Bubble Train Flow Research Articles

Theoretical Realizability of Dream-Pipe-Like Oscillating/Pulsating Heat Pipe

The state of the art of thermally self-excited oscillatory heat pipe technology is briefly mentioned to emphasize that there exists no oscillating/pulsating heat pipe (OHP/PHP) suited to long-distance heat transport. Responding to such conditions, this study actively proposes a newly devised conceptually novel type of OHP/PHP. In that heat pipe, the adiabatic section works as it were the dream pipe invented by Kurzweg. This striking quality of the proposed new-style OHP/PHP produces high possibilities of long-distance heat transport. To support such optimistic views, an originally planned mathematical model is introduced for feasibility studies. Hydraulic considerations have first been done to understand what conditions are required for sustaining bubble-train flows in a capillary tube of interest. Theoretical analysis has then been made to solve the momentum and energy equations governing the flow velocity and temperature fields in the adiabatic section. The obtained analytical solutions are arranged to give algebraic expressions of the effective thermal diffusivity, the performance index combined with the tidal displacement, and the required electric power. Computed results of those three are displayed in the figures to demonstrate the realizability of that novel OHP.

CFD studies coupling hydrodynamics and solid‐liquid mass transfer in slug flow for matter removal from tube walls

Organic matter deposition on internal surfaces constitutes a drawback that impairs the efficiency of several industrial processes. To overcome this problem, sparging a train of bubbles could be useful since its presence strongly increases the wall shear stress. A detailed numerical mass‐transfer study between a finite soluble wall and the liquid around a rising Taylor bubble was performed, simultaneously solving velocity and concentration fields. The bubble passage throws solute backward and is responsible for radial dispersion. There is also an increase in the transfer rate with enhancements between 10 and 20% (depending on liquid average velocity and bubble length) compared to single‐phase flow. Mass‐transfer coefficients along the different hydrodynamic regions around the bubble nose, liquid film, and wake were characterized and their values compared with those from literature. The results suggest a promising potential of bubble train flow to enhance organic matter removal from walls in biological systems. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2420–2439, 2017

Evaluation of Recirculation Time in Bubble Train Flow by Using Direct Numerical Simulation

In this research, hydrodynamics of teh Bubble Train Flows (BTF) in circular capillaries TEMPhas been investigated by Direct Numerical Simulation (DNS).Teh Volume of Fluid Based (VOF) interface tracking method and streamwise direction periodic boundary conditions TEMPhas been applied. Teh results show that their exists an appropriate agreement between DNS and experimental correlation results. Teh recirculation time as an important parameter, which effects teh mass transfer of gas-liquid slug flow through teh capillaries channel, TEMPhas been calculated. Teh effects of different parameters such as capillary length, capillary diameter, unit cell length, and surface tension on recirculation time has been investigated. Afterwards, teh DNS based correlation TEMPhas been proposed for BTF recirculation time in a circular capillary

Simulation of Convective Heat Transfer of Gas–Liquid Bubble Train Flow in Wet Microtube

In this paper, a direct numerical simulation of a two‐phase incompressible gas–liquid flow for simulation of bubble motion and convective heat transfer in a microtube is presented. The microtube radius is 10 μm. The interface between the two phases is tracked by the volume of fluid method with the continuous surface force model. Newtonian flows are solved using a finite volume scheme based on the PISO algorithm. Numerical simulation is done on an axisymmetric domain with a periodic boundary condition for different values of pressure gradient, void fraction, and bubble period. Mean pressure gradient is fixed for each simulation. The superficial Reynolds numbers of gas and liquid phases studied are 0.3 to 7 and 5 to 210, respectively. Numerical results are coincident with the Serizawa regime map, and there is a linear relation between the void fraction and gas flow ratio. Simulation shows local Nusselt number increases in the presence of a gas bubble.

Experimental investigations on thermo-hydrodynamics of continuous Taylor bubble flow through minichannel

Pulsating Heat Pipe (PHP) has received significant attention in the field of electronics cooling due to its simplicity, manufacturing ease and versatility. PHP involves intricate internal gas–liquid two-phase thermo-hydrodynamics. The present paper is an effort to understand this complex hydrodynamics under adiabatic and diabatic conditions. Experimental investigations are reported for air–water two-phase flow through 2.12mm horizontal circular minichannel. The influence of individual gas and liquid inlet flow rates on Taylor bubble velocity, void fraction, liquid holdup and lengths of the liquid slug and Taylor bubble, frictional pressure drop and heat transfer in continuous Taylor bubble train flow (CTB) is analysed. The findings of the present investigation could be helpful to develop mathematical model for PHP for future research.

