Ind. Eng. Chem. Res. 1987,26,2505-2508
diffusion-controlled process. 9. Conclusive Remarks Although Huffmann et al. (1957) also found that calcium ion diffusion was the rate-limiting step of the digestion process, their model did not take into account the considerable change in surface area of the ore with time. Their equation describing the digestion pocess in diluted phosphoric acid is therefore too simple and cannot be used to calculate the mass-transfer coefficients. The model presented by Serdyuk et al. (1982) was an empirical model, in which a coefficient of digestion and an undefined constant were introduced. Their model is thus only applicable within the limits of their experiments and cannot be used to calculate mass-transfer coefficients, because the relationship between the rate of digestion and the masstransfer coefficients is not well defined. The model used here does not suffer from these disadvantages. Since the digestion process is dominated by the diffusion of calcium ions from the surface of the ore into the bulk of the solution, no influence of impurities present in the process acid is expected. This was confirmed by using real product acid where the impurities did not hamper the digestion. Only if the impurities present in the acid (like excess sulfate ions) give rise to blinding of the ore particles can a reduction of the digestion process be expected. The influence of impurities in the ore can be large if the carbonate ions in the apatite structure are considered as impurities. A very low carbonate content of the ore can reduce the surface reaction step. From the foregoing, it can be concluded that the digestion of Zin phosphate ore in chemically pure phosphoric between 60 and 90 OC can be acid (30-50 wt % P205) described by a model in which calcium ion diffusion is the rate-limiting step.
Acknowledgment We are indebted to DSM for their financial support of the project.
2505
cf = CaO concentration in the bulk of the solution after complete digestion of the ore, kg m-3 c, = saturation concentration of CaO in phosphoric acid, kg
m-3 ct = CaO concentration in the
bulk of the solution at time t ,
kg m-3
f = weight fraction of CaO in the phosphate ore k = mass-transfer coefficient, m s-l
L = mass of phosphoric acid, kg Mt = mass of the phosphate ore at time t , kg R, = radius of an ore particle (mean) at time t , m t = time, s Greek Symbol
density of the Zin phosphate ore, kg m-3 Registry No. H3P04,7664-38-2; Ca, 7440-70-2; fluorapatite, 1306-05-4.
pa =
Literature Cited Becker, P. Phosphate and Phosphoric Acid, Fertiliser Science and Technology Series; Marcel Dekker: New York, 1983; Vol. 3. Bloise, R.; Shakourzadeh, K.; Baratin, F. Ind. Miner. Tech. 1984,9, 721. Calderbank, P. H.; Moo-Young, M. B. Chem. Eng. Sci. 1961,16,39. Elmore, K. L.; Farr, T. D. Ind. Eng. Chem. 1940, 32, 580. Huffmann, E. 0.;Cate, W. E.; Deming, M. E.; Elmore, K. L. J. Agric. Food Chem. 1957,5, 266. Ivanov, E. V.; Zinyuk, R. Yu.; Pozin, M. E. Zh. Prikl. Khim. 1977, 50, 1193. Jordan, D. E.; Monn, D. E. Anal. Chim. Acta 1967, 37, 42. Klok, A.; Tiggelman, J. J.; Weij, P.; van Dalen, J. P. J.; de Galan, L. Proc. Colloq. Spectrosc. Int., 24th 1985, 98. Pribil, R.; Vesely, V. Talanta 1966, 13, 233. Serdyuk, V. V.; Tereshchenko, L. Ya.; Panov, V. P.; Chekreneva, G. M. Zh. Prikl. Khim. 1982,55, 2190. Slack, A. V., Ed. Phosphoric Acid, Fertiliser Science and Technology Series; Marcel Dekker: New York, 1968; Vol. 1. Szekeres, V. L.; Kardos, E.; Szekeres, G. L. J. R a k t . Chem. 1965,4, 113. Tjioe, T. T.; Weij, P.; van Rosmalen, G. M. Proc. World Congr. Chem. Eng., 3rd 1986,2, 925. van der Sluis, S.; Meszaros, Y.; Wesselingh, J. A,; van Rosmalen, G. M. Proc. Fert. SOC.1986, no. 249. Weast, R. C., Ed. Handbook of Chemistry and Physics, 57th ed; CRC: Cleveland, OH, 1976; pp A-116, B-241.
