Application of ultrasonic multi-wave method for two-phase bubbly and slug flows

This paper proposes a measurement technique for two-phase bubbly and slug flows using ultrasound. In order to obtain both liquid and gas velocity distributions simultaneously, a new technique for separating liquid and gas velocity data is developed. The technique employs a unique ultrasonic transducer referred to as multi-wave transducer (TDX). The multi-wave TDX consists of two kinds of ultrasonic piezoelectric elements which have different resonant frequencies. The central element of 3 mm diameter has a basic frequency of 8 MHz and the outer element has a basic frequency of 2 MHz. The multi-wave TDX can emit the two ultrasonic frequencies independently. In our previous investigations, both elements were connected with two ultrasonic velocity profile (UVP) monitors to measure liquid and bubble velocity distributions. However, the technique was limited to the measurement of bubbly flows at low void-fraction. Furthermore, it was impossible to synchronize the instantaneous velocities of liquid and bubbles because of the facility limitation. In order to overcome these disadvantages, cross-correlation method is employed for the measurements in this study. In order to apply the technique to flow measurements, ultrasound pressure fields are measured. As a result, it is found that the TDX must be set 20 mm away from the test section. The technique is applied to measuring bubbly and slug flows. By the combination of 2 and 8 MHz ultrasonic echo signals, the echo signals are distinguished between reflected from particles and bubbles. Compared with the results of obtaining with the multi-wave method and a high-speed camera, it is confirmed that the technique can separate the information of liquid and gas phases at a sampling rate of 1000 Hz.     

Capacitance wire mesh imaging of bubbly flows for offshore treatment applications

The impact of ship motion on bubbly flow was emulated using a swell simulator to expose flow structure changes emerging in bubble columns relevant to offshore floating applications. Roll, roll+pitch, yaw, heave and sway were implemented at various frequencies and changes in bubbly flow resulting from the imposed motions were monitored for the first time by means of a dual capacitance wire mesh sensor to measure local gas holdup and velocity. Visualizations of the two-phase flow revealed that roll, roll+pitch, and high-frequency sway were the most impactful in terms of bubble zigzag and swirl, and bubble-clustering and segregation due to vessel dynamic inclinations. As a consequence of these motions, lateral migration of bubbles and their clustering enhanced liquid recirculation and local streamwise gas velocity. Compared to static vertical bubble column, bubbly flow pattern was barely altered by yaw and low-frequency sway except the heave displacements which tended to slowdown the bubble rise.     

Estimation of bubble size distributions and shapes in two-phase bubble column using image analysis and optical probes

A precise estimation of bubble size distributions and shapes is required to characterize the bubble column fluid dynamics at the “bubble-scale”, and to evaluate the heat and mass transfer rate in bubble column reactors. Image analysis methods can be used to measure the bubble size distributions and shapes; unfortunately, these experimental techniques are limited to resolve bubble clusters and large void fractions, and can not be applied under relevant operating conditions (e.g., high temperature and pressure). On the other hand, needle probes (i.e, optical and conductive probes) can be used to measure bubble sizes in dense bubbly flows and under relevant operating conditions; however, needle probes measure chord length distributions, which should be converted into bubble size distributions by using statistical algorithms. These algorithms rely on correlations—generally obtained for single droplets/bubbles—that predicts the bubble shapes, by relating the bubble equivalent diameter to the bubble aspect ratio. In this paper, we contribute to the existing discussion through an experimental study regarding the bubble sizes and aspect ratio in a large air-water bubble column. The experimental investigation has consisted in gas holdup, image analysis and optical probe measurements. First, the gas holdup measurements have been used to identify the flow regime transition between the homogeneous flow regime and the transition flow regime. Secondly, the homogeneous flow regime has been described at the “bubble-scale”: chord length distributions and bubble size distributions have been obtained by using an optical probe and image analysis, respectively. Based on the experimental data from the image analysis, a correlation between the bubble equivalent diameter and the bubble aspect ratio has been proposed and has been compared with existing correlations. Finally, the chord length distributions have been converted into bubble size distributions using a statistical method, supported by the aspect ratio obtained through image analysis. The proposed approach has been able to estimate correctly the bubble size distributions at the center of the column then near the wall. We have also demonstrated that the correlations used to predicts the bubble shapes are the main point of improvement in the method.     

