- h , = experimental heat transfer coefficient of mechanisms other than radiation. B.t.u. ’hr,sq. f t . - O F. = heat transfer coefficient for film convection in presence of fluidized particles, B.t.u./hr.sa. ft.-’ F. = heat transfer coefficient for film convection in absence of fluidized particles, evaluated a t G, of fluidized bed, B.t.u./hr.-sq. ft.-O F. = mass transfer coefficient, 1b.-moles/hr.-sq. ft.atm. = experimental mass transfer coefficient, kuPaMu= lb./hr.-sq. ft. = mass transfer coefficient in absence of fluidized particles, evaluated from Equation 5 a t G, of fluidized bed, Ib./hr.-sq. ft. = molecular weight of air, lb./lb.-mole = h,Dp/o = k,D,/pD, = av. partial pressure of air, atm. = saturation partial pressure of water vapor, vapor pressure corresponding to t,, atm. = partial pressure of water vapor in the air, atm. = logarithmic mean partial pressure difference, atm. = ht
hc h!
= Cpp,’cy = rate of heat transfer a t interface, by particle =
transport, via gas film, B. t.u.:’hr.-sq. ft. GD,/p, Reynolds No. based on superficial gas mass velocity
= dpDr = bulk gas temperature, temperature a t surface of
sph;ere,
O
F.
= loearithmic mean temuerature difference. ” =
O
F
mass transfer rate, 1b.-moles,’hr.-sq. ft.
GREEK cy
= gas thermal conductivity, B.t.u./hr.-ft.-”
E
P
bed void fraction, dimensionless = gas viscosity, lb./hr.-ft. = gas density, Ib./cu. ft.
x
=
(1) Botterill, J. S. M., Brit. Chem. En!. 8, 21 (1963). (2) Chilton, T. H., Colburn, A. P., Ind. Eng. Chem. 26, 1183 (1934). (3) DO”, CV. M., Jakob, M., Chem. Eng. Progr. 47, 637 (1951). (4) Emst, R., Chem.-Ingr.-Tech. 31, 166 (1959). (5) Froessling, N., Geriunds Beitr. Geophyr. 52, 170 (1938). (6) General Electric Co., “Dew Point Recorder Pamphlet,” GEI-40444A. (7) Griffith, R. M . , Chem. Eng. Sci. 12, 198 (1960). (8) Leva, M., General Discussion of Heat Transfer, London, SeDtrmber 1951. . .~ (9) Leva, M., Grummer, M., Ind. Eng. Chem. 40, 415 (1948). (10) Leva, M., Ll’eintraub, M., Grummer, .M,, Chern. Eng. Ptogr. 4 5 , 563 (1949). i l l ) Micklev. H. S..Fairbanks. D. F.. i4.I.Ch.E. J . 1. 374 1195.5). (12) Mickley; H. S., Fairbanks, D. F., Hawthorn, k.D.: Chem Ene. P?OPY. .Cvmb. S c r . 32. 51 11961\. (13) uMukhenov, I. P.,- Traber, D. G., Sarkits, V. S.,Bondarchuck, T. P., Zh. Priklud. Khim.32, No. 6, 1291 (1959). (14) Ranz, W.E., Marshall, LV. R., Jr., Chem. Eng. Progr. 4 8 , 141, 173 (1952). (15) Sarkits; V. B., Traber, D. G., Mukhlenov, I. P., Z h . Ptiklad. Khim. 32, No. 10, 2218 (1959). (16) Z6id.,33, N o . 10, 2197, 2200 (1960). (17) Thodos, G., Northwestern University, Evanston, Ill., personal communication. (18) Van Heerden. C., Nobel, A. P. P., Van Krevelen, D. LV., Chem. Ene. Sci. 1. N o . 2. 51 11951). (19) Van keerdeh, C., ‘hobel, A: P. P., Van Krevelen, D. LV., Ind. Eng. Chem. 4 5 , 1237 (1953). (20) Vreedenberg, H. A , , Chem. Eng. Sci.11, 274 (1960). (21) Vreedenberg, H. A,, J. .4fipl. Chem. 2, Suppl. Issue No. 1 . S26 11952). (22) Cqen, C.-Y.,Leva, Max, A.I.Ch.E. J . 2, 482 (1956). (23) Ll’endFr, L., Cooper, G. T., Ibid.,4 , 15 (1958). (24) b’icke, E., Fettins, F., Chem.-In,nr.-Tech. 26, 301 (1954). (25) bVicke, E., Hedden, K.: Ibid.,2 4 , 82 (1952). (26) Zcnz, F. A . , Othmer, D. F., “Fluidization and Fluid Particle Systems,” Reinhold, New York, 1960. ~~
~
2
’
-
\ - -
~
-
/
F.
