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Ind. Eng. Chem. Res. 1998, 37, 1478-1482
GENERAL RESEARCH Jet Mixing of Liquids in Long Horizontal Cylindrical Tanks Joseph J. Perona,† Tommy D. Hylton,* E. Lloyd Youngblood,‡ and Robert L. Cummins Oak Ridge National Laboratory,§ P.O. Box 2008, Oak Ridge, Tennessee 37831-6330
Large storage tanks may require mixing to achieve homogeneity of contents for several reasons: prior to sampling for mass balance purposes, for blending in reagents, for suspending settled solids for removal, or for use as a feed tank to a process. At Oak Ridge National Laboratory, mixed waste evaporator concentrates are stored in ∼190-m3 (50 000-gal) horizontal tanks, about 3.7 m (12 ft) in diameter and 18 m (60 ft) in length. This tank configuration has the advantage of permitting transport by truck and therefore fabrication in the shop rather than in the field. A survey of the literature revealed no information on mixing large storage tanks with length-to-diameter ratios greater than 2. Jet mixing experiments were carried out in two model tanks: a 0.87-m3 (230-gal) Plexiglas tank that was ∼1/6 linear scale of the actual waste tanks and a 95-m3 (25 000-gal) tank that was about 2/3 linear scale of the actual waste tanks. Mixing times were measured by the use of a sodium chloride tracer and several conductivity probes distributed throughout the tanks. Several jet sizes and configurations were tested. In the 0.87-m3 tank, jet diameters of 0.016, 0.022, and 0.041 m (0.62, 0.87, and 1.61 in.) were used. In the 95-m3 tank, jet diameters of 0.035 and 0.049 m (1.38 and 1.93 in.) were used. One-directional and two-directional jets were tested in both tanks. Mixing times for each tank were correlated with the jet Reynolds number and for the two tank sizes using the recirculation time for the developed jet. Introduction Large storage tanks may require homogenization of contents for several reasons: for sampling of the tank contents for inventory purposes, for blending in additives or reagents, for suspending settled solids for tank cleaning, or for using as a feed tank to a process. The use of mechanical mixers is often not practical for large tanks, and jet mixing is a common choice. In this method the tank contents are recirculated through a pump, often located external to the tank, and then back into the tank through a jet. The jet flows into the bulk liquid at a high relative velocity near the nozzle and expands as it flows away from the nozzle, entraining and mixing bulk fluid. In one of the earliest accounts of this method, Fossett and Prosser (1949) studied the blending of tetraethyllead in underground gasoline tanks 36 m (118 ft) in diameter by 6 m (20 ft) in depth. At Oak Ridge National Laboratory (ORNL), mixed waste evaporator concentrates are stored in 190-m3 (50 000-gal) horizontal tanks that are ∼3.7 m (12 ft) in diameter by 18 m (60 ft) in length. Wastewaters are neutralized with sodium hydroxide prior to evaporation, * To whom correspondence should be addressed. Telephone: (423) 576-2225. E-mail:
[email protected]. † Professor Emeritus of Chemical Engineering, University of Tennessee, Knoxville, TN. ‡ Retired from Oak Ridge National Laboratory. § Managed by Lockheed Martin Energy Research Corp., for the U.S. Department of Energy under Contract DE-AC0596OR22464.
and the concentrates produce a hydroxide sludge upon cooling. The tanks contain a sludge layer that is typically 0.6-1.2 m (2-4 ft) deep. The tank contents are highly radioactive, and the tanks must eventually be emptied. Work at the Savannah River Site showed that similar sludges can be suspended into the supernatant by using jets in close proximity and parallel to the tank floor (Churnetski, 1981). The resulting slurry can then be pumped out of the tank. Alternately, the sludge might be dissolved by an acid addition before the tank contents are pumped out. Work at ORNL is being carried out in two stages: mixing in the absence of sludges, reported in this paper, followed by studies of sludge mobilization. The literature on jet mixing of tanks has been surveyed by Revill (1985) and by Maruyama (1986). Most of the studies reported have been done with tanks having vertically oriented cylindrical surfaces and flat bottoms, which is also the structure of radioactive waste storage tanks at the Savannah River Site and the Hanford Site. Most commonly in the published literature on mixing, a single jet or multiple jets are located near the tank floor, oriented at an angle to the vertical; some studies, however, have been published for jets oriented vertically at the tank axis. Published mixing data for vertical jets have described results only for short tanks (i.e., those tanks with liquid height/tank diameter ratios of 0.3:1). The present study reports results for horizontal-axis tanks with length/diameter ratios of 4 and 5. An experimental study was conducted to determine mixing times for these longer tanks.
