Proposal of a new injection nozzle to improve the

Powder Technology 328 (2018) 54–74

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Proposal of a new injection nozzle to improve the experimental reproducibility of dust explosion tests Carlos Murillo a, Mariangel Amín b, Nathalie Bardin-Monnier a, Felipe Muñoz b, Andrés Pinilla b, Nicolás Ratkovich b, David Torrado a, Daniel Vizcaya b, Olivier Dufaud a,⁎ a b

Reaction and Chemical Engineering Laboratory (LRGP), University of Lorraine, UMR 7274 CNRS, 1, rue Grandville, BP 20451, 54 001 Nancy, France Chemical Engineering Department, Universidad de Los Andes, Colombia, Carrera 1 Este 19 A 40, Bogotá, Colombia

a r t i c l e

i n f o

Article history: Received 28 June 2017 Received in revised form 16 October 2017 Accepted 30 December 2017 Available online 7 January 2018 Keywords: Dust explosion CFD Euler-Lagrange Powder dispersion Agglomeration

a b s t r a c t The influence of the injection nozzle on the dispersion process of a combustible dust in the 20 L sphere is established by developing a descriptive analysis. This study compared the evolution of a dust cloud formed thanks to the standard rebound nozzle with that formed from a new symmetric nozzle. For this purpose, a CFD simulation based on a Euler-Lagrange approach characterized the physical properties of the dust-air mixture in the explosion chamber. The computational results established that the symmetric device enhanced the homogeneity of the mixture as well as the initial turbulence during the initial stage of dispersion. Nevertheless, it also constituted a more rapid turbulence decay due to a wider expansion of the gas. Thus, it constituted different sedimentation and agglomeration periods with regard to the standard device. Thereupon, the computational tools determined the most appropriate ignition delay for the dust cloud for each injection nozzle. © 2018 Elsevier B.V. All rights reserved.

1. Introduction The comprehension of the major hazards that can be associated with the formation of a combustible dust cloud is based on the proper characterization of the powder explosibility parameters in a confined environment. This analysis can be constituted by performing a set of laboratory tests that establish the explosion characteristics of the cloud according to specific standard test methods. One of these particular tests, and probably the most common one, is carried out with the 20 L apparatus that was developed by Siwek [1]. The operating procedure of this experimental setup is described in detail in various international standards. For instance, the American Society for Testing and Materials presents the main specifications of the 20 L apparatus as well as the corresponding protocol in the standard ASTM E1226-12a. Similar information is provided by the German Society of Engineers (VDI-3673) and the International Standards Organization (ISO 6184/1). The experimental setup of the standard test consists of a 20 L spherical explosion chamber connected to a pressurized canister by a solenoid valve. The sphere is surrounded by a cooling jacket with water at controlled temperature. The canister will form a confined dust cloud by

⁎ Corresponding author. E-mail addresses: [email protected] (M. Amín), [email protected] (N. Bardin-Monnier), [email protected] (F. Muñoz), [email protected] (A. Pinilla), [email protected] (N. Ratkovich), [email protected] (D. Torrado), [email protected] (D. Vizcaya), [email protected] (O. Dufaud).

https://doi.org/10.1016/j.powtec.2017.12.096 0032-5910/© 2018 Elsevier B.V. All rights reserved.

injecting a two-phase flow into the sphere through a dispersion nozzle installed at its bottom. Thereafter, the dust-gas mixture is ignited after a delay, also called tv, that is specified prior to the development of the test. In accordance with this protocol, the ignition of the cloud is preceded by the following steps: 1. The dust sample is weighed and loaded in the canister and chemical ignitors are placed in the center of the sphere. The standard ignition energy is 10 kJ (corresponding to two 5 kJ chemical ignitors) for the determination of the explosivity parameters and 2 kJ (two 1 kJ ignitors) for the minimum explosive concentration (MEC) determination. 2. The dispersion chamber is evacuated to 0.4 bar, whereas the canister is pressurized up to 21 bar(a). 3. The solenoid valve is opened and the two-phase flow forms the cloud. The third step of this protocol determines the main characteristics of the dust/gas mixture before its ignition. The dust cloud formed inside the 20 L sphere defines a transient behavior that is constituted by the fluidization of the solid sample, which induces continuous variations of the physical properties of the gas and the dispersed powder. Therefore, it will also define the propagation of the combustion flame that develops within the 20 L sphere [2]. Consequently, these changes affect the ignitability of the cloud and the violence of the explosion [3,4]. For this reason, the description of the evolution of the confined dust cloud has been considered as an aspect of major concern for the definition

C. Murillo et al. / Powder Technology 328 (2018) 54–74

of the most conservative conditions to perform an explosibility test with the 20 L apparatus. The changes occurring in both phases during the pre-ignition stage are directly associated with the initial or ‘cold’ turbulence that is generated by the injection of the high-pressure two-phase flow [5,6]. The “cold turbulence” being related to the parameter tv, the most appropriate ignition delay can be determined by studying the behavior of the dust-air mixture and the variables that are linked to its turbulence levels. Previously, some anemometry measurements were performed by Dahoe et al. in order to establish how the turbulence of the gas flow varied during the pre-ignition stage [7]. In addition, some similar analyses were reported by Pu et al. [8]. Moreover, Kalejaiye et al. developed an analysis of the solids distribution inside the explosion chamber that was based on light transmittance [9]. This study concluded that the variations of the particle size distribution of the combustible dust affected the assessment of its local concentration and that the dispersion process does not constitute a completely homogeneous dust cloud with the two injection nozzles that are commonly used in the 20 L sphere (rebound and perforated annular nozzles). This heterogeneity can have a strong influence on the experimental reproducibility, which is rather low notably with regard to the determination of the maximum rate of pressure rise. The relative standard deviation of repeatability on this parameter is generally estimated at ± 10 to 15%. In addition, various comparative tests have analyzed experimentally the influence of the shape of the injection nozzle on the development of the confined cloud. For instance, Dahoe et al. established that the size and conditions of the jets formed by the dispersion nozzle influence the initial turbulence decay rate [5]. This fact defines the influence of the injection nozzle on the evolution of the dust cloud during the preignition stage. For this reason, Sanchirico et al. performed granulometric analyses on dust samples of different solid materials before and after dispersion in the 20 L sphere. They demonstrated that the particle size distribution (PSD) of the dust collected after the dispersion process was greater with the utilization of the standard rebound nozzle with regard to the standard perforated ring [10]. In the same manner, Mercer et al. determined experimentally the variations of the velocity field of the gas flow that are defined by the geometry of the injection nozzle and the instant of the dispersion process [11]. Moreover, Krietsch et al. developed a special mushroom nozzle in order to improve the dispersion of metallic nanometric powders [12]. The samples were placed inside the explosion chamber before the dispersion process and not inside the pressurized canister. In the same manner, Zhang and Zhang analyzed the influence of the ignition delay on the explosibility parameters of corn/air mixtures with a nozzle composed of several holes at the surface [13]. This device intended to create a group of jets that are directed towards many regions of the vessel. These studies agree by concluding that the shape of the injection system constitutes an adaptable parameter to perform an explosibility test with the 20 L sphere. Then, it appears that the development of a new dispersion nozzle can be an efficient and simple solution to improve the homogeneity of the dust cloud and, as a consequence, to increase the experimental reproducibility. In addition, previous studies have demonstrated that the computational analyses become a useful tool to describe the dust dispersion within the explosion chamber. Then, the results obtained can contribute to a better comprehension of the interaction mechanisms of each solid particle with its surrounding particles and the internal walls that occur during the pre-ignition test [14,15]. At first, a new dispersion nozzle was designed, tested and the results were compared with those obtained by using a standard rebound nozzle. In parallel, the evolution of the dust-air mixture obtained with two different injection nozzles was described with a set of CFD simulations. These computational tools constitute a widely adopted methodology to characterize the phenomena associated with explosive dust clouds [16,17]. For this purpose, the computational approach has been associated with a Discrete Element Method (DEM) to represent

