Quantifying the Effect of Strong Ignition Sources on Particle Preconditioning and Distribution in the 20-L Chamber

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1 Chris T. CLONEY a,b, Robert C. RIPLEY b, Paul R. AMYOTTE a & Faisal I. KHAN c a Process Engineering & Applied Science, Dalhousie University, Halifax, NS, Canada b Martec Ltd., Lloyd's Register, Halifax, NS, Canada c Process Engineering, Memorial University, St. John s, NL, Canada Quantifying the Effect of Strong Ignition Sources on Particle Preconditioning and Distribution in the 20-L Chamber Computational fluid dynamics is used to investigate the preconditioning aspect of overdriving in dust explosion testing. The results show that preconditioning alters both the particle temperature and concentration prior to flame propagation in the 20-L chamber. A parametric study gives the fluid pressure and temperature, and particle temperature and concentration at an assumed flame kernel development time (10 ms) for varying ignitor size and particle diameter. For the 10 kj ignitor with 50 % efficiency, particles under 50 μm reach 400 K and may melt prior to flame propagation. Gases from the ignitor detonation displace the dust from the center of the chamber and may increase local particle concentration up to two times the nominal value being tested. These effects have important implications for explosive testing of dusts in the 20-L chamber and comparing 20-L data to results from larger 1-m 3 testing, where these effects may be negligible. 1. INTRODUCTION The large energy release from chemical ignitors in explosion testing can overdrive the system and alter measured explosion characteristics. Using computational fluid dynamics (CFD), the preconditioning aspect of overdriving is determined, thereby quantifying the fluid properties, particle temperature, and particle distribution prior to flame propagation. These results are beneficial to standardized testing, and to industry and policy makers relying on data from these techniques. Several studies spanning decades of work (Hertzberg et al. 1986, Cashdollar and Chatrathi 1992, Zhen and Leuckel 1997, Di Benedetto et al. 2011) have reported discrepancies due to ignitor overdriving between explosion parameters (P max, K St, MEC, and LOC) measured in the 20-L and 1-m 3 vessels. Many studies have divided the overdriving phenomena into two categories: preconditioning effects and ignitor induced pressure rise (Cashdollar and Chatrathi 1992, Going et al. 2000, Proust et al. 2007). Preconditioning occurs when the ignition energy changes the initial conditions of the flame propagation. Ignitor induced pressure rise is caused by the expansion of gaseous ignition products and particle reaction in the absence of flame propagation.

2 In an experimental study, the MEC of iron dust, lycopodium, RoRo93, Pittsburgh coal, and gilsonite was found to be dependent on ignitor energy in the 20-L vessel (Going et al. 2000). However, only the Pittsburgh coal and gilsonite showed ignitor size dependency in the 1-m 3 vessel and in general the decrease in MEC due to an increase in ignitor energy was much smaller at this testing scale. In a recent work, Proust et al. (2007) collected and summarized the results of several studies on various dusts, in which substantial discrepancies were found between P max and K St in the two standard testing vessels. Caution should be used when directly comparing these results as it is unclear whether particle size distribution or testing conditions were the same in the two vessels. With this in mind, it appears that preconditioning in the 20-L vessel may preheat the particles enough to change the phenomenology of the reaction during flame propagation. Some dusts that were found to be inexplosible in the 1-m 3 chamber have substantial rates of pressure rise in the 20-L vessel. An exploration of the combined effect of ignition energy and initial turbulence on dust-air and hybrid gas/dust-air lean mixtures has recently been conducted (Di Benedetto et al. 2011). They defined an explosion delay time as the combination of the ignition delay time and maximum rate of pressure rise induction time. For the lean mixtures tested, they found that in the 20-L vessel the mass-normalized rate of pressure rise is independent of ignition energy, except for its effect on the explosion delay time and secondary effect on the turbulence in the chamber at the beginning of flame propagation. It may be important to note that comparatively few dust-air results were reported when compared to gas/dustair results and that the ignition energy independence effect may be isolated to the hybrid testing condition. Although many aspects of overdriving and preconditioning have been investigated by exploring the effect on explosion parameters, few studies have focused on the actual dynamics of the ignitor energy release and the particle-fluid interaction prior to flame propagation. In the current work, CFD modeling is used to investigate the ignitor energy release and to quantify the gas and particle state prior to flame propagation. These results are specific to the individual particles being modeled, but should help explain some of the discrepancies found in experimental testing. The Chinook explosion and gas dynamics code (Martec Limited, NS, Canada) is used to model the blast resulting from the ignitor energy release and subsequent fluid interaction with polyethylene particles prior to flame propagation. A discussion of the testing and preconditioning process is given followed by a description of the numerical model setup and background theory. The numerical model is used to explore preconditioning dynamics in the 20-L and 1-m 3 vessels, including interaction of the shock and expanding ignition products with the particles, and non-equilibrium particle heating during the flame kernel

