Nomenclature
t$
A = dimensionless coefficient, distribution parameter, p ~ / K f
B
= dimensionless coefficient, AVo/kL
C = normalized gas phase concentration, c/Co Co = constant inlet gas phase concentration, moles/volume d p = particle diameter f = void fraction, gas volume/column volume k = mass transfer coefficient, moles/time/bed volume/concentration K = equilibrium coefficient, concentration/solids loading L = total length of adsorption column M = adsorbate molecular weight N = packing coefficient, (2d 2$)* ( A / B ) = ( A / B ) N ’ P = normalized total column pressure, P’/Po Po = inlet total pressure to column, atm. q = solids loading, moles/weight of solids T = dummy variable in Equation 6 R = gas constant s = dummy variable in Equations 5, 7 , and 8 t = time T = absolute gas temperature u = dimensionless time, k K t / p ~ u = dimensionless distance, old distance parameter, kx/Vo V = normalized gas velocity, V’/Vo Vo = constant inlet superficial gas velocity, distance/time W = normalized solid phase loading, p/p, z = distance along bed axis Y = modified distance parameter (see Equations 7 and 13) z = normalized distance, x / L a = dummy variable in Equation 7a 0 = modified performance parameter (see Equations 8 and 14) p = gas viscosity p~ = bulk density of bed, weight of solids/column volume
+
= portion of packing coefficient significant during laminar
flow C0.145 p VoL(l - f)2/Podp2gcf3when atm. c.g.s. units are employed] , J, = portion of packing coefficient significant during turbulent flow [0.00169LV>M(l - f)RTdpg,f3 when atm. c.g.s. units are employed] literature Cited
Acrivos, Andreas, Ind. Eng. Chem. 48, 703 (1956). Alonso, J. R., M.S. thesis, Worcester Polytechnic Institute, 1967. Anzelius, A., 2. Angew. Math. Mech. 6, 291 (19:f). Bird, R. B;: Stewart, W. E., Lightfoot, E. N., Transport Phenomena, Wiley, New York, 1960. Carter, J. W., Trans. Inst. Chem. Engrs. (London) 44, T253 ( 1966). Collentro, W. V., M.S. thesis, Worcester Polytechnic Institute, 1968. 6, 426 (1966). Cooney, D. O., IND.ENG.CHEM.FUNDAMENTALS Edeskuty, F. J., Amundson, N. R., J . Phys. Chem. 66, 148 (1952). Eteson, D. S., Zwiebel, Imre, A.I.Ch.E.J. 16, 124 (1969). Fosberg, T. M., Phillips, C. E., “Adsorption Dynamics in Granular Solid Beds,” Paper 14d, 62nd National hfeeting, A.I.Ch.E., Salt Lake City, Utah, 1967. Fukunaga, Paul, Huang, K. C., Davis, S. H., Jr., Winnick, Jack, Ind. Eng. Chem. Process Design Develop. 7, 269 (1968). Furnas, C. C., U . 8.Bur. Mines,liBull. 361 (1932). Hougen, 0.A,, Watson, K. M., Chemical Process Principles,” Part 111, W-iley, New York, 1947. Masamune, Shinobu, Smith, J. M., A.I.Ch.E.J. 10, 246 (1964). Meyer, 0. A., Weber, T. W., A.I.Ch.E.J. 13, 457 (1967). Needham, R. B., Campbell, J. M., McLeod, H. O., Znd. Eng. Chem. Process Design Develop. 6 , 122 (1966). Schuman, T. E. W., J . Franklin Inst. 208, 405 (1929). Vermeulen, Theodore, in (‘Advances in Chemical Engineering,” T. B. Drew, ed., 5’01. 2, pp. 147-208, Academic Press, New York, 1958. RECEIVED for review October 21, 1968 ACCEPTED April 24, 1969
EXPERIMENTAL TECHNIQUES
V A P O R I Z A T I O N OF L I Q U I D DROPLETS IN HIGH T E M P E R A T U R E A I R STREAMS GEORGE C. F R A Z I E R , JR.’,
A N D WILLIAM W. HELLIER, JRH2
Department of Chemical Engineering, The Johns Hopkins University, Baltimore, Md. 21 218 An experimental method for the study of rapid vaporization of liquid droplets in high temperature gas streams is described. Data from a prototype model are presented and discussed in terms of data obtained by other methods.
