Table I. Performance of the Porcelain Probesa
Run no.
Concentration of carbon dioxide in mole/l. in the sample from Film probe I Film probe II Drop probe I Drop probe II (1/8 in. thick) ( l / ~ 2 in. thick) ( 1 in. long) ( l / 4 in. long)
1 0,00836 0,00866 0.0110 0,01062 2 0.0079 0.00861 0.0100 0,01012 3 0.00834 0.00759 0.01166 0.01061 4 0,00765 0,00851 0.00963 0.01034 5 0.00847 0.00945 6 0,00909 0.0110 7 0,00825 0.01078 Alean 0.00829 0.00834 0.01050 0.01042 a W L = 293 lb!hr; TVC = 261 lb/hr; P = j7.8 psia; T = 21OC; concentration of carbon dioxide in the gaseous mixture = 10% by volume.
variation \vas achieved by using different thicknesses of porous probe and different probe sizes. Result,s of tests carried out, in aniiular upward f l o of ~ water aiid a 907' ~ i r - 1 0 7carbon ~ dioxide gas niisture are given in Table I. The probes \yere located 18 in. from the gas-water inlet miser. The concentration values obt'aiiied show 110 significant effect of the extent' of droplet probe surface, or of sampling rate, for either the droplet or film probe. Hence, it is likely that the concentratioii reported is reasonably close to true mean droplet or film concentrat8ioiia t this point in the apparat'us. If the liquid sampled is very close to saturat'ion, t'lieii i t may be possible that gas bubbles would be liberated in the pores of tlie porous probe. Unless the volume of gas liberated completely filled a pore, this factor xvould not' alter the efficiency of the probe as a gas-liquid separating device, although it might affect the sampling rate. However, t'wo consideratioils should be borne in mind when sampling nearly saturated solutions. First, the pressure drop across the probe can be lowered as much as desired in order to prevent flashing in tlie porous probe, although t8hesampling rate will decrease in direct proportion. Secondly, the fraction of the ten1 pressure represented by the bubble pressure of the probe gives a direct, guide as to the degree of saturation that can be t,olerated without gas flashing in the probe. Some control is possible, therefore, by selection of a porous material for t,he probe suitable for the system in which concentrations are to be measured. I
One further conclusion from the results is that the mean concentrations of solute in the film and drops were not the same, although because of interchange, these values are not as different as might be expected. Summary
The use of a liquid sampling probe of the type described here appears to make possible for the first time the determination of solute concentrations of droplets, or of the liquid phase, in a gas-liquid dispersion in a dynamic situation. The method is quite flexible, and although sampling rates are generally low, they are adequate for modern analytical methods. The probes have been used successfully in studying the absorption of carbon dioxide into water flowing in the form of a mist and of a thin film in an annular flow absorber (Jagota, 1970), Nomenclature
C1, Cz
=
C* cl, cs
= =
@La)*
=
(kLa)T =
AP &L
r
V
TVG TVL
= =
= = = =
true solute concentration in liquid a t sampling points 1 and 2, respectively, moles/l. equilibrium solubility of solute in liquid, moles/l. measured solute concentration in liquid a t sampling points 1 and 2, respectively, moles/l. apparent mass transfer coefficient based on measured concentrations, l / h r true mass transfer coefficient based on true concentrations, l/hr bubble pressure, or displacement pressure, dyn/cm2 volumetric flow rate, l./hr pore radius, cm volume of apparatus between sampling points, 1. gas flow rate, lb/hr liquid flow rate, lb/hr
GREEKLETTERS U
8
= =
surface tension, dyn/cm liquid wetting angle
Literature Cited
ilnderson, J. D., Bollinger, R. E., Lamb, 1).E., A.I.Ch.E. J . 10, 640 (1964). Jagota, A. K., Ph.D. Thesis, Department of Chemical Engineering, University of Waterloo, Waterloo, Ont., 1970. RECEIVED for review April 3, 1972 ACCEPTED November 3, 1972 This work has been supported by Atomic Energy of Canada Limited, and by the Sational Research Council. A. K. J. also wishes to acknowledge gratefully the assistance given by an International Nickel Company Research Fellowship.
