Gas Bubbles In Liquid Research Articles

Numerical modelling of bubbly flows with and without heat and mass transfer

In this paper, modelling gas–liquid bubbly flows is achieved by the introduction of a population balance equation combined with the three-dimensional two-fluid model. For gas–liquid bubbly flows without heat and mass transfer, an average bubble number density transport equation has been incorporated in the commercial code CFX5.7 to better describe the temporal and spatial evolution of the geometrical structure of the gas bubbles. The coalescence and breakage effects of the gas bubbles are modelled according to the coalescence by the random collisions driven by turbulence and wake entrainment while for bubble breakage by the impact of turbulent eddies. Local radial distributions of the void fraction, interfacial area concentration, bubble Sauter mean diameter, and gas and liquid velocities, are compared against experimental data in a vertical pipe flow. Satisfactory agreements for the local distributions are achieved between the predictions and measurements. For gas–liquid bubbly flows with heat and mass transfer, boiling flows at subcooled conditions are considered. Based on the formulation of the MUSIG (multiple-size-group) boiling model and a model considering the forces acting on departing bubbles at the heated surface implemented in the computer code CFX4.4, comparison of model predictions against local measurements is made for the void fraction, bubble Sauter mean diameter, interfacial area concentration, and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Good agreement is achieved with the local radial void fraction, bubble Sauter mean diameter, interfacial area concentration and liquid velocity profiles against measurements. However, significant weakness of the model is evidenced in the prediction of the vapour velocity. Work is in progress through the consideration of additional momentum equations or developing an algebraic slip model to account for the effects of bubble separation.

Detailed modeling of hydrodynamics, mass transfer and chemical reactions in a bubble column using a discrete bubble model

A 3D discrete bubble model is adopted to investigate complex behavior involving hydrodynamics, mass transfer and chemical reactions in a gas–liquid bubble column reactor. In this model a continuum description is adopted for the liquid phase and additionally each individual bubble is tracked in a Lagrangian framework, while accounting for bubble–bubble and bubble–wall interactions via an encounter model. The mass transfer rate is calculated for each individual bubble using a surface renewal model accounting for the instantaneous and local properties of the liquid phase in its vicinity. The distributions in space of chemical species residing in the liquid phase are computed from the coupled species balances considering the mass transfer from bubbles and reactions between the species. The model has been applied to simulate chemisorption of CO 2 bubbles in NaOH solutions. Our results show that apart from hydrodynamics behavior, the model is able to predict the bubble size distribution as well as temporal and spatial variations of each chemical species involved.

Measurement of bubble velocity components in a swirling gas–liquid pipe flow using a local four-sensor conductance probe

This paper presents a novel technique for measuring the local axial, radial and azimuthal velocity components of the gas in bubbly gas–liquid flows using a local four-sensor conductance probe. A mathematical model is presented showing how the velocity vector of a gas bubble can be calculated from seven time intervals taken from the output signals from each of the four conductance sensors located within the probe. The paper goes on to describe the construction of a local four-sensor probe and the associated electronic measurement circuitry. Results are presented showing the distributions of the mean local axial, radial and azimuthal gas velocity components in vertical, bubbly gas–liquid flows, both with and without swirl. These results were obtained using the four-sensor probe in a vertical 80 mm diameter pipe into which a swirl generator could be installed. Additional results are presented showing the local gas volume fraction distribution, also obtained from the probe, in bubbly gas–liquid flows with and without swirl. It was found, as expected, that the presence of swirl caused a significant increase in the magnitude of the measured azimuthal velocity of the gas, particularly at the pipe walls. It was also found that, at a comparatively high water flow rate, the presence of swirl caused the gas bubbles to preferentially accumulate at the centre of the pipe.

