FMRC studies of parameters affecting the propagation of dust explosions

FMRC studies of parameters affecting the propagation of dust explosions

135 Powder Technology, 71 (1992) 135-151 FMRC studies of parameters explosions F. Tamanini affecting the propagation of dust and E. A. Ural Fact...

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135

Powder Technology, 71 (1992) 135-151

FMRC studies of parameters explosions F. Tamanini

affecting the propagation

of dust

and E. A. Ural

Factory Mutual Research Corporation, 1151 Boston-Providence Turnpike, Norwood, MA 02062 (USA)

Abstract PMRC research on dust explosion propagation is reviewed. Activities to date have been directed toward quantifying the effect of turbulence on flame propagation and toward characterizing the dispersibility of dusts. Turbulence effects have been studied for the case of confined gas/air mixtures in a 1.35-m3 sphere and for the case of vented dust explosions in a 63.7-m3 chamber. In these experiments, the velocity field was measured using a new bidirectional impact probe developed as part of the program. Parallel modeling work has reached the stage of allowing for reliable predictions of turbulent confined gas explosions in simple geometries. Work is in progress to extend the model to dust/air mixtures and to allow for venting. Two laboratory techniques have been developed to measure two properties selected to characterize the dispersibility of dusts: the settling velocity of a dust cloud and the entrainment threshold of a dust layer. Dust entrainment testing has also been carried out in a 3-m long gallery under simulated explosion conditions. These results are being used as input to an effort aimed at developing a comprehensive model for dust explosion propagation in elongated structures. Preliminary results from a phenomenological version of such a model are also discussed.

Introduction The formation and permanence of a fuel/air mixture is a prerequisite for explosion propagation, regardless of whether the fuel is in the gaseous, liquid or solid phase. However, differences between gaseous and highly dispersed liquid/solid fuels (aerosols/dusts) exist with regard to the processes that are important during mixture formation. For example, molecular diffusion may be a factor to be considered with gases; it almost never needs to be in the case of liquids or solids. In addition, if turbulence is present, aerosols and dusts respond to the turbulent fluctuations through aerodynamic drag, a mechanism that does not have a counterpart in the case of a gaseous mixture. Once mixing is achieved, gravitational forces usually play an important role in the tendency of a solid fuel to separate from the mixture by settling. In gaseous mixtures, on the other hand, the corresponding effect (stratification of components of different molecular weights) can normally be neglected. Due to these factors, which affect the rate at which the mixture is being formed and which tend to promote separation of the reactants, dust/air mixtures are often characterized by strong composition gradients. This fact complicates the performance of carefully controlled experiments and adds difficulty to the modeling of dust explosions.

0032-5910/92/$.5.00

In dealing with dusts, a distinction is often made between primary and secondary explosions. While the difference in some cases is drawn around somewhat artificial criteria, the timing of the process of mixture formation with reference to ignition is the accepted discriminating element. In primary explosions, the fuel/ air mixture is generated by some kind of upset or process condition and it exists prior to initiation of the combustion event. In secondary explosions, the formation of the explosive mixture through which the flame propagates is the result of a disturbance induced by another explosion in an interconnected volume. The hazard posed by secondary dust explosions is potentially quite severe, since layered dust deposits can provide a means for the flame to propagate long distances and to involve large portions of a building or process structure. Long-range research is currently in progress at Factory Mutual Research Corporation (FMRC) to address problems relating to dust explosion hazards. With regard to dust explosion propagation, emphasis has been placed on studies of the effect of turbulence on the rate of fuel consumption by the advancing flame front and on efforts to identify and measure the dispersibility properties of dusts. This paper summarizes the results from experimental and modeling work on the effect of turbulence on explosion propagation, as well as describing the development of laboratory techniques to measure

8 1992 - Elsevier Sequoia. All rights reserved

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the dispersibility characteristics of dusts. More recent and as yet unreported data are also presented which deal with the response of dust layers to the kind of aerodynamic disturbances caused by explosions. A possible formulation for using the type of dispersibility data obtained in these studies is also discussed.

Background overview A series of large-scale tests, involving cornstarch explosions carried out in an 80-ft (24.4-m) long gallery [1,2], represents the first instance of an FMRC project which specifically addressed the question of dust explosion propagation. The main objectives of the tests were: 1) to determine the minimum dust loading on the gallery floor required to support flame propagation, and 2) to establish the effectiveness of venting in suppressing propagation. Parallel testing in a 20-ft (6.1m) long model gallery, which was done as part of the same program, had similar objectives. In view of the fact that the tests were aimed at finding answers to a set of practical questions, these results have turned out to be only partially useful in addressing fundamental issues of explosion propagation. Despite these limitations, the data from this project have provided strong guidance in the definition of a strategy aimed at understanding the mechanisms that control explosion propagation. This has helped in the formulation of a longrange dust explosion research project, whose ultimate objective is the development of a comprehensive model for explosion propagation in structures. With background turbulence representing such an important element in the list of factors affecting the rate of fuel consumption in a dust explosion, quantification of this effect has been the object of significant effort. Instrumentation for measuring the rapidly varying velocity field in a turbulent dust cloud was developed and used in tests where the severity of vented explosions of cornstarch and coal was correlated with the intensity of the turbulence [3, 41. In view of the additional complexities introduced by the combustion of the dust particles and by the dynamics of the venting process, more recent FMRC studies of turbulence effects have been focused on unvented explosions of gaseous mixtures [5]. Similarly, modeling efforts have been directed to the problem of unvented methane/air and propane/ air turbulent explosions [6]. The settling velocity of a dust cloud and the entrainment threshold of a dust layer have been selected as the two parameters necessary to characterize dust dispersibility. This choice is justified by the fact that the entrainment threshold provides a measure of the minimum strength of a perturbation capable of disrupting a dust layer. In addition, approximate for-

mulations are available to relate the rate of dust entrainment to the value of that threshold. The settling velocity, on the other hand, is a quantity that measures both the ease with which the dust can follow the turbulent fluctuations and the rate at which the dust tends to settle under the action of gravity. Two laboratory measurement techniques were developed to determine these two quantities [7, 81. Since the entrainment measurement has been found to be very sensitive to the details of the formation of the dust layer, there has been a strong incentive to develop techniques for making in situ dust entrainability measurements. Some effort, not reported here, has been devoted to this task. Recent results have also been obtained from experiments on the dispersion of dusts under conditions simulating the unsteady flow produced by a propagating explosion. These data will be discussed, along with the preliminary formulation of a phenomenological model of propagating dust explosions that makes use of the dust dispersibility information obtained from the laboratory measurements. Turbulent flame propagation in cubical enclosures Effect of test vessel and procedures Dust explosion testing is always performed with some turbulence present. This is required by the fact that formation of the dust/air cloud is normally achieved by sudden injection of a dust charge using a burst of compressed air. Ignition is then timed to occur before the turbulent fluctuations have completely died out so as not to allow the dust to settle. Standardized laboratory testing of dust explosibility [9] characterizes the reactivity of ,dusts on the basis of the maximum value of the normalized rate of pressure rise, typically referred to as K,,. This quantity is then used as input for explosion vent sizing procedures [lo]. While this approach represents the current state of the art to design protection for equipment and buildings against dust explosions, the method is not without problems, mostly related to the empirical nature of its development [ll]. The level of turbulence used in the testing is generally unknown, with its magnitude practically set by the timing of the ignition. The importance of turbulence is demonstrated by the data in Fig. 1 for cornstarch obtained in the FMRC 20-l sphere [12]. These results show that the reactivity variable KS, (the normalized peak rate of pressure rise) is a strong function of the ignition delay, while the peak explosion pressure remains almost unaffected. In the figure, the top curve corresponds to zero delay and refers to data obtained in compliance with the testing standard [9]. In a more general sense, however, the range of applicability of these results to practical explosions remains to be determined.

