Direct numerical simulation of bubble dynamics in subcooled and near-saturated convective nucleate boiling

With the long-term objective of Critical Heat Flux (CHF) prediction, bubble dynamics in convective nucleate boiling flows has been studied using a Direct Numerical Simulation (DNS). A sharp-interface phase change model which was originally developed for pool boiling flows is extended to convective boiling flows. For physical scales smaller than the smallest flow scales (smaller than the grid size), a micro-scale model was used. After a grid dependency study and a parametric study for the contact angle, four cases of simulation were carried out with different wall superheat and degree of subcooling. The flow structures around the growing bubble were investigated together with the accompanying physics. The relation between the heat flux evolution and the bubble growth was studied, along with investigations of bubble diameter and bubble base diameter evolutions across the four cases. As a validation, the evolutions of bubble diameter and bubble base diameter were compared to experimental observations. The bubble departure period and the bubble shapes show good agreement between the experiment and the simulation, although the Reynolds number of the simulation cases is relatively low.     

Flow patterns and interfacial velocities near a moving contact line

Experimental data on velocity fields and flow patterns near a moving contact line is shown to be at variance with existing hydrodynamic theories. The discrepancy points to a new hydrodynamic paradox and suggests that the hydrodynamic approach may be incomplete and further parameters or forces affecting the surfaces may have to be included. A contact line is the line of intersection of three phases: (1) a solid, (2) a liquid, and (3) a fluid (liquid or gas) phase. A moving contact line develops when the contact line moves along the solid surface. A flat plate moved up and down, inside and out of a liquid pool defines a simple, reliable experimental model to characterize dynamic contact lines. Highlighted are three important conclusions from the experimental results that should be prominent in the development of new theoretical models for this flow. First, the velocity along the streamline configuring the liquid–fluid interface is remarkably constant within a distance of a couple of millimeters from the contact line. Second, the relative velocity of the liquid–fluid interface, defined as the ratio of the velocity along the interface to the velocity of the solid surface, is independent of the solid surface velocity. Third, the relative interface velocity is a function of the dynamic contact angle.     

Modes of bubble growth in the slow-formation regime of nucleate pool boiling

The shape and size of a bubble formed slowly on a sharp- or round-edged orifice are derived with the help of a new analytical solution for the bubble profile. Two modes of formation are distinguished, depending on the natural contact angle, ?₀: bubble confined to the orifice (?₀ small); bubble spreading beyond the orifice (?₀ large: Fritz mode). The limits of the slow-formation regime in mucleate pool boiling are estimated, involving an assessment of the influences of liquid inertia, viscosity and surface-tension gradients.“Slow” formation is predicted for large cavities or high pressures and this is borne out by data for water. The Fritz mode of growth, however, is seen to be suppressed.     

Some features of spray breakup in effervescent atomizers

The near orifice spray breakup at low GLR (gas to liquid ratio by mass) values in an effervescent atomizer is studied experimentally using water as a simulant and air as atomizing gas. From the visualizations, the near orifice spray structures are classified into three modes: discrete bubble explosions, continuous bubble explosions and annular conical spray. The breakup of the spray is quantified in terms of the mean bubble bursting distance from the orifice. The parametric study indicates that the mean bubble bursting distance mainly depends on airflow rate, jet diameter and mixture velocity. It is also observed that the jet diameter has a dominant effect on the bubble bursting distance when compared to mixture velocity at a given airflow rate. The mean bubble bursting distance is shown to be governed by a nondimensional two-phase flow number consisting of all the aforementioned parameters. The location of bubble bursting is found to be highly unsteady spatially, which is influenced by flow dynamics inside the injector. It is proposed that this unsteadiness in jet breakup length is a consequence of varying degree of bubble expansion caused due to the intermittent occurrence of single phase and two-phase flow inside the orifice.     

