Bubble size measurement using wire-mesh sensors

Flow Measurement and Instrumentation 12 (2001) 299–312 www.elsevier.com/locate/flowmeasinst

Bubble size measurement using wire-mesh sensors H.-M. Prasser *, D. Scholz, C. Zippe Forschungszentrum Rossendorf e.V., Institute of Safety Research, P.O.B. 510119, D-01314 Dresden, Germany Received 27 June 2000; received in revised form 29 August 2000; accepted 19 September 2000

Abstract A wire-mesh sensor with a time resolution of 1.2 kHz was used to measure bubble size distributions in a gas-liquid flow. It is designed for a pipe of 51.2 mm diameter and consists of two electrode grids with 16 electrodes each, put in the flow direction behind each other. The local instantaneous electrical conductivity is directly measured between all pairs of crossing wires, a tomographic image reconstruction is not necessary. The resulting 16 × 16 sensitive points are equally distributed over the cross section. This resolution is sufficient to detect individual bubbles, which are imaged in several successive frames during their transition through the measuring plane. To investigate the influence on bubbles, a model of the sensor was tested in a transparent channel with a rectangular cross section of 50 × 50 mm at liquid velocities between 0 and 0.8 m/s. A comparison with high-speed video observations has shown that the sensor causes a significant fragmentation of the bubbles. Nevertheless, the measured signals still represent the structure of the two-phase flow before it is disturbed by the sensor. Bubble sizes can therefore be determined by integrating local instantaneous gas fractions over an area of the measuring points occupied by the bubble. Bubble size distributions are obtained by analysing large assemblies of bubbles. The method was applied to study the formation of slug flow along a vertical tube. The bubble size distributions obtained show the effect of coalescence as well as bubble fragmentation.  2001 Elsevier Science Ltd. All rights reserved. Keywords: Two-phase flow; Gas-liquid flow; Wire-mesh sensor; Gas fraction; Bubble size; Bubble flow; Slug flow

1. Introduction Mass, momentum and energy exchange between the phases of a gas-liquid flow strongly depend on concentration and structure of the interfacial area. The local gas fraction alone is not sufficient as a determining parameter of the phase interactions. In bubble and slug flows bubble populations must be considered. This requires measuring methods capable of delivering bubble size distributions on the experimental side. Measuring techniques for this purpose must be able to resolve individual bubbles, i.e. the spatial resolution must be at least in the range of the scale of the smallest bubble fraction to be detected. Individual bubbles in a wide range of diameters are often measured by optical methods, such as photographic and video imaging. The best resolution is achieved by pulsed laser holography

* Corresponding author. Tel: +49 351 260 2060; fax: +49 351 260 2383. E-mail address: h.m.prasser@fz-rossendor (H.-M. Prasser).

[1]. The method produces three-dimensional still pictures with a resolution of about 7 µm at exposure times of 30 ns. It was successfully used for bubble size measurements in heterogeneous stirred vessel reactors. Double exposure allows the measurement of bubble velocities. An overview of optical particle sizing techniques in multiphase flows is given by Tayali and Bates [2], including holography, particle imaging velocimetriy and sizing, laser light sheet and particle light scattering techniques. These techniques are most suitable for droplet and solid particle flows, they are always restricted to low volumetric fractions of the dispersed phase. In many cases, the flow to be investigated is characterised by higher fractions of the dispersed phase, where optical methods fail. A prominent example is the study of the transition from bubble to slug flow, which occurs at volumetric gas fractions well above 10%. With growing content of the dispersed gas fraction the flow becomes more and more opaque and an optical observation is limited to the region near the observation window. Information from the core of the flow cannot be obtained.

0955-5986/01/$ - see front matter  2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 5 - 5 9 8 6 ( 0 0 ) 0 0 0 4 6 - 7

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Nomenclature b D f H i j J k n N R t x y z V w ⌬ ⑀

local bubble identifier diameter, m frequency, Hz height, elevation, m field index, x-direction field index, y-direction superficial velocity, volume flow density, m/s field index, direction of time axis index, bubble identification number total number of bubbles radius, m time, s coordinate, m coordinate, m coordinate, m volume, m3 velocity, m/s difference, step, pitch volumetric gas fraction, 1

Indices air Bub G L level m max water 0 *

air Bubble gas liquid threshold measurement maximum water origin, initial, primary virtual

