PARTICLE IMAGE VELOCIMETRY MEASUREMENTS IN AN AERATED STIRRED TANK
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1 Chem. Eng. Comm., 189: , 2002 Copyright # 2002 Taylor & Francis /02 $ DOI: = PARTICLE IMAGE VELOCIMETRY MEASUREMENTS IN AN AERATED STIRRED TANK NIELS G. DEEN BJÒRN H. HJERTAGER Chemical Engineering Laboratory, Aalborg University Esbjerg, Esbjerg, Denmark In state-of-the-art research of multiphase flows, numerical simulations are performed time-dependently and in three dimensions. For the validation of such simulations the availability of quantitative measurement data is crucial. In this study angle resolved and angle-averaged flowfields of the liquid in the vicinity of a Rushton impeller in a stirred tank were measured with the use of particle image velocimetry (PIV). Single-phase liquid flowfields were compared with flowfields of the liquid in an aerated stirred tank. The characteristic trailing vortices in the single-phase flow were observed. When the tank was aerated, the trailing vortices disappeared. Furthermore, the flowfield turned out to be less periodic than without gas. The measured liquid velocities in the impeller-swept region were 50% lower in the case where gas was present. The absolute liquid velocity fluctuations in the presence of gas were of the same order of magnitude as in the case without gas, but when scaled with the maximum radial velocity the relative velocity fluctuations were significantly larger than in the single-phase flow. Keywords: Particle image velocimetry; Aerated stirred tanks; Gas-liquid flow; Rushton impeller Received 18 April 2000; in final form 21 March Address correspondence to Niels G. Deen, Fundamentals of Chemical Reaction Engineering, Department of Chemical Engineering, Twente University, P.O. Box 217, NL-7500 AE Enschede, The Netherlands. Tele: Fax: n.g.deen@ct.utwente.edu 1208
2 PARTICLE IMAGE VELOCIMETRY MEASUREMENTS 1209 INTRODUCTION In the design of aerated stirred tanks computational fluid dynamics (CFD) is often used. In order to validate the results of CFD simulations quantitative measurement data is crucial. For this reason many measurement results of the flow in stirred tanks have been published. Most of these publications concern measurements in single-phase flows (see, i.e., the excellent review by Ranade and Joshi (1990)). Literature concerning velocity measurements in aerated stirred tanks, however, is scarce. Lu and Ju (1987) used hot film anemometry (HFA) in order to determine liquid velocity profiles in an aerated stirred tank. Morud and Hjertager (1996) used laser Doppler velocimetry (LDV) for the measurement of gas velocities in a stirred tank. An overview of literature referred to in this work is given in Table I. A trend is seen in the use of LDV flow measurements. The advantages of this technique are its nonintrusive character and the high temporal resolution. A drawback of this technique is that it is a single-point technique. The instantaneous measurement of large flow structures is therefore not possible. Particle image velocimetry (PIV), however, is a technique that can provide whole field, instantaneous, flow characteristics. In PIV the continuous phase is seeded with small tracer particles that ideally follow the flow. The motion of the particles in an illuminated cross-section of the flow is recorded with a digital camera. Two subsequent flow images with a short exposure time delay are divided into small interrogation areas. Each interrogation area is then correlated with the corresponding interrogation area in the next image. In the resulting correlation field a distinct peak can be found. The location of the peak corresponds to the displacement of the particles in the interrogation area. The velocity is Table I Overview of Velocity Measurements in Baffled Stirred Tanks, Equipped with a Rushton Turbine Reference Measurement technique Geometrical conditions Flow type Measured quantity Costes and Couderc (1988) LDV C=T ¼ 1=2 Liquid Liquid velocity Derksen et al. (1998) LDV C=T ¼ 1=3 Liquid Liquid velocity Lu and Ju (1987) HFA C=T ¼ 1=2 Gas-Liquid Liquid velocity Morud and Hjertager (1996) LDV C=T ¼ 1=2 Gas-Liquid Gas velocity Rutherford et al. (1996) LDV C=T ¼ 1=3 Liquid Liquid velocity Sharp et al. (1998) PIV C=T ¼ 1=2 Liquid Liquid velocity Stoots and Calabrese (1995) LDV C=T ¼ 1=2 Liquid Liquid velocity Wu and Patterson (1989) LDV C=T ¼ 1=3 Liquid Liquid velocity Yianneskis et al. (1987) LDV C=T ¼ 1=2 Liquid Liquid velocity This work PIV C=T ¼ 1=2 Gas-liquid Liquid velocity