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scale conditions. The goal of developing such a model has provided motivation and a focusing point for the work described in the next section.

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With regard to the effect of turbulence on explosion propagation, work to date has been limited to gaseous mixtures in an unvented spherical enclosure. Its extension to dust/air mixtures is currently in progress. More specifically, FMRC efforts in this area have proceeded along the following lines: 1) Development of a fast-response bi-directional impact probe to measure rapidly varying flow velocities in the presence of dust. 2) Characterization of the decaying turbulent field induced by the high-pressure injection of the mixture in the test vessel. 3) Performance of unvented gas explosion tests in a 1.35-m3 sphere for five methane/air and propane/ air mixtures at different levels of turbulence. 4) Correlation of the measured mixture reactivities with the intensity of the cold flow turbulence at the time of the explosion. 5) Development of a phenomenological model for turbulent flame propagation in confined gas explosions and validation of the model by comparison with the experiment. Results

Since the importance of turbulence in dust explosions is well recognized [13], attempts have been made recently to measure the decaying turbulent field in the standard 20-l sphere apparatus [14]. Unfortunately, even after completion of the characterization of the turbulence in the laboratory apparatus through measurements of this type, difficulties still remain in establishing the necessary link to actual explosions. Some of the problems are: 1) The very strong ignition source used in the laboratory test (10 000 J) overdrives the flame propagation process in a fashion that may not be representative of most real life situations. 2) Since the intensity of the turbulence in the test decays rapidly with time, slow-igniting dusts will produce flames propagating into a turbulent field of lower intensity than dusts that ignite more promptly. 3) The turbulence levels in accidental explosions are usually not known. While research activities of the type referenced here are helping shed new light on the fundamental processes affecting flame propagation, validated dust explosion models will probably be required to provide a reliable method to extrapolate laboratory-scale results to full-

The data obtained from the experimental part of this effort are summarized here and have been described in detail in [5]. Gas explosion tests were carried out in a 1.35-m3 spherical test vessel fitted with an injection system of the design commonly used for dust explosion testing. In the experiments, the gas mixture is loaded at high pressure (300 psig, 20.7 bar (g)) in two charge vessels of 35-l capacity each and in the pre-evacuated (at 4 psia, 0.28 bar (a)) test enclosure. The injection process is interrupted when the pressure in the charge vessel drops to about 50 psig (3.4 bar (g)), at which point the air mass in the test vessel is equal to that corresponding to standard conditions. This is the same injection procedure that would be used to perform dust explosion tests. By performing repeated air injection tests with a velocity probe placed at various locations in the test vessel, measurements were obtained for the average turbulence in the sphere. Figure 2 shows the result of these measurements in a plot of the best fit to the data on average turbulence intensity, u’, as a function of time from the beginning of air charge injection. As can be seen, there is a very rapid decay of the turbulence from levels of 20-30 m s-’ to about 1 m s-’ within a time of the order of one second. While no direct

138

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Fig. 2. Measured turbulence intensity (u’) and calculated integral length scale, Taylor microscale and turbulence Reynolds number. Results for the FMRC 1.35m3 sphere and standard gas mixture injection conditions. [Modified version of figure in [5]].

measurements of turbulent scales were made, information on the integral length scale, L, and on the Taylor microscale, A, was calculated from the time variation of the data for the intensity u’. Calculated curves for these two scales and for the turbulence Reynolds number, ReL (=u’ L/u), are also shown in the figure. Results from explosion tests with 5.5% and 9.5% (stoichiometric) methane/air mixtures are shown in Figs. 3 and 4. Data are reported for three quantities: 1) Peak explosion pressure, pm: obtained from the experimental pressure record by calculating the maximum value of the smoothed curve, to remove the effect of pressure fluctuations. Equivalent turbulent burning velocity, u,,,: calcu2) lated by fitting to the early portion of the pressure rise curve (Ap from 1 to 8 psig, 0.069 to 0.55 bar (g)) the following solution from a simple analytical model assuming thin flame propagation at a constant burning velocity [5, 151:

(1) wherep, is the initial pressure, and Yis the volume of the explosion vessel. Normalized maximum rate of pressure rise, Ko: the 3) equivalent parameter for gases of the variable KS, for dusts, defined as:

The experimental data for these three variables were obtained in tests where the mixture was placed in both the charge and the test vessels, as indicated earlier (solid symbols), or in runs where all the fuel was placed in the pre-evacuated test vessel and air was injected (open symbols). The two sets of data are practically indistinguishable, indicating that initial mixing was not an issue in any of these experiments. The effect of turbulence is seen to be relatively low on the peak explosion pressure, but it is quite pronounced in the case of the two variables, uLeq and KG, more directly representative of the rate of reaction. The relative increase in reactivity due to the turbulence is greater in the case of the weaker mixture (5.5%). This may point to the possibility of underestimating the protection requirements of turbulent mixtures that display low reactivity in testing carried out under quiescent conditions. Theoretical modeling Figures 3 and 4 show curves calculated using the phenomenological model described in [6]. This model assumes that the propagation of the flame front occurs by entrainment of fresh mixture by large-scale eddies and subsequent combustion behind the macroscopic flame front by burnout of eddies of size equal to the Taylor microscale. Thermodynamic properties of the mixture are obtained from equilibrium calculations and radiative heat losses are taken into account by a mean beam length approach. The model equations are solved within the framework of a lumped-parameter formalism,

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Fig. 4. Measured and calculated explosion parameters as a function of turbulence intensity in the FMRC 1.35m3 sphere for standard injection conditions - case of 9.5% CHJair mixture (u,,=O.43 m s-r).

