Investigation of single bubbles rising in narrow rectangular channels with Particle Image Velocimetry Lutz Böhm 1,*, Matthias Kraume 1 1: Chair of Chemical and Process Engineering, Technische Universität Berlin, Berlin, Germany * correspondent author: lutz.boehm@tu-berlin.de Abstract This article deals with the fundamental PIV investigation of the rise of a single bubble in a rectangular channel with a channel depth in the range of the bubble size. A planar 2D PIV system from LaVision is used with a 5M camera and a recording frequency of 15z in maximum. Two acrylic glass channels with different channel depths (5mm and 7mm) were constructed and the bubble size was varied (3-7mm). The system is fully automated to create a large number of single bubbles on a high level of repeatability. The camera is set to two different positions with a 90 angle to be able to investigate the vector and scalar fields for images taken of the long and the short edge. Especially the investigation of the short edge proved to be fairly complex as the oscillating movement normal to the short edge in combination with a fixed position of the laser sheet makes it rather hard to get proper images of the bubble. The focus here is on the rising path and shape of the bubble, the velocity field and the vorticity induced by the bubble. The results for the camera position normal to the long edge are comparable to the literature dealing with free rising bubbles. An oscillating movement of the bubble is found which results in a serpentine like rising path. This is further explained with clockwise and anti-clockwise rotating eddies in the wake of the bubble. The results for the camera position normal to the short edge show an oscillating movement for a bubble smaller than the channel depth as well but at the same time the development of the eddies in the wake seems to be hindered by the close walls. 1. Introduction The detachment of deposition layers on flat sheet membrane surfaces with the help of aeration motivates the investigation of the rise of single bubbles in a narrow rectangular channel whereas the equivalent bubble diameter is in the range of the gap distance. The focus of this work is on the general flow behavior and the shear stress on the walls induced by the bubbles. The shear stresses are the crucial factor in the cleaning process of the membrane surface. Several groups investigated the rise of single bubbles with the help of PIV in the last 15 years. Tokuhiro et al. and Fujiwara et al. [Tokuhiro et al.1998, Fujiwara et al.2000, Fujiwara et al.2003, Fujiwara et al.2004] investigated the rise of a single bubble in a rectangular channel whereas one of the wall was a downwards moving belt which induced a shear flow in the system. Brücker [Brücker1999] investigated a bubble in a comparable system without a shear flow and gave a comprehensive explanation of the oscillating movement of the bubble which he explained with the hairpin-like vortex in the wake of the bubble. Several other authors [Funfschilling and Li2001, Liu et al.2005, Sakakibara et al.2007, Saito et al.2010] also investigated comparable systems and varied several properties such as viscosity of the liquid (even using a non-newtonian fluid) and surfactant concentration. The authors analyzed several bubble and turbulence properties. Two groups investigated systems which had constricted geometries that affected the rise of the bubble whereas one [Ortiz-Villafuerte et al.2000, assan et al.2001] had a cylindrical channel and the other [Sathe et al.2010, Sathe et al.2011] used a rectangular channel (channel depth 15mm). As the motivating system for this investigation is a flat sheet membrane module, a system with rectangular channels and a channel depth of 10mm in maximum is of interest. To the knowledge of the author such a system has not been investigated with the help of PIV yet. - 1 -
nitrogen pump of the thermostate TI 101 105 102 TCI 100 UYS 119 LIS 107 bubble separator tank for the electrolytic solution 106 flow channel 103 104 LIZL 110 servomotor M bubble cup syringe pump volume of the syringe UYS 119 EU 116 108 GR 113 115 114 UYS 119 F 118 LZL 117 122 F flow meter centrifugal pump FCRI 112 Figure 1: Flow sheet of the experimental rig (the red cuboid in the flow channel indicates the position of Fig.2) 2. Materials and Methods 2.1 The experimental rig The three parameters channel depth (5-7mm), bubble size (3-9mm) and superimposed liquid velocity (0-20cm/s) can be varied in this investigation although the results shown here are all without superimposed liquid velocity. Rectangular acrylic glass channels with different channel depths were constructed. The width is 160mm and the height is 1500mm. At the bottom of the channel the needle of a 50ml amilton Gastight syringe can be inserted into the channel through a septum. The syringe is operated with a arvard Apparatus Pump 11 Elite syringe pump which injects a specific volume of gas into a small cup which is fixed on a rotatable rod. This rotatable rod can be turned with a servo motor which again is located outside of the channel. Additionally inlets - 2 -
