System Poisons. In an effort to detect potential poisons, runs were made in which Hz, CO, and ethane were substituted for 10% or more of ethylene. No adverse effect, other than a reduction in STY proportional to the decrease in partial pressure of ethylene, was noted. I n another run, the system was made 0.1M sulfide; here, too, no adverse effect was noted. Reaction with Other Halides and Olefins. The scope of the reaction has been extended to higher olefins, substituted olefins, and the bromide system, in that 1,2-dichloropropane, 1,1,2-trichloroethane, and 1,2-dibromoethane were produced from propylene, vinyl chloride, and ethylene, respectively.
Acknowledgment
The authors thank F. Caropresso and J. Craddock, who performed the bulk of the experimentation and contributed ideas pursuant to improving the system. literature Cited (1) Benson, S. W., “Foundations of Chemical Kinetics,” Chap.
XV, McGraw-Hill, New York, 1960.
(2) Vestin, R., Acta Chem. Scand. 8, 533-57 (1954).
RECEIVED for review July 9, 1966 ACCEPTED February 3, 1967 Division of Petroleum Chemistry, 152nd Meeting, ACS, New York, N.Y.,September 1966.
PERFORMANCE CHARACTERISTICS OF SELF- ENT RA I N M ENT EJECTO R S FOUAD K H O U R Y , l M I C H A E L H E Y M A N , 2AND W I L L I A M R E S N I C K Department of Chemical Engineering, Israel Institute of Technology, Haifa, Israel The one-dimensional analysis of ejector performance is extended to include the conditions expected to prevail for a self-entrainment ejector operating a refrigeration cycle. Performance data were obtained for two ejectors operating with two fluids, butane and hexane. Experimental curves are presented for the entrainment ratio as a function of motive and suction fluid pressures and are compared to the performance predicted from the one-dimensional analysis. Compression ratio efficiencies in the range of 56 to 74y0 were obtained.
NE
of the applications of self-entrainment ejectors, in which
0 the motive and suction fluids are identical, is the ejector refrigeration cycle in which the ejector replaces the mechanical compressor of the conventional vapor-compression refrigeration cycle. Vacuum refrigeration systems in which a steamactuated ejector serves as the compressor for a water vapor system are well known, but the cold temperature is limited to approximately 40’ F. If lower temperatures are to be attained, it is necessary to use other refrigerants. Although some theoretical and experimental investigations of selfentrainment ejectors and of ejector-actuated refrigeration cycles have been reported (7, 3-8), few data are available on the performance characteristics of ejectors operating with identical motive and suction fluids. This paper reviews briefly the theoretical one-dimensional analysis by DeFrate and Hoerl ( 2 ) and extends it to include the conditions expected to prevail for an ejector operating a refrigeration cycle. Experimental results are presented for the performance characteristics of two ejectors and the results compared to the theoretical performance. Analysis of Ejector
section with supersonic velocity. The suction gas, 6, is entrained and mixes completely with the motive gas. In the subsequent analysis the mixing section was assumed to be constant area. The analysis was based on the following assumptions : 1. The flow is adiabatic and there are no shear forces at the wall. 2. The gases satisfy the perfect gas equation and the specific heats are constant. 3. Acceleration of the gases from rest to the section where mixing begins is reversible. 4. Mixing is complete and the velocity is subsonic a t the entrance to the diffuser. If the velocity is supersonic after mixing, a shock occurs before the diffuser entrance. 5. Deceleration in the diffuser is reversible. 6. The motive and suction gases at section 1 are at the same pressure. Identical suction and motive fluids are assumed in the following review of the DeFrate and Hoerl analysis. Nozzle Equations
When a gas expands reversibly and adiabatically from stagnation pressure PO to pressure PI, it will reach a velocity that can be expressed in dimensionlessform as a Mach number:
The analytical ejector model used by DeFrate and Hoerl is shown in Figure 1. Operation is as follows: Motive gas a at an elevated pressure expands through the converging-diverging nozzle and emerges into the mixing Present address, Department of Chemical Engineering, Rice University, Houston, Tex. * Present address, Central Research Department, Mobil Oil Co., Princeton, N. J.
I n accordance with the assumptions made, the motive fluid will be at sonic velocity at the nozzle throat, so that
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tion 3 and utilizing the fact that, for the case of constant area mixing, A2 will equal A I , Ala. The resulting equation is
+
cI 'r
(+)A
'3
- I}
(10)
To permit the calculation of a it is necessary also to express the over-all pressure ratios as
Suction Gas
b Figure 1.
