leaching with ivater. I t was assumed that the material removed from the residue by leaching was all CaS04.1/2 HzO, and that this material had been in solution a t the start of precipitation. Concentration products and ratio G Lvere then calculated. T h e concentration products [Ca+2],[S04-2]e \Yere calculated from the solubility data of Kurteva and Brutskus (7) a t 70’ C.: considering only those systems with SO4 concentrations less than 0.4 molal. I n this way average and 0.63 X l o p 2 were values of 1.58 X lo-?, 1.15 X calculated fer the concentration products in solutions saturated with respect to CaSO.L.’/? H20 and containing 23, 30, and 35% P20:, respectively. T h e same values were used to obtain ratio G i n experimental systems a t 65’ and 75’ C. The experimental data are summarized in Table 11. Microscopical examination of the unleached rock residues sho\ved CaS04.1,/2HQO to be present in all but two samples (1C and 2A3 Table 11). In two other samples (6B and 7), hemihydrate \\.as present as pseudomorphs after rock particles, but the rock \vas completely dissolved. The hemihydrate in the remaining samples \vas present as coating on the rock particles, either as acicular crystals or as massive coatings. Although the microscopical description of the samples can be only qualitative, ratio G of Table I1 can be correlated with the degree of coating of the rock. ll’ith values of the ratio close to 1, no nucleation of hemihydrate occurred; as the ratio approached 2.5, hemihydrate precipitated: but the rock was completely dissolved. For higher values of G? the coating of hemihydrate o n the rock particles retarded dissolution of the rock.
Thus, from knowledge of the solubility of calcium sulfate in mixtures of phosphoric and sulfuric acid it is possible to predict those compositions which will cause rock blinding in the manufacture of phosphoric acid. Acknowledgment
T h e authors were assisted in this work by members of the Phosphate and Nitrogen Research Group a t Cyanamid’s Agricultural Center, Princeton, N. J. : Lenore lViegman, George DiCicco, and Victor Palinczar. literature Cited
(1) Brutskus, E. B., Chepeleietskil, M.L., Zzu. SeXtora Fit.-Khim. Analrza, Inst. Obshch. .Yeorgan. Khtm. Akad. lVauk SSSR 20, 383-8 11950). (2)’ Car& J. H., Hill, \V. L., J . Agr. Food Chem. 4,684-7 (1956). (3) Chepeleietskii. M.L., Trans. Scz. Znst. Fertdzrers Znsectofungicides NO. 137, 10-35 (1937). (4) Copson, R. L., Newton, R. H., Lindsay, J. D., Ind. Eng. Chem. 29, 175-9 (1937). f5) Donald. R.. Schwehr, E. \V.%IVilson, H. N., J . Sci.Food Aer. 11. 677-91 (1956). ’ (6)-Hatfield, J. D.,’ Rindt, D. \V., Slack, -4. V., Znd. Eng. Chem. 51, 677-82 (1959). (7) Kurtel-a, 0. I., Brutskus, E. B., Zh. Priklad. Khim. 34, No. 8 , 1714-22 (1961). (8) Lingane, J. J., Anal. Chem. 17, 39-40 (1945). (9) S u n n , R. J., Dee, T . P., J . Sci.Food Agr. 5,257-65 (1954). (10) Tsyrlin: D. L., Zh. Prikiad. Khim. 33, 1477-82 (1960). \
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I
RECEIVED for review December 1, 1964 ACCEPTED April 13, 1965 Division of Fertilizer and Soil Chemistry, 148th Meeting, ACS, Chicago, Ill., September 1964.
HEAT TRANSFER FROM PLASMAS T O WATER=COOLED TUBES Engineering Correlations JOSEPH
F. S K R l V A N AND W O L D E M A R
VON JASKOWSKY’
American Cyanamid Co., Stamford, Conn.
Engineering studies were conducted on the heat transfer from a plasma or high temperature gas to the confining walls of a water-cooled, segmented tubular test section. Three (plasma) gases, nitrogen, hydrogen, and argon, were studied in l/2-, 1 -,and 2-inch diameter tubes, 19 inches in length. A Reynolds number range of 400 to 3500 was covered at a multitude of arc power levels. An empirical correlation relating Nusslelt number to the significant variables was developed, which can b e used to predict mixedmean axial enthalpy profiles for similar systems. A “hot core” model of the flow was used.