=
iL
literature Cited
B.t.u. latent heat of vaporization of water, _ _ lb.-mole
RECEIVED for review July 25, 1963 ACCEPTED November 22, 1963 Lliork performed under the auspices of the I!. S. Atomic Energy Commisqion at the Argonne National Labordtorv, Argonnc, Ill.
CONCENTRATION AND MASS FLOW DISTRIBUTIONS IN A GAS-SOLID SUSPENSION S . L . S O O , G . J . T R E Z E K , R . C . D I M I C K , A N D G. F . H O H N S T R E I T E R University of Illinois, Crbana, Ill.
Distributions of concentration, mass flow, and velocity of solid particles were studied with a fiber-optic probe and an electrostatic probe. Concepts concerning these distributions and electrostatic charges on solid particles were furthered and substantiated. The relation between electrostatic charge on solid particles and diffusivity of solid particles, and the difference between static loading and mass flow ratio of phases were proved.
and correlation of momentum, heat, and mass transfer in a gas-solid suspension call for a knowledge of the concentration distribution of solid particles and the velocities of the phases. Earlier studies are applicable to given concentration distributions ( 7 7 . 79) or assume constant concentration in analysis (22) and data correlation from overall average concentration (3, 27). Measurements were made by impact counter system with the assumption of similar REDICTION
Present address, Lockheed Research Laboratory, Palo Alto, Calif. 98
I&EC
FUNDAMENTALS
velocity of phases ( 7 8 ) ; the differences between velocity of phases and between mass flow and concentration distribution of particles were later recognized and presented (73). These, together with studies on dense suspensions (15), measurement by point study probe ( 2 3 ) , and measurement by capacitance (24), show that more definitive measurements need to be made. Results of earlier studies (73, 78) are further generalized in the study of boundary layer theory of gas-solid suspensions ( 7 6 ) . Methods of measurement of concentration of the particulate phase in a suspension consist of electric measurement as
applicd to aerosols ( 6 ) , optical method by light scattering (72)> counting from photographic record (171, etc., and are applicable either to the over-all measurement of large samples or relatively small numbers of particles per unit volume (light loading), The impact counter system (78) or the point study pickup (D) applies to relatively large particles as well as to light loading; both give local mass flow rather than concentration. ., It is also possible to rely on the alteration of some electric parameter such as the capacitance between two plates (24) or inductance of a coil for measurements of concentration. Basic calculations show that the desired sensitivity could not be obtained with the capacitor, while the inductance measurement would have to be limited to metallic, preferably ferromagnetic, parricles. The most straightforward method for instantaneous evaluation of the number of particles per unit volume is to rely on soirie attenuation process of a transmitted wave-that is, attenuation of light, sound, or a microwave, by the particles. Particle conceritrarion was measured utilizing the attenuation of light through the application of the principle of fiber optics (8). T h e initial configuration was suggested by Fenn (5). For the measurement of particle phase velocity (73, 76), an electrostaLic mass flow probe was developed to determine the mass flow of the particle phase. Measurements were made on a 5-inch diameter, two-phase flow system which was built as a basic research facility. The present paper concerns the measurement of the concentration distribiition and the mass flow distribution of the particle phase. The air velocities were around 130 feet per second; the particles were glass (50-micron nominal size) and magnesia (35-micron nominal size) at various loadings. The concepts concerning concentration distribution, mass flow distribution, velocity distribution of the solid particles, and electrostatic charge on solid particles were developed further from previous papers ( 7 3 , 74, 76, 78). I n particular, the relation bttween electrostatic charge on solid particles and diffusivity of solid particles, and the difference between loading (average mass ratio of phases) and mass flow ratio of phases were recognized and demonstrated. Closed-Loop Two-Phase Flow System
