Factors affecting flame propagation through dust clouds

Factors affecting flame propagation through dust clouds

FLAME PROPAGATION IN EXPLOSIVE GAS MIXTURES 185 8. DRYDEN, HUGH L.: A Review of the Statistical lent Flow. Princeton Univ. Press (Princeton), 1941...

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8. DRYDEN, HUGH L.: A Review of the Statistical

lent Flow. Princeton Univ. Press (Princeton), 1941. 7. TAYLOR, G. I.: Statistical Theory of Turbulence, I-IV. Proc. Roy. Soc. London, 151, ser. A, No. 873, pp. 421-478.

Theory of Turbulence. Quarterly of App. Math., 1, No. 1, 7-42 (Apr. 1943). 9. PRANDTL, L.: Fifth International Congress for Applied Mechanics, pp. 345 (1938).





The problem of utilizing pulverized fuel is probably as old as the idea of the Diesel engine. However, the first theoretical approach to an understanding of this type of combustion is the work of Nusselt (1). He realized the importance of the diffusion of oxygen to the surface of individual particles and the contributing, effect of radiation and predicted the formation of an inner cone in stationary dust flames, analogous to that of the Bunsen burner. An early attempt to study stationary coal dust flames experimentally was made by Fuhrmann an(t Koettgen (2). These authors could not produce stationary flames except when methane was continuously added to the mixture. Research on dust explosions, particularly by the Safety in Mines Research Board in England and by the Bureau of Mines in the United States (3), has definitely established the fact that a great variety of materials dispersed in dust clouds are capable of explosive reactions without addition of combustible gases. This, of course, does not mean that part of the reactants are not volatilized preceding or during the oxidation process. Rather, it appears that, although heterogeneous reactions form a necessary step, the self-accelerating reaction, be it the chain-reaction type or the thermal 1Work completed on manuscript August 1948. 2 Physical Chemist, Experimental Coal Mine and Dust Explosions Research Section, Explosives Branch, Bureau of Mines, Pittsburgh, Pa. 3Physical Chemist, Indian Government Scholar, at present working in the Experimental Coal Mine and Dust Explosions Research Sections, Explosives Branch, Bureau of Mines, Pittsburgh, Pa. 4 Physical Chemist, Indian Government Scholar, formerly with Explosives Branch, Bureau of Mines, Pittsburgh, Pa. Present address: National Fuel Research Institute, New Delhi, India.

explosion type, is in general an exothermic homogeneous gas reaction. With this in view, research on the mechanism of dust flames will naturally rest on two foundations: (a) Recent progress in our knowledge of stability and structure of burner flames due to the work of Lewis and yon Elbe (4) ; and (b) knowledge of radiation effects in the combustion of pulverized materials which is largely due to the contributions of Schack (5), Wohlenberg (6), and Hottel (7). THEORETICAL CONSIDERATIONS

Mallard and Le Chatelier's picture of the combustion wave (8) offers a promising working hypothesis for estimating the importance of the different factors involved in the propagation of dust flames, if it is amended by an additional term to account for the effects of radiation.

Su = u ( T b -- T , ) / b --t- bwo-aF(T~ -- T ~4) / p e r . (1)

(cp p + cd w) (T, - T~) Here, S~ is the burning velocity, ~ the coefficient of heat conductivity; Tu, Tb, T, the temperatures of the unburned and burned masses, and of ignition; ~ the emissivity of the particle surfaces; a correction factor, larger than 1, which accounts for the radiation of glowing combustion products (solids and gas); F a geometrical view factor; b the thickness of the burning zone; cp the specific heat of the gas, p its density; cd the specific heat of the dust, pd its density affd w its concentration; and r the average particle radius. In developing and applying this equation, one should be aware of its approximate character. In fact, not more can be claimed than a dimensionally correct correlation of the factors affecting



dust-flamepropagation. Also the interdependence of different parameters should be observed. For instance, factor b, for which the same value is assumed in the conductivity and the radiation terms for the sake of simplicity, certainly depends on r, w and F, since these factors affect the reaction rate. It is seen from equation t that, as b increases, the contribution of conductivity to heat transfer through the flame front decreases while that of radiation increases. By introducing the burning time of a single. particle, r, S~r can be substituted for b, where (2)