are located at the bottom of the channel through which liquid can be pumped with a defined volume flow. The system is automated with LabVIEW so that the whole process of establishing a defined liquid volume flow, inserting a bubble, releasing a bubble and recording the measurement data works automatically (Fig. 1). The automation allows a high-level of repeatability which simplifies the analysis of the data. 2.2 The PIV system The system used for this study is a FlowMaster 2D-PIV system from LaVision. It consists of a pulsed Nd:YAG Laser with a maximum double pulse rate of 15z. The images are recorded with a progressive-scan Imager Pro SX 5M CCD camera with a 12bit range and a resolution of 2456 pixel by 2058 pixel. LaVision s DaVis 8 is used for the data analysis. As the experiments are done with a multiphase flow, fluorescent particles and a cut-off filter for the lens are used to ensure that the CCD chip will not be destroyed by laser reflections from the bubble s surface. The system is investigated from two sides (Fig.2). The long (plane 1) and the short edge (plane 2) of the channel is of interest to get a general understanding of the 3D rising behavior. channel width channel depth 1 exemplary rising path rising bubble 2 y z x Figure 2: The two investigated cutting planes for the investigation of the long edge (1) and the short edge of the channel (2) - 3 -
3. Results and Discussions 3.1 Results from the long edge (plane 1) The first part of this investigation deals with the general flow behavior of bubbles rising in rectangular channels. For this, the laser is set to plane 1 (see Fig.2) and the camera is set normal to the long edge. Basic flow patterns as can be found in Figure 3 can be observed from this point of view. Two PIV analyses of the same double image are shown. The left image has a more coarse grid of interrogation windows (48x48px²) which allows a rough qualitative interpretation of the flow pattern. In the frame shown here approximately six eddies are visible in the wake of the bubble of which three are on the left side in the wake with a clockwise direction and three eddies are on the right side with an anti-clockwise direction. As it is expected, the oscillation of the bubble leads to a periodic detachment of eddies which explains their staggered appearance and therefore the typical pattern of a Kármán vortex street. Though having an almost constantly located rotational center y x Figure 3: One double image analyzed with a 48x48px² single pass (left) and a multipass algorithm with decreasing interrogation window size (right), each with the original frame 0 of the double image in the background (channel depth 5mm, bubble size 5mm) - 4 -
y x Figure 4: Rising path of a 3mm (left), 5mm (center) and 7mm (right) bubble in a channel with a depth of 5mm recorded with a frequency of 15z over time, with increasing eddy age, the rotational area of each eddy increases and the macroscopic rotational speed decreases. The right image in Figure 3 shows the result of the same double frame with a multipass analysis (interrogation window size from 96x96px² down to 24x24px², 50% overlap) which allows the visualization of a more precise vector field. Especially the central wake has a higher resolution. The interesting point here is that the birth of a new eddy is visible at the right edge of the bubble. The bubble is approximately at the point at which it has the highest angel relative to the y-direction and therefore it is in the middle of the two inversion points. An uneven pressure distribution and therefore a bubble shape deformation are co-acting with the vortex shedding [Brücker1999]. The effect of this vortex shedding is shown in Figure 4. The rising paths of three different bubble sizes are shown for a channel with a depth of 5mm. The three images shown here are put together from separate consecutive images for each recording series. Due to the limitations regarding the recording frequency the rising path cannot be resolved precisely. Still the periodicity is visible as depending on the bubble size approximately every third to fourth bubble image is almost similar. The most emphasized bubble shape deformation and rising path oscillation is visible for the 7mm bubble. For the 3mm bubble the oscillation is less emphasized. On the one - 5 -