Nomenclature A = external surface area of the phosphate ore, m2
Receiued for reuiew March 11, 1987 Accepted July 28, 1987
Efficient Methods of Inducing Air Suction by Means of Secondary Rotational Air Charge Tetsuo Akiyama,*t Taketoshi Marui,?and Motomi Konof Department of Chemical Engineering, Shizuoka University, Hamamatsu 432, Japan, and Aco Company Ltd., Chiba 272-01, Japan
Means of increasing the rate of air suction that is induced by secondary rotationary air charge from nozzles have been explored experimentally. Two factors that affect the rate of air suction were examined. One was the position of the guide vanes relative to the nozzles. The other was an impingement object a t the fluid exit. The interrelation between the position of the guide vanes and the impingement object was also studied, along with the effect of nozzle angle. Experiments have indicated that it is more advantageous to install guide vanes in the downstream rather than in the upstream of the nozzles, and the impingement object can be effectively used in a limited parameter range. The swirl flow in the straight-through cyclone is usually generated by fixed vanes or impellers, but sometimes turbocompressors can be used. A list of studies (up to Shizuoka University. Aco Company Ltd.
1966) on swirling jets issuing from vane swirlers are listed in the work by Mathur and Maccallum (1967). Experiments were carried out on swirling air flow in a sudden expansion by Hallett and Gunter (1984). The method to produce swirling flow by introducing air tangentially into a cylindrical chamber (instead of using guide vanes) was
0888-5885/87/2626-2505~01.50/0 0 1987 American Chemical Society
2506 Ind. Eng. Chem. Res., Vol. 26, No. 12, 1987 Outlet
, --T1?
Catcher 4 to
bagfilter
r
Downstream
i
t
1
Qi
Qt
upstream
2
Figure 2. Position of guide vanes. 0.31
f 01
downstream
1
I
002
I
I
004
006
I
1
t
Figure 1. Schematic diagram of the experimental apparatus.
used in the rotary flow dust collectors (Ogawa, 1984) and in other studies (Ullrich, 1960; Chigier and Beer, 1964). Recently, we reported studies on a straight-through cyclone with the suction of dust-laden air by means of secondary rotational air charge (Akiyama and Ikeda, 1986; Akiyama et al., 1986). The most important feature of this cyclone is its ability to handle the hot furnace flue gas without precooling: the secondary air charge is conveniently used to protect the cyclone wall from the heat and to drive the dust to the wall, while inducing the dust-laden gas flow toward the cyclone. I t was found, however, that under a practical range of operations, guide vanes were required to achieve a high dust collection efficiency. The installation of guide vanes sometimes resulted in the reduction of the rate of air suction by approximately 50%. Under some operational circumstances, it may become very important to have a high rate of air suction, which of course can be accomplished at the expense of high power consumption. Practically, therefore, a compromise needs to be made between power consumption and collection efficiency. The objective of the present study is to explore some possible means of increasing the rate of air suction (that is induced by the secondary rotational air charge), without resorting to high power consumption. Two factors which affect the rate of air suction were examined. One was the relative position of the guide vanes to the nozzles. The other was the impingement object installed at the fluid exit. Experiments were conducted to investigate the dependence of the rate of air suction on the rate of secondary air charge, nozzle angle, position of guide vanes, and impingement object. Experimental Section Experiments were conducted with basically the same experimental setup and procedures as the previous one (Akiyama and Ikeda, 1986). The schematic diagram of the apparatus is shown in Figure 1. The duct consists of two sections: the main duct (0.535 m long and 0.185 m in diameter) and inlet duct. Two sizes of inlet duct, 0.900 m long with 0.100 m in diameter and 0.899 m long with 0.177 m in diameter, were used. The nozzle air velocity was varied between 23 and 75 m/s with four nozzle angles: 0.26,0.44,0.61, and 0.79 rad. The secondary air flow from the blower, Q2, was controlled with valves 1and 2 and was sent into the duct tangentially through eight nozzles. This induces the primary air flow, Ql, from the inlet duct. The rate of air suction was measured by using an anemometer in the inlet duct.
0.21
L
01 0
Q2
1
008
lm3/s1
Figure 3. Dependence of Q1on Qz,Db, and position of guide vanes.