S0888-5885(97)00118-8 CCC: $15.00 © 1998 American Chemical Society Published on Web 03/12/1998
Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998 1479
Figure 1. Sketch of the tank and pipe loop setup.
Experimental Method Mixing experiments were performed with water in two model tanks. The smaller (0.87-m3 or 230-gal) tank, made of Plexiglas to permit flow visualization studies, was ∼1/6 linear scale of the actual storage tanks: that is, 0.6 m (2 ft) in diameter by 3 m (10 ft) in length. The larger (95-m3 or 25 000-gal) tank was 3 m (10 ft) in diameter by 12 m (40 ft) in length. Data were taken with a single jet placed ∼1/4 tank length from one end, pointed toward the center of the tank. This location was chosen because of its proximity to the most accessible port on the actual tanks. Jet nozzles were straight pieces of pipe or tubing 10 diameters long. The jet diameter and velocity were varied with this configuration. Tests were also made with two-directional opposed jets at this location and also at the center of the tank lengthwise. In all cases the jet was positioned close to the bottom of the tank, in the range of 1-4 jet diameters from the floor to the jet centerline. Tests were made with the suction to the pump loop at the opposite end of the tank from the jet and also at the tank center. A sketch of the Plexiglas tank piping arrangement is shown in Figure 1. The pump for the 0.87-m3 (230-gal) tank was a canned-rotor chempump (Crane model GA-1K-1S), which provided flow rates up to 8 m3/h (36 gal/min) in the recirculation loop. For the 95-m3 (25 000-gal) tank, a Gardner-Denver triplex plunger pump was used; this pump yielded flow rates up to 45 m3/h (200 gal/min). Flow rates in the recirculation loops were measured with magnetic flowmeters (Magflo). Each test began with the tank containing water in a quiescent condition. A section of the piping loop of the 0.87-m3 tank was isolated with ball valves, drained, and filled with an aqueous solution of sodium chloride. The ball valves were opened, and the pump and clock were started simultaneously. For the 95-m3 tank, the sodium chloride solution was poured into the tank near the top center. The sodium chloride concentration was measured in the tanks at four locations through the use of conductivity probes. The probes were placed near the top surface and the tank bottom at both ends where a dead space might occur. The probes were toroidal flowthrough sensors manufactured by Rosemount Analytical (model number 228). Signals from the conductivity cells were fed to Rosemount model 1054A microprocessors, which provided digitized data at 10-s intervals to data acquisition software. Conductivity versus time data were analyzed both manually and by computer for determination of mixing times. A sample conductivitytime plot is shown in Figure 2. The mixing time was determined as when the last probe had reached a horizontal orientation, indicating no long-term concentration changes, and short-term concentration changes and short-term fluctuations were within (5%.
Figure 2. Sample plot of solution conductivities at four tank locations versus time.
Figure 3. Correlation of mixing times for one-directional jets in the 0.87-m3 tank. The jets were located ∼1/4 tank length from one end of the tank and near the bottom of the tank.
Results Mixing times in the 0.87-m3 (230-gal) tank, as shown in Figure 3, were in the range of 300-1800 s as the flow rate was varied from 8 to 1 m3/h (35 to 5 gal/min). In these experiments, single jets were located ∼1/4 tank length from one end, discharging toward the middle of the tank. Jet diameters of 0.016, 0.022, and 0.041 m (0.62, 0.87, and 1.61 in.) were tested with the jet located 0.03 m (1.25 in.) above the tank bottom for the two smaller diameters and 0.04 m (1.75 in.) above the floor for the largest-diameter jet. Values of h/Dn were 2.0, 1.4, and 1.1, respectively. The results in Figure 3 show that the mixing times for the various jet diameters can be correlated with jet Reynolds number (DnFνn/µ). The temperature of the water in the tank was measured and used to obtain viscosity and density data for calculating the Reynolds number. Salt concentrations were too low to affect these properties significantly. The 0.022-mdiameter jet was raised from near the tank bottom to the tank axis, and a series of mixing times were measured. The mixing times were not greatly different. With the jet at the tank axis, mixing times were about 15% lower at a Reynolds number of 100 000 and about 20% higher at a Reynolds number of 20 000 than with the jet near the tank floor. Attempts were made to obtain mixing times with double-direction jets in the 0.87-m3 tank using this range of flow rates, but the results were chaotic and not reproducible. This lack of reproducibility was not caused by instability of the
1480 Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998
Figure 4. Mixing times in the 95-m3 tank. The jets were located ∼1/4 tank length from one end of the tank.