S, = S , ( p , / m )

is the velocity of the burned mass relative to the flame front and p,/m, the ratio of the densities of the unburned and burned gases. Equation 1 then may be written S~ -- Kpb


In developing a technique of producing uniformly dispersed dust clouds, constant dust concentrations had to be maintained during periods of time long enough to permit observations on stationary dust flames. For this purpose, vertically rising streams of dust are most easily handled.



Tb -- T~

rp, T ~ -


.w.~Fp,,(~- T'.)' (3) pd Pb r(cvP + Cd W)

where K, the thermal dittusivity, equals ~,/(cpo + c~w). We shall disregard the possibility that a slow surface reaction is rate determining and consider only the case that oxygen diffusion governs the burning of individual particles. Thus, an upper limit for the burning velocity is obtained if r is expressed in terms of the diffusion rate of oxygen: r -- p4r 2 R f u






Tb -- Ti r w k F a a ( T~ - T 4 ) ' Ti -- T~ - m D p ( % p + c~ w )

Ironsafety~aNe ~ ~ ~ Cylindricalbrass] Gasiot 2fi~


Magneticod c ]




~_~ ~k~ater'a~ r ' ~ ce


Here D is the diffusion coefficient at temperature Tu; R the gas constant; T~ the average ambient gas temperature around a particle as it passes through the reaction zone; p the average partial pressure of oxygen; M the oxygen equivalent of the fuel, expressed in grams of fuel per tool. of oxygen. Equation 3 thus assumes the form 2 KDp S~ - r~

in a dust flame is calculated to be of the order of magnitude of 2.5 cm. This value is 100 to 1,000 times greater than values that have been estimated for flames of premixed gases (9, 10). Evidently, the comparatively great thickness of the burning zone is a characteristic feature of laminar dust flames.


where k = pep~RT,,a/2/2Mp;T~ 112. To illustrate the implications of equation 5 and for the following discussion it is useful to estimate from equation 4 the burning time of a representative dust particle. For instance, for a 25-microndiameter aluminum particle, a time of about 0.01 second is obtained. Assuming a value of Sb of the order of 250 cm./sec. (from experimental data below for S,,), the thickness of the burning zone

Irondiaphrag~n '/~~-'~ A.c.magnet-'/

Pc. 423


FIG. I. Sketch of dust disperser. The procedure consisted in blowing gas jets onto a layer of the pulverized material which is continuously agitated by magnetically vibrating the iron diaphragm which forms the bottom of the container (fig. 1). The particles are cat:ried away by the gas current into a vertical pipe whose upper end is connected to a vertical glass tube which serves as the burner tube. The dust receptacle is a brass cylinder 6 inches in diameter and 4 inches high. The pipe extends into the container to a distance of 89inch from the diaphragm. Two gas jet orifices, on opposite sides, entering the receptacle 1 inch above the bottom are directed tangentially and turned downward at an angle of 45 ~. To obtain variations of the dust concentration at constant rate of flow, a valve-controlled by-pass is




provided between the top of the container and the outlet of the pipe so that the gas flm~, entraining the (lust, can be diminished while the rising cloud is diluted with practically dust-free gas. The (lust capacity of the receptahle is 2(X) grams which is sufficient, with a consumption of 6 grams per minute, I- run tests over a period of 10 minutes without refueling. A safety valve is provided to prevent flash-back. This can be actuated automatically by a melting fuse wire in the circuit of a magnetic coil. As ignition source an aluminum fuse renewal link is used. To insure laminar flow at the burner port, a length of 3 feet appeared approl)riate for the 1-inch glass tubes. It should be mentioned that the effective tube diameter in (lust streams is reduced because of the parabolic flow pattern, only those particles being lifted whose sedimentation velocity is smaller lhan the gas velocity. This correction, in our exlwriments, was less than 2 percent. This effect gives rise to a concentration gradient at the wall so thal heavier particles drop out, the amount increasing with the tube length. Therefore, the (lust concentrations were measured near the top of the burlit.r tubes. This was done by weighing filtered samples from a constant volume of (lustladen gas, aspirated from the emerging cloud. The accuracy of this methud was found to check well with the loss in weight of the receptacle during the period of sampling.


