Abstract: In this study the use of particle image velocimetry (PIV) in multiphase flows is described. Velocity fields are measured of both the continuous and the ...
MULTIPHASE PARTICLE IMAGE VELOCIMETRY MEASUREMENTS IN A BUBBLE COLUMN Niels G. Deen Chemical Engineering Laboratory, Aalborg University Esbjerg Niels Bohrs Vej 8, DK-6700 Esbjerg, Denmark
Abstract: In this study the use of particle image velocimetry (PIV) in multiphase ows is described. Velocity elds are measured of both the continuous and the dispersed phase in a bubble column. From the measurements, turbulence characteristics like the strain rate and mutual correlations between gas and liquid velocities can be derived for the validation of numerical simulations. Keywords: bubble column, bubbly ow, experimental uid dynamics, multiphase
ow, multiphase PIV 1. INTRODUCTION In the chemical process industry bubble columns are widely used because of their simple construction and the ease the operation conditions can be changed. For a proper design of these apparatus a good understanding of the prevailing multiphase
ow processes is vital. One of the major problems is understanding and subsequently modeling of turbulence. In order to validate multiphase turbulence models, a technique is needed that can provide simultaneous measurement data of whole eld, instantaneous ow characteristics of all phases. Particle Image Velocimetry (PIV) is a measurement technique that can provide such information. Previously, Oakley et al. (1997) and Gui and Merzkirch (1996) have used PIV for the velocity measurements of the continuous phase and Particle Tracking Velocimetry (PTV) to measure the velocity of the dispersed bubbles. However, it is also possible to measure the gas velocity with the use of PIV (Delnoij, 1999). That is, when two phases with a mutual slip velocity are present, two displacement peaks can be detected in the correlation function, one for each phase. An ensemble of subsequent correlation
functions is used, to increase the signal to noise ratio of the displacement peak of the dispersed phase. This multiphase PIV technique can now be applied to measure the gas and liquid velocity simultaneously, using a single camera. In this study, the multiphase PIV technique will be introduced. Its use will be illustrated with measurement results in a bubble column. Finally, its potential to derive turbulence statistics will be stressed. 2. THEORY In PIV the ow is seeded with small tracer particles. Next a cross section of the ow is illuminated with the use of a laser light sheet. The motion of the tracer particles in the cross section of the
ow is recorded with a digital camera. Every recorded image of the ow is subdivided in small interrogation areas. By comparing corresponding interrogation areas in two subsequent images, the displacement of the particles in that interrogation area can be determined. The velocity in the interrogation area, at position x, can then easily be calculated by dividing the displacement, sD by the exposure time delay between the two images, t:
Delnoij (1999) showed that the amplitude of the displacement peaks increases linearly with the number of correlation functions in the ensemble, while the amplitude of the noise peaks stays constant.
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3. EXPERIMENTAL SETUP
Fig. 1. Typical correlation function, R(s) for a gas-liquid ow, using an interrogation size of 32 pixels. 1 sD v (x; t) = (1) M t with M the magni cation of the camera. By carrying out this procedure for all interrogation areas, a velocity eld can be determined for the entire cross section. The displacement of tracer particles and bubbles in every interrogation area is determined with the use of a correlation technique. With this technique a probability is calculated for every possible displacement, s in the interrogation area. A typical example of a correlation function is shown in gure 1. In this gure two distinct peaks can be seen. The coordinates of these peaks correspond to the displacement vectors, sTD and sBD of the tracer particles and the bubbles respectively. The corresponding amplitudes of these peaks are T (s) and RB (s). Because of the large density RD D di erence between the gas and the liquid phase, there will always be a di erence in displacement between the two phases (i.e. slip velocity). Therefore the two peaks will never overlap. The correlation function can be written in the following qualitative way: T (s) + RB (s) + RF (s) R(s) = RD (2) D with RF (s) the uctuating noise peaks. To determine the displacements of tracers and bubbles, the two highest peaks in the interrogation area are determined. In order to be able to detect the displacement peaks, they need to be higher than the noise peaks. Keane and Adrian (1993) formulated a set of rules to ensure that the right peaks are detected. The most important rule is that the e ective number of particle pairs per interrogation area, NI > 7. In general this is the case for the tracer particles. However, there are only a few bubbles present in every interrogation area (i.e. NI =1 ; 2). Therefore it is hard to obey to the rule, with respect to the bubbles. To overcome this problem Delnoij (1999) suggested the use of an ensemble correlation technique. In this technique an ensemble of n subsequent correlation functions is summed:
PIV measurements have been performed in a vertical cross-section in a lab-scale bubble column. The bubble column was 200 mm wide and deep, and had a height of 1 m. Gas was introduced at a
owrate of 5.63 ml s;1 through a porous plate in the center of the bottom of the column. The size of the bubbles was approximately 2 mm. The ow was seeded with polyamid tracer particles. The particles had a diameter of 50 m and a density of 1030 kg m;3 . For the illumination an Argon ion laser was used. The laserbeam was transformed into a lightsheet with the use of a rotating mirror. The light sheet had a thickness of 3.8 mm. Images of the ow were recorded with a Texas Instruments MC1000-WU20 camera. The camera had a resolution of 1008 1016 pixels and a framerate of 15 Hz. The recorded eld of view had a size of 152 154 mm2 . The camera was operated in a way to enable short exposure time delays between two exposures, t of 2.5 ms. The velocity elds were determined with interrogation sizes of 64 pixels. Every vector was validated by comparing it with the median of the eight surrounding vectors (Westerweel, 1994). If the di erence between the vector and the median value was larger than a certain treshold, the vector was regarded as an outlier and replaced with the average of the eight surrounding vectors.