Position of Guide Vanes In the previous study, we used three kinds of guide vanes that differ in diameter, angle, and vane numbers. They were all installed in the upstream of nozzles so as not to interfere with the jetting air stream from the nozzles. In this study, the guide vanes were installed either in the upstream or downstream of the nozzles, the relative locations of which are depicted in Figure 2. The guide vanes used in the present study consist of eight vanes, 0.185 m in diameter, with vane angle dg = 0.79 rad. Illustrated in Figure 3 is the effect of the guide vanes and their position on Q1given Qz, the inlet duct diameter, Db, and the nozzle angle, On (which is 0.79 rad). The figure indicates that the installation of guide vanes has a significant effect on Q1 for Db = 0.177 m but almost none for Db = 0.100 m when the guide vanes are installed in the downstream of the nozzles. In the case of Db = 0.100 m, the energy loss due to sudden expansion is much larger than that due to guide vanes, so the guide vanes do not appear to affect Q1. This applies even in the cases of On = 0.26, 0.44, and 0.61 rad, although for brevity, the experimental data are not shown. Another important feature to be noted in Figure 3 is that the Q1 when the guide vanes are in the downstream of the nozzles is larger than the Q1 when the guide vanes are in the upstream of the nozzles by approximately 18% for Db = 0.177 m and 10% for Db = 0.100 m. To examine the function of guide vanes in more detail, velocity profiles for Db = 0.100 m were measured at 2 = 0.45 m with Qz= 0.0684 m3/s and are shown in Figure 4. An interesting point to note in Figure 4 is that the tangential as well as axial velocity when the guide vanes are in the downstream of the nozzles is larger (near the duct
Ind. Eng. Chem. Res., Vol. 26, No. 12, 1987 2507 25/---7
small cone
U 0
02
06
04
r
08
t
10
01
I-]
Figure 6. Impingement objecb and their arrangements.
Figure 4. Dependence sf velocity profiles on guide vanes. 10,
A
I
I
e’/
I key
- 0
0
05
O n [rad1
10 [
-1
O50
Figure 5. Relationship between the rate of air suction and nozzle angle.
05
10
15
Figure 7. Effect of impingement plate on the rate of air suction.
center) than when the guide vanes are not installed, although the average axial velocity is equal for both cases. When the guide vanes are in the upstream of the nozzles, the tangential velocity is larger near the wall, but the average axial velocity is smaller than that of the other flow conditions. The effect of On on Q1 is shown in Figure 5 for two flow conditions: when there are no guide vanes and when the guide vanes are installed in the downstream of the nozzles. In both flow conditions, a linear relationship can be observed between Q1 and O,/O, and is represented by a single form
- = 0.55-on + 0.45 Qi
Q1m
%
0.26 rad I0, I0.79 rad
(1)
where QIm is the maximum Q1 associated with On = eg = 0.79 rad.
Impingement Plates and Cones The diameter of the inlet duct was chosen as 0.1 m in the previous study (Akiyama et al., 1986) because the inlet duct of Db= 0.1 m was found to give the most air suction while keeping the gage pressure as well as axial velocity (near the duct center) negative in the region close to the cyclone exit. If they were positive, the dust (flowing near the center of the duct) would not be driven toward the wall and would escape without being separated from the fluid. It was thus speculated that if an appropriate object is set near the exit, then it would prevent the reverse axial flow and also reduce the flow disturbance due to a sudden flow expansion at the duct exit, in which case the rate of air suction could be increased. Three kinds of objects were used to examine their effect on air suction: a plate 0.30 m in diameter and a large and a small cone of which geometries and arrangements are depicted in Figure 6. Representative experimental results of Q1/Qlo vs Z’/D, are shown in Figure 7 for Q2 = 0.028 m3/s and Db = 0.100 m, where Qlo refers to the rate of air suction when no impingement plate is set at the fluid exit and Z’ refers to
17
Z i D , [-I
I
,
I
2508 Ind. Eng. Chem. Res., Vol. 26, No. 12, 1987 Db=0177m
05L
abiect
i
downsfream
upstream
I
Con?
L
0 0
10
05
Z/Da
15
17
[-I
Figure 9. Combined effect of impingement object and position of guide vanes on Q1.
the suction rate (Qlo = 6.65 X m3/s) that is obtainable when the guide vanes are set in the downstream of the nozzles. This appears to suggest the limited use of the impingement object.
