The Visualization of Flow Patterns on a Sphere in a Packed Bed t

An experiment was made to visualize the surface flow pattern of spheres in a packed bed. Spheres, the surface of which were coated with benzoic acid, were set within a packed bed and exposed to water flow for a certain period of time. The flow patterns on the surface were observed by the patterns of dissolution of benzoic acid. The patterns were compared with the results of visualizations by other workers using a different method. It was found that the present results are in good agreement with those results in terms of the location of separation lines and singular points on the surface.


Introduction
A packed bed is often used as an effective way of dust collection in a gas at high temperatures. When the basic mechanisms of dust capture are analysed in such a bed, the fluid motion within the bed should be taken into consideration. Also, in considering mass transfer in the packed bed, the flow around each particle is an important factor. However, there have been very few investigations of fluid motion within the bed, and a series of works by the Hanratty group (Jolls and Hanratty 1 ), Wegner et al. 2 ), Karabelas et a1. 3 )) are the only ones which dealt with visualization of the flow around an individual particle in a bed. Since particles are in contact with each other in the bed, flow structure becomes very complicated even for spherical particles.
Wegner et al. 2 ) made a test model of the packed bed consisting of transparent glass spheres. The fluid that they used in the experiment was a liquid which had the same refrac-tive index as that of the glass. To visualize the flow, a small amount of dye was injected into the flow through a nozzle installed in the sphere. They related the flow pattern on the surface to the problem of singularity caused by three dimensional separation on the boundary layer. This kind of problem has been dealt with by Lighthi11 4 ). Wegner et al. 2 ) pointed out that the contact point between spheres becomes what is called the "saddle point" on the skin friction line. They also clarified the locations of the nodal and focal points.
The flow field in the present experiment was almost the same as that of Wegner et ai. 2 ), but it was visualized in a way which was different from theirs. The method presented in this paper was based on the dissolution of solid chemicals in a liquid. That is, the sphere was coated with benzoic acid. The degree of dissolution of benzoic acid depends on the surface shear stress. As a result, the surface flow pattern was recorded in the form of streak lines. This method is easier to use than the dye injection method, particularly for a complicated flow field in a packed bed as in the present example.
In this paper, a technique of visualization using benzoic acid is described first, and then the results of the sphere in the packed bed are presented.   Figure 1 shows a single sphere hung from a string in the test section. In the packed bed experiment, many steel balls are regularly packed in a wooden box, the bottom of which is made of a mesh screen. This box is hung from strings as shown in Fig. 2 and set up in the test section of the tunnel.

2 Visualization technique
The present visualization technique was based on the phenomena of mass transfer from the surface of a body. As described above, the test sphere was coated with benzoic acid, and exposed to the flow for a certain period of time. The dissolution of benzoic acid is remarkable where the velocity gradient on the surface is steep. Therefore, the surface flow patterns could be observed at leisure after taking up and drying the test sphere.
The actual process of this kind of visualization is described next. The benzoic acid, which is a white powder at ordinary temperatures, was made molten by heating (its melting point is 122.4 o C). Three kinds of yet to be hardened steel bearing balls were used as the test spheres, the diameters of which were d = 10, 15 and 19.5 mm. A metal string used as a support was attached to the sphere. First, the surface of the spheres was coloured white using spray lacquer, while benzoic acid was coloured differently from the sphere with ink. Coating with the benzoic acid was done by dipping the sphere in to the molten benzoic acid and taking it up quickly. The film of benzoic acid could be made thinner by preheating the sphere. In this experiment, the thickness of the film was about 0.5 mm. The metal string was cut and removed when the test sphere was set in the packed bed.
If the fluid velocity was high, the benzoic acid dissolved quickly even in pure water. However, the present velocity was so low that a means for promoting dissolution was necessary. Thus, methyl alcohol was added to the water at 40% in weight. The rate of dissolution was influenced by temperature, too. Therefore, a heater was set in the tank CD to keep the pipe-line at a constant temperature by covering it with glass wool. When the temperature of the liquid was 23 to 26° C, about 10 to 15 minutes were needed for the flow patterns to be seen clearly on the spheres.

