvös number (Eo), Froude number (Fr), and Weber number (We). Based on this study, it is clear that existing dimensionless numbers in literature, i.e., Eötvös number, Froude number, Weber number, and their combinations can be used to describe flow boiling heat transfer coefficients. This combination of existing non-dimensional groups (Eo, Fr, and We) leads to good correlation with flow boiling data of different working fluids such as CO2, R134a, and R22.

On Bubble Rising in Countercurrent Flow

A single bubble of typical volume 20 mm³ ≤ VB ≤ 400 mm³ was placed in downward conically diverging flow of low and moderate viscous liquids (aqueous solutions of glycerine and of electrolytes (NaCl, Na3PO4, MgSO4), and butanol). Experiments were performed over a range of Reynolds number 60≤Re≤2200, Weber number 1≤We≤14, Tadaki number 1≤Ta≤10, Eötvös number 1≤Eo≤22, and bubble aspect ratio 0.4≤b/a≤0.9. The bubble shape, bubble position and motion were investigated by direct observation of two plane projection of bubble by high speed camera. Typical sampling frequency was 150 fps. Relatively long records, (approximately 9000 frames per one bubble observation) allow us to get relevant statistics of treated data. Bubble aspect ratio has been determined from both projection planes. Dimensionless front area of observed bubble has been introduced as suitable parameter for correlation with Eötvös number. Model of static bubble and classical Wellek correlation were employed as asymptotes. Bubble rising velocity has been determined and tested for each single bubble with respect to liquid properties. Velocity data are plotted within the frame given by several theoretical predictions for pure and contaminated liquids. Dimensional analysis is used considering viscosity and surface tension effect. New simple correlation of bubble rising velocity separating the effects of viscosity and surface tension is presented.