Prediction of pressure behind a rising bubble accelerating from rest

Numerical predictions are presented for pressure change left behind by an air bubble accelerating from rest in water. The computations are made with an implicit finite difference procedure for an axisymmetric system. The magnitude of pressure predicted compares well with the results of potential theory given by previous workers¹.     

Fluid drift caused by a rising bubble

The drift (or translation) of liquid by a rising bubble with a closed wake is shown by the motion of tracers suspended in the liquid. At low Reynolds numbers, Re, the tracers move upward continuously, while at higher Re the tracers have a looping motion. The drift is largest on the axis of rise and decays rapidly with radial distance from the axis. There are presently no models which accurately predict the drift, but the asymptotic wake expression of Batchelor provides a lower limit on the volumetric flow rate of drifted fluid.     

Mass transfer from a single rising bubble

The absorption rates of carbon dioxide, ethylene, and butene from single rising bubble of equivalent diameter 0.4–2.0 cm in water have been measured using an apparatus in which the bubble volume change with time of rise can be measured. The apparatus uses techniques previously reported but also is suitable for studies of mass transfer without and with chemical reaction at higher pressures (up to 4 atmospheres). The results have been compared with theoretical equations for rate of gas solution at the frontal surface of the bubble based upon potential flow theory and Higbie theory. The data are assessed together with those of others to show that they can be correlated well by This equation is valid for bubbles of equivalent diameter 0.6 < d < 4.0 cm and within the range 500 < N_Re < 20,000     

The dissolution of a stationary spherical bubble beneath a flat plate

The dissolution of a single stationary bubble held in place by a horizontal plate is commonly observed experimentally. For several decades the standard approach to the analysis of such dissolution data has been to apply a correction factor of ln(2)=0.69 to the Epstein-Plesset equation for an isolated bubble. In this paper, the transport equations for a stationary bubble touching a plate are solved numerically for the common case where the flow field caused by the change in system volume as the bubble dissolves can be neglected. It is found that the total bubble lifetime is not well characterised by the use of the ln(2) factor. However, in most experimental situations, the initial stages of bubble dissolution are not captured. For low gas solubilities the use of a correction factor of 0.69 to the Epstein-Plesset equation is appropriate once the initial transients have dissipated. The correction factor varies from 0.69 to 0.77 across the full range of situations described in this paper. The mathematical model is validated by comparison to experimental data.     

PIV study of bubble rising behavior

Bubble behaviors are studied in a rectangular bubble column using particle image velocimetry (PIV). Bubbles rise in a chain through a stagnant liquid. As liquid viscosity reduces, bubble rising trajectory changes from one-dimensional to three-dimensional. This transition is due to different bubble wake structures. The bubble shapes also show dissimilar characteristics in liquid of different viscosities. The instantaneous liquid flow fields measured by PIV show the diversities as bubbles rise in different paths. Based on the experimental data obtained in this study, a correlation is proposed to calculate the terminal velocity of bubbles in a chain.     

Shrinkage of an oxygen bubble rising in a molten glass

The mechanisms controlling the evolution of a bubble surrounded by molten glass are important to understand in order to improve melting in glass furnaces, particularly during a change in composition. In order to provide insight into this phenomenon, the behavior of an isolated bubble rising in molten glass is examined both experimentally and numerically.An experimental procedure developed specifically to observe, in situ, a rising bubble is described. Two soda-lime-silica compositions are tested, with low and high iron content, respectively.The numerical model used to describe bubble shrinkage is based on the results recently proposed in Pigeonneau (2009). A specific mass transfer coefficient is used for oxygen where the oxidation–reduction reaction of iron oxides is taken into account.A comparison between the experimental and numerical results shows the importance of the oxidation–reduction reaction of iron in the mass transfer of oxygen. The shrinkage rate of a pure O₂ bubble is enhanced with reduced molten glass iron content.     

Expansion of a single gas bubble rising in a column of liquid

Measurements of the expansion behavior of single bubbles of an insoluble gas by monitoring the pressure change in a gas space at the top of a closed column show that the same expansion law applies both to the bubble and the gas space, but the correct expansion law cannot be deduced from pressure measurements alone. Results from a semi-quantitative heat transfer experiment indicate that isothermal expansion should be assumed.     

