Explosion of micro particles - CFD modeling as a tool to characterize the relevant parameters of the dust dispersion

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(1)EXPLOSION OF MICRO PARTICLES: CFD MODELING AS A TOOL TO CHARACTERIZE THE RELEVANT PARAMETERS OF THE DUST DISPERSION. Carlos Hernando Murillo Rueda. Universidad de los Andes Faculty of Engineering, Department of Chemical Engineering Bogotá D.C., Colombia 2012.

(2) EXPLOSION OF MICRO PARTICLES: CFD MODELING AS A TOOL TO CHARACTERIZE THE RELEVANT PARAMETERS OF THE DUST DISPERSION. Carlos Hernando Murillo Rueda. Thesis for the Degree of Master of Engineering. Presented to: Felipe Muñoz Giraldo, PhD. Universidad de los Andes Faculty of Engineering, Department of Chemical Engineering Bogotá D.C., Colombia 2012.

(3) ACKNOWLEDGEMENTS. I would like to express my sincere gratitude to my advisor Prof. Felipe Muñoz Giraldo for the continuous support during this research project, for his patience, motivation, enthusiasm, and immense knowledge. His guidance helped me in all the time of research and writing of this thesis. Besides my advisor, I would like to thank Prof. Omar López, for his collaboration which was determinant for comprehension of basic concepts of computational fluid dynamics. This study has also been developed in collaboration with PhD Alexis Vignes in representation of the National Institute of Industrial Environment and Risks (INERIS) and PhD Laurent Perrin and PhD Olivier Dufaud in representation of the National Superior College of Chemical Industries (ENSIC). The information and support provided by these institutions has been definitive for description and characterization of the operating conditions of the Hartmann tube. Their previous work has also constituted the basis for the analysis of dispersion in the Hartmann tube and its consequences over the explosivity parameters of the material. Finally, I would like to thank the undergraduate students Wilson Molina, Sergio Rodríguez and Daniel Vizcaya for helping me during different stages of this project..

(4) CONTENT. LIST OF FIGURES .................................................................................................. 1 LIST OF TABLES..................................................................................................... 2 SUMMARY............................................................................................................... 8 INTRODUCTION ..................................................................................................... 9 1.. OBJECTIVES .................................................................................................. 11. 1.1.. GENERAL OBJECTIVE ............................................................................... 11. 1.2.. SPECIFIC OBJECTIVES ............................................................................. 11. 2. COMBUSTIBLE SOLID MATERIALS .............................................................. 12 2.1.. CHARACTERISTICS OF DUST EXPLOSIONS........................................... 12. 2.2. FLAMMABILITY PARAMETERS FOR CHARATERIZATION OF SOLID MATERIALS........................................................................................................... 15 2.3. STANDARDIZED EQUIPMENT FOR DETERMINATION OF FLAMMABILITY PARAMETERS ........................................................................... 18 2.3.1.. Modified Hartmann tube............................................................................ 18. 2.3.2.. 20 liter sphere ........................................................................................... 20. 2.3.3.. Godwert-Greenwald furnace ..................................................................... 22. 2.3.4.. Normalized hot plaque .............................................................................. 24. 3. BASIC CONCEPTS ABOUT GAS-SOLID FLOWS OF COMBUSTIBLE DUSTS 25 3.1. CLASSIFICATION OF THE INTERPARTICLE FORCES OF THE SOLID AGGREGATES. ..................................................................................................... 27 3.1.1.. Van der Waals forces................................................................................ 28. 3.1.2.. Electrostatic forces.................................................................................... 29. 3.1.3.. Magnetic forces ........................................................................................ 29. 3.1.4.. Capillary forces ......................................................................................... 30.

(5) 3.1.5.. Mechanical forces ..................................................................................... 31. 3.2. DESCRIPTION OF HYDRODYNAMIC STRESSES EXERTED BY THE CONTINOUS PHASE ON THE PARTICLES SURFACES .................................... 31 3.2.1.. Inertia stress ( ) ...................................................................................... 31. 3.2.2.. Rotary stress (. 3.2.3.. Turbulent stresses (. ) ..................................................................................... 32 ) ............................................................................. 33. 3.3. CRITERIA FOR FRAGMENTATION OF SOLID PARTICLES AGGREGATES. ..................................................................................................... 34 4. EXPERIMENTAL ANALYSIS FOR DESCRIPTION OF GAS-SOLID FLOW INSIDE THE HARTMANN TUBE ........................................................................... 36 4.1.. EXPERIMENTAL DETERMINATION OF PARTICLE SIZE DISTRIBUTIONS 38. 4.1.1. Determination of the granulometry of the solid phase with the Fraunhofer’s theory. 40 4.2.. EXPERIMENTAL METHODOLOGY ............................................................ 40. 4.3.. ALUMINUM AGGREGATES (PARTICLES BELOW 125 MICROMETERS) 41. 5. COMPUTATIONAL FLUID DYNAMICS FOR CHARACTERIZATION OF THE RELEVANT PARAMETERS OF THE DUST DISPERSION .................................. 45 5.1. DESCRIPTION OF GAS-SOLID FLOWS BY SIMULATIONS BASED ON COMPUTATIONAL FLUID DYNAMICS ................................................................. 46 5.1.1.. Reynolds Averaged Navier-Stokes Equations for fluid flow ...................... 47. 5.1.2.. Reynolds Stress Model for description of turbulence. ............................... 50. 5.1.3.. Lagrangian approach for solid particles tracking. ...................................... 52. 5.1.4.. Equations for breakup model included in particles fragmentation. ............ 53. 5.2. APPROACH DEFINED FOR THE CFD SIMULATION FOR THE BIPHASIC FLOW DESCRIPTION ........................................................................................... 54 5.2.1.. Characterization of the flow domain .......................................................... 55. 5.2.2.. Description of the boundary and initial conditions. .................................... 57. 5.2.3.. Description of dispersion through the CFD simulation .............................. 61. 5.3.. FRAGMENTATION OF MICROMETRIC ALUMINUM PARTICLES............. 64.

(6) 6.. CONCLUSIONS .............................................................................................. 66. 7. RECOMMENDATIONS ................................................................................... 67 8.. REFERENCES ................................................................................................ 68.

(7) LIST OF FIGURES Figure 1. Explosion pentagon of combustible solids .............................................. 13 Figure 2. Model for the moving flame front during a closed vessel deflagration with a burning zone of finite thickness ........................................................................... 17 Figure 3. Modified Hartmann tube (MIKE III)......................................................... 19 Figure 4. 20 liter sphere ......................................................................................... 20 Figure 5. Typical pressure versus time data obtained for a gas explosion inside the 20 liters sphere ...................................................................................................... 22 Figure 6. Godwert-Greenwald furnace ................................................................... 23 Figure 7. Scheme of the hot plaque ....................................................................... 24 Figure 8. Inertia stress caused by acceleration and changes in the flow direction. ............................................................................................................................... 32 Figure 9. Rotary stress originated by the velocity gradient in the dispersion flow .. 33 Figure 10. Turbulent stresses induced vortices in the dispersion flow ................... 33 Figure 11. Experimental setup developed for characterization of solids dispersion. ............................................................................................................................... 37 Figure 12. HELOS-R granulometer’s scheme ........................................................ 39 Figure 13. Initial particle size distribution of glass particles used in the experimental analysis. ........................................................................................... 42 Figure 14. Micrometric aluminum dispersion inside the modified Hartmann tube. . 44 Figure 15. Comparison of required simulation time for analysis of dispersion of rigid particles ................................................................................................................. 49 Figure 16. Description of the flow domain .............................................................. 56 Figure 17. Mesh grid established for numerical solution of averaged Navier-Stokes equations by the finite volume method. .................................................................. 56 Figure 18. Boundary conditions defined for the CFD simulation ........................... 58 Figure 19. Velocity magnitudes at different heights of the tube at 30 ms. .............. 62 Figure 20. Vorticity magnitude of the gas flow during the dispersion process. ....... 63 Figure 21. Mean diameter at ignition sources location during dispersion process. 64 Figure 22. Concentration profiles at different heights inside the Hartmann tube during dispersion process. The reference (0 cm) is located at the top of the dispersion nozzle. .................................................................................................. 65. 1.