This is a domain of electrical and optical needle probes. They identify the phase which is instantaneously present at the location of their sensitive tip. Due to the high time resolution of this phase detection, individual bubbles are represented in the signal as periods of contact with the gaseous phase. The electrical resistivity probe technique was proposed first by Neal and Bankoff [3]. From the contact period, i.e. the time during which the tip of the probe is covered with the gaseous phase, the chord length of the penetrated bubble is deduced. For this, information about the velocity is necessary. This may be obtained by applying double probes and evaluating the time of flight from the first probe tip to the second [4]. The probes were further improved by introducing two more sensitive tips [5,6]. These four-tip probes can measure the attack angle. This helps to increase accuracy. An excellent imaging of the instantaneous gas fraction distribution over the pipe diameter (25.8 mm) was achieved by Mori

et al. [7], where a linear 67 point-electrode probe was used in a slug flow. A recent publication on the progress of optical fibre probes has been given by Spindler and Hahne [8]. One of the basic problems of bubble size measurements with needle probes is the conversion of the primarily measured chord length distributions into distributions of the bubble diameter. The problem is theoretically solved for spherical bubbles under the assumption, that the point of penetration of the bubble by the probe is equally distributed over the circular contact area [9]. This method does not account neither for the effect of bubble deformation nor for any deflection of the bubble by the forces arising from the contact with the probe. Furthermore, the high measuring time necessary leads to high experimental efforts and makes it impossible to study time transients in two-phase flow. Large progress has recently be made in the field of radiometric tomography, using gamma, neutron or X-ray

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absorption techniques. They have a high resolution and are non-intrusive at the same time. If these methods are to be used for bubble size measurements, the measuring period must be shorter than the time necessary for the particle to travel over a distance equal to its own size. The necessary time resolution is reached by high-speed X-ray tomography relying on assemblies of pulsed Xray sources [10]. A device with 18 X-ray tubes produces sequences of two-dimensional void distributions with a time resolution of 4 ms, an advanced device with 66 tubes has a resolution of 0.5 ms. The method was recently applied to determine the shape and the volume of Taylor bubbles in a vertical slug flow in a simplified rod bundle geometry [11] and for studying the penetration of a water jet into a bulk of another immiscible fluid [12]. In both cases, a time resolution of 4 ms was reached. For medical purposes, scanned electron beam devices [13] delivering 20 frames per second were developed. This is sufficient to visualise the beating human heart, but still too slow for two-phase flow applications. The high costs of both types of devices are a major obstacle against a wide use for two-phase flow measurements. Furthermore, it is difficult to increase time resolution, because low exposure times are contradicting to low statistical errors of the obtained projections, which are necessary for a high-resolution image reconstruction. Advanced three-dimensional X-ray tomographs on the other hand [14] require several seconds up to minutes for the acquisition of the projections. They can therefore not be applied for time-resolved studies of transient flows. In front of this, wire-mesh sensors offer an interesting compromise. The disadvantage of being intrusive is compensated to a certain extent by the high time resolutions achieved at comparatively low costs. This type of sensor was initially proposed by Johnson [15] for the measurement of the average gas fraction in a cross-section. The first tomographic wire-mesh sensor with approximately 100 frames per second has been described by Reinecke et al. [16]. It is based on the measurement of the instantaneous conductivity of the two-phase mixture between all pairs of adjacent parallel wires of three electrode grids. The obtained three projections are subsequently used for a numerical reconstruction of the twodimensional gas fraction distribution. The present work is based on the wire-mesh sensor developed by Prasser et al. [17]. The conductivity of the two-phase mixture is measured at each crossing point of wires of two electrode grids directly. With this sensor a time resolution of over 1000 frames per second was achieved for the first time. Meanwhile it has been increased up to 10,000 frames per second [18], mainly by improving the electronic circuitry of the signal acquisition unit. A standard device, which has been successfully commercialised, is coupled with a personal computer via a parallel interface

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and operates at a maximum rate of 1200 frames per second. The sensor consists of two electrode grids with 16 electrodes each (Fig. 1), put in the flow direction behind each other. The local instantaneous electrical conductivity is directly measured between all pairs of crossing wires, a tomographic image reconstruction is not necessary. This results in 16 × 16 sensitive points, which are equally distributed over the cross section. In case of a tube diameter of 50 mm, this results in a spatial resolution of 3 mm, which equals the pitch of the electrode wires. The present work has paid special attention to the interaction between sensor and two-phase flow. Signals of the sensor are compared to high-speed video observations. It will be shown that this resolution is sufficient to detect individual bubbles and that bubble size and shape are well reflected by the sensor signal. A bubble is imaged in several successive frames during its transition through the measuring plane of the sensor—a necessary condition for determining the volume of the bubbles. Bubble size distributions can be obtained if large assemblies of bubbles are analysed. This method will be discussed below. After the description of the evaluation procedure and an assessment of the accuracy, the developing bubble size distribution in a vertical tube is presented to show the capabilities of the method. 2. Interaction of gas bubbles with the sensor 2.1. Experimental set-up A wire-mesh sensor consisting of 2 layers of 16 wires was integrated into a rectangular test channel made of

Fig. 1. Wire-mesh sensor with 16 × 16 measuring points for a tube of a 51.2 mm diameter.