气泡上升过程中尾流演变的VOF数值模拟

利用VOF（volume of fluid）方法对静止水中气泡的自由上升过程进行了数值模拟,研究了初始直径不同的气泡自由上升时尾流的演变过程。研究发现气泡自由上升过程中其尾流有对称脱落、过渡态和周期性脱落三种运动状态,其中过渡态是介于对称脱落和周期性脱落之间的非稳定性脱落。气泡上升过程中其形状由球形转变为椭球形。尾流的对称脱落发生在气泡处于椭球形状且沿直线上升的过程;随着气泡的继续上升,当气泡的长轴与水平方向产生夹角时,尾流就会由对称脱落转变为过渡态（非稳定性脱落）;最终,尾流会转变为周期性脱落。2.4 ~3.7 mm气泡尾流运动状态发生转变的临界Reynolds数不同,且随气泡初始直径的增大而增加。直径为2.4 ~3.7 mm气泡的尾流周期性脱落的频率为31 ~39 Hz,且频率随气泡直径的增大而减小。     

Numerical investigation on coalescence of bubble pairs rising in a stagnant liquid

In the present study, we preformed a two-dimensional numerical simulation of the motion and coalescence of bubble pairs rising in the stationary liquid pool, using the moving particle semi-implicit (MPS) method. Moving particles were used to describe the liquid phase and the vapor phase was evaluated using real vapor sate equation. The bubble–liquid interface was set to be a free surface boundary which could be captured according to the motion and location of interfacial particles. The behaviors of coalescence between two identical bubbles predicted by the MPS method were in good agreement with the experimental results reported in the literature. Numerical results indicated that the rising velocity of the trailing bubble was larger than that of the leading bubble. Both of the leading bubble and the trailing bubble rose faster than the isolated bubble. After coalescence, the coalesced bubble showed velocity and volume oscillations. The time of the volume oscillations increased with increasing initial bubble diameter. The wake flow and vortex would form behind the coalesced bubble.     

Origin of the negative wake behind a bubble rising in non-Newtonian fluids

The present work aims at understanding the behavior of individual bubbles in non-Newtonian fluids. By means of a Particle Image Velocimetry (PIV) device, the complete flow field around either a single non-spherical bubble rising in polyacrylamide (PAAm) solutions or a solid sphere settling down in the same fluids shows for the first time the similar coexistence of three distinct zones: a central downward flow behind the bubble or the sphere (negative wake), a conical upward flow surrounding the negative wake zone, and an upward flow zone in front of the bubble or the sphere. This excludes then the possible influence of the interface deformation on the negative wake. A theoretical lattice Boltzmann scheme coupled to a sixth-order Maxwell model was developed for computing the complex flow field around a solid sphere. The good agreement with the experimental measurements provides evidence that the physical mechanism responsible for the negative wake in such fluids could be related to the fluid's viscoelastic properties.     

剪切稠化流体内气泡上浮运动特性

剪切稠化流体是一种典型的非牛顿流体,研究气泡在其中的运动特性对优化设备结构、提高反应效率具有重要意义。文中采用流体体积(VOF)法,通过改变Gallilei数(Ga)、E?tv?s数(Eo)与流变指数(n),对牛顿流体(n=1)及剪切稠化流体(n>1)内气泡的形状、尾涡、终端速度和气泡周围液相黏度分布的变化进行了深入的数值研究。结果表明:气泡变形程度和尾涡尺寸随着Ga数或Eo数的增大而增加;剪切稠化效应会阻碍尾涡的形成,减小气泡的尾涡尺寸;气泡周围剪切速率的差异会导致气泡上方及尾部产生高黏度区域,该高黏度区域会随剪切稠化效应的增加而增大;气泡终端速度随Ga数的增大或流变指数n,Eo数的减小而增大。     

Charge distribution around a rising bubble in a two-dimensional fluidized bed by signal reconstruction

A signal reconstruction technique was developed recently to measure the electrostatic charge density distribution surrounding a bubble rising in a two-dimensional gas-solid fluidized bed using four induction probes flush with the outside wall of a two-dimensional fluidized bed and connected to charge amplifiers for recording induced charge signals as bubbles pass by the probes. The model was implemented in Visual FORTRAN using the LSGRR Subroutine to invert the matrix for the signal reconstruction. However, if the matrix was mathematically singular or ill-conditioned, a least-squares routine or the singular value decomposition routine provided had to be used to give approximate results. If the dimension of the matrix exceeds the permissible limit, or the number of pixels is much larger than the number of measurements, the matrix cannot be inverted using the LSGRR subroutine.This paper shows that an iterative linear back projection algorithm (LBP), often used in linear tomography, can be applied to improve the reconstruction resolution of the charge distribution around rising single bubbles in a gas-solid fluidized bed. The experimentally measured induced charges from four induction probes were then applied to reconstruct the real charge distribution around a single rising gas bubble injected in a two-dimensional column as it passed the probes. The results reconstructed using the LBP method are found to be smoother and more accurate than those obtained from the LSGRR subroutine.     

The pressure field around a two-dimensional gas bubble in a fluidized bed

Measurements of the entire pressure field around a two-dimensional bubble rising in an incipiently fluidized bed are reported. Above the center of pressure line, the field is Laplacian and reasonably well described by Davidson's theory. The pressure wake is closed. It extends for 12 bubble radii below the stagnation point and four radii on either side of the vertical axis of symmetry.     