Effect of gravity levels on the flow pattern modulation by the phase separation concept

Suspending a mesh cylinder in a tube modulates flow patterns with gas bubbles in the annular region to form thin liquid film on the wall. We investigate the effect of gravity levels on the modulated flow patterns. The volume of fluid (VOF) method simulates the slug bubble train flow in bare tube and modulated flow sections. The bubble population density along the flow direction (β) and averaged liquid film thickness (δα) synthesize a parameter β/δa to characterize the enhancement of phase change heat transfer. It is found that at the normal gravity on earth, counter-flow appears with fast upward flow in the annular region and downward liquid flow in the core region. A lower β due to sparsely populated bubbles and thin liquid film form a larger β/δa to enhance the phase change heat transfer. Convective heat transfer in liquid plugs is enhanced by the fast fluid movement in the annular region and liquid circulations at three length scales. At the miniature gravity, quasi-co-current flow happens with upward flows in both annular region and core region, except that a liquid layer inside mesh cylinder flows downward. Bubbles are more densely populated than those at the normal gravity. Liquid circulation occurs only at the bubble length scale. At the micro gravity, the two-phases are thoroughly separated with co-current flows in both annular region and core region. Gas flows slowly and the residence time of gas is increased to result in β=1. Τhe liquid film is ultra-thin. These two factors create a significantly large β/δa to enhance the phase change heat transfer. We demonstrate the effectiveness of the phase separation concept at miniature and micro gravity environment.

The phase separation in a rectangular microchannel by micro-membrane

A phase separator was formed by populating an enclosed micro-membrane at the microchannel center. When a bubble train in the bare duct interacted with the micro-membrane, a single bubble was separated into two daughter bubbles to flow in the two side regions. The separated bubbles never entered the micro-membrane inside due to the increased surfaced energy. A multiscale numerical scheme using the Volume of Fluid (VOF) method tracked the gas–liquid interface. The results identified that the separator consisted of a phase separating section and a fully phase separation section. Within the separating section, the two side regions contained confined bubble train flow. The liquid plugs were gradually shortened along the flow direction, caused by liquid flowing towards the micro-membrane inside. Liquid circulations were observed within liquid plugs. The gas–liquid could be fully separated. Within the fully phase separation section, gas was flowing in the side regions, with ultra-thin liquid films on solid walls. The separator had the potential to be used as a condenser. The heat transfer enhancement is related to Ar (the bubble project area relative to the bottom surface area) and an averaged liquid film thickness. In contrast to the bare duct section, the fully phase separation section significantly increased Ar and decreased liquid film thicknesses. The heat transfer intensity in the fully separated flow section can be ten times of that in the bare duct section.

Taylor bubble-train flows and heat transfer in the context of Pulsating Heat Pipes

Understanding the performance of Pulsating Heat Pipes (PHPs) requires spatio-temporally coupled, flow and heat transfer information during the self-sustained thermally driven flow of oscillating Taylor bubbles. Detailed local hydrodynamic characteristics are needed to predict its thermal performance, which has remained elusive. Net heat transfer in PHP is contributed by (a) pulsating/oscillating flow (b) distribution of different liquid slugs and bubbles, and, (c) phase-change process; however, its contribution is minimal. In fact, the former two flow conditions are largely responsible for heat transfer in PHPs; such flow conditions can be generated without phase-change and can also be studied independently to observe their explicit effects on PHP heat transfer. With this motivation, systematic experimental investigation of heat transfer is performed during (a) isolated Taylor bubble flow (b) continuous Taylor bubble flow and (c) pulsating Taylor bubble flow, at various frequencies (1 Hz to 3 Hz, as applicable for PHPs) inside a heated square mini-channel of cross-section size 3 mm × 3 mm. This study clearly reveals important insights into the PHP operation. Oscillating Taylor bubbles create significant disturbances in their wake which leads to local augmentation of sensible heat transfer. The implications of bubble length, wake characteristics, oscillating frequency and bubble slip velocity on the heat transfer augmentation and, in turn on thermal performance of PHPs can be clearly delineated from this study. The study also brings out the nuances in the estimation of true bubble slip under time varying Taylor bubble flows.