(;.kS M I X T U R E S

less than 6-micron (liameter, were separated from 325 mesh atomized aluminum hv elutriation in a Roller analyzer in which the conventional recepFlash back

stationary flame

Effect of concentration With the described apparatus, stationary flames of a wtriety of dusts dispersed in air or oxygen-rich nitrogen mixtures have been studied under laminar flow conditions. These flames (fig. 2) resemble Bunsen-burner flames of premixed gases in that they exhibit a well-defined inner cone and the phenumena of blmv-off and flash-back. The burning velocities were computed, on the basis of (;ouy's equation, from cone-area and flowrate measurements. The results in table 1 were obtained with I-indl burner tubes. Hence, it is concluded that in the concentration range below the stoichiometric concentration 315 reg./liter the burning velocity increases with increasing concentralitm. Since, within this range, T~ increases with w, the experimental finding is in qualilaiive agreement with equation .5.

Fffccl t!f parlicle si~e To obtain information on the effect of particle size on the burning velocity', the fines, equal to or

Before blow-off


Fie.. 2. D e x t r i n d u s t flames. TABLE 1 I


Particle ~, Concen-i size, tration, i Gas microns i mg./liter i



Ids :i Burning Ynno ~ velocity, " cm./sec.

--Atomized aluminum

: 6 to 40 i I I i


120 i Air * 1420 160 do. i 1 2 8 0 190 ,! do. 1430

0 to 4 0 I 210



19.2 22.0 23.8 25.0

tacle was replaced by the (lust disperser described above (fig. 1). Because the time requirement for collecting sufficient quantities is very high only pre[iminary experiments could be run on stationary flames. From these observations it appeared that the tendency to flash-back of these small-



particle-size (lust flames is even stronger than with those of 323-mesh in the same concentration range. Experiments on flame propagation through quiescent dust clouds can be carried out with less consumption of pulverized material. Therefore, the velocities of flames moving downward through vertical glass tubes, 1 inch in diameter and 4 feet long closed at the bottom, were measured by means of a stop watch. In this series, tests were discarded when oscillatory movements developed as the flames traveled down the tube, only the first

to obtain such flames when the diameter was equal to or smaller than 89inch. Considering the high values of b, undoubtedly characteristic of dust flames, one might expect that the burning velocity should continuously fall off from the center of the flame toward the rim layers; the latter, accordingly, would be subject to what may be called radiation quenching. Because of this effect, Lewis and yon Elbe's (5,~11) law of the constancy of the critical velocity gradient for flash-back in laminar gas flames probably does not hold for high temperature dust flames.

Fro. 3. Oscillatory flame propagating through quiescent dextrin dust dispersed in 70 percent 02. 50 cm. in general being traversed with uniform velocity. As an example of the effect of vibratory movement in a dextrin flame burning in 70 percent oxygen, figure 3 shows the finite amplitudes in which the flame velocity has increased to about 50 m./sec. Results obtained with atomized aluminum at uniform velocity are Iisted in table 2. Assuming that the observed flame velocities are proportional to the burning velocities, the results indicate.an increase in burning velocity with decreasing particle size (see additional data below for turbulent flames). Equation 5 predicts a minimum in the burning velocity S~ as a function of particle radius r. This expectation is a consequence of the radiation term, but we have been unable to obtain sufficient data to check it. A complicating factor in the effect of particle size should be mentioned here. This is the occurrence of protective surface coatings with materials like aluminum. From chemical analysis of atomized aluminum a content of oxide as high as 10 to 12 percent has to be assumed. Provided that the thickness of the alumina layer is the same for all particle sizes, it follows that the oxide content of fines would be considerably higher.

