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bubble motion and turbulence around it by hybrid PIV
Flow Measurement and Instrumentation 12 (2002) 421–428 www.elsevier.com/locate/flowmeasinst
Measurement of particle/bubble motion and turbulence around it by hybrid PIV H.M. Choi a
a, b,*
, T. Kurihara
1,b
, H. Monji1 b, G. Matsui1
b
Fluid Flow Group, Korea Research Institute of Standards and Science, P.O. Box 102, Yusong, Daejeon, 305-606, South Korea b Institute of Engineering Mechanics and System, University of Tsukuba, Tsukuba, 305-8573, Japan Received 1 March 2001; received in revised form 9 July 2001; accepted 10 September 2001
Abstract Characteristics of bubble flow are influenced by bubble motion, liquid flow and interactions between bubbles, and between a bubble and liquid phase. Thus because behavior of a single bubble and liquid around it is regarded as one of the basic elements characterizing bubble flow, the single bubble motion in stagnant water was investigated experimentally by using flow visualization and image processing methods. The bubble motion is influenced by several factors, that is, bubble size, density difference between gas and liquid, bubble shape and deformation in motion. In order to separate the effect of each factor, some solid particles with different size, shape and/or density were also measured and the characteristic of each factor was discussed. Two-dimensional water velocity field and the motion of a rising particle/bubble in the water were simultaneously measured by PIV (Particle Image Velocimetry) and PTV (Particle Tracking Velocimetry), respectively (Hybrid PIV). The experimental results showed that the large density difference between a particle and water caused high relative velocity and induced zigzag motion of the particle. Furthermore, the turbulence intensity of a bubble was about twice in the case of the spherical solid particle of similar diameter. 2002 Published by Elsevier Science Ltd. Keywords: Bubble; Particle; Velocity field; PIV; PTV
1. Introduction Dispersed two-phase flow having solid particles or bubbles in a continuous liquid phase appears often in the process of operating energy facilities such as pipelines of minerals and charcoals, various chemical plants, nuclear and steam power stations, and so on. The flow characteristics of the dispersed two-phase flow have been investigated in order to improve the efficiency and the safety of the facilities. The statistical or time average flow characteristics of the dispersed two-phase flow were revealed but it is desired to make clear the detailed flow structure changing with time. So far there are some studies of factors giving influence over the behavior of the particles or bubbles consisting of dispersed two-phase flow. Zun [1]
* Corresponding author. Tel.: +82-42-868-5310; fax: +82-42-8685028. 1 Tel: +81-298-53-5061; fax: +81-298-53-5207. 0955-5986/02/$ - see front matter 2002 Published by Elsevier Science Ltd. PII: S 0 9 5 5 - 5 9 8 6 ( 0 1 ) 0 0 0 3 0 - 9
studied the transverse lift force on a bubble generated by the velocity gradient in liquid phase. Rouhani [2] investigated the “wall–vortex effect” where bubbles are restrained by centripetal force generated at a wall. Because single bubble motion was considered as one of the basic elements characterizing bubble flow, Matsui and Monji [3] studied the size, density, shape, and deformation effects on the bubble motion compared with droplets and solid particles by using PTV (Particle Tracking Velocimetry). Further, Matsui and Monji [4,5] visualized the two-dimensional water velocity field taking the rising motion of a single bubble/particle in its surrounding fluid by Hybrid PIV (Particle Image Velocimetry). In spite of these studies, however, the detailed flow structure of dispersed two-phase flow still needs to be further clarified. In order to investigate the basic characteristics of dispersed two-phase flow, therefore, deeper studies on single particle motion are required. In this study, the effect of various factors having influence on single particle motion, such as
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particle/bubble size and shape, deformation (of bubble), and buoyancy or density difference was investigated experimentally. The behavior of the interaction between a particle or bubble and the surrounding fluid was measured using HPIV (Hybrid Particle Image Velocimetry).
