Flame propagation of boron dust particles in heterogeneous media

Flame propagation of boron dust particles in heterogeneous media

    Flame propagation of boron dust particles in heterogeneous media Mehdi Bidabadi, Masud Hassani Haghighi, Alireza Khoeini Poorfar, Sae...

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    Flame propagation of boron dust particles in heterogeneous media Mehdi Bidabadi, Masud Hassani Haghighi, Alireza Khoeini Poorfar, Saeedreza Zadsirjan PII: DOI: Reference:

S0032-5910(14)00373-8 doi: 10.1016/j.powtec.2014.04.055 PTEC 10216

To appear in:

Powder Technology

Received date: Revised date: Accepted date:

9 July 2013 15 March 2014 16 April 2014

Please cite this article as: Mehdi Bidabadi, Masud Hassani Haghighi, Alireza Khoeini Poorfar, Saeedreza Zadsirjan, Flame propagation of boron dust particles in heterogeneous media, Powder Technology (2014), doi: 10.1016/j.powtec.2014.04.055

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ACCEPTED MANUSCRIPT Flame propagation of boron dust particles in heterogeneous media

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Mehdi Bidabadi1, Masud Hassani Haghighi1, Alireza Khoeini Poorfar1*,

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Saeedreza Zadsirjan1

1) School of Mechanical Engineering, Department of Energy Conversion, Combustion Research

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Laboratory, Iran University of Science and Technology (IUST), Tehran, Iran

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Keywords: Flame propagation, Boron, Discrete sources, Thermal Model, Dust Cloud

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Abstract

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In this paper the combustion of boron dust clouds has been studied numerically in an environment with spatially discrete sources. A thermal model has been generated to estimate the flame propagation speed in various dust concentrations. Furthermore, flame speed as a function of particle diameter has been studied. The results show a very good agreement with the theoretical and experimental data. Also, in this case, a comparison between dust cloud combustion models has been made. Flame front propagation as a function of oxygen mole factor and pressure for certain particle sizes has been studied.

1. Introduction *

Corresponding author: [email protected]

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ACCEPTED MANUSCRIPT Dust explosions have been a recognized threat to humans and property for a long time. There are many comprehensive reports of explosions caused by combustion of dust

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clouds. One of the earliest reports known is Count Morozzo’s (1795) [1] detailed analysis

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of an explosion in the flour warehouse in Turin in 1785. Therefore, modeling and predicting of dust clouds combustion are so important to control and prevent explosions.

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Flame propagation speed under different conditions is a remarkable research for

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explosion prevention. Principally boron is an attractive fuel for air-breathing missile engines due to its high volumetric heat of combustion. Boron has the highest volumetric

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energy density of any element, making it attractive for use as a potential fuel. In combustor design for engines burning boron powders, information regarding laminar

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flame speed in boron-oxygen-diluents (e.g. boron-air) dust clouds and its dependency on various parameters is important for proper design of flame-bolding regions [2].

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Combustion of metallic powders is a challenging scientific subject that also has significant practical applications. Since the combustion of inorganic particles is a high exothermic chemical reaction, especially their applications in many industrial operations are significant and efficient.

King [2] theoretically studied combustion of boron dust clouds. He presented a detailed model of boron-oxygen-nitrogen dust-cloud flame considering the details of boron particle ignition and the effects of oxygen depletion so as to develop and use it for prediction of flame speed. Moreover, he investigated boron particle burning time with a simplified model similar to that of Cassel et al. [3] Many studies have been carried out by Bidabadi et al. [4-14] in order to investigate the characteristics of dust cloud's combustion.

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ACCEPTED MANUSCRIPT Foelsche et al. [15] studied the ignition and combustion of boron particles at high pressures and temperatures. Their analysis allows for the investigation of the effects of,

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particle size, temperature and pressure on boron particle ignition and combustion delay.

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Also, King [16] studied the ignition and combustion of boron particles and clouds. He investigated boron particle burn time by diffusion model.

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King [17] modeled "clean" surface boron, by diffusion-controlled droplet gasification

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formulas (d2 law) for large particles (d≥30μm). Moreover, he investigated the fundamental aspects of boron dust particles ignition. His analysis allows for the

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investigation of the effects of boric oxide coating on particle ignition time. This study derived transient differential equations describing the generation and removal of the

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oxide and associated thermal effects along with heat transfer between the particle and the surrounding. Li [18] modeled kinetic-controlled combustion formulas (d law) for small

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particles (d≤10μm).

