The minimum in-line coalescence height of bubbles in non-Newtonian fluid

The minimum in-line coalescence height of bubbles generated from a submerged nozzle was investigated experimentally in shear thinning non-Newtonian fluid at lower Reynolds number (2∼60). Carboxymethyl cellulose sodium (CMC) aqueous solution and carbon dioxide were used as the liquid phase and the gas phase, respectively. The process of the formation, movement and in-line coalescence of bubbles was visualized and recorded by a high-speed digital camera. The influences of bubble size, bubble generation frequency and liquid property on the minimum in-line coalescence height of bubbles were investigated by changing nozzle diameter, gas flow rate and the mass concentration of CMC aqueous solutions. For a given liquid, the generating frequency and size of bubbles increased but the minimum coalescence height of in-line bubbles decreased when the nozzle diameter and gas flow rate were increased. When the nozzle diameter and gas flow rate were fixed, the shear-thinning effect of CMC aqueous solution became stronger with increasing CMC mass concentration, which led to the increase in both the terminal rise velocity and average acceleration of the trailing bubble, consequently, the minimum in-line coalescence height of bubbles decreased. An empirical correlation for estimating the minimum in-line bubble coalescence height was proposed, the calculating values accords well with experimental data with a mean relative deviation only 7.6%.     

Analysis of the characteristic lengths in the bubble and slug flow regimes generated in a capillary T-junction

We present an analysis of the geometry of the continuous and disperse phases in the bubble and slug flow regimes in air–water mixtures generated in a capillary T-junction of 1  mm internal diameter. Bubble size dispersion is very low in the considered flow patterns. The concept of unit cell is used to identify two characteristic lengths of the two-phase flow, namely, the unit cell length and the bubble length. The relationship between these lengths and the gas and liquid superficial velocities, gas mean velocity, bubble generation frequency and volume average void fraction is analysed. We conclude that in the considered configuration the unit cell and bubble lengths can be predicted either by the ratio of the gas–liquid superficial velocities or the volume average void fraction.     

Bubble formation process from a novel nozzle design in liquid cross-flow

An experimental study is reported that investigated the bubble formation from a novel nozzle design in a liquid cross-flow using high speed imaging. Different configurations and orientations of the novel nozzle design were considered over a range of gas-to-liquid flow rate ratios (GLR) from 0.00031 to 0.00204. The results show that for all cases, the novel nozzle generated smaller bubbles at higher detachment frequency compared to the standard nozzle. At low liquid velocities, the novel nozzle generated bubbles that were 30% smaller in size at a detachment frequency 2–3 times higher than that for the standard nozzle. It was also found that the bubble diameter and the detachment frequency are almost independent of the liquid velocity. The underlying physical process of bubble formation and detachment in the novel nozzle under liquid cross-flow was also investigated. It was observed that the process comprised of three phases: expansion, collapse and pinch off. It was also found that the rebound force of the bubble from a side-hole under the influence of liquid drag force and hydrostatic pressure plays a key role in the early bubble detachment. The results demonstrated that the novel nozzle design performs better than the standard nozzle in the liquid cross-flow, especially at high GLRs.     

多孔介质中稳定泡沫的流动计算及实验研究

将多孔介质简化为一簇变截面毛管束,根据多孔介质的颗粒直径、颗粒排列方式、孔喉尺度比及束缚水饱和度,计算出变截面毛细管的喉道半径和孔隙半径. 在考虑多孔介质喉道和孔隙中单个气泡的受力和变形基础上,利用动量守恒定理,推导出单个孔隙单元内液相的压力分布和孔隙单元两端的压差计算公式,最终得到多孔介质的压力分布计算公式. 利用长U型填砂管对稳定泡沫的流动特性进行了实验研究. 研究结果表明:稳定泡沫流动时多孔介质中的压力分布呈线性下降,影响泡沫在多孔介质中流动特性的因素包括:多孔介质的孔喉结构、泡沫流体的流量和干度、气液界面张力、气泡尺寸,其中孔喉结构和泡沫干度是影响泡沫封堵能力的主要因素.关键词: 稳定泡沫;多孔介质;变截面毛管;流动;表观粘度;压力分布;实验研究      

Origin of regime transition to turbulent flow in bubble column: Orifice- and column-induced transitions

