Ind. Eng. Chem. Res. 1999, 38, 2505-2509
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Projection Velocities of Droplets in the Spray Regime of Sieve Tray Operation Jianmeng Chen,*,† Yunyi Liu,‡ and Tianen Tan‡ Department of Chemical Engineering, Zhejiang University, Hangzhou 310027, China, and Department of Environmental Engineering, Zhejiang University of Technology, Hangzhou 310032, China
A dual-electronic-probe technique and a multicolor high-speed stroboscopic photographic technique were used to measure the initial projection velocities of droplets on a 300 mm diameter sieve tray operating in the spray regime. The experimental results confirmed that both of these techniques can supplement each other for the measurements. A new correlation was obtained to express the relation among projection velocity, droplet size, and gas hole velocity. Introduction
Experiment and Principle
On a sieve tray operating in the spray regime, the gas-liquid dispersion consists primarily of liquid droplets dispersed in the gas, with the surface area of the droplets providing the major contribution to the interfacial area for mass transfer. A free trajectory model has been proposed by Fane and Sawistowski (1969), by which the mass-transfer efficiency of a sieve tray operating in the spray regime may be predicted. The model possesses a description of the droplet trajectories, which requires a knowledge of the initial projection velocities of the droplets into the gas space. Up to now, little work has been done in this field. On the basis of the principle that the maximum projection height above a tray is corresponding to the projection velocity of a droplet, a plate impingement method was adopted to measure the projection velocities of droplets formed at the surface of a dynamically stable froth by Aiba and Yamada (1959). Data obtained in such a way were subsequently correlated and employed in the free trajectory model by Fane and Sawistowski (1969). A photographic technique suggested by Pinczewski and Fell (1977) and Raper et al. (1979) was used to measure the projection velocities of droplets in the spray regime on a sieve tray. However, the photographic instrument they used has some shortcomings; e.g., the images of droplets in their pictures were vague under the condition of high droplet density, and thus the measured locations were usually at a high level above the tray where the droplets were scarce. Lockett (1986) stated that these results are quite different from each other. Even though a theoretical equation was proposed for predicting the projection velocity, it is not practicable because of the unknown parameters, such as the duration of vapor rush and the relative velocity between droplet and vapor rush. In this paper, a combination of a YDL-III dual-electronic-probe droplet size automatic measuring system and a ZG-9000 multicolor high-speed stroboscopic photographic system was used to investigate the projection velocity.
Apparatus. The experiment was carried out for an air-water system in a 300 mm diameter Perspex column fitted with four test sieve trays with segmental downcomers and spaced 600 mm apart. A general schematic diagram of the experimental apparatus is shown in Figure 1. At the top of the column, a rotating stream separator was used to separate the water entrainment from the air. The sieve tray has hole diameters of 10 mm and 10.1% free area. A 210 mm long and 15 mm high exit weir was used. Air was supplied by a blower and measured by a pitot tube connected to an inclined pressure gauge. Water was circulated from top to bottom in the column by a pump and was measured by a rotameter. Principle of YDL-III System. The YDL-III system was used to determine the largest droplet diameter Dm at a certain height H above the test tray. The system was developed by the authors (Chen and Tan, 1997) on the basis of the work of Pye (1971) and consists of a dual-electronic-probe sensor, a signal generator, and a microcomputer (refer to Figure 1), of which the schematic diagram for the measuring principle is shown in Figure 2. The system records the voltage pulses produced when droplets short-circuit the tips of the two probe needles across which a dc potential is applied. The separation of the needles is increased gradually. If the droplet goes through the detecting zone determined by the distance S between the two probes and its size is not smaller than S, there will be a pulse information from the recorder; otherwise, there will be no pulse. So, the pulse number recorded by the signal recorder is corresponding to the number of droplets, the size of which is not smaller than the distance in a certain period. In the measurement, the distance will automatically increase for 0.1 mm/30 s; because the probe sensor was put horizontally at a certain height H above the tray, the recorded pulse number will decrease as S increases. As S becomes large enough, the pulse number would be just zero. At this moment, S is approximately equal to the largest droplet diameter Dm that exists at the position H above the tray. When Dm is measured at different H, a relation between Dm and H can be established; this relation, in turn, shows that the maximum projection height Hm is equal to H for a droplet whose size D equals Dm.
