Dust Explosions in the Process Industries Second Edition phần 6 doc

Propagation of flames in dust clouds 32 1 Ti is the ignition temperature of the dust cloud L is the heat losses, by radiation and conduction By equating the two sides and rearranging, one obtains the expression for the minimum explosible concentration C,: (4.69) For dust concentrations above the stoichiometric concentration the heat production is constant and equal to Q x C,, whereas the heat consumption increases with the dust concentration. In this case the condition for self-sustained flame propagation will be: Cs X Q 2 L + (Ti - To)(C x cd + dg x c,) By rearranging, Jaeckel’s theoretical upper explosible limit becomes equal to: (4.70) (4.71) Jaeckel considered a constant volume explosion. In a typical real case, a dust explosion is probably neither a pure constant pressure nor a pure constant volume process, since pressure will gradually build up in the unburnt cloud, although the flame may not be fully confined in volume. As can be seen from Equations (4.69) and (4.71), a substitution of c, by cp increases CI and decreases C,. The loss L is difficult to estimate, and Jaeckel suggested, as a first approximation, that the loss factor L be neglected. If this is done, and c, is replaced by cp, Equations (4.69) and (4.71) can be written: (4.72) (4.73) If the left-hand sides of the Equations (4.68) and (4.70), representing the heat production, are denoted Hp, it is seen that for 0 < C < C,, Hp is a linear function of C, and for C > C, it is constant and independent of dust concentration. If the ignition temperature is considered to be independent of dust concentration and the loss L is neglected, and the right-hand sides of the equations (4.68) and (4.70) representing the heat consumption, are denoted H,, H, becomes a linear function of the dust concentration. According to Jaeckel’s simple model, the condition of self-sustained flame propagation is: Hp 3 H, (4.74) Zehr (1957) suggested that Jaeckel’s theory be modified by replacing the assumption of an ignition temperature of finite value by the assumption that dust flames of concentra- tions near the minimum explosible limit have a temperature of loo0 K above ambient. Zehr further assumed that the combustion is adiabatic and runs completely to products of 322 Dust Explosions in the Process Industries the highest degree of oxidation, and that the dust particles are so small that the dust cloud can be treated as a premixed gas. The resulting equations for the minimum explosible concentration in air are: 1000 M 107 m + 2.966[Qm - CAZ] CI = wm31 for constant pressure, and 1OOOM 107 m + 4.O24[Qm - CAU] c, = wm31 (4.75) (4.76) for constant volume. Here M is the mole weight of the dust and m the number of moles of O2 required for complete oxidation of 1 mole of dust. Q, is the molar heat of combustion of the dust, CAI the enthalpy increase of the combustion products and CAU the energy increase of the combustion products. Schonewald (1971) derived a simplified empirical version of Equation (4.75) that also applies to dusts containing a mass fraction (I - a) of inert substance, a being the mass fraction of combustible dust: C,/a c; = 1 - 2.966(1 - a)c,CI/a (4.77) where the minimum explosible dust concentration without inert dust is C, = - 1.032 + 1.207 X lO6/Q0, Qo being the heat of combustion per unit mass (in J/g), as determined in a bomb calorimeter. As can be seen from Freytag (1965), Equations (4.75) and (4.76) were used in F. R. Germany for estimating minimum explosible dust concentrations, but in more recent years this method has been replaced by experimental determination. Table 4.11 gives examples of minimum explosible dust concentrations calculated from Equations (4.75) and (4.76), as well as some experimental results for comparison. The calculated and experimental results for the organic dusts polyethylene, phenol resin and starch are in good agreement. This would be expected from the assumptions made in Zehr’s theory. However, the result for graphite clearly demonstrates that Zehr’s assump- tion of complete combustion of any fuel as long as oxygen is available, is inadequate for other types of fuel. The results for bituminous coal and the metals also reflect this deficiency. Buksovicz and Wolanski (1983) postulated that at the minimum explosible concentration, flames of organic dusts have the same temperature as lower limit flames of premixed hydrocarbon gadair. They then proposed the following simple semi-empirical correlation between the heat of combustion (calorific value) Q [KJ/kg] of the dust, and the minimum explosible concentration C, [g/m3] in air at normal pressure and temperature: CI = 1.55 x lo7 x Q-’.21 (4.78) The assumptions implied confine the applicability of this equation to the same dusts to which Zehr’s Equations (4.75) and (4.76) apply. For