in which properties are assumed to be uniform in the burnt and unburnt mass. The model contains essentially one free parameter, the laminar burning velocity, whose value must be obtained from experiment (0.08 and 0.43 m s-’ are used for 5.5 and 9.5% methane in air, respectively). The calculated curves were obtained by running the theoretical model for the laminar case (u’ = 0, quiescent conditions) and for nine levels of turbulence at the time of ignition. The run corresponding to the highest turbulence is represented by the rightmost point of the calculated curves. As can be seen, the curves for the slow burning mixtures (5.5%, Fig. 3) extend to lower values of turbulence than those for the more reactive mixture (9.5%, Fig. 4), due to the greater extent of turbulence decay taking place in the case of the first mixture during the slower flame propagation process. The calculated results and the experimental data are both plotted at abscissa values obtained by taking the average of the turbulence intensity during the portion of the pressure curve relevant to the variable being plotted. Note that this eliminates the error that is introduced when explosions of different propagation

rates are correlated to the intensity of the decaying turbulence field at the time of ignition. Agreement between theory and experiment is seen to be quite good, particularly in reflecting the effect of turbulence on two very different portions of the pressure rise curve: the early stage, represented by the variable u~,,~; and the subsequent development, as described by the variable KG. It implies that the entire shape of the pressure curve is reproduced well by the model. This result is quite gratifying, particularly since it comes from a model that provides limited options for fine tuning. The combustion sub-model is believed to be the principal contributor to this initial success. Further development work and extensions of the model to more complex situations (dusts, vented explosions) will decide whether this formulation is still promising. Vented dust aplosiom The effect of turbulence on dust explosions was investigated in a series of large-scale vented tests carried out with cornstarch and a bituminous coal in a 2250ft3 (63.7 m3) chamber. This work has been documented in [3,4]. Following an approach similar to that described

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in the previous section, the turbulence produced in the test chamber by the dust injection process was first quantified by taking several measurements during air discharge runs (no dust). The results from the averaging of measurement pairs at twenty-three different locations in the chamber volume are qualitatively similar to the data shown in Fig. 2 and have been reported in [3, 41. These data show that the turbulence intensity decays roughly linearly with time during the active portion of the injection process, and at a faster rate following completion of the air discharge. The effect on the discharge process due to the presence of a dust was studied by a limited number of tests and found to be two-fold. First, since the dust causes additional flow resistance, the rate of release of the air from the charge is slowed down, thus taking a longer time to complete. This is documented by the time variation of the pressure in the charge tanks. The second effect, which is illustrated by the turbulence data in Fig. 5, appears to be that the presence of dust increases the intensity of the turbulence during the latter portion of the active injection phase and during the subsequent decay of the velocity fluctuations. These results, the details of which may need to be confirmed by additional testing, demonstrate the need to account for the presence of a dust charge because of its impact on the evolution of the source for the turbulence field (i.e. the time dependence of the injection flow). This has implications on the control of turbulence in laboratory tests of dust explosibility, where typical procedures call for experiments at different dust loadings. Furthermore, while the available data are in this respect inconclusive, the influence of the dust particles on the decay of the velocity fluctuations may also need to be taken’into account.

Another element which complicates the performance of testing with careful control of turbulence levels is the fact that dusts display differences in the rate of growth of the initial flame kernel. This was evident in the vented explosion tests performed in the 2 250-ft3 chamber for two dusts, cornstarch and a bituminous coal, which differ widely in ignition energy requirements. In these tests, the effective ignition time, calculated from a cubic fit to the early portion of the pressure curve, lagged behind the time of firing of the ignition source by about 30-80 ms for cornstarch and 200-350 ms for the bituminous coal. To account for this effect, data from the explosion tests were correlated with respect to the average turbulence of the background flow during the time of pressure rise from 20% to 80% of maximum. Results for the severity of these vented dust explosion tests as a function of background turbulence intensity are shown in Fig. 6. The variable plotted on the ordinate of the figure is thevalue for the maximum normalized rate of pressure rise, KS,, that the explosion would have displayed had it taken place under unvented conditions. These KS, values were calculated from the reduced explosion pressures measured in the tests using a simple model of vented explosions [3]. This quantity was chosen for the presentation of the results, in place of the measured vented reduced pressures themselves, to incorporate the effect of differences in vent areas in the tests (A, Vmzn typically equal to 0.35 for cornstarch, to 0.086 for the coal tests). As can be seen, the difference in mixture reactivity between the cornstarch and the coal tested is quite large, a factor of about 3-10, depending on the level of turbulence at which the comparison is made. On the other hand, standard 20-I sphere data [3, 9, 121, perhaps owing to the strength of the ignition

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Fig. 5. Effect of a dust charge of 250 g mm3 of cornstarch on the time evolution of the RMS of the instantaneous velocity for standard injection conditions in the FMRC 2250-ft” chamber. paken from [4]].

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Fig. 6. Explosion severity for vented tests in the FMRC 2250ft’ chamber, based on values of K,, calculated from an analytical model. Data plotted as a function of the mean turbulence intensity during pressure rise from 20 to 80% of maximum. &eft and right horizontal error bars represent turbulence intensities at 80% pressure rise and at nominal ignition time.

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source, would indicate a narrower spread between the two dusts with K,, values of 144 and 74 bar m s-l (a factor of about 2) for cornstarch and coal at 250 g mT3. Even with all other injection parameters held constant, dust loading has an effect on the turbulence development. Since no turbulence measurements were carried out for the charge corresponding to 500 g mW3, the result from the only vented test at this concentration is plotted by using the turbulence data obtained for 250 g mV3. This is clearly incorrect, and the actual turbulence intensity for that test was probably higher than the value at which the data point is plotted. The horizontal arrows reflect this uncertainty. As indicated earlier, the data are plotted at an average turbulence level. The high and the low limits of the horizontal error bars correspond to the turbulence intensities at the nominal ignition time and at the time of 80% pressure rise. The greater extent of these bars in the case of coal confirms the fact that this dust, due to its relatively low reactivity, was exposed to a broader range of turbulence intensities than the cornstarch. Unless the timing of the explosion with respect to the decaying turbulence field is carefully taken into account, it is easy to attribute to the intrinsic reactivity of the dust a result that is in fact mostly due to the level of turbulence actually experienced by the mixture.

Characterization of dust dispersibility of

dispersibility

the conditions for dust must and mixed with an oxidizer (usually air) to generate The dispersibility of a dust is, just as important the reactivity the material and the level of turbulence the environment, this property directly affects the amount The aerodynamic disturbances responsible for credust cloud are and last anywhere from a fraction For an explosion the disturbance must be of sufficient strength and to: 1) Remove the from its place Mix dust with air form a flammable mixture; and the dust from settling until arrival of propagating the dispersibility dust must done in such that three the dispersion sequence are This be achieved two fundamental parameters: the for particles from layer the entrainability the

dust); and the terminal velocity of particles, how closely the dust particles follow the and resist settling. test methods appear to be available two parameters with sufficient accuracy, two were developed powders according to these two the settling velocity apparatus which used to compare the

and lift-off apparatus, according to their ease of entrainment

dust layers air stream.

