Measurement of Bubble Velocity using Spatial Filter Velocimetry

Transcription

1 Lisbon, Portugal, 9 July, Measurement of Bubble Velocity using Spatial Filter Velocimetry Takaaki Matsumoto, Shigeo Hosokawa,*, Akio Tomiyama : Graduate School of Engineering, Kobe University, Kobe, Japan * correspondent author: hosokawa@mech.kobe-u.ac.jp Abstract Spatial filter velocimetry (SFV) based on spatial filtering of time-series particle images proposed by Hosokawa and Tomiyama is applied to a bubble column to examine its applicability to multi-scale bubble velocity measurement. PTV measurement of the bubble velocity is also carried out for comparison. The edge detection process is added in the SFV processing to reduce the size of image pattern and to obtain accurate velocity data. It is demonstrated that SFV is able to measure the bubble velocity in various spatial scales with higher accuracy than PTV. The measured mean bubble velocity does not depend on the interrogation size in the measurements. To the contrary, standard deviation of measured bubble velocity becomes higher as the interrogation size decreases due to the superposition of interfacial wave velocity on the measured velocity. Simultaneous measurement of bubble and liquid velocities is also carried out for a planar bubble plume. The results clearly show that SFV can measure bubble velocity and structural velocity as well.. Introduction To understand multi-scale structure of bubbly flows, it is important to measure bubble velocity in various scales. has been measured by an electric conductance probe [], an optical fiber probe [], WMT [3], PTV [4] or PIV [5]. Since contact of a sensor with a bubble may reduce the bubble velocity and increase the uncertainty in velocity measurement, imaging-based methods such as PIV and PTV are preferable for accurate measurement of bubble velocity. Though simultaneous measurement of bubbles and liquid velocities is required to understand bubbly flows, it is not easy to realize it by using contact methods such as the electric/optical probe or WMT. The image based methods have advantages in the simultaneous measurement. PTV measures a translation distance of each bubble, and therefore, it is difficult to apply it to a flow with a high bubble number density, in which bubble overlapping in recoded images frequently occurs. Measurement of interfacial velocity is also difficult in PTV measurements. On the other hand, PIV measures translational velocity of a pattern, and therefore, it can measure interfacial velocity and bubble velocity even for overlapped bubble images. However, deformation of bubbles and a difference in velocities of bubbles in an interrogation area change the pattern of bubble images during the time interval of a set of images, and reduce the accuracy of the measured velocity. This is mainly due to the evaluation of velocity only from two images with the time interval. Hosokawa and Tomiyama proposed spatial filter velocimetry (SFV) based on spatial filtering of time-series particle images [6]. SFV has been proved to measure fluid velocity with accuracy as high as LDV. This high accuracy is a result of velocity evaluation not from two images but from several time-series images. Since SFV detects the motion of images by using a spatial filter function, it has a potential of accurate velocity measurement of a pattern such as bubble or bubble interface. In this study, we apply SFV to a bubble column to examine its applicability to multi-scale bubble velocity measurement. Effects of pattern size in images on the measurement are discussed through a simulation and an experiment. Simultaneous measurement of liquid and bubble velocities using SFV is also demonstrated for bubbly flow in a planar bubble plume. -