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Measurement results of the multiphase ow in a bubble column were shown in gure 2. From these
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4. RESULTS When the column is operated in the described mode, a bubble plume rises through the center of the column. In that area liquid is dragged upward by the bubbles. Large vortices in the liquid are present just next to the bubble plume. A down ow of liquid is observed near the walls of the bubble column. The measured gas and liquid velocity elds are shown in gure 2 (Delnoij et al., 1999). 5. DISCUSSION
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Fig. 2. Velocity elds in a vertical cross section in a bubble column. Left: instantaneous liquid eld, using n =1. Right: pseudo instantaneous gas velocity, using n =15. The reference vectors are 0.60 m s;1 : (Delnoij et al., 1999). gures it becomes clear that the multiphase PIV technique is able to produce quantitative measurement data of whole eld, ow characteristics of both phases. The complex structures in the liquid ow illustrate the time-dependent and 3dimensional character of the ow. When the liquid and gas ow elds in gure 2 are compared, it can also be seen that there is a strong relationship between the gas and liquid velocity. The vortices that were observed visually, are also present in the measured liquid velocity eld. The gas velocity eld is derived with the use of the ensemble correlation technique. The timescale of the measurements is therefore increased from 2.5 ms to about 1 s. The result is that all the transient structures in the gas ow are smoothed, so the gas velocity in the bubble plume seems to be uniform. 6. FUTURE WORK The described technique is able to produce instantaneous ow elds for the liquid velocity. Instantaneous information of the gas phase however has not been derived yet. This step is a necessary one for further research. One possibility to determine the instantaneous gas ow eld, is to use the pseudo-instantaneous gas ow eld as a feedback. When this is done, turbulence statistics (i.e. velocity uctuations) of the gas-phase can also be calculated, from the instantaneous gas ow eld. Turbulence statistics of the ow can be determined, by measuring time-series in the order of 100 ow elds. The relation between the uctuations in the gas and liquid velocities can be used for models of the mutual in uence of the gas and
liquid phase. From the ow elds strain rate elds can also be derived. These can for example be used in large eddy simulations (LES). 7. ACKNOWLEDGEMENTS The software for the digital PIV analysis (PIVware) originated from the Laboratory for Aero and Hydrodynamics, Delft University of Technology, The Netherlands. 8. REFERENCES Delnoij, E. (1999). Fluid dynamics of gas-liquid bubbble columns- a theoretical and experimental study. PhD thesis. University of Twente. Delnoij, E., J. Westerweel, N. Deen, J. Kuipers and W. van Swaaij (1999). `Ensemble correlation PIV applied to bubble plumes rising in a bubble column'. Fourth conf. on G-L and G-L-S Reactor Eng. GLS99. Gui, L. and W. Merzkirch (1996). `Phaseseparation of PIV measurements in twophase ow by applying a digital mask technique'. ERCOFTAC Bulletin pp. 45{48. Keane, R. and R. Adrian (1993). Flow Visualization and Image Analysis. (ed. F.T.M. Nieuwstadt). chapter Theory of cross-correlation analysis of PIV images, pp. 1{25. Oakley, T., E. Loth and R. Adrian (1997). `A two-phase cinematic PIV method for bubbly
ows'. J. Fluids Eng. 199, 707{712. Westerweel, J. (1994). `Ecient detection of spurious vectors in particle image velocimetry data'. Exp. Fluids 16, 236{247.