Development of dust dispersibility measurements

has been developed

to measure the

range and controllable air pulse the material The device has dust size operating from a pm (sub-sieve range) up to which provides coverage the particle most interest from the explosion The settling velocity apparatus has been described in [7]. tall cylinder high nominally (0.3 m) in diameter. The cloud is formed near the top of apparatus and down onto dust collecting platform resting load cell. The the output the load cell with time for subsequent data analysis. The cylindrical enclosure is sealed top bottom air currents, and any fugitive dust emissions. The dust dispersion mechanism was designed dust clouds with no initial vertical momentum. two vertical opposed nozzles, (25 in diameter, separated by an adjustable gap. The the bottom the lower nozzle and is dispersed air pulse. The shear stress the dispersion jet the sample, well as orifice formed by mouths the nozzles, provide efficient such as cornstarch. The from orifice forming a radial jet a relatively high velocity, that flow impinges on outer wall of cylindrical enclosure, and the cloud spreads the upward and The operating conditions of apparatus were selected the efficiency dispersion for most cohesive dust used the program. The VS. time plot recorded the data accan be viewed fall time probability distribution with time referenced to instant Each point in

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normalized weight curve represents the mass fraction of particles whose fall times are shorter than the value read from the abscissa, for a fall height of 1.8 m. A more convenient characterization of the cloud settling process is to use particle velocities instead of fall times. This conversion is done assuming that the time required for the particles to reach their terminal velocity is small compared to the fall time, and that thevertical dimension of the initial cloud is small compared to the fall height. A plot of settling velocity distribution for cornstarch is given in Fig. 7. The vertical axis indicates the mass fraction of particles with settling velocities greater than the value on the abscissa. Also shown in this plot with the solid line are the data for cornstarch mixed with 1 wt.% of an anti-static additive, Aluminum Oxide-C pigment. This additive, which consists of very tine (approximately 20 nm size) and highly conductive particles, is used to improve the flowability of powders. As seen in Fig. 7, Aluminum Oxide-C substantially reduces the settling velocities of cornstarch, which is indicative of reduced agglomeration and better dispersion. The mass mean settling velocity of the Aluminum Oxide-C/cornstarch mixture is 1.12 cm s-l, from Fig. 7. Assuming a density of 1.6 g crnm3 for cornstarch particles, the mass mean aerodynamic size is calculated to be 15.3 pm. This diameter is in remarkable agreement with mass mean diameters of 14 pm and 16 pm obtained from previous measurements for the same dust using a Coulter counter [l]. The aerodynamic particle size corresponding to the mass mean settling velocity of non-cohesive powders should ideally be equal to the diameter of equivalent spherical particles. Some deviation is expected for nonspherical particles such as coal dust. Therefore, the satisfactory operation of the apparatus has been verified by comparing the aerodynamic particle size to that obtained from direct measurements for Lycopodium

Fig. 7. Settling characteristics of a cornstarch dust cloud measured in the FMRC settling velocity apparatus.

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Lip-off apparatus The FMRC lift-off apparatus was developed to determine the aerodynamic forces required to remove a powder layer deposited on a surface. It consists of two parallel aluminum disks, as shown in Fig. 8. The dust layer is deposited on the lower disk, which is 15 in (0.38 m) in diameter. The upper disk is 12 in (0.30 m) in diameter with a 1 in (25 mm) diameter hole at the center. Along one radius, windows are placed in the upper plate to allow observation of dust lift-off during testing. Controlled suction is applied through the center hole using a blower. A pressure measurement made at the wall of the suction pipe is used to measure the air flow rate. The edges at the outer and inner diameter on the lower side of the upper plate are rounded with a l/2 in (12.7 mm) radius of curvature to reduce inlet and outlet effects. The surfaces of the two plates facing the flow are polished to a 32 microinch (0.8 pm) finish. Air moves radially inward between the two disks accelerating towards the center due to a reduction in the effective cross-sectional area. In addition to this radial variation, the local air velocity is controlled by means of changing the gap between the plates (l/8 to l/2 in, 3.2 to 12.7 mm) and by adjusting the air flow throughput (up to 110 cfm, 0.052 m3 s-l). Under these operating conditions, average radial air velocities span the range 0.9 to 62 m s-‘. A detailed review of the existing literature on the aerodynamic forces acting on particles in a dust layer has been given elsewhere [7]. When the particles are deep inside the boundary layer, the aerodynamic environment to which they are subjected can be described by the surface shear stress alone. Under the experimental conditions of the lift-off apparatus, the flow between the two disks is estimated to be laminar and of boundary layer type. This is characterized by a developing region near the inlet, where its thickness is increasing in the flow direction. Further downstream, the boundary layer

Fig. 8. Schematic view of the FMRC lift-off apparatus. [Taken from [S]].

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thickness decreases due to flow acceleration. A simple integral boundary layer model, used to calculate the local wall shear stresses as a function of distance between the disks and the rate of flow through the apparatus, predicts that the wall shear stress in the apparatus ranges from 0.025 to 25 Pa. The dust layer is deposited on the bottom plate of the apparatus, and is subjected for one minute to air flow at the rate required to cause dust removal at a radius greater than 1.5 in (38 mm). The dust removal pattern typically consists of a completely clean area free from dust particles near the center of the plate, and a practically undisturbed area sufficiently away from the center. The transition between these two zones has a combination of dusty and clean areas of varying thicknesses. In the data reduction, the radius at which 50% of dust particles are removed is determined by employing a gravimetric method and by visual inspection, with good agreement between the two methods. A critical shear stress for entrainment is then calculated from the value of this radius and from calibration data on the apparatus. Dust layers to be tested were at first formed using the settling velocity apparatus described in the previous subsection. Deposition runs with cornstarch used 0.5, 2 and 4 g. Cornstarch loads in excess of 4 g were found to exceed the capacity of the dispersion mechanism. The critical aerodynamic wall shear stress data obtained for these layers are plotted (square symbols) in Fig. 9 as a function of layer density. Avery strong dependence of critical shear stress on layer density is apparent from this plot. It should be noted that the layer density of 15 g me2, obtained for the maximum dust load allowable in the settling apparatus, is not adequate to represent dust layers that may pose an explosion threat for most applications. The formation of layers greater than 15 gm -’ would require multiple deposition runs in the

100

1 LAYER DEN&Y

(g/rn2)

Fig. 9. Layer thickness dependence of the aerodynamic surface shear stress required for 50% removal. Data for cornstarch obtained for three different deposition methods. [Taken from

Ml.

settling velocity apparatus. In this mode of operation, experience has shown that it is practically impossible to obtain smooth deposits. Even within the 0 to 15 g rnd2 range, the method of increasing the dust charge in the dispersion device to increase the layer density does not completely isolate the effect of layer density on lift-off characteristics, since the settling velocities measured in the apparatus used to form the layer are strongly affected by the sample weight. To separate these two factors, the layer thickness was controlled independently from the deposition rate by using an elutriation type continuous deposition chamber. The powder sample is placed at the bottom of a tube where it is fluidized by an upward air flow. Two flow rates termed ‘slow’ and ‘fast’ deposition were used to form a series of cornstarch layers. Critical wall shear stress data for these layers are plotted as diamonds and triangles in Fig. 9. The lift-off shear stress appears to decrease with increasing layer density both for the fast and slow deposition layers. However, the absolute magnitude of the 50% dust lift-off shear stress is almost a factor of three smaller for fast VS. slow deposition rates. This strong dependence on the deposition rate also explains the steeper slope observed for the settling apparatus data shown in the same figure since, in that case, increasing sample mass not only has the effect of increasing layer thickness but also of increasing the deposition rate and the size of the depo’siting agglomerates. The strong dependence of the lift-off parameters on the method and rate of deposit formation creates a practical problem in the application of this methodology to field conditions. First of all, the two deposition rates employed in the continuous deposition apparatus may not necessarily bracket all conceivable real deposits. Furthermore, for powders with strong cohesive forces between the particles, the measured lift-off parameter may also depend on the nature of the surface itself. Therefore, a portable version of the apparatus has been developed to take measurements on actual deposits and has been used for preliminary measurements not reported here. For the purpose of a generic classification of dusts according to their dispersibility, however, choosing a ‘standard’ deposit formation technique should be adequate. A ‘standard method’ was selected based on the use of the settling velocity apparatus with 2 g of dust sample. Tests were also carried out with Lycopodium, sand, and Pittsburgh seam bituminous coal dust layers prepared using the standard deposition method. Within experimental scatter, the critical shear stress values measured for all these dusts were very similar, but substantially lower than those for cornstarch. Unlike cornstarch, these dusts are free-flowing and are expected to have minimal cohesive tendencies. To con-

