3. Experimental Techniques and Data Processing

Transcription

1 3. Experimental Techniques and Data Processing 3.1 Introduction The use of accurate and non-intrusive techniques in two-phase flow measurements assures that the results obtained correspond to the real situation for undisturbed flow. Data obtained in this way can be used with confidence for further model testing or model parameters fitting. This is the main reason why only non-intrusive techniques were used in the current work. This chapter should be understood as a reference of experimental techniques used in this work. Then, Chapters 4 and 5 will be devoted to the actual presentation and discussion of the experimental results. Therefore, the present chapter is a prerequisite to the following chapters and the reader should be always able to find here specific information or details concerning the experiment, reactor and flow loop design. A brief theoretical background for each data acquisition technique is given here, as well as, the description of the experimental procedures, data processing, statistical evaluation and uncertainty estimation. Furthermore, this chapter briefly compares the advantages and disadvantages of all employed techniques and it tries to give an overall outlook on the amount of experimental work carried out. Some of the techniques used in this work include new ideas and result from the improvement of previous work, particularly for the image processing and the

2 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 49 Laser Doppler Velocimetry (LDV) measurements. The techniques that are described in this chapter are following: image processing technique for standard imaging and also for BIV (bubble image velocimetry) and combined BIV-LIF (Laser Induced Fluorescence); pressure drop and pressure fluctuations measurements in single- and two-phase flow; Laser Doppler Velocimetry (LDV) in two-phase flow. In general, research work in two-phase flow starts with the determination of flow regime transitions, which in the present case, were identified in both the unpacked and the packed reactors. Visual observation of movies obtained by a standard Charge Coupled Device CCD camera was performed to identify flow patterns and to find the transitions between them. Since, visual observation is rather subjective and the transitions between two flow patterns are always spread off on a broad range of fluid velocities, the visual flow pattern determination has more an informative than a quantitative character. The main objective of image processing and bubble image velocimetry experiments was to obtain information about gas volume fraction, interfacial area and bubble velocities simultaneously with their size and shape characteristics. The image processing technique was used to collect the data from a broad range of gas and liquid velocities with the purpose to correlate the gas volume fraction and interfacial area for various flow regimes. Differently, the BIV measurements were carried out only in the bubble and slug regimes with the focus on bubble velocity and bubble size determination. Both methods provide relative accurate data especially in bubbly and slug regimes but certain assumptions have to be taken that will be discussed later. The combined BIV-LIF technique was used as an alternative to the BIV to demonstrate its feasibility in the 2D transparent system. This technique is based on the scanning of the light emitted by a fluorescent dye when illuminated with light of certain wavelength. In this way, better phase discrimination can be obtained than in the standard BIV technique. More details about BIV-LIF technique will be given later in this chapter. Pressure drop and pressure dynamics measurements were destined to provide data about local pressure drop in single- and two-phase flow in a rectangular channel. Moreover, gas averaged volume fraction can be extracted from this data for the flow in unpacked reactor. From the monitoring of pressure fluctuations at two different positions, bubble velocity can be calculated using cross-correlation techniques.

3 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 50 Finally, the LDV technique will provide information about the local mean liquid velocity together with the Reynolds stresses. From its nature, LDV is supposed to produce the highest accuracy data if compared to the other mentioned techniques. However, it is feasible only for bubbly and slug regimes due to the difficulties arising from the presence of an ambiguous signal coming from the gas-liquid interface. Even when using a gas phase discriminator technique that will be discussed later, measurements in the churn regime are difficult, because of the high complexity of the dynamics of this kind of flow regime. 3.2 Flow Loop and 2D Reactor Design In this section, the basic description of the flow loop and reactor are given. The flow loop is composed of a 2D acrylic reactor, a liquid reservoir, variable-area gas and liquid flowmeters, a liquid positive-displacement pump, an air compressor and tubing with all necessary fittings. All experiments were performed on an acrylic 2D reactor shown in Figure 3.1 where the left part of the image shows the 2D multiphase reactor and on the right part is shown the controlling equipment, such as flowmeters and regulation valves. In Figure 3.2, a schematic drawing of the flow loop, together with the different data acquisition channels for all experimental techniques is depicted. 1 Phase separator 2 Central reactor section 3 Bottom section with gas sparger 4 Gas flowmeters 5 Liquid flowmeters 6 Liquid reservoir Figure 3.1 Photograph of experimental set-up including the 2D gas-liquid reactor and its flow loop.

4 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 51 The 2D acrylic reactor is shown schematically in Figure 3.3. It is composed of three main parts: the bottom chamber with liquid inlet and gas sparger; the central section is the 2D reactor itself and consists of two parallel vertical transparent acrylic plates; and finally the upper chamber, which contains the gas-liquid separator. From the reactor design drawn in Figure 3.3, it can be seen that the interior of the bottom chamber is gradually narrowed towards the top in order to allow a smooth passage of fluids into the measuring central section. Just above the liquid entrance, a liquid deflector was placed to avoid discontinuities on the gas distribution. The gas was introduced through the sparger, an acrylic tube with 40 orifices of diameter m drilled at m equal spacing, covering the whole width of the bottom chamber. The sparger was aligned with the vertical axis of the central reactor section. This kind of perforated tubular sparger provides a reasonably uniform distribution of the gas phase across the measured section, although some maldistribution in the bubble concentration profiles were found at certain flow conditions particularly at small gas superficial velocities. Figure 3.2 Schematic drawing of the experimental set-up including the 2D reactor and its flow loop and the data acquisition equipment.