CORRESPONDENCE
Streaming Potential Fluctuation around a Cylinder in Water SIR: The purpose of this correspondence is to modify our earlier comments (Alujumdar and Douglas, 1971a) 011 the fiiidiiigs of Liu, et al. (1970). Specifically, we had disputed the sigiiificant effect of turbulence on the Strouhal number for cylinders in cross-flow of water. These comments were based on our o ~ v nmeasurements in a wind tunnel which showed 110 influence of the free stream turbulence level or scale on the Strouhal number for cylinders (Alujumdar and Douglas, 140 Ind. Eng. Chem. Fundam., Vol. 12, No. 1, 1973
1971b). Concurring observations have been made by Surry (1969) aiid Petty (1970) among others. Very recent experimental studies a t Stanford on the Strouhal number for cylinders in cross-flow of a liquid have partially nullified our earlier comments and lent support t o the data of Liu, et al. (1970), but not necessarily to their hypothesis that "when the scale of the free stream turbulence is larger than the diameter of the cylinder there is a lowering
of the Strouhal number." 11orrom- and Kline (1971) obtained the following correlation for the Strouhal number, St, for circular cylinders in flow of water S t = 0.187
- 4.15/Re
(50 < R e
< 150)
which is i-97, below Rosliko's correlation measured in air S t = 0.212
- 4.5/Re
(50 < Re
< 150)
where both S t and the Reynolds number, Re, are based on the cylinder diameter (Roshko, 1953). Klemp and Xcrivos (1971) made a flow visualization study of vortex shedding from circular cylinders using air bubbles in oil. Morrow and Kline have noted t h a t t,here is better agreement betLveen correlations for water and oil Ohan for either liquid with the air correlations of Roshko (1953) or the more recent one of Tritton (1959). Thus, there is a yet unclear distinction between the Strouhal number in liquids and that in air. LTnfortunat'ely, these studies were not being extended t o higher Reynolds numbers t'o check if the asymptotic value of S t = 0.21 for R e > 500 is the same for both air aiid liquids. The data of Liu, et al. (1970), indicate a lower S t in n.ater flow for R e = 7000. To the authors' knowledge there has not been tematic study of the influence of stream turbulence 011 the Strouhal number of blunt bodies in liquid flow.
The authors wish t o apologize for any inadvertent inconvenience our earlier comments may have caused the readers. Literature Cited
Klemp, J., Acrivos, A,, Department of Chemical Engineering, Stanford Cniversity, Stanford, Calif., unpublished data quoted by T. B. Morrow and S. J. Kline, 1971. Liu, H., Binder, G., Cermak, J. E., ISD. ENG.CHEV.,FUND YM. 9, 211 (1970). LIorrow. T. B.. Kline. S. J.. Iteoort 3ID-2.5. Thermosciences Division, Alkchanical Engineering Ilepaitment, Stanford University, Stanford, Calif., 1971. lIujumdar, A-S., Ilouglas, W. J. 31.,INU. ESG.C H r x . , Fcsu (M. 10, 323 (1911a). Xujumdar, A. S., Douglas, W. J. AI., Phys. Fluids, 13, 1233 t1971b).
Petty, I). G., paper presented at 17th Euromech Conference. . .. . .. Cambridge University, England, 1970. Roshko, A., .\IACA Tech. S o t e 2913 (19.5'3). Surrv, D., Ph.1[I.The&, University of To ronto. 1960. Tritton, D. J., J . FlzizcZJlech., 6 , 4"(1959).
Dsp ar t m e nt oj' Chemical Engineering JlcGill University Jlontreal, Quebec, Canada
A . S.AUupmdar*l TI'. J . -11. Douglas
Correspondence should be sent to the author at the Pulp and Paper Research Institute of Canada, Pointe Claire, Quebec, Canada.
A Study of Steam Injection into Wet Scrubbers SIR:In a recent article by Lancaster and Strauss (1971), experimental work has been reported on the mechanism of particle collection in condensation scrubbers. X felv quest'ioiis arise regarding the analysis of their results. Lancaster and Strauss proposed t h a t the scrubber performance is given b y Q
=
-0.2
0.3,
[za1 -_
-1
where Q is the steam injection rate, Ib/lb of air, 1 - 7 = penetration with steam injection, and 1 - qo = penetration wit'hout' steam injection. This relabionship would mean that at a steam injection rate of 0.2 lb/lb of air the penetration kvould be zero, or the collection efficiency would be loo%, which seems unrealistic. They furt'lier stated that the scrubber performance depends upon the quantity of steam injected rathey than the quantity of steam condensed. The values for the quantity of steam condensed have not been reported. The example they have cited to justify this statement is also not true for a n actual situation, since it does not take into account the condensation due to heat losses from the unit. In a pipeline scrubber operating a t constant gas and steam flow rates, the steam condensation rate would primarily depend upoil two factors : (a) thermodynamic conditions of the incoming gas stream such as temperature, pressure, and humiditj-, aiid (11) heat-transfer characteristics of the pipeline (for heat losses) such as diameter, wall thickness, thermal conductivity, and outside temperature. Exlierimelits on similar lilies in our laboratory have slioivii that for a 1)articular pipeliue condensation scrubber operating at n fixed gas flon- rate the amouiit of steam condensed is
3
Figure 1. Scrubber performance related to the steam injection rate in a pipeline scrubber
proportioiial to the amount of steani injected (in the range of our interest). Theoretically, scrubber performance should relate to the amouiit of steam condensed on the particles, which would be a certain fraction of the total steam condensed. Since in this case the quantity of steam injected happens to be proportional to the quantity of steam condensed, fortuitously the scrubber perforniaiice is also related to the quantity of steam injected. Figure 1 i-: a plot between the steam injection rate erpressed Ind. Eng. Chem. Fundam., Vol. 12, No. 1 , 1973
141