3 development time. A parametric study shows the effect of ignitor size and particle diameter on the quasi-static fluid temperature and pressure, and particle temperature and concentration in the 20-L vessel at an assumed flame kernel development time (10 ms). 2. BACKGROUND The steps in the explosion testing process are discussed with respect to overdriving and the preconditioning phenomenon is explored. A description of the 1D spherical model used to investigate preconditioning is given along with the theory and assumptions involved Explosion Testing Process The typical explosion testing process involves pneumatic dispersion of the dust, ignitor detonation after a delay time, flame kernel development, and flame propagation. A schematic detailing a typical pressure history is given in Figure 1. The time-scales shown in the figure are adapted from Di Benedetto et al. (2011) for the 20-L chamber and include time delay of the outlet valve (t d ), ignition delay time (t v ), time from ignitor detonation to flame propagation (defined here as flame kernel development time, t fd ), and flame propagation time (t p ). Similar steps with longer time-scales occur in the 1-m 3 chamber as described by Proust et al. (2007). The goal in the current work is to investigate preconditioning of the fluid-particulate system during flame kernel development, and to attempt to quantify changes from the nominal testing state prior to flame propagation. Pressure Preconditioning alters the initial state of the flame propagation P max 0 td (30-50) tv (60-120) tfd (~10) tp Time (ms) Figure 1. Schematic of the pressure history and associated time-scales involved in the 20-L explosion testing process. Preconditioning occurs during the flame kernel development time denoted by t fd.

4 Preconditioning is a complex process dependent on many variables including ignitor strength, particle diameter, and particle thermo-physical properties. A schematic showing the ignitor detonation process for an idealised spherical ignitor located at the center of the vessel is shown in Figure 2. The detonation results in expansion of the gaseous ignition products which drive a shock wave through the testing vessel. As the shock passes through the particles they are accelerated outward and heated. Behind the shock wave, the ignition products further displace particles from the center of the vessel, changing the concentration from the initial nominal value. In a very short time (on the order of hundreds of micro-seconds) the ignition products reach the maximum expansion diameter, and the shock reflects from the wall of the vessel. Several reverberation periods of shock reflection, gas expansion and contraction occur during the flame development time. Electrical Detonation Ignition Products Expansion and Blast Shock Reverberation and Kernel Development Flame Propagation and Pressure Rise IG IP S F IP S F Preconditioning Aspects: 1) Shock heating and acceleration 2) Ignition products displace and heat particles 3) Quasi-static vessel pressure and temperature increase 4) Particle heating due to nonequilibrium thermodynamic state 5) Flame propagation through preconditioned fluid and particulate phase Figure 2. Schematic showing ignitor detonation process and flame kernel development. The ignitor (IG), shock wave (S), gaseous ignition products (IP), and fireball (F) are denoted. Several aspects of the ignitor detonation process may be involved in preconditioning the fluid-particulate system, some of which are listed in the bottom of Figure 2. The shock reverberation and detonation products expansion rapidly heats the fluid in the vessel causing a non-equilibrium state with the particles. The particles then exchange heat continuously until equilibrium is reached with the fluid or they are ignited by the flame Numerical Model A 1D spherical model is used to investigate the effect of ignitor preconditioning in the 20- L and 1-m 3 chambers. A schematic showing the initial conditions of the simulation and the domain decomposition is given in Figure 3. The ignitor is modeled directly after ignition as a 2 cm sphere of high density and energy gas. The mass of the ignition products is 1.2 g for a 5.0 kj ignitor (Hertzberg et al. 1986) and is scaled according to