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organic glass (Fig. 2). The dimensions of the inner cross section of the channel were 50 × 50 mm. The pitch of the wires is 3.125 mm, the distance between the two layers is 1.5 mm. Wires have a diameter of 0.12 mm. Except the rectangular cross section, the sensor is identical to the wire-mesh sensor in Fig. 1. The channel was connected to the circuit of a twophase flow test loop. It was supplied from below with water at room temperature. At several positions below the sensor, air can be injected through a small steel tube, which can be varied in diameter. The transparent walls of the channel allow an optical observation of the sensor and the bubbles from aside. The wires are fixed in small orifices directly in the wall, so that the view is not obstructed by any fixing parts. For the visual observation, the test facility is equipped with a high-speed video device. In the experiments presented below, a resolution of 240 × 256 pixel was used at a speed of 1000 camera frames per second. The rate of the wire-mesh sensor was accurately set to the same frequency. Both camera and wire-mesh sensor measurement were started synchronously. 2.2. Disturbance caused by the sensor In Fig. 3 selected frames of a high-speed record are presented, which show the process of the penetration of one single bubble through the wire-mesh sensor. When the bubble comes in contact with the wires of the first plane, it is cut into slices. Between the fragments of the bubble, water bridges in the form of thin lamellae maintain a certain electrical contact between the transmitter and receiver wires. When the bubble crosses the second grid of wires, it is also cut in the second direction. This results with the appearance of a cloud of small bubbles. Though some of the small fragments recombine, the bubble is heavily disturbed by the sensor.

Fig. 2.

Transparent test channel with integrated wire-mesh sensor.

Fig. 3.

Bubble fragmentation caused by the wire-mesh sensor.

The process of bubble fragmentation was observed for nearly all the analysed bubbles independently of their size and the velocity of the water, which was varied from 0–0.8 m/s. However, with growing bubble size the process of recombination by coalescence of the fragments becomes more and more effective and the initial shape of the bubble is more and more restored (see Fig. 4). Further it was observed that in case of resting water (vL = 0 m/s) the bubbles sometimes are significantly slowed down, before they penetrate the sensor. This effect disappears at low water velocities of about 0.1 m/s. This can

Fig. 4. Comparison between video observation and measured gas fraction distributions, method of extracting virtual side views from the gap between the electrode grids.

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probably be explained by the balance between inertial forces and the surface tension. With growing velocity the inertia of the liquid becomes dominant.

2.3. Signal of the wire-mesh sensor

Despite the fragmentation caused by the sensor, the bubbles are represented in the measuring signal in their previous shape, i.e. the bubbles are displayed as they are before they come in contact with the sensor. In Fig. 4 side views obtained by the camera are compared to the corresponding instantaneous gas fraction distributions measured by the sensor. The local instantaneous gas fractions were calculated assuming a linear dependency between local conductivity and gas fraction, as described in [17]. It is clearly visible, that the sensor signal represents the undisturbed image of the bubble. Another method for a comparison is given by constructing virtual side views of both camera record and wire-mesh signal. For this purpose, the pixel row belonging to the gap between the two electrode planes is extracted from a sequence of frames. These lines are combined to a new bitmap file by stacking them in a vertical column, beginning from the top and moving downwards with increasing time. The procedure is illustrated on the right side of Fig. 4. In the next step, the resulting grey-scaled image is discriminated and transformed into a contour image. The sensor signal is also transformed into an Eulerian side view by calculating projections of the two-dimensional instantaneous gas fraction distributions in the direction of the camera view. The result of the projection was defined as the maximum of the local gas fractions were found along the projecting lines. The resulting sequences of one-dimensional projections were plotted in the same way as the pixel row extracted from the camera images. Finally, the bubble contours obtained from the camera images were overlaid. In these combined images, it is clearly visible, that the sensor shows the shape assumed by the bubble in the moment of its passing through the electrode planes (Fig. 5 and Fig. 6). Obviously the main disturbance that may influence the signal is given by the appearance of the water bridges in the wake of the wires of the first plane of electrodes. Through these water bridges, a certain electrical current can flow. This is the case for the medium-size bubbles in Fig. 6. For this reason the measured local gas fraction does often not reach exactly 100% inside the bubble. Nevertheless, the image does not show the formation of fragments, because the water bridges are much smaller than the spatial resolution of the sensor. In the case of the large bubble shown in Fig. 6, the water can completely drain from the gap between the electrode layer and the gas fraction reaches 100%.

Fig. 5. Comparison between virtual side projections of the sensor signal (clouds) with virtual side views obtained by the high-speed camera (contours).