Theoretical studies on the design criteria of double-sensor probe for the measurement of bubble velocity

This paper presents a study of the design criteria and the theoretical calibration factor of a double-sensor probe for the measurement of bubble velocity in two-phase flows. Due to the finite probe spacing between the two probe tips, any lateral motion of a bubble can complicate the interpretation of the measured value. To quantify the measurement error, a rigorous derivation was carried out for spherical bubbles to bridge the measured value with the true bubble velocity. Afterwards, the mean measurable value was then obtained by use of proper probability density functions identified via a necessary coordinate transform. It was discovered analytically that the measurable velocity might approach infinity if the probe spacing is too small compared to the bubble size. For practical applications, the probe spacing should be greater than roughly one half of the bubble diameter in order to avoid such a singularity problem. Numerical results indicate that the calibration factor, defined as the ratio of the mean bubble velocity to the average measured value, depends only on the relative bubble velocity fluctuation, if the probe spacing is about 0.5–2 times the bubble diameter. The relative bubble velocity fluctuation was then correlated with the standard deviation of the inverse measurable speed that can be readily obtained in the experiment. These results are also applicable for moderate non-isotropic velocity fluctuations. Finally the appropriate sample size was provided using a Monte Carlo approach.     

Shock wave propagation in bubbly liquids at small gas volume fractions

It is well known that shock wave propagation in liquid media is strongly affected by the presence of gas bubbles that interact with the shock and in turn affect the gas bubbles. An explicit form of a wave equation was obtained from a set of equations for wave propagation in bubbly liquid (Caflisch et al., 1985a) in this study. Shock wave propagation in bubbly mixtures was considered with the solution for the obtained wave equation, of which homogeneous and particular solutions provide the pressure field due to the shock profile and bubble- bubble interaction, respectively. The gas behavior inside a spherical bubble under the shock wave was obtained by a set of homologous solutions for the mass and momentum conservation equations. The energy equation for the gas inside the bubble was solved analytically with help of the homologous solutions. The bubble wall motion in compressible medium was obtained from the Keller-Miksis equation. The heat transfer from/to the bubble was obtained by solving the energy equation for the gas inside the bubble and for the liquid outside the bubble wall. The relaxation oscillations behind the shock front, which were calculated using the Keller-Miksis equation with the solutions of the obtained wave equation, are in close agreement with those obtained in shock tube experiments for a uniform bubbly flow by Kameda et al. (1998). Heat exchange between the gas bubbles and the liquid and the interaction between bubbles were found to be very important factors to affect the relaxation oscillations in the shock front.

     

Uncertainty and intrusiveness of three-layer wire-mesh sensor

A wire-mesh sensor (WMS) has been applied to estimate the bubble velocity of an air-water bubbly flow in a vertical channel with a square cross-section. The WMS provides instantaneous cross-sectional gas fraction distributions which are measured by detecting the local electrical conductivity between two electrode wires crossing each other at right angles. The applied WMS has three planes of wire grids separated by 1.5 mm in the axial direction. The wires of the central grid are used as transmitter electrodes, while the wires of the two external grids are connected to the receiver inputs of the electronic unit. In this way, the sensor has two measuring planes, located between the transmitter grid and both receiver planes. Individual bubble diameters are calculated from the measured gas fraction data by using a bubble identification algorithm, and the bubble velocity is evaluated by cross-correlating the instantaneous gas fraction profiles. In case of WMS measurements, the intrusive effects caused by the wires cannot be neglected. In this study, the effect of the intrusive WMS on the bubble velocity was studied by high speed camera (HSC) observation. Bubble parameters were extracted from both WMS and HSC data. A comparison of bubble size and velocity was carried out for each bubble individually. It was found that bubbles are strongly decelerated when they collide with the wire grids in case of low liquid velocities. The effect decreases with growing liquid velocity and finally turns into a slight acceleration which corresponds to the degree of the cross-section obstruction by the wires.     