MEASUREMENT TECHNIQUE FOR ANALYSIS IN TWO-PHASE FLOWS INVOLVING DISTRIBUTED SIZE OF DROPLETS AND BUBBLES USING INTERFEROMETRIC METHOD — PLANAR SIMULTANEOUS MEASUREMENT OF SIZE AND VELOCITY VECTOR FIELD

Not only the size and velocity distrib ution but also the spatial information of those instantaneous properties of individual droplets and bubbles are required to understand the complex behavior of dispersed multi-phase flow. In the present paper, an interferometric laser imaging technique investigating two-phase flow characeristics was demonstrated examining the simultaneous measurement of planar distributions on particle size, velocity vector and number density concentration from a frozen image, and the time series information was obtained by processing sequential imagtes of the interferogram. The measurement results with velocity vectors were precisely discriminated by size, the transient spray showed the significant difference of their flow behavior. Interferometric technique was further applied to investigate the characteristics of the size distribution of microscale gas bubble in liquid and to measure such bubbly flows on the different basis as air injection bubbly flow, electrolytic hydrogen and oxygen bubble injection and alcoholic beverages with gas bubbles.

Manipulation of Fluid Objects with Acoustic Radiation Pressure

Conditions are summarized for manipulating and stabilizing fluid objects based on the acoustic radiation pressure of standing waves. Examples include (but are not limited to) liquid drops, gas bubbles in liquids, and cylindrical liquid bridges. The emphasis is on situations where the characteristic wavelength of the acoustic field is large in comparison to the relevant dimension of the fluid object. Tables are presented for ease of comparing the signs of qualitatively different radiation force parameters for a variety of fluid objects.

Interface pressure calculation based on conservation of momentum for front capturing methods

A new method for the calculation of interface pressure for front capturing methods is developed. This method is based on the calculation of the pressure force at each interfacial cell face using the exact pressure due to the portion of the cell face that is occupied by each fluid. Special formulations for the pressure in the interfacial cells are derived for different orientations of an interface. This method (referred to as pressure calculation based on the interface location (PCIL)) is applied to the time evolution of a two-dimensional initially stagnant liquid drop in a gas, as well as, a gas bubble in liquid (gravity effects are not considered). A two-fluid, PLIC-VOF method is used to simulate the flow numerically. Both the continuum surface force (CSF) and the continuum surface stress (CSS) methods are used. A wide range of Ohnesorge numbers and density and viscosity ratios of two fluids are tested. It is shown that the new method reduces the spurious currents by up to three orders of magnitude for the cases tested.

Propagation through nonlinear time-dependent bubble clouds and the estimation of bubble populations from measured acoustic characteristics

For several decades the propagation characteristics of acoustic pulses (attenuation and sound speed) have been inverted in attempts to measure the size distributions of gas bubbles in liquids. While this has biomedical and industrial applications, most notably it has been attempted in the ocean for defence and environmental purposes, where the bubbles are predominantly generated by breaking waves. Such inversions have required assumptions, and the state–of–the–art technique still assumes that the bubbles undergo linear, steady–state monochromatic pulsations in the free field, without interacting. The measurements always violate, to a greater or lesser extent, these assumptions. The errors incurred by the use of such assumptions have been difficult to quantify, but are expected to be most severe underneath breakers in the surf zone, where the void fraction is greatest. Very few measurements have been made in this important region of the ocean. This paper provides a method by which attenuation can be predicted through clouds of bubbles which need not be homogeneous, nor restricted to linear steady–state monochromatic pulsations. To allow inversion of measured surf zone attenuations to estimate bubble populations with current computational facilities, this model is simplified such that the bubble cloud is assumed to be homogeneous and the bubbles oscillating in steady state (although still nonlinearly). The uses of the new methods for assessing the errors introduced in using state–of–the–art inversions are discussed, as are their implications for oceanographic and industrial nonlinear bubble counters, for biomedical contrast agents, and for sonar target detection in the surf zone.