5 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 52 The central reactor section is composed from two rectangular acrylic plates of dimensions m. The plates are connected along the sides by means of two internal acrylic strips that define the column gap thickness. The strips were manufactured with precision (2.00±0.01) 10-3 m, that should ensure a constant and highly accurate value of the crosssection area at any downflow position. To study the effect of structured packing, the reactor may be filled with acrylic discs in 2D regular diamond-shape-pattern packing as shown in Figure 3.4. Packing particles of m thickness were manufactured by slicing a (10.0±0.1) 10-3 m diameter acrylic rod and were placed and glued to the back acrylic wall by using a computer-designed matrix. The horizontal distance between the centres of each particle is m and the vertical distance between two rows of particles is m, resulting in a bed porosity of ε p = 0.6. The accuracy of the particle position with respect to the designed pattern structure was kept within ± m. Figure 3.3 Detailed drawing of the 2D reactor: a) frontal view; b) side view.

6 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 53 The gas-liquid separator in the upper chamber was designed to maintain a stable level on the free liquid surface in order to avoid unwanted changes in the hydrostatic pressure inside the reactor. The upper chamber also includes a liquid shower and a gas inlet for future use in downflow regime. The acrylic liquid reservoir has a capacity of m 3 and together with the reactor and pump creates a closed loop designed to minimise external liquid contamination. The liquid phase was pumped using a magnetic-coupled positive displacement micropump (Pacific Scientific, model C) with an external rpm controller coupled to the computer, resulting in a constant and well-known liquid flow rate introduced to the flow loop. The micropump is capable to deliver m 3 /s of water and to develop maximum pressure Pa. The liquid flow rate can be also measured and controlled manually by means of variable-area flowmeters (Cole Parmer model 60648) that were used especially for calibration purposes. The precision of the flowmeters can be estimated as a 1% of the maximum. For the gas phase, filtered air is delivered by a compressor (Hydrovane, model HFP07) with a maximum capacity of Q G, max = m 3 /s air that allows to reach superficial gas velocities more than 2 m/s. The gas rate was measured and controlled by the set of three variable-area flowmeters (Gilmont, model GF-4540, Cole Parmer, model 60648). Figure 3.4 Photograph of central reactor section filled with structured packing.

7 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING Experimental Flow Ranges and Fluid s Physical Properties The experimental studies were conducted at steady-state flow conditions, for different pairs of liquid and gas fluxes for both the unpacked and the packed reactor. The ranges of liquid superficial velocity in the bed void space, U LS = Q L (ε P A cs ), and gas superficial velocity in the bed void space, U GS = Q G (ε P A c s ), are given in Table 3.1 for each individual experiment technique. Here, Q L and Q G are the liquid and gas flow rates, respectively, and A cs is the reactor cross-sectional area. The widest ranges of liquid and gas superficial velocities were used only for the image processing and pressure drop measurements. In the case of image processing, the chosen ranges of gas and liquid superficial velocities include bubbly, slug and churn regimes, and in the experiments with packing even annular flow patterns were observed. On the other hand, the LDV and pressure fluctuation experiments were carried out only in bubbly and slug regimes, due to the experimental difficulties encountered at high U GS. Tap water and filtered air were used as the working fluids at ambient pressure and airconditioning controlled temperature of (21±1) C. For the image processing and the BIV- LIF technique, a dye had to be added the liquid-phase to enhance the signal-to-noise ratio, i.e., to increase the contrast between the gas and liquid phases. Since the multiphase hydrodynamics parameters are highly sensitive to the physical properties of fluids, these parameters were measured for each set of experiments. The gasliquid surface tension, σ G L, was determined by means of a ring tensiometer (KRÜSS, model K6). This device determines the force needed to pull a platinum-iridium ring out from the solution. A set of ten measurements were performed and the mean value of these measurements was used. For the tap water and the water solution containing Rhodamine B value of σ G L = 7.2 ± 0.2 ( ) 10 2 J m 2 was obtained, but a different value was measured for the solution containing bromophenol sodium salt, where σ G L = ( 6.6 ± 0.2) 10 2 J m 2. Another parameter related to the surface forces effect, the air-water-acrylic contact angle, γ GLS, was measured. It was obtained by acquiring images of a stagnant liquid drop on an horizontal acrylic plate and the angle between the acrylic surface and gas-liquid boundary was determined by direct measuring, as shown in Figure 3.5. A value of γ GLS = ( 108 ± 2) o was obtained for all measured solutions, including solutions containing Rhodamine B and

8 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 55 bromophenol sodium salt. The viscosity of the liquid solutions was considered constant and equal µ L = Pa s. Figure 3.5 Example of an image for contact angle measurement. Table 3.1 Gas and liquid superficial velocity ranges used for each experimental technique. Technique Liquid phase U LS [m/s] U GS [m/s] No Packing With Packing No Packing With Packing Image Processing BIV BIV + LIF Tap water + 2 ppm bromophenol sodium salt Tap water Tap water + 2 ppm Rhodamine B Pressure Dynamics LDV Tap water Tap water

9 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING Acquisition Grids Obtaining experimental data at various spatial locations allows performing the accurate validation of simulation results and can be also used for the correlation purposes in future. Since gas-liquid flow patterns in the 2D reactor develop very quickly downstream, the data acquisition positional grid for all experimental techniques should be fine enough to cover most of the reactor sections, especially at the reactor bottom and top. Therefore, for profiling studies, the lateral spatial resolution with spacing close to 0.01 m was used. Since different acquisition techniques are being used, not all the measuring points coincide but the scanning axial positions for each technique were chosen to match as close as possible. Figure 3.6 shows the acquisition grids used for each experimental technique described below. A Cartesian coordinate system, with dimensionless coordinates X, Y and Z was used to describe the measuring positions with origin of the coordinate system located on the intersection of the column bottom edge and column centreline. The coordinates X, Y, and Z were normalised with respect to the half of the column width. Thus, the left column wall corresponds to Y = -1.0 and the top column edge lies on X =6.0. The scanning grids for each individual technique can be described as follows: The scanning grid used for image processing is shown in Figure 3.6 a. Images were acquired at four axial positions X = 0.7, 1.7, 2.9, and 4.8 and at three lateral locations Y = -0.75, -0.5, and encompassing the half of the column width. Due to a large range of U LS and U GS covered by this technique, images were acquired only in one half of the column width with the implicit assumption of flow axi-symmetry. In all the other experimental techniques, the profiling was done over the whole lateral profile. Figure 3.6b represents the scanning grit used in the BIV measurements that were performed at three axial positions X = 0.6, 3.0, and 5.5 representing the image centres. At each axial position, images were taken at three equally spaced lateral locations Y = -0.5, 0.0, and 0.5 to encompass the whole column width. As in the previous case, the scanning locations were partially overlapped. A similar acquisition grid was used in the BIV-LIF measurements. Bubble velocity measurements by pressure transducers were performed at practically the same downstream positions as in the imaging case covering the whole column