5 energy content for other sizes (specific energy is held constant). An ignitor conversion efficiency of 50% is assumed throughout the study, except when comparing with experimentally determined values. The remainder of the testing vessel is filled with an initially quiescent cloud of polyethylene particles (500 g/m 3 ) in air at ambient conditions. D/A Dust/Air Mixture: Dust Concentration = 500 g/m 3 Pressure = 101,325 Pa Temperature = 298 K r IP (2 cm Dia.) Δr Ignition Products: Mass Specific Energy = 1.2 g (5.0 kj Ignitor) = 2083 kj/kg Figure 3. Schematic showing initial conditions and domain decomposition for the 1D spherical model. The ignition products (IP) and quiescent dust-air (D/A) mixture are denoted. A resolution of = 0.5 mm was used in both the 20-L and 1-m 3 simulations. Due to the nature of 1D models, large scale fluctuations or rotational flow in the vessel will not be captured. Furthermore, although particle momentum and heat transfer have terms which capture Reynolds number effects, turbulent fluctuations are not modeled. Both laminar and turbulent fluctuations affect particle burning and flame propagation (Amyotte et al. 1988); however, the effects may be minimal on preconditioning due to the short time-scales involved. A turbulence intensity of 1 to 5 m/s in the 20-L vessel is given by Skjold (2003) as reported by Proust et al. (2007). At 10 ms these would only produce movement up to 5 cm or less, which may have a low impact on particle movement and heating during preconditioning. It may also be important to note that the ignitor detonation is a much simplified version of the physical process. Chemical ignitors generally expand as a jet and have sparking and possible multi-point ignition (Zhen and Leuckel 1997). Both of these phenomena have been discussed for gas combustion (Cattolica and Vosen 1987, Rychter 1989) but little research has been completed for the effect on dust explosion. Although this combined with asymmetry and often using two ignitors for explosion tests make capturing the earlytime dynamics of the ignitor energy release difficult, the results section shows that the model compares well with experimentally determined pressure rise in the 20-L chamber with no dust. The transient results and particle interaction produced by the model should provide insight into the preconditioning phenomenon and a basis to further investigate non-ideal ignitor effects.

6 2.3. Numerical Theory The theoretical background, conservation equations, and associated model assumptions are given. A very good description of the assumptions involved in a similar 1D planar model for dusty shock tubes is given by Igra et al. (1987). A recent description of the current model used in the Chinook code to investigate 1D planar detonation of aluminum particle clouds is given by Zhang et al. (2009). The conservation equations are solved on the 1D finite-volume mesh using a flux-vector splitting scheme. The number density of the particles is assumed large enough such that the solid phase can be modeled as a continuum. The particles are assumed to be uniform in size and spherical in shape. The fluid phase follows the ideal gas law and conduction is not modeled. The conservation equations for the two phases include Particle Mass: ( 1 ) Fluid Mass: ( 2 ) Particle Momentum: ( 3 ) Fluid Momentum: ( 4 ) Particle Energy: ( 5 )

7 Fluid Energy: ( 6 ) where r is the radial coordinate, is the local concentration of the particulate phase (kg/m 3 ), and is the density of the fluid phase (kg/m 3 ). The subscripts and denote the particle and gas phase respectively, while is the volume fraction (-), is the velocity (m/s), is the pressure (Pa), and is the specific energy (J/kg) of the denoted phases. Two more conservation equations are required to track the number density of the particles and the concentration of fluid materials (air and ignition products are considered in the current model). Number Density: ( 7 ) Species Mass Fraction: ( 8 ) where is the number density (1/m 3 ) of the particulate phase and is the mass fraction of j th fluid material (-). The local particle concentration and number density are defined assuming spherical particles: ( 9 ) ( 10 ) where is the particle diameter (m). The summation of the volume fractions of the two phases must equal unity ( ). The source terms on the right hand side of the conservation equations govern phase momentum exchange (, N/m 3 ), heat exchange (, J/m 3 -s), particle mass transfer due to particle/gas reactions (, kg/m 3 -s), fluid mass transfer due to inter-phase gaseous