HE phenomenon of vaporization of small droplets, as well Tas their condensation, is fundamental to the formation, stability, and dispersal of aerosols. In many situations of interest, the characteristics and behavior of the droplets may influence or determine the gross characteristics of larger systems of which they are a part. In particular, in the area of combustion of liquid fuels the vaporization rate of small fuel droplets may be the rate-limiting step in the total process. Present address, Chemical and Metallurgical Engineering, University of Tennessee, Knoxville, Tenn. 37916 Present address, Department of Chemical Engineering, University of hlaryland, College Park, Md. 20740.
Interest in this, as well as other areas, has prompted a considerable number of investigations into various aspects of small drop phenomena (Bitron, 1955; Essenhigh and Fells, 1960; Ranz and Marshall, 1952). However, basic questions are still unanswered, especially with respect to the rapid vaporization of droplets in high temperature air streams, aside from the purely hydrodynamic processes. Among these are the extent of the deviation from vapor pressure-temperature equilibrium at the droplet surface during vaporization, the sensitivity of the vaporization rate to the form of the mixture “rule” for the transport properties of both polar and nonpolar vapor mixtures, and VOL.
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the range in vaporization rates and droplet size over which quasi-steady state may be considered a good approximation. The development of answers to these questions has been impeded by the mathematical difficulties associated with the nonlinear, governing differential equations. This latter difficulty is pointed up for multicomponent systems in particular by the form of the Mason-Saxena relation (Mason and Saxena, 1958) for the conductivity, A, of nonpolar gas mixtures : n
L t = C Ai/[1 i=l
+ C Gik.d.il n
(11
k=l
where Gib
= 1.065 (1 -I-
Mi/Mk)-‘12
X
Hence the mixture conductivity depends on the composition through the mole fractions, z3. Because of the form of this dependence on composition, as well as other factors, the energy and mass conservation balances in general form a set of nonlinear differential equations. Only special cases of the conservation equations appear to have been treated (Goldsmith and Penner, 1954; Williams, 1965). Thus, to determine the range over which vaporization rates estimated from a simple theory hold, and to guide further developments of the theory, quantitative data are desirable over a wide range of experimental conditions. At least two experimental difficulties have to be overcome in the quantitative study of vaporization phenomena of small droplets-that is, droplets in the size range below the order of few hundred microns. First, sprays of droplets are normally produced in nonuniform sizes. Hence one has the additional problem of determining the size distribution function in the study of vaporization in sprays. This is difficult with many liquids of interest, as their droplets tend to evaporate during the time they are collected and measured. However, Bitron (1955) conducted an experiment of this type using dibutyl phthalate. Secondly, the droplets must be either fixed in space or their motion “stopped” photographically. The droplets have been fixed (Godsave, 1953; Ranz and Marshall, 1952), but this tends to produce a lower limit on the size range that can be studied, and the extent to which the droplet holder affects the results is not readily known.