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firm the result, the cornstarch tests were repeated with 1 wt.% A&0,-C added, to suppress cohesive forces and improve the flowability of the dust. When tested in the lift-off apparatus, the cornstarch/A.&O,-C mixture gave results comparable to the other free-flowing dusts. For the free-flowing powders tested, the critical shear stress appears to be weakly dependent on the particle size. In the experiments, sand and coal dust were separated to five size fractions using a conventional sieve-shaker. The sand data showed a slight reduction in the critical shear stress with increasing particle size. The same trend was not apparent in the case of the coal dust. Eflect of oil treatment on the entrainability of grain dust

The characterization of the effect of oil treatment on grain dust entrainability provides a useful practical application for the lift-off apparatus. Soybean oil or mineral oil applied to grain in trace amounts ( < 0.03%) has been found to significantly reduce the grain dust production during handling. Even at these reduced rates of emission, however, dust accumulation over exposed surfaces still occurs. One sample of both treated and untreated grain dust, and two other oil treated samples were obtained from grain handling facilities. All treated samples emanated from g;ain treated with 180 to 220 ppm mineral oil. These samples were sifted using a conventional sieve shaker, and tests were performed on two different size groups of each sample, i.e, less than 75 pm and 75 to 125 pm. The critical shear stresses measured for standard layers of these eight grain dust samples are shown in Fig. 10. Comparison of the critical shear stresses for untreated and treated sample 1 indicates that the treated dust deposits should be more difficult to entrain in an explosion situation. It is also apparent from Fig. 10 that the larger grain dust particles are 2

PARTICLE SIZE : DZB LT 75 /an

9

0

Sample 1 Untreated

Fig. 10. Critical shear stresses for dust lit-off measured for standard layers of untreated and treated grain dust. [Taken from

Ml.

more easily entrainable, compared to smaller particles. Substantial differences in the critical shear stresses measured for treated samples originating from different plants can also be noted in the data. Furthermore, since the oil treatment significantly reduces the generation of dust in the first place, the dust layers should form much more slowly, thus further increasing the critical shear stress of the actual layers. The two size fractions of the treated and untreated sample 1 were also tested in the settling velocity apparatus, which directly measures the distribution of the settling velocity over the mass of sample. The measured settling velocities of the treated samples are higher compared to the untreated samples, especially in the larger size group. Considering that in an explosion situation the particle dispersion forces are likely to be much weaker compared to those employed in the settling velocity apparatus, a stronger effect of oil treatment on the settling velocities can be anticipated. Increased settling velocities would imply that lifted particles would stay suspended for shorter time periods, thereby reducing the hazard.

Testing under simulated explosion conditions

Experiments were carried out in the intermediate scale, 20-ft (6.1 m) long model gallery described in [l]. The gallery cross-section was nominally 1 ft X 1 ft (0.3 x0.3 m). To achieve better control over the reproducibility of the experiment, an air burst was used instead of a primary explosion to produce the flow through the gallery. The original primary explosion chamber was removed and a converging nozzle was created by the insertion of two baffle plates. Air flow through the gallery was generated by the sudden discharge of an air tank through a pipe section approximately 20 in long and 1 in diameter (508 by 25.4 mm). The internal free volume of the air tank was 0.52 ft3 (0.028 m’), corresponding to a storage of 244 g of air at a pressure of 120 psig (8.3 bar). At this charge pressure, the time constant of discharge was typically 45 ms. The inlet nozzle into which the air tank discharges simulates an ejector design, thereby allowing for a multifold increase in the total flow rate through the gallery. The test section located 13 ft (4 m) downstream into the straight section of the gallery is equipped with a 12 x 14 in (0.30 X 0.36 m) removable bottom plate. Test dust layers were formed on this plate under controlled laboratory conditions. Transducers were placed to measure the pressure inside the air tank and at four locations along the length of the gallery. Velocity probes were installed at two stations in the center of the gallery cross-section.

145

In the tests performed, the air tank discharged quite reproducibly and the process was essentially completed within 100 ms of the valve opening. Records of the static pressures inside the gallery display a rather noisy signal and an oscillatory behavior. The pressure trace recorded at the upstream transducer is characterized by a longer first positive pulse and a shorter first negative pulse than traces recorded further down the gallery. This is consistent with a pressure wave traveling downstream and reflecting from the open end. Starting with the third positive pulse, these phase delays disappear and the oscillations take the form of a standing wave of frequency consistent with an equivalent pipe length of 22 ft (6.7 m). The peak static overpressure inside the gallery was found to be approximately proportional to the air tank charge overpressure, with values as high as 1.6 psig (0.11 bar) observed for the most intense discharge. The velocities measured by the two velocity probes placed at two different locations agreed well with each other, but displayed significant noise during the injection period. An example of a filtered (280 Hz cutoff) velocity trace is shown in Fig. 11. In this test, the air tank was charged to 118 psig (8.1 bar) and instantaneous peak velocities in excess of 60 m s-l were recorded. The smooth line seen in Fig. 11 was calculated using a theoretical model (to be described elsewhere) and appears to be a reasonable representation of the mean velocities. The model prediction also agreed well with the velocity data from a test which was run with the air tank charged to 60 psig (4.1 bar). The peak static pressure rise, hp,,, correlated well with the smoothed peak velocity, U,,, through the equation: @,,=

! pa&, L

where p and a denote the density and the speed of sound, respectively. This equation can be derived using the acoustic approximation for a right running compres-

‘~~~,‘~~~1’,,,~‘~~~~‘~,~~‘~,,,‘~,~~’~~~”~~”1

.2

.3

.4

.5

.6

.7

.8

sion wave produced by a left running (reflection of the compression wave from the open end) rarefaction wave. Two types of dust layers with different critical shear stress values were tested. Cornstarch layers were deposited on the test plate in the deposition chamber under slow deposition conditions as described earlier. These layers had a nominal density of 10f 1 g me2 and their critical shear stress was measured to be 5.8 Pa. Lycopodium layers were prepared manually by sprinkling 4 g of dust on the test plate using an ordinary salt shaker and by tapping the plate on the sides to form a uniform layer of a nominal density of 37 g m-‘. The critical shear stress for these layers was measured to be 0.2-0.3 Pa in the laboratory lift-off apparatus. Tests were performed at various air tank charge pressures. After the air blast exposure, the mass of the remaining layer was measured and the entrained mass fraction was calculated. High-speed movie records showed no evidence of surface creep. Small amounts of dust deposits were observed to accumulate downstream of the test plate, probably indicating deposition of entrained particles. The fraction of dust removed during the tests in this series is plotted against the peak smoothed velocity in Fig. 12. Considering the fact that Lycopodium layers were approximately four times denser than the cornstarch layers, the Lycopodium layers appear to be much more easily entrained when compared to the cornstarch layers. The tests with cornstarch layers at higher peak flow velocities show that, in this region, increases in the peak flow velocity provide only a slight gain in the fraction of dust removed. This is partially due to imperfect flatness of the test plate. It was found that at small and intermediate dust removal fractions, dust was always removed in certain areas of the test plate. Two of the dust entrainment tests (one for cornstarch, one for Lycopodium) were recorded on high-speed (500 frames per s) movies viewing a 4-ft (1.2 m) length of

0 .Q

1

TIME (Seconds)

Fig. 11. Measured and calculated flow velocity in the 20-ft (6m) gallery under simulated explosion conditions.