8 reactions (, kg/m 3 -s), and changes to number density due to fragmentation and agglomeration effects (, 1/m 3 -s). The momentum exchange is determined using the drag coefficient and slip-velocity between the phases, while the heat exchange is determined using the Nusselt number, thermal conductivity, and temperature difference: ( 11 ) where is the drag coefficient (-), is the particle Reynolds number (-), is the Nusselt number (-), is the fluid thermal conductivity (W/m-K), Pr is the Prandtl number (-), and is the temperature of the denoted phase. In the current work forces due to gravity, buoyancy, pressure gradients, and Basset forces are assumed negligible in the small preconditioning time-scale. Radiation is assumed negligible and the Biot number is small. Recent numerical studies have shown that the Biot number assumption is valid up to a particle diameter of a couple of micro-meters (Di Benedetto et al. 2010). The drag coefficient and Nusselt number correlations are from Gilbert et al (1995) and Drake (1961) respectively, as provided by Saito et al. (2003): ( 12 ) ( 13 ) The thermal conductivity is calculated as a function of temperature using a power law: ( 14 ) ( 15 ) where is the reference thermal conductivity, is the reference temperature, and n is the power exponent taken as W/m-K, 273 K, and 0.81, respectively. The other source terms (,, and ) are assumed to be zero in the current work. Physically this signifies that "inert particles" are being used, no reaction occurs between gaseous species in the ignition products and oxygen or nitrogen in the air, and no particle fragmentation or agglomeration is modeled. Although the particles have the material

9 properties of polyethylene particles they are made "inert" by not modeling particle reactions. This allows preconditioning to be studied in isolation from flame propagation. The solid flow is assumed dilute and the particle phase is incompressible ( = 0 and = constant). This is only a valid assumption at small particle volume fractions. The ideal gas law is used for both of the fluid materials (air and high density ignition products). A non-physical low-temperature is reported by the ideal gas equation-of-state (EOS) when the ignition products are highly expanded. However, it is only local in time and has limited effect on the quasi-static solution. A more detailed gas expansion EOS such as Jones-Wilkins-Lee (JWL) for detonation may provide a better model. Due to the Biot number assumption the temperature gradient in the particle is assumed to be negligible. The particle temperature is calculated assuming constant temperature melting, using a piece-wise function: ( 16 ) where is the particle temperature (K), is the melting temperature (K), is the latent heat of melting (J/kg), and is the specific heat of the particle phase (J/kg-K). Particle evaporation or pyrolysis is not modeled. The polyethylene material properties are based on the work of Di Benedetto et al. (2010). Melting temperature and latent heat of melting vary with specific polyethylene sample. Representative values of 400 K and 200 kj/kg were used in the current work and are similar to those given in the literature (Drobny 2005, Vasile and Pascu 2007). 3. RESULTS AND DISCUSSION The numerical model is used to investigate preconditioning dynamics in the two standard testing vessels. Ignitor detonation with no dust in the 20-L vessel is compared to experimental data, and particle and fluid preconditioning in both the 20-L and 1-m 3 vessels are explored. Several aspects such as shock-particle interaction, fluid-particle interaction, particle heating and acceleration, and other non-equilibrium effects prior to flame propagation are captured in the results. A parametric study determines the effect of ignitor size and particle diameter on the particle and fluid state prior to flame propagation in the 20-L vessel. The assumed flame kernel development time is 10 ms in the current work.