Liquid Nozzle Sonic Driver Droolet
4
Figure 1. 808
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Regulated Liquid Source
Experimental arrangement
FUNDAMENTALS
These difficulties can be minimized in the experimental approach described here. This approach is based on the observation of a well-defined stream of small droplets generated by induced breakup of a liquid jet emanating from a fine capillary tube. The breakup is induced in this case by longitudinal vibrations generated in the capillary by a 20-watt sonic driver. This technique of producing small droplets of uniform size has been developed and applied in the study of certain other small droplet phenomena (Magarvey and Taylor, 1956; Park and Crosby, 1965). Prototype vaporization studies were conducted by directing the droplet stream through the potential core of an elevated, known temperature air jet near the exit of a 14inch i.d. tubular furnace. A schematic of the experimental arrangement is shown in Figure 1. The furnace tube was filled with 3/16-inch alumina spheres to enhance the heat transfer between the tube and the air stream. A uniform, laminar, air velocity profile a t the exit of the furnace tube was produced by the use of a series of three nonwoven, nickel, 100-mesh, Lektromesh screens, placed in the furnace tube normal to the air flow. The details of this technique of flow smoothing have been described (Kooyman, 1969; Walker and Westenberg, 1958). In these first experiments, the air velocity was 326 em. per second, the Reynolds number based on the furnace tube diameter, Reo, was 1190, and that based on the screen grid diameter, Red, was 4.7. Red is thus well below the critical value of -40 for the generation of turbulence by screens (Schubauer el al., 1950), so the flow was laminar in the experiments reported on here. Walker and Westenberg’s (1958) hot wire measurements and diffusion experiments in a similar setup operating under similar conditions substantiate this, and show, further, that the velocity profile in the test region (the zone downstream of the last screen but within about 1 inch of the screen) is uniform to within 8%. This method of flow straightening provides a convenient method of studying droplet vaporization in streams of different incident air turbulence intensities as well as in the laminar regime. For such studies the turbulence can be generated by the last screen in the series by setting the parameters such that, Red > Ree= 40. The turbulence downstream of such screen-type grids has been characterized by a number of investigators (Grant and Nisbet, 1957; Tsuji and Hama, 1953). The droplet stream was passed across the air stream, as illustrated in Figure 1, approximately 1/2 inch from the furnace tube. The Reynolds number of the 440-micron droplets discussed below, based on the velocity of the droplet relative to the air stream, is 25.3. This magnitude is sufficiently small to make deflection of the droplets by the air stream negligible. The trajectory is essentially straight over the width of the observation zone, which is approximately 2 em. in this case. A photographic record of the vaporization process was made by the use of a Graflex camera with a shutter speed of 1/400 second. The Kodak Royal-X Pan film was illuminated by use of a Strobotac set a t a suitable multiple of the droplet frequency and placed behind the droplets. A series of close-up lenses was attached to the regular camera lens so that a magnification of 4% was achieved. Larger magnifications may be required for observing droplets in a size range smaller than that of the prototype runs. In view of the fact that the components of an optical system cannot be placed too close to the hot furnace tube, the use of holography as developed for the study of aerosols (Silverman et al.,
Figure 2.
Freon 1 13 droplets in a 669" C. oir stream
Time t is that required for a droplet of initial mas$ mo to be reduced to m. Equation 2 is of the form one obtains from a quasisteady energy balance with all properties held confitant. Within the experimental error, the data of Figure 3 are correlated by the form, Equation 2, and the vaporization constant, K , for the Freon 113 droplets under these conditions is 56 seconds per sq. cm. This is in the lower end of the range of values for a number of volatile liquids evaporating in high temperature gas streams as summarized by Essenhigh and Fells (1960), which is considered reasonahle in view of the relatively low latent heat of vaporization of this material (so00 cal. per gram mole a t the normal boiling point). The vaporization data of Figure 3 may also be interpreted in terms of a mass transfer coefficient, kc, as defined by Ranz and Marshall (1952):
7 pt= I a m . 1.; 669'C do= 0.044 cm.
i
3 l i m e . f x 10 ,rec.