Sketch of ejector
and the ratio of the nozzle exit area to the throat area calculated by a material balance becomes
and
Ejector Performance with Vapor Mixing Section
By combining the continuity, momentum, and energy equations written between sections l and 2, the Mach number of the combined motive and suction gas at 2 is
where
and the pressure ratio is
I n an ejector refrigeration cycle the refrigerant is vaporized at pressure Poa with thermal energy supplied, for example, by a solar collector and serves as the motive fluid for the ejector. The low pressure refrigerant at POb is entrained from the evaporator and the combined streams leave the ejector at Po8 and are condensed. Part of the liquid from the condenser is returned to the vaporizer by a pump and the remainder is returned to the evaporator through an expansion valve. Optimum ejector design charts for an ejector-operated refrigeration cycle have been presented by Heymann and Resnick (4), who assumed that the motive and suction fluids would be supplied to the ejector at or very close to the vapor pressures corresponding to the temperatures prevailing in the boiler and evaporator. Assuming that the Clausius-Clapeyron equation is obeyed, it can be integrated between the limits ToG, Poa, and POb to yield
rob,
Toa = 1
\-I
PI
TOb
k At Poa
+ J l n -Poa POb
where
I n the foregoing equations To2 is the stagnation temperature of the gas at section 2 and a is the entrainment ratio, wb/wa. m
(7)
Upon substituting Equation 13 into 9 the expression for the entrainment ratio becomes
The pressure increase brought about in the diffuser as a result of the deceleration can be obtained by rearrangement of Equation 1
Gross divergence from the assumption of ideal gas behavior would be expected if the fluids, at any point in the ejector, entered the two-phase vapor-liquid region. The thermodynamic properties of the two fluids used in the experimental programs, butane and hexane, were inspected to determine if this possibility could occur. For both fluids, adiabatic, reversible compression of the saturated vapor results in superheating, and subsequent compression of the mixed vapor from pressure P I to PO3 does not bring the vapor back to the saturation condition.
l+ff Diffuser
and the gas will leave the diffuser at the stagnation temperature, T03, which is equal to TO^. Performance Equations
The entrainment ratio can be written as
and can be related to the area ratio A2/At with the aid of Equa332
I L E C PROCESS DESIGN AND DEVELOPMENT
Performance Curves, Envelope Curve, and Optimum Ejector
If the fluid properties, J and k , and the ejector areas, A t , A I , , and A2, are all specified, a performance curve relating a to PO,, Pob, and PO3 can be calculated. As a result of the assumptions made in the development of the performance
0.01
2
3
4
Figure 2.
5
6 7 6 8 . 1
O(
2
3
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2
5 6 7 8 9 1
3
4
5
Theoretical performance curves and envelope curve
equations, however, only two of these four performance variables are independent. This point can be clarified by examining the equations. If, for example, values are selected for Poa and POb, then, according to Equations 1 and 3, P I is determined. The value of a! is also determined from Equation 15. Po3 is calculated from Equations 4 to 14. These equations, however, involve CY and PI,which are now determined once Poa and PO0 have been set, and, as a result, Po3 is also determined. A performance curve can, therefore, be presented graphically as a plot of Poa/Pob us. CY for a given set of the parameters A2/A1,A l , / A t , k , and J . For a given set of ejectors, all with the same values for A2/At, k , and J but with different values for A1,/Al, a family of performance curves w7ill be obtained. An “envelope curve” can be drawn enclosing the performance curves and giving the maximum possible entrainment ratio for any value of Poa/Pob. This envelope curve represents the locus of optimum ejectors and permits the prediction of the entrainment ratio to be expected and, also, the determination of the optimum area ratios for any given ratio of motive to suction fluid pressures. A typical set of theoretical performance curves is shown in Figure 2. This figure was prepared for a fluid with J = 0.15, k = 1.11, and A 2 / A l = 7.5. Heymann and Resnick ( 4 ) present graphical procedures for determining the optimum ejector design for self-entrainment ejectors.
Log a Figure 3. Sketch of performance curve with critical flow in suction fluid
area ratio A1,/A2. I t is possible, however, that for certain values of the design and operating parameters the ratio POh/P1 will be less than the critical ratio and the suction fluid will be at critical flow conditions. Under these conditions the suction fluid a t cross section 1 would, therefore, be not a t PI but at Pb* = rcPOh and the suction fluid would undergo a sudden pressure drop from Pb* to P I at this point. The velocity of the suction fluid would then be determined only by the suction stagnation conditions, POb and Too, and
Critical Flow in Suction Fluid
I n the analytical development presented above it was assumed that both the suction and motive fluids expanded from their respective stagnation pressures to the common pressure, PI. The motive fluid is at sonic velocity a t the nozzle throat; hence, pressure P I at the exit of the diverging section is a function of the motive fluid inlet pressure, PO,,and
The entrainment ratio becomes
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px
c
yl
0
W
0
.-E $E a i al
L
a 0) ii
1 334
l&EC PROCESS DESIGN AND DEVELOPMENT
Id 8 6
4
2
PCU
Po b
IO' 8
6
4
2
I .01
2
3
Figure 6.