Pressure waves in bubbly liquids

It is well known that sound propagation in liquid media is strongly affected by the presence of gas bubbles that interact with sound and in turn affect the medium. An explicit form of a wave equation in a bubbly liquid medium was obtained in this study. Using the linearized wave equation and the Keller-Miksis equation for bubble wall motion, a dispersion relation for the linear pressure wave propagation in bubbly liquids was obtained. It was found that attenuation of the waves in bubbly liquid occurs due to the viscosity and the heat transfer from/to the bubble. In particular, at the lower frequency region, the thermal diffusion has a considerable affect on the frequencydependent attenuation coefficients. The phase velocity and the attenuation coefficient obtained from the dispersion relation are in good agreement with the observed values in all sound frequency ranges from kHz to MHz.     

Experimental study of bubbly swirling flow in a vertical tube using ultrasonic velocity profiler (UVP) and wire mesh sensor (WMS)

Two-phase air-water bubbly swirling flow through a pipe is a complex turbulent flow and its prediction is still challenging. The present paper describes the experimental investigation of the air-water bubbly swirling flow in vertical co-current flow. Swirling flow is induced by a twisted tape in a 20 mm inner diameter pipe. The flow is investigated using Ultrasonic velocity profiler (UVP), which allows the measurement of liquid and gas velocities simultaneously. Furthermore, simultaneous measurement of void fraction is performed using Wire mesh sensor (WMS). The experimental results reveal that swirling flow has significant impact on bubbles’ distribution. In low liquid flow rate, the average bubble velocity is fairly uniform along the radial position and void fraction increases in the near wall region. However, increasing liquid flow rate at constant gas flow rate leads to increase in void fraction in the core region, this is mainly due to drift velocity which is affected by centrifugal force. Experimental findings and parametric trends based on the effects of swirling flow are summarized and discussed.     

Accurate mass flow and density of bubbly liquids using speed of sound augmented Coriolis technology

Speed of sound augmented Coriolis technology utilizes a process fluid sound speed measurement to improve the accuracy of Coriolis meters operating on bubbly liquids. This paper presents a theoretical development and experimental validation of speed of sound augmented Coriolis meters. The approach utilizes a process fluid sound speed measurement, based on a beam-forming interpretation of a pair of acoustic pressure transducers installed on either side of a Coriolis meter, to quantify, and mitigate, errors in the mass flow, density, and volumetric flow reported by two modern, dual bent-tube Coriolis meters operating on bubbly mixtures of air and water with gas void fractions ranging from 0% to 5%. By improving accuracy of Coriolis meters operating on bubbly liquids, speed of sound augmented Coriolis meters offer the potential to improve the utility of Coriolis meters on many existing applications and expand the application space of Coriolis meters to address additional multiphase measurement challenges.The sources of measurement errors in Coriolis meters operating on bubbly liquids have been well-characterized in the literature. In general, conventional Coriolis meters interpret the mass flow and density of the process fluid using calibrations developed for single-phase process fluids which are essentially incompressible and homogeneous. While these calibrations typically provide sufficient accuracy for single-phase flow applications, their use on bubbly liquids often results in significant errors in both the reported mass flow, density and volumetric flow. Utilizing a process fluid sound speed measurement and an empirically-informed aeroelastic model of bubbly flows in Coriolis meters, the methodology developed herein compensates the output of conventional Coriolis meters for the effects of entrained gas to provide accurate mass flow, density, volumetric flow, and gas void fraction of bubbly liquids.Data presented are limited to air and water mixtures. However, by influencing the effective bubble size through mixture flow velocity, the bubbly liquids tested exhibit decoupling characteristics which spanned theoretical limits from nearly fully-coupled to nearly fully-decoupled flows. Thus, from a non-dimensional parameter perspective, the data presented is representative of a broad range of bubbly liquids likely to be encountered in practice.     