(8) LIST OF TABLES Table 1. Determining factors of a dust explosion. .................................................. 14 Table 2. Technical specifications of the ignition sources used in the Hartmann tube ............................................................................................................................... 19 Table 3. Fitting parameters for the turbulent stresses in a solid particles dispersion flow ........................................................................................................................ 34 Table 4. Classification of lenses and measurement ranges of the HELOS-R granulometer. ......................................................................................................... 39 Table 5. Initial particle size distribution of glass particles used in the experimental analysis. ................................................................................................................. 42 Table 6. Mean diameter at ignition sources location during dispersion process. ... 43 Table 7. Parameters considered for the transport of Reynolds stresses with the RSM turbulence model. ......................................................................................... 51. 2.

(9) LIST OF VARIABLES. : Contact area between two surfaces [m2] : Radius in the parent parcel before aggregates fragmentation [m] : Ratio of particle pairs per unit cross-section to particle pairs per unit volume [-] : Fraction of the smaller contacting particle's surface area that is in contact with adjacent particles per contact [-] : Coordination number of solid aggregates [-] : Constant defined by the wall roughness [-] : Drag coefficient defined according to the Stokes-Cunnigham equation [-] ̅ : Diameter to determine the order of magnitude of the average size of the sample [μm] : Particle´s diameter [m] : Aggregate’s diameter [m] ∆ : Differential normal distance from the tube walls [m] : Void fraction in solids aggregates [-] : Inter-particle force per unit contact area [N] : Brownian force components [N] : Force between particles per contact unit [N] : Electrostatic force between the particles and the disperse liquid [N] : Drag force coefficient [s−1] : Electrostatic force between two particles [N] : Magnetic force between the particles [N]. 3.

(10) , ,. : Van der Waals force between two spheres [N] : Van der Waals force between two flat surfaces [N]. : Additional body forces exerted on the particle [m·s−2] : Intensity of the magnetic field [T] : Hamaker constant [J] : Turbulence intensity [%] : Kinetic turbulent energy of the continuous phase [m2·s−2] : Boltzmann constant [m2·kg·s-2·K-1] : Deflagration index [St] : Relevant dimension in the pipeline [m] : Kolmogorov’s length scale [m] ℓ: Turbulent length scale [m] : Mach number [-] : Dispersion level of the analyzed sample [-] : Ohnesorge number [-] : Gas pressure [Pa] : Initial pressure of the air injection in the Hartmann tube [barg] : Turbulent Prandtl number [-] : Gas static pressure [Pa] : Number of atoms per cubic centimeter in the two interacting particles [cm-3] : Radius of the new formed particle after aggregates fragmentation [m]. : Reynolds number defined according to the aggregates diameter [-]. 4.

(11) : Reynolds number defined according to the particles diameter [-] : Effective mean surface area per particle [m2] ,. : Spectral intensity [-]. : Velocity of the front flame due to the expansion of the burnt mixture [m·s−1] : Velocity of the front flame due to the change in the number of gas molecules by the conversion of unburnt into burnt mixture [m·s−1] : Burning velocity of solid particles inside the 20 liters sphere [m·s−1] : Gas temperature [K] : Taylor number [-] : Time elapsed until the activation of the ignition sources of the Hartmann tube [s] : Contact potential difference between two surfaces [V] : Gas velocity [m·s−1] : Particle velocity [m·s−1] : Mean velocity of the gas flow [m·s−1] : Gas velocity at a differential normal distance from the tube walls [m·s−1] : Gas velocity near the Hartmann tube walls [m·s−1] : Gas the friction velocity [m·s−1] : Mean volume per particle [m3] : Relative velocity between the gas flow and the particle [m·s−1] : Volume of the 20 liters sphere [m3] : Weber number [-] : Mass fraction of the sample that is larger than a given particle size [-]. 5.

(12) Greek letters : Angle of contact between the solid and the liquid [rad] : Gas expansion coefficient [Pa] : Heat capacity ratio of the gas [-] ̅ : Diameter to determine the order of magnitude of the average size of the sample [m] δ. : Flame thickness of particles combustion [m] : Kronecker delta function [-]. : Permittivity of the air [F·m−1] : Adjustment variable for directions of velocity perturbations [-] : Particle’s combustion time [s] : Von Kármán constant [-] : Volumetric magnetic susceptibility of the medium [A·m−1] : Volumetric magnetic susceptibility of the particle [A·m−1] : Wavelength of the fastest-growing unstable surface wave on the parent particle. [m] ,. : London’s constant [-]. : Gas viscosity [Pa·s] : Turbulent gas viscosity [Pa·s] : Magnetic permeability of vacuum [H·m−1] : Kinematic viscosity of the fluid [m2·s−1] : Gas density [kg/m3] : Particle’s density [kg/m3]. 6.

(13) : Surface tension [N·m−1]. : Solid phase stress that favors particles aggregation [N·m−2] : Inertia stress exerted by the gas flow on the solid surface [N·m−2] : Rotary stress exerted by the gas flow on the solid surface [N·m−2] : Standard deviation for adjustment of air injection profile [s] : Turbulent stress exerted by the gas flow on the solid surface [N·m−2] : Breakup time of fragmentation model [s] : Shear stress on the wall [Pa] : Most unstable wave’s length [m] : Rotation vector [m] : Average rate of dissipation of turbulence kinetic energy per unit mass [W/kg]. 7.

(14) SUMMARY A descriptive study of combustible dusts clouds has been developed in order to analyze phenomena of segregation and fragmentation of solid aggregates during a typical characterization test performed on a Hartmann tube. This apparatus, which is designed for determination of specific flammability parameters of combustible dusts, has been described from two complementary perspectives for description of flow characteristics and discussion of their influence on variations of the particle size distribution of the solid sample, which imply an uncertainty level in evaluation of ignitability and severity of combustible dusts. An experimental overview has been performed by development of a setup designed to couple granulometric systems and a high speed camera. The results obtained during this stage of the project have classified the dispersion process of aluminum micrometric particles according to the variation of mean diameter. In this order, an instability period has been evidenced during the first 40 ms of dispersion and it has been established that a stability period can be reached after 60 ms, which is a parameter suggested for dust ignition during a characterization test of this type of materials. Afterwards, the technical specifications of this equipment have been modeled with an Eulerian-Lagrangian approach in ANSYS Fluent TM in order to describe the flow conditions developed by the two phases. This study has identified the vorticity structures of the gas flow inside the dispersion tube and their influence of development of regions with high solids concentration. This analysis has also described the transient conditions associated to each phase, which, have defined a flow linked to a gulf effect at the bottom of the tube and a flat profile at higher elevations. Finally, a direct comparison has been performed to determine the validity of the posed model for description of gas-solid systems inside the Hartmann tube. The similarity in the evidenced concentration profiles of the dust clouds allows considering this approach as an important alternative for description of dispersion phenomena of combustible dusts during a flammability characterization test.. 8.