Discussion The primary objective of the present study was to find efficient methods of inducing air suction by means of secondary rotational air charge. In other words, we have been concerned primarily with the fluid dynamical aspect of the air suction. From the viewpoint of designing the straight-through cyclone (with the air suction), however, the dust collection efficiency is also a matter of equal importance. By use of the inlet duct of Db = 0.100 m, the dust collection efficiency was measured for Q2 = 0.0415 m3/s with glass beads of 16 pm in average diameter. The glass beads were provided by means of a vibration feeder in the primary air flow at the concentration level of 0.003 kg/m3. The secondary air charge from the nozzles in turn provided swirling motion to the primary air flow, driving the glass beads toward the wall. At the exit of the main duct, the glass beads were caught in the annular space of the catcher and were sucked into a bag filter through the use of a vacuum pump. The dust collection efficiency was 95% (with Q1 = 0.0585 m3/s) and 92% (with Q1 = 0.0532 m3/s) when the guide vanes were installed in the downstream of the nozzles, respectively, and 85% (with Q1 = 0.0585 m3/s) when no guide vanes were installed. Somewhat unexpectedly, we thus attained a higher rate of air suction with equal or slightly higher dust collection efficiency when the guide vanes were installed in the downstream rather than in the upstream of the nozzles. This tendency was observed with other experimental conditions as well. The velocity profiles in Figure 4 seem to give a partial answer for the cause of the enhanced air suction and dust collection efficiency. The tangential as well as axial velocity, when the guide vanes are in the downstream of the nozzles, is larger than, when the guide vanes are in the upstream of the nozzles. The dust collection efficiency was measured also with the impingement object at the fluid exit, but no appreciable change in the dust collection efficiency was observed. The rate of air suction increases as Db increases. Practically, however, there are two factors that must be accounted for in determining the size of Db. First, dust collection efficiency must be maintained at a certain level: a large Db would deteriorate the dust collection efficiency, because the gage pressure, as well as the axial velocity (near the center of the cross-sectional area), may not become negative for a large Db.Second, the fluid velocity in the
inlet duct must be fast enough to send dust into the main duct: an increase in Q1 is achieved at the expense of slow inlet velocity, given the rate of secondary air charge. A quantitative comparison between the present type of straight-through cyclone and a reverse-flow cyclone has been made in our previous paper (Akiyama et al., 1986). It has been demonstrated that the energy loss within the present straight-through cyclone is comparable with a standard reverse-flow cyclone.
Conclusions Means of increasing the rate of air suction, induced by secondary rotational air charge from the nozzles, have been explored. The experimental apparatus consists of two sections: the main and inlet duds. Two sizes of inlet ducts were used, along with four different nozzle angles. First, the effect of guide vane position relative to the nozzles was investigated in terms of air suction efficiency. The installment of guide vanes was found to have a significant effect on Q1for Db = 0.177 m but almost none for Db = 0.100 m, provided guide vanes were installed in the downstream of the nozzles. The rate of air suction as well as the dust collection efficiency, when the guide vanes are in the downstream of the nozzles, may be higher than when the guide vanes are in the upstream of the nozzles. Second, the effect of impingement objects on Q1was investigated. A plate or a cone was installed at the fluid exit, and Q1 was measured. It was found that Q1 can be increased with the installation of an impingement object in the case of 8, = 0.44 but not for 8, = 0.61 or 0.79 rad; also, the effect of the position of the guide vanes (relative to the nozzles) is a more dominant factor than the impingement object. Therefore, the usefulness of the impingement object appears limited. Nomenclature D, = diameter of main duct, m Db = diameter of inlet duct, m Q1 = rate of air suction, m3/s Qlo = rate of air suction without impingement object in Figures 7 and 9, m3/s Qlm = Q1 for 8, = 0.79 rad in Figure 5 , m3/s Q2 = rate of secondary air charge, m3/s r = R/Ra R = radical coordinate, m R, = radius of main duct, m V = tangential velocity, m/s W = axial velocity, m/s 2 = axial coordinate, m 2’= distance between the duct exit and impingement plate,
m
Greek Symbols 8, = guide vane angle 8, = nozzle angle
Literature Cited Akiyama, T.; Ikeda, M. Znd. Eng. Chem. Process Des. Deu. 1986,25, 907. Akiyama, T.; Marui, T.; Kono, M. Znd. Eng. Chem. Process Des. Dev. 1986,25, 914. Chigier, N. A.; Beer, J. M. JBasic Eng. 1964, 86, 788. Hallett, W. L. H.; Gunter, R. Can. J . Chem. Eng. 1984, 62, 149. Mathur, M. L.; Maccallum, N. R. L. J . Znst. Fuel 1967, 40, 214. Ogawa, A. Separation of Particles from Air and Gases; CRC: Boca Raton, FL, 1984; Vol. 2, Chapters 1 and 2. Ullrich, H. Forsch. Geb. Zngenieurwes. 1960, 26, 19. Received f o r review March 13, 1987 Revised manuscript received August 7, 1987 Accepted September 4, 1987
