is applied, additional pulses result each time the sum of the externally applied field, Eo sin ut, plus the field resulting from accumulated wall charge is again sufficient to produce breakdown. Perhaps the most convincing evidence for this mechanism is the observation that after the applied voltage reaches its peak value and declines, current pulses flow in a direction opposing the applied field. This occurs because the wall charge field opposes the applied field to produce breakdown. Thus Harries and von Engel (1951) found the potential drop across their discharge space a t 5 Torr was about 700 V, even though applied voltages of up to 6 kV were used. Manley (1943) found the internal field was 28 kV/cm for a range of reactor types and electrode spacings in air a t atmospheric pressure. I will assume, as Van Drumpt suggests, that at the low powers involved in his silent electric discharge, the production of active species is the rate-determining step. This was also found to be the case at low power in the radiofrequency glow discharge (Bell, 1967; Flamm, 1973). Since conversion is low, it might be assumed that the rate of formation of active species will be proportional to time and insensitive to the extent of reaction. During each current pluse discussed above, an approximately constant unit of conversion should then occur. Since the number of pulses will increase with the applied voltage, then too should conversion. The findings of Harries and Von Engel (1957) differ somewhat from those of Kher and Kelkar (1962) and Manley (1943) in that the proportionality between voltage and the number of pulses is not exact. If such is the case for the present system, there should be a closer propor-
tionality between the number of current pulses and conversion than between applied voltage and conversion. Nomenclature d = discharge reactor gap, cm EO = peak electric field, V/cm f = frequency of applied field, sec -1 u d = drift velocity of ions, cm/sec Vb = breakdown voltage of gas, V Greek Letters v = collision frequency of ions, sec - 1 w = angular velocity of applied field, sec - I Literature Cited Bell, A. T., Sc.D. Thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1967. Cooper, W. W., Mickley, H. S., Baddour. R. F., Ind. Eng. C h e m . , Fundam. 7, 400 (1968). El-Bakkal J., Loeb, L. B., J. Appl. Phys. 33, 1567.(1962). Fite, W. L., Advan. C h e m . Ser. No. 80, 15 (1969). Flamrn, D. L., lnd. Eng. C h e m . , Fundam. 12,276 (1973). Francis, G., Proc. Phys. SOC. London, S e c t . 6 66, 137 (1955). Fuji, S., Take,mura, N., Advan. C h e m . Ser. No. 21, 334 (1959). Gross, B., 6nf.J. Appl. Phys. 1, 259 (1950). Harries, W. L., von Engel, A , , Proc. Phys. SOC., London S e c t . 6 64, 916 (1951). Joshi, S. S., Narasirnhan, V., Curr. Scl. 9, 535 (1940). Katakis, D., Bersis, D., J. Appl. Phys. 36, 1298 (1965). Kher, V. G., Kelkar, M. G., J. Sci. Ind. R e s . , S e c t . 6 21, 293 (1962). Manley, T. C., Trans. Elecfrochem. SOC. 64,83 (1943). Moser, A., Igarischev, N., 2. Elektrochem. 16, 613 (1910). Van Drurnpt, J. D., lnd. Eng. Chem., Fundam. 11, 595 (1972).
Teras A&M Uniuersity College Station, Texas 77843
Daniel L.Flamm Receiuedfor reuiew March 5 , 1973 Accepted August 30, 1973
CORRESPONDENCE
Fully Developed Turbulent Boundary-Layer Flow of a Fine Solid-Particle Gaseous Suspension
Sir: The paper by Boothroyd and Walton (1973) starts from the premise that the addition of solid particles to a gas flow results in the partial suppression of the gas turbulence and presents the results of an experimental investigation which is said to show that there is strong suppression of gas turbulence near the wall of a pipe. However, it will be shown here that the premise is incorrect, and that one factor was not taken into account in analysis of the experimental data. The authors’ Figure 1 shows curves for data on heat transfer and pressure drop: values of Nu,/Nuo for 1-, 2-, and 3-in. tubes at Reynolds number of 35,000 from Boothroyd and Haque (1970), and values of fJf0 for the same tube sizes and Re from Boothroyd (1966), for mixtures of air and 15 p weight-average (“0-40” p range) zinc particles. Comparison of a sample of those data with the data of other investigators shows that some of the Figure 1 curves are incorrect. Heat Transfer. Let us make a comparison of values of h, at a loading of 8 lb of solids per pound of air. Booth92
Ind. Eng. Chem., Fundam., Vol. 13, No. 1, 1974
royd and Haque, in an example of a calculation for the 1-in. tube, list an air flow of 0.0289 lb/sec. This enables us to calculate the viscosity apparently used in the specified Re and to estimate the corresponding temperature; the other air heat transfer properties can then be evaluated at that temperature. We can presumably assume the same properties for the other two tube sizes, and calculate ho’s on that basis, without introducing too much error. Then, a t the Re and loading noted, the curves of h,/ho indicate that the values of h, would be 6.06 for 1-in., 16.0 for 2-in., and 15.3 for 3-in. tubes. Wilkinson and Norman (1967) also ran experiments in 2-in. tubes. The mean bulk temperature was a minimum of 181°F and a maximum of 392°F for all runs with all solids and loadings (Wilkinson, 1972); taking the average of the extremes as a reasonable temperature at which to evaluate gas properties for our purpose, we can calculate ho from the specified Re. The curves (their Figure 3) indicate that using 40-p Ballotini at a loading of 8, h, is 15.5 at Re of about 20,000 and h, is 22.7 at Re of 44,900. Considering the assumptions that