3 1210 N. G. DEEN AND B. H. HJERTAGER determined by dividing the measured displacement with the exposure time delay. Sharp et al. (1998) used PIV to measure the liquid velocity in a stirred tank. The time averaged velocity fields show the classical jet flow and the trailing vortices coming from the impeller blades. These results agree very well with LDV results of other researchers. However the instantaneous results presented by Sharp et al. (1998) reveal a much more complex flowfield. An interesting extension of the PIV technique to simultaneously determine the velocities of both the continuous and the dispersed phase was demonstrated by Delnoij et al. (1999). In this technique two peaks are detected in every interrogation area. The peaks correspond to the displacement of the continuous phase (i.e., the particles) and the dispersed phase (i.e., the bubbles). The use of this method in this work is not feasible, however. In order to limit the out-of-plane loss of pairs (i.e., see Keane and Adrian (1992)) the exposure time delay should be smaller than 0.25 ms. For a bubble slip velocity of 0.20 m s 1, the current experiment would result in a relative displacement between the phases of 1 pixel. Because this value is so small, the two displacement peaks will overlap, and it will no longer be possible to discriminate between the two phases. In this work PIV was used to determine the influence of the presence of gas on the liquid velocity field. Measurements were performed in the impeller region of a stirred tank equipped with a Rushton impeller. The results are compared with LDV data from the literature. The influence of the presence of gas on the velocity and turbulence characteristics of the liquid phase will be discussed. EXPERIMENTALTECHNIQUE PIV measurements were performed in a standard stirred tank (H=T ¼ 1), with a dished bottom and a tank diameter of T ¼ m. The stirred tank has exactly the same dimensions as the one described in Morud and Hjertager (1996). A six-bladed Rushton impeller with a diameter of D ¼ T=3 was placed in the center of the stirred tank (C ¼ T=2). Both the impeller blade width (l) and the impeller blade height (w) are equal to 0.25 D. Four baffles of 1=10 T in diameter are equally placed around the tank. The tank was filled with distilled water. Similar to Morud and Hjertager (1996), 4 g NaCl l 1 was added to the water in order to obtain a noncoalescing system. Gas is supplied through a small tube, which is located under the impeller. The tube is perforated at the bottom. The flow was seeded with Dantec polyamide particles of 50±20 mm diameter and 1030 kg m 3 density. The volume fraction of the particles
4 PARTICLE IMAGE VELOCIMETRY MEASUREMENTS 1211 was A 15 Hz New Wave MiniLase double pulsed Nd:YAG laser with a beam-expanding lens was used to create a lightsheet with a depth of 3 mm. A 30 Hz Kodak Megaplus ES 1.0 camera was used to record px 2 images of the flow. A digital encoder is mounted on the central shaft. The encoder generates 360 TTL pulses per rotation of the shaft. A Dantec PIV 2100 processor synchronized the laser and the camera with the use of the encoder signal in such way that measurements were performed at a prescribed angle of the impeller blades with respect to the measurement plane, y. The rotation speed of the impeller was 360 rpm. This corresponds to a Reynolds number Re ¼ ND 2 =n of and a tip velocity U tip of 1.4 m s 1. According to PIV design rules of Keane and Adrian (1992), the exposure time delay between images was set to 0.25 ms. Two measurement series were carried out in an area of mm 2, midway between two baffles. The plane of measurement was located in the vicinity of the Rushton impeller (i.e., r=r ¼ 0 to 0.53 and 2z=w ¼ 3.4 to þ3.2). The first series was taken without gas supply. The power number was determined by measuring the difference in power draw between a filled and an empty tank. The measured power number N P ¼ P=rN 3 D 5 was equal to 6.0. The second series was taken with a gas flow of 0.5 VVM (i.e., Q G ¼ 7.2*10 5 m 3 s 1 ). This corresponds to an aeration number N A ¼ Q G =ND 3 of The measured power number for the second series was 3.8. The flowfield was measured at six different angles behind the impeller blades, y ¼ 0, 10, 20, 30, 40, and 50. The images were divided in interrogation areas of px 2 with an overlap of 50%, which corresponds to an area of mm 2. The PIV technique determines a velocity that is spatially averaged over each area. Sufficiently small areas were used in order to capture the scales of turbulence. The data was validated in three steps. The images of the particles were in the order of 2 4 px. In the correlation analysis this gives displacement peaks of the order 3 6 px. Vectors originating from displacement peaks wider than 6 px are rejected in the first validation step. In the next validation step all vectors originating from displacement peaks with a SNR of less than 1.2 are removed. In the last step every vector is compared with the mean of the eight surrounding vectors. If the norm of the difference between the vector and the local mean exceeds 0.2, the vector is regarded as an outlier. For more details, see Westerweel (1994). For the determination of ensemble-averaged velocity fields and turbulence characteristics, 100 and 150 images were used for the measurements in liquid flow and gas-liquid flow, respectively. More images were used for the measurements in the gas-liquid flow, because the data contains more noise.