Fig. 6. Signals of bubbles with different size: clouds, virtual side projections calculated from the sensor signal; contours, virtual side views obtained by the high-speed camera; curve, maximum of local gas fraction in the current line; ⑀, instantaneous maximum gas fraction.

3. Bubble size measurement 3.1. General approach The wire-mesh sensor delivers a sequence of twodimensional distributions of the local instantaneous gas

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fraction, measured in each mesh formed by pairs of crossing wires, a transmitter wire i and a receiver wire j. This results in a three-dimensional data array ⑀i,j,k. The elements of this distribution are characterised by the triplet of indices [i,j,k]. Here, i and j are the numbers of the corresponding pairs of crossing electrode wires. The crossing point defines the location of the given mesh. k is the number of the instantaneous gas fraction distribution in the time sequence. These indices correspond to coordinates x, y of the local measurement in the cross section and the current time t in the following way: k x⫽i⌬x⫹x0; y⫽j⌬y⫹y0; t⫽k⌬t⫽ fm

(1)

Here, ⌬x and ⌬y denote the electrode pitches (in our case ⌬x = ⌬y =3 mm), and fm the measuring frequency, and ⌬t = 1/fm the time step respectively, x0 and y0 are constants defining the origin of the coordinate system. Any single value of ⑀i,j,k denotes, to which extent the corresponding mesh [i,j,k] is filled with the gaseous phase. The time necessary for the fluid element to travel through the sensor depends on the velocity. The total gas volume flowing through one mesh of the sensor during the measuring period ⌬t can be expressed as VG,x,y,t = ⑀x,y,twG,x,y,t⌬x⌬y⌬t. Here, wG,x,y,t is the axial component of the instantaneous local gas phase velocity. In general, a bubble occupies more than one mesh. Furthermore, due to the high time resolution, it is generally mapped in several successive two-dimensional gas fraction distributions. The volume of a given bubble can be found, if we manage to identify which elements [i,j,k] of the threedimensional gas fraction distribution ⑀i,j,k belong to the bubble:

冘

VBub⫽⌬x⌬y⌬t

⑀i,j,kwG,i,j,k ∀[i,j,k]苸Bubble

(2)

From the bubble volume, an equivalent bubble diameter can be calculated:

冑6

DBub⫽3

p

VBub

(3)

In this respect, a bubble is defined as a set of elements [i,j,k], where gas is present, which are in contact with each other and which are surrounded by elements consisting of the liquid phase, i.e. by other elements, where the gas fraction equals zero. In general, in a distribution ⑀[i,j,k], a large number of bubbles is present. The task to obtain bubble size distributions can therefore be subdivided into the following steps: 앫 Identification of bubbles, i.e. assigning each element [i,j,k] to one of N bubbles or to the area occupied by the solid liquid phase,

앫 integrating the local instantaneous gas fraction over the elements belonging to the given bubble to obtain the bubble volume according to Eq. (2) and transfer to an equivalent diameter, Eq. (3), 앫 calculation of a statistical distribution with the equivalent bubble diameter as variable. A general problem is the availability of the gas phase velocity wG,i,j,k. It is still not possible to measure the local instantaneous gas velocity over the entire cross section, nor the velocity of every bubble that crosses the measuring plane. To separate the problem of measuring the velocity, it is possible to factor it out in Eq. (2), if the bubble velocity is used as an approximate, i.e. wG,i,j,k⬵wBub. In the result, a related bubble volume V˜ Bub can be defined, which is independent from the velocity. It is measured in units of m2s, the corresponding related ˜ Bub according to Eq. (3) is measured bubble diameter D in units of (m2s)1/3. VBub ˜ ⫽V ⬵⌬x⌬y⌬t wBub Bub

冘

⑀i,j,k∀(i,j,k)苸Bubble

(4)

The high-speed video imaging can deliver an estimate ˜ Bub. This allows a direct of related bubble diameter D assessment of the accuracy of the bubble size measurement of the sensor separately from the accuracy of any velocity information. For this purpose, the bubble volume was determined from time sequences of pixel rows as it was described in Section 2.3 (see Fig. 5). From the bubble contours, related bubble volumes are estimated by assuming a rotational symmetry of each individual axial layer of the bubble. Since the vertical axis is a time axis, the obtained volumes are related ones in units of m2s, they are transformed into related diameters using Eq. (3). A closer look at the virtual side projections shows that the contours taken from the gap between the electrode layers (Fig. 5, left side) shows the distortions of the bubbles caused by the cutting effect of the electrode wires. These deformations disturb the determination of related bubble volumes from the contours. For this reason, virtual side views were also extracted from a pixel row 5 mm below the sensor (Fig. 5, right side). In this case, the contours obtained from the camera signal are still free of the influence of the sensor, but shifted to an earlier time, while the bubble volume can be assumed to remain constant at this short distance. With known velocities, related volume can afterwards be transformed into the real volume by multiplying with the corresponding bubble velocity. In case of the diameter, a multiplication by the cube root of the velocity must be performed. There are different possible approaches to obtain velocity information: 앫 The gas phase velocity can be approximated by the