Figure 6. Comparison of mixing times for the 0.035-m doubledirectional jet at two locations in the 95-m3 tank. Table 1. Mixing Time Data
Dn (m)
flow rate (m3/h)
mixing time (s)
590 473 1510 748 728 468 338 366 1220 898 672
95-m3 Tank, Single Jet, Tank Length from the End of the Tank 11.5 1.68 80.0 17.0 2.48 110 26.3 3.84 182 45.2 6.58 311
4500 2640 1500 840
0.035 0.035 0.035 0.035 0.035 0.049 0.049 0.049 0.049
95-m3 Tank, Double Jet, Tank Length from the End of the Tank 11.4 1.63 46.9 22.7 3.26 86.7 28.8 4.15 119 28.8 4.15 119 34.1 4.91 141 11.4 0.829 34.6 17.0 1.24 51.9 22.7 1.66 69.0 45.4 3.32 138
2760 1290 882 882 660 4740 2430 1650 720
0.035 0.035 0.035 0.035 0.035
95-m3 Tank, Double Jet in the Center of the Tank (Lengthwise) 11.7 1.69 59.2 14.0 2.01 67.9 22.9 3.32 116 28.4 4.08 143 34.1 4.91 170
3390 2610 1440 930 815
0.016 0.016 0.022 0.022 0.022 0.022 0.022 0.022 0.041 0.041 0.041
conductivity probes. Perhaps this particular mixing configuration would provide a suitable application for chaos theory. Mixing times in the 95-m3 (25 000-gal) tank were measured with single and double jets located ∼1/4 tank length from one end, using jets with inside diameters of 0.035 m (1.38 in.) and 0.049 m (1.93 in.). Experiments were also made with a double jet in the center of the tank lengthwise. All mixing tests in the 95-m3 (25 000gal) tank were performed with the jets positioned 0.15 m (6 in.) from the bottom of the tank, giving h/Dn values of 4.3 for the smaller jet and 3.1 for the larger jet. For the single jet, mixing times ranged from 840 to 4500 s as the flow rate was varied from 45 to 11 m3/h (200 to 50 gal/min), as shown in Figure 4. For the double jet of the same size and location, mixing times were within 15% of those for the single jet at the same flow rates, although the jet velocities (and Reynolds numbers) were half of those of the single jet. At a given flow rate, mixing times were significantly lower with the 0.035-m (1.38-in.) jet than with the larger jet. Mixing times for the different sizes of double jets at the 1/4-tank-length location were correlated by the jet Reynolds number, as shown in Figure 5. The 0.035-m (1.38-in.) double jet was moved to the center position of the tank (lengthwise). A series of tests were made over the flow rate range of 11-34 m3/h (50150 gal/min). In Figure 6 the mixing times are compared with those obtained with the jet located 1/4 tank
jet Reynolds number (×1000)
0.87-m3 Tank, Single Jet, Tank Length from the End of the Tank 3.95 5.64 89.0 5.77 8.23 130 1.10 0.799 18.0 2.52 1.83 40.7 3.86 2.79 62.0 5.43 3.93 87.0 7.20 5.21 116 8.11 5.88 131 1.77 0.375 15.4 3.84 0.811 33.3 7.74 1.64 67.0
1/
Figure 5. Correlation of mixing times for double-directional jets in the 95-m3 tank. The jets were located ∼1/4 tank length from one end of the tank.