starch, Equation (4.78) gives Cl = 114 g/m3, which is somewhat higher than the value of 70 g/m3 found experimentally by Proust and Veyssiere (1988), but close to that calculated by Zehr for constant pressure. For polyethylene, Equation (4.78) gives 36 g/m3, in close agreement with both exper- iments and Zehr’s calculations. Propagation of flames in dust clouds 323 Table 4.11 data published by Freytag (1 965). Comparison with experimental data Minimum explosible dust concentrations calculated by the theory of Zehr (1957). Most Dust type Phenol resin Maize starch explosible dust explosible dust concentration Lunn (1988) also investigated this group of materials and obtained further support for the hypothesis that the minimum explosible concentration of organic dusts that burn more or less completely in the propagating flame, is primarily a function of the heat of combustion of the dust. Shevchuk et af. (1979), being primarily concerned with metal dusts, advocated the view that a discrete approach, considering the behaviour and interaction of individual particles, is necessary for producing an adequate theory for the minimum explosible dust concentra- tion. They analysed the distribution of a heat wave in a dilute suspension of monosized solid fuel particles in a gas, assuming no relative movement between particles and gas, no radiative heat transfer, and that the rate of heat production qp during combustion of a single particle of mass mp was constant during the entire burning lifetime fb of the particle, and equal to qp = QmP/tp, where Q is the heat of combustion of the particle material. The resulting equation for the minimum explosible dust concentration, assuming that the 324 Dust Explosions in the Process Industries Powder type Aluminium Magnesium rmum Iron Mawanew average flame temperature equals the ignition temperature Ti of the dust cloud as determined in a heated-wall furnace, was: TI Eqn. (4.72) Eqn. (4.79) [Kl [g/m3] [glm3] 920 25 51 890 29 62 600 21 44 590 52 107 730 62 129 (4.79) Here TO is the ambient temperature, cg and cd the heat capacities of gas and dust material, pg the gas density and F a special particle distribution factor resulting from this particular analysis, and which causes Equation (4.79) to differ from Jaeckel’s Equation (4.72). Using Ti data from Jacobson et al. (1964), Shevchuk et al. compared Equations (4.72) and (4.79) as shown in Table 4.12. Reliable experimental data for metal dusts are scarce. However, Schlapfer (1951) found a value of 90 g/m3 for fine aluminium flakes, which indicates that both equations underestimate the minimum explosible concentration considerably, Equation (4.72) by a factor of nearly four and (4.79) by a factor of nearly two. One main reason for this is probably the use of the ignition temperature Ti as a key parameter. Mitsui and Tanaka (1973) derived a theory for the minimum explosible concentration using the same basic discrete microscopic approach as adopted later by Nomura and Tanaka (1978) for modelling laminar flame propagation in dust clouds, and discussed in Section 4.2.4.4. Working with spherical flame propagation, they defined the minimum explosible dust concentration in terms of the time needed from the moment of ignition of one particle shell to the moment when the air surrounding the particles in the next shell has been heated to the ignition temperature of the particles. If this time exceeds the total burning time of a particle, the next shell will never reach the ignition temperature. Because this heat transfer time increases with the mean interparticle distance, it increases with decreasing dust concentration. By using some empirical constants, the theory reproduced the trend of experimental data for the increase of the minimum explosible dust concentration of some synthetic organic materials with mean particle size in the coarse size range from 100-500 pm particle diameter. Nomura, Torimoto and Tanaka (1984) used a similar discrete theoretical approach for predicting the maximum explosible dust concentration. They defined this upper limit as the dust concentration that just consumed all available oxygen during combustion, assuming that a finite limited quantity of oxygen, much less than required for complete combustion, was allocated for partial combustion of each particle. Assuming that oxygen diffusion was the rate controlling factor, they calculated the total burning time of a particle in terms of the time taken for all the oxygen allocated to the particle to diffuse to the Propagation of flames in dust clouds 325 particle surface. In order for the flame to be transmitted to the next particle shell, the particle burning time has to exceed the heat transfer time for heating the gas surrounding the next particle shell to the ignition temperature. Equating these two times defines the maximum explosible dust concentration. Two