10 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 57 width. However, the gas volume fraction was scanned only in two sections at height of 0.2 m. The bottom section starts at the position X =1.0 and the upper one at the position X = 3. 5, as can be seen from Figure 3.6c. LDV data was acquired at five downstream positions X = 0.7, 1.5, 3.0, 4.5, and 5.5 and at 20 lateral measuring positions equally spaced by 0.01 m. For the packed reactor, a different scanning scheme was used in order to capture points both inside the channels formed by two neighbour particles and in the centres of chambers formed by four adjacent solid particles, as shown in Figure 3.6d. a) b) Figure 3.6 c) d) Experimental grid used at: a) imaging, b) BIV, c) pressure fluctuations measurements and d) LDV.

11 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING Imaging Two different imaging techniques were used in the experimental characterisation of the multiphase flow: standard imaging and Bubble Image Velocimetry. Regardless of their similar background, each of these two techniques uses different equipment and different data processing. Besides, the standard imaging technique was aimed to obtain the correlation between the gas volume fraction and interfacial area in broad range of flow conditions and the BIV was focused on the measurements of the bubble velocity and bubble size in bubbly and slug regimes. Because of these distinct differences, a separate description of each technique is necessary. In the next subsections, the description of data acquisition and data processing for the standard imaging technique is given Image Acquisition The standard imaging equipment consisted on a colour CCD camera (SONY, V800-E) positioned in front of the reactor, two halogen lamps, a light diffuser and a computer with a frame grabber board, as shown in Figure 3.1. The light from the halogen lamps, reflected from the diffuser situated about 0.3 m behind the reactor, produced well-dispersed and uniform background illumination. To obtain a high contrast between the liquid and gas phases, 2 ppm of bromophenol blue sodium salt dye was added to the tap water. Images, captured by the camera at shutter speed 1/10000 second, were digitised at a grabbing frequency 3 Hz. The size of each frame was pixels with a resolution of 8 pixels/mm. At each flow condition and local scanning position, an ensemble of 200 frames was digitised and analysed. This standard imaging technique was only used for the gas volume fraction and interfacial area measurements since the frame size was not large enough to perform accurate bubble size measurements. However, the later BIV experiments with the high-resolution PIV camera overcame this drawback, thus allowing the bubble size and bubble velocity measurements Image Processing The grabbed frames were analysed using a new image-processing algorithm written for NIH Image, a shareware software package for image processing. New features were developed and attached to NIH Image to enhance its performance for multiphase flow acquisition, namely: Euclidian distance map; pruning; feature-and; and hybrid median

12 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 59 filter. These processing algorithms and techniques are described in detail in Russ (1994) and were implemented in Pascal code compiled by Code Warrior (Metrowerks). A brief introduction and description of these algorithms is given in Appendix A. General use video cameras usually do not allow digitising captured frames with a colour resolution of 24 bits per pixel. Only expensive, special purpose scientific cameras have this option. Instead of 24-bit/pixel resolution, the so-called 8-bit pseudo-colour compression is often used. This compression is based on the analysis of the 256 most frequent colours occurring in the frame that are then used to code the colour information. Due to this 8-bit pseudo-colour image compression there are many noisy pixels (e.g. pixels that have different colour than the true one) scattered within the image and a colour diffusion near the object boundaries is observed. Therefore, it is very hard to identify small objects by simple thresholding of a pseudo-colour image or its HSI (hue-saturationintensity) equivalent. Moreover, the size of the larger objects determined in this way is considerably smaller than their true size. For the precise determination of the bubble shape, it is very useful to use the natural boundary of the bubbles, created by the light reflection and absorption on a bubble meniscus. Especially in the bubble regime, bubbles are clearly delineated by these boundaries. At higher flow rates, the bubble boundaries become blurred that sometimes results in the breaking of the boundary line and the loss of the information about the exact bubble shape. Due to the reasons mentioned above, the gas phase identification was conducted as a combination of two separate processes described in the next two sections: object (bubble) boundaries determination and fluid identification Identification of the Bubble Boundaries The eight main steps the of image processing algorithm are represented by the sequence of images shown in Figure 3.7. The grabbed image, such as the one shown in Figure 3.7a, is first converted to grey scale followed by the subtraction of the background image. The background image corresponds to the same window as the original one but without presence of gas phase. It was taken at the same light conditions and the same camera set-up as for the other frames used for analysis. It is normally used to correct a non-uniform background illumination. In the case of the packed column, in order to distinguish the fixed solid phase, a particle mask image, consisting of black packing particles, was also used.