The effect of the VOF–CSF static contact angle boundary condition on the dynamics of sliding and bouncing ellipsoidal bubbles

The static contact angle is the only empiricism introduced in a Volume of Fluid–Continuum Surface Force (VOF–CSF) model of bubbly flow. Although it has previously been shown to have a relatively limited effect on the accuracy of velocity and shape predictions in the case of large gas bubbles sliding under inclined walls (e.g. Cook and Behnia, 2001), it may have a more determining influence on the numerical prediction of the dynamics of smaller ellipsoidal bubbles which were shown by Tsao and Koch (1997) to bounce repeatedly when sliding under inclined walls at certain wall inclinations. The present paper reports on the influence of surface tension and the static contact angle on the dynamics of an ellipsoidal air bubble of equivalent diameter D_e = 3.4 mm. The bubble Eötvös and Morton numbers are Eo = 1.56 and Mo = 2 × 10⁻¹¹ respectively. The computational results are achieved with a Piecewise Linear Construction (PLIC) of the interface and are reviewed with reference to experimental measurements of bubble velocity and interface shape oscillations recorded using a high speed digital camera. Tests are performed at plate inclination angles θ ∈ {10°, 20°, 30°, 45°} to the horizontal and computational models consider three static contact angles θ_c ∈ {10°, 20°, 30°}. The static contact angle has been found to have a significant effect on the bubble dynamics but to varying degree depending on the plate inclination. It is shown to promote lift off and bouncing when the plate inclination angle reaches 30° in a way that does not necessarily reflect experimental observations.     

NUMERICAL STUDY OF THE BEHAVIOR OF A BUBBLE ATTACHED TO A TIP IN A NONUNIFORM ELECTRIC FIELD

In order to investigate the effects of a nonuniform electric field on the behavior of a bubble, a numerical study on the shape of a bubble attached to a conducting tip on a supporting wall is performed. The equilibrium bubble shape is determined by solving the free boundary problem that consists of the governing equation for electric field and the normal stress condition at the bubble surface. A numerically generated composite orthogonal coordinate system is employed to solve the free boundary problem. A bubble on a tip is found to be extended in the direction parallel to the applied electric field. The elongation increases steeply with an increase of the electric field strength and the height of the tip. It is also observed that a highly elongated bubble has a shape with slender waist. The bubble shape obtained from numerical studies are qualitatively similar to the shapes observed in experiments. If the contact radius is maintained during bubble deformation, the contact angle and the aspect ratio increase with the increase of the electric field strength and the tip height. On the other hand, if the contact angle is fixed during bubble deformation, the contact radius decreases as the electric field strength increases. In order to estimate the effect of electric field on the bubble departure volume, the surface tension force and the downward electric force exerted on a bubble are also computed for a bubble of fixed volume under the fixed contact angle condition. The sum of the two forces is found to decrease with increasing strength of nonuniform electric field. This fact suggests that the bubble departure volume decreases in a nonuniform electric field.     

Validation of a Two-Dimensional Hyperbolic System Modelling a Gas Fluidized Bed

Numerical solutions of a gas fluidized bed model in two space dimensions are presented. This model is hyperbolic and contains particle pressure, but no particle viscosity. The results are compared with experimental data available in the literature for a wide variety of phenomena. Investigated are: the rise velocity of a single, isolated bubble; the frequency of variation of bubble diameter with time; bubble splitting; bubble frequency and the coalescence of a bubble chain formed by gas injected through a single orifice; analysis of the coalescence of bubbles aligned vertically, as well as that of those not in vertical alignment; the formation of slugs in narrow beds; and, eruption at the bed surface. The simulation results show both qualitative and quantitative agreement with the literature. This revised version was published online in July 2006 with corrections to the Cover Date.     

Liquid flow patterns about barbotage bubbles

This paper summarizes the results of a flow visualization study on the liquid motion around barbotage bubbles during growth and departure. Flow patterns, as well as for the first time, instantaneous velocities, are reported as a function of time and location about the bubbles. The experiments, employing the hydrogen-bubble technique and high-speed cine photography, were with: water as the liquid, air as the bubbled gas, orifice diameters of 0.116 and 0.252 cm, and different air flow rates; the two limiting cases of constant supply pressure and constant volumetric flow rate were covered. It was found that the liquid around a barbotage bubble assumes two velocity maxima, the first an outward maximum during bubble growth and the second in the opposite direction approximately at the time of bubble departure; further, liquid velocities were found to be higher close to the bubbling site. Certain differences in liquid velocities between the constant pressure and constant flow cases are explained in terms of available theoretical solutions to the bubble growth rate. Qualitative comparisons of the barbotage liquid flow patterns and those recently reported for boiling flow patterns are also presented.     