(15) INTRODUCTION The dust clouds dispersions have constituted an area of main interest in the loss prevention research due to the diverse hazards associated to facilities that handle metallic and organic solids and are exposed to different types of accidents. This fact constitutes the main aspect for the consideration of specific safety parameters to design facilities and for the implementation of protocols that provide acceptable risk levels for plants of the mentioned industries. Previous studies have established that dispersion and subsequent ignition of solids have different mechanisms and potential consequences according to the particle diameter of the aggregates present in the biphasic system. Considering this hypothesis, the focus of the research work described in this document has been directed towards the evaluation and characterization of systems composed by aggregates of micrometric particles dispersed in air. The description of the agglomeration and fragmentation mechanisms of these species will provide experimental and simulation results that will constitute the source of information required for a flammability parameters determination that takes into account the mentioned phenomena. The research work developed so far has been performed in aqueous suspensions but has not been accomplished for micrometric powders dispersed in dust clouds. This fact has posed the necessity of a descriptive model for the dispersion of combustible solids that characterizes their behavior by considering the hydrodynamic stresses exerted on the agglomerates surfaces during the gas-solid flow development. Diverse apparatus have been standardized for the determination of the ignitability and severity characteristics of combustible solids. The Hartmann tube or Mike III and the 20L sphere are commonly referenced as some of the approved setups for characterization procedures of combustible materials. For this reason, the gassolid flow, developed inside the former, was evaluated to analyze the dispersion mechanisms that constitute the main factors for variations in particle size distributions during a typical test performed with the mentioned equipment. In this context, the research work presented in this document was focused on the determination of an accurate model that implements the hydrodynamic stresses exerted over an agglomerate surface in order to analyze the influence of the technical specifications of a Hartmann tube on the uncertainty level associated to an experimental characterization of a combustible material. In addition, the results obtained in this study can be extrapolated to ideal systems (homogeneous monodisperse suspension, for instance). Additionally, this problem will be. 9.

(16) addressed by the evaluation of the behavior of the biphasic flow observed in the standard apparatus in order to link the agglomerate breakage to the turbulent hydrodynamic conditions induced by the dispersion according to the simulation and experimental data. The case study considered for this project is based on the characterization of the dispersion of aluminum micrometric particles agglomerated in a dust cloud by the consideration of the material properties and the system conditions. By the determination of a model that describes this type of biphasic systems, the influence of the transport conditions of the agglomerate particles can be determined. The reduction of the uncertainty level with the results obtained from different perspectives can provide a procedure to determine the validity of the fragmentation data obtained in the Hartman Tube and the 20 liters sphere. This analysis has been enhanced with the analysis of the influence of aluminum properties in the safety parameters that establish the probability and severity of explosions of ultrafine particles in dust clouds by the description of the dispersion process during the stages previous to the material ignition.. 10.

(17) 1. OBJECTIVES. 1.1. GENERAL OBJECTIVE Characterize the dispersion of aluminum micrometric particles agglomerated in a dust cloud considering the material properties and the system conditions. By the determination of a model that describes this type of biphasic systems, the influence of the transport conditions of the agglomerate particles can be determined.. 1.2. SPECIFIC OBJECTIVES . Develop a procedure to determine the validity of the fragmentation data obtained in the Hartman Tube and the 20 liters sphere.. . Describe the behavior of the agglomerates in a biphasic flow according to the hydrodynamic stresses exerted over their surface.. . Analyze the influence of aluminum properties in the safety parameters that establish the probability and severity of explosions of ultrafine particles dispersed in dust clouds.. 11.

(18) 2. COMBUSTIBLE SOLID MATERIALS. Dust explosions demonstrate a characteristic behavior. The accidents related to these mixtures are most common in the flour milling, grain storage, and coal mining industries. For this reason, events can be quite substantial in risk analysis performed for these processes. Previous studies performed with specialized equipment have provided valuable information about the origin and consequences of several hazards related to dust explosions. The results obtained so far are based on specific properties of the dispersed material and have been determinant in the analysis of combustible and explosive species because they have been helpful to determine specific safety parameters that can be useful for areas classification and organization of hazardous gases and dust clouds according to their degree of reactivity and the severity of events associated to their combustion.. 2.1. CHARACTERISTICS OF DUST EXPLOSIONS. The ignition of a combustible solid is defined by the association of the five elements shown in Figure 1 (Crowl & Louvar, 2002). Every flammable material must be in an atmosphere with presence of a comburant gas that allows the explosion propagation and an ignition source that provides the required energy for combustion. However, a solid substance also requires some additional aspects for the initiation of the combustion process. The material must be in suspension inside a confined environment that assures a concentration inside the explosivity limits of the material. Crowl affirmed that deflagrations caused by powder combustion are more common than detonations for dust clouds, but, the hazards associated can be significant because of the powders’ capability to generate reactions in series and affect people and structures (Crowl & Louvar, 2002). The minimal requirements to consider a dust cloud as an explosive mixture have been listed by this author.. 12.

(19) Combustible. Confineme. Suspensi. Ignition source. Oxygen. Figure 1. Explosion pentagon of combustible solids. These minimum conditions for ignition are defined by the environment conditions and some properties of the solid phase. Several studies (Cashdollar, 2000; Skjold, 2003) have discussed the influence of these variables on micrometric powders explosions. The main factors that affect the ignitability and the explosivity are summarized in the . Given the large number of reactive powders that can be handled in hazardous industries as well as the large number of possible combinations between the various influencing factors (particle size, moisture ...), it is therefore necessary to determine the characteristics of the explosion in standardized equipment (Cashdollar, 2000). The parameters used for characterization of confined explosions caused by dust clouds can be determined with the results obtained in closed vessels equipped with the instruments necessary to establish the development of the expanding wave inside the vessel.. 13.

(20) COMBUSTIBLE DUST COMBURANT SUSPENSION CONFINEMENT INFLAMMATION CONCENTRATION. PARAMETERS THAT DEPEND ON THE NATURE OF THE PROCESS. PARAMETERS THAT DEPEND ON THE COMBUSTIBLE/COMBURANT. Table 1. Determining factors of a dust explosion. (Vignes, 2008).     . Particle’s surface Particle size distribution Particle’s shape Particle’s porosity Oxide layer, fusion enthalpy, vaporization enthalpy, thermal conductivity, density, heat capacity, etc Chemical composition Heat of combustion Inert content Humidity Volatile components content.    . Initial pressure Initial temperature Thermal conductivity Density. Chemical properties.  . Chemical composition (inert, oxygen, etc.) Relative humidity. Dispersion.  . Dispersion degree Agglomeration. Hydrodynamic.   . Turbulence velocity Turbulence level Temporal and spatial distribution of turbulence. . Confinement level.      . Volume Shape Obstacles Heat losses through the walls Radical recombination on the walls Potential secondary explosions. Ignition source.   . Type (Cf. Norm EN 1127,1998) Energy (power, duration) Source location. Mixture quality.  . Spatial and temporal mixture of mass concentration Spatial and temporal mixture of particle size. Physical properties. Chemical properties. Physical properties. Confinement level Geometry Others.     . 14.