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accurately the gas-solid fluidization characteristics of the combustible dust cloud [18]. Finally, the numerical results were compared to the previous set of experimental tests. 2. Materials and methods 2.1. The 20 L dispersion sphere The descriptive study of the behavior of a combustible dust cloud in the 20 L sphere is hard to accomplish due to the absence of a visualization window with a sufficiently large diameter. For this reason, a whole new dispersion vessel was constructed in order to obtain a visualization field from different views. The apparatus shown in Fig. 1 was built with stainless steel and was installed on the outlet valve of the experimental setup in order to replace the original chamber. Some modifications were included in the design of this vessel to make it suitable for a dispersion analysis. For this purpose, five windows have been placed in the structure of the chamber to provide several points for the visualization of the dust cloud: four circular windows located at the lateral extremes of the apparatus and another one at the top. On the one hand, the lateral windows are made of borosilicate with a diameter of 9.7 cm and are sustained by flanges. They were utilized for the data acquisition through in situ granulometric analyses (Helos Vario - Sympatec GmbH) and Particle Image Velocimetry (PIV) measurements. On the other hand, the window that is located at the top of the vessel is made of polymethyl methacrylate and has a diameter of 14 cm. This window was used for the recording of the dispersion process with a PhantomV91 highspeed video-camera and for cleaning purposes. It should be added that, if this new vessel can withstand the pressure variation due to the dust dispersion, it was not designed to withstand explosion overpressures. This experimental setup was considered for the descriptive tests according to the following procedures: i) Particle Image Velocimetry: The high-speed camera was placed in front of one of the four lateral windows and was adjusted to visualize the geometric center of the sphere. The recordings were obtained for an interrogation window of 2.95 cm × 2.80 cm with an image resolution of 480 × 480 pixels and a framerate of 6410 fps. The analysis envisaged the description of the velocity field with two different positions of the standard rebound nozzle: parallel and perpendicular to a continuous laser sheet that illuminated the interrogation window. Subsequently, 0.6 g of micrometric wheat starch were charged into the storage canister of the standard apparatus in order to obtain a nominal dust concentration equal to 30 g/m3. A dispersion test was carried out according to the specifications of the standard procedures. This fact allowed describing the evolution of the velocity field during the first 120 ms when no ignition occurs. For this purpose, a set of five replicate tests was performed for each configuration of the injection nozzle. ii) Granulometric analyses: The same weight that was considered for the PIV analyses was determined for the wheat starch samples used in these tests. Another dispersion test established the evolution of the particle size distribution during the 120 ms elapsed after the arrival of the bulk of the dust cloud to the geometric center of the sphere, in which a laser beam is positioned. For this purpose, the granulometric data were registered in measurement cycles of 1 ms and reported for intervals of 5 ms. A set of five replicate tests was performed for the granulometric analysis in order to verify the repeatability of the tendencies evidenced in the experimental results. 2.2. Design of a new nozzle The scheme of the standard rebound nozzle is shown in Fig. 2. A The geometry of this nozzle clearly implies that two main directions will be

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Fig. 1. Dispersion sphere and experimental setup A) Vacuum system B) Venting C) Valve for manometer D) Lateral window E) Upper window F) Tube for the outlet valve G) Lamp H) Granulometer HELOS/KR I) High-speed video camera J) Analysis PC.

promoted during the dispersion process: an upward jet corresponding to the injection of dust through the three internal holes and two lateral jets oriented in the direction of the plates. The injection of the particle-laden flow was recorded with the standard rebound nozzle. Fig. 3 A, B and C present the first stages of the flow injection seen from the top of the dispersion chamber. As expected, Fig. 3 B and C clearly identify three jets that constitute the two-phase flow in the dispersion chamber: two jets that are directed towards the extremes of the nozzle plates (forming a bow-tie shape) and the one that develops in the middle of it. The dust repartition between these jets is clearly unequal and the two lateral fronts expand quicker than the upward jet due to the high pressure drops in the internal holes. Moreover, Fig. 3 C shows a high concentration zone that was observed in the middle of the sphere. This variation of the dust cloud was produced when the two fronts of the lateral flows collided. This collision was evidenced for micrometric wheat starch after 7 ms of dust dispersion. A similar behavior was also observed by Du et al. [19]. The asymmetrical shape of the rebound nozzle inducing an asymmetrical distribution of the solid phase within the sphere, a new nozzle was designed to improve the initial homogenization of the dust cloud. As shown in Fig. 2. B, the new system was based on the standard rebound nozzle characteristics (surface areas of the injection holes, distances between the plates, etc.). Nevertheless, the new nozzle is

distinguished from the standard system by its symmetrical shape which is intended to spread out the combustible dust inside the dispersion vessel under a more homogeneous distribution [20]. Fig. 3 shows a significant difference in the distribution mechanism of the dispersed phase between the two nozzles within the vessel. With the symmetric nozzle, two fronts can be identified in the injection: a rising front which develops in the middle of the frame and is attributed to the hole located in the center of the nozzle and a lateral front identified by the broken line in Fig. 3 E. The latter circular front is evidenced from the base of the nozzle and is directed towards the internal walls of the sphere. The most remarkable characteristic of the distribution of the combustible dust relies on the uniform spreading of the sample that comes from the bottom of the vessel. This condition apparently reduces the heterogeneity of the bulk of the cloud (Fig. 3 F). In both cases, when the dust fronts will collide at the top of the vessel, a downward flow will still be produced in the middle of the dispersion chamber. These visual observations have been compared to quantitative measurements (PSD, velocity fields) performed on wheat starch and numerical simulations. 3. CFD simulations The dispersion process of micrometric wheat starch was described computationally in order to perform a comparative analysis of the evolution of the dust clouds formed with the two injection nozzles. For this purpose, a set of CFD simulations based on the Eulerian-Lagrangian approach was developed with the software STAR CCM+ 10.06.010-R8. This formulation was considered because, under usual test conditions, the global volume fraction of dust dispersed in the sphere ranges between 10−6 and 10−3 cubic meters of solid per cubic meter of mixture. For instance, some validation tests have been carried out with 0.6 g of wheat starch (ρp: 610 kg·m−3), which corresponds to a nominal concentration of 30 g·m−3 and a volume fraction of 2·10−5 m3 solid per m3 mixture. 3.1. Eulerian-Lagrangian approach The Eulerian formulation envisaged the description of the gas flow as a continuous phase through the numerical solution of the NavierStokes equations. In accordance with this definition, the characteristics of the flow can be predicted through the conservation of mass, momentum and energy.

Fig. 2. Comparison of the standard rebound nozzle (A) with the symmetric nozzle (B).

Continuity :

∂ρ þ ∇ ðρuÞ ¼ 0 ∂t

ð1Þ


57

Fig. 3. Injection of a combustible dust (wheat starch – 65 μm – ρp: 610 kg·m−3) developed with the standard rebound nozzle (A, B, C) and with the symmetric nozzle (D, E, F).

Momentum :

Energy : ρC p

DðρuÞ ¼ −∇p−∇ τ þ ρg þ F int Dt

DT ∂ ln ρ Dp ¼ −∇ q− −∇τ : u Dt ∂T p Dt

ð2Þ

ð3Þ

The numerical solution of these equations is coupled with a turbulence closure model through the finite-volume method. This method establishes that the conditions of the flow will be determined by the conditions of a discretized domain. Moreover, the medium-density particle-laden flow develops is submitted to the influence of the interaction with the surrounding particles (Fint). For this reason, the CFD simulations were developed according to the two-way coupling formulation. The influence of the solid phase in a two-way formulation is associated with the particle response time. For instance, the agglomerates with a short response time (small diameter) increase the dissipation rate of turbulence energy. On the contrary, high response times represent high Reynolds particle numbers. This fact enhances the production of turbulence energy if this dimensionless number reaches a value of 400 due to vortex shedding [21]. In accordance with this statement, the CFD simulations were developed according to a two-way coupling formulation since the momentum exchange between the dispersion gas and the combustible dust constitutes an important factor in the evolution of the dust cloud [4]. 3.1.1. Detached Eddy Simulations model (DES) The evolution of eddies formed inside the 20 L sphere was predicted with the Detached Eddy Simulations model, which is a hybrid turbulence formulation that uses either the Reynolds Averaged Navier Stokes

(RANS) or the Large Eddy Simulation (LES) treatment depending on the regions of the flow domain. This hybrid turbulence model has been previously considered for the description of unsteady airflows in enclosed spaces [22,23]. Moreover, an experimental characterization analysis carried out by Wang et al. concluded that the description of the particle distribution pattern in a two-phase flow is more representative in unsteady conditions with an anisotropic turbulent energy dissipation model [24]. For this reason, this model has been previously implemented in characterizations of turbulent particle-laden flows in which combustible particles are dispersed [25]. The DES model is a three-dimensional unsteady numerical solution scheme that functions as a subgrid-scale model in the regions where the grid density is fine enough for the LES approach and as a RANS model in regions where it is not [26]. Therefore, it utilizes a zoning methodology to take advantage of RANS and LES methods. For this purpose, it defines a RANS model (Shear Stress Transport k-ω) for the boundary layer and the LES approach (Smagorinsky-Lilly) on the flow field containing vortices with disperse scales (away from the region where RANS works) [27]. The main aspects of these formulations are briefly described as follows: • Shear Stress Transport k-ω: This RANS model is based on the calculation of the turbulent kinetic energy of the fluid flow (k) and its specific dissipation rate (ω). The transport equations of this model are envisaged to blend the formulation of the k-ω, which provides an accurate description of the near-wall region, with the free-stream independence of the k-ε model [28]. For this purpose, the second RANS model is converted into the k-ω formulation. This method is considered for the description of adverse pressure gradient flows, airfoils and transonic shockwaves. This is achieved with the inclusion of the

58


turbulent shear stress in the definition of the turbulent viscosity (μ t) [28]. The two parameters of the turbulence model are calculated with the following transport equations: ∂ ∂ ∂ ðρkui Þ ¼ ðρkÞ þ ∂t ∂xi ∂x j

∂k Γk ∂x j

∂ ∂ ∂ ðρωui Þ ¼ ðρωÞ þ ∂t ∂xi ∂x j

Γω

!