Measurement of local heat transfer coefficient during gas–liquid Taylor bubble train flow by infra-red thermography

In mini/micro confined internal flow systems, Taylor bubble train flow takes place within specific range of respective volume flow ratios, wherein the liquid slugs get separated by elongated Taylor bubbles, resulting in an intermittent flow situation. This unique flow characteristic requires understanding of transport phenomena on global, as well as on local spatio-temporal scales. In this context, an experimental design methodology and its validation are presented in this work, with an aim of measuring the local heat transfer coefficient by employing high-resolution InfraRed Thermography. The effect of conjugate heat transfer on the true estimate of local transport coefficients, and subsequent data reduction technique, is discerned. Local heat transfer coefficient for (i) hydrodynamically fully developed and thermally developing single-phase flow in three-side heated channel and, (ii) non-boiling, air–water Taylor bubble train flow is measured and compared in a mini-channel of square cross-section (5mm×5mm; Dh=5mm, Bo≈3.4) machined on a stainless steel substrate (300mm×25mm×11mm). The design of the setup ensures near uniform heat flux condition at the solid–fluid interface; the conjugate effects arising from the axial back conduction in the substrate are thus minimized. For benchmarking, the data from single-phase flow is also compared with three-dimensional computational simulations. Depending on the employed volume flow ratio, it is concluded that enhancement of nearly 1.2–2.0 times in time-averaged local streamwise Nusselt number can be obtained by Taylor bubble train flow, as compared to fully developed single-phase flow. This enhancement is attributed to the intermittent intrusion of Taylor bubbles in the liquid flow which drastically changes the local fluid temperature profiles. It is important to maintain proper boundary conditions during the experiment while estimating local heat transfer coefficient, especially in mini-micro systems.

Simulation of slug flow systems under laminar regime: Hydrodynamics with individual and a pair of consecutive Taylor bubbles

Slug flow is an extremely important gas–liquid flow pattern that can be frequently found in oil extraction processes causing instabilities and randomness in the hydrodynamic environment of an oil well. The dynamics of individual and a pair of Taylor bubbles rising in vertical columns of stagnant and co-current liquids was numerically studied using the volume of fluid (VOF) methodology implemented in the commercial code ANSYS FLUENT. The first step was to validate the application of the numerical code to slug flow with in-house experimental data about the rising of single Taylor bubbles obtained by photographic studies and PIV/PST measurements. Then, the application of this CFD tool was extended to a system with a pair of Taylor bubbles. The numerical results of the single Taylor bubble velocity, frontal bubble shape, liquid film thickness, wall shear stress in the stabilized film, axial velocity in the liquid film, bubble shape at the rear, wake volume and length are favorably compared with available experimental and theoretical values. Regarding systems with a pair of consecutive Taylor bubbles, which are the structural units of continuous slug flow, the hydrodynamics was simulated under stagnant and co-current liquid flow conditions, with physical properties that can be representative of some gas–oil systems. The behavior of the most important hydrodynamic features, as the bubbles approach process evolves, is addressed to infer the major effects caused by this kind of bubble–bubble interaction. The information gathered about the bubble–bubble interaction can be crucial to improve already developed bubble train flow simulators.

Lattice Boltzmann study of mass transfer for two-dimensional Bretherton/Taylor bubble train flow

This work presents a procedure for the determination of the volumetric mass transfer coefficient in the context of lattice Boltzmann simulations for the Bretherton/Taylor bubble train flow for capillary numbers 0.1<Ca<1.0. We address the case where the hydrodynamic pattern changes from having a vortex in the slug (Ca<0.7) to not having it (Ca>0.7) [1]. In the latter case the bubble shape is asymmetric and cannot be approximated through flat surfaces and circular circumferences as is often done in the literature [2,3]. When the vortex is present in the slug, the scalar concentration is well mixed and it is common to use periodic boundary conditions and the inlet/outlet-averaged concentration as the characteristic concentration. The latter is not valid for flows where the tracer is not well mixed, i.e. Ca>0.7. We therefore examine various boundary conditions (periodic, open, open with more than 1 unit cell) and definitions of the characteristic concentration to estimate mass transfer coefficients for the range of capillary numbers 0.1<Ca<1.0. We show that the time-dependent volume averaged concentration taken as the characteristic concentration produces the most robust results and that all strategies presented in the literature are extreme limits of one unified equation. Finally, we show good agreement of simulation results for different Peclet numbers with analytical predictions of van Baten and Krishna [2].