Estimation of the liquid velocity field in two-phase flows using inverse analysis and particle tracking velocimetry

In bubbly two-phase flow, the gas phase and liquid phase have different flow fields. The relative velocity of the two phases depends on the motion characteristic of the bubbles. The mathematical expression for the motion of a small bubble at low Reynolds number is already established. Using the equation, the liquid velocity along the trajectory of the bubble is calculated inversely using the motion equation. Whole field liquid flow structure is also estimated using a spatial and/or temporal interpolation method. This paper proposes an algorithm for estimating the liquid phase flow field from measurement data on bubble motion. In order to verify this principle, Taylor–Green vortex flow and Karman vortex shedding from a square cylinder have been chosen. The results reveal that by combining the inverse analysis and PTV with the spatio-temporal post-processing algorithm one can reconstruct well the carrier phase flow of the gas–liquid two-phase flow.     

Quantitative comparison between volume-of-fluid and two-fluid models for two-phase flow simulation using OpenFOAM

This study compared numerical characteristics of volume-of-fluid (VOF) and two-fluid models for the two-phase flow simulation by using open-source computational fluid dynamics software (OpenFOAM). In both models, the pressure-implicit method for pressure-linked equations was solved to obtain transient pressure and velocity fields. For the simulation of subgrid-scale bubbles, the VOF model was coupled with a Lagrangian discrete bubble model (DBM). In the single bubble rising case, kinematic and dynamic parameters predicted by the two-fluid model were poor. However, in the bubbly flow case, this model predicted the gas and liquid velocities well and, similarly, the liquid front position in the free surface flow case. On the other hand, the VOF model was less accurate in describing bubbly flow, despite the inclusion of the DBM. While the two-fluid model is recommended for the simultaneous simulation of separated and dispersed flows, the VOF model is more effective for separated flows.     

超声空化对细微流道中固体颗粒的运动特性研究

针对细微流道中的多相流调控问题,研究超声空化效应对微流道内固体颗粒运动特性的影响。利用Fluent有限元技术对空化气泡溃灭的过程进行模拟,得在超声声压作用于近壁区的气泡时,气泡凹陷、破壁、溃灭的演变过程,并对其周围流场的速度矢量分布进行研究,仿真结果显示,空化气泡溃灭能够产生射向壁面的高速微射流,其最大速度达到28m/s,进而确定细微流场观测实验的最优参数;利用高速摄像机对细微流道中气泡的演变过程进行观测实验,并与仿真实验结果进行对照,观测实验结果表明,利用超声空化效应能够实现对固体颗粒向流道壁面运动的有效引导,为实现细微流道的流场调控、提高加工精度等问题提供理论支持。     

An experimental and numerical study on hydrodynamic characteristics of horizontal annular type water-air ejector

A water-driven annular type ejector loop is designed and constructed for air absorption. Fabricated ejector unit is horizontally installed in the loop, and annular water jet at the throat entrained atmospheric air through the circular pipe placed at the center of the ejector. The tested range of water flow rate is 160 L/min to 320 L/min and volumetric flow rate of water and air and local pressure are quantitatively measured using LabVIEW signal express program. For the quantitative measurement of bubble velocity, cinematic PIV technique using a high speed camera is adapted. In post processing, each bubble is used as seeding particles and ensemble averaged bubble velocity field at vertical plane of the ejector system is finally acquired. In the range of experiment, the bubble size distribution at downstream of the ejector seems to be quite uniform so that the flow can be classified as a homogeneous bubbly flow. In case of low range of water flow rate, the transition from bubbly flow to stratified flow occurs at the atmospheric outlet condition. As a comparative study, a numerical simulation on the same ejector shape is performed to understand the more detail hydrodynamic characteristics in the annular type ejector system. Homogeneous bubbly flow regime is used as default two-phase flow regime, and void fraction at the vertical plane of the ejector system is qualitatively compared with that of experiment. In volume flow rate comparison, numerical prediction agrees well with that of experiment where the homogeneous bubbly flow is maintained.     