∂ω ∂x j

þ Gk −Y k þ T k

ð4Þ

! þ Gω −Y ω þ Dω þ T ω

ð5Þ

The previous transport equations comprise various terms for the determination of the effective diffusivity (Γk & Γω), production (Gk & Gω), dissipation (Yk & Yω), cross-diffusion (Dω) and sources (Tk & Tω) of each variable. These terms establish the turbulent viscosity of the fluid flow along with the parameters k and ω as the flow properties of the domain. This procedure is performed according to the calculation scheme implemented in the commercial CFD codes [28]. • Large Eddy Simulations: The LES model establishes an approach that is based on the partial simulation of the large eddies and the partial modeling of the small eddies that compose the fluid flow [29]. The classification of the turbulent eddies according to their size allows describing the main characteristics of the flow. The large eddies are responsible for the transport phenomena of the bulk of the flow whereas the small ones determine the energy dissipation [30]; hence the former are dictated by the geometry and conditions of the domain and the latter tend to be more isotropic [28]. For this reason, this turbulence model is conceived to track the behavior of the larger eddies only. For this purpose, a spatial filtering is performed on the unsteady Navier-Stokes equations before the calculations. This classification passes the large eddies and rejects the small ones by developing the following convolution in the flow domain: 0 0 0 0 0 ϕðx; t Þ ¼ ∭V Κ x; x ; ΔLES ϕ x ; t dxi dx j dxk

ð6Þ

in which ϕ is the filtered value of the fluid flow property ϕ, ΔLES is the filter cutoff width, Κ is the filtering kernel of the LES model and x′i is one of the convolution variables for the position of the gas flow. This approach requires an additional expression to take into account the effects attributed to the omitted eddies. For this particular case, the Smagorinsky-Lilly formulation was considered to model the behavior of the small eddies. This turbulence model estimates the behavior of the small eddies according to the filtered values of the velocity field (u∗i ): ∂ui ∂u j 1 þ τij ¼ −2μ t Sij þ τ kk δij ¼ −μ SGS 3 ∂x j ∂xi

!

1 þ τkk δij 3

for the regions that would require a high refinement due to their closeness to the walls. Despite the fact that both models add different terms in the momentum equations (Reynold stresses and subgrid-scales), it is possible to combine both formulations in a simulation. The switch from RANS to LES is performed by reducing the eddy viscosity in the LES zone appropriately. This procedure is accomplished by calculating the length scales of each turbulence model, which are averaged with the corresponding delayed function [28]. This coupling can be established because the turbulence models do not carry any information about their derivation after being introduced into the momentum equations [31]. For this case study, Fig. 4. A and B give a representation of this zoning and the main boundaries between RANS and LES within the 20 L sphere with the standard rebound nozzle and the symmetric nozzle respectively. 3.1.2. Lagrangian approach: combustible dust Furthermore, a Lagrangian treatment was considered for the solid phase. This formulation considers the dispersed phase (combustible dust) as a population of discrete entities that can interact with thecontinuum conservation equations. Thereupon, the motion of each particle inside the flow is traced according to a momentum balance defined for every dispersed particle. Thus, the following expressions (8 and 9) define the treatment of the model for the discrete phase:

ms

" # ρp −ρ dup 18μ C D Rep þ F ¼ ms u−u þ g p x 2 ρ dt ρp dp 24

with : Rep ¼

ρu−up dp μ

ð8Þ

ð9Þ

The particle acceleration is determined by the drag force exerted by the continuous phase on the dispersed phase, the buoyancy effects and the acceleration terms attributed to additional forces (Fx), such as pressure gradient, lift or added mass ones. Moreover, this scheme allows considering the particle-particle interactions that are constituted by the collisions of the dispersed phase. Therefore, the main advantage of this model is associated with its capability of resolving every impact force of the particle [32]. For this purpose, it can constitute a stochastic or deterministic technique for the discrete element method. Nonetheless, the main disadvantage of the Eulerian-Lagrangian model relies on the computational cost that is required for the calculation process.

ð7Þ

in which τij represents the local subgrid stresses, τkk is the isotropic part of the subgrid-scale stresses, S∗ij is the rate-of-strain tensor for the resolved scale, δij is the Kronecker delta function and μ SGS is the dynamic subgrid viscosity. The requirements of the LES formulation make it unsuitable for the description of the gas flow in the near-wall regions. In fact, the computational resources that were available for this analysis do not allow considering a CFD analysis based on a formulation like this for the whole domain. Nevertheless, the flow domain also consists of several regions that define the core turbulent region as a zone that generates significant energy dissipation rates. Sun et al. have posed the LES as an appropriate alternative for the description of certain flows with high Reynolds numbers that are characterized by a complex vorticity [27]. The RANS treatment was considered as a complementary alternative

Fig. 4. Scheme of the repartition of the LES and RANS zones used to model the turbulence of the gas-solid flow in the 20 L sphere.


Schellander established that the calculation efforts rise by the square of the number of particles [32]. A correction factor is included in the calculation of the drag coefficient (CD) in order to take into account the ovoid shape of a starch agglomerate [33], which constitutes a different drag force on the dispersed particles with regard to that observed on a spherical particle. The correction established by Haider & Levenspiel for nonspherical particles [34] defines a correlation based on the shape factor of the combustible dust (Eqs. 10 to 15). This parameter depends on the ratio SF between the surface area of a sphere having the same volume as the particle (ssphere) and the actual surface area of the particle (sp). The shape factor was set equal to 0.71 for the wheat starch parcels [35]. This value is consistent with previous scanning electron microscopy observations, which were performed on such wheat starch particles to determine their shape [33]. CD ¼

24 b3 Rep 1 þ b1 Rebp2 þ b4 þ Rep Rep

ð10Þ

59

parameter that was considered for the momentum balance of the dispersed phase. kt 1−ϑ ¼ kn 1−ϑ 2

ð18Þ

Despite the fact that there is not an absolute value for this physical property of the combustible dust in the literature, the Poisson's ratio could be fixed from the data found in it since the span associated with the references considered is quite small. For instance, Mangwandi et al. determined a value of 0.23 for the Poisson's ratio of a porous powder [37], while Jia et al. considered a value of 0.3 for cohesive fine particles [38]. The latter value was used to compute the value of the tangential coefficient of restitution (et), which was considered to estimate the normal coefficient of restitution (en) with the equations proposed by Freireich et al. who established that the coefficient can be calculated from the stiffness ratio of the material (kt /kn) [39].

b1 ¼ exp 2:3288−6:4581S F þ 2:4486S2F

ð11Þ

b2 ¼ 0:0964 þ 0:5565S F

ð12Þ

b3 ¼ exp 4:9050−13:8944S F þ 18:4222S2F −10:2599S3F

ð13Þ

en ¼ et

b4 ¼ exp 1:4681−12:2584S F −20:7322S2F −15:8855S3F

ð14Þ

Finally, Moreover, the two-way coupling formulation considers the momentum balance of the discrete phase for the determination of the fluid-particle interactions. In this manner, the particle-fluid interactions are initially defined as the drag force exerted by the gas flow on the particle. Thereafter, the momentum exchange between both phases establishes that this magnitude is also considered as a source term in the momentum balance of the dispersion gas (Fint). This condition determines the effects of the fluid-particle interactions in any subsequent calculation of the continuous phase flow field [28].

with : S F ¼

ssphere sp

ð15Þ

The first term of the additional forces (Eq. 16) considers the significant pressure gradients in the fluid. Additionally, the second term takes into account the shear lift induced by the velocity gradients in the fluid that are orthogonal to the relative motion of a solid particle. Finally, the last term calculates the normal (Fab, n) and tangential (Fab, t) contact forces exerted on a particle a by other colliding particles (b) according to the soft-sphere collision model. Thus, this scheme estimates each contact force from a spring-dashpot formulation that is defined by the normal (kn) and tangential (kt) spring constants and the corresponding restitution coefficients (en and et). Further details about this collision model were provided by [36]. ( ms F x ¼ ms

) ! X

ρ ∂u ρπ 3 dp u−up Ω þ up þ C SL F ab;n þ F ab;t ρp 8 ∂xi ∀b ∈ contactlist

ð16Þ The normal and tangential spring constants of the DEM method were defined according to Eq. 17. These parameters are treated indifferently by the CFD commercial code utilized in this study. Hence, the adjustment of these parameters of the model did not differ between the normal and tangential components of the spring constants. In accordance with this statement, the corresponding values of both parameters were established in the same way by considering the diameter d50 of the particle size distribution (62.5 μm) and the solid's density (ρp = 610 kg·m− 3), the relative velocity between two colliding particles (upr) and assuming a maximum overlap (δ = 0.10).

k¼

πu2pr 3δ2

d50 ρp

ð17Þ

The coefficient of restitution of the micrometric wheat starch was estimated according to the strain ratio of the powder. The Poisson's ratio (ϑ) of the material was implemented in Eq. 18 to calculate the