4
5 6 7 6 9 . 1 0
a
2
3
4
5
67891.
2
3
4
Theoretical and actual performance of ejector 1 with butane
or, for the ejector-operated refrigeration cycle, a = - - - ' O b (1 + J l n
At Poa The performance curve is sketched in Figure 3 by line A B D . Segment A B represents subsonic flow in the suction fluid. At point B the ratio P1/Pob reaches the critical ratio and line segment B D is obtained by Equation 18. The dashed line, BC, represents the entrainment ratio that would be expected according to Equation 15, which requires that the suction fluid be supersonic at P I . Experimental
The properties of the fluid have relatively little effect on the performance of self-entrainment ejectors and the equations developed are insensitive to small variations in k and J. The fluids used, hexane and n-butane, were chosen primarily because of their availability and their suitability for use with the facilities and utilities available in the laboratory. Hexane properties of interest are k = 1.08 and J = 0.10 (calculated a t Toa = 200' F.). Corresponding values for n-butane are 1.11 and 0.15. Two ejectors were designed and built. Ejector 1 was designed to give optimum performance when operating with nbutane at the following conditions: P O , = 151 p.s.i.a., POb = 13.8 p.s.i.a., and Po3 = 37.4 p.s.i.a. These pressures would correspond to the following temperatures in an ejector refrigeration system: boiler temperature T , = 178' F., evaporator temperature T E = 28' F., and condenser temperature T , = 80' F . * These conditions correspond to PO. 10.8 p.s.i.a. ( T , = 139' F.). Pob = 0.97 D.s.i.a. ( T , = 35' F.), and Po? = 2.63 p.s.i.a. (Tc'=--73' F.) for hexane- The optimum dt&n ratios that result are A2/At = 7.5, A1,/At = 3.5, and the maximum entrainment ratios to be expected are 0.407 for nbutane and 0.370 for hexane.
Table I. Ejector Dimensions Ejector Dimensions 1
Dlb, mm. Inner Outer
DI,, mm. D2,mm. Da, mm. D t , mm. Ala,sq. mm. AI,, sq. mm. A2, s q . mm. A t , sq. mm. AdAt A 2/A t
7.0 8.6 4.68 6.84 20.0 2.5 19.59 17.19 36.73 4.906 3.5 7.5
2 8.0 8.75 5.86 6.84 20.0 2.5 9.26 26.96 36.73 4.906 5.5 7.5
Ejector 2 was designed for the following conditions: Poa = 214 p.s.i.a. (T. = 208' F.), Pob = 8.2 p.s.i.a. (TE = 5' F.), and PO3 = 46.7 p.s.i.a. ( T , = 93' F.) for n-butane, and PO, = 14.9 p.s.i.a. ( T , = 157' F.), POb = 0.63 p.s.i.a. (TE = 20°F.), and Po3 = 3.28 p.s.i.a. ( T , = 82' F.) for hexane. The resulting ratios are A2/At = 7.5, A1,/At = 5.5, and a = 0.07 for n-butane and 0.08 for n-hexane. For both ejectors the throat area was set by the capacity of the ancillary equipment to supply motive fluid. The boiler was able to supply approximately 120 pounds per hour of fluid and this in turn required that the nozzle throat diameter be no more than 2.5 mm. Area AIb is in the form of an annulus with inside diameter Dlb' and outside diameter Dlb''. The dimensions of the two ejectors are given in Table I and dimensional drawings are shown in Figures 4 and 5. Brass was used as the material of construction and Teflon as the gasketing material. Theoretical performance curves are shown in Figures 6, 7, 8, and 9. The experimental setup was essentially as follows: A steamheated boiler, 6 inches in diameter, with a volumetric capacity of 16 liters supplied the motive gas to the ejector through a rotameter. The boiler was equipped with a sight glass over its entire height and with appropriate temperature- and VOL. 6
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Id
10
8
8
6
6
4
4
2
2 POa -
5% k b
PO0
IO'
1.0
8
.8
6
.6
4
.4
2
.2
I
0.I .01
3
2
4
5
6780.1
OC
3
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5 6 78910
3
2
Figure 7. Theoretical and actual performance of ejector 1 with hexane
.01
2
3
Figure 8. 336
4
5
6 ? 80,l
2
3
4
5
6 ?89.LO
Theoretical and actual performance of ejector 2 with butane
I h E C PROCESS DESIGN A N D DEVELOPMENT
2
4
.01
2
Figure
3
9.