MULTI-SCALE CHARACTERISTICS OF CHAOS BEHAVIOR IN GAS-LIQUID BUBBLE COLUMNS

The multi-value phenomenon of correlation dimension appearing in chaos analysis of time series of pressure fluctuation obtained from gas-liquid bubble columns was studied. Its relationship with multi-scale flow behavior and possible application in the identification of flow regime and regime transition in bubble columns were investigated. The results indicated that the multi-value phenomenon of correlation dimension results from the multi-scale behavior existing in the heterogeneous churn flow regime in bubble columns. When a bubble column is in the homogeneous flow regime, only one correlation dimension is found at a specified superficial gas velocity, indicating that single-scale behavior is dominant in the system. When a bubble column is in the heterogeneous churn flow regime, multi- (generally three) correlation dimensions can be obtained, showing the appearance of multi-scale behavior. Therefore, the formulation of an effective flow model depends on an appropriate multi-scale analysis for bubble columns. Flow regime and regime transition can be characterized by the structure and structure variation of the plot of the correlation integral versus radius of the hyper-sphere. On the basis of the above analysis, a complementary potential methodology called correlation integral analysis for the identification of flow regime and regime transition in gas-liquid bubble columns is recommended.

Turbulence energy distributions in bubbling gas–liquid and gas–liquid–solid flow systems

The turbulence energy distributions in the gas–liquid bubble column system and the effect of solids on the turbulence are investigated using the laser Doppler velocimetry and the particle image velocimetry. The superficial gas velocity employed ranges from 0.025 to 7.5 cm/s , covering such bubble-flow conditions as single-bubble chain, bubbly flow and churn-turbulent flow. Turbulence induced by rising bubbles through bubble wakes is also examined. Experimental results indicate that the bubble-induced turbulence dominates over the liquid shear-induced turbulence in turbulence generation under the operating conditions of this study. The development of the flow field and the turbulence energy of the liquid-phase in the nozzle region are probed. Furthermore, a self-similarity phenomenon is observed in a two-phase flow system. The analysis of the power spectra in gas, liquid and solid phases indicates that the Kolmogorov −5/3 law is obeyed in the inertial range. The presence of solids reduces the transition frequency from the energy-containing range to the inertial range. The effect of the solids on the liquid-phase turbulence is complex. It depends on solids properties and flow field around particles. A criterion based on the variation of a parameter defined by U g ( r)/ u mf is proposed to account for the effect of the solids on the liquid-phase turbulence. The prediction based on this criterion matches well with the experimental results.

A mathematical model and numerical simulation of pressure wave in horizontal gas-liquid bubbly flow*

Abstract By using an ensemble-averaged two-fluid model, with valid closure conditions of interfacial momentum exchange due to virtual mass force, viscous shear stress and drag force, a model for pressure wave propagation in a horizontal gas-liquid bubbly flow is proposed. According to the small perturbation theory and solvable condition of one-order linear uniform equations, a dispersion equation of pressure wave is induced. The pressure wave speed calculated from the model is compared and in good agreement with existing data. According to the dispersion equation, the propagation and attenuation of pressure wave are investigated systemically. The factors affecting pressure wave, such as void fraction, pressure, wall shear stress, perturbation frequency, virtual mass force and drag force, are analyzed. The result shows that the decrease in system pressure, the increase in void fraction and the existence of wall shear stress, will cause a decrease in pressure wave speed and an increase in the attenuation co...

Balance of Liquid-phase Turbulence Kinetic Energy Equation for Bubble-train Flow

In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k—epsilon and the two-phase k—l model is evaluated.

Discrete simulation of gas‐liquid bubble columns and gas‐liquid‐solid fluidized beds