calculated values were given, namely 1400 g/m3 for terephthalic acid of 40 pm particle diameter and 4300 g/m3 for aluminium of 30 pm particle diameter. The ignition temperatures for the two particle types were taken as 950 K and 10oO K respectively. Bradley et al. (1989) proposed a chemical kinetic theoretical model for propagation of flames of fine coal dust near the minimum explosible dust concentration. It was assumed that the combustion occurred in premixed volatiles (essentially methane) and oxidizing gas, the char particles being essentially chemically passive. The predicted minimum explosive concentrations were in good agreement with experimental values (about 100 g/m3 for 40% volatile coal, and 500 g/m3 for 1&15% volatiles) 4.3 NON-LAMINAR DUST FLAME PROPAGATION PHENOMENA IN VERTICAL DUCTS This section will treat some transitional phenomena that are observed under conditions where laminar flames could perhaps be expected. This does not include fully turbulent combustion, which will be discussed in Section 4.4. Buksowicz et al. (1982) and Klemens and Wolanski (1986) describe experiments with a lignite dust of 52% volatiles, 6% ash and < 75 pm particle size, in a 1.2 m long vertical duct of rectangular cross section of width 88 mm and depth 35 mm. The duct was closed at the top and open at the bottom. Dust was fed at the top by a calibrated vibratory feeder yielding the desired dust concentration. The ignition source (an electric spark of a few J energy or a gas burner flame) was located near the open bottom end. Flame propagation and flame structure were recorded through a pair of opposite 80 mm X 80 mm glass windows. Diagnostic methods included Mach-Zehnder interferometry, high-speed fram- ing photography, and high-frequency response electrical resistance thermometry. Figure 4.31 shows a compensation photograph of a lignite dust/air flame propagating upwards in the rectangular duct. The heterogeneous structure of the flame, which is typical for dust flames in general, is a striking feature. This is reflected by the marked temperature fluctuations recorded at fixed points in the flame during this kind of experiments, as shown in Figure 4.32. The amplitudes of the temperature oscillation with time are substantial, up to loo0 K. The very low temperature of almost ambient level at about 1.1 s in Figure 4.32b shows that at this location and moment there was probably a pocket of cool air or very dilute, non-combustible dust cloud. Klemens and Wolanski (1986) were mainly concerned with quite low dust concentrations. From quantitative analysis of their data they concluded that the thickness of the flame front was 11-12 mm, whereas the total flame thickness could reach 0.5 m due to the long burning time (and high settling velocities) of the larger particles and particle agglomerates. The flame velocities relative to unburnt mixture of 0.5-0.6 m/s were generally about twice the velocity for lean methane/air mixtures in the 326 Dust Explosions in the Process Industries Figure 4.31 Compensation photograph of a 80g/m3 lignite dust/air flame in a vertical rec- tangular duct of width 88 mm (From Buksowicz, Klemens and Wolanski, 1982) same apparatus. This was attributed to the larger flame front area for the dudair mixture, and to the intensification of the heat and mass exchange processes in the dudair flame. Even for Reynolds’ numbers of less than 2000 (calculated as proposed by Zeldovich et al. (1980)) eddies, generated by the non-uniform spatial heat generation rate caused by the non-uniform dust cloud, could be observed in the flame front. Gmurczyk and Klemens (1988) conducted an experimental and theoretical study of the influence of the non-uniformity of the particle size distribution on the aerodynamics of the combustion of clouds of coal dust in air. It was suggested that the non-homogeneous particle size, amplified by imperfect dust dispersion, produces a non-homogeneous heat release process, and leads to the formation of vortices. Propagation of flames in dust clouds 327 Figure 4.32 Temperature variation with time at four fixed locations in a 103 g/m3 lignite/air dust flame propagating in a vertical duct of 88 mm x 35 mm rectangular cross section. Temperature probe locations: a = 2 mm from duct wall; b = 6 mm from duct wall; c = 26 mm from duct wall; d = 44 mm from duct wall (= duct centre) (From Klemens and Wolanski, 7 986) Deng Xufan et al. (1987) and Kong Dehong (1986) studied upwards flame propagation in airborne clouds of Ca-Si dust and coal dust, in a vertical cylindrical tube of i.d. 150 mm and length 2 m. The tube was open at the bottom end and closed at the top. The Ca-Si dust contained 58% Si, 28% Ca, and 14% Fe, Al, C etc. and had a mean particle diameter of about 10 pm. The Chinese coal dust from Funsun contained 39% volatiles and 14% ash and had a median particle