The possible events during bubble formation on an orifice were investigated using a rectangular bubble column (30 cm × 30 cm × 100 cm). The gas flow rate through a single orifice was adjusted from 0.1 dm³/min to 5.0 dm³/min covering a high flow rate regime. At the high gas flow rate, the bubble formation process was complicated by diverse events, such as wake effect, channeling, and orifice-induced turbulent flow. The detachment period could be used to discern the bubble formation steps because it was strongly affected by the above events. The bubble size distribution around the orifice was also analyzed to gain a clearer understanding of the bubble formation process. Above the rate of 3.0 dm³/min through a single orifice, the detachment period converged to a value of 25 ms irrespective of the orifice diameter. The bubble size distribution also showed little difference in this range of gas flow rate. This could be explained by the development of turbulent flow around the orifice. A 0.15 m in-diameter bubble column was tested to investigate the effect of orifice-induced turbulent flow on the regime transition in which the homogeneous flow regime is converted into the heterogeneous flow regime in the column. Obvious distinction between the orifice- and column-induced transitions was observed.     

The problem of a gas bubble in plane ideal fluid flow

We study the problem of two-dimensional fluid flow past a gas bubble adjacent to an infinite rectilinear solid wall.Two-dimensional ideal fluid flow past a gas bubble on whose boundary surface-tension forces act (or a gas bubble bounded by an elastic film) has been studied by several authors. Zhukovskii, who first studied jet flows with consideration of the capillary forces, constructed an exact solution of the problem of symmetric flow past a gas bubble in a rectilinear channel [1]. However, Zhukovskii's solution is not the general solution of the problem; in particular, we cannot obtain the flow past an isolated bubble from his solution. Slezkin [2] reduced the problem of symmetric flow of an infinite fluid stream past a bubble to the study of a nonlinear integral equation. The numerical solution of this problem has recently been found by Petrova [3]. McLeod [4] obtained an exact solution under the assumption that the gas pressure p₁ in the bubble equals the flow stagnation pressure p₀. Beyer [5] proved the existence of a solution to the problem of flow of a stream having a given velocity circulation provided p₁p₀.We examine the problem of two-dimensional ideal fluid flow past a gas bubble adjacent to an infinite rectilinear solid wall. The solution depends on the value of the contact angle . The existence of a solution is proved in some range of variation of the parameters, and a technique for finding this solution is given. The situation in which =1/2 is studied in detail.     

Semi-empirical prediction of bubble diameter in gas fluidized beds

Theoretical expressions for bubble diameter in both small and large particle fluidized beds are derived by the application of two phase theory and gas flow continuity. Comparison with experimental data suggests that the numerical and analytical solution of these expressions, combined with empirical bubble frequency relations, can provide an accurate prediction of bubble size and its parametric trends.Several commonly employed empirical correlations of bubble diameter are shown to be derivable from a common theory, with differences among the correlations ascribed to variations in flow regime and bubble frequency.     

Nucleate pool boiling in microgravity: Recent progress and future prospects

Pool boiling on flat plates in microgravity has been studied for more than 50 years. The results of recent experiments performed in sounding rocket are presented and compared to previous results. At low heat flux, the vertical oscillatory motion of the primary bubble is responsible for the increase in the heat transfer coefficient in microgravity compared to ground experiments. The effect of a non-condensable gas on the stabilisation of the large primary bubble on the heater is pointed out. Experiments on isolated bubbles are also performed on ground and in parabolic flight. The effect of a shear flow on the bubble detachment is highlighted. A force balance model allows determining an expression of the capillary force and of the drag force acting on the bubble.     

Modeling of bubble behaviors and size distribution in a slab continuous casting mold

Population balance equations combined with Eulerian–Eulerian two-phase model are employed to predict the polydispersed bubbly flow inside the slab continuous-casting mold. The class method, realized by the MUltiple-SIze- Group (MUSIG) model, alongside with suitable bubble breakage and coalescence kernels is adopted. A two-way momentum transfer mechanism model combines the bubble induced turbulence model and various interfacial forces including drag, lift, virtual mass, wall lubrication, and turbulent dispersion are incorporated in the model. A 1/4th scaled water model of the slab continuous-casting mold was built to measure and investigate the bubble behavior and size distribution. A high speed video system was used to visualize the bubble behavior, and a digital image processing technique was used to measure the mean bubble diameter along the width of the mold. Predictions by previous mono-size model and MUSIG model are compared and validated against experimental data obtained from the water model. Effects of the water flow rate and gas flow rate on the mean bubble size were also investigated. Close agreements by MUSIG model were achieved for the gas volume fraction, liquid flow pattern, bubble breakage and coalescence, and local bubble Sauter mean diameter against observations and measurements of water model experiments.     