(21) 2.2. FLAMMABILITY PARAMETERS FOR CHARATERIZATION OF SOLID MATERIALS. The variations in flammability parameters attributed to distinctions in the variables mentioned above have given more importance to the procedures of characterization of combustible solids. For this reason, the analyses performed have been developed as standardized tests. The ISO 6184-1 (1985), which follows the standards of the Bureau of Mines in the United States establishes that explosive tests should be performed in a cylindrical enclosure of 1 m3, whereas the measurements can be extrapolated to an industrial scale. However, most of explosibility measurements are performed with the 20 liters sphere (Vignes, 2008). The flammability parameters discussed in this section can be considered to determine the ignitability and severity of the explosion of a given combustible solid. Matsuda affirms that sensitivity or susceptibility to dust explosion can be described by a combination of the minimum values of explosive dust concentration, oxygen concentration, minimum ignition energy (MIE) and minimum ignition temperature (MIT) (Matsuda, Yashima, Matsuda, Matsui, Miyake, & Ogawa, 2001). Among these dust explosion parameters, the committee of the Association of Powder Process Industry and Engineering has adopted the minimum explosive dust concentration (MEC) as a sensitivity index, based on the long-term investigation. These parameters will be discussed below. . Explosion limits: For most dusts, the lower explosion limit is between 20 g/m3 and 60 g/m3 and the upper explosion limit is between 2 kg/m3 and 6 kg/m3. The minimum explosive concentration (MEC) is commonly determined in normalized spheres of 20 L or 1 m3, but can also be determined with a modified Hartmann tube.. . Minimum ignition temperature (MIT): Temperature value for which the combustion reaction begins spontaneously, producing a phenomenon called autoignition. The MIT is defined as the lowest temperature of a hot surface in contact with a cloud of combustible dust or a dust layer ignites spontaneously. At this temperature, the production of heat by the chemical reaction so just exceeds the loss of heat through the walls of the system. The MIT of a dust cloud is measured using standard furnaces, which can be the vertical Godbert-Greenwald or the horizontal BAM. This parameter can also be measured with a layer of particles on standardized a hot plate.. 15.

(22) . Minimum ignition energy (MIE): Energy required for a given cloud of particles to sustain ignition and inflammation in a medium at an initial temperature Tu while the burning medium is at a final temperature Tad, the flame adiabatic temperature. The MIE depends on the specific chemical or mixture, the concentration, the system pressure and the temperature. The MIE of a dust cloud can be assessed by electrical, electrostatic and mechanical sparks. The MIE is generally determined using the standard vertical Hartmann tube (Mike III).. . Maximum overpressure (Pmax): This parameter is likely to be reached in the enclosure during the explosion. A first approach for its determination assumes that this variable is independent of the volume of the vessel. . Maximum rate of pressure increase (dP/dt)max: It indicates the robustness of an explosion. Thus the explosive behavior of different materials can be compared on a relative basis.. . Deflagration index ( /. ): It indicates the robustness of an explosion. It can be (: /. (1). Dahoe et al studied the explosion of coal in a 20 liters spherical vessel in order to determine validity of the cube-root law used for the estimation of the deflagration index (Dahoe, Zevenbergen, & Lemkowitz, 1996). This author affirmed that the flame thickness must be taken in count for the estimation of this scale-up parameter. Considering the model proposed by Dahoe for the , it is possible to interpret the mechanism of rigorous determination of explosion of the dust cloud in a deeper way. The modified cube-root law proposed by Dahoe considers the flame development inside the explosion chamber of the sphere to adjust the classification of the severity. This author states that the flame thickness (δ ) corresponds to the width of the burning zone inside the vessel. In this zone, the mixture suffers the transition from unburnt to burnt mass according to a linear relationship. The value for this length considering the burning velocity of the particles ( ) and the time required for their combustion ( ) with the following equation: (2). 16.

(23) The unburnt mixture ahead of the flame front moves with the sum of and . Hence, the flame front enters the unburnt mixture with the burning velocity , which determines the mass consumption rate and the rate of heat production and of the unburnt mixture. This scheme is represented in Figure 2. Figure 2. Model for the moving flame front during a closed vessel deflagration with a burning zone of finite thickness (Dahoe, Zevenbergen, & Lemkowitz, 1996). The flame thickness and the burning velocity are considered as key parameters in this work since they cause the maximum rate of pressure rise to occur at an earlier time than the maximum explosion pressure. These variables were related to the dust concentration, the properties of the material, the flow conditions and the thermostatic state of the cloud to obtain an equation that allows estimating the deflagration index according to the dependence of this parameter on the flame thickness, which was evidenced in the experimental results. The adjusted equation for this model is: /. Where f δ/R. (3). is of the form: (4). 17.

(24) The mechanism considered by this author provides useful information about the mechanism of expansion of the explosion wave and describes the phenomena occurring during the transport of the particles after the ignition of the combustible. Additionally, Dahoe established that maximum pressure and the maximum pressure rate can be located at indifferent points for dust explosions. The experimental results indicated that the rate reaches a top value near the end of the explosion, when a part of the flame front contacted the vessel wall while the other is still propagating inside the vessel. 2.3. STANDARDIZED EQUIPMENT FOR DETERMINATION OF FLAMMABILITY PARAMETERS The dust explosivity classification of a combustible dust can be developed with different apparatus designed to determine its ignitability and the severity of an induced explosion. The material is classed as explosive if a positive result is obtained in a qualitative test performed with one of the tests discussed in this section.. 2.3.1. Modified Hartmann tube This setup has been developed by the US Bureau of Mines to determine the minimum ignition energy (MIE), the minimum explosive concentration (MEC) of combustible dusts and gases. This apparatus consists of a vertical tube with a volume of 1,2 liters coupled with an ignition system. The ignition source installed inside the tube can be an electrode or a hot coil. Moreover, a pressure sensor can be incorporated at the top of the equipment. The methodology considers the location of a small quantity of the analyzed material (0,1 grams approximately) at the bottom of the tube. Afterwards, the sample is dispersed around the ignition source with the injection of compressed air at 7 barg.. 18.

(25) Figure 3. Modified Hartmann tube (MIKE III) (Mannan, Dust Explosibility Characteristics, 2005; Vignes, 2008). The scheme shown in Figure 3 poses the main elements that compose the standardized setup. The pressurized air is stored inside a 50 cm3 reservoir and is released during 30 ms approximately. A mushroom-shaped deflector is adapted as the injection nozzle that determines the distribution of the gas flow that allows considering a homogeneity condition for the mixture until the activation of the brass electrodes that constitute the ignition sources. The time elapsed until the ignition of the dust cloud ( ) can be adjusted to take into account the variations attributed to the material sample. Other technical specifications of the ignition electrodes are listed in Table 2: Table 2. Technical specifications of the ignition sources used in the Hartmann tube Parameter Equipment with inductance on the discharge circuit. Value L = 1mH – 2mH. Equipment without inductance on the discharge circuit. L 0,025 mH. Material of the electrode. Tungsten or stainless steel. Electrode diameter Distance between the electrodes. d = 2mm 6 mm minimum. 19.

(26) 2.3.2. 20 liter sphere The 20 l sphere test is used, like the Hartmann vertical tube, for both qualitative and quantitative determinations. The general approach taken in this scheme is to use these spheres to determine also the other explosibility characteristics. Thus, the spheres are used to determine the minimum explosive concentration and the minimum ignition energy. The analysis of the results obtained for dust clouds is similar to that used for gas explosions (Mannan, Dust Explosibility Characteristics, 2005). This apparatus was initially developed by Siwek in 1988 in order to determine the maximum pressures and the maximum rate of pressure increase, which, is used to establish the deflagration index of combustible substances according to the correlation described by Equation 1. This apparatus shown in Figure 1Figure 4 is built with stainless steel and is constituted by a spherical chamber whose volume is 20 liters. Additionally, the equipment is coupled with a cooling system that allows dissipating the heat of combustion released during the explosion of the analyzed substance by water circulation.. Figure 4. 20 liter sphere. The sphere is supported by control unit (KSEP 310) and a measurement control system (KSEP 332). A reservoir of 0,6 liters is connected to the explosion chamber and pressurized until 20 bars gauge. This recipient has a quick opening valve that 20.