AbstractA computational scheme for three‐dimensional (3‐D), discrete simulation of bubble dynamics in gas‐liquid bubble columns and gas‐liquid‐solid fluidized beds is presented. This scheme describes the motion of the gas, liquid, and solid phases, respectively, based on the level‐set interface tracking method, the locally averaged time‐dependent Navier‐Stokes equations coupled with the Smagorinsky Sub‐Grid Scale stress model, and the Lagrangian particle motion equations. Various gas, liquid, and solid interactive forces are considered, which include those due to drag, added mass, interfacial tension, bubble‐particle collision and particle‐particle collision. The accuracy and validity of the simulation based on this scheme is examined through computational experiments on some well‐known bubbling phenomena including the rise behavior of a single gas bubble in liquids and the bubble formation process from an orifice embedded in liquids. The computed bubble rise velocity, bubble shapes and their fluctuations, and bubble formation behavior in liquids show a good agreement with existing theories and experimental findings. The simulation is extended to investigate the effects of solids concentration on bubble formation and rise behavior. It is found that the bubbles are less coalesced in a fluidized bed with a higher solids concentration. A circulatory motion of particles with an upward flow in the center region and a downward flow near the wall, and a lateral solids concentration distribution in a gas‐liquid‐solid fluidized bed can also be predicted. The bubble formation and rise behavior in a multi‐nozzle bubble column are simulated, and the limitation of the Smagorinsky Sub‐Grid Scale stress model is discussed. © 2004 American Institute of Chemical Engineers AIChE J, 50: 288–301, 2004

Numerical Aspects of Bubble Column Simulations

A numerical study of gas-liquid bubble flow in a square cross section bubble column was carried out. The Euler-Euler approach was used to describe the equations of motion. The effects on the solution of the numerical modeling of the convective terms and of the inlet condition were investigated. Upwind first order and higher order, oscillation free, Flux Corrected Transport (FCT) schemes were tested for both the phase fraction equations and for the momentum equations. Different inlet conditions, constrained on the mass flux inlet, were modeled and tested in order to show the sensitivity of the solution on the inlet condition. The solver used to simulate the gas-liquid flow is FLOTRACS-MP-3D, which originally used a Partial Elimination Algorithm (PEA) for solving the momentum equations. It has been upgraded with a coupled solver for the momentum equations. The numerical results are compared with the experimental data of Deen (2001).

Balance of Liquid-phase Turbulence Kinetic Energy Equation for Bubble-train Flow

In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k-e and the two-phase k-l model is evaluated.

1178. 急拡大を伴う鉛直円管内空気―水系気泡流に対する1次元2流体モデルの適用性

Experiment and numerical calculation were made on the multi-dimensional behavior of upward gas-liquid bubbly flow in a vertical pipe with an axisymmetric sudden expansion. The variation of the void fraction distribution in the sudden expansion was measured at the different axial and radial positions using a point-electrode resistivity probe for various gas and liquid flow conditions. Based on the measured void fraction distribution in the sudden expansion, the axial profiles for the phase distribution parameters were evaluated in the sudden expansion. Numerical calculations were carried out to predict the cross-sectional averaged void fractions along the flow direction by using the one-dimensional two-fluid model considering the phase distribution parameter to verify the applicability of the computations. From these results, it concretely pointed out that some multi-dimensional modeling or modifications for numerical simulation would be needed and the distribution parameter was one of the most important parameters for one-dimensional two-fluid model to evaluate accurately the void fraction distriblltions affected by the multi-dimensional channel geometry.

Acoustical correction to the bubble dynamics equation for elastic media

Nonlinear oscillations of microbubbles are being investigated extensively for innovative medical and industrial applications. The Rayleigh–Plesset equation successfully describes the dynamics of gas bubbles in liquids and viscoelastic media. To model bubble dynamics in weakly compressible elastic media such as soft tissue, effects of shear stress should be taken into account. These effects were included recently by the authors in a model for bubble oscillations that differs from the Rayleigh–Plesset equation by a single term associated with nonlinear elasticity of the medium surrounding the bubble. Here, we augment this dynamical equation to account for acoustic radiation and thus describe nonlinear bubble oscillations in slightly compressible elastic media. The bubble is assumed to be spherical and the surrounding elastic medium to be isotropic. The analysis is performed in Eulerian coordinates, and attention is devoted to terms associated with radiation loss. Our analysis builds on results obtained by Prosperetti and Lezzi [J. Fluid Mech. 168, 457 (1986)] for a bubble in liquid. The stress tensor for the elastic medium is expressed through invariants of the Green deformation tensor in spherical coordinates. Explicit expressions for components of the stress tensor are obtained using Mooney’s potential function. [Work supported by IR&D at ARL:UT.]