1 Single sphere
The visualization method presented here was checked by using it for a certain well-known flow before it was applied to the packed bed. Such confirmation is particularly important at low fluid velocities. The fluid velocities in this work were adjusted to be so low that similarity in flow based on the Reynolds number could be obtained between the present packed bed and actual ones. That is, the particle size was 10 to 20 mm in the present flow, while it is much smaller in ordinary packed beds. The superficial fluid velocities were in the order of several em/sec in this experiment. If the density of the coated material (benzoic acid) is different from that of the fluid, true flow patterns cannot be obtained at low velocities due to the effect of gravity. Therefore, a preliminary experiment was done in which the flow around a single sphere was visualized in a uniform stream by using the method presented here. Figure 3 shows a photograph of the pattern  Fig. 6 Array of spheres in the packed bed symbols were obtained at a velocity u less than 1.5 cm/s. The disagreement observed at low velocities came from the effect of gravity, as has been mentioned. The specific weight of benzoic acid is larger than 1 (1.2659 at l5°C). Therefore, when the flow approaches the sphere upwards at very low velocities, the dissolved material tends to fall down along the surface of the sphere, indicated by the large values of e. This phenomenon was observed by the naked eye as well. Based on the above result, visualization at velocities less than 2 cm/s was avoided in the present experiment.

2 Packed bed
Generally, particles in an actual bed have a variety of sizes and shapes. Also, the geometrical position of particles with respect to each other is irregular. However, the present study dealt with only three cases where spheres of a constant diameter were packed regularly, as shown in Fig. 6. Cases (1) and (2) have the same packing structure, called tetrahedral or rhombohedral packing, but these are treated separately in this work because flow fields in them differ depending on the relative direction of the uniform flow to the bed. Case (3) is called cubic packing. The number of contacts of the sphere is 12 in cases (1) and (2), and it is 6 in case (3 ).
The present bed consisted of 4 or 5 layers, and the test sphere were set in the third layer from the front facing the uniform flow. The coordinate system used in this paper is shown in Fig. 7, where e, <I> and R are the components of the spherical coordinate, and Z is the vertical axis with the downward direction which is   Fig. 6 (1) positive. The direction perpendicular to the paper is chosen as the X-axis. Figure 8 shows the results of case (1 ). Wegner et al. Z) also presented the results of this case. Figs. 8 (1) and (2) are side-views observed from the position <I>= 0 and 45°, while Fig. 8 (3) is a KONA No. 5 (1987) picture seen from the top e = 180°. For convenience of explanation, a sketch is given for each photograph. The dark parts correspond to the places of much benzoic acid. It is found from these pictures that a characteristic flow field which is closely related to three-dimen-  Fig. 8. The present flow pattern is almost the same as Wegner's results except that the focal point cannot be observed in this work. What is noted here is that the benzoic acid remained in the form of curved streaks connecting separation zones. This means that the shear stress is SQ small along these streaks that a separation of the three dimensional boundary layer occurs there. The visualization for case ( 1) was made at a Reynolds number of from 210 to 380, in which the patterns obtained were the same as those in Fig. 8. The results for case (2) in Fig. 6 are shown in Fig. 10. The patterns are quite different from those in Fig. 8. Neither the focal point nor the nodal point can be observed clearly in the pictures. Experiments on this packing were made at the Reynolds number Re = 70 ~ 460, but the results were almost the same within this range. However, at a high Reynolds number, several streaks were observed near the apex, as shown in Fig. 11. It is not clear at this stage in the present work whether these streaks are characteristic of such high Reynolds numbers or of the sort of packing.
KONA No.5 (1987) Fig. 12 Result of visualization in the case of Fig. 6(3) Figure 12 shows the results of cubic packing. A curve catenary-like is observed around the central part. A line similar to this was sketched by Karabelas et al. 3 ). Figure 12 shows that longitudinal streaks appear alternatively from the bottom to the central part. These streaks were not observed in Karabelas' experiment where the cubic bed consisted of only one layer.