2. Experimental apparatus and instrumentation Figure 1 shows the experimental apparatus that consists of a particle/bubble injector, a vertical pipe with a test section and a separator tank. The test section and the particle/bubble injector are part of the vertical pipe and the test section is located at 30D above the particle/bubble injector. Here, D is an inner diameter of the vertical pipe. The vertical pipe is made of transparent acrylic pipe of 40 mm inner diameter and 2 m long. The vertical pipe was filled with stagnant water and solid particles/bubbles were injected into the stagnant water. The rising velocity of the single bubble/particle was zero at the injector, and then became constant due to the buoyancy. The density of solid particles employed in the experiment was smaller than that of water. At the test section, the motion of the particle or bubble and the water velocity were measured simultaneously by the HPIV.
The specification of the solid particles and bubbles employed in the experiment are shown in Table 1. The solid particles were three kinds of spherical particles and two kinds of non-spherical particles. For the spherical particles, the diameters were 5.6, 7.1 and 9.5 mm, and the density close to that of the liquid. Additionally spherical particles of 10 mm diameter but different densities were used (the types were solidsFa andFb). The two kinds of non-spherical particles were a hemisphere (solidFc) and an oblate spheroid (solidFd). The sizes of the bubbles were 5.7, 7.3, 9.1 and 12.4 mm in equivalent spherical diameter. The equivalent diameter of each bubble was calculated from the volume of the displacement of the injection syringe. Figure 2 illustrates the schematic of the test section and HPIV system. At the test section, a water jacket 30 cm long was attached to prevent the distortion of visual images. A time series of two-dimensional water velocity field was measured by PIV. In the PIV, a light sheet of a YAG pulse laser passed the longitudinal cross-section of the pipe and the flow image on the laser sheet was taken by a CCD camera. The resolution of the image was 0.115 mm/pixel. The tracer was fluorescent and its size and density were 10 µm diameter and 1500 kg/m3, respectively. The velocity of the water was calculated by the cross correlation between two flow images the time interval of which depended on the flow velocity and was 2 to 5 ms. The particle/bubble motion was measured by PTV. A stroboscope and a CCD camera were used to take an image of the particle/bubble. The back light system of the stroboscope located opposite the CCD camera was useful for taking a clear contour of the particle/bubble image. In order to avoid interference between the PIV and PTV, optical filters with different ranges of wavelength were used for the stroboscope and CCD cameras, respectively.
3. Results and discussion 3.1. Particle/bubble motion and velocity and vorticity fields in the surrounding flow
Fig. 1.
Schematic diagram of experimental apparatus (D=40 mm).
The particle image taken by PTV was combined with the PIV results. Before combining the images taken with PIV and PTV, we put a reference object into the measurement section, obtained the basic parameters such as the bubble location, size of 1 [pixel], etc. and made corrections to the images. While observing the images at 8 points of the reference object with 3 cameras, we arranged the focus of the cameras until the size of the images became the same. A background image with no flow of bubbles was prepared before experiments. After subtracting the background images from the images taken with PTV, we determined the value of the threshold and digitized contouring images of bubbles. And
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Table 1 Specifications of test particles/bubbles Particles/bubbles
Diameter (mm)
Density (kg/m3)
Shape
Solids
5.6 7.1 9.5 10 10 7.9 9.4
860
Sphere
Solid Solid Solid Solid
a b c d
Bubbles
5.7 7.3 9.1 12.4
57.3 647 955 233
1.18
Hemisphere of d=10 mm Oblate ellipsoid Major axis length 10.6 mm Minor axis length 4.5 mm Oblate ellipsoid
Spherical cap
the solidF9.5, solidFa, bubbleF9.1 and bubbleF12.4, respectively. The time interval of each image was 35 ms. The arrow shows the velocity at each point and the color shows the vorticity around the axis perpendicular to the image. The expanded uncertainty of vorticity was analyzed to be U95=2.4×10⫺2. The spherical solid particle of 9.5 mm diameter moved in a straight line and rose in the stagnant water as shown in Fig. 3. The flow directly below the particle was straight and the wake structure was symmetric. In the case of solidFa, the density difference between the particle and water was large. Under such a condition, the particle moved in a zigzag way, and a vortex was shed when the direction of the particle motion changed, as shown in Fig. 4. As the density difference between the spherical solid particle and the surrounding water became larger, the particle motion changed from straight to zigzag. In the case of bubbleF9.1 shown in Fig. 5, the vortex shedding was similar to the case of solid a. When the particle shape became oblate, the vortex developed at its bottom end. In case of the bubble, the direction of motion seemed to change while changing the aspect ratio. The bubble of the larger diameter (bubble 12.4 shown in Fig. 6) produced bigger vortexes than those by the bubble of 9.1 mm diameter. 3.2. Time averaged rising and transverse velocities of particles/bubbles
Fig. 2.