Propagation of diffusion front in reactive, heterogeneous media consisting of two spatially separated phases are common in many fields such as chemical kinetics, combustion, biology, etc. [19]. Often, the approach used for modeling front's propagation in discrete systems is to average the source terms with a spatially continuous function [18]. Goroshin et al. [20] studied the effects of the discrete nature of heat sources on flame propagation in particulate suspensions. They have illustrated the effect of the discrete nature of the heat sources on flame propagation by comparing flame speeds calculated both from continuous and discrete models in lean aluminum and zirconium particle-gas suspensions. It has been reported in their work that lower flame speeds and a weaker

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ACCEPTED MANUSCRIPT dependence of the speed on oxygen concentration are predicted by the discrete flame model.

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Tang et al. [21] investigated the effect of discreteness on heterogeneous flames and

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propagation limits in regular and random particles. Also Mendez et al. [22] studied the speed of reaction-diffusion fronts in spatially heterogeneous media.

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In the present study, the effects of particle size, oxygen mole fraction and dust

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concentration on flame propagation of micron-sized boron dust particles are studied theoretically. The discrete heat source method provides the dust combustion model, from

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ignition process to final state which includes steady flame propagation, flame quenching or even explosion. This is a powerful developing method. Beside wide range of models

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generated for dust particle's combustion which involve mass transfer and chemical kinetic that make them complicated problems, the present thermal model uses a novel approach

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in order to theoretical simulation of inorganic dust particle's combustion. The model is based on conduction heat transfer mechanism.

2. Thermal model

The mechanism of the dust cloud's combustion is a very complex process. The difficulty of the study is as a result of various processes such as: heating, evaporation, mixing with oxidizer, ignition, burning and quenching of particles in the dust cloud. In study of flame propagation in dust clouds, particle size and dust concentration play very important roles. Also, the interaction between the particles in the mixture always makes the dust combustion an unstable process. Heat transfer is the dominant phenomenon in the process of flame propagation in dust clouds.

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ACCEPTED MANUSCRIPT When the ignition system provides the minimum amount of energy to the dust cloud, the temperature of particles in the first layer is increased to the ignition

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temperature. As these particles start to burn, they act as heat sources in the dust cloud

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system and cause the temperature of the surrounding region to rise. The temperature rise

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in the other particles is calculated as the sum of thermal effects from the burned and burning particles. In case a high-enough temperature is provided, the combustion process

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will proceed to the other particles as shown in Figure 1. The temperature increase of

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particles in the preheated zone as a result of only conduction heat transfer mechanism is expressed based on the superposition principle.

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A thermal model based on heterogeneous combustion in three-dimensional space which

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relies on the following assumptions has been generated: 1. The particle is spherical and the flame diameter remains constant and is equal to the

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particle diameter.

2. The thermal properties of the media and particles are independent of temperature. 3. There is an equal and constant space between the particles distributed in the dust cloud. 4. A constant rate of energy release is considered during the combustion of a single particle.

5. For simplicity, the radiation heat transfer in the boron dust cloud is neglected and only conduction heat transfer has been considered. A relation for burning time of a single boron particle is presented by king [16]. As mentioned earlier, the mode of the combustion of micron-sized boron particles is a diffusion-controlled regime. Also boron undergoes a heterogeneous combustion in

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ACCEPTED MANUSCRIPT oxygen with the oxide coating on the particles. The burning time of boron particles in diffusion-controlled regime can be obtained from the following relation:

B

8 g DO2 , ln(1  0.677X O2 , )

d p2,I

(1)

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tb 

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Where t b is the burning time of boron particle in diffusion- controlled regime,  B

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is the boron particle density, d p ,I is the initial diameter of the boron particle,  g is the

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ambient gas density, g DO2 , is the density-diffusion product, and X O2 , is the mass

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fraction of oxygen in the ambient gas far from the particle surface. Moreover, the combustion time of boron particles from d1 law expression has

rp ,I k R PY O2 ,

(2)

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tb 

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calculated to generate simplified closed-form flame speed expression [2]:

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Where the parameters are defined in the nomenclature table. To model the single-particle combustion and the time-place temperature distribution of its domain, the energy equation in spherical coordinates is used: 1  2 Ta (r , t ) 1 Ta (r , t ) (r ) 2 r r r  t

(3)

   k A Ta (r , t )  q  Heaviside(  t ),@ r  rp  p  r   Ta (, t )  0  T (r , 0)  0   a    Ta ( r , t ) is T (r , t )  T , and T is the ambient temperature. The boundary and initial

conditions of the above equation are also shown above.