Vorticity [1/s] y x Figure 5: Vorticity patterns for a 3mm (left), 5mm (center) and 7mm (right) bubble in a channel with a depth of 5mm hand side, this is due to the smaller amplitude of the oscillation and on the other hand the investigation of the rise of several 3mm bubble showed the effect that the oscillation was not similar for the different bubbles. Looking at the fluid particle shape map in Clift et al. [Clift et al.1978], the 3mm bubble is in the range of the boundary line between a spherical and a wobbling shape. Therefore it cannot be predicted if the bubble will oscillate at all or not. Another property to describe the oscillation and the according vortex shedding is the vorticity. This property is shown in Figure 5 for the three different bubble sizes. ere in comparison to the flow patterns shown in Figure 3, it is even more clear to see the counter-rotating eddies on each side of the bubble wake visualized by the color red and blue for clockwise and anti-clockwise rotational direction. Additionally the information can be extracted from the images that the vorticity value range roughly doubles and the area affected by the bubble massively increases with increasing bubble diameter. 3.2 Results from the short edge (plane 2) The second part of this investigation deals with the general flow behavior of bubbles rising in rectangular channels with a special interest in the behavior in confined geometries. Although the same geometry is used as in section 3.1, the results for the long edge are basically according to results for free rising bubbles as the bubble is free to oscillate in the x-y-plane. For the short edge investigation, the laser is set to plane 2 (see Fig.2) and the camera is set normal to the short edge. For all parameter combinations the walls have a strong effect on the bubble behavior in comparison to unconfined geometries. It is worth mentioning here that the movement in the x-y-plane is responsible for a problem in the investigation of the y-z-plane. As the laser sheet is fixed at one position, depending on the amplitude of the bubble oscillation the centroid of the bubble will move out of this plane and the bubble will therefore be cut at different positions or even will not be cut by - 6 -
Vorticity [1/s] y z a) b) c) d) Figure 6: a) Rising path, b) original image used for the vector and scalar field, c) flow pattern and d) vorticity for recordings of the short edge (channel depth 7mm, bubble size 3mm) - 7 -
laser plane at all. In Figure 6a in the image showing the rising path this is the reason why no bubble is visible at a y-position of 30mm and 165mm. Still a differentiation can be done for the parameter combinations with a bubble diameter smaller than the channel depth and the parameter combinations with a bubble diameter equal or larger than the channel depth. For a bubble size smaller than the channel depth one example is shown in Figure 6. Although the geometry confines the potential rising path still an oscillation of the bubble and therefore a movement of the bubble normal to the wall is visible. It is expected that this oscillation is according to a shape deformation as shown for the x-y-plane but due to the problem of the x-y-plane oscillation the different bubble shapes (e.g. visible in Fig. 6a) cannot solely be assigned to the bubble shape deformation but also to the different cutting planes. The effect of the oscillation is also visualized by the flow pattern where the serpentine like flow structure below the bubble is illustrated (Fig.6c). Unlike the flow pattern in the x-y-plane eddies are not visible. If in such a confined geometry the hairpin-vortex mentioned above for unconfined geometries would be apparent as well, eddies should be visible. There are two possible explanations for the lack of eddies in this image. Either the resolution of the image is not high enough so that small eddies cannot be visualized or the creation of the eddies is hindered by the small available space. as Looking at the vorticity plot in Figure 6d, a fairly high vorticity is apparent in the system. This indicates the potential of the flow which is blocked by the walls. Again vorticities of alternating prefixes can be found in y-direction although here these are