Effect of interfacial forces and turbulence models on predicting flow pattern inside the bubble column

The numerical approaches have been used in many studies to predict the flow pattern inside the bubble column reactors because of the difficulties that are still found in designing and scaling-up the bubble columns. This review makes an effort to show suitable interfacial forces i.e., drag force, lift force, turbulent dispersion models and virtual mass and turbulence models such as standard k–ɛ model, Reynolds Stress Model, Large Eddy Simulation to predict flow pattern inside the bubble column using Eulerian–Eulerian. The effect of various interfacial forces and turbulence models on gas–liquid velocity and gas hold-up in bubble column is critically reviewed.     

基于气泡群相间作用力模型的加压鼓泡塔流体力学模拟

目前,多数文献报道了冷态加压湍动鼓泡塔内流动特征,并且通过实验数据回归相关经验关联式。然而,此类关联式适用范围有限,难以直接外推到工业鼓泡塔反应器条件。因此,在FLUENT平台上建立了基于气泡群相间作用力的、动态二维加压鼓泡塔计算流体力学模型。通过数值模拟考察了操作压力为0.5~2.0 MPa,表观气速为0.20~0.31 m·s^-1,内径0.3 m鼓泡塔内流场特性参数分布,并且与冷态实验数据进行比较。结果表明,采用修正后的气泡群曳力模型、径向力平衡模型以及壁面润滑力模型描述气泡群相间作用力,能够较为准确地反映平均气含率和气含率径向分布随操作压力和表观气速变化的规律。     

Design and selection of sparger for bubble column reactor. Part II: Optimum sparger type and design

Bubble columns are widely used for conducting gas–liquid and gas–liquid–solid mass transfer/chemical reactions. Sparger is the most important accessory because it decides the bubble size/rise velocity distribution. These, in turn, govern the radial and axial hold-up profiles, the liquid phase flow pattern and hence the performance of bubble columns. In particular, the sparger design is critical if the aspect ratio is low and the sparger design dominates the performance of the bubble column. However, systematic procedure for the selection of sparger design and type are not available in the published literature. This is the specific objective of the present work. In Part I, the performance of different spargers, including the newly developed wheel type of sparger is discussed. Thus the important considerations required for the sparger design are highlighted. The bubble column used in the manufacture of hydrogen peroxide has been considered as a case for illustration.     

Bubble column research in Japan

Many experimental studies on the bubble column have been reported by Japanese researchers since around 1960. They include studies of bubble behaviour, bubble size distribution, transition from the homogeneous bubbly flow regime to the heterogeneous liquid circulation regime, liquid velocity distribution, longitudinal liquid mixing, hydrodynamic modelling, the gas holdup, and the volumetric coefficient of gas-liquid mass tranfer k_La. Studies covered various modified bubble columns, such as the airlift reactor with an external or internal loop, the packed bubble column, and others. Performance of three-phase bubble columns, which deal with suspensions or emulsions, and their use as bioreactors or chemical reactors were also studied.     

Flow regimes and mass transfer in counter-current bubble columns

Counter current bubble columns have the feature that specific gas-liquid interfacial area and gas holdup are larger than those for standard and cocurrent bubble columns. In this study, three different flow regimes, churn-turbulent flow, bubble flow and bubble down-flow, have been observed in a counter-current bubble column and correlations of gas holdup and volumetric liquid-phase mass transfer coefficient have been proposed as functions of operating variables such as the superficial velocities of gas and liquid, the gas-liquid slip velocity and the liquid properties.     

INVISCID LIQUID CIRCULATION IN BUBBLE COLUMNS

For circulation in axi-symmetric (cylindrical) bubble columns, the recently developed mathematical model^25,26 has been used along with the criterion of minimum circulation strength to determine the height of each circulation cell in a tall column. This is then used to derive a theoretical expression, first of its kind, for gas hold-up inside a bubble column. The predictions of this equation as well as the equation derived here for axial liquid velocity at column axis have been compared with available data and the comparison is found to be excellent for both the variables. An explicit relation is derived for the average liquid circulation velocity. The model is also used to derive an expression for liquid axial dispersion coefficient which compares almost exactly with Deckwer et al.'s⁴ correlation.