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ACCEPTED MANUSCRIPT q is the rate of heat release of a single particle from its surface during the burning time

which is defined as below [23]:

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q  Ak p (T f T  )rp,1I

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(4)

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The space-time temperature distribution of particles has been obtained through the whole domain by Bidabadi et al. [24] as stated below:

T s  T a (i , j , k )(ri , j ,k , t ig ) i

j

k

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rp  (r  rp ) 2 (r  rp ) 2   Ta (r , t )  (T f  T ) erfc( )  Heaviside(t   )erfc( ) r  4 t 4 (t   )   

(5)

(6)

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Ta is the space-time distribution of temperature around a single burning particle

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and beyond, and Ts is the total effect of burning and burned particles which is indicative

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of the temperature of medium fluid around a particle in the preheated zone. T∞ = 600K and Tf =2358K [2] are the considered values in basic case. Table 1 shows other properties of boron particle and properties of air. The space between the target particle and each particle placed at i, j, k is presented by: ri , j ,k  L i 2  j 2  k 2

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Where L is the space between two adjacent layers which is defined by the following equation by Bidabadi et al. [24]: L  ( d 3p  p / 6Cd )1/3

(8)

Where  p is the particle density and C d is the dust cloud concentration and d p is the particle diameter.

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ACCEPTED MANUSCRIPT The flame propagation speed is defined as the ratio of the space between two adjacent layers to the difference of their ignition times [24]. As mentioned earlier, since

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micron-sized particles are being dealt with, the formulation presented by [2] is utilized

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here. Fig. 1 shows the spatial distribution of particles in dust cloud.

Figure 1. The spatial distribution of particles in dust cloud: Layer n −1(burned particles), layer n (burning

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particles), and layer n +1 (preheating particles) [24].

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The ignition time of a single particle in a layer can be the representative of the

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ignition time of the mentioned layer. The particle is assumed to be positioned at the

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origin of the local coordinate system [24].

Table 1- Thermo physical properties of boron particle and air used in base case King [2]

3. Results and discussion

A computer code with Matlab software has been generated to calculate the burning speed of each layer after the release of energy from the ignition system. The logic and algorithm of the program is shown in Fig.2. In the considered algorithm, following the release of energy, at first, the temperature of the first layer caused by the ignition system at the considered location is calculated. When the temperature of the first layer’s particles reaches the ignition temperature, it is recorded as the ignition time of first layer and the calculations continue to find the ignition times of the other layers. 8

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Figure 2. Flowchart for estimation of the ignition time of boron particles

Beyond the first layer (n > 1), the preheating of layers is influenced by the burning of the

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preceding layers in addition to the ignition system. Thus, when a layer’s temperature

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reaches the ignition temperature, the relevant time is recorded as the ignition time of that

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layer. Flame propagation speed is determined by dividing the distance between two adjacent layers by the difference between ignition times of these two layers. If we

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assume that conduction is the only mechanism of flame propagation, the rise of particle's temperature will be a function of thermal diffusivity. The higher this value, the sooner the

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adjacent layers reach the ignition temperature and the flame propagation speed increases.

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The present discrete model's results for the estimation of flame propagation speed shown

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in Fig. 3 illustrate better agreement with the experimental data [2] in comparison with the theoretical simplified model by King [2]. Fig. 3 demonstrates that, despite the use of simplified model's burning time [2], the results of the discrete model are much closer to the experimental results [2]. Indeed, in combustion modeling of boron dust cloud, continuous model isn't as accurate as discrete sources of energy. However, it should be pointed out that the results of the present discrete model show a discrepancy with the ones of the detailed model and the reason for such a difference can be due to the fact that the detailed model considers the effect of oxygen depletion and ignition delay time which have been neglected here; therefore its results would be more accurate and closer to the experimental data.

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ACCEPTED MANUSCRIPT Figure 3. The change of flame propagation speed with initial oxygen mole fraction under atmospheric

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pressure and initial temperature of 300 Kelvin with particle diameter of 5μm

Fig. 4 shows the variation of flame propagation speed as a function of dust concentration

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for boron dust cloud with 2m diameter.

2m boron dust cloud

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Figure 4. Flame propagation speed as a function of dust concentration (kg/m 3) for

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As it is observed in Fig. 4, with the increase of dust concentration, flame propagation speed tends to increase. It is obvious that with the increase of dust concentration, the

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distance between fuel sources decreases which causes augmentation of heat conduction

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and increase of flame propagation speed.

Figure 5 shows that for boron particle diameters smaller than 10 micron, the flame speed rises dramatically when the particle diameter decreases. Due to use of simplified burning time, it seems that King's flame speed simplified model [2] has better agreement with discrete results.