2 Lisbon, Portugal, 9 July, Measurement method. Principle of SFV Spatial filter velocimetry has been developed for velocity measurement of particles following fluid flows [6]. Before applying SFV to bubble velocity measurements, the principle of SFV is briefly introduced below. Figure shows a schematic of SFV. Time-series particle images are recorded by a video camera (image acquisition step). distribution I(x, y, t) in an interrogation area (measurement region) in each image is multiplied by a spatial filter function F SF (x, y, t), and the integral intensity I SF (t) of the spatially-filtered I(x, y, t) is calculated at each recording time (spatial filtering step): Light sheet Camera Time-series particle images x Flow + particles Image acquisition step Time y I L X I ( t = F dxdy SF ) Measurement region SF v x x Spatial filter I (x, y, t ) F SF (x, y, t ) Spatial filtering of particle image Calculation of integral intensity of filtered image Spatial Filtering step Integral intensity I SF ( t ) f = / t = V X /L X t Frequency f (Velocity V x ) Frequency analysis V X = L X / t = L X x f Time Time Frequency/velocity evaluation step -- Time Fig. Principle of spatial filter velocimetry I SF ( t) = y x I( x, y, t) F SF ( x, y, t) dxdy () where t is the time and x and y are the coordinates in the interrogation area. When a particle is moving in x direction with the velocity v x, the integral intensity I SF (t), which is calculated by using a periodic spatial filter function F SF (x) with the wavelength L x in x direction, periodically oscillates with the frequency f = v x /L x as shown in Fig.. Hence, the particle velocity v x can be measured by evaluating the frequency f of the integral intensity I SF (t) (frequency/velocity evaluation step). The other velocity component v y, which is perpendicular to v x, can be measured by using a periodic spatial filter function F SF (y) with the wavelength L y in y direction. Thus, we can evaluate magnitudes of two velocity components of each particle in an arbitrary interrogation area in the imaging plane from the time-series particle images. A moving spatial filter function is used to

3 Lisbon, Portugal, 9 July, determine the direction of velocity like the frequency shifting in LDV measurement. Details on SFV can be found in Hosokawa and Tomiyama [6].. Application to bubble velocity measurement When a bubble size in images is small compared with the wavelength of spatial filter, we can apply SFV to bubble velocity measurement without any difficulty. On the other hand, I SF (t) does not seriously change with t when a pattern size is larger than the size of an interrogation area and the pattern covers the interrogation area. Thus, degradation in periodic oscillation of I SF (t) may occur when the bubble size is comparable with or larger than the size of an interrogation area. Hence, we carried out a simulation to make clear the dependence of I SF (t) on the ratio of the bubble size d to the interrogation size L. Bubble shape was assumed to be spherical and synthetic time-series images of a bubble moving with a constant velocity V B were generated to simulate I SF (t) as shown in Fig.. The wavelength and cycle of spatial filter in the simulation were fixed at 6 pixels and 5, respectively. The ratio d/l ranged from. to. I SF (t) normalized by its maximum value is shown in Fig. 3 (a). The red curve in the figure shows the integral value of non-filtered intensity I(x, y, t) normalized by its maximum value. The oscillation of I SF (t) is periodic for small d/l (d/l =.). The oscillation of I SF (t) at high d/l consists of two frequencies. One is the high frequency component which corresponds to the wavelength of the spatial filter. The other is low frequency component which corresponds to the change in the integral value of I(x, y, t). The amplitude of the high frequency component is about a half of that of the low frequency component at d/l >.. Hence, the increase in bubble size (pattern size) makes velocity evaluation difficult. Refinement of pattern of bubble image could be effective to remove this difficulty. We, therefore, applied an edge detection processing to the images to reduce the scale of the pattern. I SF (t) of images of detected bubble edges are shown in Fig. 3 (b). The edge detection process clearly reduces the low frequency component and good periodic signals are obtained in I SF (t) not only for small d/l but also for large d/l. Therefore, we adopted the edge detection process to evaluate bubble velocity. V B Time I SF SF d L Bubble Image Spatial Filter Time Time Fig. Schematic of simulation of integral intensity 3 measurement 3. Experimental setup SFV was applied to measurement of bubble velocity in a bubble column. Figure 4 shows a schematic of the experimental setup. The size of the column was 4(W) x 7(D) x 8(H) mm. Water was filled in the column, and the water level was 7 mm from the bottom of the column. Air was supplied from the compressor (Hitachi, SRL-.), and injected into the column through nozzles (diameter:.5 mm, number: 35) located at the bottom. The gas volumetric flux ranged from 3. x -3 to.3 x - m/s. The bubble diameter varied from 3 to 8 mm. Time-series bubble images were recorded by using a high-speed camera (Redlake Motion Pro HS, frame rate: 3, fps, resolution: 65 µm/pixel) at two elevations (x = and 5 mm from the bottom). Horizontal (y) distributions of bubble velocity were measured from the time-series bubble images by using SFV. A cosine function was used for the spatial filter F SF, and a wavelet analysis was adopted to evaluate the frequency of I SF. PTV measurements of bubble velocity were also carried out for comparison. was measured by LDV (DANTEC, 6X series) at the same elevations. -3-