After the stream passes throQgh the constant speed radial-type blower, it is returned to the brass tube through a galvanized 20gage sheet metal tube. A damper located at the fan discharge along with two rubber-seated butterfly valves allows the flow velocity to be varied. A cyclone-type particle separator incorporated in series with the loop system through a butterfly valve allows the particles to be sepaiated from the gas and the system to be purged if a diiTerent solid-gas mixture is desired. The volume of the closed-loop system is 23 cu. feet. At steady condition and maximum air velocity of around 130 feet per second, the temperature of the circulating air at stead!- stare is 95' to 105' F. (at a room temperature of 75' E'.) ; thus, approximately 1.67 pounds of air W B S circulated. Besides the instrumentation discussed below, the test loop is equipped with a velocity and temperatuie profile-measuring apparatus in the form of a Pitot static rube and an impact thermocouple. A section equipped with \vindo\vs is incorporated for observation and photography. Rapid traverse of probes is made possible by a motordriven probe stand. I n this flow system, the motor turns a lead screw which drives a block holding the probe and associated components. Microswizches and a stepping relay are employed to reverse the probe at the end of each travel. Auxiliary switching to halt or manually traverse the probe at any point in the cycle is provided. The test section is mounted betweeri two flanges \\ith bolts at 45'. so that the traverse can be made at various directions with respect to gravity to check againsr nonsymmetry of both concentration and mass flow profiles over the pipe diameter. Over the range of experimentation the profiles were symmetric with respect to the center of the pipe. The closed-loop system makes possible large loading of solid particles! heretofore impractical in a once-through duct used earlier with feeder and collector (77, 78). However, calibrations by normalization as presented below still have to be checked with those of mass flow distribution and concentration distribution with feeder and collector (Figure 1 ) ; this makes possible checking against deposition at corners and turns of the closed loop. With the closed loop and prolonged tests: zhe particles tend to break up, particularly in the fan. The glass particles, originally sieved \virhin the range of 210 and 250 microns, eventually settle a t the distribution as shown in Figure 2: from counting under a microscope with distribution of size around 50 microns. The magnesia particles, originally sieved at 105 to 125 microns, eventually break up to the distribution as sho\vn in Figure 3, with distribution of particle size around 35 microns. The range of loading \\.a flow. as in the mass pickup ( 4 ) . For this purpoje a ball probe (Figure 7) was built, with a measuring circuitry utilizing most of the components employed in the optical probe system, except that the ball probe needs no provision for bucking the output of the probe. T h e current produced by impact of the particles against the ball is fed directly into the Keithley 6-10-R electrometer, which permits ampere. An adjustmeasurements of currents as lo\c as able damping constant is provided by a number of capacitors. I n the electrometer itself. the input impedance in ohms is the reciprocal of the current range at which it is set. For the current ranges of 10~-6and lo--$ ampere full scale, which are most often used with the ball probe, the input impedance \could rherefore be l o h and 109 ohms, respectively. Darnping times ranging from 0.1 to 10 seconds were found to be ideal for removing the turbulent fluctuations present in the output from the probe. T h e turn-around point when the probe approached the wall of the duct was marked with a spiked pulse on the recorder chart, caused by pickup from the coil of the stepping relay used in the probe traverse circuit. With the reversing microswitches carefully positioned, the radial position of the probe could be determined accurately by a linear measurement along the chart between the wall marks. For convenience in handling the d a t a the traverse speed was set so that a linear length of chart equal to the diameter of the duct \cas unrolled during the time required for the probe to traverse across the duct. I n the design of the ball probe itself. d n effort was made to maintain a high rcsistance to ground by using glass sleeving to insulate the lead to the ball from the hypodermic tubing serving as the probe shaft. 'ro be acceptable, the probe had ro h a w a t least a lO"-ohm resistance so as not to shunt the signal to ground. 'l'his required careful washing with distilled \cater and acetoce after the stainless steel ball was soldered to the inner conductor. \I'ith a reasonable amount of care it was possible to maintain a lO"-ohm or greater resistance to ground. \Vith these resistances. I) l${, or less of the probe output was shunted to ground and the electrometer readings were taken. \vith no further correction, as the absolute current produced a t the ball.