* Corresponding author. Telephone: +86-571-8320386. Fax: +86-571-8320611. E-mail:
[email protected]. † Zhejiang University of Technology. ‡ Zhejiang University.
10.1021/ie980519s CCC: $18.00 © 1999 American Chemical Society Published on Web 05/19/1999
2506 Ind. Eng. Chem. Res., Vol. 38, No. 6, 1999
Figure 1. Schematic diagram of the experimental apparatus.
Figure 2. Principle of the two-electronic-probe sensor method.
From the free trajectory model, when the effect of flotation and friction on the droplet motion is neglected, for a droplet size D, its projection velocity can be derived (refer to the appendix) as follows:
v0 ) xv2 + 2gH ) x2gHm
(1)
which has also been proposed without large discrepancy (Jeronimo and Sawistowski, 1979). When the gas hole velocity uh is changed, the relation between v0 and uh can be obtained for a definite droplet size. Principle of the ZG-9000 Stroboscopic System. The ZG-9000 system consists of a rapidly changing multicolor light source, a microcomputer controlling instrument, and a camera. It differs from the abovementioned traditional photographic instrument mainly by the light source to which two colors of red and yellow are applied. The light source is a high-intensity electronic flash of duration 10-8 s which has a sufficiently short exposure to minimize blurring of the droplet image (see Figure 6). A definite interval was set up between the flashes. Therefore, the experiment could obtain pictures in which two different color images for any droplet will appear. From the interval of the two flashes and the distance of the two different color images, the velocity at a given height above the tray can be obtained, and thus the corresponding projection velocity can be
calculated further by eq 1. It is advantageous of the different color images, and thus it is suitable to measure the droplet population near the tray in high density. The equipment arrangement finally adopted is shown in Figure 3. The light source and camera are mounted on each side of the column. To avoid the disturbance of liquid film on the column wall to the droplet images, two windows made of optical glass are fitted at the distance through which the light travels. Between the target droplets and the window nearby the camera, a pipe of 50 mm i.d. is used to avoid the disturbance of the other droplets which is not located in the sharp focus plane of the objective lens. The flash of duration and the interval of flash were experimentally determined as 0.1 or 0.2 and 2.0-4.0 ms, respectively. Both of these techniques have their advantages and disadvantages. As a noncontacting method, the use of the photographic technique alone has less disturbance to the target droplets and captures the droplet images directly. Meanwhile, because the pictures are taken in such a short time, the technique obtains less information especially for large size droplets and thus leads to statistical uncertainty. Although this particular disadvantage is overcome in the electronic technique by means of detecting large size droplets with a much longer measuring time, the electronic technique itself suffers from the disadvantage of a contact disturbance (because the volume of the sensor is much smaller than that of the plate of the impingement method mentioned above, the disturbance to the droplet-gas flow is usually small) and indirect results. It was therefore decided to use a combination of both the photographic and electronic techniques to obtain a much more accurate droplet projection velocity. Separate velocities from each of the techniques were combined to yield the final droplet projection velocity. Results and Discussion In accordance with the results by Fane and Sawistowski (1969), Jeronimo and Sawistowski (1974), Pinczewski and Fell (1971), Raper et al. (1979), and the present measured data, the relationship among the
Ind. Eng. Chem. Res., Vol. 38, No. 6, 1999 2507
Figure 3. Schematic diagram of the photographic experiment.
Figure 4. Hm vs D at different hole velocities (L ) 2.86 m3/m‚h).