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average gas phase velocity, i.e. it is assumed that wG,x,y,t⬵wG=JG/⑀¯ . Non-uniformity over the cross section and fluctuations in time are neglected. This is a satisfying approximation in case of rising turbulent two-phase flow in a vertical tube, when it is operated in forced convection. It is characteristic for such a flow, that the velocity profile of the liquid phase is rather flat. Due to the slip of the gas phase, the difference between gas velocity in the center and near the wall is further decreased. The relative measuring error in terms of bubble diameter units arising from this simplification is additionally decreased by a factor 3 compared to the relative error of the gas velocity due to the cubic root in Eq. (3). 앫 Local gas velocities averaged over an integration period of several seconds can be measured by operating two wire-mesh sensors placed in a certain distance behind each other. The conductivity signals obtained at identical crossing points of the two sensors can be cross-correlated. In the result, a two-dimensional distribution of the gas velocity averaged of the measuring time can be obtained. These profiles of the average gas velocity would provide a better approximate, than wG, i.e. wG,x,y⬵wG,x,y,t. This method was tested with a certain success [19], but there are still open questions to be answered. 앫 With increasing time resolution, the two sensors can be brought closer to each other. This makes it possible to measure the time of flight of individual bubbles. This method is also still under development. Examples of bubble size distributions in a vertical tube presented in this paper in the next section were calculated using the average phase velocity wG. The experiments were performed at constant flow rates of gas and liquid. The superficial velocity JG was known from a measurement of the gas flow rate before injecting. The average volumetric gas fraction ⑀¯ was found by averaging the instantaneous gas fraction distributions measured by the sensor over time and cross section. For the assessment of the accuracy, distributions of the related bubble diameter are compared, which were obtained by the wire-mesh sensor and a high-speed video device synchronously.

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to fill two-dimensional areas until a border of a given quality is reached. In case of the bubble identification, a similar procedure works upon three-dimensional array. The fill is achieved by a recursive call of a procedure that sets the content of an element of bi,j,k to the current value of a bubble counter nbub, if the same bubble identification number is found at least in one of the neighbouring elements, and if the local gas fraction indicates the presence of gas. For the presence of plain liquid in an element, b is set to 0. This is also the value the elements bi,j,k have to be set to before the fill is started. The structure of the recursive fill procedure is shown in Fig. 7. The fill process is terminated, when there is no more neighbour having a local instantaneous gas fraction ⑀i,j,k greater than a certain threshold ⑀Level. This termination level is necessary, because in practise the signal is affected with noise. In consequence, the measured gas fraction is not exactly zero in the region of plain liquid. If we set the threshold to zero, the fill algorithm would run from one bubble to another through the plain liquid area via random channels with small positive errors of the local gas fractions. The procedure has to be called with a start element that has a gas fraction greater than the threshold ⑀Level, which has to be found in the gas fraction array. As a second condition, the start element must not yet be identified to belong to any bubble. The search for a start element and the subsequent fill procedure must be repeated while new start elements are found in the data array. The counter nBub has to be initialised and incremented after the completing of one run of the fill procedure. In practice, at higher gas fraction the following serious difficulty occurs: bubbles may appear very close to each other, so that the same element is touched by two bubbles from different sides. The gas fraction in this element may be greater than the threshold and the bubbles are erroneously united by the fill algorithm. An

3.2. Identification of bubbles The goal is to mark all elements [i,j,k] belonging to one and the same bubble with an identifier, in our case with an integer number, which is assigned exclusively to that bubble. For that purpose, a bubble identification array bi,j,k of the same dimensions as ⑀i,j,k is defined. The identification of a bubble in the gas fraction distribution ⑀i,j,k was carried out by a so-called recursive fill algorithm. Recursive fill procedures are used in image processing

Fig. 7. Structure of the recursive fill algorithm to identify a bubble in a 3D array of local instantaneous gas fractions.