2D lattice Boltzmann investigation of saturated pool boiling using a tunable surface tension model: Prandtl number effects on film boiling

In this paper, the saturated pool boiling is investigated using lattice Boltzmann method. The written FORTRAN code is validated in two aspects: For flow, the thermodynamic consistency test and Laplace law are applied and for heat transfer, the space- and time- averaged Nusselt number is compared with Berenson analytical solution in film boiling regime. In addition, the results of bubble generation and departure are compared with some well-known analytical solutions to show the accuracy of the code. It is confirmed that bubble departure diameter and the departure frequency are related to the gravity acceleration with powers of ? 0.505 and 0.709, respectively, which is in a very good agreement with the existing analytical expressions. The present model has the ability to tune different surface tensions independent of liquid/vapor density ratio, which was unreachable using other existing numerical models of boiling. Thus, the sole effects of surface tension on boiling can also be taken into consideration using the present model. It is also shown that the departure diameter is related to the surface tension with a power of 0.485, which is in good agreement with the analytical expressions. Temperature contours are shown together with flow lines to have a better viewpoint for studying the bubble’s behavior. An intensive temperature gradient is observed in the necking area at the departure time. All the four boiling regimes in the boiling curve are simulated under constant temperature boundary condition. The Prandtl number effects on vapor bubble dynamics in the film boiling regime are investigated using the improved Shan and Chen model for the first time. Results revealed that bubbles are more resistant to depart from the vapor blanket with increasing the Prandtl number.     

Hydrodynamics of a bubble formed at vent pipe exit

In this paper, the hydrodynamics of a bubble formed during transient injection of air through a tube submerged in a pool of water has been studied. The experiments were performed by injecting air through vertical tubes varying in diameter from 0.9 to 9.5 cm and located in the middle of a 45 cm dia. and 120 cm high plexiglas chamber. The plexiglas chamber was partly filled with water and was open at the top to the outside. Data for bubble growth and vent line pressure histories are obtained under different upstream pressure conditions. Effect of presence of an orifice in the vent line on bubble growth has also been investigated.A theoretical model describing the bubble growth at the exit of a vent pipe submerged in a pool of water is developed. Predictions of bubble radius, line static pressure and uplift on the bottom of the test chamber have been made and are found to compare well with the data. Insertion of an orifice in the pipe line between the solenoid valve and the vent exit has been found to inhibit the bubble expansion as well as alter the bubble oscillation characteristics.     

Fluidization and bubbling behavior of potash particles in a deep fluidized bed

Most existing models for predicting bubble size and bubble frequency have been developed for freely bubbling fluidized beds. Accurate prediction of bubbling behavior in deep fluidized beds, however, has been a challenge due to the higher degree of bubble coalescence and break up, high probability of the slugging regime, partial fluidization, and chaotic behavior in the bubbling regime. In this work, the bubbling and fluidization behavior of potash particles was investigated in a deep fluidized bed employing a twin-plane electrical capacitance tomography (ECT) system. Solid volume fraction, average bubble velocity, average bubble diameter, and bubble frequency in both bubbling and slugging regimes were measured at two different bed height ratios (H/D = 3.5 and H/D = 3.78). This work is the first to illustrate a sequential view of bubbles at different superficial gas velocities in a fluidized bed. The results show that both the bubble diameter and rising velocity increased with increasing the superficial gas velocity for the two bed heights, with larger values observed in the deeper bed compared to the shallower one. Predicted values for bubble diameter, bubble rise velocity and bubble frequency from different models are compared with the experimental data obtained from the ECT system in this work. Good agreement has been achieved between the values predicted by the previous models and the experimental data for the bubble diameter and bubble rise velocity with an average absolute deviation of 16% and 15% for the bed height of 49 cm and 13% and 8% for the bed height of 53 cm, respectively.     