Figure 5.
-TO
Straight-through fiber optics p r o b e
PHOTOCELL
t
c
-8'
Figure
6.
Probe with built-in light source
I
'l'he background current caused by dust particles in air \vas checkTd. Such a background current, measurable.
1
1
,,-STAINLESS
Figure 7.
STEEL
Electrostatic ball probe
Evaluation of Data
Concentration Distribution. Since the probe detects only a change in light intensity, AZ> between the bulb and the receiving rod responding to the concentration of solid particles in the gap, ir is necessary to convert the scale from intensity t o particle concentration. For the case of straight glass rods: the change in light intensity is the difference bmveen the light intensity with the zero particle condition and the given concentration. These changes were measured. using the I'Veston densitorneter. in terms of the light transmitted. IVith the probe as shown in Figure 6, this was obtained from the total output of the phototube in each case (without bucking voltage). using the bucking circuit. T h e major voltage output \vas cancelled, so that fine deviation could be detected across a tube diameter; in effect. the sensitiviry was such that a 3 to 10% light iritensity \could correspond to a full scale deflection (1 00 divisions) of the recorder. T h e intensity variarion. or voltage variation. due to the particle concentration was counted from rhe zero particle reading. Evaluation of the particle concentration involves a normalizing procedure with respect to total mass M, of solid pa titles in the pipe:
length
p,, 2at
where p p is the concentration of solid particles (mass per unit volume), r is the radius measured from the axis of the pipe, and R is the radius of the pipe. Since any local change in light across the tube diameter would be caused by a local change in particle concentration, the particle concentration must be proportional to the change in intensity or voltage. or
and pp
2ar dr = K
( A Z j 2ar dr = M , length
(4)
where K is the optical scale factor, and .Zip 'length is the mass of particles per unit length of the pipe. This is in effect normalizing local variation across the tube diameter to the total mass of particles of the system: _A f P_ ~-~ ~
length
M, ~~~~~~
~
~~~~
(volume of system)
(cross-sectional area)
(5)
T h e volume of the system can be related to the mass of air entrained in the system. since it is closed, so that \vr have
dr
VOL. 3
NO. 2
MAY
1964
101
at the center (subscript o), or at least very neaily SO (13). Therefore, the above measured value of p P at thr center gives
uo is the fluid velocity determined by Pitot static tube. ‘The above shows that K , is a constant for a given distribution. Hence, the mass flows a t various radii are determined. Figures 10 and 11 give the mass flow distribution of glass particles and magnesia particles. From the relation in Equation 10 we can determine three important quantities. One is u p , the mean ve1ocit)- of the particle phase (Figure 12) ; another is the total flow rate in a recirculating system
K=0.834xl~uqI33.2 fp
I
I
0.5
1.5
2
I 2.5
RADIUS, inches
which can be compared to metering by the s c r e ~ vfeeder ( 7 7 ) . T h e value of Allpgives a check of earlier assumptions in concentration distribution. T h e third quantity Lvhich can be determined here is the average value of charge LO mass ratio. T h e above implies
Figure 8. Concentration distribution of 50-micron glass pariicles in air 5-inch diameter pipe
where M a is the mass of air entrained by the system, mp* is the = 1 / p where p is the density mass ratio of solid to gas, and of air a t the flow condition. Thus
K =
my*
7rR2p
lR
= -
mp* nR2p
27r 2: ( A I ) ~ ( A Y )
(AI) 27rr dr
Particle Diffusivity. T h e above knowledge of conceiitrations of solids and charge to mass ratio also permits determination of diffusivity of particles, by using the procedure of So0 (74):
(7)
Integration was carried out numerically on curves obtained from the recorder. K’s for each loading were determined and then the local value of the density corresponding to a local change in light intensity was computed. K has the dimension of density and is a function of the total particle mass. T h e concentration distribution measurements obtained for glass beads and magnesia powder are shown by Figures 8 and 9. T h e density in each case increases a t the wall as theoretically predicted (73, 74) and measured (24). Mass Flow Distribution. T h e ball probe gives the current distribution as
where e is the permittivity. can be calculated :
Do.the diffusivity of the parricies.