0 sffiffiffiffiffiffiffiffiffiffiffiffiffi1 kt et ¼ − cos@π 2:5 A kn kn kt

ð19Þ

ð20Þ

3.2. Flow domain Fig. 4. C and D present the structures that were considered for the simulation of the dispersion process of a dust sample in the 20 L sphere. The flow domain consists of two different bodies that represent the canister and the dispersion sphere. The four cylindrical sections that are observed in the scheme correspond to the windows that were installed on the prototype for the experimental data acquisition. Moreover, three internal elements were also considered for the definition of the flow domain. The electrodes used for connecting the ignition sources were represented by the two cylinders that are seen in the middle of the flow domain. In addition, the standard rebound nozzle (Fig. 4. C) or the symmetrical nozzle (Fig. 4. D) were also represented at the bottom of the chamber. The injection valve was not considered rigorously for the definition of the geometry; hence, it is represented by an elbow that is located at the base of the sphere. 3.3. Initial and boundary conditions The 20 L sphere was conceived as a closed system. Thus, it is only composed of internal walls and there is no inlet or outlet condition in the geometry. All the internal walls have similar momentum specifications since they are defined with a no-slip condition for the gas flow and a reflect condition for the solid particles dispersed in the cloud. Nevertheless, these walls are differenced by their thermal specifications. As previously said, the dispersion chamber is covered by the cooling water that flows around the vessel surface; hence it was defined as a boundary whose temperature is constant and equal to 300 K. On the contrary, all the other internal walls were defined as adiabatic walls. Moreover, the initial conditions of the flow domain have been set according to the operating protocol of the apparatus. In accordance

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distribution that was determined experimentally by granulometric sedimentation analyses (Fig. 5). These analyses were performed in quiescent air in order to establish the aggregation level of the combustible dust during the absence of high fragmentation stresses in the dispersion gas. Obviously, by using a different dispersion technique, such as laser granulometry with dry injection system, or a different dispersion medium, such as water or organic solvent, the particle size distribution would have been different. Clearly, the most appropriate technique of PSD analysis would be the one corresponding to the most representative dispersion conditions encountered under industrial conditions or to the one encountered in the 20 L sphere during the tests (see Section 4.4). However, as one of the aim of this study was to highlight the influence of fragmentation, PSD obtained by sedimentation was chosen as a reference. 3.4. Meshing parameters Fig. 5. Initial particle size distribution of the micrometric wheat starch samples.

with this statement, the two bodies (the sphere and the canister) are filled with air at the temperature of the environment (300 K). Moreover, the velocity field of the whole flow domain represents a quiescent amount of air. This fact implies that the velocity of the fluid and its initial turbulent kinetic energy are null. However, there are only two initial conditions that differ in the two bodies. The first dissimilarity relies on their initial static pressure. The dispersion sphere is evacuated before the injection of the dust-air mixture until 0.4 bars whereas the storage canister is pressurized until 21 bar(a). This pressure difference causes the transonic flow that develops within the explosion chamber before the ignition of the cloud. Moreover, the solids are placed inside the canister as a surface injection. For this purpose, the whole internal surface of the body was set as the initial location of the 937,650 solid parcels. The initial size distribution of this discrete phase was implemented in the CFD simulations with a size discretization that corresponds to the

The meshes of the 20 L sphere are composed of polyhedral-shaped cells (Fig. 6). This selection allows considering a fewer finite-volumes in the spatial discretization of the flow domain. In addition, it is possible to obtain a less diffusive, more stable and more accurate numerical solution of the flow field properties with this grid structure with regard to a tetrahedral mesh. Moreover, the polyhedral grid was structured with the implementation of a surface remesher method. This model was included in order to retriangulate the surfaces and reduce the skewness of the mesh. The refinements of the meshes were considered for the surroundings of the interface of the bodies and the injection nozzle. The behavior of the two-phase flow was considered for the setting of the meshing parameters listed in Table 1 according to a preliminary grid convergence test. The refinement regions were chosen after performing several tests that determined that the pressure changes at these locations are relevant to the development of the flow in the zones located near the nozzle

Fig. 6. Mesh of the flow domain of the 20 L sphere with the standard and symmetric rebound nozzles A. Standard rebound nozzle B. Symmetric nozzle.

C. Murillo et al. / Powder Technology 328 (2018) 54–74 Table 1 Parameters of the advancing layer method defined for the meshes of the 20 L sphere. Parameter

Geometry with the standard rebound nozzle

Geometry with the symmetric nozzle

Maximum growth rate Surface size (mm)

1.3 Minimum: 0.8 (dispersion nozzle) Maximum: 16.0 (separated cells) Sphere: 753,039 Canister: 9935 Total: 762,974 Sphere: 5,190,994 Canister: 59,188 Total: 5,250,182

1.3 Minimum: 0.75 mm (dispersion nozzle) Maximum: 15.0 (separated cells) Sphere: 787,839 Canister: 9935 Total: 797,774 Sphere: 5,427,774 Canister: 59,126 Total: 5,486,900

Number of cells

Number of faces

and the calculation stability. Afterwards, it was observed that the refinement of the cells situated near the visualization windows of the sphere was also important since there is an important change of momentum of the two phases in these regions. Hence, the size increase defined from the cells of the walls towards the core of the flow domain established a maximum growth rate of 1.3 and a surface proximity based on 2 points per gap. In accordance with these considerations, the following meshing parameters were specified in Table 1. Finally, the first 50 time steps were simulated with a Courant number equal to 1 in order to describe properly the propagation of the gas injection through the chamber. Thereafter, the computational results showed an efficient calculation stability and convergence with the time step previously defined. Thus, the Courant number was increased to 20 to reach rapidly a converged solution without compromising the calculation stability [40]. Finally, the computation of the velocity field and the trajectories was performed with a server Intel Xeon × 5650 with 12 processors of 2.66 GHz installed with a set of 48 GB of RAM. The calculation time required for the simulation of 100 ms of dust dispersion is approximately 6.5 days.

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4. Results and discussion 4.1. Stages of dust dispersion The finite amount of injected gas constitutes a transient dispersion process that defines different turbulence conditions in the dust cloud. This condition was evidenced experimentally by developing a Digital Particle Image Velocimetry (DPIV) analysis in the dispersion sphere. This study established the evolution of the velocity field in an interrogation window located in a region that corresponds to the ignition zone of the explosion chamber. Fig. 7 presents the mean values of the two velocity components of the dispersed particles in the laser sheet along with their maximum fluctuations of the velocity field (error bars). This chart shows that the mean values of the horizontal component are considerably lower than that of the vertical direction during the dispersion. Moreover, the experimental data also evidence a decrease of the fluctuations as the dust-air mixture is injected into the sphere. This result can be explained by the continuous energy dissipation of the turbulent two-phase flow. The development of a downward flow in the middle of the vessel after the collision of the lateral jets (Fig. 3. B) explains the behavior of the two velocity components. In fact, the erratic behavior of this variable is developed by the jets that constitute the internal pressure gradients and the turbulent eddies of the flow. Particularly, the mean value of the horizontal component at the ignition zone (geometric center) is approximately zero during the whole dispersion period because of the collision of the jets in the middle of the sphere. On the contrary, the vertical component presents different behaviors due to the downward flow induced by the previous jets collision and the subsequent redistribution of the dispersed dust. Fig. 7 shows that the downward flow lasts 20 ms approximately and is followed by an upward flow that reaches its peak at 80 ms and finishes 20 ms after it. Moreover, Fig. 7 shows that the perpendicular position of the standard rebound nozzle has a different behavior with regard to the

Fig. 7. Evolution of the velocity components of the particles with the standard rebound nozzle within the 20 L sphere.

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one observed with the perpendicular one. In general, the former has lower fluctuations and mean velocities because the latter considers the bow-tie region formed by the two rising jets. These differences are more remarkable for the vertical velocity during the time period elapsed between 50 and 100 ms. These dissimilarities of the velocity components of the dispersed particles confirm that the asymmetry of the injection device might promote the heterogeneity of the dust cloud; hence it is possible to divide the dispersion process into different stages for the analysis of the effects of the modification of the injection device on the local flow conditions. The experimental results established that the dispersion process consists of three regimes: High turbulence, transition and stability. The frames associated with each regime are shown in Fig. 8, which shows that the number of particles in the interrogation window increases as the size of the vortexes and the turbulence levels decrease. Moreover, an additional frame (200 ms) has been included to show the increase of the particles density in the recorded images that is caused by the dust sedimentation occurring during the final stage. During the first 50 ms, the bulk of the dust cloud is characterized by a high turbulence and the fluctuations of the particles velocities range between ±18 m·s−1. When most of the sample has been discharged into the vessel, the velocity fluctuations start to decrease, down values inferior to ± 3 m·s− 1 at 100 ms: this is done during the transition stage. From 100 ms, the turbulence level is not high enough to maintain the chaotic behavior of the dust particle; hence the influence of the sedimentation phenomenon becomes clearly visible. Similar observations were made by of Dahoe et al. and Mercer et al. by analyzing anemometry results [7,11]. They observed that the velocity reaches its maximum fluctuations during the first 10 ms of dust dispersion. This period is followed by a continuous decrease of this variable during the next 30 to 40 ms. After 100 ms, their results show that the velocity fluctuations are negligible and the vertical velocity is clearly negative. Therefore, the sedimentation becomes the predominant phenomenon. Despite the similar operating conditions with both nozzles, the evolution and duration of the three dispersion stages are different for each particular case. As a consequence, the analysis of the numerical simulations has been split into two parts: i) the analysis of the initial discharge of the mixture during the first 10 ms of the dust injection; ii) the development of the dust cloud from 10 to 100 ms. Finally, the impact of these stages on the particle size distribution of the dust cloud will be discussed. 4.2. Influence of the nozzle on the initial development of the dust dispersion (0–10 ms) 4.2.1. Effect on the fluid flow Initially, it can be seen in Fig. 9 and Fig. 10 that the two injection devices generate different conditions of the dispersion jets within the