Schematic of test section and hybrid PIV system.
then we eliminated the residual noises and placed images to be compared with the analyzed images taken with the PIV. Figures 3 to 6 show typical results composed of the particle or bubble image, velocity and vorticity fields for
Figure 7 shows the time averaged rising velocities of the particles and bubbles in stagnant water. The location of the particle or bubble was obtained from the centroid of the particle or bubble. The expanded uncertainty of the time average velocity was U95=2.1×10⫺2. In the cases of solidsF5.6 to 9.5 whose density was not so different from that of the water, the rising velocity increased with the particle diameter. In the cases of solidFa and solidFb, the rising velocity increased with den-
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Fig. 3. Average velocity and vorticity field (solidF9.5).
Fig. 4.
Fig. 5.
Average velocity and vorticity field (solidFa).
Average velocity and vorticity field (bubbleF9.1).
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Fig. 6.
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Average velocity and vorticity field (bubble 12.4).
The averaged radial velocity of each particle/bubble (Fig. 8) was calculated by taking the mean value of the absolute radial velocities through the measuring field. Solids 5.6Fto 9.5 showed small radial velocity. Because these particles moved straight up, the radial velocity may be small. SolidFa, whose density was much smaller than that of the water, rose in a zigzag way and the radial velocity was large. The hemisphere solidFc revolved but its radial movement and velocity were small. 3.3. Interaction between particles/bubbles and their wakes
Fig. 7.
Rising velocity of particles and bubbles.
sity difference between the particle and the water. The rising velocity of the oblate spherical solid particle (solidFd) was slower than that of the solidF9.5, even if their equivalent diameters were almost the same. In the cases of bubbles, the shape of bubbles deformed and were faced with resistance, which in turn attenuated the buoyancy effect in accordance with the diameter of the particles. Thus, the rising velocities of bubbles were almost the same even if their diameters were different. The values of the rising velocities were either slower than or in agreement with the results obtained by Moris et al. [6] in the case of the solid particles, and those by Peebles et al. [7] in the case of the bubbles. We analyzed that the slower velocities were caused by the existence of the pipe wall. The slow velocities were better observed in the case where the particles/bubbles had a larger diameter.
3.3.1. Axial and radial velocity distribution in wake Figure 9 shows the distributions of the dimensionless axial velocity v/V0 (v: axial velocity of water, V0: average rising velocity of the particle) and the dimensionless radial velocity u/V0 (u: radial velocity). In the figures, the origin is taken at the center of the particle image and
Fig. 8.
Radial average velocity.
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Fig. 9.
Axial (v) and radial (u) velocity distribution in wake.