(17) Equation 15 is plotted in Figure 13.
where d is the diameter of the probe, n p is the number of particles per unit volume, q is the average charge per particle, and u p is the mean velocity of the particles at a given radius. Equation 8 is rewritten as:
i
= ?! 4 d2npmp
(A)
up =
d2ppup
(A)
(9)
where q , m p is the average charge to mass ratio induced on the solid particles by impact with the wall ( 9 ) and resultant charge distribution. Therefore, for a narrow size range of particles, q / m , is very nearly constant, and the mass flow of solid particles is given by: ppup =
K,1
(10)
\vhere KeEis the constant of proportionality. K,,, can be determined from the condition at the center of the pipe lvhere our previous theoretical study gave : uo E u p 0 102
l&EC
FUNDAMENTALS
(11)
Discussion
T h e above data were further evaluated according to the theoretical basis (73, 74, 76) and the results were compared to those from our earlier experiments ( 7 3‘1 and to those of \’an Zoonen ( 2 4 ) . In these experiments. gravity effect is nr:ligible. Table I presents the concentration arid mass flow data of various sources, covering a wide range of flow rate ratios of solid to air (item 12). Because of the difference benveeii the velocity profiles of solid and gas. the mass ratio (;24,, :Ifa) a i d arel ~different. a) \virh the former the flow rate ratio ( L l ~ p , ’ L always at a higher value. The velociry of the solid particles a t the center of the pipe does not differ from that of the gas in fully developed turbulent pipe floiv in the range of loading of the present experiments, but lags tonsiderably in die case of very high loading of \.an Zoonen’s experimonts. hlthough Van Zoonen stated that his resiilts tend to fluctuate. analysis of his data and comparison \vith our results indicate that his results are consistent and correct in magnitude. In spite of
mc
5 4 9 v)
‘9 2-3
0
z u6138.3fpr
I I
RADIUS, inches Figure 9. Concentration distribufion of 35-micron magnesia particles in air 5-inch diameter pipe
.8
I
1
RADIUS, inches I 1.5
.5
Figure 1 1 .
1
I
I
0
2
2.5
h.ass flow distribution of magnesia in air 132 feet per second
,
L_1__:
I
I .5
J
- .-5 I 1.5 2 7 RADIUS, INCHES’ GAS PHASE VELOCITIES: -AIR ALONE -WITH IO 1b.GLASS Ib.GLASS WITH 20 -WITH 30 Ib.GLASS SOLlDPHASEVELOC1TIES:--WITH I O Ib.GLASS ._ .-s -.-z20 Ib GLAS .............. WITH WITH -0.75 lb.Mg0 WITH 1.75lb.Mg0 WITH 2.75 1b.MgO ~
/..
-------
----
the range of average mass flo\v of particles (itern 3 ) , the mass floiv distribution (items 5 and 6) and the concentration distribution (items 8 and 9)follo\v the same trend. as does the slip velocity of solid particles a t the \\-all (item 10). Their being similar, hoivever. is due to the narroit’ range of turbulent sushension parameter (77) (item 1 3 ) :
\\.here dli?is the intensity of turbulence of the gas, p is the density of the gas and p its viscosity. 0, is the 1,agrangian scale of turbulence of the gas, & is the density of the solid material;
Figure 1 2 .
Velocity distribution of particles
and pipe flov pararpeter of turbulent suspension ( 73) (item 14) :
where R is the pipe radius, and u, is the maximum gas velocity. From the distribution. one further sees rhat the approximations ( 7 3 ) : u p
=
up,
+ iu,,
-
u p u ) (1 -
VOL. 3
NO. 2
6)
(20,
1 I,,
MAY
1964
103
Table I.