Local Nusselt number enhancement during gas–liquid Taylor bubble flow in a square mini-channel: An experimental study

Taylor bubble flow takes place when two immiscible fluids (liquid–liquid or gas–liquid) flow inside a tube of capillary dimensions within specific range of volume flow ratios. In the slug flows where gas and liquid are two different phases, liquid slugs are separated by elongated Taylor bubbles. This singular flow pattern is observed in many engineering mini-/micro-scale devices like pulsating heat pipes, gas–liquid–solid monolithic reactors, micro-two-phase heat exchangers, digital micro-fluidics, micro-scale mass transfer process, fuel cells, etc. The unique and complex flow characteristics require understanding on local, as well as global, spatio-temporal scales. In the present work, the axial streamwise profile of the fluid and wall temperature for air–water (i) isolated single Taylor bubble and, (ii) a train of Taylor bubbles, in a horizontal square channel of size 3.3 mm × 3.3 mm × 350 mm, heated from the bottom (heated length = 175 mm), with the other three sides kept insulated, are reported at different gas volume flow ratios. The primary aim is to study the enhancement of heat transfer due to the Taylor bubble train flow, in comparison with thermally developing single-phase flows. Intrusion of a bubble in the liquid flow drastically changes the local temperature profiles. The axial distribution of time-averaged local Nusselt number (Nu¯z) shows that Taylor bubble train regime increases the transport of heat up to 1.2–1.6 times more as compared with laminar single-phase liquid flow. In addition, for a given liquid flow Reynolds number, the heat transfer enhancement is a function of the geometrical parameters of the unit cell, i.e., the length of adjacent gas bubble and water plug.

A model of a bubble train flow accompanied with mass transfer through a long microchannel

A model of a bubble train flow accompanied with mass transfer in a long capillary tube is developed. In contrast to models presented in literature, our modeling approach accounts for expansion of gas bubbles and flow velocity increase along the channel due to the pressure drop caused by friction losses. The model performance is illustrated by a number of computational examples. The distributions of the bubble velocity and the volumetric mass transfer coefficient along the channels of different diameters are presented. The deviation of the dissolved gas concentration from the saturation concentration along the channel is used as a characteristic of closeness of a fluid system to the phase equilibrium. The calculations explicitly demonstrate that the deviations of gas–liquid mixture flows from equilibrium in long capillary channels of small diameters are small. The effect of the channel diameter, the channel length, and the bubble nucleation frequency on the deviation of the system from equilibrium is also studied.

Numerical investigation of the stability of bubble train flow in a square minichannel

The stability of a train of equally sized and variably spaced gas bubbles that move within a continuous wetting liquid phase through a straight square minichannel is investigated numerically by a volume-of-fluid method. The flow is laminar and cocurrent upward and driven by a pressure gradient and buoyancy. The simulations start from fluid at rest with two identical bubbles placed on the axis of the computational domain, the size of the bubbles being comparable to that of the channel. In vertical direction, periodic boundary conditions are used. These result in two liquid slugs of variable length, depending on the initial bubble-to-bubble distance. The time evolution of the length of both liquid slugs during the simulation indicates if the bubble train flow is “stable” (equal terminal length of both liquid slugs) or “unstable” (contact of both bubbles). Several cases are considered, which differ with respect to bubble size, domain size, initial bubble shape, and separation. All cases lead to axisymmetric bubbles with the capillary number in the range of 0.11–0.23. The results show that a recirculation pattern develops in the liquid slug when its length exceeds a critical value that is about 10%–20% of the channel width. If a recirculation pattern exists in both liquid slugs, then the bubble train flow is stable. When there is a recirculation pattern in one liquid slug and a bypass flow in the other, the bubble train flow may be stable or not depending on the local flow field in the liquid slugs close to the channel centerline. These results suggest that a general criterion for the stability of bubble train flow cannot be formulated in terms of the capillary and Reynolds number only, but must take into account the length of the liquid slug.

A qualitative computational study of mass transfer in upward bubble train flow through square and rectangular mini-channels