13 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 60 To remove noise that does not belong to the bubble boundaries, the double thresholding combined with the feature-and algorithms were used (Appendix A). For this reason, the original image was duplicated and a copy, labelled image A, was filtered by the hybrid median filter. This filter is an efficient tool in removing randomly scattered noise smaller than half of the filter kernel diameter. In the next step, the image was threshold in such a way that only fragments of boundaries with the maximum pixel s value, i.e. black colour, representing boundaries were obtained as shown in Figure 3.7b. The original image, labelled image B, was also threshold but at a smaller threshold level than in previous case, with purpose to produce a complete delineation of the boundaries accepting some noise around, as indicated in Figure 3.7c. Then, the noise was slightly eliminated by an erosion algorithm where pixels with more than 6 white neighbours were cancelled. Finally, both original and copied images were combined by the feature-and algorithm. Objects from image A were used as markers to select only those objects from image B whose position match with those of markers. The resulting image shown in Figure 3.7d was then skeletonised to get single pixel edges. Free branches were pruned by repeatedly erasing any pixels that touch only one black pixel and the result is shown in Figure 3.7e Gas Phase Identification In the original acquired images, the bubbles are represented as white objects and the liquid phase by cyan colour. Therefore, a red filter can be used to enhance contrast between the two phases. Since cyan and red are complementary colours, the cyan colour is absorbed resulting in a dark grey colour. On the contrary, the white bubbles are well transmitted through the red filter so a relatively high contrast between the two phases can be obtained. Hence, the original image was electronically filtered by a red filter and smoothed. Then, the non-uniform illumination effect was removed by subtracting the background image, and the resulting image was then modified by the hybrid median filter to eliminate the noise. In the next step, the image was converted to a binary one and the result was eroded and dilated (see Russ, 1993) and it is shown in Figure 3.7f. This image was overlapped with the image obtained for edge detection (Figure 3.7e), and the result is shown in Figure 3.7g. The boundary detection method produces better defined objects than the gas phase identification method, but it is not capable to distinguish the difference between the phases.

14 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 61 a) b) c) d) e) f) g) h) Figure 3.7 Step-by-step example for the image processing algorithm.

15 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 62 A secondary drawback of the boundary detection algorithm appears to be the appearance of touching objects that may introduce errors in the quantitative analysis. Therefore, the objects in Figure 3.7g were completely filled with grey and the Euclidian distance map algorithm was applied to separate the touching objects. In this way, all touching objects were split and the effect of this operation together with the noise removal technique, described in the next section, can be seen in Figure 3.7h Noise Removal After image processing, some noise objects are often present because of a non-ideal threshold value or insufficient contrast between the measured bubbles and the background liquid. Since these objects are usually of small size and irregular shape they can be removed by size filtering or, in present case, by comparison of particular objects areas obtained by two different techniques. The drawback of this filtering process is that small bubbles may disappear from the analysis and large noise may not be filtered. By visual inspection of acquired images, the following criteria for noise filtering were chosen. All objects whose area delineated by the boundary detection procedure is smaller than 0.5 mm 2 are erased; all objects up to 1.5 mm 2 detected by this method are accepted. If the area of an object delineated by the boundary detection is greater than 1.5 mm 2, the area detected by the gas phase identification must be at least 20% of the area obtained by the boundary detection; otherwise, object is deleted. The first condition indicates that all objects with equivalent diameter d e < m are filtered out. This condition should not considerably affect the calculated gas volume fraction but it can affect the value of the interfacial area especially in churn flow regime where a large number of small bubbles is present Measured Gas Phase Parameters The above described image processing technique allowed the determination of two gas phase parameters: local gas volume fraction and interfacial area.

16 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 63 The determination of the gas volume fraction was based on the assumption that each bubble is a 2D thin object with an image projected area, A z, determined by the bubble perimeter, P z,i, and with a maximum thickness, δ, equal to the reactor gap size. If the liquid film surrounding the bubbles is neglected, (De Swart et al., 1996; Wilmarth and Ishii, 1997) for each image frame with N bubbles, the gas volume fraction can be calculated as ( ) 1 N A z, i α = W x W y (3.1) i=1 where W x and W y are image dimensions. The bubble interfacial area concentration was determined as a s = 2αδ 1 + W x W y ( ) 1 N P z, i (3.2) i=1 where the first term on the right side accounts for the area of all objects, projected in the frontal and rear directions, and the second term is the contributions from perimeters of the narrow objects. 3.6 Bubble Image Velocimetry The principle of this technique is similar to the image processing technique described before. The main difference is in the use of more sophisticated devices such as a pulsed light source and a high-resolution PIV camera. The PIV system allows measuring of bubble velocity and obtaining other parameters from enlarged images that improves the quality of the acquired frames and consequently the accuracy of the analysed data Experimental Set-Up The typical set-up for the BIV and the combined BIV-LIF techniques is presented in Figure 3.8. As the light source, the dual YAG laser (TSI, model Y12-15) with a maximum power of 12 mj per pulse was used. The use of two lasers gives essentially unlimited control of the time between pulses that allows measuring both very high and low velocities. It can operate at a repetition rate of double pulses up to 15 Hz. The outgoing

17 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 64 laser beam was diverged by means of a negative spherical lens and dispersed by the white photo reflector also used in the image processing technique. Figure 3.8 Schematic layout of the experimental set-up used for BIV-LIF. Better light dispersion and a practically uniform illumination was obtained by a white diffusive glass located behind the reactor. In this way, high quality frames were obtained and captured by the cross-correlation digital camera (TSI, model PIV 10-30) with a spatial resolution of pixels and a maximum frame rate of 30 frames per second. This technique has the capability to capture sequential frames with a very short time between them. These double images are digitised in real time and grabbed by the frame grabber (TSI, model ). For each flow condition, a set of 200 double-frames was captured with double frame frequency of 0.5 Hz. The separation time between two consecutive frames was set according to the fluids superficial velocity and it varied in the range from to 0.01 s. The YAG laser pulses and the camera exposure were synchronised by an external synchroniser (TSI, model ) controlled by a PC computer. The fluids used in these experiments were tap water and filtered air under ambient conditions. An example of an image obtained in this way is shown in Figure 3.9a. A second technique involving a variation of BIV combined with LIF is based on the use of a liquid containing fluorescent dye that when illuminated by a laser light of a certain