vessel. On the one hand, the geometry of the rebound nozzle establishes a jet that is mainly altered by the holes that compose the device and the only plates that contribute significantly to the shape of the jet are the top plates (Fig. 2. A). On the other hand, the utilization of the symmetric nozzle represented a major alteration of the initial trajectory of the injected flow since it is also significantly affected by the base plates. This fact implies that the standard rebound nozzle constitutes a smaller obstruction that may cause a reduced change of momentum in the two-phase flow. Moreover, a comparison of the lateral view and the front view of the standard rebound nozzle (Fig. 9) shows that the initial distribution of the gas flow is not homogeneous. The lateral view shows the flow that is attributed to the three internal injection holes whereas the front view shows how the major part of the injected flow is directed towards the internal walls of the vessel. This condition induces the formation of two large vortexes in the zones near the walls in the equatorial region of the sphere. These results correspond to the two rising fronts that were discussed above. During the first 8 ms of the dust dispersion, the vortex structures grow and rise due to the high mass flow that is caused by the high pressure difference between the canister and the dispersion chamber. Afterwards, the energy dissipation begins to reduce the size of these structures. On the contrary, the velocity field developed by the symmetric nozzle constitutes a different profile with regard to the standard injection system. The lateral and front views of Fig. 10 do not have significant differences in the distribution of the injected gas flow, which implies more homogeneity of the dust cloud during the initial stage of dust dispersion. In addition, this distribution causes some variations in the vortex observed in the middle of the sphere since they have a toroidal shape due to the symmetric injection of the pressurized fluid. Moreover, the development of the internal jets with the symmetric nozzle causes higher velocities during the first 10 ms of dust dispersion. Therefore, it represents a more rapid injection of the dust-air mixture. This fact represents higher turbulence levels submitted to higher dissipation rates during this initial stage of dispersion. If proved, this could have a significant effect notably on the particle size distribution. This point will be discussed later on (Section 4.4). 4.2.2. Dispersibility of the combustible dust with the different injection nozzles One of the major concerns on the development of a flammability test relies on the homogeneity assumption on the solids concentration of the dust cloud. For this reason, the influence of the geometry of the dispersion nozzle on the initial distribution of the solid phase must also be established with the comparison of the particle size distributions shown in Fig. 11 and Fig. 12 The computational results identify the particles segregation in the dispersion sphere. Initially, it is possible to observe some initial lumps at the center of the sphere. At this moment, the

Fig. 8. Flow regimes in the 20 L sphere.


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Fig. 9. Velocity magnitude of the gas flow with an injection performed with the standard rebound nozzle.

central jets have similar characteristics for both injection devices since the solids fraction injected in the central holes is considerably low. Nevertheless, the lateral jets that collide at the top of the sphere after 4 or 5 ms of dust dispersion create rapidly the downward flow that collides subsequently with the central jet. The evolution of the lateral jets is mainly dictated by the inertial effects of the gas flow. This condition is observed in the first instants of the

dispersion process which shows that the highest elevation is achieved by the smallest particles. This condition was also determined numerically by Kosinski and Hoffmann who established that the fluidization of the dust particles in absence of external forces (e.g. magnetic fields) is mainly defined by the drag force exerted on the surface of the solid [41]. In addition, the inertial effects are also clearly evidenced during the first 10 ms of the dispersion process, especially with the symmetric

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Fig. 10. Velocity magnitude of the gas flow with an injection performed with the symmetric nozzle.

nozzle. The inferior views of Fig. 11 and Fig. 12 show that the trajectories of the solid particles inside the sphere are slightly directed towards one of the sides of the chamber. This condition is observed because the storage canister is mounted on the right side of the apparatus. Therefore, the pressurized two-phase flow follows the path of least resistance and channels to one of the sides of the sphere [11]. In accordance with this statement, the complete uniformity of the dust cloud would require the montage of the canister just below the sphere.

These conditions show that the symmetric nozzle results in a condition that approaches the assumption of the nominal concentration during the first 6 ms of the dispersion process since it distributes the combustible dust homogeneously within the explosion chamber. The angles of the plates of this nozzle develop the expanded jets at upper heights and with larger sizes with regard to those generated by the standard device in the dispersion chamber. Consequently, the momentum loss of the two phases during this initial stage cannot be considered in


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Fig. 11. Particle size distribution of the combustible dust injected with the standard rebound nozzle.

the same way for the two injection systems. The symmetric nozzle induces an important collision at the top of the sphere that subsequently creates a downward flow. In addition, this nozzle is submitted to greater friction effects that are caused by the contact with the internal walls of the apparatus. For this reason, the collision at the top is not clearly evidenced for this injection system.

4.3. Influence of the nozzle on the final development of the dust dispersion (10–100 ms) 4.3.1. Effect on the fluid flow The previous section established that the injections of the dust-air mixture by different injection nozzles generate different behaviors

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Fig. 12. Particle size distribution of the combustible dust injected with the symmetric nozzle.

during the first 10 ms of dust dispersion. These variations have a direct repercussion on the dynamics of the two-phase flows during the subsequent stages of dust dispersion. This section will discuss the influence of the geometry of the nozzle on the evolution of the dispersion process. Fig. 13 and Fig. 14 present the behaviors of the velocity magnitude of the gas flow that were calculated for the two bodies that compose each flow domain. Fig. 13 shows that the high velocities at the outlet of the dispersion nozzle are sustained during the first 60 ms approximately. This condition verifies the experimental result obtained by Dahoe et al. who determined that this is the duration of the injection process [5]. This fact constitutes an important aspect of the characterization of the explosion tests since it

locates the standard ignition delay (tv) at the end of the injection process. Similarly, Fig. 14 establishes that the injection performed with the symmetric nozzle lasts 60 ms as well. Nonetheless, it generates a different velocity field because it achieves a faster energy dissipation due to the wider distribution of the jet. This fact constitutes a faster injection of the gas flow with this device with a higher velocity decay during the next stages of dust dispersion. Thereupon, the propagation of the jets from the walls to the center of the sphere shows that the random behavior of the gas flow is reached by the standard nozzle after 40 ms whereas the symmetric device generates this condition approximately 20 ms before. Another remarkable difference in the velocity fields is observed in the injection zone of the dispersion sphere. Two vortex structures are


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Fig. 13. Velocity magnitude in the canister and the dispersion chamber of the 20 L sphere with the standard rebound nozzle.

formed between the plates of the symmetric nozzle due to the partial confinement generated by the angle of the lower plates. This fact represents an additional factor for energy dissipation with the utilization of this injection device. On the contrary, the gas flow develops a linear jet with the standard rebound nozzle, whose strength decreases as the dispersion process evolves. Nevertheless, the results determine that

the asymmetry that was identified in the early stages of dispersion becomes a determining factor only during the charge of the dust-air mixture because the velocity field is determined by the internal turbulence dissipation after it. The injection of pressurized air generates a continuous pressure increase in the dispersion sphere as the injection develops. Fig. 15

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Fig. 14. Velocity magnitude in the canister and the dispersion chamber of the 20 L sphere with the symmetric nozzle.

shows that this fact constitutes a transient behavior of the velocity magnitude of the fluid flow characterized by an increasing behavior during the first 6 ms and a decreasing tendency during the next stages of dust dispersion. This tendency is not similar for both cases since the velocity decay is more rapid with the symmetric nozzle. This condition induces a difference of 12 m·s−1 after the first 40 ms. This dissimilarity allows concluding that the sedimentation phenomenon will occur before with an injection performed with the symmetric nozzle. Moreover, the velocity magnitude in the pressurized canister presents the

evolution of the injection during the dispersion process. During the first 15 ms, an oscillatory behavior in the storage canister. This condition is due to the high velocity fluctuations that are generated by the arrival of the jet to a quiescent field. Furthermore, Fig. 16 describes the behaviors of the three components of the gas velocity. These flow variables have oscillatory tendencies that clearly show how the gas flow behaves during the first two stages of dispersion. The inertial effects observed by Mercer et al. explain why the velocity oscillations in the direction of the X-axis


Fig. 15. Mean velocity magnitude in the canister and the dispersion chamber of the 20 L sphere.