jet velocity (m/s)
1/
0.049 0.049 0.049 0.049
1/
4
4
4
length from the end of the tank. Mixing times are ∼2025% longer with the jet in the center of the tank. Mixing time data are presented in Table 1. Correlation of Mixing Times Lehrer (1981) developed a theoretical model for mixing in free turbulent jets, which he then applied to the tank mixing time data of Fossett and Prosser (1949) and of Fox and Gex (1956). Lehrer defined the entrainment ratio as that of the mass flow rate in the fully developed
Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998 1481 Table 2. Developed Jet Lengths tank size (m3) 0.87 0.87 0.87 95 95 95
jet locationa
Dn (m)
from end from end 1/ from end 4 1/ from end 4 1/ from end 4 center
0.016 0.022 0.041 0.035 0.049 0.035
1/
4
1/
4
distance to the number of Dn’s to the end end of the of the tank tank (m) 2.3 2.3 2.3 9.1 9.1 6.1
145 103 56 260 185 174
a The description “1/ from end” indicates the jet was located 4 ∼1/4 tank length from one end of the tank.
jet to the mass flow rate of the injected stream (i.e., (Qe + Qn)/Qn). His thesis was that the time required for jet mixing a tank is inversely proportional to the entrainment ratio. The ratio of entrained liquid flow rate to jet flow rate is as follows (Revill, 1985):
Qe z )β Qn Dn
(1)
The empirical factor β depends on the jet Reynolds number in the laminar region but is only a weak function of Re for the turbulent jets of interest in this work. When Qe is large compared with Qn, the ratio in eq 1 approximates the entrainment ratio. The recirculation time for the developed jet is equal to the recirculation time calculated with the flow rate through the jet nozzle multiplied by the factor Dn/L. If the time required to mix a tank is proportional to the recirculation time for the developed jet, a correlation of the following form is indicated (Maruyama, 1986):
tm ) (constant)tR(Dn/L)
(2)
Determination of the length L of the fully developed jet is not straightforward. The turbulent jet entrains liquid and expands as it moves away from the nozzle, and its velocity slows until at some point it no longer entrains liquid. The centerline jet velocity and concentration may be approximated as (Revill, 1985):
vc 6Dn ≈ vn z
(3a)
Cc 4.5Dn ≈ Cn z
(3b)
Equations 3a and 3b show that the velocity and concentration fall in inverse proportion to the distance from the nozzle. The mixing effect of a turbulent jet is generally considered insignificant after about 400 jet diameters (Revill, 1985). When the jet impacts the end of a tank, it may be considered to be broken up and no longer a jet. In our experiments with the 0.87-m3 tank, the smallest single jet (0.016 m diameter) was about 150 diameters from the end of the tank. With the 0.035-m (1.38-in.) jet in the 95-m3 (25 000-gal) tank, the distance to the end was about 260 diameters. In all other cases the jets were located shorter distances from the ends of the tanks. Table 2 lists the distances (in terms of jet diameters) between the jet nozzles and the end of the tank. In most of the experiments reported in this paper, the jet is located near the floor of the tank. The developing jet contacts the floor of the tank a short distance away
Figure 7. Correlation of mixing times for both model tanks. The length of the developed jet is calculated as the distance from the nozzle to the end of the tank.