Figure 5. Relation of X to uh.
projection velocity, gas hole velocity, and droplet size is suggested as
v0 ) auhbDc
(2)
where a, b, and c are the parameters to be determined. After eq 2 is substituted into eq 1, taking the logarithm of the equation yields
log Hm ) log X + 2c log D
(3)
a2 + 2b log uh 2g
(4)
where
log X ) log
Figure 6. Photograph of droplets.
where log X is definite for a certain given uh and, therefore, there is a linear relation between log Hm and log D in eq 3. The slope and intercept of the lines are 2c and log X, respectively, and can be obtained from the measured data with the YDL-III (see Figure 4). X may be evaluated for the different uh, and from the relationship of X ∼ uh (see Figure 5), the parameters of a and b are able to be evaluated further. When the data shown in Figures 4 and 5 are regressed, a ) 0.219, b ) 0.797, and c ) 0.261 were obtained. Therefore, the projection velocities of the droplets can be expressed as
v0 ) 0.219uh0.797D-0.261
(5)
The white-black images of typical pictures from ZG9000 are shown in Figure 6. Two images of a droplet at two different heights on the tray are depicted as two circles (in the original color picture, they are yellow and red). The droplet size can be calculated by the size of the circle and the amplifying time used in the photog-
raphy. The projection velocity can be deduced by eq 1 from a velocity calculated by the distance between the images and the flash interval. Under the operating conditions of the gas hole velocity 13.54 m/s and liquid loading 2.86 m3/m‚h, the projection velocity vs droplet size measured by ZG-9000 is shown in Figure 7. It is clear that, although there is a great deal of scattering, v0 tends to decrease with an increase of the droplet size. To make a comparison between the measured results from YDL-III and ZG-9000, substitution of the above values in eq 5 gives results as shown by the solid line in Figure 7. The agreement between them is reasonably well. Under the operating condition of the gas hole velocity 23.55 m/s, the comparisons of the projection velocities from references and from this work are shown in Figure 8. It can be seen that the difference between the results of Fane and Sawistowski (1969) and Jeronimo and Sawistowski (1974) is obvious, and the data of Raper et al. (1979) scatter randomly. However, the present results lie between the data of the former workers (Fane and Sawistowski, 1969; Jeronimo and Sawitowski, 1974) and agree resonably with the data of Raper et al. (1979).
2508 Ind. Eng. Chem. Res., Vol. 38, No. 6, 1999 L ) volumetric liquid flow rate per unit length of the weir, m3/m‚h t ) time, s uh ) gas hole velocity, m/s us ) superficial gas velocity, m/s v ) vertical velocity of the droplet, m/s v0 ) vertical projection velocity of the droplet, m/s X ) intervariable in eq 3 Greek Letters FG ) gas density, kg/m3 FL ) liquid density, kg/m3
Appendix In accordance with the free trajectory model (Fane and Sawistowski, 1969), the differential equation for droplet motion above sieve trays can be derived from Newton’s law Figure 7. Data and curve of v0 vs D (uh ) 13.54 m/s, L ) 2.86 m3/m‚h).
FL - FG 3CD(v - us)|v - us|FG dv v dv ) ) -g dt dH FL 4DFL (A1) If a droplet flies from the tray, the relation between the height of the flying droplet and the flying velocity can be expressed by the integral of eq A1 as
H)
∫vv (F 0
v dv L - FG)g/FL + 3CD|v - us|(v - us)FG/4DFL (A2)
When v equals zero, the droplet gets its maximum height, which can be given as
Hm )
Figure 8. Comparison between the present and other works (uh ) 23.55 m/s).
Conclusions The projection velocities of droplets in the spray regime on a sieve tray were investigated by a dualelectronic-probe technique in combination with a multicolor high-speed stroboscopic photographic technique. The results from the two techniques supplement and confirm each other. With the gas hole velocity varying in the range of 13.54-24.96 m/s, the projection velocity of droplet can be expressed by eq 5. Acknowledgment This work was supported by the National and Zhejiang Provincial Natural Science Foundations of China (Grants 29170288 and 293018). Nomenclature a, b, c ) parameters in eq 2 CD ) drag coefficient D ) droplet size, mm g ) gravitational acceleration, m/s2 H ) height above the sieve tray, m Hm ) maximum projection height of the droplet, m
∫0v (F 0
v dv F )g/F + 3C L G L D|v - us|(v - us)FG/4DFL (A3)
Equations A2 and A3 reflect the relation among H, v, and v0 and between Hm and v0, respectively. From the measured data of H and v or Hm, v0 could be obtained. However, because eqs A2 and A3 are too complicated in integration, v0 cannot be obtained directly. For such a situation, Jeronimo and Sawistowski (1979) proposed that the effect of flotation and friction on droplet motion can be ignored without great discrepancy (