THE field of chemical synthesis in plasma jet reactors (3, 4 ) has now reached thz stage a t \\hich it is desirable to have detailed information (concerning the thermal interactions betiveen plasmas and thcir confining walls (70). The purposes of the present study werz principally three:
1. To delineate the significant variables and to determine over-all heat transfer coefficients. 2. To develop engineering correlations necessary for scale-up. Present address, Department of Aerospace and Mechanical Sciences, Princeton University, Princeton, N. J.
3. To extend the above results to the formulation of approximate expressions descriptive of the axial enthalpy profile for use in kinetic rate equations. I n order to make practical use of plasmas in chemical processing, reactions and operations must be carried out on a time scale and in a configuration which is more or less determined by the plasma itself. Accepting these limitations, then, attack on this problem must, by necessity, be of a n empirical nature. The problem of heat transfer in undeveloped flow with variable fluid properties is sufficiently complex to defy analytical solution. I n addition, there are inherent uncertainties in the plasma state VOL. 4
NO. 4 O C T O B E R 1 9 6 5
371
Rectifiers
Pressure flow Elec frical (except Water Temperalure Thermometer)
Panel with aft Meters
1
Control Console Safety Vacuum
Plosmojet Head
Two Heat €#changers
Jhermomefers
i
Exhaust into, Atmosphere
Figure 1.
P-
Schematic diagram of experimental apparatus
as to ionization and dissociation (for diatomic gases) levels as well as to the approach to thermal equilibrium. Furthermore, because of the increase of gas viscosity with temperature and the throughput limitations of small-scale (below 1 megawatt) plasma jet units, the flow regime encountered is in the laminartransition range (by Reynolds number). T o allow sufficient tube length to establish a stable velocity profile is not practical. By the time such a profile is established, the energy is sapped by cooling, the plasma character is destroyed, and one has left only a warm gas to study. Apparatus and Procedure
Figure 1 is a schematic diagram of the experimental facility. The plasma jet head, control console, and power supplies were capable of covering a range of 5 to 100 kw., with 50 to 707, of this power being absorbed by the arc gas. The power supplies were of the welding rectifier type. Gas is fed from a compressed gas cylinder, enters the arc unit tangentially, and leaves through the front electrode as an extremely hot jet of plasma. Electrical energy is converted into thermal, and the gas-XI, for example-is dissociated and ionized to an extent dependent on the power input. “Equilibrium” temperatures as high as 3100°, 6800°, and 8700’ K. were obtained a t this point for HI?Ne, and argon, respectively. T h e plasma then passed into a water-cooled copper nozzle (Figure 2, with Table I). The purpose of this section was to achieve some approach to thermal equilibrium and to expand the plasma smoothly to the test section diameter, since the front electrode of the plasma unit could not be made to match all three test sections. Considerably reduced in enthalpy as a result of heat loss to the nozzle, the subsonic gas stream then passed into a series of 10 cylindrical water-cooled test sections, insulated from each other by Bakelite spacers and sealed by O-rings. The exit diameter of the nozzle matched the internal diameter of the test section. Temperatures a t the inlet to the test section were as high as 2400’, 5200°, and 6200’ K. for HI, NI, and A, respectively. Velocities a t this point varied from 65 feet per second for argon in the 2-inch test section t o 2000 feet per second for N fin the ‘/I-inch test section. The latter was not sonic be-
Table l.
Figure 2.
Transition piece
1200P
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!
1
,
1
,
l
,
1
,
1
,
1
,
1
,
1
,
1
,
BOUNDARY LAYER I
Nozzle Dimensions (Inches)
Front
Electrode Diameter
0.125 0.250 0.500
0.25
B 0.112
0.5 1.0
0,224 0,447
A
C 10’ 10’ loo
D 0.5 0.5 0.5
E
0.5 1.0
2.0
F 0.5
0.5 0.5
~
372
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
HEAD
NOZZLE
X.X
X.0
TEST SECTION
Figure 4.
Schematic diagram of plasma jet assembly
cause of the high temperature involved. T h e test section was followed by heat exchangers containing a multiplicity of cooling coils transverse to the flow. The exit gas temperature was 60' C. or less. T h e cooling water for the electrodes, nozzle, test section, and heat exchanger were separate systems, each having its own pump and flowmeter. Pressure taps were provided in the nozzle and each component of the test section. Temperatures were measured by thermometers graduated to 0.1' C. Gas flows were measured by calibrated orifices and water flows by calibrated rotameters. Voltage and current inputs \