Concentration and Mass Flow Distributions of Solid Particles Glass Particles .Magnesia Particles Glass ( 7 3 ) 10 20 2 75 0 75 1 75 8.79 5 39 0 2695 0 598 0 946 0.0273
CQtdJSt (24, Fig. 5)
-
1. 2. 3.
0.2742 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. Pipe material 19.
Particle size (nominal),
0 447
133.2 128 1,560 1 0.397 0 1.735 2 1.562 1 1 1.902 0 0.205 12 6 4 97 8 0.1465 0 0.017 0 1.14 1 2.14 2 12 7.2 Brass
4 643 40 822 647 876 212 13 1465 011 14
0 0137
0 0304
138 3 1 472 0 423 0 0863 1 485 1 60 0 264 0 448 0 249 0 125 0 281 1 504 3 29 0 242
137 6 1 452 0 486 0 1918 1 462 1 52 0 318 1 048 0 551 0 125 0 127 1 355 2 62 0 51 Brass
Table II.
10
20
0.75
23.7
(630) (330) 0.467 0,892 29.7 31.1 1,362 1.13 0.1054 0.118 13.2 25.3 1 ,362 1.00 3.27 3.21 0.32 0.35 55.7
106.5
0,085 1.25 2.30
Unrecorded, 5-cm. dia. 20-1 50
Glass ( 73)
Catalyst ( 2 4
0.0273 3.39 0.528 0.388 2.16 1.23 7,96 106 74 21
3 0 0 1 1 10 108 77 5
84 466 450 91 10 3
1.031 0.778 0.1805 2.70 1.15 96 77 30
can be checked by determining constants rn and a from present results as presented in Figures 8, 9, and 12 (items 15 and 16). These values vary over a small range in spite of the large variation in size of particles and speeds. T o compare to the results of So0 (76) governing slip condition, the value of particle slip parameter
was computed as given in item 17 of Table I, showing that the slip (at the wall) occurs at Ka values from 0.2 to 10.0. I t was recognized earlier that, in the pipe flow of a gas-solid suspension, there must be a drift component of the solid particles besides diffusion to give the measured solid distribution. Diffusion alone, regardless of the dependence of diffusivity to radius. would end u p with uniform concentration distribution of solid particles at fully developed pipe flow, even if the diffusivity varied with the radius. Distributions in concentration with higher values near the \Val1 are attributed to the electrostatic charge induced on the solid particles by impact with the wall ; and the drift is due to electrostatic repulsion by self-field (7-1). The present results further substantiate this fact. l&EC
1.67 1.67 0.19 0.18 0.0763
Glass, 3in. dia. 100-250
Magnesia Part ides ____ 1.75 2.75
and
104
100 1.65 0.45
(140) 0.198 27.8 1 .52 0.536 5 6 1.612 3.27 0.18
Diffusivity and Electrostatic Charge of Solid Particles
Glass Particles 1. M p , lb. 2. M p , Ib./sec. , m. sec. 3. M P / r R z Ib./sq. 4. .Km,lo8 lb./sq. in. sec. am 5. ( g / m p y ; 10-6 coul./kg. 6. [ & J ~ / & ] ~ , , Ib./sq. in. 7. 8. $ 1 9. Do, sq. rn./sec. 10. Pipe temp., ' F. 11. Ambient temp., F. 12. Relative humidity, %
136 9 1 480 0 491 0 304 1 480 1 526 0 328 1 65 0 876 0 125 0 078 0 81 2 13 0 81
35
50
fi
0 0481
~
FUNDAMENTALS
1.106 0.725 0.020 2.72 1.59 98 77 30
1.415 0.568 0.0183 2.28 1.88 101 77 30
0.198
0.467
0.892
2 7
1 33
1 27
1 26
2 35 1 30 2 7 85 85
572 350 8
6 6 4 0 9 45
5 59 3 4 13
Table I1 presents the relation of diffusivity and electrostatic charges in solid particles. In the case of the first five columns (of the table), the charge to mass (qt m p ) ratio (item 5) was was calculated (item 9) ; measured first and the diffusivity (Do) the value of D oof the glass particles checks with the earlier measurements (77, 20) within the order of magnitude. The values of q"mp for the last four columns were calculated from their values of D o . For both glass particles and MgO particles, the charge to mass ratios induced by copper pipe are similar in magnitude, and all positive in sign as measured. The glass particles used in our previous study (73) carried much larger charges because glass pipe was used, although the sign of charge was not determined. Charge distribution at impact and separation is affected by the surface. Surfaces having exactly similar Fermi levels will not induce charges ( 9 ) . The q 'mP from Van Zoonen's experiments are deemed reasonable, although the material of the pipe is not reported. nor t h e type of catalyst. The average field, E, at the surface of the particles is given by ;
(23) The value of E varies from 800 volts per meter for magnesia panicles to 900 volts per meter for glass panicles i n rhe above.