diameter by mass of 13 pm. The dust clouds were generated by vibrating a 300 pm aperture sieve, mounted at the top of the combustion tube and charged with the required amount of dust, in such a way that a stationary falling dust cloud of constant concentration existed in the tube for the required period of time. The dust concentration was measured by trapping a given volume of the dust cloud in the tube between two parallel horizontal plates that were inserted simultaneously, and weighing the trapped dust. Ignition was accomplished by means of a glowing resistance wire coil at the tube bottom, after 10-20 s of vibration of the sieve. Upwards flame velocities and flame thicknesses were determined by means of two photodetectors positioned along the 328 Dust Explosions in the Process Industries tube. For the Ca-Si dust, flame velocities were in the range 1.3-1.8 m/s, and the total thickness of the luminous flame extended over almost the total 2 m length of the tube. The net thickness of the reaction zone was not determined. Figure 4.33 shows a photograph of a Ca-Si dust flame propagating upwards in the 150 mm diameter vertical tube. Figure 4.34 gives the average upwards flame velocities in clouds of various concentra- tions of the Chinese coal dust in air. On average these flame velocities for coaVair are about half those found for the Ca-Si under similar conditions. The data in Figure 4.34 indicate a maximum flame velocity at about 500 g/m3. If conversion of these flame velocities to burning velocities is made by Figure 4.33 vertical combustion tube (From Deng Xufan et at., 1987) Photograph of upwards flame propagation in a Ca-Si dust cloud in the 150 mm i.d. Propagation of flames in dust clouds 329 assuming some smooth convex flame front shape, the resulting estimates are considerably higher than the expected laminar values. This agrees with the conclusion of Klemens and Wolanski (1986) that this kind of dust flames in vertical tubes will easily become non-laminar due to non-homogeneous dust distribution over the tube volume. Figure 4.34 Upwards flame velocity versus con- centration of dry coal dust in air in vertical tube of i.d. 150 mm, open at bottom and closed at top. Coal dust from Funsun in P. R. China, 39% vola- tiles and 14% ash. Median particle diameter by mass 13 prn, and particle density 2.0-2.5 g/cm3 (Data from Kong Dehong, 1986) In the initial phase of the experiments of Proust and Veyssiere (1988) in the vertical tube of 0.2 m x 0.2 m square cross section, non-laminar cellular flames as shown in Figure 4.35 were observed. In these experiments the height of the explosion tube was limited to 2 m. Over the propagation distance explored, the mean flame front velocity was about 0.5 ds, as for the proper laminar flame, but careful analysis revealed a pulsating flame movement of about 60 Hz. A corresponding 60 Hz pressure oscillation, equal to the fundamental standing wave frequency for the one-end-open 2 m long duct, was afso recorded inside the tube. Further, a characteristic sound could be heard during the propagation of the cellular flames. Proust and Veyssiere, referring to Markstein’s (1964) discussion of cellular gas flames, suggested that the observed cellular flame structure is closely linked with the 60 Hz acoustic oscillation. However, there seems to be no straightforward relationship between the cell size and the frequency of oscillation. It is of interest to relate Proust and Veyssiere’s discussion of the role of acoustic waves to the maize starch explosion experiments of Eckhoff et al. (1987) in a 22 m long vertical cylindrical steel silo of diameter 3.7 m, vented at the top. Figure 4.36 shows a set of pressure-versus-time traces resulting from igniting the starcwair cloud in the silo at 13.5 m above the silo bottom, i.e. somewhat higher up than half-way. This kind of exaggerated oscillatory pressure development occurred only when the ignition point was in this region. The characteristic frequency of 4-7 Hz agrees with the theoretical first harmonic standing wave frequency in a 22 m long one-end-open pipe (22 m = i wave length). The increase of frequency with time reflects the increase of the average gas temperature as combustion proceeds. It is interesting to note that the peak amplitude occurs at about 2 s after ignition. The pulsating flow probably gradually distorts the flame front and increases the combustion rate. The oscillatory nature of this type of explosion could be clearly seen on video recordings. ‘Packets’ of flames were ejected at a frequency matching exactly that of the pressure trace. Similar oscillations were also generated in experiments in the 236 m3 silo when the vent was moved from the silo roof to the cylindrical silo wall, just below the roof (Eckhoff et al., 1988). 