Nonlinear Bubbling Hydrodynamics in a Gas-Liquid Bubble Column with a Single Nozzle

In this work, the chaotic bubbling mechanism in a gas-liquid bubble column with a single nozzle was investigated. The signal for the analysis was the time series of pressure fluctuations measured from a pressure transducer probe placed in the bubble column close to the nozzle. In order to study the bubbling process, statistical analysis, qualitative and quantitative non-linear analyses were carried out for the pressure fluctuations. Power spectra used as standard statistical measures provided preliminary evidence that bubbling in the middle values of gas flow rates may be chaotic in nature. Phase plots provided a qualitative means of analyzing the fine geometry structure of the attractor reconstructed from the bubbling time signal. Positive finite estimates of the Kolmogorov entropy provided a quantitative evidence of behavior consistent with chaos. Besides previous diagnostic tools, the local non-linear short-term prediction was also used as a supplement method. It was found that the bubbling process exhibits a deterministic chaotic behavior in a certain range of the gas flow rate. When increasing the gas flow rate, the sequence of periodic bubbling, primary and advanced chaotic bubbling, and jetting or random bubbling were successively observed. However, no clear period doubling sequence leading to chaotic behavior was observed. The sharp loss of the ability to predict the pressure signal successfully with the non-linear prediction method provides a strongest evidence of the presence of the chaotic bubbling. The variations of the non-linear invariants, such as the Kolmogorov entropy and the correlation dimension together with the plot of the correlation integral with the operation conditions, might be developed as potential and effective quantitative tools for flow regime identification of the bubbling process.

A combined resonance-Doppler technique for studying bubble evolution in liquids

Gas bubbles in liquids have been studied for decades with a variety of optical and acoustic techniques. The evolution of a bubble consists of several stages, including formation and growth at a nozzle, detachment and resonance, and rise towards terminal velocity. Most existing techniques can monitor only a single aspect of the bubble behaviour. This work describes an acoustic technique to monitor all stages of an air bubble's evolution. The technique uses a combination of passive acoustic listening and active ultrasonic Doppler observation to study millimetre-sized air bubbles in liquid. A hollow cylindrical piezoelectric transducer, located around the nozzle used to produce the bubbles, detects the resonance of the bubble following its detachment. An ultrasonic Doppler system, positioned several centimetres above the nozzle, monitors both the growth and the rise of the bubble, including shape oscillations and the terminal velocity through the use of joint time-frequency analysis. Because all aspects of the bubble evolution are affected by the properties of the liquid, by monitoring the bubble evolution with this technique the rising bubble can potentially be used as a tool to characterize the liquid.

Symmetry in bubble dynamics

The paper reviews some aspects of application of symmetry groups for analysis of nonlinear dynamics of gas bubbles in liquid: scaling bubble pulsation, dynamics of tethered bubble, distribution of coagulating bubbles.

Nonlinear bubble dynamics in viscoelastic media

Microbubbles are already widely used for biomedical and clinical purposes, and are further being investigated for innovative medical and industrial applications. In most cases, the Rayleigh–Plesset equation for a gas bubble in liquid is used. In this paper we present a more general equation for gas bubble dynamics in viscoelastic media such as soft tissue. The equation, describing oscillations of a spherical bubble in an isotropic, incompressible medium, contains an integral over an elastic energy density function that depends on two invariants of the strain tensor. For moderate bubble oscillations one may use Landau’s cubic expansion of energy density, which contains five elastic moduli—shear and bulk moduli corresponding to quadratic terms, and three moduli (A, B, and C) corresponding to cubic terms. With energy density expressed through invariants of the strain tensor in spherical coordinates, the total elastic energy for an incompressible medium becomes an explicit function of bubble radius and contains only two of the five moduli, the shear modulus and modulus A. Compared to the Rayleigh–Plesset equation, the resulting equation has additional terms associated with shear force and elastic nonlinearity. Further modifications of this equation account for weak compressibility, viscosity, surface tension, radiation loss, and elastic shells.