Effect of radiation No direct experiment on this factor has been made so far. Indirect evidence can be found in the difficulty of producing stationary dust flames on tubes of small diameter. In fact, with none of the luminous flames studied has it been possible


Atomized aluminum Particle size range, microns

Concentration, reg./liter

Flame velocity, cm./sec.


100 200

35 45

80% 0-6 and t 20/% 6-40 j

140 250

100 60

Effect of turbulence Since the molecular transport coefficients of heat and matter are factors in the numerator of equation (5), turbulent conditions should greatly increase the rate of flame propagation through dust clouds. More specifically, turbulence might increase K across the combustion wave as well as D around individual particles. Large-scale turbulence, obviously, can contribute little apart f r o m indentations in the flame front which might lead to both deficiencies and excess of oxygen by mixing combustion products with unburned reactants, and vice versa. If the scale of turbulence becomes commensurate with the thickness of the burning zone or less, the more effectively should eddy fluctuations assist in mixing vaporized or gasified fuel components (aluminum vapor, CO) and the available oxygen. When the values of K and D reach that of the turbulence exchange coefficient, ,, the behavior of the dust flame, which was a true diffusion flame under laminar flow conditions, will

FLAME PROPAGATION IN EXPLOSIVE GAS MIXTURES approximate that of a turbulent flame of premixed gases (12). This prediction is supported by experiments on closed-end (bottom) ignition of quiescent atomized aluminum dust clouds in 4-foot long, 1-inch wide glass tubes. Flame velocities of 100 to 150 m./sec. were recorded photographically on a rotating film. If one takes the observed velocity as Sb and estimates a ratio of 10 for pu/m, burning velocities S~ of the order of 10 to 15 m./sec, are derived from the continuity equation 2.


Flame velocities of the order of only 5 to 10 m./sec. are found, probably because small-scale turbulence is less developed. However, a striking increase of the flame velocity with increasing energy of ignition is observed, probably because of the persistence in the flame, of turbulence produced by the ignition source. Even more pronounced turbulence effects are observed on applying the MacDonald-Evans (13) technique to the 2-inch tubes. After a grid is inserted close to the ignition point in the 2-inch tube, flame velocities of the

Fro. 4. (top) Closed end ignition flame of atomized aluminum, 0-40 microns. FIG. 5. (bottom) Closed end ignition flame of atomized aluminum; 80 percent 0-6 microns, 20 percent 6-40 microns. Under the conditions of the experiment the unburned mass ahead of the flame is moving with considerable absolute velocity, Sb -- S~, i.e., 90 to 135 m./sec. Provided that it is permissible to apply concepts which apply strictly to stationary flow, this corresponds to Reynolds numbers of the order of 100,0130. Hence the conclusion is drawn that owing to turbulence burning velocities about 50 times greater than under laminar flow conditions can be attained in dust flames. Figure 4 shows a flame of 130 mg./liter 325-mesh atomized aluminum reaching a maximum velocity of 220 m./sec. (average 100 m./sec.). Figure 5 shows a dust flame produced in a mixture of 80-percent fines and 20-percent 325-mesh atomized aluminum of 140 mg./liter reaching nearly twice the average velocity of the coarser mixture, and 295 m./sec, maximum velocity. These observations are in line with the results on the effect of particle size given above for laminar flames (table 2). Experiments conducted with 2-inch-diameter tubes throw further light on the role of turbulence.

order of 100 m./sec, result with the smallest ignition energy that was used for the 1-inch tube experiments. SUMMARY The Mallard-Le Chatelier picture of the combustion wave is amended by adding a term for radiant heat transfer. On introducing the rate of oxygen diffusion toward individual particles an expression for the burning velocity in dust clouds is obtained, representing its dependence on thermal conductivity, burning and ignition temperatures, radiation characteristics of the dust cloud, dust concentration and particle size. This serves as working hypothesis in conducting experiments on the effect of those factors upon stationary dust flames and flames traveling through quiescent dust clouds. Results obtained with atomized aluminum are: 1. On the lean side of the stoichiometric ratio the burning velocity increases with increasing concentration.