had to be made for this comparison, the results of the two investigations may be said to show a rough check a t the loading selected. On the other hand, a t a loading of 8 in 0.669-in. i.d. tubes, Farbar and Morley (1957) indicate (their Figure 4 line) an h, of 45.6 for 50-p weight-average (range ca. 9-220 p ) cracking catalyst at Re of 27,000, and Farbar and Depew (1963) indicate (their Figure 5 line) an h, of 47 for 30-fi closely sized solid glass spheres at Re of 26,500. There is something considerably wrong with the data on 1-in. tubes, as indicated both by comparison with results of other investigators on larger and smaller tubes and by comparison with its own authors’ results on larger tubes. Equation 2 is incorrect. (1) The addition of solids to a gas flowing through a heat transfer apparatus will almost invariably result in a change in MTD (the mean temperature difference); the ratio of heat fluxes, with and without solids, is therefore almost invariably not the same as the ratio of h’s, since h is flux/MTD. (2) Heat flux is the product of quantities flowing, specific heat, and temperature range, not temperature p e r se as shown. Moreover, it is not clear what the authors intend by referring to wall heat flux and setting up their equation in terms of radial velocity in the pipe. The film theory of heat transfer postulates a stationary film of fluid between the pipe wall and the bulk stream, with heat transfer across the film occurring by conduction. If eq 2 is intended to propose that the film theory is wrong and that the flux depends on the physical movement of fluid to and from the wall, some proof should be provided. Pressure Drop. When solids are introduced into a flowing gas stream the resulting mixture has a greater mass flow rate and a higher density than the original solids-free gas. The authors, however, have defined friction factor for the mixture on the basis of m i x t u r e pressure drop and gas mass flow and density; this attributes the difference between gas and mixture pressure drop solely to a change in friction factor. The curves that are marked f,/fo should actually be labeled AP,/APo. The pressure drop line for 1-in. tubes indicates that 1.0 lb of solids can flow through the test apparatus with 1.0 lb of air, using only about one-third the frictional pressure drop that would be needed for 1.0 lb of air alone, or 4.0 lb of solids can flow through with 1.0 lb of air using only about two-thirds the frictional pressure drop that would be needed for 1.0 lb of air alone. The data are obviously incorrect. Farbar (1949) determined pressure drop with the same catalyst and in the same size tube that was later used by Farbar and Morley for their heat transfer investigation. At a loading of 5, the value of APJAPO is about 3.0 at Re of 14,300 and about 4.0 a t Re of 19,900. At the same loading the Boothroyd curves indicate AP,/APo of 2.5 for 2-in. tubes and 2.6 for 3-in. tubes, both at Re of 35,000. The check is not good, but a t least there is no aura of the impossible about the indicated ratios. For the usual gas-solids mixtures, where the volume of
the solid particles is negligible in comparison with the volume of the gas, the net effect on pressure drop of the increase in both mass flow and density as solids are added, provided that f, = fo, would be
At a loading of 5 , AP,/APo would be 6 on that basis. As can be seen from the examples given above, the actual ratios are lower than 6, showing that the addition of solids to the flow has decreased the original gas friction factor. The Measure of Turbulence. The Reynolds number is accepted as the measure of turbulence. In a given apparatus at a given viscosity, an increase in Re, indicating an increase in turbulence, results in an increase in ho and a decrease in fo. The addition of solids to a gas flow (above some minimum ratio, say W,/W, of 2) results, as we have already noted, in increased h and decreased f . Based on both criteria the addition of solids has increased turbulence. The Effect of a Tracer Gas. The authors injected a C02-He mixture through a porous graphite collar into air or air-zinc mixtures flowing in a 3-in. tube. Samples were obtained downstream from the injection collar and tracer concentrations were determined. What was apparently overlooked in interpretation of the data is that each particle in these flowing gas-solids mixtures is in suspension in the gas and therefore is acted on by any imposed radial flows. A stream from any tiny pore in the graphite will give up part of its energy each time it impinges on a solid particle. If the concentration of particles is high enough, the tracer streams will lose their radial velocity completely. The authors’ Figure 4 suggests that W s / W gof about 5 for these zinc particles provided a high enough concentration of particles to reduce tracer radial velocity to substantially zero as soon as it came through the collar, since higher loadings with greater particle concentrations had no additional effect. The decreased tracer radial dispersion when solids were added was interpreted as evidence of decreased turbulence, but decreased radial dispersion would have to be expected as tracer inlet radial velocity was reduced or eliminated by the interaction noted. Literature Cited Boothroyd, R. G., Trans. lnst. Chern. Eng. 44,306 (1966). Boothroyd, R. G., Haque, H.,J. Mech. Eng. Sci. 12, 191 (1970). Boothroyd, R. G., Walton, P. J.. Ind. Eng. Chern., Fundarn. 12, 75 (1973). Farbar, L., Ind. Eng. Chem. 41,1184 (1949). Farbar, L., Depew, C. A , , Ind. Eng. Chern., Fundarn. 2,130 (1963). Farbar, L., Morley, M. W., Ind. Eng. Chem. 49,1143 (1957). Wilkinson, G. T., personal communication, 1972. Wilkinson, G. T., Norman, J. R., Trans. Inst. Chern. Eng. 45, T314 (1967),
253 East 202nd Street Bronx, N . Y.
W. J. Danziger
Received for reuieu; August 20, 1973 Accepted October 31, 1973
Fully Developed Turbulent Boundary-Layer Flow of a fine Solid-Particle Gaseous Suspension
Sir: It so happens that I can refute completely all of Danziger’s criticisms. Apart from some statements (e.g., his eq 1) which are quite grossly inaccurate, I consider that many of his general views are definitely outdated in the light of modern developments. Such matters can be
answered effectively by reference to other literature in the field. I feel sure that readers may assess much of our controversy for themselves without my further comment. Here I concentrate on the less obvious issues which have been raised. Ind. Eng.
Chern., Fundarn., Vol. 13, No. 1, 1974 93