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overestimation of bubble sizes would be the consequence. This would recommend the choice of a threshold as large as possible. But in this case, small bubbles in the range of the spatial resolution of the sensor would be neglected, because they do not occupy the control volume (mesh) completely and, consequently, the gas fractions remain well below 100%, as observed during the experiments at the transparent test channel (Fig. 6). Furthermore, a high threshold truncates the bubbles too early and elements at the bubble periphery are lost. This causes an underestimation of bubble sizes. The two latter effects lead to the wish to decrease the threshold as much as possible. In practice, an optimum between these contradicting tendencies cannot be found for the absolute threshold ⑀Level. Obviously, the main problem is that the fixed threshold termination fails when the signal level characteristic for plain liquid is not reached between neighbouring bubbles. The algorithm should nevertheless be able to distinguish bubbles, which are separated only by a local minimum of the gas fraction, without causing small bubbles to be neglected. This was achieved by the so called differential threshold method. In this case, the fill process is started in a local maximum of the gas fraction. It is terminated when the local gas fraction becomes less than the gas fraction in the local maximum ⑀max minus a so called differential threshold ⌬⑀Level. For this purpose the fill procedure shown in Fig. 7 can remain unchanged, if the former absolute threshold ⑀Level is adapted to each bubble individually, using the expression ⑀Level = ⑀max ⫺ ⌬⑀Level. The local maximum must fulfil the following conditions: (1) neither the element itself nor its neighbours must not yet be occupied by a bubble (bi,j,k = 0), (2) the local gas fraction ⑀i,j,k must be maximum, i.e. among the elements fulfilling condition (1) the one with the highest gas fraction must be searched. The differential threshold must be set to a value slightly greater than the magnitude of the statistical fluctuations of the raw sensor signal, otherwise bubbles would be divided into unrealistic fragments. The resulting individual threshold ⑀Level is close to the maximum gas fraction in the bubble, and the fill algorithm identifies only the core of the bubble, i.e. elements at the periphery remain unclassified. By the introduced conditions (1) and (2), which the start element must fulfil, it is excluded that the fill process for the next bubble is started in an element belonging to the neighbourhood of the already identified bubble core, i.e. in an element, which may belong to the already identified bubble. In the next step, it is necessary to assign the peripheral elements to the bubbles. This is solved by assigning the bubble identification number of an element already identified to its neighbours. For this purpose, a cellular automaton algorithm was adapted. In this stage of the bubble identification process, no new bubble identification numbers are generated. At higher gas fractions,

such an element may have neighbours belonging to more than one bubble. In this case, the element gets the number of the neighbour bubble, which has the highest sum of local gas fractions in the elements contacting the new element. This method was chosen, because the mentioned sum of local gas fractions in the neighbours characterises the magnitude of the contact area between the new element and the identified bubble. It seems to be appropriate to assign the new element to the bubble, with which it has the greatest contact area. Nevertheless, a significant influence of the choice of the latter described criterion on bubble size distributions was not found. 3.3. Quantification of bubble characteristics When the bubble identification is completed, the calculation of the related bubble volume has simply to be carried out according to Eq. (4). The affiliation of an element of the gas fraction distribution to a given bubble is characterised by the assigned bubble identification number bi,j,k. Eq. (4) is therefore up-dated as follows: V˜ Bub,n⬵⌬x⌬y⌬t

冘

⑀i,j,k

(5)

∀i,j,k:n⫽bi,j,k

→

The centre of mass R Bub,n=(xBub,n,yBub,n,tBub,n) of the bubble is calculated by averaging the coordinate vector →

R i,j,k= (x,y,t) of the elements [i,j,k] belonging to the bubble weighted with the local instantaneous gas fraction: →

R Bub,n⬵

冘

→

⑀i,j,kR i,j,k

(6)

∀i,j,k:n⫽bi,j,k

As an additional information, the maximum gas fraction inside the bubble can be found:

⑀max Bub,n⫽ MAX (⑀i,j,k) ∀i,j,k:n⫽bi,j,k

(7)

In a similar way of integration, any momentum of inertia of the bubble can be determined, which allows the characterisation of the departure from a spherical shape. 3.4. Bubble size distributions Bubble size distributions are constructed by summarising the contribution of the bubbles of a given range of diameters to the integral volumetric gas fraction. These partial gas fractions d⑀/dDBub are plotted against the equivalent bubble diameter DBub. An integration over this kind of bubble size distribution restores the average volumetric gas fraction. Often the resulting curves are very uneven at large diameters, because there are only a few large bubbles, which carry most of the gas volume.

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In these cases, the class width of the bubble size distribution are increased with growing bubble diameter to have at least 5 bubbles in each class. 3.5. Comparison to high-speed video observations The direct comparison to high-speed video records allows the accuracy of the bubble size measurement to be assessed in a quantitative way. For this purpose, the gas flow is adjusted to such a value, that separately rising gas bubbles were formed. Due to the constant gas flow, the volume of the bubbles was nearly constant during one test. The size of the bubbles was varied by using three different gas injection orifices (inner diameters: 0.5, 3 and 8 mm). Experiments were carried out varying the liquid velocity (0, 0.05, 0.2, 0.4, 0.6, 0.8 m/s) in order to study its influence. A number of bubbles was recorded by the high-speed camera as well as by the wire-mesh sensor during a measuring period of 7.838 s. Eulerian side projections (see Figs. 5 and 6) were constructed and related bubble diameters were estimated as described above. The agreement between the related bubble diameters obtained by the sensor respectively by the camera is shown in Fig. 8. The experiments with the large orifice show a larger scattering of the optical diameter compared to the wire-mesh values. This hints at growing measuring errors of the camera measurements with increasing bubble size due to the departure from a rotational symmetry of the bubbles. In the future it is planned to perform a stereoscopic visualisation. This

Fig. 8.