5. SC:~ACK,A. : Industrial Heat Transfer, John Wiley Company, 1933. 6. WOHLENBERG, W. F., AND MORROW, D. G.: Trans. Amer. Soc. Mech. Engrs., 47, 127 (1925). 7. HOSTEL, H. C.: In Heat Transmission, by W. H. McAdams, McGraw-Hill, 1942.

2. The burning velocity increases with decreasing particle size in the range studied. 3. The failure to produce stationary dust flames with burner tubes smaller than 89 diameter indicates an effect of "radiation quenching" close to the rim in high temperature dust flames. 4. A striking increase in the flame velocity of closed end ignited dust flames is attributed to turbulence. The experimental results are in qualitative agreement with theoretical expectations.

HASLA~, R. T., AND HOTTEL, H. C.: Trans. Amer.

Soc. Mech. Engrs., FSP, 50, 9 (1928). 8. MALLARD, E., AND LE CHATELIER, H. L.: Ann. des mines, 4, 274 (1883). 9. LEWIS, B., AND VON ELBE, G.: Combustion, Flames and Explosions of Gases, Cambridge University Press, 1938, p. 219. 10. ZEI~OVlTCH, Y., AND SE~XNOV, N.: J. Expt. & Theoret. Phys., U.S.S.R., 10, 1116 (1940). 11. vow" ELBE, G., AND MENTSER, M.: J. Chem. Phys., 13, 89 (1945). 12. DAMKOEHLER,G.: Zeitschrft. f. Elektrochem., 46, 601 (1940). 13. EVANS, M. W., SCHEER,M. D., ANDL. J. SCHOEN: Tech. Rep. No. 7, Project Squid, Bur. Aeronaut. and Office of Naval Research. (1947).


1. NUSSELT, W.: Zeitschrft. Verein Deutscher Ingenieure, pp. 124 and 914 (1924). 2. FUHRMANN,E. A., ANDKOETTGEN,H.: Zeitschrft. f. physikal Chem., A169, 388, 1934. 3. HARTMANN,I.: Ind. & Eng. Chem., 40, 752 (1948). 4. LEwis, B., ANDYONELBE, G.: J. Chem. Phys., 11, 75 (1943).



As part of an investigation being conducted at the NACA Cleveland laboratory to determine the effect of structure on the flame speed of a fuel, a study of the relation of unsaturation and of chain length to the uniform flame movement in a quiescent fuel-air mixture for 16 straight-chain hydrocarbons up to six carbon atoms in length and for four cyclic hydrocarbons has been made in a horizontal glass tube with an internal diameter of 2.5 centimeters. Coward and Hartwell (1) have shown that the fundamental flame speed of a fuel, or the burning rate at any point normal to the surface of the flame, is constant over the flame surface and is dependent only upon the fuel-air composition of the mixture. Several investigators (2-5) have shown that in a tube closed at one end and ignited from the open end, the flame travels through the combustible mixture with a uniform velocity over a part of the 1 Flight Propulsion Research Laboratory, N.A.C.A.

tube length. The magnitude of this uniform velocity for any fuel at a constant temperature and pressure is dependent upon (a) the fuel-air ratio of the mixture, (b) the diameter of the tube, and (c) the direction of propagation, that is, whether upward, downward, or horizontal. The uniform flame velocity, that is, the linear rate of flame travel through the tube, is equal to the product of the fundamental flame speed times the area of the flame surface divided by the crosssectional area of the tube. Thus, by measurements of the uniform flame velocity, the fundamental flame speeds of different combustible mixtures can be relatively compared. All results reported herein are presented as the variation of the uniform flame velocity with mixture composition and are given in graphical form. Acknowledgment is made to the American Petroleum Institute Research Project 45 at the Ohio State University Research Foundation for contributing four of the hydrocarbons used in this study.