4 広川ハゲ 6 mm 6th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 9 July, d / L =. d / L = d / L = d / L = d / L = (a) Particle image d / L = d / L = d / L = (b) Particle edge image Fig. 3 Effect of bubble size on I SF Compressor 7 mm. Bubble column 4 mm Point of air injection mm φ.5 mm 35 Tank x Z Tank y Nozzle plate 5 mm mm 8 mm 8 mm 4 mm Nozzle 7 mm Regulator Valve Nozzle Drain Fig. 4 Schematic of experimental apparatus -4-

5 Lisbon, Portugal, 9 July, 3. Results and discussion Examples of I SF (t) in various interrogation area (75x 75, 5 x 5, x pixels) are shown in Fig. 5 (a). The periodic oscillations of I SF (t) are observed for large interrogation sizes (75 x 75 and 5 x 5 pixels). On the other hand, I SF (t) in the small interrogation size ( x pixels) shows a low frequency fluctuation as we have discussed in section.. This is because bubbles sizes ( 3 pixels) are comparable to the interrogation size. The edge detection process was applied to bubble images to reduce the scale of pattern, and I SF (t) of the bubble edge images are shown in Fig. 5 (b). By the edge detection, the low frequency oscillation is clearly attenuated, and good periodic signals are formed in I SF (t) not only for the large interrogation areas but also for the small interrogation area. Axial mean velocities U B of bubbles measured by SFV and PTV at J G =.3 m/s are shown in Fig. 6. Here, y is the distance from the left wall of the bubble column. The interrogation region of SFV was 75 x 75 pixels (6 x 6 mm). U B in the SFV measurement was calculated from, instantaneous bubble velocities. The bubble velocity in PTV measurement was measured from a translation distance of bubble center between two consecutive images (frame rate: 3 Hz), and U B was calculated from 5 bubble velocities at each measurement point. The error bars of PTV data show the standard deviation of the data. The mean bubble velocities measured by SFV agree very well with those measured by PTV in both elevations. This result shows that SFV measures the bubble velocity with the same accuracy as or higher accuracy than PTV. Edge detection I SF I sf (t) (t) I SF I sf (t) I SF I (t) sf I SF sf (t) (t) I SF I sf (t) I SF I sf (t) (t) t [s] (a) Original image.5..5 t [s] (b) Bubble edge image Fig. 5 Integral intensity of filtered bubble image -5-

6 Lisbon, Portugal, 9 July,.3 U B [m/s].. x= mm 5 mm SFV PTV Fig. 6 Measured axial mean velocity of bubbles.3..8 Scale of interface oscillation Bubble size U B [m/s].. Average ±5% N C = 4 N C = 5 N C = L [mm] u' B [m/s].6.4. N C = 4 N C = 5 N C = L [mm] (a) Mean bubble velocity (b) Standard deviation of bubble velocity Fig. 7 Effects of interrogation size The interrogation area of SFV can be set at an arbitrary size. Dependences of measured axial mean velocity U B of bubbles and standard deviation u B of axial bubble velocities on the interrogation size L are shown in Fig. 7. The data were obtained at the center of the column (y = mm) at x = 5 mm for J G =.3 m/s. The red and black symbols show data for fine (33 µm/pixel) and coarse resolutions ( µm/pixel) of bubble images, respectively. The cycle number N C of spatial filter in an interrogation area ranged from 4 to 6. Note that the gradient U B y of bubble velocity distribution was almost zero at the measurement point as shown in Fig. 5, and therefore, the effect of the velocity gradient on the variation of measured bubble velocity is negligible. U B does not depend on L and the variation of U B is within +5% irrespective of L and N C as shown in Fig. 7 (a). Therefore, we can correctly measure U B at any interrogation size. On the other hand, u B takes a high value for L <.5 mm and a low value for L > 3 mm which corresponds to the bubble size. u B decreases with increasing L in the range of.5 < L < 3 mm. When the interrogation size is much larger than the bubble size, a bubble is regarded as a point in the image plane and its translation velocity governs the oscillation of I SF (t). On the other hand, interface velocity of a -6-