5

10

15

Peak

20

Velocity

25

30

35

40

(m/s)

Fig. 12. Dust entrainment as a function of peak flow velocity from tests in the 24%ft(6-m) gallery under simulated explosion conditions.

146

the gallery. The film was examined to determine the beginning and the end of the dust entrainment from the plate. The latter was more difficult to assess. In both tests, entrained dust was confined to the lowest l/8 (approximately 1.5 in, 38 mm) of the gallery crosssection, within the field of view of the camera. Towards the end of the Lycopodium test, dust eddies reaching as high as 3 in (76 mm) from the gallery floor were noted. In the test with cornstarch, performed with the air tank charged up to 60 psig (4.1 bar), the first dust pickup was observed to occur at about the time at which the gas velocity reached its maximum (25 m s-l). Entrainment from the dust layer terminated when the flow velocity had dropped only to 18 m s-l. In the test with Lycopodium, the air tank was charged to 40 psig (2.8 bar). The first pickup occurred when the flow velocity was around 17 m s-l. The dust entrainment continued for 650-800 ms into the transient, when the flow velocity had dropped to 5-6 m s-l. These data indicate that a correlation of percent dust removed with the peak flow velocity as shown in Fig. 12 would tend to make the difference in the entrainability of cornstarch and Lycopodium layers appear to be less than it should, since the density of the Lycopodium layer was four times greater. Because of this, the flow velocity corresponding to the time at which dust entrainment has stopped may be a better measure of entrainability. These values are also shown in Fig. 12 for the two tests for which high-speed movies were analyzed. Assuming a fully developed flow, in a duct lined with galvanized steel, the shear stresses corresponding to these velocities can be calculated to be 0.87 Pa for the cornstarch layer and 0.077 to 0.11 Pa for the Lycopodium layer. These values are lower than the critical shear stresses of 5.8 and 0.2-0.3 measured in the laboratory lift-off apparatus, respectively, for the same two layers. The large difference in the case of the cornstarch layer can be attributed to the fact that the flow was not fully developed when the dust entrainment ceased, which was very early in the transient. In the Lycopodium test, the flow was close to being fully developed, and the discrepancy is significantly smaller. Part of the residual difference in this case may be explained by the fact that the shear stress required to maintain entrainment is less than that required to initiate it. For example, it has been found [16] that the ratio of these two shear stresses is 64% for desert sand. Pressure fluctuations observed in the experiments and mechanical vibrations induced by the air tank discharge could also be partly responsible for the discrepancy in the critical shear stress. These comparisons show that work is still needed before dust dispersibility data from laboratory

tests and results from dust entrainment experiments under actual or simulated conditions can be unified.

Explosion propagation in elongated structures Propagation tests in 20- and SO-jIgalleries The test program described in [l, 21 was undertaken to investigate the following technical issues relating to propagation of dust explosions in elongated structures: 1) what is the minimum amount of fuel on the floor of a gallery which is required to support flame propagation; and 2) can vents be effective in reducing explosion overpressures and in preventing flame propagation. Tests were carried out with cornstarch in the model gallery described in the previous section (20-ft long (6.1 m) and 1 by 1 ft in cross-section (0.3 by 0.3 m)) and in a large-scale facility, SO-ft long (24.4 m) and 8 by 8 ft in cross-section (2.4 by 2.4 m). Both facilities had one end open, and the other end connected to a chamber where a cornstarch dust explosion provided the initiating event. A uniform dust layer was laid on the gallery floor in controlled amounts to simulate different levels of dust accumulation. To study the effect of turbulence enhancing mechanisms, tests were performed both with and without obstacles in the two galleries. The testing in the model gallery produced pressures as high as 13.4 psig (0.92 bar) and flame velocities up to 160 m s-l. In these tests, the presence of dust on the gallery floor was found to enhance the severity of the explosion. In the large-scale gallery, explosion pressures reached peak values of 5.3 psig (0.37 bar), but were more typically in the range 2-3 psig (0.14-0.21 bar). Flame velocities of 50-90 m s-l were observed in these tests. The relatively low pressures developed in the large-scale tests are attributable to the use of a weak dust dispersion source for the primary explosion. With no obstacles in the gallery, the presence of dust on the gallery floor made a negligible contribution to the severity of the explosion in the 80-ft gallery. Concerns for the structural integrity of this test facility advised against performing tests with blockages and fuel on the floor of the unvented gallery. To interpret the test results, a criterion for flame propagation through the length of the gallery was first established based on the measured level of radiant energy ahead of the flame front. It was found that flame propagation could be achieved at nominal dust loadings as low as 75-100 g mm3. In the absence of obstacles, the dust entrained from the floor was observed to remain confined roughly to the bottom one third of the gallery height. Obstacles, on the other hand, had the clear effect of dramatically enhancing the vertical

147

mixing, thereby filling the entire gallery cross-section with dust shortly after entrainment. While effective at reducing overpressures, venting along the gallery roof was not successful at preventing flame propagation. Due to the limitations of these experiments, it is difficult to generalize their conclusions. The value of minimum dust loading for flame propagation, for example,‘may have been affected by the short length of the test gallery preventing full development of the secondary explosion front before it reached the open end. For the same reason, the information that was collected on the amount of dust entrained may be difficult to use. Despite these problems, current studies of dust entrainment and modeling efforts on dust explosion propagation will provide opportunities to better understand these results. Theoretical estimates of dust entrainment rates The discussion of the results from the entrainability

tests has brought out the importance of calculating entrainment rates. Reliable methods for making estimates do not appear to be available, however. For the purpose of demonstrating the effect of the critical shear stress on the dust entrainment rates, the model proposed by Mirels [17] is used here mostly because it is based on physical reasoning. This model treats the dust entrainment in the boundary layer as a blowing effect, which reduces the wall shear stress according to the expression:

G GO

rw -=-= -Lo

ln (l+B) B

(4)

where T__~and C, are the wall shear stress and the friction coefficient in the absence of dust entrainment, while TV and Ci represent the same parameters in the presence of dust entrainment. The friction coefficient here is defined as the ratio of the surface shear stress to the free stream dynamic pressure. Its value depends on the boundary layer properties and, for turbulent flows, on the surface roughness. Although the variation of the friction coefficient with the surface roughness is well known for fully developed turbulent pipe flow, judgment would have to be used in the selection of the appropriate friction coefficient for the present application in cases where the dust layer thickness is comparable to or larger than the characteristic scale of the solid surface roughness. The non-dimensional blowing parameter, B, in eqn. (4) is defined as:

B=Z

ni”

c, p,u,

where ni”, p_, U, represent dust entrainment rate, free stream density, and velocity, respectively. The key

,/;‘,,, = 0.1 Pa j

ot 0

10

20

FREE

30

40

STREAM

50

60

VELOCITY

Fig. 13. Calculated entrainment [Taken from [8]].