For circulation in two-dimensional bubble columns a new mathematical model is developed. The predictions of bubble envelope shape and bubble envelope area compare well with published data. The predictions of number of circulation cells in the horizontal direction also compare well with published data.     

INVISCID LIQUID CIRCULATION IN BUBBLE COLUMNS

For circulation in axi-symmetric (cylindrical) bubble columns, the recently developed mathematical model^25,26 has been used along with the criterion of minimum circulation strength to determine the height of each circulation cell in a tall column. This is then used to derive a theoretical expression, first of its kind, for gas hold-up inside a bubble column. The predictions of this equation as well as the equation derived here for axial liquid velocity at column axis have been compared with available data and the comparison is found to be excellent for both the variables. An explicit relation is derived for the average liquid circulation velocity. The model is also used to derive an expression for liquid axial dispersion coefficient which compares almost exactly with Deckwer et al.'s⁴ correlation.

For circulation in two-dimensional bubble columns a new mathematical model is developed. The predictions of bubble envelope shape and bubble envelope area compare well with published data. The predictions of number of circulation cells in the horizontal direction also compare well with published data.     

基于径向力平衡的鼓泡塔二维流体力学模型

提出了一种鼓泡塔二维轴对称流体力学模型,模型中将气泡所受的升力以及湍动扩散力作为形成塔内气含率稳定分布的主要机制.采用Fluent 6.3流体力学软件求解模型,能得到稳定的二维流场,气含率与液速分布与实验值吻合良好,模型能准确反映表观气速(0.12～0.62 m·s^-1)以及塔径(ø200 mm、ø500 mm、ø800 mm)对流型的影响.利用该模型对更大直径鼓泡塔的流动参数进行了预测,结果与文献给出的经验关联式相符.     

Characteristics of flow fields in the gas–liquid mini-bubble columns with particle image velocimetry measurements

As a new type of gas–liquid microreactors, the gas–liquid mini-bubble column has potential applications. However, few studies on the flow fields in the mini-bubble column can be found at present. In this work, particle image velocimetry (PIV) was used to visually study the velocity fields, vorticity fields and bubble dynamics in the gas–liquid mini-bubble columns with column inner diameters of 1–3 mm and mini-bubble diameters ranged from 0.7 to 1.3 mm. It is found that with the increase of superficial liquid velocity, bubbles rose from almost straight line to Z-shaped or S-shaped trajectory, and the bubble trajectory changed from one-dimension to three-dimension; when the bubble velocity changed, the bubble size and gas holdup decreased; bubble terminal velocity was controlled by bubble buoyancy and flow resistance, and increased slightly with bubble coalescence. These findings may provide basic reference for the design and scale-up of such a mini-bubble column reactor.     

Hydrodynamics of a Tapered Bubble Column

The hydrodynamic behavior of a single‐stage tapered bubble column using an air‐water two‐phase system has been studied. The experimental results indicate that the holdup increases with increasing superficial gas velocity and bubble slip velocity, while it remains constant with increasing superficial liquid velocity. The gas flow rate has a subtle effect on pressure drop owing to the dynamic pressure recovery stemming from the increase in flow area in the axial direction. The results further suggest that the tapered bubble column shows higher holdup with lower energy dissipation than the conventional bubble columns under similar hydrodynamic conditions. The experimental values of the holdup are in excellent agreement with the well‐known Akita and Yoshida correlation available in the existing literature. Also, the performance of the tapered system has been shown to be much better than that of conventional columns under similar conditions in water/alkaline scrubbing of fly ash and SO₂ either alone or in combination.     