18 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 65 wavelength, emits a light of different wavelength, usually smaller. If a bandpass filter, which solely permits passage of the dye emitted light, is located in front of the camera lens, the light signal coming from the gas phase disappears. The resulting image is similar to that shown in Figure 3.9b. The shift in wavelengths between the excitation and the emitted lights must be sufficiently large to filter out the excitation light, so fluorescence dye Rhodamine B with concentration of 2 ppm was added to the tap water. Its extinction maximum is almost identical with the YAG laser light wavelength, which is m and the emitting maximum peaks close the m. Obviously, this phase discrimination facilitates image analysis, since only a minimum image processing is needed. This technique was used to demonstrate the feasibility of the laser-induced fluorescence in the BIV experiment and as a preliminary test for future use of fluorescent particles in PIV experiments. However, here the main result was the acquisition of twophase flow parameters, such as gas volume fraction and bubble size for the gas-liquid system with the liquid phase containing Rhodamine B. As it will be shown later, the addition of Rhodamine B has a profound effect on bubble coalescence rate and consequently on bubble size and its distribution. Figure 3.9 a) b) Typical images obtained with the PIV camera for: a) BIV and; b) BIV-LIF Data Processing As in the previous case, the NIH image software package was used to enhance and process the images. Data was taken only for the bubbly and slug regimes, where a relatively well defined bubble interface occur. Moreover, as can be seen from Figure 3.9a, the quality of the acquired images is adequate, with a good delineation of the bubble boundaries.

19 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 66 Therefore, the processing algorithm could be substantially simplified. First, the background and particle mask images were subtracted and the resulting image was automatically threshold. Then the dilation and erosion procedures were used to remove small noise particles and finally the images were analysed. Bubbles that intersected the image boundaries were not included for the bubble velocity and bubble size measurements. To measure the bubble velocity, it was necessary to determine the position of all bubbles inside a frame and found their corresponding counterparts in the consecutive frame. The corresponding bubbles in these two consecutive frames (called frame 1 and frame 2) were found in the following manner: i. the bubble geometric centres and the bubble areas were calculated for each bubble in frame 1 and in frame 2; ii. for each bubble in frame 1, all bubbles in frame 2 with geometric centres that lay within a certain radius scanning radius from the geometric centre of the bubble in frame 2 were searched; iii. the corresponding bubble pair was found by comparison of bubble sizes found in the previous step, the bubble in frame 2, whose size best matched the bubble size in the frame 1 was marked as the corresponding bubble pair. The scanning radius, in the previous step ii, was determined from the maximum assumed bubble velocity for a particular flow condition. In this way, typically only one or two bubbles were found in the frame 2 within the scanning radius. The bubble velocity was then calculated as of the difference between the geometric centres of the bubbles in frame 1 and in frame 2 divided by the pulse separation time. Simultaneously with the bubble velocity, the bubble diameter was measured for each bubble. In 3D columns, bubble diameter is usually defined as the mean volume-to-surface ratio and is known as the Sauter mean diameter. However, in 2D columns, it is useful to replace the Sauter mean diameter by the diameter of cylinder of volume equal to the bubble volume and length equal to the column gap, e.g., the area equivalent diameter, d e, as d e = 4A B π (3.3)

20 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 67 where A B is the bubble area measured by BIV technique. Besides the gas volume fraction and interfacial area, other bubble properties, concerning the bubble shape were determined. The bubble shape may be described by shape descriptors (Russ, 1993) each capturing some aspects of the shape but none in a unique way. By measuring the bubble area, A i, bubble perimeter, P z,i, bubble maximum and minimum diameter, d max and d min, the following three shape factors can be determined. The Form Factor, defined as Form Factor = 4πA i (3.4) 2 P z,i varies with the surface irregularities while the Aspect Ratio is obtained as a ratio of maximum to minimum diameters Aspect Ratio = d max d min (3.5) is a measure of the overall elongation. A third descriptor, the Roundness, indicates how much a bubble differs from circular shape and is defined as Roundness = 4 A i (3.6) 2 πd max 3.7 Pressure Dynamics Measurements In this section, the pressure technique, used for the total pressure drop, gas volume fraction and bubble velocity measurements, is described. Although similar equipment was used for the both measurements, the layout and arrangement of pressure transducers for the gas volume fraction measurements differs from the alignment used for the bubble velocity measurements. Therefore, they are described in two separate subsections Total Pressure Drop and Gas Volume Fraction Indirect measurements of the total pressure drop and gas volume fraction were carried out at two axial positions using two variable reluctance transducers (VALIDYNE, model DP- 15). These fast response transducers use interchangeable membranes that allow

21 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 68 measurements in various pressure ranges. For the gas volume fraction measurements, the diaphragms with working range from 0 to 8600 Pa were used. The diaphragms were calibrated for the experimental conditions with the transducers already in place. Care was taken to remove air from the tube and from the pressure cavities in order to avoid attenuation and non-linearity of the pressure signal. The transducers are excited by a 5 V rms 3 khz signal that was then demodulated by the carrier demodulator to DC analogue signal. This signal was passed to the 12 bit A/D board (National Instrument, model MIO- 16E) and processed by LabView software. All cables and wires were shielded to avoid additional noise from the external electrical circuits. The connections for one of the transducers used for the gas volume fraction measurements is depicted in Figure 3.10a. The two connections between the pressure transducer and the pressure taps were made of stainless steel tubes of internal diameter 10-3 m. In all the cases, the transducer bodies were positioned above the monitoring point because in this way, fewer bubbles enter the taps and removing of the bubbles that enter the tube is easier. These measurements were performed at two positions 0.15 and 0.45 m downstream from the column bottom that allows comparison with the results obtained by the imaging technique. In both cases, the distance between the pressure taps was 0.20 m. For each flow condition, the acquisition of 200 s of data track was performed at a sampling frequency of f s = 200 Hz Calculation of Gas Volume Fraction In case of gas volume fraction measurements, it was assumed that the average pressure difference, T p, measured by the transducers is solely the sum of the liquid single-phase frictional pressure drop, F p L, and the hydrostatic pressure drop of the gas-liquid mixture p T = p F L + d 1 2 g[ ρ L (1 α) + ρ G α] (3.7) where ρ L and ρ G are the liquid and the gas densities, d 1 2 is the distance between pressure taps, g is the gravitational acceleration, and α is the gas volume fraction. Once the total pressure drop is obtained from Equation 3.7, the gas volume fraction can be calculated as long as the reasonable estimate for the frictional pressure drop is know.