5 1212 N. G. DEEN AND B. H. HJERTAGER RESULTS The ensemble-averaged velocity field of the liquid phase is displayed in Figure 1. From Figure 1a the classical jet stream coming out of the impeller blade is observed. In contrast to the results of other researchers (i.e., Wu and Patterson (1989), Costes and Couderc (1988), Derksen et al. (1998)), the jet is directed downward. This may be a consequence of the dished bottom. One circulation cell underneath the jet is observed. The upper circulation cell probably falls outside the area of measurement. The asymmetric positioning of the circulation cells is probably due to the downward directed jet. Figure 1b shows the ensemble-averaged velocity field of the liquid phase when gas is supplied to the tank. The major difference between the flowfields in Figures 1a and 1b is the jet coming out of the impeller. When gas is present, the jet is no longer directed downwards, but as an effect of the gas is pulled upwards. This correspondends with observations of Lu and Ju (1987). It can also be seen that in the presence of gas the maximum velocity in the jet is a factor 2 lower and is spread out over the entire impeller blade. In the center of the tank (the bottom left part of the plot) gas bubbles are rising and entrained in the impeller stream. Liquid is dragged upward in the wake of the bubbles. From Figure 1b it can be seen that the velocities in this area are larger than in the case without gas. Angle resolved ensemble-averaged velocity fields without gas are shown in Figure 2. The development of the flowfield after the passage of Figure 1. Velocity field of the liquid phase, ensemble-averaged, averaged over all angles. (a) without gas; (b) with gas.
6 PARTICLE IMAGE VELOCIMETRY MEASUREMENTS 1213 Figure 2. Velocity fields of the liquid phase, ensemble-averaged, angle resolved, without gas. (a f) 0, 10, 20, 30, 40, and 50 behind the impeller blade, respectively.
7 1214 N. G. DEEN AND B. H. HJERTAGER an impeller blade is seen. The trailing vortices can clearly be distinguished. The eye of the lower vortex is moving horizontally at a height of 2z=w ¼ 0.9. The upper vortex is moving along a horizontal line at a height of 2z=w ¼þ0.2. Both vortices are located lower than observed by Yianneskis et al. (1987), Stoots and Calabrese (1995), and Derksen et al. (1998). Yianneskis et al. (1987) observed the center of the upper vortex at 2z=w ¼þ1.0, while both Stoots and Calabrese (1995) and Derksen et al. (1998) observed the lower vortex at a height of 2z=w ¼ 0.5. For angles of 40, 50, and 0 the upper vortex becomes less clear. This corresponds to experimental and computational observations of Derksen and Van den Akker (1999). The angle resolved ensemble-averaged velocity fields in the presence of gas are shown in Figure 3. There is a large difference between the flowfields in Figures 2 and 3. It seems that the presence of gas diminishes the presence of trailing vortices in the ensemble-averaged flowfield. This is in correspondence with CFD results of Ranade and Deshpande (1999). They performed a detailed simulation of the model problem of gas-liquid flow over a single impeller blade. When gas was introduced from a sparger below the impeller blade, it destroyed the symmetrical vortices. However, this disagrees with the measurements of Lu and Ju, who still observed the vortices. When the flowfields for 10, 20, and 30 are compared, it is observed that the influence of the position of the impeller blade on the flowfield is less pronounced than in the unaerated case. In Figures 4 and 5 axial profiles of, respectively, the radial and the axial liquid velocities are shown. The data was measured at a vertical line just outside the impeller blade, at r=r ¼ The profile of the radial liquid velocity is compared with data of Costes and Couderc (1988), Wu and Patterson (1989), and Derksen et al. (1998). As mentioned earlier, the maximum radial velocity is located below the centerline of the impeller. The maximum radial velocity is lower than measured by other researchers. However, the magnitude of the measured axial component of the velocity is much larger than reported by Costes and Couderc (1988). Therefore the maximum length of the velocity vectors in this work and the work of Costes and Couderc correspond very well. Axial profiles of the radial and axial liquid velocity fluctuations are shown in Figures 6 and 7. In these figures both the angle resolved and the angle-averaged profiles are shown. The angle resolved rms velocities were calculated as follows: u 0 ¼ 1 X 50 X N ju y;i U y j 6N y¼0 i¼1 ð1þ with U y the mean velocity at angle y.