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.     

Blasenbildung und Phasengrenzfläche beim Dispergieren von Gasen in Flüssigkeiten an einzelnen Gaszulauföffnungen

Bubble formation during the injection of helium, nitrogen and sulfur hexafluoride through single orifices into water, ethanol and the refrigerant R11 (CFCl₃) was investigated at pressures up to 21 bar. The gas flow rate was varied from low values within the regime of single bubbles up to the onset of coales-cence. Systematic measurements indicate that there exists a relationship between the bubble volume and the pressure fluctuations within the liquid near the bubble, which seems to be independent of system pressure and gas flow rate. A comparison of the experimental results for the bubble volume generated at capillary orifices with a semiempirical correlation from literature shows good agreement for atmospheric pressure as well as for higher pressures, whereas the results for sharp-edged orifices cannot be described by this calculation method. These data together with the results for the capillary at high gas flow rates could be correlated, however, by an empirical equation which only contains the specific interfacial area and gas density.     

Generator geometry effect on wave dispersion of a gas in a liquid

The influence of the channel diameter and length of the hydrodynamic oscillation generator on gas bubble dimensions in the case of wave dispersion of a gas in a liquid is experimentally investigated. The technique of measuring the bubble diameters based upon the computer analysis of the gas-liquid jet photos is presented. It is shown that on the gas flow rate range from 0.5 to 32 dm³/min the mean diameter of the gas bubbles produced by wave dispersers in water is estimated by an interval from 0.45 to 0.75 mm in optimum performance regimes.     

Transition of plug to slug flow and associated fluid dynamics

Transition of plug to slug flow is associated with bubble detachment from elongated bubble tail or bubble entrainment inside the liquid slug. The mechanism responsible for this transition was earlier identified by Ruder and Hanratty (1990) and Fagundes Netto et al. (1999) based on the shape of the hydraulic jump observed at elongated bubble tail region. The transition mechanism reported by Ruder and Hanratty (1990) and Fagundes Netto et al. (1999) was only based on their flow visualization study. Plug to slug transition and associated dynamics of bubble detachment from the elongated bubble is analysed in the present paper using flow visualization and local velocity measurements. Experiments are reported for 13 different inlet flow conditions of air and water phases. Images of plug/slug flow structures are captured at a rate of 4000 FPS using FASTCAM Photron camera and the local values of axial liquid velocity are measured using LDV system synchronised with a 3D automated traverse system. LDV measurement of local liquid velocity in the liquid slug and liquid film establishes the reason for detachment of bubbles from the slug bubble tail.     

The motion of long bubbles through viscoelastic fluids in capillary tubes

The penetration of long gas bubble through a viscoelastic fluid in a capillary tube has been studied in order to investigate the influence of viscoelastic material properties on the hydrodynamic coating thickness and local flow kinematics. Experiments are conducted for three tailored ideal elastic (Boger) fluids, designed to exhibit similar steady shear properties but substantially different elastic material functions. This allows for the isolation of elastic and extensional material effects on the bubble penetration process. The shear and extensional rheology of the fluid is characterized using rotational and filament stretching rheometers (FSR). The fluids are designed such that the steady-state extensional viscosity measured by the FSR at a Deborah number (De) greater than 1 differs over three orders of magnitude (Trouton ratio = 10³–10⁶). The experiment set up to measure the hydrodynamic coating thickness is designed to provide accurate data over a wide range of capillary numbers (0.01 < Ca < 100). The results indicate that the coating thickness in this process increases with an increase in the extensionally thickening nature of the fluid. Experiments are also conducted using several different capillary tube diameters (0.1 < D < 1 cm), in order to compare responses at similar Ca but different flow De. Suitable scaling methods and nonlinear viscoelastic constitutive equations are explored to characterize the displacement process for polymeric fluids. Bubble tip shapes at different De are recorded using a CCD camera, and measured using an edge detection algorithm. The influence of the mixed flow field on the bubble tip shape is examined. Particle tracking velocimetry experiments are conducted to compare the influence of viscoelastic properties on the velocity field in the vicinity of the bubble tip. Local shear and extension rates are calculated in the vicinity of the bubble tip from the velocity data. The results provide quantitative information on the influence of elastic and extensional properties on the bubble penetration process in gas-assisted injection molding. The bubble shape and velocity field information provides a basis for evaluating the performance of constitutive equations in mixed flow. Received: 19 January 1999 Accepted: 30 June 1999     