H.M. Choi et al. / Flow Measurement and Instrumentation 12 (2002) 421–428
the abscissa denotes the dimensionless radial distance x/d from the center of the particle image. The y-coordinate in the figure is taken parallel to the pipe axis. Here, d is the particle diameter. As was anticipated, v/V0 had the maximum value at the nearest point to the center for all the particles/bubbles. In the case of solidF9.5, the maximum value of v/V0 was about 0.6 at the point x/d=0 and y/d=0.6. In the case of bubbleF9.1, the maximum value of v/V0 exceeded 0.6 at the point x/d=0 and y/d=0.5, and the values were about 0.6 at the point x/d=0 and y/d=0.63 which is similar to the case of solidF9.5. It is noticeable that the value of v/V0 was quite large and 0.9 at the point x/d=0 and y/d=0.55 in the case of bubbleF12.4. Furthermore, remarkable backflow was found in the range of x/d=⫺1.0 to 1.5, which was due to the stagnant water and the pipe wall. The point of the maximum value of the radial flow depends on the particle type and the wake structure. In the case of solidF9.5, the maximum value was taken at the point y/d=2, while it was taken at the point y/d=0.57 in the case of solidFa, and at y/d=0.5 in the case of the bubbleF9.1. In the case of solidF9.5, the particle moved straight and pulled fluid toward the particle center from the backward point a distance twice the particle diameter. 3.3.2. Distribution of turbulence intensity in wake Figure 10 shows the distribution of turbulence intensity (2u2+v2)/2V20 at the point of y/d=0.6 in the wake. The expanded uncertainty of turbulence intensity was U95=2.1×10⫺2. In the case of the spherical solid particle (solidF9.5), the distribution of turbulence intensity showed a similar tendency to the distribution of v/V0 in Fig. 9, because the transverse velocity u was small. On the other hand, in the case of solidFa whose density was much smaller than that of water, the profile of the turbulence intensity was different from that of v/V0. The solid
Fig. 10.
Turbulence intensity.
427
a moved widely in the transverse direction, and thus the wake region was wide on x/d. Also, the intensity of turbulence by the particle was quite high. In the case of bubbleF9.1, its turbulence intensity at the point of y/d=0.6 was about twice that of the solidF9.5 because the bubble motion was zigzag. 3.3.3. Distribution of average Reynolds stress in wake Figure 11 shows the distribution of Reynolds stress (⫺u⬘v⬘/V20) at the point of y/d=0.6 in wake. u⬘ and v⬘ are the fluctuations of axial and radial velocities, respectively. The expanded uncertainty of Reynolds stresses was U95=3.0×10⫺2. The Reynolds stress distribution in the case of solidF9.5 was different from those in the cases of bubbleF9.1, bubbleF12.4 and solidFa due to the different flow pattern in the wake, that is, a velocity profile and vortex shedding shown in Figs 4 and 9.
4. Conclusion The experiments clarified how the motion of the single particle/bubble was influenced by its size, shape, deformation, and buoyancy among other factors. At the same time, it allowed us to learn the interaction between the motion of the single particle and the surrounding fluid by using the Hybrid PIV. The following are the main experimental results. 1. The rising velocity increased with diameter for the spherical solid particles under constant density, while the rising velocity of bubbles did not change much with its diameter. For bubbles, the buoyancy effect in accordance with the diameter was attenuated with the resistance due to deformation. 2. The rising velocity of spherical solid particles increased with density difference between the solid particle and liquid. The motion of the spherical solid
Fig. 11.
Reynolds stress.
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particle also changed from straight to zigzag as the density difference increased. 3. The turbulence intensity of a bubble of 9 mm diameter was about twice of intensity of the spherical solid particle with similar diameter.
[3]
[4]
[5]
References [6] [1] I. Zun, The transverse migration of bubbles influenced by walls in vertical bubbly flow, Int. J. Multiphase Flow 6 (6) (1980) 583–588. [2] Z. Rouhani, Effect of wall friction and vortex generation on the
[7]
radial distribution of different phase, Int. J. Multiphase Flow 3 (1) (1976) 36–50. G. Matsui, H. Monji, Behaviour of a single particle/droplet/bubble in vertical liquid flow, two-phase flow modeling and experimentation 1995, Edizioni ETS, 1995, pp. 789–795. G. Matsui, H. Monji, et al., PIV measurement of flow field around a bubble, in: 1st European–Japanese Two-Phase Flow Group Meeting, Portoroz, Slovenai, 1998. H. Monji, G. Matsui, et al., Measurement of velocity field and a particle/bubble motion by PIV and PTV, in: 9th International Symposium on Flow Visualization, 2000, p.1352. S.A. Moris, A.J. Alexander, An investigation of particle trajectories in two-phase flow systems, J. Fluid Mech. 55 (1972) 193–208. F.N. Peebles, H.J. Garber, Studies on the motion of gas bubbles in liquids, Chem. Eng. Prog. 49 (2) (1953) 88–97.