8 PARTICLE IMAGE VELOCIMETRY MEASUREMENTS 1215 Figure 3. Velocity fields of the liquid phase, ensemble-averaged, angle resolved, with gas. (a f) 0, 10, 20, 30, 40, and 50 behind the impeller blade, respectively.
9 1216 N. G. DEEN AND B. H. HJERTAGER Figure 4. Axial profiles of the radial liquid velocity at r=r ¼ 0.37, ensemble-averaged, averaged over all angles, with and without gas. The angle-averaged rms velocities were calculated as follows: u 0 ¼ 1 X 50 X N ju i Uj 6N y¼0 i¼1 ð2þ with U the angle-averaged mean velocity: U ¼ 1 6 X y¼0::50 U y ð3þ Figures 6 and 7 clearly demonstrate that the velocity fluctuations for the liquid-only case exist in a periodic part and a random part. This distinction was also made by Wu and Patterson (1989) and Derksen and Van den Akker (1999) for the velocity fluctuations and the turbulent kinetic energy. Except for their vertical position, the trends shown in Figures 6 and 7 correspond well with those found by Wu and Patterson (1989). For all measurements high values of the velocity fluctuations are found in the positions of the trailing vortices. It is seen that in the
10 PARTICLE IMAGE VELOCIMETRY MEASUREMENTS 1217 Figure 5. Axial profiles of the axial liquid velocity at r=r ¼ 0.37, ensemble-averaged, averaged over all angles, with and without gas. liquid-only case the random velocity fluctuations in the impeller-swept region are approximately 70% of the total velocity fluctuations. The contribution of the nonrandom fluctuations (i.e., periodical velocity fluctuations) diminishes with increasing distance from the impeller blade. Furthermore, it is observed that the velocity fluctuations are in the same order of magnitude when the tank is aerated. However, when the velocity fluctuations would be scaled with a characteristic velocity like the maximum radial velocity, the turbulence intensities in the presence of gas are much higher than without gas. As mentioned earlier, the position of the impeller blades with respect to the plane of measurement has a minor influence on the flowfield for the aerated case. This is also expressed in the fact that the periodic velocity fluctuations are negligible, i.e., the difference between the angle-averaged and angle-resolved velocity fluctuations is very small. CONCLUSIONS Angle-resolved and angle-averaged flowfields of the liquid in the vicinity of a Rushton impeller in a stirred tank were measured with the use of particle image velocimetry (PIV). Single-phase liquid flowfields were
11 1218 N. G. DEEN AND B. H. HJERTAGER Figure 6. Axial profiles of the radial liquid velocity fluctuations at r=r ¼ 0.37, ensembleaveraged, with and without gas. Top: angle averaged, bottom: angle resolved.
12 PARTICLE IMAGE VELOCIMETRY MEASUREMENTS 1219 Figure 7. Axial profiles of the axial liquid velocity fluctuations at r=r ¼ 0.37, ensemble-averaged, with and without gas. Top: angle averaged, bottom: angle resolved.