(27) injects the content of the dust container during the 10 ms after the opening command. The sphere is connected to the chamber with a plaques disperser. The ignition source is composed by two pyrotechnical igniters that provide 10 kJ of total energy. These elements induce the inflammation of the material after 60 ms according to the predominant turbulence level at the ignition moment. The igniters are located at the center of the explosion chamber. Additionally two piezoelectric pressure sensors have been installed and connected to a collection data system supported by two amplifiers in order to determine the internal pressure of the equipment. This equipment provides information for determination of profiles similar to the one shown in. Figure 5, which can be used to establish the maximum pressure and the increase rate of this variable. 21.

(28) Figure 5. Typical pressure versus time data obtained for a gas explosion inside the 20 liters sphere (Crowl & Louvar, 2002). 2.3.3. Godwert-Greenwald furnace There are two types of furnaces for determinations of the MIT of a dust cloud. The vertical equipment is known as the Godwert-Greenwald furnace and the horizontal apparatus is known as the BAM (Bundes Anstalt für Materialsprüfung) furnace. The first setup is shown in Figure 6:. 22.

(29) Figure 6. Godwert-Greenwald furnace. The vertical setup is by a vertical tube coupled with an electrical heating system. The upper part of the furnace is connected to the pod containing the dust by means of a glass connection. The dust is dispersed inside the apparatus after opening an electrovalve that sets the discharge of compressed air from a reservoir. The base of the tube is open to the atmosphere. The furnace is located on a support that allows observing the lower part of the tube with an inclined mirror. The installed thermocouples have been calibrated for the range between 20°C and 1000°C, on a linear base in order to guarantee a precision of 1% for the measures above 500°C and 3% for measures below 300°C.. 23.

(30) 2.3.4. Normalized hot plaque The methods for determination of the minimum ignition temperature of a combustible dust have been listed in the norm CEI 1241-2-1. The first part of the international standard is related to determination of MIT of a dust layer located on a hot surface. It is possible to consider an inflammation of the dust layer if glow or flames appear during the test. Moreover, this test is positive if the surface temperature reaches 450°C or increases 250°C. This apparatus is represented in Figure 7. The hot plaque and the regulation device must satisfy some minimum conditions related to the uniformity and constancy of the temperature. These requirements are accomplished by calibration of the regulator and the equipment devices.. A. B. C. D. E. F. G.. Hot plaque Edge Heating filament Heating device support Heating regulation Ring to deposit of the dust Thermocouple inside the plaque that is supported by the heating regulation H. Thermocouple inside the plaque that is supported by the recorder I. Thermocouple inside the dust layer that is supported by the recorder J. Screw adjustment of the height of thermocouple K. Spring. Figure 7. Scheme of the hot plaque. 24.

(31) 3. BASIC CONCEPTS ABOUT GAS-SOLID FLOWS OF COMBUSTIBLE DUSTS. Combustion of solids materials, and especially dust explosion, is particularly influenced by the dispersion characteristics of the particles in the comburant gas. As highlighted by Echkoff (Eckhoff R. , Understanding dust explosions. The role of powder and science technology, 2009), the most important properties of the dust dispersion are : i) the particle shape, ii) the particle size distribution, iii) the agglomeration degree, iv) the dust concentration within the cloud and v) the degree of turbulence of the suspension. The influence of the last four parameters will be discussed in the present article. The effect of the particle size distribution on dust explosion has already been extensively studied (Bouillard, Vignes, Dufaud, Perrin, & Thomas, 2010) (Eckhoff R. , Prevention and mitigation of dust explosions in the process industries: A survey of recent research and development, 1996). It is generally considered that, by reducing the particle size, the dust ignitability increases as well as its explosivity (Soundararajan, Amyotte, & Pegg, 1996); (Matsuda, Yashima, Matsuda, Matsui, Miyake, & Ogawa, 2001); (Callé, Klaba, Thomas, Perrin, & Dufaud, 2005); a modification of the powder diameter having notably a strong influence on the ratelimiting step of the oxidation and on the persistence of the cloud. However, the expression “particle size” is too inaccurate and appropriate particle size characteristics should be chosen in order to represent such phenomena. Despite the fact that the volume mean diameter is often chosen for the sake of convenience and for industrial applications, it is not always the best indicator in terms of reactivity. Dust ignition being strongly linked to the presence of small particles, due for instance to the presence of powder attrition or erosion (Amyotte, Pegg, & Khan, 2009), the entire particle size distribution brings relevant information, especially the analysis of the fine tail of the distribution (Eckhoff R. , Understanding dust explosions. The role of powder and science technology, 2009). This remark is even more accurate when dealing with nanoparticles. The degree of agglomeration of the powder plays also a significant role in the dust explosion phenomenon. On the one hand, if the agglomerates are not broken by the dispersion process, they tend to behave as a large single particle of the size of the agglomerate (Eckhoff R. K., Assessment of Ignitability, Explosibility, and Related Properties of Dusts by Laboratory-Scale Tests, 2003), burning with the same combustion regime. On the other hand, for dispersion processes of higher intensities, the particle size distribution of the pure powder does not correspond to 25.

(32) the characteristics of the dust suspension. For very small particles (often below 10 µm) and especially for nanopowders, the interparticle attractive forces cannot be neglected and the agglomerate cohesive strength impacts the dust ignition. For instance, Bouillard et al (Bouillard, Vignes, Dufaud, Perrin, & Thomas, 2010) have established that the minimum ignition temperature (MIT) of carbonaceous particles suspensions decreases down to 670°C when the primary particle size decreases, but increases for particles having BET diameters of 23 and 3 nm. Indeed, this parabolic trend can be explained by the strong agglomeration level of those powders, having respectively agglomerates diameters of 23 and 10 µm. Similar behaviors have also been observed by Trunov (Mohana, Trunov, & Dreiz, 2009) in the case of aluminum nanoparticles, demonstrating that aggregates could be more easily ignited than deagglomerated nanoparticles. This effect seems to be mainly due to local self-heating of the agglomerates. In order to oxidize such powders, the amount of energy corresponding to the agglomerate cohesive strength should then be added to the minimum ignition energy of the primary particles. Eckhoff (Eckhoff R. , Understanding dust explosions. The role of powder and science technology, 2009) also proposes to consider a global dispersibility parameter related to the minimum work needed to break the interparticle bonds in order to quantify the influence of the agglomeration degree. In addition, turbulence can affect the properties of the initial dust cloud and the flame propagation. In the present work, the explosion-induced turbulence has been ignored in order to focus only on the turbulence of the initial dust cloud. Turbulence can both have a promoting effect on the dust explosivity (Eckhoff R. K., Pressure development during explosions in clouds of dusts from grain, feedstuffs and other natural organic materials, 1977) or a quenching effect on the flame kernel growth (Glarner, T., 1984). It has obviously an impact on the mixing of fuel and oxidizer, on the efficiency of the heat transfer, but also on the dust concentration distribution in the cloud as well as on the agglomeration degree of the powder. All these considerations must then be taken into account when measuring safety parameters related to dust explosion. During the 20th century, several standardization techniques have been developed in order to experimentally determine the flammability and explosivity of combustible powders. Such parameters describe the explosive behavior of the mixture and also provide useful information for facilities handling this type of materials. Among these methods, the modified Hartmann tube and the 20 liters sphere constitute the most frequently used equipment for determining quantitative parameters such as the minimum ignition energy (MIE) (IEC 1241-2-3) and the minimum explosive concentration (MEC). The 20 liters sphere also provides pressure profiles that characterize the explosion severity of a combustible cloud composed by the gas and the solid disperse phase (ISO 6184-1). However, it appears that the tests conditions set by these standards do not systematically lead to the determination of the most. 26.