10 3.1. Ignitor Detonation With No Dust in the 20-L Chamber The ignitor detonation in the 20-L chamber with no dust was simulated using the numerical model. The overpressure and ignition products mass fraction profiles 0.1 ms after deployment of a 5.0 kj ignitor (nominal) are shown in Figure 4. The ignition products expansion drives a shockwave through the vessel, shown as a discontinuous pressure increase. The mass fraction results vary from 1.0 (100 % ignition products) to 0.0 (100 % air) and the shock wave has a peak pressure of 3.2 bar at 0.1 ms. Figure 4. Numerical results showing the shock wave (S) and ignition products (IP) expansion 0.1 ms after deployment of a 2.5 kj ignitor (5.0 kj nominal) in the 20-L chamber containing air (A) with no particles. The expansion-contraction motion of the ignition products and shockwave reverberation rapidly pressurizes and heats the fluid in the vessel. A series of simulations with different ignitor sizes are compared to experimental results (Hertzberg et al. 1986) in Figure 5. Equivalent energies (40-60 % efficiency) determined by Hertzberg et al. (1986) are the input for the ignition products. It was later expressed by Cashdollar and Chatrathi (1992) that the ignitors used in the experimental work given in Figure 5 contained paper caps and that the new plastic cap ignitors should have higher efficiencies due to less loss of explosive prior to use. For the remainder of the current work an efficiency of 50 % is assumed for all ignitor sizes. The quasi-static pressure (volume-averaged over the vessel) compares well with the experimental results suggesting that the ignitor detonation model used here is sufficient for determining the quasi-steady pressure in the vessel. The shock reverberation and expansion-contraction motion of the ignition products increases the pressure causes the transient oscillations. The periodic oscillations can be seen in the experimental 1-m 3

11 results reported by Zhen and Leuckel (1997, Figure 4) and commonly appear as noise in the 20-L vessel due to lack of time resolution. The ignition energy "release time" is normally reported as approximately 10 ms (Hertzberg et al. 1986, Going et al. 2000) but here it is assumed that 10 ms is meant to represent the time from ignitor deployment to the first increase of the explosion pressure rise curve (flame kernel development time). The actual ignition energy release time can be taken as the rise-time from Figure 5, and appears to be from approximately 0.2 to 2 ms depending on ignitor strength. Figure 5. Numerical results showing quasi-static overpressure in the 20-L chamber with no dust for different ignitor sizes. Experimental results and equivalent energy for the igniton products is taken from Hertzberg et al. (1986) Preconditioning Dynamics in the 20-L Chamber Numerical results with the same ignitor size shown in Figure 4, and with polyethylene particles ( = 500 g/m 3 ) of different diameters are shown in Figure 6. The ignition products mass fraction from the simulation with no dust is shown for reference. There is very little change in the mass fraction profile due to the addition of dust this early in the energy release. The shock wave heats and accelerates the particles outward. The degree of heating appears to be largely influenced by the particle diameter. The expansion of the ignition products compresses the particles and displaces them from the center of the vessel changing the concentration from the nominal value. An interesting aspect is that the ignition products appear to fully displace the smallest particles, but the inertia of the larger particles cause a portion them to remain in the ignition products.

12 Very small particles such as nano-powders are likely to be in mechanical and thermal equilibrium with the fluid. Due to the increase in reactivity at this scale the particles may ignite due to shock heating prior to flame propagation. On the other hand larger particles may be trapped inside the ignition products and burn with the hot gases from the ignitor reaction prior to flame propagation. Both of these phenomena would lead to ignitor driven pressure rise and are different facets of overdriving than preconditioning. Figure 6. Numerical results showing polyethylene particle concentration (left) and temperature (right) of three particle sizes 0.1 ms after ignitor detonation in the 20-L chamber with a 2.5 kj ignitor (5.0 kj nominal). An initial particle concentration of 500 g/m 3 is modeled. The shock reverberation and expansion-contraction motion of the ignition products rapidly heat the fluid causing a non-equilibrium state with the particles. The transient fluid and particle temperature increase is shown in Figure 7 for different particle and ignitor sizes. The particle heating has a double effect of increasing the particle temperature, but also of decreasing the temperature of the fluid. The particles are continually heated until they reach equilibrium with the fluid or they react due to flame propagation (not modeled here). These results suggest that for small particles which reach equilibrium with the fluid, preconditioning heating will terminate prior to flame propagation. For larger particles the flame propagation may occur during a dynamic state in which the particle temperature is still increasing. Since the flame propagation takes a finite interval of time and may further compress and heat the particles, the dust which is consumed later in the explosion test may be hotter than during the early flame propagation. This effect may change the phenomenology of the reaction during the later times and lead to an acceleration effect during the flame propagation.