Hydrodynamic characterization of a needle sparger rectangular bubble column: Homogeneous flow, static bubble plume and oscillating bubble plume

In this work a detailed experimental hydrodynamic characterization of a needle sparger rectangular bubble column has been performed. The liquid velocity profiles and bubble plume oscillation frequency have been measured by means of laser Doppler anemometry (LDA), and the bubble velocity map by particle image velocimetry (PIV). In this way, the influence of the superficial gas velocity, liquid height and aeration pattern on the column flow structure was analysed. A highly uniform upward flow structure with down flow near the walls was obtained by means of a full-length aeration pattern. This flow structure was preserved even for high gas fractions values. The partial-length aeration patterns with the aerated zone (defined as the aerated width divided by the column width) larger than 0.7 provide a bubble plume and two pure liquid vortical structures in the column bottom, although they are static in nature. With aerated zones lower than 0.6, an oscillating bubble plume is obtained. A non-dimensional analysis of bubble plume oscillation frequency shows a dependence of bubble plume behaviour with the aerated zone. In this way, two different types of bubble plume oscillations, namely confined bubble plume oscillation and free bubble plume oscillation, are introduced and analysed.     

Stability analysis of bubble columns: Predictions for regime transition

A criterion for the transition from the homogeneous to the heterogeneous regime in a bubble column is developed based on the theory of linear stability. Hydrodynamics of bubble column is described by two-fluid model incorporating the interphase forces like drag force and added mass force. Added mass force affects the hydrodynamics of gas-liquid flows significantly and is formulated by taking into account the bubble deformation. A proper understanding of the nature of gas-liquid interface (clean or contaminated) is desired for the reliable predictions of the added mass coefficient. Data from the literature on the transition in bubble columns is critically analyzed. A good agreement has been obtained between the experimental transition gas hold-up and the predictions of the same obtained by the theory developed in this work.     

Sparged loop reactors

Circulating bubble columns or loop reactors form one of the important classes of modified bubble columns. The present paper analyses the performance of external loop air lift reactors (EL-ALR). The EL-ALR has many advantageous features especially at large scale. These arise from its feature of having controlled liquid circulation which is the key parameter for the design and operation of EL-ALR contactors. Therefore, a reliable and generalised circulation model has been presented. The reliability of the model depends on the accuracy of the predictive methods for the gas hold-up and the two-phase fractional pressure drop. Detailed analysis of these fundamental parameters of gas-liquid flows has been presented. The effects of design (area ratio of riser to downcomer, height to diameter ratio and volume of reactor) and operating (gas flow rates and sparging locations) parameters on the performance of the EL-ALR have been analysed in detail. A rational basis has been developed for the estimation of pressure drop, mixing time and mass transfer coefficient. An optimum combination of design and operating parameters has been suggested and a criterion has been developed for the optimum location of spargers. An attempt has been made to provide critical analysis of the published information and to construct a coherent picture of EL-ALR.     

Stability analysis of a bubble column

The aim of the paper is to study the transition between homogeneous and heterogeneous flows in bubble columns, by taking into account the destabilizing effects of both added mass force and deformation of the bubbles. The transition is expressed in terms of instability of a uniform bubbly flow. Special attention is paid to closure relations involving pressure terms at the gas–liquid interface. The models presented in this paper give instructive information on the transition between homogeneous and heterogeneous flows in bubble columns, highlighting the respective weight of physical phenomena, modeled in terms of closure relations introduced in the two-fluid model.     

鼓泡塔中浮力驱动环流特征及反应器放大

针对鼓泡塔一维流动模型,应用新分析方法首次给出环流特征参数（如速度转折点、最大Reynolds剪应力及其位置以及最大回流速度点）的具有明确物理含义的理论表达式,并比较了该关系式与既有结果的异同,分析了气含率分布与Reynolds剪应力的相互关系,提出一种基于流体动力学相似的鼓泡塔放大准则,即以所导出的最大Reynolds剪应力作为特征量,若几何尺寸不同的两个塔满足流体动力学相似,则该剪应力近似相等或具有相同的量级,对比分析表明,该准则对直径介于0.14～5.5m的鼓泡塔近似成立。     

The plug flow model for mass transfer in three-phase fluidized beds and bubble columns

The plug flow model (PFM), overwhelmingly used to describe mass transfer in bubble columns and three-phase fluidized beds, has never been critically tested. This study analyzes the PFM single parameter, K_La, to quantify mass transfer in the forementioned systems. Particular attention is paid to the mass transfer features of the zone near the distributor (grid zone) largely ignored until now. This study, carried out under the largest gas and liquid flow rates ever published, for similar types of systems, indicates the presence of two well defined mass transfer zones. These features invalidate, for design purposes, the use of the PFM. However, it still can be used as a qualitative mass transfer indicator. This has permitted a comparison between the mass transfer efficiency of bubble columns and three-phase fluidized beds with the conclusion that three-phase fluidized bed of 0.5 cm particles can compete successfully with bubble columns.     