Interaction between partitioning porous plate and rising bubbles in a trayed bubble column

In a trayed bubble column, the structure of the partitioning plate plays an important role on the bubble behavior. This study examined the effect of the opening ratio and pore size of the plate on the bubble break-up frequency and bubble size distribution. The sieve tray was used as the partitioning plate. The opening ratio was closely related to gas cap development. The stagnation of bubble flow and a gas cap were observed with an opening ratio less than 48.5%. The gas cap increased with decreasing opening ratio and increasing superficial gas velocity. The main effect of the sieve tray could be categorized into the additional drag force and bubble break-up depending on the sieve pore size. When the sieve pore size was smaller than the Sauter diameter of the bubble swarm, the movement of rising bubbles was interrupted by the drag force applied by the surrounding mesh lines. On the other hand, when the sieve pore size was larger than the Sauter diameter, the bubbles were affected by the additional bubble break-up. After the bubbles penetrated the sieve tray, the bubble size distribution shifted to a smaller one and the Sauter diameter decreased.     

Mass transfer of a rising bubble in molten glass with instantaneous oxidation-reduction reaction

The mass transfer around a rising bubble has been studied within the field of glass melting processes. Due to the large value of liquid viscosity, creeping flow was used. The rising bubble is assumed to have a clean interface with a total mobility and the exact solution of Hadamard or Rybczynski was used to define the velocity field around the bubble. The mass transfer of oxygen in the soda-lime-silica glass melt where oxidation-reduction reactions of iron oxides occur is also described.The dimensionless mass transfer coefficient, Sherwood number, was determined as a function of the Péclet number based on the terminal rise velocity of the bubble. Two different techniques have been used: the first based on the boundary layer theory and the second using a finite element method.In order to take into account the oxidation-reduction reaction in a unified framework, a modified Péclet number has been defined as a function of two dimensionless numbers. The first is strongly linked to the equilibrium constant of the chemical reaction and the second is the glass saturation, defined as the ratio of oxygen concentration in the bulk to that at the bubble surface. The Sherwood number, taking into account the chemical reactions, increases with iron content as well as with glass reduction (i.e. small saturation level).From an application point of view, the determination of a modified Péclet number is important because it is possible to use a similar expression (determined without the reaction) by replacing the classical Péclet number by the modified one proposed herewithin.     

Shape oscillations and path transition of bubbles rising in a model bubble column

We investigate experimentally the occurrence of shape oscillations accompanied by path transition of periodically produced air bubbles rising in water. Within the period of bubble formation, the induced velocity is measured to examine bubble-liquid and bubble-bubble interactions. The flow is produced in a small-scale bubble column with square-shaped cross section. A capillary aerator produces bubbles of size 3.4 mm at a frequency of 5 Hz. Measuring techniques employed are high-speed imaging to capture bubble shape oscillations and path geometry, and laser-Doppler anemometry (LDA) to measure the velocity in the liquid near the rising bubbles. The experimentally obtained bubble shape data are expanded in Legendre polynomials. The results show the occurrence of oscillations by the periodicity of the expansion coefficients in space. Significant shape oscillations accompanied by path transition are observed as the second-mode oscillation frequency converges to the frequency of the initial shape oscillations. The mean velocity field in the water obtained by LDA agrees well with potential theory. An analysis of the decay of the induced flow shows that there is no interaction between the flow fields of two succeeding 3.4 mm bubbles in the rectilinear path when the bubble production frequency is lower than 7.4 Hz.     

单气泡沿倾斜绝热表面运动特性的LBM方法研究

气泡沿斜面运动现象在工业生产中广泛存在,采用格子Boltzmann方法(LBM)研究单个气泡沿倾斜绝热表面的运动过程,考察气泡的初始直径、斜面倾角、Eotvos数(Eo)对气泡的变形和气泡形心与斜面垂直距离的影响,探讨相同初始直径的气泡沿斜面运动的稳定终态速度与倾角和Eo之间的关系。通过模拟得出气泡沿斜面的运动规律:斜面倾角越大,气泡前后端不对称性越大;气泡在上升过程中,形心轨迹与斜面保持平行;当倾角大于45°时,形心与斜面的垂直距离和Eo变化一致,当小于45°时,变化相反;相同初始直径气泡的稳定终态速度随倾角和Eo的增加而增加。     

The influence of flow rate on the decrease in pressure beneath a conical pile

The decrease in the stress at the bottom of a sandpile exhibits the preparation dependence known to occur for granular materials. By using a grid-based tactile pressure sensor, we carefully measured the progressive development of the pressure profile at the bottom of conical piles formed by funneling rice grains onto the sensor. A significant decrease in the stress was observed at small flow rates, but it gradually disappeared at greater flow rates. This result is helpful in understanding the stress distribution within sandpiles.