7 Lisbon, Portugal, 9 July, bubble governs the oscillation of I SF (t) when the interrogation size is comparable to the scale of interfacial wave. Figure 7 (b) indicates that only bubble translation velocity was captured for L > 3, and local interface velocity was captured for L <.5. In other words, u B for L > 3 indicates variation in bubble translation velocity, and u B for L <. 5 indicates the sum of interfacial oscillation and the variation in bubble translation velocity. This result also indicates that the scale of the interface oscillation is about.5mm, which is about a half of bubble diameter. These results clearly demonstrate that SFV can measure bubble velocity in multi-scale only by changing the size of interrogation area. SFV was applied to bubbly flow at a higher void fraction to examine its applicability to overlapped bubble images. Examples of bubble images and I SF (t) at J G =.3,.6 and.3 m/s are shown in Fig. 8. The interrogation area was 3 x 3 pixels (5 x 5 mm). The number of overlapped bubble images increases as J G increases, and most of bubbles are overlapped in the image at J G =.3 m/s. I SF (t) calculated from these bubble images possesses periodic oscillations not only for the low J G but also for the high J G in spite of the presence of many overlapped bubble images. J G =.3 m/s J G =.6 m/s I sf SF (t) I SF I sf (t) J G =.3 m/s I sf I SF (t) (t) t [s] Fig. 8 Bubble images and integral intensities of filtered bubble image The horizontal distributions of axial mean velocity U B measured by SFV are shown in Fig. 9 together with the axial mean velocity U L of the liquid phase measured by LDV. U B gradually increases with y at x = mm at J G =.3 m/s, and it becomes flatter at the higher elevation (x = 5 mm). At J G =.6 m/s, the gradient of U B in the near wall region becomes steeper, and U B at the measurement point nearest to the wall is smaller than that at J G =.3 m/s. To the contrary, the horizontal distributions of U B in the center region are more or less flat. These results indicate that as J G increases, the downward flow in the near wall region becomes stronger and the horizontal width of the downward flow region becomes narrower due to high updraft induced by bubbles in the center region. Further decrease in U B is observed in the near wall region at J G =.3 m/s. The distribution of U L is similar to that of U B in each condition, and the relative velocity between