have a greater amplitude than the components in the direction of the Y-axis [11]. The amplitudes of the horizontal components remain of the same order of magnitude during the whole process for the standard nozzle but not with the symmetric nozzle because of a higher energy dissipation. On the contrary, the vertical component (Fig. 16C) shows the rapid decay that was discussed above during the first 40 ms as well as the subsequent stabilization. The comparison of the gas velocities in the geometric center of the sphere (Fig.16. A to C) and the whole dispersion chamber (Fig.16. D to E) shows that their behaviors follow the same tendencies for the energy decay rate. However, the highest velocities are reached in the middle of the explosion sphere due to the development of the downward flow. Therefore, it is possible to determine that the assumption of complete homogeneity in the gas flow must be considered with caution for dust cloud ignitions occurred during the first 50 ms. This condition was also seen in the anemometric analyses performed by Dahoe et al. in different regions of the 20 L sphere [7]. Despite the variations of the dust concentration that are caused by the particles settlement, the selection of the ignition delay of a combustible dust cloud must not only be fixed by the sedimentation of the combustible dust. In fact, this parameter must also be set according to the variations of the turbulence levels. The computational results have shown that the computed velocity fields exhibit many differences that constitute an important variation of the turbulence levels of the dust cloud. Thus, the ignition delays should not be the same if the injection nozzle is modified. For this reason, this analysis has also considered the variation of the turbulent kinetic energy in the two bodies that compose the flow domain of the CFD simulation. The mean value of this variable for the case studies considered is shown in Fig. 17. This chart shows the same behavior as that observed by Di Benedetto et al. [6]. For each nozzle, the gas flow induces a rapid increase of the turbulence levels during the first milliseconds that is followed by a longer turbulence decay: 4.3.2. Dispersibility of the combustible dust with the different injection nozzles The injection process showed that the dust cloud has a chaotic behavior that defines a random distribution of the dispersed phase all over the sphere. This condition has constituted some basic considerations about the standard test method. For instance, the assumption of the uniformity of a turbulent dust cloud formed within the 20 L sphere allows estimating its minimum explosible concentration as the nominal concentration of a well-dispersed dust sample. However, the computation of the velocity field has shown that the dispersion conditions are also influenced by the injection nozzle. Thus, it is necessary to establish how the dispersed particles respond to the turbulence of the gas flow. For this analysis, a spherical region (diameter: 3 cm) was arbitrary defined as the control volume in order to represent the zone where the ignition spark is formed. Nevertheless, when using strong ignition sources

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as 2 × 5 kJ chemical ignitors, it should be underlined that the initial flame kernel can be greater than the proposed spherical region. However, the cloud composition at the center of the sphere is still a parameter of interest in order to study the effect of the initial dust cloud properties on its explosivity. Moreover, when using weaker ignition sources, 100 J chemical ignitors or sparks for instance, the assumption of a spherical ignition zone of a few centimeters diameter is certainly relevant. Fig. 18 shows the comparison of the dust concentration in the control volume that is obtained with each injection nozzle. On the one hand, the standard device clearly evidences instantaneous concentrations that differ significantly from the nominal concentration generated by 0.6 g of wheat starch (0.03 kg/m3). During the first 60 ms, the local concentration can be several times higher than the nominal value. This fact constitutes a higher ignitability of the dust cloud during certain moments because the high solids concentration favors the flame propagation without consuming the most of the energy provided by the ignitors (concentration below 0.75 kg/m3). On the other hand, the symmetric nozzle distributes the combustible dust to generate a dust concentration at the geometric center that does not differ considerably from the nominal value. Hence, the ignitions are not submitted to great variations of the mass of the combustible powder near the ignitors and the uniformity assumption is more valid. Unfortunately, this distribution also implies a lower explosibility of the dust cloud as it will be discussed in the following sections. Additionally, it is possible to identify a period during which the concentrations established by the two nozzles are quite similar. After 80 ms of dust dispersion, the velocity of the gas flow has decreased to velocities below 20 m/s at the geometric center and the continuous displacement of the solid particles is lower. Hence, the fluctuations of the solids concentration decrease drastically and approach to the nominal value.

4.4. Variation of the Particle Size Distribution in the 20 L sphere The variations of the Particle Size Distribution (PSD) of the micrometric wheat starch within the 20 L sphere were also considered for the classification of the dispersion stages of the flammability test performed with this apparatus. This condition can be analyzed by taking into account the relation between the turbulence levels of the twophase flow and the fragmentation and agglomeration phenomena of the dust. In fact, the manufacturer of the 20 L test apparatus (Kühner AG) affirmed that the combination of the outlet valve and the dispersion nozzle might lead to a particle size reduction in the course of dispersion due to their grinding effect on the dust particles [9,42]. In accordance with this statement, the manufacturer usually recommends performing a complementary dispersion test in order to collect and analyze the solid sample. Thus, the fragmentation of the dust can be established from a comparative analysis between the PSD determined prior to the dispersion test and the one that is obtained after it. Nevertheless, this procedure poses as its main drawback the significant difference between the conditions of the dispersion test and the test used to establish the PSD of the collected sample. The variations of the PSD were established with some granulometric analyses that were carried out in situ to establish the fragmentation levels of the solid agglomerates during the dispersion process. These analyses are important because the broad PSD can be thought as a series of narrow size distributions that make a contribution to the explosibility of the solid material [43]. These tests were performed with the experimental set-up that is shown in Fig. 1 (elements H and J). Firstly, the height of the incident laser beam was adjusted to pass through the middle of the dispersion sphere. This zone was considered as the region of main interest because it constitutes the location of the ignition spark inside the sphere. Despite the fact that the homogeneity of the dust cloud has been controverted by the results obtained from different experimental approaches [5,9,19], the geometric center of the dispersion vessel can be considered for this analysis because it will

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Fig. 17. Evolution of the turbulent kinetic energy during the dispersion process.

establish the condition of the solid aggregates in the region where the combustion of the first fraction of the dust cloud is developed. Fig. 19. A shows the evolution of the PSD of the combustible dust during the dispersion process that developed from an injection performed with the standard rebound nozzle. The results exhibit an important shift of the size distributions respect to the initial PSD. Indeed, the diameter d50 decreased from 65.20 μm to 15.95 μm during the first 15 ms. Furthermore, the experimental results obtained for this analysis established that the size distributions of the wheat starch had a low variation in the region of interest during the dispersion process. This condition can be associated with the continuous displacement of the solid particles in the turbulent eddies that are developed by the two-phase flow. Nevertheless, the three dispersion stages that were proposed by Du et al. [19] could be identified in Fig. 20: The first stage was observed during the first 50 ms of dust dispersion. This time-lapse is characterized by an important reduction the diameter d50. During this period, the largest standard deviations are observed due to the temporary pass of the lump injected through the three holes in the middle of the dispersion nozzle (0–10 ms) as well as the fragmentation of most of the injected particles. During the intermediary stage of dispersion, the turbulence of the fluid flow is high enough to keep a reduced agglomeration level in the solid aggregates in spite of its continuous decrease. Moreover, the quick augmentation of the diameters analyzed with these tests is evidenced in the third

Fig. 19. Particle Size Distributions in the 20 L sphere after the injection with different nozzles A) Standard rebound nozzle B) Symmetric nozzle.

stage, which is attributed to the agglomeration and sedimentation phenomena in the middle of the dispersion chamber. This final stage is considered to begin for micrometric wheat starch after 100 ms of dust dispersion approximately. The analysis of the fragmentation phenomenon also describes some important characteristics of the dust dispersion and its ignitability.

Fig. 18. Variations of the dust concentration in a spherical region (diameter: 3 cm) located at the ignition zone of the 20 L sphere.

Fig. 16. Mean values of the three components of the velocity field computed in the 20 L sphere Dispersion chamber: A. Transversal (X-axis) B. Transversal (Y-axis) C. Axial (Z-axis) Geometric center: D. Transversal (X-axis) E. Transversal (Z-axis) F. Axial (Y-axis).

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Fig. 20. Diameter d50 at the geometric center of the sphere.

Previously, Calvert et al. stated that the small aggregates of the cohesive dust disperse by disintegration, whereas large aggregates disperse by particles gradually peeling from the cluster surface [44]. This condition is associated with the force propagation across the aggregate. For this reason, the drag force may be responsible for a partial dispersion of the combustible dust. Despite the fact that the turbulent conditions were capable of breaking up even the smallest aggregates, the diameter d50 of the PSD remained at a value of 16 μm. This fact implies that the largest aggregates could only be fragmented until this size. This condition is determined by the shear rate generated by the dispersion medium and the cohesion forces. For this reason, the dust fragmentation is more determinant for the dispersion process of nanometric dusts. This fact is evidenced because their agglomeration degrees are considerably determined by the particle interactions, which mainly correspond to Van der Waals forces [45]. Moreover, this condition also establishes the level of homogeneity that might be expected during a typical flammability test respect to other cohesive powders. For this reason, the cohesive behavior of the dust represents an important aspect for the determination of the ignition delay of the powder. Furthermore, the symmetrical rebound nozzle was also tested with the experimental protocol that was followed for the standard injection system. Fig. 19. B presents the evolution of the PSD of the wheat starch that was determined for the device that was constructed for this study. The results show a similar fragmentation level for the dust and a modest

variation of the particle size distribution as well. Previously, Kalejaiye et al. established that the reduction in particle size is mainly attributed to the shear stresses exerted on the aggregates during their pass through the outlet valve rather than the impaction against the injection nozzle [9]. In other words, the high velocity of the particle-laden flow through the valve is mainly responsible for the reduction in the particle size and not the action of the dispersion nozzle. In accordance with this statement, the contribution of the nozzle on the fragmentation of the dust can be considered as a minimum. This condition explains the high similarity between the profiles obtained with both injection systems. Nevertheless, the granulometric analyses also show that the flammability parameters that are determined with this injection nozzle can be more sensitive to the variations of the ignition delay defined for the test. This condition can be evidenced after observing how the presence of the large aggregates is favored as the dispersion process develops. This condition poses that the influence of the nozzle relies on the trajectories and the segregation of the two-phase flow. Indeed, the presence of a unique front directs most of the aggregates to the geometric center of the dispersion chamber. This condition enhances the sedimentation process of the solid phase when the turbulence levels are low enough. This characteristic is clearly evidenced in Fig. 20. Despite the fact that the symmetrical rebound nozzle provides a greater reduction of the diameter d50, this injection system has an important increase in the value of this variable and its fluctuations after the first 70 ms dispersion. This condition shows that the dispersion developed with the new injection system can be divided into the same stages that were proposed by Du et al. for the standard device [19]. These results determine that the ignition delay that should be defined for the wheat starch in the 20 L sphere should not be greater than 80 ms for the symmetrical rebound nozzle and 90 ms for the standard device. Finally, the results clearly evidence that the granulometric analyses constitute a useful tool for the implementation of a specific nozzle in a flammability characterization test. For this reason, it is recommended to analyze the variations of the particle size distribution of a combustible dust in order to determine the ignition delay that brings the most conservative conditions for the flammability test by taking into account the physical properties of the solid material. 4.5. Effects of the variation of the dispersion nozzle on the explosibility characteristics of the dust cloud The ignition delay constitutes an important factor if the weight of the dust sample is high enough to define a significant change of the solid concentration. Indeed, the characterizations of a combustible dust that

Fig. 21. Influence of the injection pressure on the flammability parameters of wheat starch determined in the 20 L sphere.


