Figure 2: Principle of GPVS and ILIDS.

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1 Summary Bubbly flows appear in many industrial applications. In electrochemistry, bubbles emerge on the electrodes in e.g. hydrolysis of water, the production of chloride and as a side-reaction in metal plating. Bubbles also appear in the continuous casting of steel, waste water treatment, fermentation processes and many other domains. All of these industries benefit from advances in the experimental bubble measurement devices they use to characterise the bubbly flow. For measuring the diameter and velocity of these gas bubbles, a non-intrusive, planar measuring technique is preferably used. These techniques have the advantage that they do not disturb the flow and they can provide a spatial overview (e.g. of an entire electrode) with a single measurement. The most common 2D optical technique that satisfies these criteria is backlighting (or shadowgraphy). Here, the bubbles are illuminated from the back and their shadow is recorded by a camera (figure 1(a)). This technique has several disadvantages though. The most important one being that all the bubbles between the light source and the camera are imaged. Therefore, one does not know the distance between the bubble and the camera precisely. As the magnification of the camera depends on this distance (in general), sizing errors are the inevitable result. Figure 1: The five optical 2D measuring techniques that were investigated in this thesis, illustrated on a single bubble (a) Backlighting (b) ILIDS (c) GPVS (d) Glare Circles (e) LMS xix

2 Figure 2: Principle of GPVS and ILIDS. Another technique, called Interferometric Laser Imaging for Droplet Sizing (ILIDS), was developed over 20 years ago but is recently becoming a serious competitor for measuring spherical droplets (Koenig et al. [1986], Ragucci et al. [1990], Glover et al. [1995]). In this technique, a laser-sheet is created and placed at an angle with the viewing direction of the camera. Only droplets in this plane (of several mm thick) are imaged by the camera and therefore, the above mentioned issue with backlighting is almost absent here. ILIDS is based on the fact that light that is scattered towards the camera is coming from specific points on the droplet surface; the so-called glare points. Although this technique was developed for droplets, the principle is illustrated on bubbles in figure 2. This figure shows that when these glare points are imaged outfocus, an interference pattern as shown in figure 2 (and 1(b)) emerges. The frequency of this interference pattern is used to size the bubble. In a technique closely related to ILIDS, the camera is placed in-focus and only two glare points are visible as shown in figure 2 and 1(c). As demonstrated by Hess [1998], the distance between these glare points can also be used to size the bubble. Throughout the text, this technique will be denoted by Glare Point Velocimetry and Sizing (GPVS). However, these optical techniques were mainly developed for droplets. Because measuring bubbles is that important for e.g. the electrochemical industry, Note that other interaction orders also reach the camera but these have a significantly lower intensity and are therefore not visible in the image (or at least for the shown position of the camera). xx

3 the main goal of this thesis was to develop non-intrusive 2D optical techniques for bubble sizing. As the investigation of ILIDS on droplets had already shown that this technique (and GPVS) has many advantages compared to backlighting, the original aim was to investigate how the measuring principles of GPVS and ILIDS could be transferred to measuring gas bubbles. The first results in this respect were reported in Dehaeck et al. [2005] (chapter 3). Here, three new configurations were proposed to measure bubbles with GPVS (including the one of figure 2). It was shown numerically how these configurations were more accurate, applicable in larger bubble concentrations and lead to smaller velocity errors than the only configuration known at this time for the measurement of bubbles with ILIDS (Niwa et al. [2000]). In one of these configurations, a second laser-sheet was used that is opposed to the original one, which creates a third glare point. With this extra information it is possible to measure the refractive index of the liquid, as was shown experimentally. This extra point can also be used to detect non-spherical bubbles. This is vital as numerical simulations have showed that the sizing error on bubbles with a non-sphericity of 10% can go up to 16%! With the proposed configuration, this error can be reduced to approximately 4%. Chapter 4 then investigates how to implement these improvements in GPVS to bubble measurements with ILIDS (a combination of Dehaeck and van Beeck [2007d] and Dehaeck and van Beeck [2007e]). This resulted in a new ILIDS configuration in which the same non-sphericity detection is achieved with a single laser-sheet. Next to this, a complete uncertainty analysis of ILIDS was performed for the first time, both for bubbles and droplets. One of the innovative results here was that the sizing error for measuring non-spherical droplets (of 10%) can go up to 5.5% (appendix B). This analysis also showed that the calibration of ILIDS is one of its most important error sources. This fact is relatively unknown in the ILIDS community as most researchers do not mention their calibration procedure, nor the associated uncertainty. To clarify the differences in the various calibration procedures, they were compared theoretically and experimentally. Based on this analysis, it was shown how to optimise the calibration. As the original goals, i.e. develop new configurations for sizing bubbles with GPVS and ILIDS, were reached in the two previous chapters, other techniques were also investigated or newly developed in the remainder. In this respect, chapter 5 (based on Dehaeck and van Beeck [2007a]) introduces a novel image processing algorithm, which can detect ellipsoidal shadows of a variable size in an image (e.g. figure 1(a)). To this end, the algorithm of Rad et al. [2003], xxi