330 Dust Explosions in the Process Industries Figure 4.35 Photograph of a typical cellular flame in 150 g/m3 maize starch in air, at 7.5 m above the ignition point. Upwards propagating flame in a vertical duct of 0.2 m x 0.2 m cross section (From Proust and Veyssiere, 7 988) [...]... corresponding specific interface surface area He then assumed a differential equation of the form: 338 Dust Explosions in the Process Industries d(1-’) - M + B + A dr (4.84) where M represents the influence of mechanical processes such as stretching, breakage, impact and coalescence B represents the influence of the burning, whereas A represents influences of other processes such as wrinkling, smoothing... laminar burning velocity As the methane/air flame approached the end of the tube, the average flame speed W had reached the same value of 60 -70 m/s irrespective of the ignition delay (initial turbulence), which means that the obstacle-induced turbulence played the main role in the latter part of the combustion In the dust cloud, however, the high final flame speed of about 70 m/s is only reached in the. .. types of brown coal, a maize dust, and a wood dust, all dusts being finer than 75 km particle size Figure 4.50 shows the average turbulent burning velocity for maize dust/ air in the loop as a function of the average normalized turbulence intensity 350 Dust Explosions in the Process Industries Figure 4.49 Laboratory-scale flow loop for studying influence of turbulence on the propagation of dusvair flames:... predict the kind of oscillation shown in Figure 4. 36 The calculations in fact showed that before the flame reached the open end, the air velocity at the open end could become negative, i.e the air would flow inwards Further reflections would cause the flow to reverse again Artingstall and Corlett suggested that this theoretical result could help to explain the pulsating flow observed in some actual dust explosions. .. ,at an initial pressure P2 % P I In some apparatuses the dust is initially placed on the high-pressure side of the dispersion air valve, as indicated in Figure 4.39, whereas in other apparatus it is placed downstream of the valve Normally, the mass of dispersion air is not negligible compared with the initial mass of air in the main vessel This causes a significant rise of the pressure in the main vessel... lower than for a dried dust Therefore ignition of the moist dust with a continuous source is not possible until the turbulence has decayed to a sufficiently low level, below the critical level for Propagation of flames in dust clouds 343 ignition of the dried dust In other words: As the moisture content in the dust increases, the ignition delay also increases Therefore the strong influence of moisture content... interval after opening of the dust dispersion valve These sources vary from electric sparks, via exploding wires to various forms of electrically triggered chemical ignitors An important inherent feature of all apparatus of the type illustrated in Figure 4.39 is that the dispersion of the dust inevitably induces turbulence in the main vessel The level of turbulence will be at maximum during the main... anemometer The turbulence intensity v ’ , 344 Dust Explosions in the Process industries assuming isotropic turbulence, was determined from the rms (root mean square) and mean velocities extracted from the hot-wire signal in the absence of dust As pointed out by Semenov (1 965 ), a hot-wire probe senses all velocities as positive, and therefore a positive mean velocity will be recorded even if the true... Flame jet too weak for igniting secondary cloud; (b) Flame jet will ignite secondary cloud (From Schuber, 1989) 3 56 Dust Explosions in the Process Industries dust properties were conducted with comparatively low initial turbulence in the dust clouds Schuber correlated his experimental MESG values with the product of minimum electric spark ignition energy and the dimensionless minimum ignition temperature... turbulence intensities at the moment of ignition The turbulence intensities were measured by means of a bi-directional impact probe For a given dust, dust concentration and vent characteristics, the maximum pressure in the vented explosion increased systematically with increasing initial turbulence intensity in the experimental range 2-12 d s Hayes et al (1983) investigated the influence of the speed . of the particle material. The resulting equation for the minimum explosible dust concentration, assuming that the 324 Dust Explosions in the Process Industries Powder type Aluminium. 322 Dust Explosions in the Process Industries the highest degree of oxidation, and that the dust particles are so small that the dust cloud can be treated as a premixed gas. The resulting. determined by means of two photodetectors positioned along the 328 Dust Explosions in the Process Industries tube. For the Ca-Si dust, flame velocities were in the range 1.3-1.8 m/s, and the