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Table 2 Comparison between the dispersion conditions developed by the standard rebound nozzle and the symmetric injection device. Parameter

Standard rebound nozzle

Symmetric nozzle

Gas velocity

Two large jets (lateral) and a reduced jet (central) are generated during the injection. The injection of the pressurized gas lasts 60 ms approximately.

A large expanded jet and a reduced jet (central) are generated during the injection. The injection of the pressurized gas lasts 10 to 20 ms less than the injection with the other nozzle. This nozzle defines higher velocities during the first stage of dispersion but is characterized by a more rapid decrease of the gas velocity. This nozzle posed the highest turbulence peak (110 J/kg) but had a shorter period of high turbulence (0–40 ms).

Turbulence levels

Solids distribution

Particle size distribution

The initial velocities (0–10 ms) are slower but the gas flow maintains high velocities during a longer period of time. This nozzle maintains a high turbulence level for a longer period of time (0–60 ms) but its maximum turbulence level is lower than that obtained with the other nozzle (84 J/kg). The dust-air mixture is injected towards the two lateral windows of the sphere. Thus, the heterogeneity of the mixture is considerably higher during the first 10 ms of dust dispersion The dust concentration at the ignition has more fluctuations The reduction of the particle size distribution is lower with the utilization of this nozzle. However, the dust agglomeration is not clearly observed during the first 100 ms.

are performed at high concentrations are defined by the ignition delay. If this parameter is too short, the cloud may still be in a developing stage in which the dust is not fully dispersed within the sphere. On the other hand, the dust explosions can be weakened if the mixture is ignited too late because the dispersed particles have agglomerated and settled down. These conditions define the main characteristics of the flame propagation [46]. Fig. 21 show the results of explosivity tests carried out at 10 kJ (two 5 kJ chemical ignitors) with both nozzles at different ignition delays and dust concentrations. Fig. 21 shows that an explosion carried out with a concentration of 125 g/m3, which is very close to the MEC, is not affected by a variation of the ignition delay when the standard rebound nozzle is utilized. This fact is evidenced because the concentration is too low. Indeed, there is not too much energy available for the combustion process. Nevertheless, some important characteristics can still be analyzed from the results obtained. The explosions that were carried out at 20 ms of dust dispersion are exposed to an important uncertainty level that is attributed to the high turbulence level of the two-phase flow that is developed during the charge of the mixture into the vessel. The fluctuations, represented by the error bars, decrease as the ignition delay time increases due to the reduction of the turbulence of the flow. In fact, this condition is evidenced because the high turbulence constitutes a quenching effect on the flame kernel growth [47]. Furthermore, there is a decrease of the two flammability parameters determined with symmetrical nozzle when the cloud is ignited at 110 ms. This condition can be explained by the changes in particle size distribution that were observed thanks to the granulometric analyses. In fact, the trajectories followed by the solid particles within the sphere create a wider distribution of the dust. Despite the fact that the symmetrical nozzle accomplishes a higher fragmentation level during the dispersion process, it is submitted to more significant fluctuations of the particle size for ignitions occurring after the first 80 ms. These characteristics were evidenced with the explosions performed with a concentration of 500 g/m3 as well. This concentration reveals these characteristics more clearly because the variations of the internal conditions of the cloud have an effect on a greater amount of mass that represents more available energy for the combustion process. In fact, the explosivity parameters of the standard nozzle at 110 ms are similar to those determined with the new nozzle at 60 ms. In this manner, these results corroborate the conclusion obtained with the lower concentration, which establishes that a long ignition delay constitutes an operating drawback for the symmetrical nozzle. 5. Conclusions The design of a new dispersion nozzle was proposed to promote the homogeneous distribution of a combustible dust-air mixture within the

The dust-air mixture is injected towards the walls without a predominating direction. Thus, the nominal concentration is a more valid assumption for this nozzle. The homogeneous distribution reduces the variations of the dust concentration The initial turbulence levels are higher with this nozzle. Thus, the initial fragmentation is greater with this nozzle but the rapid turbulence and velocity decay promote the solids agglomeration and sedimentation after 80 ms.

20 L sphere. This device allows forming a well-dispersed dust cloud that intends to validate the homogeneity assumption that is usually considered to perform an explosibility test with this standard apparatus. The modifications on the geometry of the dispersion nozzle induced the changes in the physical characteristics of the dust cloud that are listed in Table 2: The symmetric nozzle developed for this study constituted a solids distribution device that established a concentration in the ignition zone that did not differ significantly from the nominal concentration. Nonetheless, the utilization of this injection device also increased the decay rate of the turbulence levels. Thus, it also represented the development of the agglomeration and sedimentation phenomena at earlier periods due to a higher energy dissipation. For this reason, it is necessary to adapt the ignition delay of the explosibility test by identifying the high and low turbulence periods. Therefore, it is compulsory to determine the fluidization conditions that promote the agglomerates fragmentation and the homogenization of the dust cloud through a computational analysis based on the physical properties of the combustible dust. In this manner, the ignition delay of a given dust-air mixture can be determined appropriately. Acknowledgements This project was developed as a scholarship granted by the French Ministry of Higher Education and Research. In addition, this study was also supported by the Research Vice-Rectory of the University of Los Andes, who constituted a funding source for the development of the computational study. References [1] R. Siwek, Reliable determination of the safety characteristics in 20-l apparatus, Proceedings of the Flammable Dust Explosion Conference, St. Louis: Missouri 1988, pp. 529–573. [2] A. Di Benedetto, V. Di Sarli, The role of turbulence in the validity of the cubic relationship, J. Loss Prev. Process Ind. 43 (2016) 593–599. [3] S. Callé, L. Klaba, D. Thomas, L. Perrin, O. Dufaud, Influence of the size distribution and concentration on wood dust explosion: experiments and reaction modelling, Powder Technol. 157 (2005) 144–148. [4] T. Skjold, Selected aspects of turbulence and combustion in 20-litres explosion vessels, Development of Experimental Apparatus and Experimental Investigation, University of Bergen, 2003. [5] A.E. Dahoe, R.S. Cant, B. Scarlett, On the decay of turbulence in the 20-liter explosion sphere, Flow Turbul. Combust. 67 (2001) 159–184. [6] A. Di Benedetto, P. Russo, R. Sanchirico, V. Di Sarli, CFD simulations of turbulent fluid flow and dust dispersion in the 20 liter explosion vessel, AICHE J. 59 (2013) 2485–2496. [7] A.E. Dahoe, R.S. Cant, M.J. Pegg, B. Scarlett, On the transient flow in the 20-liter explosion sphere, J. Loss Prev. Process Ind. 14 (2001) 475–487. [8] Y.K. Pu, J. Jarosinski, V.G. Johnson, C.W. Kauffman, Turbulence effects on dust explosions in the 20-liter spherical vessel, Symposium (International) on Combustion, Elsevier 1991, pp. 843–849.