22 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 69 a) b) Figure 3.10 Pressure transducers alignment for: a) gas volume fraction measurements and; b) bubble velocity measurements. The liquid single-phase pressure drop is a function of mean liquid velocity, U = α, L U LS where U LS is the liquid superficial velocity. If the function F p = f ( U L ) (3.8) L is known from direct measurements in single-phase liquid flow, the gas volume fraction can be iteratively calculated as follows: a first estimate of the gas volume fraction is used to calculate the frictional pressure drop from Equation 3.7; then a new value of α is obtained from Equation 3.8. This process is repeated until a difference between the values of α in two consecutive iterations is within a certain limit (< ) Pressure Fluctuations and Bubble Velocity Measurements For the pressure fluctuations measurements, different membranes with working range from 0 up to 860 Pa and sensitivity close to 1 Pa were used. These highly sensitive membranes allow the detection of very small bubbles passing through the monitored section.

23 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 70 The transducer connections used for the bubble velocity measurements are depicted in Figure 3.10b, where the transducers are referred to as T I and T II. The differential transducer connection was chosen due to its better accuracy compared to absolute pressure measurements with one pressure chamber open to the atmosphere. Absolute pressure measurements have the advantage of no interference between signals coming from the upper and bottom pressure taps. On the other hand, the differential alignment allows measuring of bubble velocity in the particular reactor section and subtracts the noise coming from the fluid above this section. The upper reference taps 3 and 4 are situated close to the column wall where the bubble concentration is relatively small. In this way, the interference due to direct bubble traversing over the pressure tap is suppressed and only the signal coming from the upper reactor section is scanned most of the time. Pressure fluctuations measurements were carried out at three different vertical positions X =0.8, 3.0, and 4.8 and in a range of gas fluxes covering bubbly and slug regimes. The distance between the pressure taps was d 1 2 = m, which is a compromise between the measurement accuracy (the larger d 1 2, the better the accuracy) and the signal-to-noise ratio, which decreases with decreasing d 1 2. The sampling frequency, f S, for the bubble velocity measurements was set to 1000 Hz and a sample size of 16 kb was used that is equivalent to 16 s in track duration. Then, the cross correlation functions and the power spectra of 16 consecutive tracks were calculated and averaged. In this way, a total of 256 kb points were sampled and analysed corresponding to 260 s of track duration Cross-Correlation Function and Bubble Velocity The calculation of bubble velocities was based on cross-correlation techniques (Bendat and Piersol, 1969). From two pressure signals p I and p II, the cross-correlation function, R pi, p II, can be calculated. This function describes the dependence of one set of data on another set, thus it can be used to measure the time required for a signal to pass through a given system. An unbiased estimate of the cross-correlation function for two digitalized pressure signals, obtained at the sampling frequency f S, can be obtained from R PI,P II (n t ) = N n 1 p N n I (i) p II (i + n) (3.9) i=1

24 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 71 where p I ( i) and ( i n) p II + are the pressure signals at instants of time i t and ( i + n) t measured by T I and T II, respectively, N is number of data points in each waveform, t = 1 f is the time shift between two signals and n is the number of points expressing S the time slot between the two cross-correlated pressure signals. The mean bubble velocity, U G, can then be calculated from the time shift, function maximum occurs t peak, at which the cross-correlation U G = d 1 2 t peak (3.10) Power Spectra In the present work, the power spectrum of the pressure signal will be used to discuss different sources of oscillations in multiphase columns and to demonstrate its variations in different flow regimes. The power spectrum indicates how the energy is distributed over the frequencies, and was calculated using the Fast Fourier Transformation described, for example, by Bendat and Piersol (1969). The square of the real part of the Fast Fourier transform function is called the power spectrum and is defined as G x ( f S ) = 1 2π ( ) x(t)exp i2πft dt 2 (3.11) where f S means the signal frequency. 3.8 Laser Doppler Velocimetry The LDV technique was developed in the middle of the seventies (Durst et al. 1976) and it has been extensively improved during the last three decades. The theory behind this powerful technique is quite complex and received extensive attention in the last years. Currently, LDV systems involve sophisticated mainly electronic and optical components. More details of the LDV principles and description of each system component can be found elsewhere (TSI manuals, 1991). Here, the principle of this technique is briefly explained.

25 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING Description of Technique Usually, a laser source is used to produce a monochromatic and coherent light beam, which is collimated and then separated to two or four beams. These are then carried by optical equipment to the optical probe. Here, the beams are focused and crossed by transmitting optic into a small controlling volume in a distance equal to the focus distance of the transmitting optics. The crossing beams of the same wavelength create an interference pattern composed of planar layers of high and low intensity light, usually called fringes. When a moving particle passes through the fringes, it scatters light of a certain frequency called the Doppler frequency. This scattered light is proportional to the velocity of a particle crossing the controlling volume. The velocity normal to the fringes can be calculated from the frequency of the scattered light if the distance between fringes is known. Photo-detectors convert the received scattered light into an electrical-voltage signal using the photo-multiplier system. The typical voltage signal obtained from signal processor is composed of a Gaussian shape peak the pedestal and a number of smaller peaks imposed on it. The frequency of these smaller peaks, Doppler frequency, is determined by the velocity of the particle passing through the control volume. A basic LDV system cannot distinguish between forward or reverse flows and low velocity flows because the frequency of the signal goes to zero at zero velocity of a particle. The frequency shift eliminates this ambiguity by the superposition of a known frequency signal onto the main frequency for one of the beams of each colour. This is performed in the Bragg cell of the multicolour beam separator, in order to bring the measured frequency into the range of the signal processor and to resolve the directional ambiguity of a moving particle Experimental Set-Up The LDV system used in the present work operates in backscatter mode (the light is transmitted and received from the same optical probe) and two velocity components can be measured simultaneously. A schematic representation of the experimental set-up is presented in Figure 3.11 and two different views of the LDV equipment are shown in Figure 3.12 and Figure 3.13.