(33) representative, or even the safest, parameters with regard to the industrial context (Janes, Chaineaux, Carson, & Le Lore, 2008). For instance, the ignition delay time, which is the delay between the dust dispersion into the test vessels and its ignition, is inadequate for most of the powders and even more for nanoparticles. As previously stated, the flame propagation being linked to the suspension hydrodynamics, a better knowledge of the initial suspension characteristics will enable an informed choice of the tests conditions. The aim of this work is then to study the particles suspension in a turbulent flow, which characteristics will match those encountered in our standardized equipment as for instance the 20L sphere, the modified Hartmann tube or an explosion tube designed for the study of flame propagation (Sanchirico, Di Benedetto, GarciaAgreda, & Russo, 2011). In this article, we will focus on the explosion tube. Two complementary approaches have been used. On the one hand, computational fluid dynamics (CFD) simulations have been carried out to study the hydrodynamic of such suspensions. The biphasic flow simulation will be based on an EulerLagrange approach. With regard to the high solid loading, it is compulsory to characterize the particle/particle interactions and the potential fragmentation or agglomeration, but also to take the action of the particles upon the fluid into account. On the other hand, in situ particle size measurements and high-speed video cameras have been used to validate the model by identifying the particle size distributions, the agglomeration degree and the dust concentration within the experimental setup as a function of time. This document presents an analysis that has been developed at micrometric and sub-micrometric scales to evaluate the behavior of the disperse phase in air by simulating the conditions inside the specific experimental apparatus. The latter will be briefly described as well as the micro and nanopowders used in this study. The CFD model, its assumptions, experimental validation, limitations and accuracy associated with scale analyzed will then be developed.. 3.1. CLASSIFICATION OF THE INTERPARTICLE FORCES OF THE SOLID AGGREGATES. Debrincat considered a simple description proposed by Rumpf for the agglomerates fragmentation considering their separation through a planar fracture process that produces two halves per Agglomerate (Debrincat, Solnordal, & Van Deventer, 2008). According to that proposition, Debrincat et al have developed a classification of inter-particle forces to model the behavior of the dispersed units considering the material properties and also the influence of specific aspects. 27.

(34) related to the transport fluid conditions such as the stream moisture. This categorization is briefly discussed up next:. 3.1.1. Van der Waals forces These forces are also known as dispersion or London forces and can be defined as short-range interactions associated to the instantaneous polarization of the molecules of the substances present in the solid. If two or more interacting surfaces are close enough to induce forces of this type, an electromagnetic field is formed due to the generation of electrical and magnetic polarizations. Israelachvili summarized the van der Waals forces main features as follows (Israelachvili, 1997):  These forces can be repulsive or attractive, and in general the dispersion force between two molecules or large particles doesn’t follow a simple power law.  The dispersion forces not only bring molecules together but also tend to align them. However, the effect of this orientation is weak.  The dispersion interaction of two bodies is affected by the presence of other bodies nearby. This feature is denominated the non-additivity principle of an interaction. The following equations have been proposed by Lee-Desautels (Lee-Desautels, 2005) in order to model the van der Waals forces between two spheres and two flat surfaces respectively: ,. (5). ,. (6). Where is the contact area of the two surfaces, is the particle diameter, is the Hamaker coefficient and represents the separation distance. The Hamaker coefficient depends on the London’s constant , and the number of atoms per cubic centimeter in the two interacting particles ( ): The principal difficulty for the modeling of the dispersion forces on agglomerates of solid particles lies on their arrangement and the irregular contact area. Besides, the. 28.

(35) distance between the particles can be influenced by the asperities on their surfaces. Debrincat affirms that the Hamaker constant value might be in the range between 10-21 and 10-19 J.. 3.1.2. Electrostatic forces Debrincat states that the adhesion of particles is influenced by the electrostatic forces. In some cases, these interactions don’t characterize the principal interparticle attractions, e.g., when the distances between the particles are short the values of other interactions such as the van der Waals forces increase considerably and define the interaction model established for the agglomerate. This author also refers to the work of Rumpf that proposes the following equation for the electrostatic force of attraction due to a potential difference between a sphere and a flat plate: (7) is the permittivity of the air and is the contact potential difference Where between the considered surfaces, this variable may range from 0 to 0,05 V according to the dispersed material properties. As mentioned above, these forces might be more significant if the interactions considered in the model are long-range (Debrincat, Solnordal, & Van Deventer, 2008).. 3.1.3. Magnetic forces The magnetic forces are long-range forces that must be considered when the interacting surfaces have magnetic dipole moments. These interactions let aggregates of ultra-fines in slurries remain together and can join heteroaggregations of hematite and magnetite particles if their sizes are less than 10 μm as well. If the studied material has these characteristics, the modeling of the biphasic system should include these forces in the analysis of the agglomerate system. Debrincat establishes an equation to include the parameters associated to the implementation of the magnetic interactions of the solid particles:. 29.

(36) |. |. (8). is the magnetic permeability of vacuum, is the intensity of the Where magnetic field, the gradient function of in the radial direction is defined by and and are the volumetric magnetic susceptibility of the particle and medium respectively (Debrincat, Solnordal, & Van Deventer, 2008). 3.1.4. Capillary forces If the relative humidity of the atmosphere and the hygroscopicity of the solid cause a high degree of moisture in the agglomerate, predominant capillary forces can be generated because of the water retention in the powder. The adsorbed water in equilibrium with the atmospheric humidity affects the inter-particle forces in one of two ways:  The adsorbed layers of moisture will decrease the effective separation distance between particles.  The water retained between two particles will form capillary bridges that increase the interaction forces. These results indicate the affection of the inter-particle forces according to the thickness of the moisture layers due to the reduction of the distance between the surfaces of two particles and the promotion of the van der Waals interactions and the formation of bridges that reinforce the cohesion of the units that compose the agglomerate. However, Debrincat affirms that these forces disappear at distances in range of 0,005-0,5 . The forces generated by static capillary bridges can be described by the following equation: (9) Where corresponds to the angle of contact between the solid and the liquid and defines the degree of wetting of the specified particles, the surface tension is represented by .. 30.

(37) 3.1.5. Mechanical forces Other forces that might contribute in holding the particles together can be related to friction between the particles and the interlocking of the irregular ones. These mechanical forces are defined by the contact area of the particles in the aggregate. For this reason, the principal variables that influence this type of forces are the particle size and its roughness. These forces haven’t been studied deeply due to the difficulty in the determination of the variables mentioned in this paragraph.. 3.2. DESCRIPTION OF HYDRODYNAMIC STRESSES EXERTED BY THE CONTINOUS PHASE ON THE PARTICLES SURFACES Previous works and simulations have classified the hydrodynamic stresses associated to the biphasic flow of solid particles aggregates in order to propose simple and effective models that describe the dispersion system. Weiler has established the following categories for a model to explain the behavior of a dispersion of dry powder agglomerates (Weiler, Wolkenhauer, Trunk, & Langguth, New model describing the total dispersion of dry powder agglomerates, 2010): 3.2.1. Inertia stress ( ) This stress is caused by aggregated particles accelerations and shifts in the flow direction and is associated to the resistances per surface area of agglomerate. The maximum inertia stress can be considered when the relative velocity between the fluid and the solid particles reaches a maximum value as well. This happens when the model assumes a resting agglomerate in an air stream. During the acceleration process, the relative velocity between the fluid and the particles decreases, reducing the inertia stress too. Finally, it’s important to establish the short-time scales for the induction of the stress. The following figure shows a scheme of this stress classification:. 31.