13 Figure 7. Numerical results showing non-equilibrium quasi-static fluid and polyethylene particle temperature for two particle sizes. Both are modeled with a 2.5 kj ignitor (5.0 kj nominal) and a 1.25 kj ignitor (2.5 kj nominal) Preconditioning Dynamics in the 1-m 3 Chamber Due to the size of the 1-m 3 chamber and mass of dust relative to the ignitor energy, preconditioning should not be as important as in the 20-L chamber. Numerical results showing the effect of a 10.0 kj ignitor (nominal) in the 1-m 3 chamber are shown in Figure 8. Particle concentration profiles at selected times after ignitor deployment are shown for small particles (10 μm) and the quasi-static fluid and particle temperature is shown for large particles (100 μm). The ignitor products still displace the dust from the center of the chamber, but the change from the nominal concentration is much less than in the 20-L vessel. Since the energy release of the ignitor is small compared to the size of the chamber, the increase in quasi-static temperature of the fluid is only 0.6 K, and has little effect on the quasi-static particle temperature. The temperature oscillations are weaker and have a lower frequency as the shock must transverse a farther distance in the 1-m 3 chamber. Several reasons exist for the reduction of preconditioning effects in the 1-m 3 chamber. The mass and energy release of the ignitor is small relative to the mass of dust and fluidparticle energy in the vessel. Furthermore, the shock from the ignitor detonation decays exponentially in space and shock heating does not contribute to particle heating far away from the vessel center. It is interesting to note that the experimental results of Going et al. (2000) show that Pittsburgh coal and Gilsonite have an ignition energy dependence in the 1-m 3 chamber. These numerical results suggest that in their case the dependence is not due to preconditioning effects, but other aspects of overdriving such as ignitor induced particle reaction.

14 Figure 8. Numerical results showing polyethylene particle concentration at selected times for 10 μm particles (left) and quasi-static polyethylene particle and fluid temperature for 100 μm particles (right), in the 1-m 3 vessel with a 5.0 kj ignitor (10.0 kj Nominal) Parametric Study Preconditioning in the 20-L chamber is further studied by determining the effect of particle size and ignitor strength on the quasi-static fluid temperature and pressure, and particle temperature and concentration at a representative flame kernel development time. These results should give an indication of the state of the fluid-particle system at the start of flame propagation. The pressure and temperature of the fluid phase at the 10 ms flame development time are given in Figure 9. In general larger ignitors increase the temperature and pressure of the fluid more than smaller ignitors. Since the smaller particles heat up faster they remove more energy from the fluid reducing its temperature and pressure. The preconditioning pressure increase is sometimes used as an offset for the measured P max during dust explosion testing. However, to the authors' knowledge the pressure has not been determined to be a function of both the ignitor strength and particle size. The changes in fluid pressure and temperature may also have important implications for hybrid gas/dust explosion testing. It may be important to note that the flame development time may not be the same under these conditions. The particle temperature is plotted for particle diameters from 10 to 500 μm and nominal ignition energies from 1 kj to 10 kj in Figure 10. In general the particle temperature increases with increasing ignitor size and decreasing particle diameter. The effect seems to level out at lower particle diameters, suggesting that a lower limit applies. This limit may be the diameter at which the particles reach equilibrium with the fluid prior to 10 ms.