Figure 5. Flame speed as a function of particle size

Fig. 6 illustrates the comparison of flame propagation speed as a function of particle initial oxygen mole factor. For a considered particle size, the flame front speed in king's detailed model [2] has higher value comparing to the flame speed in other models.

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ACCEPTED MANUSCRIPT Figure 6. The change of flame propagation speed with initial oxygen mole fraction under atmospheric

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pressure and initial temperature of 600 Kelvin with particle diameter of 2μm

Flame propagation speed for boron dust cloud in the presumed discrete media as a

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function of pressure for different models is demonstrated in Fig. 7. As it is seen, with the

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rise of pressure, flame speed decreases. The detailed model of predicting flame speed has been modeled with d2 law [2]. As it is mentioned it has the burning time independent of

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pressure, thus it has constant value in different values of pressure. Also, it can be

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observed that the discrete model is in agreement with king’s simplified model [2].

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Figure 7. Flame speed as a function of pressure in different models

The two probable effective potential error-producing assumptions associated with

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discrete model are mentioned below: 1. Neglect of the effect of radiation heat transfer 2. Neglect of the effect of oxygen depletion.

4. Conclusions In this paper, flame propagation of boron dust particles in an environment with spatially discrete sources is numerically investigated. A computer code has been generated in order to study the effects of dust concentration and particle size on flame propagation speed. Flame propagation speed is studied as a function of particle size for

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ACCEPTED MANUSCRIPT fuel-rich boron-air suspension. It is shown that as the particle size increases, the value of flame speed decreases. Furthermore, flame speed as a function of oxygen mole fraction

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for certain particle diameters is illustrated. It is observed that flame front speed tends to

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have higher values as the oxygen mole factor increases. Moreover, it can be concluded that for boron dust cloud, front flame speed decreases with rise of pressure. Results from

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the presented model are in good agreement with the theoretical model and experimental

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data. The results of the presented discrete model demonstrates a good compatibility with the ones of experimental data and detailed model. Nonetheless, as mentioned earlier, due

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to the fact the effects of radiation heat transfer and oxygen depletion have been neglected

A Cd d D i,j,k

kp kR L n P

q. r t

tb T X

Y O 2 ,

Particle Surface Area Dust concentration Diameter Diffusivity coefficient Components of Cartesian coordinate Conduction coefficient

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Nomenclature

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in this study, a difference between the aforementioned results can be observed.

Constant in burning rate expression Distance of of two adjacent particles or layers Layer's number, number of Pressure Heat transfer rate to a particle, heat release by Igniter Radius of , radial distance Time Burning Time Temperature Mass fraction Oxidizer mole fraction

Subscripts a

Ambient , Burning zone, absorption

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Greeks

   

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Thermal diffusivity Dimensionless distance Density Particle burning time

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Initial particle Summation of effects, particle per Ambient property

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Boron Conduction Flame Ambient gas Due to igniter Particles in layer per unit area Oxygen in the ambient gas

B c f g ig L O2 ,  p,I s

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References

2009, pp. 20–21.

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[1] R.K. Eckhoff, Dust Explosions in the Process Industries, Third edition, Elsevier Science, New York,

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[2] King, M. K, Predictions of laminar flame speed in boron-oxygen-nitrogen clouds, Proceeding of fifteenth international symposium on combustion, 1974, pp.467-477. [3] Bidabadi M, Rahbari A and Alizadehheidari M. The analytical investigation of the premixed combustion in cylindrical micro – combustor. Proc IMechE, Part C: J Mechanical Engineering Science 2011; 225(4): 931–938.

[4] Cassel, H. M., Das Gupta, A. K., and Gunaswamy, S.: Third Symposium on Combustion, Flame and Explosion Phenomena, p. 185, Williams and wilklns, 1949. [5] Bidabadi M, Haghiri A and Rahbari A. The effect of Lewis and Damkohler numbers on the flame propaga-tion through micro-organic dust particles. Int J Therm Sci2010; 49(3): 534–542. [6] Bidabadi M, Montazerinejad S and Fanaee A. An ana-lytical study of radiation effect on the ignition of mag-nesium particles using perturbation theory.Latin Am Appl Res2010; 40: 351–357. [7] Bidabadi M, Moallemi N, Shabani A, et al. Analysis of size distribution and ignition temperature effects on flame speeds in aluminum dust clouds. Proc IMechE, Part G: J Aerospace Engineering 2010; 224(1): 113–119.

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ACCEPTED MANUSCRIPT [8] Bidabadi M, Azimi M and Rahbari A. The effects of radiation and particle size on the pyrolysis of biomass particles. Proc IMechE, Part C: J Mechanical Engineering Science2010; 224(3): 675–682. [9] Bidabadi M, Shahrbabaki Shabani A, Jadidi M, et al. An analytical study of radiation effects on the

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premixed laminar flames of aluminium dust clouds.Proc IMechE, Part C: J Mechanical Engineering

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Science2010; 5(12): 2194–2202.