8 Lisbon, Portugal, 9 July, bubbles and the liquid phase is about. m/s, which is almost the same as terminal velocity of a bubble with the same diameter, irrespective of measurement positions and conditions..3 G ( ).3 G ( ) U B,U L [m/s].. U B,U L [m/s].. -. x = mm 5mm J G =.3m/s.3 -. x = mm 5mm J G =.6m/s G ( ) U B,U L [m/s].. -. x = mm 5mm J G =.3m/s Fig. 9 Measured bubble and liquid velocities Figure shows the histograms of bubble and liquid velocities at four measurement points (y = 3, 4, 8, mm) on x = mm for J G =.3 m/s. The peak locking, which is frequently observed in PIV measurement, is not observed in the histograms measured by SFV. The difference between peaks in velocity histograms of bubble and liquid velocities is about. m/s, and the maximum velocity of U L is almost the same as the maximum velocity of U B. This is reasonable judging from the flow around single bubbles [7, 8]. The widths of the histograms of U L are almost the same as those of U B except in the near wall region (y = 3 mm) where viscous damping of fluctuation of liquid velocity may be strong. The width of the histogram of U B does not depend on the position so much. This result implies that the fluctuation of U L is mainly induced by variation in bubble velocity, which is a result of oscillatory motion of bubbles. These results show that SFV can measure bubble velocity accurately not only for isolated bubble images but also for overlapped bubble images. 4 Simultaneous measurements of liquid and bubble velocities We have confirmed that SFV can accurately measure bubble velocity from bubble images as well as liquid velocity from particle images. In this section, we demonstrate simultaneous measurement of liquid and bubble velocities in a planar bubble plume using SFV. A schematic of the experimental apparatus is shown in Fig.. The height, width and gap size of the test section were 33, and 3 mm, respectively. Air and water at atmospheric pressure and room temperature were used for the gas and liquid phases, respectively. Air was supplied from the compressor (Hitachi, SRL-.), and -8-

9 広川ハゲ 6th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 9 July, planar air bubbles were released from the nozzle locating at the bottom of the test section. The nozzle inner diameter was.4 mm and the gas volumetric flux was.5 m/s. The bubble diameter ranged from 6 to 8.5 mm. Distributions of liquid and bubble velocities were measured at three elevations (, and 5 mm from the bottom). Polystyrene particles of µm diameter were added to water. The particles were illuminated by a diode laser (GIGA*LASER, X33B) and LED flat lamp was used as a backlight for imaging bubble shapes. Time-series images were recorded by using a high-speed camera (Redlake Motion Pro HS, frame rate: fps, resolution:.9 mm/pixel). PDF PDF PDF U [m/s] y = 3 mm PDF U [m/s] y = 4 mm U [m/s] U [m/s] y = 8 mm y = mm Fig. Bubble and liquid velocity distributions on J G =.3 m/s at x = mm Compressor 3 mm mm Photograph of test section. Tank 5 mm mm mm 3 mm 33 mm 5 mm mm mm Lens LED Regulator Valve Diode Laser Test section High speed camera Fig. Schematic of experimental apparatus -9-

10 Lisbon, Portugal, 9 July, Image processing procedure is shown in Fig.. The background image was subtracted from original images to obtain subtracted images [9]. The bubble region in the subtracted image was detected by using a labeling process. The particle and bubble images were generated by masking the bubble region and by inversing the bubble region, respectively. Finally, SFV processing was applied to particle and bubble images to obtain liquid and bubble velocities, respectively. Original image Background Subtraction Subtracted image Detection of bubble region Inverse bubble region (Mask for particles) Bubble region (Mask for bubbles) Masking subtracted image Particle image Bubble image SFV process for particle images SFV process for bubble images Fig. Image processing procedure 7 x [mm] 6 5 x = 5 mm.3 x [mm] x = mm.5 [m/s] x [mm] x = mm Fig. 3 Measured liquid and bubble velocities (left: liquid velocity, right: bubble velocity) -