toward the wall, and velocity is less than or equal to that of the stream at the core, but is finite a t nearly 20y0 core velocity at the wall in the range studied. T h e fluid follows nearly the turbulent velocity law ( 7 ) , but the particles follow nearly linearly with distance from the wall to nearly * / g power. The over-all mass flow ratio and mass ratio of solid to gas are not equal; the latter is usually nearly twice as large as the former. Correlation of drift of solid particles toward the wall because of electrostatic forces and diffusion of solid particles toward the core because of concentration gradient is valid. Magnitudes of charge to mass ratio and diffusivity were reasonable, and the latter checks with earlier results. From these considerations, the concentration distribution is not expected to he uniform even for micro-sized particles. Ac knowledgmeni
Figure
13. Plot of
Equation 15
Support of Project SQCID is appreciated. G . F. Ilohnstreiter designed the test duct and early phase of the optical probe toward his M.S. thesis a t the University of Illinois. G. J. Trezek performed measurements and further developed the optical probe, and R. C. Dimick designed the circuitry and mass flow probe, each working toward fulfillment of the requirements of graduate study. M. W. Wolf performed the numerical computations. Nomenclature
No electric breakdown (2) occurred under the prevailing humidity. T h e ranges of temperature and humidity data in our experiment are shown in Table 11. T h e average charge to mass ratios obtained in Table I1 are particular to the test system. T h e present result is due to the brass pipe, galvanized pipe, and blower combination ; the magnitude of charge is also affected by the flow velocity and number of impacts (due to turbulence) with the walls. The charges induced as given in the data of the previous study cited (7,?) are particular to the glass pipe and the surfaces of that system, This consideration applies also to Van Zoonen's experiments (24). Two stations of measurements a t 3 feet apart were taken in one continuous loop and no differences were recorded. However, this is not expected to be true for all systems. The above approximation with an average charge to mass ratio and the correlation by Equation 15 actually neglected the fact that, with particles of a given size distribution, the size distribution at various radii would differ. This is due to different forces on particles of different sizes. The electrostatic effects are negligible in a liquid-solid suspension where particle velocity and fluid velocity are directly proportional (70). Electrostatic charge carried by solid particles constitutes a new parameter to be contended with in the study of gas-solid and gas-liquid suspensions. Many more experiments are also needed for further generalization. The concentration distribution due to electrostatic effect affects friction, heat transfer, and mass transfer in gas-solid systems. The charge carried by solid particles is expected to be significant in the solid-gas reactions. The high temperature phenomenon has been previously presented ( 7 5). Conclusions
The nature of the concentration, mass flow, and velocity distributions of solid particles is such that the concentration increases toward the wall of the pipe, mass flow decreases
B'
= =
I K
= = = = = = =
= = = =
M, R
=
d
=
i
=
81
=
rn
=
rn, rn,*
= = =
n,
q r u
up
= = = =
interaction parameter of electrostatic forces and turbulent diffusion particle diffusivity electric field light intensity optical scale factor turbulent suspension parameter pipe flow parameter of turbulent suspension particle slip parameter mass flow constant total mass of air in system total flow rate of air total mass of solid particles in system total flow rate of solid particles radius of pipe diameter of solid particles electric current through probe Lagrangian scale of turbulence constant for velocity distribution of particles mass of particle mass ratio of solid to gas number of solid particles per unit volume charge on particle radius velocity of air velocity of solid particles