26 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 73 The laser beam produced by 5W Argon-Ion Laser (Coherent, Innova 305) was collimated and driven to the multicolour beam separator (TSI, Colorburst model 9802); by the two adjustable mirrors. In the beam separator, the laser beam was split into two green beams with wavelength λ= m, and two blue ones with λ= m. Figure 3.11 Experimental set-up used for LDV technique. These were focused to the optical couplers connected to the fibre-optical cables that carry the beams to the 82 mm optical probe (TSI, model 9253). The optical probe, which transmits the four laser beams and receives the scattered light, was mounted on an automatic 3D positioning system called a traverse table (TSI, ISEL). The traverse table allows automatic measurements on a pre-set grid by precise displacement of the optical probe. The scattered light captured by the optical probe is carried to the multicolour receiver (TSI, Colorlink 9230) where it is converted to the voltage signal. The signal processor (TSI, IFA 750) receives a voltage signal from the photo-multiplier system, and this signal is then filtered, analysed and converted into velocity information. The PC computer coupled with signal is used to collect velocity data and to provide complete velocity statistics for LDV data. In order to improve the signal-to-noise ratio and to increase the data rate, seeding particles are often used in LDV measurements. In order to properly describe the trajectory of fluid elements and not to disturb flow, the seeding particles should be neutrally buoyant, i.e., their density should be close to that of the liquid and the particle size should be as small as possible. On the other hand, they should be large enough to provide good quality Doppler

27 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 74 signal. Therefore, the particle size of the same order as fringe spacing appears to be a good compromise. As seeding particles, hollow glass spheres of mean diameter 10-5 m (Dantec, HGS-10) with density 1.05 kg/m 3, were added to the liquid phase to improve signal-to-noise ratio and data rate. 1 - Laser source (Argon-Ion, 5 watts) 2 Beam separator (TSI, Colorburst model 9802) 3 - Optical couplers (TSI, model 9271) Figure 3.12 Partial view on the LDV optical system. 83-mm optical probe (TSI, model 9253) mounted on traverse table 1 - Signal receiver (TSI, Colorlink 9230) 2 - Signal processor (TSI, IFA 750) 3 - IBM PC 350+ software (TSI, FFW 1.0) 4 - Oscilloscope (ITT, OX 750B) Figure 3.13 View of the LDV data acquisition system reprinted from Panacek, 1999)

28 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING Signal Discrimination in Multiphase Flow In two-phase flow, two different kinds of LDV signals can be encountered: one from the seeding particles and one from bubbles. The signal coming from the seeding particles is characterised by a well-known Gaussian pedestal plus a Doppler frequency imposed on it. The larger particles such as air bubbles reflect fringes that travel in space and these can be detected by the probe. The resulting signal has in principle similar characteristics to the previous case, except for the different amplitude. Since bubble interface works as a moving mirror, it reflects the laser beam and creates fringes moving in the space. In flat narrow columns, bubbles are strongly distorted by the presence of the reactor walls and their shape is similar to discs of rounded corners, i.e., its curvature is not constant along the surface. In this way, the information from the reflected signal is ambiguous and therefore it should be excluded from the measurement. Furthermore, a zero velocity signal may be present due to the displacement of the controlling volume in the gas phase. If a bubble passes through the controlling volume, the controlling volume is displaced due to the different refractive index of the gas phase. If the displacement is sufficiently large, the controlling volume intersects with the rear acrylic wall resulting in zero velocity signals due to its reflection from the wall. To avoid ambiguous signals coming from the gas-liquid interface or from the reflection from acrylic wall, a light detector positioned in the forward scattering direction was used. It consisted of a light attenuator, a fast response photo-diode (HAMAMATSU, model S1226), and an operational amplifier connected in a simple electronic circuit, which scheme is shown in Figure The analogue signal from the light detector was digitised and linked to the LDV signal processor. The decision criteria for bubble detection was set to 5% bellow the mean level of the light intensity detected if only the liquid phase is present. This ensured that the signal was triggered almost instantaneously after the bubble interface detection and on the other hand, small discrepancies in the light intensity were not confused with signals coming from bubbles. The photodiode response on the bubble presence was verified by the PIV camera whose shutter was triggered by the signal coming out from the photodiode. The image illustrated in Figure 3.15 confirms that the photodiode responds almost immediately to the passage of a bubble through the photodiode pinhole.