Measurement of particle/bubble motion and turbulence around it by hybrid PIV H.M. Choi a
a, b,*
, T. Kurihara
1,b
, H. Monji1 b, G. Matsui1
b
Fluid Flow Group, Korea Research Institute of Standards and Science, P.O. Box 102, Yusong, Daejeon, 305-606, South Korea b Institute of Engineering Mechanics and System, University of Tsukuba, Tsukuba, 305-8573, Japan Received 1 March 2001; received in revised form 9 July 2001; accepted 10 September 2001
Abstract Characteristics of bubble flow are influenced by bubble motion, liquid flow and interactions between bubbles, and between a bubble and liquid phase. Thus because behavior of a single bubble and liquid around it is regarded as one of the basic elements characterizing bubble flow, the single bubble motion in stagnant water was investigated experimentally by using flow visualization and image processing methods. The bubble motion is influenced by several factors, that is, bubble size, density difference between gas and liquid, bubble shape and deformation in motion. In order to separate the effect of each factor, some solid particles with different size, shape and/or density were also measured and the characteristic of each factor was discussed. Two-dimensional water velocity field and the motion of a rising particle/bubble in the water were simultaneously measured by PIV (Particle Image Velocimetry) and PTV (Particle Tracking Velocimetry), respectively (Hybrid PIV). The experimental results showed that the large density difference between a particle and water caused high relative velocity and induced zigzag motion of the particle. Furthermore, the turbulence intensity of a bubble was about twice in the case of the spherical solid particle of similar diameter. 2002 Published by Elsevier Science Ltd. Keywords: Bubble; Particle; Velocity field; PIV; PTV
1. Introduction Dispersed two-phase flow having solid particles or bubbles in a continuous liquid phase appears often in the process of operating energy facilities such as pipelines of minerals and charcoals, various chemical plants, nuclear and steam power stations, and so on. The flow characteristics of the dispersed two-phase flow have been investigated in order to improve the efficiency and the safety of the facilities. The statistical or time average flow characteristics of the dispersed two-phase flow were revealed but it is desired to make clear the detailed flow structure changing with time. So far there are some studies of factors giving influence over the behavior of the particles or bubbles consisting of dispersed two-phase flow. Zun [1]
* Corresponding author. Tel.: +82-42-868-5310; fax: +82-42-8685028. 1 Tel: +81-298-53-5061; fax: +81-298-53-5207. 0955-5986/02/$ - see front matter 2002 Published by Elsevier Science Ltd. PII: S 0 9 5 5 - 5 9 8 6 ( 0 1 ) 0 0 0 3 0 - 9
studied the transverse lift force on a bubble generated by the velocity gradient in liquid phase. Rouhani [2] investigated the “wall–vortex effect” where bubbles are restrained by centripetal force generated at a wall. Because single bubble motion was considered as one of the basic elements characterizing bubble flow, Matsui and Monji [3] studied the size, density, shape, and deformation effects on the bubble motion compared with droplets and solid particles by using PTV (Particle Tracking Velocimetry). Further, Matsui and Monji [4,5] visualized the two-dimensional water velocity field taking the rising motion of a single bubble/particle in its surrounding fluid by Hybrid PIV (Particle Image Velocimetry). In spite of these studies, however, the detailed flow structure of dispersed two-phase flow still needs to be further clarified. In order to investigate the basic characteristics of dispersed two-phase flow, therefore, deeper studies on single particle motion are required. In this study, the effect of various factors having influence on single particle motion, such as
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H.M. Choi et al. / Flow Measurement and Instrumentation 12 (2002) 421–428
particle/bubble size and shape, deformation (of bubble), and buoyancy or density difference was investigated experimentally. The behavior of the interaction between a particle or bubble and the surrounding fluid was measured using HPIV (Hybrid Particle Image Velocimetry).