(38) Figure 8. Inertia stress caused by acceleration and changes in the flow direction.. The equation that characterizes the inertia stress has been defined according to the Reynolds number according to specific parameters related to the agglomerate ) and the relative velocity of the system fluid ( ): diameter ( (10) that determines the inertia stress exerted on the solid surface is The coefficient established by the Reynolds number defined for the aggregates: √. 0,4. (11) (12). 3.2.2. Rotary stress (. ). This stress is introduced by the velocity gradient (. /. ) in a shear flow.. It occurs during the transportation of the agglomerate within the shear zone. During a stepwise deagglomeration in a constant shear zone, becomes smaller with the power of two of the decreasing agglomerate size. The equation used by Weiler in his model for the dispersion of dry powder agglomerates are based on the aggregate properties and the previous description of the flow profile: (13). 32.

(39) Figure 9. Rotary stress originated by the velocity gradient in the dispersion flow. 3.2.3. Turbulent stresses (. ). These stresses are originated by the vortices formed according to the flow regime and can be divided in shear stresses and impaction stresses. The first ones cause the disintegration of micron sized agglomerates and are attributed to the vortices of comparable length scale. The main parameters for the determination of the intensity of the micro-turbulences are the viscosity of the fluid νkin, the energy of the dissipation rate ε and the size of the involved vortices.. Figure 10. Turbulent stresses induced vortices in the dispersion flow. The Kolmogorov microscale ( ) joins the parameters mentioned above and classifies the micro-turbulences. The turbulent flows have large sizes vortices ( 58 ) while the laminar flows are associated to small-size vortices ( 3 ) and intermediate sizes are in the range between these two values. The equation to determine the Kolmogorov microscale is: ,. (14). The turbulent stresses can be estimated according to the following equation which has been adjusted with the respective flow parameters ( to ) listed in Table 3.. 33.

(40) (15). Table 3. Fitting parameters for the turbulent stresses in a solid particles dispersion flow (Debrincat, Solnordal, & Van Deventer, 2008; Weiler, Wolkenhauer, Trunk, & Langguth, New model describing the total dispersion of dry powder agglomerates, 2010) STRESS. KOLMOGOROV LENGTH SCALE 3. 0,260. 1,000. 0,500. 0,000. -1,000. Shear stress. 3 ,7 7 , 58 58. 0,068 0,490 1,900. 1,000 3,000 1,000. 1,000 0,250 0,666. 2,000 1,000 0,666. 1,000 1,000 0,000. Impaction stress. 3 , 58. 0,051. 3,000. 0,250. 1,000. 1,000. 3.3. CRITERIA FOR FRAGMENTATION OF SOLID PARTICLES AGGREGATES. Debrincat et al have associated the stresses exerted over the surface of the agglomerate with the breakup of the aggregates. The studies developed in previous research have established that agglomerates will break up if the turbulent stresses overcome the agglomerate stresses. This condition can be validated through the evaluation of the Weber number that relates these stresses (Debrincat, Solnordal, & Van Deventer, 2008): (16) The agglomerate stress must be estimated at its surface in order to determine the affection degree of the hydrodynamic stress. If the value of the Weber number is greater than one, the agglomerate will fragment. (17) It is possible to establish the force on the particles by substituting this evaluated stress in the following equations:. 34.

(41) . Model for mono-sized spherical particles proposed by Rumpf: (18) Where is the void fraction, is the coordination number, is the particle diameter and is the force between particles per contact unit (Debrincat, Solnordal, & Van Deventer, 2008).. . Model for Irregular particles proposed by Cheng: 1. (19). Where is the ratio of particle pairs per unit cross-section to particle pairs per unit volume, is the fraction of the smaller contacting particle's surface area that is in contact with adjacent particles per contact, is the effective mean surface area per particle, is the mean volume per particle, and is the inter-particle force per unit contact area (Debrincat, Solnordal, & Van Deventer, 2008).. 35.

(42) 4. EXPERIMENTAL ANALYSIS FOR DESCRIPTION OF GAS-SOLID FLOW INSIDE THE HARTMANN TUBE. The Hartmann tube is commonly used in the first stages of characterization of materials to perform tests that determine ignition sensitivity of powders whose particle diameter is smaller than 420µm by exposition of the material in the form of a dust cloud to an ignition source. This apparatus is an experimental setup composed by three different elements that have been designed and standardized for determination of the minimum explosive concentration (MEC) and the minimum energy required for ignition (MIE). Nevertheless, this apparatus has been implemented in qualitative analyses associated to the explosions. The assembly shown in Figure 11 consists of a vertical tube mounted onto a dust dispersion system which is composed by a dispersion nozzle connected to a gas injection wire. Powder samples of different size distributions are dispersed in the tube with pressurized air and attempts are made to ignite the resultant dust cloud by a spark generated by the discharge of a capacitor at two electrodes (ignition sources) or a glowing wire coil (SQ-25) that possibly cause an ignition (Erlend & Eckhoff, 2006). By moving one of the electrodes towards the other electrode with high speed, the moment of spark discharge can be determined. Spark delay times vary from 60 ms to 180 ms with a defined energy transmitted. The apparatus has been modified, for performance of granulometric analyses, by the adaption of a square transversal section. This fact has allowed the determination of variations in the particle size distribution (PSD) during the transient dispersion process. Additionally, an aspect of main interest discussed on this document lies on the verification of the degree of homogeneity in the mixture by the description of segregation regions of the solid phase. For this reason, the further discussion is focused on description of gas injection and dispersion time. 36.

(43) which must guarantee the necessary mixing level for high precision and accuracy of the experimental data obtained in a typical test. Weiler et al have classified the hydrodynamic stresses exerted on the disperse phase’s surface according to the turbulence phenomenon (Weiler, Wolkenhauer, Trunk, & Langguth, New model describing the total dispersion of dry powder agglomerates, 2010) by establishing the effects attributed to the gradients of velocity and collisions on solids fragmentation. In this order, it is necessary to determine the instantaneous size distributions to identify variations in it that have an influence on the experimental flammability characterization results.. Figure 11. Experimental setup developed for characterization of solids dispersion. a. Dispersion tube b. Granulometer c. Dispersion nozzle d. Gas inlet. During this study, granulometric analyses have been performed with solids dispersions of materials with different rigidity levels in order to determine their particle size distribution during the transient dispersion process, in which, different 37.

(44) stresses are exerted on the surface of every particle and agglomerate. The experimental setup shown in Figure 11 has been constituted with an adjustable support for a granulometer type HELOS-R provided by SympatecTM. This section poses the modifications performed on the original Hartmann tube that have allowed determining the variations in particle size distributions and the subsequent description of the confined gas-solid flow.. 4.1. EXPERIMENTAL DETERMINATION OF PARTICLE SIZE DISTRIBUTIONS. This apparatus possesses an optic system which is composed by a laser emission and detection device. A characterization of particle size distributions can be performed by laser scattering with 32 different detectors located in a circular arrangement. The incident beam is generated by a 5mW Helium-Neon source and can be adapted with different sizes (2mm – 13 mm). The system has several Fourier lenses that provide a high precision and accuracy in measurements for a specific size range. The Fraunhofer’s theory has been considered for PSD determination. This approach considers opaque and non-porous particles. The particles dispersed in the dust cloud possess a random and ideal movement. These facts allow establishing that the laser scattering is proportional to the particle size. The laser has been located at the same height of ignition sources in order to compare the mean size determined by the granulometric analyses and the CFD simulations. The experimental tests have been performed with two different materials whose mean size is in the micrometric scale.. 38.