In this paper we present a new method for numerical simulation of conjugate mass transfer of a dilute species with resistance in both phases and an arbitrary equilibrium distribution coefficient. The method is based on the volume-of-fluid technique and accounts for the concentration jump at the interface by transforming the discontinuous physical concentration field into a continuous numerical one. The method is validated by several test problems and is used to investigate the mass transfer in upward bubble train flow within square and rectangular channels. Computations are performed for a single flow unit cell and a channel hydraulic diameter of 2 mm. The simulations consider the transfer of a dilute species from the dispersed gas into the continuous liquid phase. Optionally, the mass transfer is accompanied by a first-order homogeneous chemical reaction in the liquid phase or a first-order heterogeneous reaction at the channel walls. The results of this numerical study are qualitative in nature. First, because periodic boundary conditions in axial direction are not only used for the velocity field but also for the concentration field and second, because the species diffusivity in the liquid phase is arbitrarily increased so that the liquid phase Schmidt number is 0.8 and the thickness of the concentration and momentum boundary layer is similar. Two different equilibrium distribution coefficients are considered, one where the mass transfer is from high to low concentration, and one where it is vice versa. The numerical study focuses on the influence of the unit cell length, liquid slug length and channel aspect ratio on mass transfer. It is found that for the exposure times investigated the liquid film between the bubble and the wall is saturated and the mass transfer occurs by the major part through the bubble front and rear so that short unit cells are more efficient for mass transfer. Similar observations are made for the homogeneous reaction and for the heterogeneous reaction when the reaction is slow. In case of a fast heterogeneous reaction and when the main resistance to mass transfer is in the gas phase, it appears that for square channels long unit cells are more efficient, while large aspect ratio rectangular channels are more efficient than square channels, suggesting that for these conditions they might be more appropriate for use in monolithic catalysts.

Optical sectioning for microfluidics: secondary flow and mixing in a meandering microchannel

Secondary flow plays a critical function in a microchannel, such as a micromixer, because it can enhance heat and mass transfer. However, there is no experimental method to visualize the secondary flow and the associated mixing pattern in a microchannel because of difficulties in high-resolution, non-invasive, cross-sectional imaging. Here, we simultaneously imaged and quantified the secondary flow and pattern of two-liquid mixing inside a meandering square microchannel with spectral-domain Doppler optical coherence tomography. We observed an increase in the efficiency of two-liquid mixing when air was injected to produce a bubble-train flow and identified the three-dimensional enhancement mechanism behind the complex mixing phenomena. An alternating pair of counter-rotating and toroidal vortices cooperated to enhance two-liquid mixing.

Numerical simulation of gas–liquid two-phase flow and convective heat transfer in a micro tube

Numerical simulation of an air and water two-phase flow in a 20 μm ID tube is carried out. A focus is laid upon the flow and heat transfer characteristics in bubble-train flows. An axisymmetric two-dimensional flow is assumed. The finite difference method is used to solve the governing equations, while the level set method is adopted for capturing the interface of gas and liquid. In each simulation, the mean pressure gradient and the wall heat flux are kept constant. The simulation is repeated under different conditions of pressure gradient and void fraction. The superficial Reynolds numbers of gas and liquid phases studied are 0.34–13 and 16–490, respectively, and the capillary number is 0.0087–0.27. Regardless of the flow conditions, the gas-phase velocity is found approximately 1.2 times higher than the liquid-phase velocity. This is in accordance with the Armand correlation valid for two-phase flows in macro-sized tubes. The two-phase friction coefficient is found to be scaled with the Reynolds number based on the effective viscosity of the Einstein type. The computed wall temperature distribution is qualitatively similar to that observed experimentally in a mini channel. The local Nusselt number beneath the bubble is found notably higher than that of single-phase flow.

A model for the residence time distribution of bubble-train flow in a square mini-channel based on direct numerical simulation results

This paper presents an original method for evaluating the liquid phase residence time distribution in bubble-train flow using data from direct numerical simulations (DNS). The method is a particle method and relies on the uniform introduction of virtual particles in the volume occupied by the liquid phase within a single flow unit cell. The residence time distribution is obtained by statistical evaluation of the time needed by any particle to travel an axial distance equivalent to the length of the flow unit cell. Residence time curves are evaluated from DNS data of bubble-train flow in a square mini-channel for different lengths of the flow unit cell. The curves obtained are well fitted by an exponential relationship, which has been developed on basis of a two-tanks-in-series compartment model, where the first tank is a plug flow reactor and the second is a continuous stirred tank reactor.

Exploring the flow of immiscible fluids in a square vertical mini-channel by direct numerical simulation

The three-dimensional flow structure of a bubble-train flow in a square capillary of 2 mm width is investigated numerically. Using the volume of fluid method for tracking the phase-interface direct numerical simulations in a cubic flow unit cell are performed for a void fraction ε=33% and two different values of the capillary number ( Ca B=0.205 and 0.043). Comparison of computed global flow parameters with available experimental data shows good agreement. Though for both capillary numbers the bubble is fully axisymmetric, quite different flow structures in the bubble and in the liquid slug are observed. This suggests that the flow conditions in miniaturized devices for chemical processing involving two-phase flow in square or rectangular mini- or micro-channels are very sensitive, indicating a certain potential for careful optimization.

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.