2. Experimental apparatus and instrumentation Figure 1 shows the experimental apparatus that consists of a particle/bubble injector, a vertical pipe with a test section and a separator tank. The test section and the particle/bubble injector are part of the vertical pipe and the test section is located at 30D above the particle/bubble injector. Here, D is an inner diameter of the vertical pipe. The vertical pipe is made of transparent acrylic pipe of 40 mm inner diameter and 2 m long. The vertical pipe was filled with stagnant water and solid particles/bubbles were injected into the stagnant water. The rising velocity of the single bubble/particle was zero at the injector, and then became constant due to the buoyancy. The density of solid particles employed in the experiment was smaller than that of water. At the test section, the motion of the particle or bubble and the water velocity were measured simultaneously by the HPIV.
The specification of the solid particles and bubbles employed in the experiment are shown in Table 1. The solid particles were three kinds of spherical particles and two kinds of non-spherical particles. For the spherical particles, the diameters were 5.6, 7.1 and 9.5 mm, and the density close to that of the liquid. Additionally spherical particles of 10 mm diameter but different densities were used (the types were solidsFa andFb). The two kinds of non-spherical particles were a hemisphere (solidFc) and an oblate spheroid (solidFd). The sizes of the bubbles were 5.7, 7.3, 9.1 and 12.4 mm in equivalent spherical diameter. The equivalent diameter of each bubble was calculated from the volume of the displacement of the injection syringe. Figure 2 illustrates the schematic of the test section and HPIV system. At the test section, a water jacket 30 cm long was attached to prevent the distortion of visual images. A time series of two-dimensional water velocity field was measured by PIV. In the PIV, a light sheet of a YAG pulse laser passed the longitudinal cross-section of the pipe and the flow image on the laser sheet was taken by a CCD camera. The resolution of the image was 0.115 mm/pixel. The tracer was fluorescent and its size and density were 10 µm diameter and 1500 kg/m3, respectively. The velocity of the water was calculated by the cross correlation between two flow images the time interval of which depended on the flow velocity and was 2 to 5 ms. The particle/bubble motion was measured by PTV. A stroboscope and a CCD camera were used to take an image of the particle/bubble. The back light system of the stroboscope located opposite the CCD camera was useful for taking a clear contour of the particle/bubble image. In order to avoid interference between the PIV and PTV, optical filters with different ranges of wavelength were used for the stroboscope and CCD cameras, respectively.
3. Results and discussion 3.1. Particle/bubble motion and velocity and vorticity fields in the surrounding flow
Fig. 1.
Schematic diagram of experimental apparatus (D=40 mm).