70

80

90

100

(m/s)

rates based on Mirels’ model.

assumption in the model is that the entrainment rate ti” is just sufficient to reduce the surface shear to the critical value for that particular layer. In lieu of actual measurements, the model was validated [17] using a data correlation obtained for saltating desert sand to estimate the critical shear stresses. Unfortunately this correlation is applicable only to non-cohesive dusts of relatively large size (of the order of 100 pm). On the other hand, the critical shear stresses measured in the lift-off apparatus should be very suitable for this type of estimate. Dust entrainment mass fluxes calculated using eqns. (4) and (5) are plotted in Fig. 13 as a function of free stream velocity. The calculations have been carried out using two different friction coefficients, C,,= 0.0025 (lower three curves), and 0.0125 (upper three curves). These two friction coefficients are selected to bracket the wide spectrum of relative roughness to diameter ratios from 5 x 10m5, to 0.02, for completely turbulent pipe flow. As expected, the wall roughness has a significant effect on the calculated dust entrainment rates. The three curves shown for each friction coefficient were calculated for the critical shear stresses of 0.1 Pa, representing most free flowing (non-cohesive) dusts, 2 Pa typical of standard cornstarch layers, and for 8 Pa, the maximum value measured for cornstarch. It should be noted that critical shear stress values as high as 16 Pa were measured for some ‘non-standard’ oiltreated grain dust layers. It is apparent from Fig. 13 that for a given surface roughness and free stream velocity, the value of critical shear stress determines whether any dust will be entrained or not. The calculated entrainment rates demonstrate avery strong dependence on the critical shear stress. Phenomenological modeling of dust explosion propagation in elongated structures

For the purpose of describing some of the features of propagating explosions, a possible phenomenological

148

model using the type of data on dust dispersibility introduced in the preceding sections is discussed here. Consider a primary explosion (of a gas or a dust mixture) that takes place in a room vented through a long gallery laden with combustible dust deposits. For the dust particles to participate in the explosion, they must be lifted off the surface by the flow induced by the primary explosion, remain in suspension until the arrival of the flame front and attain ignition. Self-sustained flame propagation is possible only if the suspended dust concentration at the time of flame front arrival exceeds the Lower Explosibility Limit (LEL) of the dust. The vent flow not only lifts and suspends the dust particles, but it also transports them. A simple integral model can be set up to illustrate the key features of this process. The dust density pi, averaged over the gallery cross-section, varies with time, t, and distance, X, along the length of the gallery and is given by:

where rri” = entrained mass flux (Fig. 13), u =vent flow velocity, VT= settling velocity of dust particles, H= height of the gallery. The form of eqn. (6) implies that the suspended dust fills the entire cross-section of the gallery, as was observed in explosion tests with obstacles in the gallery [l]. In the tests with no obstacles discussed above, the suspended dust was confined to approximately the lower l/S of the gallery cross-section so that H in this case should be taken as the height of the suspended dust layer. For this situation, the density, pi, would represent an average value within the dust boundary layer, which is a more meaningful quantity to judge the likelihood of a self-sustaining propagation. An analytic solution of eqn. (6) can be easily obtained for the special case of constant vent flow velocity, u. In this case, assuming a fully developed flow throughout the gallery, the entrained mass flux is constant until depletion of the layer. For an unlimited supply of dust in the layer, the maximum dust concentration increases until it reaches its steady state value hSS =ni”/V, for which the dust entrainment is balanced by the settling of the particles. If the nominal dust density bN,,,,, (calculated by dividing the layer surface density by the height of the dust suspension) is greater than bSS, the maximum dust density will tend to approach the latter value and never attain bNO”. On the other hand, when ,&&,m is smaller than hSS depletion of the dust layer comes into play and the maximum dust concentration reaches PDN,,,,,, but still cannot exceed it. Near the inlet of the gallery the dust layer will deplete at time tD,= &/rh”, where n$ represents the initial layer density. At locations further down the gallery, the depletion time increases due to partial settling of

the dust entrained upstream. Therefore, eqn. (6) is coupled with the conservation the layer mass:

m”(x, t)=m”-

jni”dti

0

in this case equation for

j&x,

t>VTdt

0

An analytic solution of eqns. (6) and (7) has been derived. Calculated dust density profiles indicate that up until the time of depletion, the suspended dust concentration builds up in a uniform fashion in most of the gallery. At the inlet (developing) region, which lengthens in time, the concentration is independent of time and increases along the flow direction. After the time of depletion, the developing region is convected downstream by the flow velocity, while the dust density remains constant and uniform in the rest of the gallery. The constant density contours calculated for this constant velocity flow case and for bNO,,,/p,,sS= 0.5 are given in Fig. 14. The domain of flammable mixtures corresponding to times and locations with suspended dust densities greater than the LEL is shown by the shaded area. A self-sustained secondary explosion is possible only if the flame from the primary explosion enters this domain. The history of dust density at several stations along the gallery is given in Fig. 15. The analytic solution obtained for the postulated simple propagation process confirms the intuitive expectation that the suspended dust density, thus the likelihood and severity of a secondary explosion, should increase with increasing entrained mass flux and decreasing settling velocity. The entrained mass flux, on the other hand, is expected to increase with decreasing critical shear stress, as was discussed under Theoretical estimates of dust entrainment rates. The solution has also demonstrated that flammable dust/air mixtures are

E z 0

0

2.5

Fig. 14. Constant density contours calculated by the simplified dust entrainment and transport model.