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[9] O. Kalejaiye, P.R. Amyotte, M.J. Pegg, K.L. Cashdollar, Effectiveness of dust dispersion in the 20-L Siwek chamber, J. Loss Prev. Process Ind. 23 (2010) 46–59. [10] R. Sanchirico, V. Di Sarli, P. Russo, A. Di Benedetto, Effect of the nozzle type on the integrity of dust particles in standard explosion tests, Powder Technol. 279 (2015) 203–208. [11] D.B. Mercer, P.R. Amyotte, D.J. Dupuis, M.J. Pegg, A. Dahoe, W.B.C. de Heij, J.F. Zevenbergen, B. Scarlett, The influence of injector design on the decay of pre-ignition turbulence in a spherical explosion chamber, J. Loss Prev. Process Ind. 14 (2001) 269–282. [12] A. Krietsch, T.-M. Romahn, M. Scheid, U. Krause, Modified setup of 20-L-sphere for the determination of safety characteristics of nano powders, Chem. Eng. Trans. 31 (2013). [13] Q. Zhang, B. Zhang, Effect of ignition delay on explosion parameters of corn dust/air in confined chamber, J. Loss Prev. Process Ind. 33 (2015) 23–28. [14] A. Di Benedetto, P. Russo, P. Amyotte, N. Marchand, Modelling the effect of particle size on dust explosions, Chem. Eng. Sci. 65 (2010) 772–779. [15] C. Murillo, O. Dufaud, N. Bardin-Monnier, O. López, F. Munoz, L. Perrin, Dust explosions: CFD modeling as a tool to characterize the relevant parameters of the dust dispersion, Chem. Eng. Sci. 104 (2013) 103–116. [16] W. Cao, Q. Qin, W. Cao, Y. Lan, T. Chen, S. Xu, X. Cao, Experimental and numerical studies on the explosion severities of coal dust/air mixtures in a 20-L spherical vessel, Powder Technol. (2017) 17–23. [17] A. Tascón, Á. Ruiz, P.J. Aguado, Dust explosions in vented silos: simulations and comparisons with current standards, Powder Technol. 208 (2011) 717–724. [18] Y. Yang, C. Zi, Z. Huang, J. Wang, M. Lungu, Z. Liao, Y. Yang, H. Su, CFD-DEM investigation of particle elutriation with electrostatic effects in gas-solid fluidized beds, Powder Technol. 308 (2017) 422–433. [19] B. Du, W. Huang, L. Liu, T. Zhang, H. Li, Y. Ren, H. Wang, Visualization and analysis of dispersion process of combustible dust in a transparent Siwek 20-L chamber, J. Loss Prev. Process Ind. 33 (2015) 213–221. [20] C. Murillo, Experimental and Numerical Approaches to Particles Dispersion in a Turbulent Flow: Application to Dust Explosions (in English), Université de Lorraine, 2016. [21] S. Elghobashi, On predicting particle-laden turbulent flows, Appl. Sci. Res. 52 (1994) 309–329. [22] M. Wang, Q. Chen, Assessment of various turbulence models for transitional flows in an enclosed environment (RP-1271), HVAC&R Research. 15 (2009) 1099–1119. [23] Z.J. Zhai, Z. Zhang, W. Zhang, Q.Y. Chen, Evaluation of various turbulence models in predicting airflow and turbulence in enclosed environments by CFD: part 1—summary of prevalent turbulence models, HVAC&R Research. 13 (2007) 853–870. [24] M. Wang, C.-H. Lin, Q. Chen, Advanced turbulence models for predicting particle transport in enclosed environments, Build. Environ. 47 (2012) 40–49. [25] H. Zhou, K. Cen, J. Fan, Detached eddy simulation of particle dispersion in a gas-solid two-phase fuel rich/lean burner flow, Fuel 84 (2005) 723–731. [26] C. Mockett, A Comprehensive Study of Detached Eddy Simulation, Univerlagtuberlin, 2009. [27] D. Sun, Q. Li, H. Zhang, Detached-eddy simulations on massively separated flows over a 76/40° double-delta wing, Aerosp. Sci. Technol. 30 (2013) 33–45. [28] Ansys Inc., ANSYS FLUENT 12.0 Theory Guide, 2009. [29] R. Schiestel, Modeling and simulation of turbulent flows, ISTE; Wiley, London: Hoboken, NJ, 2008. [30] H. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, 2 edition Prentice Hall, Harlow, England; New York, 2007. [31] M.L. Shur, P.R. Spalart, M.K. Strelets, A.K. Travin, A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities, Int. J. Heat Fluid Flow 29 (2008) 1638–1649. [32] D. Schellander, CFD Simulations of Particle Laden Flows: Particle Transport and Separation, Anchor Academic Publishing, 2014. [33] O. Dufaud, M. Poupeau, I. Khalili, N. Cuervo, M. Christodoulou, R. Olcese, A. Dufour, L. Perrin, Comparing pyrolysis gases and dusts explosivities: a clue to understanding hybrid mixtures explosions? Ind. Eng. Chem. Res. 51 (2012) 7656–7662. [34] A. Haider, O. Levenspiel, Drag coefficient and terminal velocity of spherical and nonspherical particles, Powder Technol. 58 (1989) 63–70. [35] J.D. Wilson, D.B. Bechtel, T.C. Todd, P.A. Seib, Measurement of wheat starch granule size distribution using image analysis and laser diffraction technology, Cereal Chemistry Journal 83 (2006) 259–268. [36] N.G. Deen, M. Van Sint Annaland, M.A. Van der Hoef, J.A.M. Kuipers, Review of discrete particle modeling of fluidized beds, Chem. Eng. Sci. 62 (2007) 28–44. [37] C. Mangwandi, Y.S. Cheong, M.J. Adams, M.J. Hounslow, A.D. Salman, The coefficient of restitution of different representative types of granules, Chem. Eng. Sci. 62 (2007) 437–450. [38] T. Jia, Y. Zhang, J.K. Chen, Y.L. He, Dynamic simulation of granular packing of fine cohesive particles with different size distributions, Powder Technol. 218 (2012) 76–85.

[39] B. Freireich, J. Litster, C. Wassgren, Using the discrete element method to predict collision-scale behavior: a sensitivity analysis, Chem. Eng. Sci. 64 (2009) 3407–3416. [40] CD-Adapco, STAR-CCM+ Version 10.04, User Guide, 2015. [41] P. Kosinski, A.C. Hoffmann, An Eulerian–Lagrangian model for dense particle clouds, Comput. Fluids 36 (2007) 714–723. [42] A. Kühner, Operating Instructions for the 20 Litre Apparatus 5.0, Basel, Switzerland, 1994. [43] P.R. Amyotte, K.J. Mintz, M.J. Pegg, Y.-H. Sun, K.I. Wilkie, Laboratory investigation of the dust explosibility characteristics of three Nova Scotia coals, J. Loss Prev. Process Ind. 4 (1991) 102–109. [44] G. Calvert, A. Hassanpour, M. Ghadiri, Analysis of aerodynamic dispersion of cohesive clusters, Chem. Eng. Sci. 86 (2013) 146–150. [45] F. Henry, Dynamique des systèmes nanodispersés: application au cas de l'agglomération des nanoparticules (in French), Université de Lorraine, 2013. [46] J. Yuan, W. Huang, H. Ji, N. Kuai, Y. Wu, Experimental investigation of dust MEC measurement, Powder Technol. 217 (2012) 245–251. [47] T. Glarner, Mindestzündernergie-Einfluss der Temperatur, VDI Ber. 494 (1984) 109–118.

Nomenclature Symbols

bi: Parameter for the calculation of the drag coefficient, [−] CD: Drag coefficient between the solid particle and the fluid, [−] CSL: Coefficient of the shear lift force, [−] dp: Particle diameter, [m] Dω: Cross-diffusion of the turbulent kinetic energy and the specific dissipation rate (k-ω model), [J·m−5] en: Tangential coefficient of restitution, [−] et: Normal coefficient of restitution, [−] Fab, n: Normal component of the contact force of the particles a and b, [N] Fab, t: Tangential component of the contact force of the particles a and b, [N] Fx: Additional forces exerted on a dispersed particle (Lagrangian approach), [m·s−2] g: Gravitational acceleration, [m·s−2] k: Turbulent kinetic energy of the fluid flow (SST k-ω model), [m2·s−2] kn: Normal spring constant, [N·m−1] kt: Tangential spring constant, [N·m−1] ms: Mass of a solid particle, [kg] Rep: Reynolds number based on the particle diameter, [−] S∗ij: Rate-of-strain tensor for the resolved scale in the Large Eddy Simulation model, [s−1] SF: Shape factor of the combustible dust, [−] ssphere: Surface area of a sphere having the same volume as the solid particle, [m2] sp: Surface area of the solid particle, [m2] Tk: Source of turbulent kinetic energy (k-ω model), [W·m−3] Tω: Source of specific dissipation rate (k-ω model), [J·m−5] u: Fluid flow velocity, [m·s−1] u∗i : Component of the velocity filtered in the Large Eddy Simulation model, [m·s−1] up: Particle velocity, [m·s−1] upr: Relative velocity of two colliding particles, [m·s−1] x'i: Convolution variable for the position of the gas flow, [m] Yk: Dissipation of the turbulent kinetic energy (k-ω model), [W·m−3] Yω: Dissipation of the specific dissipation rate (k-ω model), [J·m−5] Greek symbols

ΔLES: Filter cutoff width, [m] Γk: Effective diffusivity of the turbulent kinetic energy (k-ω model), [J·s·m−3] Γω: Effective diffusivity of the specific dissipation rate (k-ω model), [J·s·m−3] δ: Maximum overlap of two colliding particles, [−] δij: Kronecker delta function, [−] Κ: Filtering kernel of the LES model, [−] μ: Dynamic viscosity of the fluid, [Pa·s] μSGS: Dynamic subgrid viscosity, [Pa·s] ϑ: Poisson's ratio, [−] ρ: Fluid density, [kg·m−3] ρp: Particle density, [kg·m−3] τij: Local subgrid stress, [Pa] τkk: Isotropic part of the subgrid-scale stress, [Pa] ϕ: Filtered fluid flow property, [−] Ω: Angular velocity of the fluid flow, [s−1] ω: Specific dissipation rate of the turbulent kinetic energy of the fluid flow (SST k-ω model), [s−1]