The particle image taken by PTV was combined with the PIV results. Before combining the images taken with PIV and PTV, we put a reference object into the measurement section, obtained the basic parameters such as the bubble location, size of 1 [pixel], etc. and made corrections to the images. While observing the images at 8 points of the reference object with 3 cameras, we arranged the focus of the cameras until the size of the images became the same. A background image with no flow of bubbles was prepared before experiments. After subtracting the background images from the images taken with PTV, we determined the value of the threshold and digitized contouring images of bubbles. And
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Table 1 Specifications of test particles/bubbles Particles/bubbles
Diameter (mm)
Density (kg/m3)
Shape
Solids
5.6 7.1 9.5 10 10 7.9 9.4
860
Sphere
Solid Solid Solid Solid
a b c d
Bubbles
5.7 7.3 9.1 12.4
57.3 647 955 233
1.18
Hemisphere of d=10 mm Oblate ellipsoid Major axis length 10.6 mm Minor axis length 4.5 mm Oblate ellipsoid
Spherical cap
the solidF9.5, solidFa, bubbleF9.1 and bubbleF12.4, respectively. The time interval of each image was 35 ms. The arrow shows the velocity at each point and the color shows the vorticity around the axis perpendicular to the image. The expanded uncertainty of vorticity was analyzed to be U95=2.4×10⫺2. The spherical solid particle of 9.5 mm diameter moved in a straight line and rose in the stagnant water as shown in Fig. 3. The flow directly below the particle was straight and the wake structure was symmetric. In the case of solidFa, the density difference between the particle and water was large. Under such a condition, the particle moved in a zigzag way, and a vortex was shed when the direction of the particle motion changed, as shown in Fig. 4. As the density difference between the spherical solid particle and the surrounding water became larger, the particle motion changed from straight to zigzag. In the case of bubbleF9.1 shown in Fig. 5, the vortex shedding was similar to the case of solid a. When the particle shape became oblate, the vortex developed at its bottom end. In case of the bubble, the direction of motion seemed to change while changing the aspect ratio. The bubble of the larger diameter (bubble 12.4 shown in Fig. 6) produced bigger vortexes than those by the bubble of 9.1 mm diameter. 3.2. Time averaged rising and transverse velocities of particles/bubbles
Fig. 2.
Schematic of test section and hybrid PIV system.
then we eliminated the residual noises and placed images to be compared with the analyzed images taken with the PIV. Figures 3 to 6 show typical results composed of the particle or bubble image, velocity and vorticity fields for
Figure 7 shows the time averaged rising velocities of the particles and bubbles in stagnant water. The location of the particle or bubble was obtained from the centroid of the particle or bubble. The expanded uncertainty of the time average velocity was U95=2.1×10⫺2. In the cases of solidsF5.6 to 9.5 whose density was not so different from that of the water, the rising velocity increased with the particle diameter. In the cases of solidFa and solidFb, the rising velocity increased with den-
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Fig. 3. Average velocity and vorticity field (solidF9.5).
Fig. 4.
Fig. 5.
Average velocity and vorticity field (solidFa).
Average velocity and vorticity field (bubbleF9.1).
H.M. Choi et al. / Flow Measurement and Instrumentation 12 (2002) 421–428
Fig. 6.
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Average velocity and vorticity field (bubble 12.4).
The averaged radial velocity of each particle/bubble (Fig. 8) was calculated by taking the mean value of the absolute radial velocities through the measuring field. Solids 5.6Fto 9.5 showed small radial velocity. Because these particles moved straight up, the radial velocity may be small. SolidFa, whose density was much smaller than that of the water, rose in a zigzag way and the radial velocity was large. The hemisphere solidFc revolved but its radial movement and velocity were small. 3.3. Interaction between particles/bubbles and their wakes
Fig. 7.
Rising velocity of particles and bubbles.
sity difference between the particle and the water. The rising velocity of the oblate spherical solid particle (solidFd) was slower than that of the solidF9.5, even if their equivalent diameters were almost the same. In the cases of bubbles, the shape of bubbles deformed and were faced with resistance, which in turn attenuated the buoyancy effect in accordance with the diameter of the particles. Thus, the rising velocities of bubbles were almost the same even if their diameters were different. The values of the rising velocities were either slower than or in agreement with the results obtained by Moris et al. [6] in the case of the solid particles, and those by Peebles et al. [7] in the case of the bubbles. We analyzed that the slower velocities were caused by the existence of the pipe wall. The slow velocities were better observed in the case where the particles/bubbles had a larger diameter.
3.3.1. Axial and radial velocity distribution in wake Figure 9 shows the distributions of the dimensionless axial velocity v/V0 (v: axial velocity of water, V0: average rising velocity of the particle) and the dimensionless radial velocity u/V0 (u: radial velocity). In the figures, the origin is taken at the center of the particle image and
Fig. 8.