Investigation of flow structures and transport phenomena in bubble columns using particle image velocimetry and miniature pressure sensors

The bubble column reactors are usually operated in a heterogeneous regime where the liquid phase turbulence is generated by the bubble motion and the velocity gradients in the mean motion. The turbulent flow comprises of fluid elements moving in a random fashion with different sizes and energies, called ‘flow structures’. Both the large and small scale flow structures within a reactor play an important role in governing the local momentum, heat and mass transfer. The current work is focused on the estimation of the time averaged flow pattern and flow structures. The experimental data has been collected using miniature pressure sensors, PIV+shadowgraphy and LDA. The data was subjected/analyzed to/with multipoint linear stochastic estimation (MLSE), wavelet transforms, image processing and eddy isolation (EIM) to identify the flow structures. Two bubble columns have been used: a narrow rectangular (2D) column and a cylindrical (3D) column. Wavelet transforms (WT) were applied to isolate individual structures from PIV data to get their shape, size and energy in the 2D column. MLSE has been used to obtain the velocity profiles from pressure fluctuation signals. This data, augmented by PIV and LDA data, is subjected to WT and EIM to get the eddy age and its energy distribution. The data of the eddy shape size and energy was used to predict the mass transfer coefficient in the cylindrical bubble column as a test case. Overall, in this work we present a methodology to utilize the experimental data to get a better insight of the dynamics of flow structures, and propose a path forward for the deeper understanding of transport phenomena in bubble columns.     

Enhancement in gas holdup in bubble columns through use of vibrating internals

Including internals in bubble columns is known to enhance the gas holdup. In this paper, a method to achieve this objective substantially has been proposed via the use of vibrating helical spring internals. Experimental observations on effect of vibrating internals such as vibrating helical springs on gas holdup in bubble columns are presented. Effects of superficial gas velocity, H/D ratio (height of the static liquid to column diameter ratio), volume fraction of helical springs, and thickness of the helical spring wires on hydrodynamics parameters are studied. Increase in gas holdup up to 135% is observed by using vibrating helical spring internals in bubble columns compared to bubble columns without internals. This method offers a simple, cost‐effective, and easy way to enhance gas holdup even at high gas fluxes. It has been reported that this enhancement stems from the fact that the vibrating springs breakup the gas into fine bubbles, which effectively reduces their rise velocity and enhances their average residence time in the liquid column.     

On the drag force of bubbles in bubble swarms at intermediate and high Reynolds numbers

An accurate and fast simulation of large-scale gas/liquid contact apparatusses, such as bubble columns, is essential for the optimization and further development of many (bio)chemical and metallurgical processes. Since it is not feasible to simulate an entire industrial-scale bubble column in full detail from first principles (direct numerical simulations), higher-level models rely on algebraic closure relations to account for the most important physical phenomena prevailing at the smallest length and time scales, while keeping computational demands low. The most important closure for describing rising bubbles in a liquid is the closure for the drag force, since it dominates the terminal rise velocity of the bubbles.Due to the very high gas loadings used in many industrial processes, bubble–bubble (or ‘swarm’) interactions need to be accounted for in the drag closure. An advanced front-tracking model was employed, which can simulate bubble swarms up to 50% gas hold-up without the problem of (numerical) coalescence. The influence of the gas hold-up for mono-disperse bubble swarms with different bubble diameters (i.e. Eötvös numbers) was quantified in a single drag correlation valid for the intermediate to high Reynolds numbers regime . Also the physical properties of the liquid phase were varied, but the simulation results revealed that the drag force coefficient was independent of the Morton number. The newly developed correlation has been implemented in a larger-scale model, and the effect of the new drag closure on the hydrodynamics in a bubble column is investigated in a separate paper (Lau et al., this issue).