Experimental study on bubble departure characteristics in subcooled nucleate pool boiling

The boiling models use departure diameter and frequency in closure relations for the calculation of nucleate boiling heat flux. These parameters are normally derived from empirical correlations which depend heavily on experiments. While these parameters are studied mostly for saturated conditions, there is not sufficient data for the values of departure diameter and frequency in subcooled boiling. In this work, the bubble departure characteristics, i.e. the departure diameters and frequency have been measured using high speed visualization experiments with subcooled demineralized water at atmospheric pressure for nucleate pool boiling conditions. The water pool dimensions were 300 mm × 135 mm × 250 mm with four different heating elements to carry out the parametric studies of bubble departure behavior. The considered parameters were heater surface roughness, heater geometry and heater inclination along with the experimental conditions like degree of subcooling (ΔT_sub = 5−20 K), superheat (ΔT_sat = 1−10 K) and the heat flux. The departure diameters and frequencies were directly measured from the images captured. It was intended to generate the subcooled nucleate pool boiling data under a wide range of conditions which are not present in the literature. The departure diameter was found to increase with the wall superheat, heater size and the inclination angle while the liquid subcooling and surface roughness produced a damping effect on the diameter. The departure frequency was found to increase with the wall superheat and the inclination angle, but decreases with an increase in the heater size. The frequency increases with the degree of subcooling except very close to the saturation, and is unaffected by the surface roughness beyond a certain superheat value.     

Numerical simulations of spontaneous capillary rises with very low capillary numbers using a front-tracking method combined with generalized Navier boundary condition

We propose a front-tracking method that considers a moving contact line with a generalized Navier boundary condition (GNBC) and with a delta function distribution approximated on the grid scale. A method of evaluating the interfacial balance at the contact line in the form of a body force, which is straightforward with the front-tracking method, cannot give a natural flow field. In contrast, the proposed method using the GNBC, which includes the unbalanced Young’s force as stress on the wall, can give a very stable and reasonable flow field. The proposed front-tracking method was applied for the capillary rise of a liquid in a tube, in which the velocity-dependent contact angle dominates the dynamic characteristics. The validity of the proposed method was confirmed by comparing simulation results with experimental measurements and simple theoretical models. The results of the present simulations with adjusted non-dimensional slip parameters agreed very well with experimental measurements. Under the present simulation conditions, the linearity of the GNBC allows the correlation between the dynamic contact angle and the contact line’s velocity to follow a simple linear expression that involves the difference of the cosine with the capillary number. The non-dimensional slip parameter, which represents the dynamic nature of the moving contact line, can therefore be easily adjusted to reproduce experimental observations under small-capillary-number conditions.     

Bubble nucleation characteristics in pool boiling of a wetting liquid on smooth and rough surfaces

Quantitative measurements are obtained from high-speed visualizations of pool boiling at atmospheric pressure from smooth and roughened surfaces, using a perfluorinated hydrocarbon (FC-77) as the working fluid. The boiling surfaces are fabricated from aluminum and prepared by mechanical polishing in the case of the smooth surface, and by electrical discharge machining (EDM) in the case of the roughened surface. The roughness values (R_a) are 0.03 and 5.89 μm for the polished and roughened surfaces, respectively. The bubble diameter at departure, bubble departure frequency, active nucleation site density, and bubble terminal velocity are measured from the monochrome movies, which have been recorded at 8000 frames per second with a digital CCD camera and magnifying lens. Results are compared to predictions from existing models of bubble nucleation behavior in the literature. Wall superheat, heat flux, and heat transfer coefficient are also reported.     

Parametric study on impinging-jet liquid sheet thickness distribution using an interferometric method

 The effects of several influencing parameters on the thickness distribution of a liquid sheet formed by two impinging jets are examined using a simple interferometric method which can provide sharp and clear fringe images in spite of very simple optical setup. The parameters changed in this study are the impinging angle, orifice diameter, liquid jet velocity, and liquid viscosity. The experimental results are compared with existing theoretical predictions. A larger impinging angle, smaller orifice diameter, and a higher azimuthal angle are found to result in thinner liquid sheets, although jet velocity itself does not have any effect on the sheet thickness. Higher viscosity, on the other hand, is found to yield a thicker liquid sheet, which has not been considered in the theoretical analysis so far. The theoretical models used for comparison predict the same trend as the experimental results, but the thickness values are overestimated at low azimuthal angles. This discrepancy is gradually lessened as the azimuthal angle is increased. More refined theoretical modeling that decreases this difference and includes the effect of physical properties of liquid is necessary. Received: 26 May 2000/Accepted: 8 November 2000     

Points singuliers d'une ligne de contact mobile

It is proposed to represent the dynamics of a moving contact line by an Onsager like mobility relation between the contact angle and the speed of the moving line, including an Arrhenius factor small enough in many physical situations to be the limiting factor for the motion. The liquid-vapor interface is then in quasiequilibrium, which allows one to analyse a dynamical wetting transition. This approach predicts well the formation of angular points on the rear edge of droplets sliding on a tilted plane.     