Radial average velocity.
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Fig. 9.
Axial (v) and radial (u) velocity distribution in wake.
H.M. Choi et al. / Flow Measurement and Instrumentation 12 (2002) 421–428
the abscissa denotes the dimensionless radial distance x/d from the center of the particle image. The y-coordinate in the figure is taken parallel to the pipe axis. Here, d is the particle diameter. As was anticipated, v/V0 had the maximum value at the nearest point to the center for all the particles/bubbles. In the case of solidF9.5, the maximum value of v/V0 was about 0.6 at the point x/d=0 and y/d=0.6. In the case of bubbleF9.1, the maximum value of v/V0 exceeded 0.6 at the point x/d=0 and y/d=0.5, and the values were about 0.6 at the point x/d=0 and y/d=0.63 which is similar to the case of solidF9.5. It is noticeable that the value of v/V0 was quite large and 0.9 at the point x/d=0 and y/d=0.55 in the case of bubbleF12.4. Furthermore, remarkable backflow was found in the range of x/d=⫺1.0 to 1.5, which was due to the stagnant water and the pipe wall. The point of the maximum value of the radial flow depends on the particle type and the wake structure. In the case of solidF9.5, the maximum value was taken at the point y/d=2, while it was taken at the point y/d=0.57 in the case of solidFa, and at y/d=0.5 in the case of the bubbleF9.1. In the case of solidF9.5, the particle moved straight and pulled fluid toward the particle center from the backward point a distance twice the particle diameter. 3.3.2. Distribution of turbulence intensity in wake Figure 10 shows the distribution of turbulence intensity (2u2+v2)/2V20 at the point of y/d=0.6 in the wake. The expanded uncertainty of turbulence intensity was U95=2.1×10⫺2. In the case of the spherical solid particle (solidF9.5), the distribution of turbulence intensity showed a similar tendency to the distribution of v/V0 in Fig. 9, because the transverse velocity u was small. On the other hand, in the case of solidFa whose density was much smaller than that of water, the profile of the turbulence intensity was different from that of v/V0. The solid
Fig. 10.
Turbulence intensity.
427
a moved widely in the transverse direction, and thus the wake region was wide on x/d. Also, the intensity of turbulence by the particle was quite high. In the case of bubbleF9.1, its turbulence intensity at the point of y/d=0.6 was about twice that of the solidF9.5 because the bubble motion was zigzag. 3.3.3. Distribution of average Reynolds stress in wake Figure 11 shows the distribution of Reynolds stress (⫺u⬘v⬘/V20) at the point of y/d=0.6 in wake. u⬘ and v⬘ are the fluctuations of axial and radial velocities, respectively. The expanded uncertainty of Reynolds stresses was U95=3.0×10⫺2. The Reynolds stress distribution in the case of solidF9.5 was different from those in the cases of bubbleF9.1, bubbleF12.4 and solidFa due to the different flow pattern in the wake, that is, a velocity profile and vortex shedding shown in Figs 4 and 9.
4. Conclusion The experiments clarified how the motion of the single particle/bubble was influenced by its size, shape, deformation, and buoyancy among other factors. At the same time, it allowed us to learn the interaction between the motion of the single particle and the surrounding fluid by using the Hybrid PIV. The following are the main experimental results. 1. The rising velocity increased with diameter for the spherical solid particles under constant density, while the rising velocity of bubbles did not change much with its diameter. For bubbles, the buoyancy effect in accordance with the diameter was attenuated with the resistance due to deformation. 2. The rising velocity of spherical solid particles increased with density difference between the solid particle and liquid. The motion of the spherical solid
Fig. 11.
Reynolds stress.
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particle also changed from straight to zigzag as the density difference increased. 3. The turbulence intensity of a bubble of 9 mm diameter was about twice of intensity of the spherical solid particle with similar diameter.
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