from the nozzle and is affected by it. Several investigators have reported studies of jets developing from a circular nozzle above a plane surface (e.g., Newman et al., 1972; Rajaratnam and Pani, 1974; Davis and Winarto, 1980). These studies show that the influence of the wall is to cause the jet to spread laterally (parallel to the wall) to a much greater extent than vertically. Davis and Winarto (1980) report experiments on velocity distributions and turbulent properties of jets for h/Dn values of 0.5-4. The ratio of spreading rates approaches 8.5 at large distances from the nozzle. Measurements of turbulence and Reynolds stress were generally consistent with the spreading rates. The drop in maximum jet velocity with distance from the nozzle was not quite as fast for the wall jets as for a free jet. The shear on the floor is not a large factor in the overall momentum balance. Entrainment ratios could not be obtained from these studies. In the present tank experiments, the jets were developing not above a plane surface but above a cylindrical surface. The effects of the curvature of the surface on the spreading rates and turbulence properties are not known. Using the distances from the jet nozzles to the ends of the tanks for values of L, the data were plotted as indicated by eq 2 and shown in Figure 7. The best line through the data points has a slope of about 28, indicating that approximately 28 volumes must be circulated through the entrained jet to achieve good mixing for this tank configuration. In comparison, Maruyama et al. (1982) show that about 5-6 tank volumes is sufficient for good mixing with tanks having length-to-diameter ratios of 0.5-1.0. Conclusions Jet mixing times were measured for long horizontal tanks with length-to-diameter ratios of 4 and 5. Mixing times in the 0.87-m3 tank decreased from 1800 to 300 s (30 to 5 min) as the jet Reynolds number was increased from 15 000 to 130 000. Mixing times for various jet diameters were correlated with the jet Reynolds number. With a single jet in the 95-m3 (25 000-gal) tank, mixing times decreased from 4500 to 840 s (75 to 14 min) as the jet Reynolds number was increased from 80 000 to 311 000. For a double jet of the same diameter and location, mixing times were not significantly different from those of the single jet at the same flow rate. At a given flow rate, mixing times were significantly lower with a 0.035-m (1.38-in.) double jet than with a
1482 Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998
0.049-m (1.93-in.) double jet. The concept of correlating mixing times with the recirculation time of the developed jet was found to be valid. About 28 tank volumes must be recirculated through the entrained jet for good mixing with tanks of this configuration.
h ) hour in. ) inch m ) meter min ) minute mS ) millisiemens s ) second
Acknowledgment The work described in this paper was performed at Oak Ridge National Laboratory, which is managed by Lockheed Martin Energy Research Corp., for the U.S. Department of Energy under Contract DE-AC0596OR22464. Nomenclature Symbols Cc ) concentration at the centerline of a developed jet Cn ) concentration of fluid leaving the jet nozzle Dn ) jet nozzle diameter h ) height of the jet nozzle centerline above the floor L ) length of the developed jet Qe ) flow rate of the fully developed jet Qn ) volumetric flow rate through the jet nozzle Re ) jet Reynolds number ) DnFνn/µ tm ) mixing time tR ) recirculation time constant ) VT/Qn vc ) velocity of the jet at the centerline vn ) velocity at the jet nozzle VT ) tank volume z ) distance from the jet nozzle β ) empirical factor ) f(Re) µ ) liquid viscosity F ) liquid density Units ft ) foot gal ) gallon
Literature Cited Churnetski, B. V. Prediction of Centrifugal Pump-Cleaning Ability in Waste Sludge. Presented at the American Nuclear Society Winter Meeting, San Francisco, 1981. Davis, M. R.; Winarto, H. Jet Diffusion from a Circular Nozzle Above a Circular Plane. J. Fluid Mech. 1980, 101, 201-221. Fossett, H.; Prosser, L. E. The Application of Free Jets to the Mixing of Fluids in Bulk. Proc.sInst. Mech. Eng. 1949, 160, 224. Fox, E. A.; Gex, V. E. Single-Phase Blending of Liquids. AIChE J. 1956, 2, 539. Lehrer, I. H. A New Model for Free Turbulent Jets of Miscible Fluids of Different Densities and a Jet Mixing Time Criterion. Trans. Inst. Chem. Eng. 1981, 59, 247. Maruyama, T. Jet Mixing of Fluids in Vessels. In Encyclopedia of Fluid Mechanics; Gulf Publishing Company: Houston, TX, 1986; Vol. 2, Chapter 21. Maruyama, T.; et al. Jet Mixing of Fluids in Tanks. J. Chem. Eng. Jpn. 1982, 15, 342-348. Newman, B. G.; et al. Three-Dimensional Wall Jet Originating from a Circular Orifice. Aeronaut. Q. 1972, 23, 188-200. Rajaratnam, N.; Pani, B. S. Three-Dimensional Turbulent Wall Jets. Proc. Am. Soc. Chem. Eng., J. Hydraul. Div. 1974, 100, 69-83. Revill, B. K. Jet Mixing. In Mixing in the Process Industries; Harnby, N., Edwards, M. F., Nienow, A. W., Eds.; Butterworth: London, 1985; Chapter 9.
Received for review February 3, 1997 Revised manuscript received January 28, 1998 Accepted February 3, 1998 IE970118X