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should improve the accuracy of the optical measurement. Further, the scattering of the measuring points is significantly increased for the small injection capillary at the lowest liquid velocity (JWater =0.05 m/s), which is caused by a slow-down of the bubbles when they contact the electrode grid. This effect disappears with growing liquid velocity. In general, a slight overestimation of the bubble diameter is observed.

4. Application example: evolution of a two-phase flow along a vertical tube 4.1. Experimental test facility Measurements were performed at the MTLOOP test facility [20], a two-phase flow test loop of the Institute of Safety Research. It can be operated either with airwater or steam-water mixture, in the latter case up to parameters of 2.5 MPa and 225°C. For the present investigations, the loop was operated with air at atmospheric pressure and 30°C. A vertical test section of 4 m height and 51.2 mm inner diameter (Fig. 9) was used. Air was injected through a number of orifices in the wall of the tube. The superficial velocity can be varied between 0 and 12 m/s for the air and 0 to 4 m/s for the water respectively. The air flow rate was measured under normal conditions. The superficial velocity was calculated from a flow rate corrected according to the actual temperature and pressure at the location of the wire-mesh sensor. The tests were carried out under steady-state con-

Comparison of related bubble diameters, obtained from high-speed video observations and measured by the wire-mesh sensor.

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virtual sectional views of the flow, shown in Fig. 10. For this purpose, a time sequence of instantaneous gas fraction distributions over the tube diameter is plotted in a vertical column. In Fig. 10, height and width of the column correspond to the same geometric scale, so that the bubbles are displayed in their realistic shape (with the accuracy of the velocity assumption). It is clearly visible, that the previous primary bubbles are both coalescing and fragmenting along the tube length. In the end, the flow pattern changes from bubble to slug flow. It has to be kept in mind, that the Eulerian sectional views display a “frozen” flow pattern, i.e. the flow is visualised as it is, when it crosses the sensor plane. That means, for example, that in a real sectional view the picture in the first column (z* = 30 mm) would have changed to the picture in the second column (z* = 80 mm) at z = 50 mm a.s.o. 4.3. Choice of differential threshold for the bubble size measurement The differential threshold in the bubble identification algorithm is a parameter which has to be adjusted empirically. If it is chosen too low, some of the bubbles will be artificially divided into unrealistic fragments. In the opposite case, neighbouring bubbles can be identified as one bubble. The right choice depends on the noise level of the raw signal of the wire-mesh sensor.

Fig. 9.

Vertical test section for air-water experiments.

ditions. The wire mesh sensor was located at certain distances above the injection device, which were varied from 30 mm to 3133 mm, i.e. the inlet length was varied from 0.6 to 60 L/D. In the following, results will be presented for one selected test. In this test, the superficial velocity of the liquid was 1 m/s, the superficial gas velocity was 0.5 m/s. The air was injected through 8 orifices in the wall of the tube, which had a diameter of 4 mm. All orifices were located at the same height and were equally distributed over the perimeter. 4.2. Observed flow patterns The average velocity introduced in Section 3.1 was used to define a virtual z*-axis (z* = wG⌬t) to construct

Fig. 10. Virtual sectional views of the air-water flow in a vertical tube at different distances (H) between air injection and wire-mesh sensor position, JWater = 1 m/s, JAir = 0.5 m/s, gas injection through 8 orifices of ⭋4 mm in the wall.

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For determining the right threshold, the air-water flow straight above the gas injection in Fig. 10 (H = 30 mm) was used. In this case, quite large bubbles are formed. Due to the short distance, they arrive at the sensor position still as they were generated. Nevertheless, at higher gas flow, the bubbles come very close to each other. This is an ideal case of adjusting the threshold. For illustrating the effect of changing the differential threshold, the sensor signal was processed to obtain virtual side projections through the back half of the circular flow channel, as shown in Fig. 11. These side projections clearly show the comparatively large and almost uniform primary bubbles formed by the 4 mm orifices. The bubble identification algorithm was run with the sensor data for this case with three different values of the differential threshold (0, 10, 30%). The bubble identification numbers assigned to the elements of the three-dimensional gas fraction array ⑀i,j,k were used to colour the pixels of the virtual side projection. In this way, different bubbles in Fig. 11 were painted in different colours. If the threshold is set to the minimum, the majority of the bubbles is divided into unrealistic fragments (Fig. 11a), i.e. the colour changes inside one and the same bubble. When the threshold is increased to 10%, the unrealistic fragmentation disappears (Fig. 11b). When ⌬⑀Level is further increased, the algorithm starts to unite bubbles, as shown in Fig. 11c, i.e. neighbouring bubbles obtain an identical colour. Correspondingly, the sharp peak of the bubble size distribution, shown in the lower part of Fig. 11b, reflects the observed uniform size of the bubbles best at the optimal threshold value of 10%. An increase of the threshold leads to a widening of the distribution towards higher bubble diameters, a decrease to a widening of the distribution towards low diameters. It is also useful to analyse the dependency of the average