29 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 76 Figure 3.14 Scheme of electrical connection of photodiode and operational amplifier. Figure 3.15 Verification of photodiode trigger signal Experimental Procedure Two velocity components and Reynolds stresses values were collected for nine combinations of liquid and gas fluxes in bubbly and slug regimes. The hardware and software settings are also reported in Table 3.2. The hardware settings, band-pass filters and frequency shift, were adjusted according to the expected frequency of the Doppler signal, which depends on fluid velocity. This calculation was based on the expected average flow velocity and on the optical fringe spacing. The value of the expected Doppler frequency plus the frequency shift was then placed into the frequency limits of band-pass filters. For each set of flow conditions, a waveform of 5000 samples in coincidence mode was collected to calculate the average of the liquid velocity components and the corresponding Reynolds stresses. Taking U and V to be the instantaneous velocity components in the x

30 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 77 and y directions, respectively, the mean velocity components, U and V, have been calculated using the transit time weighting to correct for velocity bias: N U = U (i)τ burst (i) τ burst (i ) (3.12) i =1 N i=1 where N is the number of samples collected at each grid point and τ burst is the burst time for each sample. Table 3.2 Laser beam characteristics and LDV software settings Beam 1 Beam 2 Argon-Ion laser source: Nominal light power 2.5 W 2.5 W Wavelength in vacuum m m Beam diameter m m Beam distance leaving optics m m Half-angle of intersection in air Half-angle of intersection in water Scanning volume: Smaller semi-axis in water m m Larger semi-axis in water m m Fringe spacing in water m m Number of fringes in water Processor settings: Frequency shift at at U LS = 0.06 m/s 100 khz 100 khz U LS = 0.20 m/s 500 khz 500 khz Signal filter at U LS = 0.06 m/s khz khz at U LS = 0.20 m/s khz khz Signal-to-noise ratio 1 db 1 db Decomposing each instantaneous velocity component on its mean and its fluctuating part U =U + u and V = V + υ (3.13)

31 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 78 the normal Reynolds stresses ρ L u u and ρ L v v can be calculated in the following way ρ L u u = ρ L (UU U 2 ) and ρ L v v = ρ L (VV V 2 ) (3.14) where UU and VV were obtained from UU = N pts i U i ( ) 2 τ burst N pts τ burst i N pts and VV = V i i ( ) 2 τ burst N pts τ burst i (3.15) The tangential Reynolds stress ρ L u υ were obtained in similar way ρ L u υ = ρ L (UV U V ) (3.16) where UV is obtained from UV = N i N UV τ τ (3.17) overlap i overlap with the overlap time, τ overlap, being the smallest of the two measured burst times for each coincident detection of the two velocity components, U and V. 3.9 Specific Aspects of Statistical Data Analysis Statistical and uncertainty analysis is one of the most important parts for the description and evaluation of any experimental technique and procedure. It is sometimes surprising how little space is devoted to uncertainty analysis in scientific publications. This analysis is of great importance for the evaluation and comparison of different experimental techniques and plays an important role in the validation of new theoretical models and simulation results. To establish the experiment accuracy, all possible sources of uncertainty should be discussed. Usually, the uncertainties and errors of each experimental technique originate from instrumental inaccuracy and from the statistical processing of the measured data. The instruments uncertainty depends on many factors, such as: overall resolution and precision of the each system involved; calibration procedure; data storage; accuracy of measured secondary quantities; etc. The second source of uncertainty arises from the experimental procedures. Here, other parameters, such as the sample size, duration of data acquisition, sampling frequency and statistical methods used for data post-processing, are of great importance.

32 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING Uncertainty Analysis in Imaging and BIV Technique In this section, an attempt to estimate the accuracy of the imaging technique is presented. The error involved in neglecting of bubble transverse shape is evaluated and the evaluation of the confidence interval of the measured data is presented In the previous section, describing the image processing techniques, the calculations of gas volume fraction and interfacial area were based on the assumption that bubbles are thin disks of thickness equal to the column gap thickness. Since in these calculations the liquid film encompassing a bubble was neglected, the data obtained in this way is expected to be greater than the actual values and Equations 3.1 and 3.2 can only be viewed as two upper limit estimates for the values of α and a i. In order to elucidate how much space is actually occupied by a bubble in the narrow slot between the two plates, an analysis of the lateral bubble profiles was performed. To accomplish this task, one of the lateral acrylic bands, which normally define the gap thickness, was removed and the central part of the reactor was submerged into a large transparent tank filled with water. Then, a syringe was used to inject bubble of different sizes at the column bottom. The flow field was illuminated from the side by a laser sheet produced by the YAG laser and the images of rising bubbles were taken by the PIV camera. Figure 3.16a shows typical frontal and lateral views of bubbles larger than the reactor gap size. It is clearly shown in the lateral view that the bubbles do not encompass the entire reactor gap. Similar images for more than 100 single bubbles, rising in a stagnant liquid, of different sizes in the range from to m were analysed. It was found that the average value of the ratio between the area occupied by gas, A bubble, and the area of a rectangle given by the product of the bubble vertical size, given by d x, and gap thickness δ is Abubble Cα = 0.69 ± 0.03 (3.18) δd x This value is slightly higher than the geometrical ratio of 0.65 suggested by Mishima et al. (1988). The dependence of the correction factor C α on the bubble length measured in stagnant liquid is illustrated on Figure 3.16b. It can be seen that C α does not vary significantly for bubble sizes greater than the reactor gap, hence its mean value can be used

33 EXPERIMENTAL TECHNIQUES AND DATA PROCESSING 80 as a good estimate for the correction factor of the gas volume fraction with relative error less then 5%. The data for the interfacial area concentration was corrected in a similar way based on geometrical considerations. The estimation of the correction factor was based on the assumption that bubbles retained the shape of a rotational ellipsoid with semi-axis defined by the bubble chord length, d x, and the gap thickness, δ. Then the ratio of the surface area of the rotational ellipsoid to the area of the cylinder defined by the gap thickness and bubble chord length gives the estimation of the correction factor as C a = A ellipsoid πδd x 0.77 ± 0.03 (3.19) A second source of uncertainty arises from the estimation of the mean value of the measured parameters such as gas volume fraction, interfacial area and bubble size. The variation of gas volume fraction and other related parameters with respect to time appears quite random and chaotic, since it depends on many parameters such as the distributor properties and the bubble-bubble interactions C d X [mm] Figure 3.16 a) b) Bubbles of different sizes and: a) their frontal and lateral views in a stagnant liquid; b) correction factor C α as a function of bubble vertical size.