On sampling bias in multiphase flows: Particle image velocimetry in bubbly flows

Measuring the liquid velocity and turbulence parameters in multiphase flows is a challenging task. In general, measurements based on optical methods are hindered by the presence of the gas phase. In the present work, it is shown that this leads to a sampling bias. Here, particle image velocimetry (PIV) is used to measure the liquid velocity and turbulence in a bubble column for different gas volume flow rates. As a result, passing bubbles lead to a significant sampling bias, which is evaluated by the mean liquid velocity and Reynolds stress tensor components. To overcome the sampling bias a window averaging procedure that waits a time depending on the locally distributed velocity information (hold processor) is derived. The procedure is demonstrated for an analytical test function. The PIV results obtained with the hold processor are reasonable for all values. By using the new procedure, reliable liquid velocity measurements in bubbly flows, which are vitally needed for CFD validation and modeling, are possible. In addition, the findings are general and can be applied to other flow situations and measuring techniques.     

Experimental PIV and LIF characterization of a bubble column flow

Experimental 2D Particle Image Velocimetry (PIV) measurements, with uniform background lighting and Laser Induced Fluorescence (LIF) of the tracking particles, were performed in order to characterize the air-water biphasic flow and the 2D bubble column rising velocity in static water. Some applications require knowledge of the simultaneity of two-phase flow characteristics. The two phase flow air/water are common application in industry as chemical, hydraulic and nuclear industry, water treatment by aeration, and measurements are implemented to characterize the behaviour of the air bubbles column flow. The bubble flow studied in this paper is related to the optimization of the aeration in hydraulic turbines with micro-bubbles. The first step of this study, presented in the paper, is a complete characterization of a bubble column issued from a metallic sparger with holes of 0.5 mm diameter. For its complete characterization is determined simultaneously, via image processing technics, the flow velocity field induced by the column of bubbles in water, and the bubbles features: the bubble ascension velocity, diameter variation, interfacial area and shape factor. The results are compared with bibliographical data.     

A parametric study on bubbly lubrication of high-speed journal bearings

The influence of aerated oil on high-speed journal bearings is examined by classical thermohydrodynamic lubrication theory coupled with analytical models for viscosity and density of the air–oil mixture in the fluid-film bearing. Convection to the walls, mixing with supply oil and recirculating oil, and some degree of journal misalignment are considered. The parameters considered for the study of bubbly lubrication are oil aeration level, air bubble size, shaft misalignment and shaft speed. The results show that air bubbles can more clearly bring on increasing load capacity under high-speed operation of a plain journal bearing than under previous normal speed operation. Moreover, the load capacity may be increased more by oil aeration under the conditions of shaft misalignment and increasing speed.     

Form drag coefficient quantification on rising bubbles using particle image velocimetry

Two-phase flow transport heavily depends on the generalized interfacial drag force term in the two-fluid model. The impact of accurate design and prediction associated with thermal energy systems is highly sensitive to multi-phase heat transfer characteristics. Because of this, the interfacial drag force has been studied with rigor for some time. The steady state drag force component in particular has been well characterized for rising single bubbles but has not been previously experimentally separated into its skin and form drag components. Historically, experimental studies were unable to measure the pressure distribution around a bubble to determine the form drag force along the bubble interface. This paper presents the outcomes of an experimental study wherein a new experimental method was developed which, for the first time, separates the form and skin drag coefficients on rising bubbles. Eleven air bubbles sizes representing spheroidal, ellipsoidal, and transition to spherical cap regimes (10²<Re<10⁴) were studied in a water test loop with velocity fields measured via particle image velocimetry; pressure fields were then synthesized from these velocity fields through the Queen2 algorithm. The skin and form drag coefficients were separated for single bubbles which showed a nominal trend of increasing form drag contribution with increasing Reynolds number. This work presents a new method and new outcomes for rising bubbles over several bubble regimes and includes a comprehensive uncertainty characterization of the resulting data.     