15 Figure 9. Effect of polyethylene particle diameter and ignitor size on fluid pressure and temperature in the 20-L chamber at a 10 ms flame kernel development time. Figure 10. Particle temperature at a flame kernel development time of 10 ms for varying particle size and ignition energy. The horizontal dashed line shows the polyethylene particle melting temperature and the vertical dashed line separates the combinations in which the particles are in thermal equilibrium (within 10 K) with the fluid during flame propagation. In general the increase in average particle temperature is significant and may change the limiting combustion step of the particles and the overall phenomenology of the flame propagation. For the largest ignitor tested (10 kj nominal) the majority of the particles in the vessel may be in a fully or partially melted state during flame propagation. This could have important implications for metallic powders as melting the oxide layer of the particles could greatly enhance the reaction with the bare metal underneath. For fibrous

16 particles or plastics the effect may be reversed and agglomeration of the melted particles may reduce testing explosion likelihood and severity. Quantifying the particle concentration at the 10 ms flame development time is difficult as the particles are not evenly distributed throughout the vessel. Also, for the larger ignition energy local numerical instabilities in the particle concentration are found due to the high speed solver having difficulties calculating the near static flow, and the Euler particle phase interaction with the solution boundaries. Because of these issues, a more qualitative approach to reporting the effect of ignition energy and particle diameter on concentration is given in Figure 11. Under this system the ignitor strength-particle size combinations are given a ranking from N (particle concentration fluctuates around the nominal value at 10 ms) to 2X (concentration is two times the nominal value in the outer portion of the vessel). S denotes that particles are displaced from the center of the vessel but only a small change from the nominal concentration is found throughout. Figure 11. Qualitative representation of the particle concentration at a 10 ms flame development time (left) and particle concentration profiles for 10 μm particles (right) for varying ignition energies and example qualitative ratings. N denotes that the concentration fluctuates close to the nominal value throughout the vessel and S that a portion of the particles are displaced from the vessel center. The other notations are used to describe the approximate increase in particle concentration from the nominal value (i.e. 2X denotes that the concentration reaches two times the nominal value at the exterior portion of the vessel). Example value assignments are shown in the right side of Figure 11 for 10 μm particles. Although this method depends on a somewhat subjective judgment by the authors, the results still show that in the 1D spherical model large ignitors can greatly change the particle concentration from its nominal value. More research in this area with a

17 quantitative method of measurement and determining multi-dimensional effects may further increase the understanding of the effect of large ignitors on the initial particle concentration during flame propagation. The qualitative results show that the concentration of dust particles can be altered from the nominal dust loading even for small ignitors such as those used in explosibility testing. Results such as those presented by Going et al. (2000) in which MEC is dependent on ignitor size, may be partially explained by the particles being displaced from the center of the vessel. If larger ignitors have more of a tendency to displace the particles than smaller ones, smaller nominal amounts of dust will be required to achieve the actual explosible concentration in the outer section of the vessel, and a lower MEC value may be recorded. 4. CONCLUSION Computational fluid dynamics was used to investigate the preconditioning aspect of ignitor overdriving in the 20-L and 1-m 3 explosion testing vessels and to quantify the fluid-particle state prior to flame propagation. A 1D spherical model was developed and showed that preconditioning may significantly alter the testing condition in the 20-L chamber with polyethylene particles, but may be negligible in the 1-m 3 vessel. The dynamics of the ignitor energy release were investigated showing that many factors may lead to preconditioning effects including shock heating and acceleration, interaction with the expanding products from the ignitor detonation, and non-equilibrium heating by the fluid. The ignition energy is dispersed throughout the vessel increasing the temperature of the fluid in approximately 0.2 to 2 ms, depending on ignitor size. The fluid then heats the particles until thermal equilibrium is reached or they ignite due to flame propagation. The results indicate that equilibrium may be reached for smaller particles, but for larger particles the temperature may still be increasing due to fluid heating during flame propagation. A parametric study determined the effect of ignitor size and particle diameter on the fluid pressure and temperature, and particle temperature and concentration, in the 20-L vessel at a 10 ms flame development time. The particle temperature varies widely depending on ignitor size and particle diameter. With the 10 kj ignitor the majority of particles may be partially or fully melted. This may have important implications for metallic powders or fibrous and plastic dusts. The expanding ignition products may alter the nominal dust loading concentration during flame propagation. As the size of the ignitor increases more dust is displaced from the center of the vessel. This could cause the MEC to decrease as less dust is required to reach an explosible concentration at the outer portion of the vessel during flame propagation.

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