(45) Figure 12. HELOS-R granulometer’s scheme. The criterion defined for the measurement method is based on the laser diffraction caused by the particles present in the optical path and whose sizes are in the range between 0,1 and 8750 micrometers. The various existing lenses are listed in Table 4. The tests have contemplated the use of R3 lens after taking into account the size ranges of the analyzed samples. Table 4. Classification of lenses and measurement ranges of the HELOS-R granulometer.. TYPE OF LENS SIZE RANGE OF DISPERSE PARTICLES R1 100 nm – 35,0 μm R2 250 nm – 87,5 μm R3 500 nm – 175,0 μm R4 500 nm - 350 μm R5 500 nm - 875 μm R6 500 nm - 1750 μm R7 500 nm - 3500 μm R8 500 nm - 8750 μm. 39.

(46) 4.1.1. Determination of the granulometry of the solid phase with the Fraunhofer’s theory.. The experimental protocol defined for the characterization of non-porous opaque particles is based on the Fraunhofer’s theory. This alternative was chosen because this model requires less prior information about the optical characteristics of the dispersed material (refractive index and shape factor). It is possible to consider the distribution of particles and agglomerates in the powder cloud is ideal and its motion is random. For this reason, it is stated that the degree of diffraction of the laser beams is proportional to particle size on which an impact. During a typical characterization test, a concentric pattern called "Airy disk" is defined by light and shade stripes during data collection. According to the theory proposed by Fraunhofer, the intensity of the diffracted beam is affected by the radius of the particles in the diffraction spot. The color changes of the rings constitute points of cancellation of the pattern; therefore, the diffraction angle is defined by the first null point.. 4.2. EXPERIMENTAL METHODOLOGY. The methodology used to develop a randomized two-phase flow characterization includes different stages associated with setting up equipment and placement of material: . Equipment cleaning: Cleaning is performed in the glassy walls of the equipment to remove particles present from previous tests or environmental conditions. This procedure involves a rinse with a concentrated solution of ethanol and subsequently with the placement of a film which prevents adhesion of particles by static charges.. 40.

(47) . Material preparation: Placement of a sample of 0,8 grams of previously characterized aluminum particles at the base of the tube. Subsequently, equipment’s software is adjusted to specify the parameters required by the granulometer such as density and form factor.. . Parameter settings of granulometric system: The data collection can be manipulated with the software WINDOX 5TM. It is possible to adjust the equipment to record data between a period that begins 50 ms before detection of an optical concentration of 2% and 50 ms later. The results presented correspond to statistical analyses performed every 10 ms with measurements performed every millisecond. Additionally, it is necessary to adjust the lens before the test to ensure its proper targeting. If there are no contingencies that hinder the collection of samples, we proceed to take a reference measurement that constitutes the comparison value for the equipment.. . Adjustment of the injection system: A check is performed on the system that generates the gas pulse in order to check the pressure in the line and verify the deactivation of the ignition sources.. . Gas Injection and data analysis: After activating the granulometer and the injection system simultaneously, a data analysis is developed to identify the evolution of particle size distribution.. 4.3. ALUMINUM AGGREGATES (PARTICLES BELOW 125 MICROMETERS). The combustible solid posed for this paper consists of micron-sized aluminum particles. The analyzed samples are characterized by a PSD below 125 μm, in which, the size of most solid aggregates is 80 μm. This material spontaneously forms aluminum oxide when exposed to the atmosphere. The formed film becomes an effective barrier to prevent further reaction of the aluminum with the environment. The induced ignition of this material is caused by a local disruption of the protective layer produced by the supply of sufficient energy (Chiffoleau, G, Newton, B, Holroyd, NJH, & Havercroft, S, 2006). 41.

(48) Figure 13. Initial particle size distribution of glass particles used in the experimental analysis.. The particle distribution has been adjusted to a continuous function in a certain range by adjustment of the Rossin-Ramler, which defines the mass fraction of the sample that is larger than a given particle size ( ) with Equation 19: (20) Where ̅ is the diameter that sets the order of magnitude of the average size of the sample and is the exponent that sets the degree of dispersion in the distribution. From the data presented in Table 7, the coefficients were determined by the software required to characterize CFD the dispersed phase in its initial condition. Table 5. Initial particle size distribution of glass particles used in the experimental analysis. PARAMETER Size diameter larger than 10% of the sample (μm) Size diameter larger than 16% of the sample (μm) Size diameter larger than 50% of the sample (μm) Size diameter larger than 84% of the sample (μm) Size diameter larger than 90% of the sample (μm) Size diameter larger than 99% of the sample (μm) Diameter to determine the sample’s magnitude order (μm) Dispersion level. 42. VALUE 26,63 33,18 57,41 76,75 80,60 86,36 64,91 3,489.

(49) After the identification of initial conditions of the PSD, the evolution of mean size distribution at the ignition electrodes elevation was characterized. The results, shown in Table 6, evidence a reduction of the analyzed variable of the tested sample during the first 60 ms of dispersion, because the initial mean diameter is 57,41μm and the distribution has decreased until a mean value of 23 μm. Table 6. Mean diameter at ignition sources location during dispersion process.. Time after reaching the Mean diameter (µm) ignition sources elevation (ms) 30 53,72 40 23,19 50 24,68 60 24,05 Figure 14 presents the initial stages of micrometric aluminum dispersion. The images have been taken with a high speed camera. This device has been adjusted with a resolution of 1632x1200 pixels to register the biphasic flow development with 1016 frames per second. The internal conditions evidence a homogeneous distribution, in which, the aggregates dispersed in the dust cloud rise with a characteristic profile that is similar to a plug-flow. This behavior can be associated to fragmentation phenomenon after considering the similar rising velocity in the dust cloud. The particle size distribution inside the distribution varies significantly due to hydrodynamic stresses exerted by the gas flow. At the bottom of the tube, the injected air flows at transonic conditions and the solids particles possess low velocities that favor rotation and drag forces that reduce the reduce the mean size of the analyzed sample (Weiler, Wolkenhauer, Trunk, & Langguth, New model describing the total dispersion of dry powder agglomerates, 2010). Nevertheless, it is necessary to take into account that the collision probability at the bottom of the tube is higher. This fact constitutes an important factor for fragmentation and aggregation of solid phase.. 43.

(50) a. b. c. d. e. f. Figure 14. Micrometric aluminum dispersion inside the modified Hartmann tube. a. 10 ms c. 20 ms d. 30 ms e. 40 ms f. 50 ms g. 60 ms.. 44.

(51) 5. COMPUTATIONAL FLUID DYNAMICS FOR CHARACTERIZATION OF THE RELEVANT PARAMETERS OF THE DUST DISPERSION. A computational fluid dynamics simulation, based on an Euler-Lagrange approach, has been developed to describe the dispersion of aluminum micrometric particles in a standardized setup designed for characterization of solid combustible materials, known as Hartmann tube or Mike III. The analysis performed on the biphasic flow development determined the regions of high solids concentrations and the zones with high vorticity that cause variations on the particle size distribution and therefore on their mechanism of combustion. In that context, the CFD study was directed towards the assessment of flow conditions pertaining to the agglomeration and fragmentation of particles dispersed in a standardized Hartmann tube setup. This preliminary analysis was focused on the characterization of biphasic turbulent flows within this equipment in order to study the influence of flow conditions on fragmentation dynamics. Due to the apparent worsening effects of agglomerates, this study was complemented with granulometric analyses that constituted the main source for the information required to adapt the fragmentation model and describe the variations in particle size distributions accurately. The study of dispersion of solid particles inside the Hartmann tube also analyzed the homogeneity assumption and some operating recommendations that have been defined for an experimental characterization of solid combustible materials in order to evaluate the performance of the equipment designed for this purpose. Afterwards, the dispersion process has been classified according to the variations in particle size distribution. The minimum delay for ignition has been recommended with a value of 60 ms after considering the distribution of discrete phase inside the tube and the variations in mean diameter at the elevation of ignition electrodes.. 45.