Axial development of subcooled boiling flow in an internally heated annulus

For the main purpose of database construction in order to develop the interfacial area transport equation, axial developments of local void fraction, interfacial area concentration, bubble Sauter mean diameter, interfacial velocity, and bubble number density were measured in boiling water bubbly flows in a vertical-upward internally heated annulus using a double-sensor conductivity probe. The annulus channel consisted of an inner rod with a diameter of 19.1 mm and an outer round tube with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. A total of 11 data sets were acquired consisting of four inlet liquid velocities, 0.500, 0.664, 0.987 and 1.22 m/s, two heat fluxes, 100 and 150 kW/m², and two inlet liquid temperatures, 95.0 and 98.0°C. The axial developments of the flow parameters were discussed based on the measured data in detail. In addition to the database construction, the measured data validated recently proposed constitutive equations for the distribution parameter, drift velocity, and bubble Sauter mean diameter, which will improve the accuracy of the drift-flux model in subcooled bubbly flow.     

鼓泡流化床中流动特性的多尺度数值模拟

鼓泡流化床因其较高的传热特性以及较好的相间接触已经被广泛应用于工业生产中,而对鼓泡流态化气固流动特性的充分认知是鼓泡流化床设计的关键.在鼓泡流化床中,气泡相和乳化相的同时存在使得床中呈现非均匀流动结构,而这种非均匀结构给鼓泡流化床的数值模拟造成了很大的误差.基于此,以气泡作为介尺度结构,建立了多尺度曳力消耗能量最小的稳定性条件,构建了适用于鼓泡流化床的多尺度气固相间曳力模型.结合双流体模型,对A类和B类颗粒的鼓泡流化床中气固流动特性进行了模拟研究,分析了气泡速度、气泡直径等参数的变化规律.研究表明,与传统的曳力模型相比,考虑气泡影响的多尺度气固相间曳力模型给出的曳力系数与颗粒浓度的关系是一条分布带,建立了控制体内曳力系数与局部结构参数之间的关系.通过模拟得到的颗粒浓度和速度与实验的比较可以发现,考虑气泡影响的多尺度曳力模型可以更好地再现实验结果.通过A类和B类颗粒的鼓泡床模拟研究发现,A类颗粒的鼓泡床模拟受多尺度曳力模型的影响更为显著.      

Pressure drop of two-phase dry-plug flow in round mini-channels: Effect of moving contact line

In the present experimental study, the pressure drop of the two-phase dry-plug flow (dry wall condition at the gas portions) in round mini-channels was investigated. The air–water mixtures were flowed through the round mini-channels made of polyurethane and Teflon, respectively, with their inner diameters ranging from 1.62 to 2.16 mm. In the dry-plug flow regime, the pressure drop measured became larger either by increasing the liquid superficial velocity or by decreasing the gas superficial velocity due to the increase of the number of the moving contact lines in the test section. In such a case, the role of the moving contact lines turned out to be significant. Therefore, a pressure drop model of dry-plug flow was proposed through modification of the dynamic contact angle analysis taking account of the energy dissipation by the moving contact lines, which represents the experimental data within the mean deviation of 4%.     

Numerical and Experimental Study of Bubble Dynamics in Contact with a Solid Surface

A complex numerical and experimental method is proposed for studying 3D dynamics of a bubble contacting with a surface in the presence of an acoustic field. The numerical approach is based on the boundary element method for potential flows, which is most efficient for solving the problems in a 3D formulation. The use of heterogeneous computer architectures consisting of central graphic processors and becoming more and more popular makes it possible to increase the scale of the problem and sufficiently reduce the calculation time. The mesh destabilization problems are solved using a spherical filter. To describe the contact line dynamics, a semi-empirical law of motion is used. The experimental method is based on high-speed recording and optical microscopy. An air bubble contacts with the inner surface of an experimental cell made from acrylic glass and filled with distilled water. The acoustic field in the cell generated by a disk-shaped acoustic radiator is measured using a hydrophone. The behavior of the bubble contacting with a hydrophillic surface is considered for the cases of a fixed or moving contact line. The shape and volume oscillations of the bubble are investigated. The results of numerical simulations agree qualitatively with the experimental data.