not strictly separated by a serpentine like center line as it was found in the x-y-plane. For bubble sizes equal or larger than the channel depth (not shown here) the oscillation in the y-zplane is not as pronounced. Still a bubble shape deformation will happen but this property is not further investigated here. 4. Conclusions This article deals with the fundamental PIV investigation of the rise of a single bubble in a rectangular channel with a channel depth in the range of the bubble size resulting in vector and scalar fields for images taken of the long and the short edge. The focus here is on the rising path and shape of the bubble, the velocity field and the vorticity induced by the bubble. The results for the camera position normal to the long edge are according to findings for free rising bubbles. An oscillating movement of the bubble is found which results in a serpentine like rising path. This is further explained with clockwise and anti-clockwise rotating eddies in the wake of the bubble. The results for the camera position normal to the short edge show an oscillating movement for a bubble smaller than the channel depth as well but at the same time the development of the eddies in the wake seems to be hindered by the close walls. In the future further experiments will be done to quantify the flow properties mentioned above. Additionally a high speed camera will be used to investigate properties such as the rising path and bubble shape in more detail as for these the direct knowledge of liquid flow around the bubble is not necessary and especially a higher recording frequency can be reached which is important to properly reconstruct the bubble behavior regarding these properties. - 8 -
References Brücker, C. (1999). Structure and dynamics of the wake of bubbles and its relevance for bubble interaction. Phys. Fluids, 11(7):1781 1796. Clift, R., Grace, J., and Weber, M. (1978). Bubbles, Drops and Particles. Academic Press, New York. Fujiwara, A., Danmoto, Y., and ishida, K. (2003). Bubble deformation and surrounding flow structure measured by PIV/LIF and shadow image technique. In ASME Conference Proceedings, 1323 1324. Fujiwara, A., Danmoto, Y., ishida, K., and Maeda, M. (2004). Bubble deformation and flow structure measured by double shadow images and PIV/LIF. Exp. Fluids, 36:157 165. Fujiwara, A., Tokuhiro, A., and ishida, K. (2000). Application of PIV/LIF and shadow-image to a bubble rising in a linear shear flow field. In Proc 10th international symposium on applications of laser technique to fluid mechanics, 38, 2. Funfschilling, D. and Li,. Z. (2001). Flow of non-newtonian fluids around bubbles: PIV measurements and birefringence visualisation. Chem. Eng. Sci., 56(3):1137 1141. assan, Y.-A., Ortiz-Villafuerte, J., and Schmidl, W.-D. (2001). Three-dimensional measurements of single bubble dynamics in a small diameter pipe using stereoscopic particle image velocimetry. Int. J. Multiphase Flow, 27(5):817 842. Liu, Z., Zheng, Y., Jia, L., and Zhang, Q. (2005). Study of bubble induced flow structure using PIV. Chem. Eng. Sci., 60(13):3537 3552. Ortiz-Villafuerte, J., Schmidl, W. D., and assan, Y. A. (2000). Three-dimensional PTV study of the surrounding flow and wake of a bubble rising in a stagnant liquid. Exp. Fluids, 29:202 210. Saito, T., Sakakibara, K., Miyamoto, Y., and Yamada, M. (2010). A study of surfactant effects on the liquid-phase motion around a zigzagging-ascent bubble using a recursive cross-correlation PIV. Chem. Eng. J., 158(1):39 50. Sakakibara, K., Yamada, M., Miyamoto, Y., and Saito, T. (2007). Measurement of the surrounding liquid motion of a single rising bubble using a dual-camera piv system. Flow Meas. Instrum., 18(5-6):211 215. Sathe, M. J., Mathpati, C. S., Deshpande, S. S., Khan, Z., Ekambara, K., and Joshi, J. B. (2011). Investigation of flow structures and transport phenomena in bubble columns using particle image velocimetry and miniature pressure sensors. Chem. Eng. Sci., 66(14):3087 3107. Sathe, M. J., Thaker, I.., Strand, T. E., and Joshi, J. B. (2010). Advanced PIV/LIF and shadowgraphy system to visualize flow structure in two-phase bubbly flows. Chem. Eng. Sci., 65(8):2431 2442. Tokuhiro, A., Maekawa, M., Iizuka, K., ishida, K., and Maeda, M. (1998). Turbulent flow past a bubble and an ellipsoid using shadow-image and piv techniques. Int. J. Multiphase Flow, 24(8):1383 1406. Acknowledgements This work was financially supported by DAAD D/10/46059, DFG KR 1639/18-1 and DFG SFB/TR63 inprompt. During the experiments I was supported by Eva Lenhart. - 9 -