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bubble diameter from the differential threshold (Fig. 12). With growing threshold, the number of identified bubbles decreases, because the number of unrealistic fragments decreases. This is reflected by a growth of the average bubble diameter. At threshold values in the range between 5 and 10%, this growth stops for low gas fractions. A further increase of ⌬⑀Level does not cause changes of the bubble size and its distribution. This is an indication for the optimal choice of a threshold of 10%. In the case of higher gas fractions, the bubble size continues to grow due to unrealistic bubble unification, but with a much lower gradient of the curve. A similar behaviour was found for all flow regimes investigated in the vertical test channel. The value of the differential threshold of ⌬⑀Level = 10% was chosen for the bubble size analyses as a result of this investigation.

4.4. Evolution of the bubble size distribution along the vertical tube

In Fig. 13 the evolution of the bubble size distribution at the flow conditions of Fig. 10 is shown. At z* = 30 mm the maximum of the bubble size distribution corresponds to the size of the primary bubbles (D0). With growing height, the coalescence leads to the appearance of a bimodal bubble size distribution, which is fully established at z* = 1532 mm. This indicates the transition to slug flow. Bubbles with a diameter greater than the tube diameter (51.2 mm) must be understood as strongly deformed plug bubbles (see Fig. 10). The large bubble fraction is still further developing with increasing height. At the same time, bubbles smaller than the primary bubbles appear due to fragmentation.

Fig. 11. Effect of changing the differential threshold on bubble size distributions (different colours = different bubbles recognised) (JWater = 1 m/s, JAir = 0.5 m/s).

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Fig. 12. Measured average bubble diameter as a function of the differential threshold at different superficial air velocities (experiments in the vertical pipe, ⭋51.2 mm, H = 30mm, JWater = 1 m/s, parameter: average volumetric gas fraction [%]).

Fig. 13. Evolution of the bubble size distribution along the vertical tube, JWater = 1 m/s, JAir = 0.5 m/s, gas injection through 8 orifices of ⭋4 mm in the wall.

4.5. Distortion of the bubble size distribution by the wire-mesh sensor The observations of the bubble breakdown in the mesh of the sensor (Fig. 3) caused us to check the influence of a wire-mesh sensor to the signal of a second one placed behind it by a small distance. Two sensors were operated in the test channel (Fig. 9), the distance

between the measuring planes was 35 mm. In Fig. 14 results are shown for two different situations: a bubble flow with about 13% gas fraction and a slug flow with approximately 30% gas fraction. Both gas fractions were realised by different combinations of the superficial velocities, i.e. at different mixture velocities. It was expected that the bubble size distribution measured by the two sensors would differ significantly. In

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Fig. 14. Effect of a wire-mesh sensor on the bubble size distribution, vertical tube, ⭋51.2 mm, distance between air injection and sensor H = 3033 mm, air injected through 19 tubules equally distributed over the tube cross section.

fact, the bubble break down in the first sensor caused a shift of the bubble size distribution to smaller diameters (Fig. 14). Nevertheless, both distributions are still quite close to each other. The characteristic shape of the distribution remains unchanged. The most intensive influence of the first sensor on the signal of the second one was found at the lowest superficial velocities investigated.

5. Conclusion The wire-mesh sensor provides detailed information about the structure of the two-phase flow. It is successfully used to visualise the air-water flow in a vertical pipeline. From the primary measuring data it is possible to obtain void fraction profiles as well as bubble size distributions. It was shown that the sensor causes a significant fragmentation of bubbles. Nevertheless, the measured signals still represent the structure of the twophase flow before it is disturbed by the sensor. Moreover, bubble size distributions measured by two sensors put one behind the other, differ only slightly. Measured bubble sizes are in a satisfactory agreement to reference measurements carried out by a high-speed video device. Experiments were carried out in a vertical tube to study the evolution of the flow structure with growing distance from the gas injection. The bubble size distributions clearly show the effect of coalescence and fragmentation.

Acknowledgements The author would like to express special thanks to Mr D. Baldauf for the skilful work of constructing and manufacturing the transparent test channel.

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