Figure 3. Vaporization of Freon 113 droplets in a n air stream
1964; Thompson et al., 1966) is a promising technique for obtaining the desired information while maintaining an adequate distance from the hot zone. A stream of Freon 113 (CCLFCCIF,) droplets passing through a 669' C. air jet is shown in Figure 2 (Hellier, 1968). The liquid was injected a t room temperature, approximately 20' C. helow its normal boiling point. The droplet residence time in the hot gas stream was approximately 5 msec. before measurements of its size and position were recorded. This initial residence time served as a preheat period. A 20-mil i d . capillary was used in this case with a sonic driver frequency of 1350 see.-'. The initial droplet diameter, 6, is 0.044 cm., the wave length is 0,109 cm., and the speed relative to laboratory coordinates is 186 cm. per second. With this information and the measured diameter of each droplet shown, the diameter as a function of time, d ( t ) , can he computed and the vaporization rate can be deduced. These data are provided in Figure 3, where the least-squares line through the data is shown. The diameters of the droplets were measured on the RoyalX Pan photographic negative by the use of a Joyce-Loebl Mark 111 B microdensitometer. This instrument is reported to he capable of a resolution of the order of 1 micron, which yields a minimum error of about 0.1% in the measurement of the -2-mm. droplet images. However, the resolution of the Royal-X Pan film with our developing technique k estimated to be in the range of 65 to 75 line pairs per mm., so the minimum error in measurement of these droplets is about 0.7%. This value could be reduced by use of Tri-X film. The maximum deviation of from the least squares line in Figure 3 is 10.5%, which yields a maximum deviation in droplet diameter from the mean of -5%. In view of the magnitude of the above-mentioned errors inherent in the measuring technique, most of this scatter is attributed to the
ko = TA./APA
(3)
For these droplets, kc"0.15 g./(sq. cm.) (see.) (atm.), which is higher by a factor of about 4 than the value obtained from the low temperature correlation of Rana and Marshall. Their correlation was based by and large on vaporization data from suspended droplets, so the discrepancy between the experimentally determined value of ko and the value obtained from their Correlation for this case is probably due to different modes and amplitudes of oscillation in the present free droplets as well as the fact that the temperature of the present study w&swell above the range of Ranz and Marshall. This discrepancy points up the need for caution when using the low temperature, fixed droplet correlations, as pointed out by Ranz and Marshal1,hut estimates based on their results would appear to he conservative. An extension of these experiments into a higher temperature and smaller droplet size range is planned with both combustible and noncombustible liquids. Acknowledgment William Hellier appreciates the support in the form of a fellowship provided by NASA. Freon was supplied through the courtesy of E. I. du Pont de Nemours & Co., Inc., Freon Products Division. Nomenclature
d do Gix
= droplet diameter, screen grid diameter, cm. = initial droplet diameter, em. = quantity defined under Equation 1, uondimen-
ko
= maas transfer coefficient, g. mass/ (sq. cm.-see.-
K
= vaporization constant, see./sq. cm. = droplet mass, initial droplet mass, g. = molecular weight of species k, g. mass/g. mole = number of species in mixture = partial pressure of diffusing vapor, total pressure,
sional atm.) wt, mo
Mk 12
PA,
rn
atm. VOL.
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of species A per unit area, measured at the interface, g. mass/(sq. cm.-sec.) = critical Reynolds number, nondimensional Re Rea, ReD = Reynolds number based on screen grid diameter, and on furnace tube diameter, both nondimensional t = time, see. = ambient air stream temperature, ’ C. T, TAi
= rate of vaporization
GREEKLETTERS Xi, ,A,, Xko
of species i and of mixture, respectively, cal./ (sec.-cm.-’ K.) = translational thermal conductivity of species k , cal./ (sec.-cm.-’ K.) = thermal conductivity
literature Cited
Bitron, M. D., Znd. Eng. Chem;;47, 23 (1955). Essenhigh, R. H., Fells, Ian, Combustion of Liquid and Solid Aerosols.” in “The Phvsical Chemistrv of Aerosols.” General Discussion of Faraday society, p. 208, ”1960.