4
5
6 7 8 9 . 0
2
3
4
5
6
2
789ID
Theoretical and actual performance of ejector 2 with hexane
I'0 8
6
4
2
..P P.b
.01
2
3
4
Figure 10.
5
6 7 8 9 . 1
o(
2
3
4
5
678S1.0
Experimental results with butane Ejector 1
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Id 8
6
4
2
eP-L
IO'
8 6
4
2
-01
3
2
4
5 6 7 89.1
Figure 11.
&
2
3
4
5 6 7891.0
Experimental results with hexane Ejector 1
I' 0 8 6
4
4B 2I
.o I
2
Figure 12.
3
4
5 6 7 8 9 . 1
2
Experimental results with butane Ejector 2
338
o(
I h E C PROCESS DESIGN A N D DEVELOPMENT
3
4
IO’ 8 6
4
2
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I
I
I
1
.01
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I I l l 1 1
1
1 I l l
Figure 13.
5
d
6 7 8 0 . 1
I
I
i I l ! ! I
I
I
i
I I l l i J
2
3
4
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6 789l.O
Experimental results with hexane Ejector 2
pressure-measuring and control devices. The motive fluid entered the ejector from a superheater set to provide several degrees of superheat to the vapor. The ejector took suction from the evaporator, a vessel identical in construction to the boiler, and the combined vapors entered a condenser. Condensate flowed by gravity to an intermediate storage tank, from whence it could either return to the evaporator through a valve or be pumped by an air-operated piston pump to the boiler. The equipment was well instrumented and equipped with control devices to permit accurate control of temperatures and pressures. Appropriate overpressure devices and venting were provided. Performance data were obtained for both ejectors and for both butane and hexane, in a series of runs in which the motive pressure and, hence, motive fluid rate were held constant while the suction pressure was measured as a function of suction fluid rate over the range of zero suction flow (minimum suction pressure) to the maximum suction flow possible. T o be able to compare the actual performance curves with the theoretical curves, it was also necessary to carry out “directed” experiments in which the discharge pressure was controlled. Experimental Results
The results are presented graphically in Figures 10 to 13, in which the performance curves are presented for a, the entrainment ratio, as a function of Poa/Pob. I n all cases, a increases as Poa/POb decreases, or for a constant motive pressure, an increase in the entrainment ratio requires an increase in the suction pressure and the minimum suction pressure is obtained at zero entrainment, as would be expected. In the results shown in Figures 10 and 12 the discharge pressure sought its own level in accordance with the suction conditions. Figures 11 and 13 represent “directed” experiments in which the discharge pressure was held constant.
Comparison with Theory
To compare the experimental results with the theoretical development the performance curves for Po,/Poa us. a must be drawn in such a manner that the ratio Por/Poa at each point will match the theoretical value. The theoretical results shown in Figures 6 to 9 are presented as two curves, one for the dependence of PO./POb on a and the second for PO3/POa on a. To compare the theoretical results for PO,,/POb as a function of a with the experimental results the experimental and theoretical curves for P03/PO. us. a must be identical. This comparison is made possible by virtue of “directed” experiments. The procedure for constructing the experimental curve will be illustrated by an example. For ejector 1 with hexane at an entrainment ratio of 0.05 the theoretical value for Por/Poa from Figure 7 is 0.233. Turning to Figure 11 we note that a series of runs was made at the same value for P03/POa. At a = 0.05 the experimental value for PO,/POb was 11.0. This value is shown in Figure 7 as the experimental value for Poa/Pob at this same entrainment ratio. The experimental performance curves shown in Figures 6, 7, and 9 were built up in this manner. Because of the paucity of experimental data for ejector 2 operating on butane, it was impossible to carry out the procedure outlined above and the experimental curve shown in Figure 8 is the same as that shown in Figure 12. The shapes of the theoretical and experimental curves are similar except for Figure 8, in which a comparison is not valid because PO3 varied freely, as noted above. The dashed lines show the theoretical ejector performance where no correction is made for sonic flow in the suction fluid. The experimental results show that the sonic flow correction is necessary. A numerical comparison between the theoretical and experimental results can be made if we define an ejector efficiency as VOL. 6
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P re
R where the compression ratios are for the same values of the entrainment ratio. These values were almost constant over the entire range of the performance curves. The efficiency of ejector 1 was approximately 6670 with butane and 74% with hexane. Ejector 2 had an efficiency of 56Y0 when operating with hexane. The lower efficiency of ejector 2 may possibly be attributed to its smaller suction cross section as compared to ejector 1, with the balance of the dimensions being similar. I n addition, because of the nozzle wall thickness, area AI, Alb is not equal to A:!as was assumed in the theory.