dz - intensity of turbulence 2/2= intensity of turbulence of solid particles =
va
=
specific volume of air
GREEKLETTERS = constant for density distribution of particles 8, K = proportionality = permittivity p = viscosity of air p = density of air pI = density of particle cloud pp = density of solid material $ = dimensionless density gradient LY
SUBSCRIPTS o
=
a'
=
center of pipe wall of pipe VOL. 3
NO. 2 M A Y 1 9 6 4
105
References
(1) Bald\vin! I*. V., \Valsh. T. J . , A.I.Ch.E. J . 7, 53-61 (1961). (2) Cobine. J. D.. .'Gaseous Conductors," p , 183, Dover Publications, S e w York. 1958. (3) Depe\v. C. A . . '.Heat 'Iransfer to Flowing Gas-Solid hlixtures in a Vertical Circular Duct," L n i v . Calif. Tech. Rept.; Contract No. 2-7405-En~-48.Julv 1960. (4) Dimick. R. Cy. Trezek: G. J., Rei. Sci. Instr. 34, 981 (1963). (5) F r n n ? J . B.. private communication. 1959. (6) Hinckle, D. I>.. Orr, C.. Dallavalle. J. M., J . Coiioid Sci. 9 , 70--80 (195.5). (7) Hinze. J . 0...,Turbulence," p. 479, McGraw-Hill. New York. 1953. (8) Kapany, N. S.."Fiber Optics," Appendix N by J. Strong, "Concepts of Classical Optics.'' \ V . H. Freeman and Co.! San Francisco. 3958. (9) Montgomery. D. J . ? Solid State Phys. 9, 139-97 (1959). (10) Newitt. D. M.. Richardson. J. F.. Shook: C. A , . Proc. Svmposium on Interaction between Fluids and Particles, 3rd C o n q e s s of European Federation of Chem. Engineering, pp. 87-101, Institution of Chem. Engineers, Idondon. 1962. (1 1) Peskin. I- mass transfer. and accurate knoivledge of the mode of contacting is necessar!' for successful reactor design. Although orifice mixers have been used for many years for gas-liquid and liquid-liquid reactions. they have not been subjected to s! stematic study. nor has the mode of operation been critically examined and compared \vith the more costly agitated-tank reactors. This study \vas undertaken to provide some quantitative as \vel1 a.s qualitative insights into this important but some\vhat neglected area. Specifically the effects of plate design (hole size and number of holes). ulate spacing. gas rate, m d liquid rate have been studied using the catalyzed air oxidation of aqueous NarSO3 for determining contacting efficiency and high-speed motion pictures for observing flow characteristics. .I'he a i r - S a r S 0 3 system has been studied thoroughly in agitated-tank reactors, and thus the resdts on orifice plates are immediatel!- comparable rvith those of previous Lvork. NIIVSTRIAL
106
I&EC FUNDAMENTALS
Previous Investigations
The performance of agitated-tank. gas-liquid contaclors using the air-SasSOs system has been studied rather extensivel!. ( 7 , 6L?.72). The air-NazS03 system \vas found desirable for these studies because the mass transfer rate is controlled by the liquid-film resistance. and the catalyzed reaction proceeds so rapidly that the mass transfer rate. and rhus the contacting efficiency. may be examined over wide ranges of conditions. Kinetic studies on the air-Sa2S03 system have been performed (2. 70). and it has been demonstrated that the transfer rate is relatively independent of sulfite ion concentration. The use of orifice mixers and their applications in petroleum refining have been discussed by Morrel and Bergman (5). More recently. Scott et al. ( 9 ) and McDonough et ai. ( 3 ) found that the formation of interfacial area in immiscible liquids b>orifice mixers is a function of the change in kinetic energy across the mixing orifice. the energy required to overcome the