[10] Bidabadi M, Gh Barari, Azimi M, et al. Theoretical study of a perfectly volatile particle triple

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flame.Int J Recent Trends Eng2009; 1(5): 26–29.

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[11] Bidabadi M and Rahbari A. Novel analytical model for predicting the combustion characteristics of premixed flame propagation in lycopodium dust particles. J Mech Sci Tech2009; 23(9): 2417–2423.

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[12] Bidabadi M and Rahbari A. Modeling combus-tion of lycopodium particles by considering the temperature difference between the gas and the par-ticles. Combust Explo Shock Waves 2009; 45(3): 278285

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[13] Bidabadi M, Fereidooni J, Tavakoli R, et al. Premixed filtration combustion of micron and sub-micron

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par-ticles in inert porous media: a theoretical analysis. Korean J Chem Eng2011; 28(2): 461–469.

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[14] Haghiri A and Bidabadi M. Modeling of laminar flame propagation through organic dust cloud with thermal radiation effect. Int J Therm Sci 2010; 49(8): 1446–1456. [15] R.O. Foelsche, R.L. Burton, and H. Krier 1999 Boron particle ignition and combustion at 30-150 atm, Combustion and Flame 117:32-58.

[16] King, M. K., J. Ignition and Combustion of Boron Particles and Clouds Spacecraft Rockets19:294 (1982)

[17] King, M. K., "Boron Particle Ignition In Hot Gas Streams," Comb. Sci. Tech, 8, 255 (1974). [18] Li, S. C., and Williams, F. A., In Combustion of Boron-Based Solid Propellants and Solid Fuels. Boca Raton: Begell House/CRC Press, p. 248. 1993. [19] J. Xin, Front propagation in heterogeneous media, Siam Rev. 42 (2000), 161-230. [20] S. Goroshin, J.H.S. Lee, Y. Shoshin, Effect of the discrete nature of heat sources on flame propagation in particulate suspensions, 27th Symposium (International) on Combustion, The Combustion Institute, USA, 1992, pp. 743–749.

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ACCEPTED MANUSCRIPT [21] F.D. Tang, A.J. Higgins, S. Goroshin, Effect of discreteness on heterogeneous flames: Propagation limits in regular and random particle arrays, Comb. Theory and Modelling 13 (2009) 319-341. [22] V. Mendez, J. Fort, H.G. Rotstein, S. Fedotov, Speed of reaction-diffusion fronts in spatially

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heterogeneous media, Phys. Rev. E 68 (2003), 041105.

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[23] H. Hanai, H. Kobayashi, T. Niioka, A numerical study of pulsating flame propagation in mixtures of gas and particles, Proc. Combust. Inst. 28 (2000) 815-822.

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channels, J. Loss Prev. Process Ind. 26 (2013) 172-176.

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[24] M. Bidabadi, S. Zadsirjan, S.A. Mostafavi, Propagation and extinction of dust flames in narrow

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Figure 1. The spatial distribution of particles in dust cloud: Layer n −1(burned particles), layer n (burning particles), and layer n +1 (preheating particles) [24].

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Figure 2. Flowchart for estimation of the ignition time of boron particles

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Figure 3. The change of flame propagation speed with initial oxygen mole fraction under atmospheric pressure and initial temperature of 300 Kelvin with particle diameter of 5μm

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Figure 4. Flame propagation speed as a function of dust concentration (kg/m3) for 2m boron

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Figure 5. Flame speed as a function of particle size

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Figure 6. The change of flame propagation speed with initial oxygen mole fraction under atmospheric pressure and initial temperature of 600 Kelvin with particle diameter of 2μm

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Figure 7. Flame speed as a function of pressure in different models

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Table 2- Thermo physical properties of boron particle and air used in base case [2]

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T

600

 DO ,

1.2 0.15

kR

0.05

K

K

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2

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Tignition

Unit

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T flame

Value 2358

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Property

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K kg / m 3

m2 / s cm atm .sec

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Graphical abstract

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ACCEPTED MANUSCRIPT Highlights: 

A thermal model based on discrete dust combustion in three-dimensional space has



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been generated so as to study the flame propagation of boron dust cloud. The presented model is an effective model for the better prediction of the different

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aspects of dust explosions and a better design of safety systems.

As the particle size increases, the value of flame speed decreases



With the increase of the oxygen mole fraction, the value of flame speed tends to rise.

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