+
Acknowledgment
The financial assistance of the Fohs Foundation and of the Israel National Council for Research and Development is gratefully acknowledged. Nomenclature
A B
=
D
=
g
= acceleration of gravity
cross-sectional area
= dimensionless grouping defined by Equation 4
diameter
= force-mass conversion factor AHrs = latent heat of vaporization J = dimensionless grouping defined by Equation 14 k = ratio of specific heats M * = Mach number referred to velocity of sound attained by gas in adiabatic, reversible expansion from local stagnation condition
gc
T w W a qp
absolute pressure critical pressure ratio gas constant absolute temperature mass flow rate = molecular weight = entrainment ratio = ejector efficiency = = = = =
SUBSCRIPTS a = motive gas b = suction gas t = motive nozzle throat 0 = stagnation condition 1 = cross section a t nozzle exit 2 = cross section a t diffuser entrance 3 = cross section at diffuser exit Literature Cited
(1) Danilov, R. L., Sisoyev, L. P., Annexe 1960-63, Supplement au Bulletin de 1’Institut International du Froid, p. 155. ( 2 ) DeFrate, L. A,, Hoerl, A. E., Chem. Eng. Progr. Symp. Ser. 5 5 , No. 21, 43 (1959). (3) Girardon, P., Annexe 1960-63, Supplement au Bulletin de 1’Institut International du Froid, p. 161. (4) Heymann, M., Resnick, W., Israel J . Technol. 2,242 (1964). (5) Mizrachi, J., Solomiansky, M., Zisner, T., Resnick, W., Bull. Res. Council Israel 6C, 1 (1957). (6) Ward, G. T., J . Eng. SOC.Uniu. Kuala Lumpa, Malaya 3, No. 1, 25 (1957). (7) Work, L. T., Haedrich, V. W., Znd. Eng. Chem. 31, 468 (1939). (8) Zhadan, S. Z., Annexe 1960-63, Supplement au Bulletin de 1’Institut International du Froid, p. 169. RECEIVED for review August 15, 1966 ACCEPTEDFebruary 13, 1967
BATCH MIXING OF VISCOUS LIQUIDS ROGER
T. J O H N S O N
Chemstrand Research Center, Inc., Durham, N . C. Mixing times with six-bladed turbines, a marine propeller, and a helical ribbon blender are compared for the agitation of viscous Newtonian liquids. A correlation is developed between a dimensionless mixing number and the Reynolds number. Mixing times are shorter with the turbine than for a propeller of the same diameter at a given Reynolds number. W a l l baffles further reduce mixing times. With turbines and propellers, unmixed tori are formed and the time for diffusion into them determines the mixing time. With a helical blender, no unmixed zones are formed and in viscous systems efficiencies based on the power required for mixing are much greater for. the helix than for conventional agitators. A plot of power number vs. Reynolds number is presented.
preparation of polymers frequently involves mixing of viscous liquids. The importance of efficient mixing is frequently ignored, because very little of a quantitative nature can be found in the literature to provide a guide to what constitutes satisfactory mixing. Inefficient mixing in polymer systems can have a pronounced effect on molecular weight distribution and reaction rate. Saunders and Frisch (8) report the large effect of agitator speed on prepolymer viscosity in polyurethane preparation. I n the fiber industries, inhomogeneities in spinning dopes can often be traced to inefficient mixing. These in turn give rise to problems in the spinning of fibers, so that a better definition of agitation requirements would be useful. A step in this THE
340
I & E C PROCESS DESIGN AND DEVELOPMENT
direction is the correlation of relative mixing times for various agitators and agitation systems which is attempted in this paper. Discussion
Earlier investigators have used mixing times derived in various ways, as a measure of mixing effectiveness. Fox and Gex (7) used the time for neutralization of a basic solution. Nagata, Yanagimoto, and Yokoyama ( 5 ) used color change in a n iodine solution. Kramers and his co-workers (3) used fluctuations in conductivity. In this work, the time for uniform dispersion of a dye solution was used. This work was intended to provide a comparative measure of mixing times for various agitators. No generalized correla-