Godsave, G. A. E., “Fourth Symposium on Combustion,” pp. 818-30, Williams & Wilkins, Baltimore, 1953. Goldsmith, M., Penner, S. S., Jet Propulsion 24, 245 (1954). Grant, H. L., Nisbet, I. C. T., J. Fluid Mech. 2, 263 (1957). Hellier, W. W., Jr., M.S. essay, Johns Hopkins University, Baltimore, Rld., 1968. Kooyman, W. J., Ph.D. dissertation, Johns Hopkins University, Baltimore, Md., 1969. Magarvey, R. H. Taylor, B. W., Rev.Sci. Znstr. 27, 944 (1956). Mason, E. A., Saxena, S. C., Phys. Fluzds 1, 361-9 (1958). Park, R. W.,Crosby, E. J., Chenz. Eng. Sci. 20, 39-45 (1965). Ranz, W. E., Marshall, W. R., Chem. Eng. Progr. 48,173 (1952). Schubauer, G. B., Spangenberg, W.G., Klebanoff, P. S., “Aerodynamic Characteristics of Damping Screens,” NACA Tech. Note 2001 (1950). Silverman, B. A., Thompson, B. J., Ward, J. H., Appl. Meteorol. 3, 792 (1964). Thompson, B. J., Parrelit, G. B., Ward, J. H., Justh, Bruce, Appl. Meteorol. 6, 343 (1966). Tsuji, H., Hama, F. R., J . Aero??.Sci. 20, 848 (1953). Walker, R. E., Westenberg, A. A., J . Chem. Phys. 29, 1139 (1958). Williams, Forman A,, “Combustion Theory,” Chap. 3, AddisonWesley, Reading, Mass., 1965. RECEIVED for review March 29, 1968 ACCEPTEDApril 7, 1969 Work supported in part by the Esso Education Foundation
IMPROVED CONDUCTIVITY SYSTEM FOR MEASUREMENT OF TURBULENT CONCENTRATION FLUCTUATIONS ROBERT S. TORREST’ A N D WILLIAM E. R A N 2 Department of Chemical Engineering, University of Minnesota, Minneapolis, Minn.
A microelectrode conductivity probe and associated electrical system suitable for concentration fluctuation measurement in turbulent shear flow of ionic solutions are described. Simplified probe design permits controlled reduction of electrode surface and ease of handling. Probe sampling volumes on the order of 5 X lo-’ cc. are readily obtained. The electrical system has a reduced noise to signal ratio of about 0.03% with the half-power frequency a t 10 kcps. System output voltages are directly proportional to the mean Concentration and variance of the fluctuations, allowing use for the measurement of high intensity fluctuations. The electrical systems employed with microelectrode conductivity probes described in the literature were best suited for low intensity fluctuation measurements in flows of uniform mean concentration.
HE experimental study of some of the statistical aspects
Tof mass transfer in turbulent flow fields has received ever-
increasing attention during the last decade. Measurements in a free turbulent smoky air jet (Rosenweig et al., 1961), a ducted jet with recirculation (Becker et al., 1967), and gridgenerated turbulence in a water tunnel (Gibson and Schwarz, 1963) are good examples of what has been done. Ideally, the sensors used should respond to fluctuating concentrations at a given point in the flow at frequencies up to 10 kcps. or more. When the sensor must be inserted into the flow, in contrast to nondisturbing-for example, opticaltechniques, the probe must be sufficiently strong without distorting the flow significantly. These practical requirements may cause the best resolution to fall short of that required accurately to resolve the highest frequency fluctuations. 1 Present address, Shell Development Co., Houston, Tex. 77001.
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FUNDAMENTALS
This paper is concerned with a microelectrode probe and the associated electrical system developed for the measurement of fluctuating point values of solution electrical conductivity in turbulent shear flows. Conductivity measurements lead directly to the mean concentration of ionic tracers and the variance of the concentration fluctuations. Results for turbulent mixing and chemical reaction obtained with the system described here have been presented (Torrest, 1967). The system, although basically similar to that used by Lawrence (1965), seems to be improved in ease of operation and signal-noise ratio. The details of this kind of electrical system suited for measurements of high “intensity”-root mean square--fluctuations in shear flows have not been described in the literature. Other techniques for concentration measurement in turbulent liquid flow include light scattering or absorption methods. However, for measurement of “point” values of concentration fluctuations, the major competitor with con-