4 which was already capable of detecting circles, was extended to detect ellipses and made considerably faster. Chapter 6 (based on Dehaeck and van Beeck [2007b]) investigates the appearance of bright circles inside the shadows of bubbles as shown on figure 1(d). It will be demonstrated how these circles are also caused by glare points. In fact, the appearance of these glare circles was already predicted theoretically by van de Hulst and Wang [1991] and Bongiovanni et al. [1997]. However, experimental results and the idea to use them to measure the diameter and refractive index of the bubble has not been demonstrated so far (to our knowledge). Next to an analytical derivation of the necessary formulae, we show experimentally that bubble diameter measurements based on this glare circle are approximately one order of magnitude more precise. However, perhaps more interesting is the application of this glare circle to measure the refractive index of the surrounding liquid. We demonstrated how to obtain this quantity accurate up to the second decimal without the need for a calibration! In chapter 7 (based on Dehaeck and van Beeck [2007c]), another improvement of regular backlighting is introduced: Laser Marked Shadowgraphy (LMS). This technique is a combination of backlighting and GPVS (figure 1(e)). In this way, backlighting benefits of the good localisation of the measurement volume offered by the laser-sheet. This decreases the sizing error caused by the uncertainty in the distance bubble-camera. It also avoids the sizing of outfocus bubbles. We showed experimentally how regular backlighting could lead to sizing errors of up to 20% due to the sizing of out-focus bubbles whereas LMS can limit this error to 1%. Nevertheless, sizing spherical bubbles is done preferably with GPVS due to the increased precision it brings. Now, GPVS also benefits from the collaboration with backlighting as the presence of the circular shadows makes the image processing more robust. This is because a black circle with two bright points at specific locations is a much stronger signature than just two glare points that should be at the same pixel row. This technique was then applied to measure bubble diameter distributions in an electrochemical reactor. Now, the only piece of the puzzle that is missing is a good calibration method for the in-focus techniques (GPVS, backlighting, glare circle sizing and LMS). This is remedied in chapter 8 in which an algorithm based on the Fourier transform is proposed. Experiments have shown that this technique is capable of calibrating targets that are placed at an angle with the viewing direction of the camera, a situation quite common in GPVS. The resulting change in the magnification across the field of view (caused by the varying distance bubblexxii

5 camera) can be measured and used as a calibration curve to obtain more accurate results. Finally, in chapter 9, the introduced techniques are compared on the basis of working domain (stand-off distance of the camera versus the bubble diameter), precision and achievable void fraction. These comparisons showed that each presented technique has its own preferred working domain. Thus, the following guidelines were extracted concerning which 2D optical technique to use in a given situation: When the bubbles are not spherical (i.e. larger than 1mm) the choice is clear: LMS. This technique was introduced in chapter 7 and is the only technique able to obtain quantitative data in this case. Backlighting can provide this information as well, but its measurement volume is not welldefined. As a result, void fraction measurements are inaccurate and outfocus bubbles are measured as well, which leads to large measurement errors. Note that in some occasions, the localisation can be provided by the experimental set-up, e.g. bubble formation on a single needle, in which case regular backlighting is sufficient. When the bubbles are spherical there are different possibilities. When the diameter distribution of a dilute cloud of micro-bubbles (<0.5mm) should be measured, the ILIDS configuration suggested in chapter 4 is probably the best option. With this technique, regular lenses can be used at a comfortable stand-off distance. However, one should take into account that velocity measurements and the localisation of the bubbles for the void fraction maps are one order of magnitude less accurate than the bubble diameter. When the void fraction in the bubble cloud is too large to avoid overlapping images with ILIDS or when the velocity measurements should have a better resolution or when one needs to measure close to the wall, in-focus techniques are necessary. For moderate bubble concentrations, using LMS (chapter 7) provides the best compromise. The increased robustness of the image processing over regular GPVS is its main advantage. However, GPVS (chapter 3) still appears to be the best option to measure in high bubble concentrations. This is due to the fact that only those bubbles between the measurement volume and the lens are important and not the ones between the laser-sheet and the backlighting source as for LMS (and backlighting). xxiii