13 1220 N. G. DEEN AND B. H. HJERTAGER compared with flowfields of the liquid in an aerated stirred tank. The characteristic trailing vortices in the single-phase flow were observed. When the tank was aerated, the trailing vortices disappeared. Furthermore, the flowfield turned out to be less periodic than without gas. In the presence of gas, the measured velocities in the impeller-swept region were about 50% lower. The absolute liquid velocity fluctuations with and without gas are in the same order of magnitude, but when related to the maximum radial velocity the relative velocity fluctuations in the presence of gas are significantly larger than in the single-phase flow. The measurement results show the large impact of the gas-phase on the liquid velocity field. These results are of vast importance in the validation of numerical simulations of multiphase flow. ACKNOWLEDGMENTS The following funds are gratefully acknowledged for their financial support to the laser laboratory at Aalborg University Esbjerg: Lida og Oscar Nielsens fond, Fabrikant Mads Clausens fond, Esbjerg seminarie fond, Direktør Ib Henriksens fond, Fabrikant P. A. Fiskers fond, Obelske fond, and DONG s Jubilæumslegat. LIST OF SYMBOLS C D H l N N A N P P R r Re Q G T U U U y u 0 w z impeller clearance, measured from the tank bottom, m impeller diameter, m liquid level, measured from the tank bottom, m width of the impeller blade, m impeller rotation speed, s 1 aeration number (Q G =ND 3 ), dimensionless power number (P=rN 3 D 5 ), dimensionless power drawn by the impeller, J s 1 tank radius, m radial coordinate direction, measured from the center of the impeller, m Reynolds number (ND 2 =n), dimensionless gas flow, m 3 s 1 tank diameter, m liquid velocity, m s 1 angle-averaged mean liquid velocity, m s 1 mean liquid velocity at angle y, ms 1 liquid rms velocity, m s 1 height of the impeller blade, m axial coordinate direction, measured from the center of the impeller, m Greek letters y angle between the position of the impeller blade and the measurement plane, degrees n kinematic viscosity, m 2 s 1
14 PARTICLE IMAGE VELOCIMETRY MEASUREMENTS 1221 Subscripts r radial coordinate direction, measured from the center of the impeller tip at the tip of the impeller blade z axial coordinate direction, measured from the center of the impeller REFERENCES Costes, J. and Couderc, J. P. (1988). Chem. Eng. Sci., 43, Delnoij, E., Westerweel, J., Deen, N. G., Kuipers, J. A. M. and van Swaaij, W. P. M. (1999). Chem. Eng. Sci., 54, Derksen, J. J., Doelman, M. S. and van den Akker, H. E. A. (1998). Three-dimensional phase-resolved LDA experiments in the impeller region of turbulently stirred tank. Paper presented at Int. Symp. on Applications of Laser Techniques to Fluid Mechanics, Lisbon. Derksen, J. J. and van den Akker, H. E. A. (1999). AIChE J., 45, Keane, R. D. and Adrian, R. J. (1992). Appl. Sci. Res., 49, Lu, W. M. and Ju, S. J. (1987). Chem. Eng. J., 35, Morud, K. E. and Hjertager, B. H. (1996). Chem. Eng. Sci., 51, Ranade, V. V. and Deshpande, V. R. (1999). Chem. Eng. Sci., 54, Ranade, V. V. and Joshi, J. B. (1990). Chem. Eng. Res. Des., 68, Rutherford, K., Mahmoudi, S. M. S., Lee, K. C. and Yianneskis, M. (1996). Chem. Eng. Sci. Des., 74, Sharp, K. V., Kim, K. C. and Adrian, R. J. (1998). Dissipation estimation around a Rushton turbine using particle image velocimetry. Paper presented at Int. Symp. on Applications of Laser Techniques to Fluid Mechanics, Lisbon. Stoots, C. M. and Calabrese, R. V. (1995). AIChE J., 41, Westerweel, J. (1994). Exp. Fluids, 16, Wu, H. and Patterson, G. K. (1989). Chem. Eng. Sci., 44, Yianneskis, M., Popiolek, Z. and Whitelaw, J. H. (1987). J. Fluid Mech., 175,
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