149

Non-Dimensional

Time

(t/t&

Fig. 15. Calculated dust concentration cations along the gallery.

histories

at selected

lo-

formed beyond a certain distance from the inlet of the gallery. Therefore, if the strength of the primary explosion is insufficient to project its flame beyond this distance, a secondary explosion is not likely. Even for the continuous flow case considered here, flammable mixtures at a given point, are sustained only for a finite period of time. Therefore, timing of the flame front arrival is one of the. key factors deciding the likelihood of a secondary explosion. This timing is not only governed by the volume of the primary chamber and crosssectional’area of the gallery, but by factors such as the strength of the primary explosion, its ignition location, and the geometry of the primary chamber. As discussed in the section Turbulent flame propagation in cubical enclosures, turbulence in the primary chamber would increase the severity of the primary explosion which in turn affects the flow velocity in the gallery, the entrained mass flux, and the timing of the flame front arrival. Flow induced turbulence is also known to increase the speed at which explosions propagate in elongated structures [l]. However, its effect on the probability of a secondary explosion is not clear at the moment. If the turbulence generating obstacles are located sufficiently close to the dust boundary layer, the resulting turbulence can enhance the entrained mass flux, thus increasing the suspended dust densities. However, this type of turbulence can also increase the vertical extent of the suspended dust cloud due to improved mixing over the entire gallery height, and reduce the suspended dust density, thereby preventing the formation of a flammable mixture. This outcome was in fact observed in some of the tests reported in [l] where the value of nominal dust concentrations in the gallery was about 100 g me3. Current

work and future activities

In the presentation of the results of research on dust explosion propagation, emphasis has been placed on

the importance of turbulence. In this regard, however, only background turbulence has been considered and the question of turbulence generated by the propagation process itself still remains to be addressed. In addition, the work on turbulence completed to date has been limited to gas/air mixtures. After the reported achievements in the development of velocity measurement techniques and the availability of a preliminary turbulent combustion model, the study of the effect of turbulence on the flame propagation in dust/air mixtures can now be undertaken with confidence. Experiments are being planned using cornstarch in the 1.35-m3 sphere under conditions similar to those reproduced in the tests with methane and propane. Extension of the model to the case of dust combustion will proceed in parallel. The phenomenological models of dust entrainment and explosion propagation described in the last two sections are preliminary and need further validation and necessary refinements. These two aspects are currently receiving attention. A parallel effort is also in progress to develop a simple model for the unsteady dynamics of the flow induced by an explosion in a connected volume. While initially directed to the study of the impact of ducts on the effectiveness of explosion vents, this type of analysis is also being undertaken for application to the explosion propagation problem, where it will eventually account for the development of the flow through the gallery. The ultimate goal of FMRC research on dust explosion propagation is the development of a comprehensive methodology to assess the propensity of dusts to form explosive mixtures and to quantify explosion hazards. The dispersibility characteristics of the material are expected to define the spatial extent and the concentration in dust clouds that can be generated during handling of the material. In addition to these properties, details of the geometry involved are important in defining the magnitude and duration of the fluid dynamic disturbance produced by an explosion, relative to the advancement of the flame front. These details need to be considered in situations where the achievement of flame propagation depends on accurate timing between the formation of the dust/air mixture and availability of an ignition source. A practical situation of interest is where the fuel loading is not the same over different portions of a gallery. The issue here is how long and how clean a section of the gallery should be in order to prevent explosion propagation. The techniques under current development are applicable to somewhat idealized situations. Actual engineering problems are likely to include complexities that are beyond the reach of these simpler models. A more detailed description of the geometry, for example, will almost certainly be necessary, forcing the use of advanced numerical techniques and number-crunching power. Prior to this step, however, the sub-models

150

handling the physical processes will have been tested by validation against experiment, for the kinds of simpler

the FMRC Test Center have contributed aspects of the work described here.

to various

situations where geometric complexities are not present. List of symbols Conclusions

The research presented in this paper summarizes the progress to date and future plans of FMRC activities directed to the problem of dust explosion propagation. The effect of turbulence on the rate of flame propagation has been studied for the case of flammable gas mixtures subjected to the kind of turbulence environment reproduced in dust explosion testing. The same type of detailed study is about to begin using dust/air mixtures. These results will eventually be extended to account for the case where the turbulence is not introduced externally, but is generated by the interaction between the expanding flow and solid boundaries. Two laboratory techniques have been developed to characterize the dispersibility of dusts through measurements of the settling velocity of a dust cloud and the entrainment threshold of a dust layer. Preliminary testing has also been carried out in a 20-ft (6.1-m) long gallery to study the dust entrainment process under simulated explosion conditions. These experimental efforts are being supplemented by the development of a phenomenological model of dust explosion propagation that simulates the response of the dust to the unsteady flow generated by explosions. This approach to the modeling of dust explosjon propagation is necessary to understand the important processes involved and to develop means to tackle simple problems. However, the reality presented by actual engineering situations is such that refinements to the current approach may be necessary in order to handle the complications introduced by real geometries. Use of advanced numerical techniques may be in order at the point where the study of simpler cases has generated sufficient confidence in the fundamental soundness of the physical sub-models.

G H

KG

m” ni” P t U

u U t.eq

V

VT x

speed of sound, m s-l nondimensional blowing parameter (defined by eqn. (5)), friction coefficient, height of the gallery, m normalized maximum rate of pressure rise in a confined gas explosion (defined by eqn. (2)), bar m s-l same as KG, but for a dust explosion, bar m s-l dust layer density (mass per unit area), kg m -2 dust entrainment mass flux, kg rnp2 s-l pressure, Pa time, s vent flow velocity, m s- ’ gas m s-’ equivalent turbulent burning velocity, s-’ volume, m3 of dust m s-’ distance from the inlet of m

Greek letters

4P7AP P PD

pressure gas suspended shear

density

Subscripts

maximum 0

in parameters initial

absence free

dust

References

Acknowledgements

F. Also F. 4-8, F.

Most of the work described in this paper has been carried out as part of an internally-sponsored, longrange research program on explosions. The authors gladly acknowledge the support of Factory Mutual Research Corporation (FMRC), and the guidance and encouragement provided by Bob Zalosh and Cheng Yao. Members of the Explosion Section of FMRC Fire and Explosion Research Department (Jeff Chaffee, Richard Jambor and Robert Monti) and personnel from

F. PlantlOperations 9, 1990, 52-60. Tamanini J. Chaffee, Symp. on The Institute, PA, pp. Orleans, July 1990. Tamanini, Tech. J. OQ2E4.m 1990. A. FMRC Rep. I. April E. Ural, Int. Dynamics Explosions Reactive Ann MI, 24-28, AL4A Aeronaut. 132 73.

FMRC Rep. I. Fire Explosion Ninth Meeting,

and April

L.

July Report

FMRC

France, Rep.

I.

151 9 ASTM El22688, Am. Sot. Test. Mater., Philadelphia, PA, USA. 10 NFPA68, National Fire Protection Association, Quincy, MA, USA, 1988. 11 W. Bartknecht, DustExplosions - Course, Prevention, Protection, Springer-Verlag, Berlin, 1989. 12 R. Burke, FMRC Tech. Rep. J. I. OQ2El.RK; May 1988. 13 P. R. Amyotte, S. Chippett and M. J. Pegg, Prog. Energy Cornbust. SC& 14 (1989) 293.

14 Y. K. Pu, J. Jarosinski, V. G. Johnson and C. W. Kauffman, Twenty-Third Symp. (Znt.) Combust., The Combustion Institute, Pittsburgh, PA, 1990, pp. 843-849. Orleans, France, July 22-27, 1990. 15 J. Nagy, J. W. Conn and H. C. Verakis, Explosion Development in a Spherical Vessel, US Bureau of Mines, R. I. No. 7279, 1969. 16 R. A. Bagnold, The Physics of Blown Sands and Desert Dunes, Methuen, London, 1941. 17 H. Mirels, ‘Blowing Model for Turbulent Boundary-Layer Dust Ingestion,’ AIAA J., 22 (1984) 1582.