A non-intrusive probe for bubble profile and velocity measurement in horizontal slug flows

A new technique was developed for measuring the profile and mean velocity of elongated bubbles in horizontal air–water slug flows. It is based on the capacitance between two thin electrodes mounted on the external surface of a dielectric pipe, and has advantages in relation to the traditional parallel wire technique, since it is not intrusive, the presence of impurities in the liquid phase has no influence on the probe response, and it is applicable to very low electrical conductivity liquids, such as oils and deionized water. Tests were performed in an experimental facility with a 5 m long, 34 mm internal diameter Plexiglas pipeline. The elongated bubble mean velocity was determined by using a cross correlation technique applied to the signals coming from two identical capacitance probes, mounted 50 mm distant from each other. The results were compared with an empirical correlation from the literature. Discordance was observed only for flows near the flow pattern transition regions in the flow pattern map.     

Effects of prong-wire interferences in dual hot-wire probes on the measurements of unsteady flows and turbulence in low-speed axial fans

Support needles of Dual Hot Wire (DHW) anemometers induce significant inaccuracies for flow angle and turbulence measurements in the case of X-array probes with prongs perpendicular to the flow plane. At certain angular ranges of the incident flow, a wake interference is established between the sensors which leads to a practical limitation of the device. In the case of turbomachinery environments, this is even more critical due to the inherent unsteadiness of the flow direction rotor downstream.In the present work, the measurement deviation caused by hot-wire probes operated under interference effects has been studied and evaluated, in both steady and unsteady conditions, especially for turbomachinery flows. New designs of DHW probes without prong-wire interference effects in their operative angular ranges were developed for validation. In particular, both V-type and Z-type interference-free probes are compared to a classic X-type probe susceptible for prong-wire interferences. Firstly, a steady calibration is performed to show the baseline deviation of the X-array probe in the measurement of the velocity magnitude, the flow angle and the turbulence intensity. Typical errors up to 10–13% in velocity, 5.5–7 deg in angle and 1.5–2.5 points overestimation in turbulence levels are observed. Also, unacceptable inaccuracies are found in the turbulence spectra of the measurements.Following, the impact of the interference for unsteady flow measurements is highlighted comparing the performance of the three probes within the single stage of a low-speed axial fan. The unsteady measurements of the X-array probe have revealed similar averaged discrepancies to those observed in the steady performance, but the instantaneous deviations can be as high as a 20% in velocity and 16–18 deg in flow angle in those regions (rotor wakes) with large unsteady velocity gradients and turbulence generation. Turbulence intensity measured in the rotor wakes is also excessively higher.     

Comparison between wire-mesh sensor and ultra-fast X-ray tomograph for an air–water flow in a vertical pipe

A comparison between ultra-fast X-ray CT and a wire-mesh sensor is presented. The measurements were carried out in a vertical pipe of 42 mm inner diameter, which was supplied with an air–water mixture. Both gas and liquid superficial velocities were varied. The X-ray CT delivered 263 frames per second, while the wire-mesh sensor was operated at a frequency four times higher. Two different gas injectors were used: four orifices of 5 mm diameter for creating large bubbles and gas plugs and a sintered plate with a pore size of 100 μm for generating a bubbly flow. It was found that the wire-mesh sensor has a significantly higher resolution than the X-ray CT. Small bubbles, which are clearly shown by the wire-mesh sensor, cannot be found in the CT images, because they cross the measuring plane before a complete scan can be performed. This causes artifacts in the reconstructed images, instead. Furthermore, there are large deviations between the quantitative information contained in the reconstructed tomographic 2D distributions and the gas fractions measured by the sensor, while the agreement is very good when the gas fraction is obtained by a direct evaluation of the X-ray attenuation along the available through-transmission chords of the tomography set-up. This shows that there is still potential for an improvement of the image reconstruction method. Concerning the wire-mesh sensor it was found that the gas fraction inside large bubbles is slightly underestimated. Furthermore, a significant distortion of large Taylor bubbles by the sensor was found for small liquid velocities up to 0.24 m/s. This effect vanished with growing superficial water velocity.