11 Lisbon, Portugal, 9 July, Measured bubble and liquid velocities are shown in Fig.3. Each vector indicates the mean velocity vector calculated using about 5, instantaneous velocities during 5 seconds in each interrogation area. The center of the test section is located at y = 5 mm. The bubbles pass trough the center region (around y = 5 mm), and the widths of the bubble passing regions at x = and 5 mm become wider than that at x = mm. The bubble velocity does not depend on the position so much. The liquid velocities take higher values in the region where bubbles pass through, and the liquid flows down in the near wall region due to the liquid circulation induced by bubbles. The relative velocity between bubbles and the liquid phase is about.5 m/s irrespective of elevations, and it is almost the same as the bubble terminal velocity [, ]. These results clearly demonstrate the potential of SFV for simultaneous measurements of liquid and gas velocities in two-phase flows. 5. Conclusion Spatial filter Velocimetry (SFV) based on spatial filtering of time-series particle images was applied to bubble velocity measurement. Effects of pattern size in recorded image on the measurement were discussed based on synthetic bubble images, and an edge detection process was added to preprocessing of images to improve the accuracy. Then, SFV was applied to bubbly flow in a bubble column to examine its applicability to bubble velocity measurement. Simultaneous measurement of liquid and bubble velocities was also carried out for a planar bubble plume. The main conclusions obtained are as follows: () Size of image pattern should be smaller than the interrogation size to obtain good periodic oscillation in the integrated intensity. The edge detection process is effective to reduce the size of image pattern and to obtain accurate velocity data. () The bubble velocities measured by SFV in a bubble column agree well with those measured by PTV, and therefore, SFV measures the bubble velocity with the same accuracy as or higher accuracy than PTV. (3) Measured mean velocity of bubbles does not depend on interrogation size. To the contrary, standard deviation of measured bubble velocity becomes higher as interrogation size decreases due to superposition of interfacial wave velocity on the measured velocity. This result demonstrates that SFV can measure bubble velocities in multi-scale only by changing the interrogation size. (4) SFV is applicable to simultaneous measurement of bubble and liquid velocities using timeseries images of bubbly flow. Acknowledgement The authors gratefully acknowledge Mr. Kyosuke Kitahata (Kobe University) for his assistance to experiments. This work has been partly supported by the Japan Society for the Promotion of Science (grants-in-aid for scientific research (C) No. 5667). References [] Lucus, G.P. and Mishra, R., 5, Measurement of Bubble Velocity Components in a Swirling Gas-Liquid Pipe Flow using a Local Four Sensor Conductance Probe, Measurement Science and Technology, Vol. 6, pp

12 Lisbon, Portugal, 9 July, [] Guet, S., Fortunati, R.V., Mudde, R.F. and Ooms, G, 3, Bubble Velocity and Size Measurement with a Four-Point Optical Fiber Probe, Particle and Particle System Characterization, Vol., pp [3] Wangjiraniran, W., Motegi, Y., Richter, S., Kikura, H. Aritomi, M. and Yamamoto, K., 3, Intrusive Effect of Wire Mesh Tomography on Gas-Liquid Flow Measurement, Journal of Nuclear Science and Technology, Vol. 4, No., pp [4] Hosokawa, S. and Tomiyama, A., 9, Multi-fluid Simulation of Turbulent Bubbly Pipe Flows, Chemical Engineering Science, Vol. 64, pp [5] Cheng, W., Murai, Y., Sasaki, T. and Yamamoto, F., 5, Bubble Velocity Measurement with a Recursive Cross Correlation PIV Technique, Flow Measurement and Instrumentation, Vol. 6, pp [6] Hosokawa, S. and Tomiyama, A.,, Spatial Filter Velocimetry based on Time-series Particle Images, Experiments in Fluids, Vol. 5, No. 6. [7] Tokuhiro, A., Maekawa, M., Iizuka, K., Hishida, K. and Maeda, M., 998, Turbulent Flow Past a Bubble and an Ellipsoid using Shadow-image and PIV Techniques, International Journal of Multiphase Flow, Vol. 4, pp [8] Hosokawa, S., Moriyama, S., Tomiyama, A. and Takada, N., 3, PIV Measurement of Pressure Distributions about Single Bubbles, Journal of Nuclear Science and Technology, Vol. 4, No., pp [9] Honkanen, M. and Nobach, H., 5, Background Extraction from Double-frame PIV Images, Experiments in Fluids, Vol. 38, pp [] Grace, J.R., and Harrison, D., 967, The Influence of Bubble Shape on the Rising velocities of Large Bubbles, Chemical Engineering Science, Vol.. pp [] Hosokawa S. and Tomiyama A., 6, Effects of Bubble Wake on Coalescence Between Planar Bubbles, Journal of Fluid Science and Technology, Vol., No., pp