Three-dimensional CFD simulation of bubble–melt two-phase flow with air injecting and melt stirring

This paper reports on progress in developing CFD simulations of gas bubble–metallic melt turbulent flows induced by a pitched-blade impeller with an inclined shaft. Foaming process of aluminum foams, in which air is injected into molten aluminum composites and the melt is mechanical stirred by the impeller, has been investigated. A two-fluid model, incorporated with the Multiple Reference Frames (MRF) method is used to predict the three-dimensional gas–liquid flow in the foaming tank, in which a stirring shaft is positioned inclined into the melt. Locally average bubble size is also predicted by additively solving a transport equation for the bubble number density function, which accounts for effects of bubble breakup and coalescence phenomena. The computed bubble sizes are compared with experimental data from our water model measurement and reasonable agreements are obtained. Further, simulated results show that the volume averaged total and local gas fractions are generally increased with rising impeller speed and gas flow rate. The local averaged bubble size increases with increasing gas flow rate and orifice diameter and decreasing liquid viscosity, and decreases also with rising rotation speed of the impeller.     

Bubble chains in large diameter gas fluidized beds

Using statistically based measuring methods for the determination of local bubble size distributions and local average bubble shapes in gas fluidized beds, bubble characteristics have been measured in a fluidized bed column of 1 m diameter where quartz sand (minimum fluidizing velocity 0.0135 m/sec) was fluidized with air at velocities ranging from 0.05 to 0.30 m/sec. The results present experimental evidence that bubbles within large diameter fluidized beds do not rise completely randomly distributed in space but rather in the form of bubble chains which is in agreement with industrial operating experience in large scale fluid bed systems. Since the formation of bubble chains considerably reduces the residence time of the bubble gas this finding is of significance for the performance of fluidized bed reactors. The influence of the operating parameters on the extent of the bubble chain formation has been investigated and possible consequences of these results are discussed.     

Vapour bubble growth and detachment at the wall of shear flow

N-pentane micro-bubbles are created on a small heated film flushed-mounted at the lower wall of a horizontal channel. The bubble growth and detachment in the shear flow are filmed with a high-speed video camera. The time evolutions of the bubble radius and bubble centre position are measured from image processing. The growth rate is determined and compared to models of the literature. The experimental results are also used to estimate the different forces acting on the bubble during its growth and after its detachment.     

Fluctuation characteristics of two-phase flow splitting at a vertical impacting T-junction

In order to investigate the fluctuation characteristics of two-phase flow splitting at a T-junction, particular attention was paid on Churn flow which had the strongest fluctuation comparing with bubble flow and annular flow. The main tube of the T-junction was vertical and the two branches were horizontal. All three pipes connecting to the junction were of 15 mm inner diameter. A statistical analysis based on Root Mean Square (RMS) was applied to temporal differential pressure signals and gas flow rate signals. The Power Spectral Density (PSD) was also employed to reveal their peculiar features in frequency domain as well. The effects of the extraction flow ratio and the gas and liquid superficial velocity upstream on fluctuation characteristics of gas-liquid two-phase flow splitting at the T-junction were investigated in detail. It is found that there is a wide fluctuation in both differential pressure and gas flow rate downstream at every extraction ratio (W₃/W₁) and the fluctuation intensity increases as W₃/W₁ increasing. It is also made clear that increasing either water superficial velocity or gas superficial velocity in inlet causes fluctuation to become more intensive.     

Stability of a numerical algorithm for gas bubble modelling

A free-surface-tracking algorithm based on the SOLA-VOF method is analysed for numerical stability when modelling gas bubble evolution in a fluid. It is shown that an instability can arise from the fact that the bubble pressure varies with its volume. A time step stability criterion is introduced which is a function of the natural oscillation period but does not depend on the mesh size. This dependence suggests that the instability is likely to arise in the case of a general motion of a bubble, especially if break-up occurs. The effect is shown using linear Fourier analysis of the discretized equation for radial bubble oscillation and demonstrated numerically using a CFD code FLOW-3D. One- and three-dimensional situations are considered: a bubble in a fluid bounded by two concentric surfaces and a bubble floating in a fluid chamber with and without gravity. In cases where no analytical solution is available, a numerical method for the stability time step limit calculation is suggested based on finding the natural oscillation frequency. The nature of the instability suggests that it can be a feature of any numerical algorithm which models transient fluid flow with a free surface.