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Chemical Engineering Journal xxx (2012) xxx–xxx

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Chemical Engineering Journal

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A reaction engineering approach to modeling dust explosions

Vimlesh Kumar Bind a,b, Shantanu Roy a,⇑, Chitra Rajagopal b

a Department of Chemical Engineering, Indian Institute of Technology – Delhi, Hauz Khas, New Delhi 110 016, Indiab Center for Fire, Explosive and Environment Safety, Defence Research and Development Organization, Timarpur, Delhi 110 054, India

h i g h l i g h t s

" We present a two-scale reaction engineering model for dust explosions." Particle scale model incorporating transport effects and kinetics is presented." Quasi-homogeneous (dust-) cloud scale CFD model linked to particle-scale model." Model validated for aluminum (metallic) and starch (organic) dust explosions." Presented case study demonstrates applicability to real situations.

a r t i c l e i n f o

Article history:Available online xxxx

Keywords:Dust explosionMulti-scale modelingCFDCombustion

1385-8947/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.cej.2012.07.026

⇑ Corresponding author. Tel.: +91 11 2659 6021; faE-mail address: [email protected] (S. Roy).

Please cite this article in press as: V.K. Bind et10.1016/j.cej.2012.07.026

a b s t r a c t

Dust explosions are a major hazard frequently encountered in vital sectors like food, energy, defense(propellants and explosives) and pharmaceuticals. These explosions emanate from rapid combustion ofclouds of suspended fine particles in the micron range. Quantitative estimation of dust explosion prop-agation is crucial to their mitigation, and for providing estimates of physical quantities that determinethe explosion behavior for design of safety systems. In this contribution, a multi-scale reaction engineer-ing approach for modeling dust explosions has been presented. In the model, two scales are considered.At the particle scale, a detailed model involving various transport steps is written and solved for a varietyof different boundary conditions. This model is used to build an effective reaction rate term which isincorporated in the dust cloud-scale CFD model through an appropriate source term. The CFD modelfor the effective dust cloud mixture is then executed to model the propagation of the dust explosion. Val-idation of the developed CFD model has been carried out for two different kinds of dust particles, alumi-num (metallic dust) and starch (organic dust), for experimental data published in literature. Finally, acase study has been presented which shows the applicability of present approach in modeling real situ-ations. It is demonstrated that using the same physics and estimated kinetic parameters from particlescale model or smaller scale experiments, fairly satisfactory prediction for dust explosions in real geom-etries could be obtained.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

Dust explosions involve rapid combustion of fine, combustibledust particles (generally in the micron size range). Following thisrapid combustion, typically the pressure of product gases, in theenclosure containing the dust-oxidizer mixture, increases manyfolds within a fraction of second. This causes the ‘‘explosion’’ andcan potentially cause collapse of the enclosure itself, or lead to sec-ondary dust explosions which could be equally damaging to life andproperty even at some distance from the original point of the explo-sion. Historically the first recorded incidence of a dust explosionwas at an Italian flourmill in 1785, although it was almost certainly

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al., A reaction engineering appr

not the first to occur [1]. These hazards are frequently encounteredin vital industries and sectors of a country including agriculture,food processing, coal mining, defense (involving solid, granularexplosives and propellants), plastic, wood and other materials pro-cessing, and pharmaceuticals. In these industries, various unit oper-ations like storage, grinding, transportation and pneumaticconveying are susceptible to dust explosion hazards. Several excel-lent texts are now available which provide excellent reviews of thisimportant but relatively less studied safety hazard (for example, seethe works of Eckhoff [1], Field [2], Palmer [3] and Field [4]). How-ever, most of these books deal with dust explosion as a safety andhazard issue, discuss ways of mitigating and preventing these, butfew treat the underlying physics in great detail.

Proper understanding of dust explosion phenomena is neces-sary for design of any preventive or protective system to prevent

oach to modeling dust explosions, Chem. Eng. J. (2012), http://dx.doi.org/

http://dx.doi.org/10.1016/j.cej.2012.07.026

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2 V.K. Bind et al. / Chemical Engineering Journal xxx (2012) xxx–xxx

such hazards causing accidents. Since the explosions result in rapidpressure build-up and heat localization, it is crucial to estimate the(primarily convective) transport rates with accuracy, so that a pro-tection system could be designed and safety protocols may beestablished. This is of particular relevance since experiments aredifficult to perform in these situations, and investigations leadingto quantitative estimates can only be performed in well-designed,small-scale laboratory units, such as the classical Siwek 20L appa-ratus (e.g. [5]). Dust explosion experiments in actual process plantsare rarely performed, due to the prohibitively high cost and risk in-volved ([6] is a notable exception).

Extensive work on modeling dust explosions using CFD [7–9] inconjunction with input from laboratory scale experiments [10–12]has revealed that much more work is needed on the basic physicsand chemistry. Ogle [13] was perhaps the first one to emphasizethe need of dust explosion prediction using material propertiesof the explosible mixture. Ogle [13] has developed a model for sim-ulation of aluminum/air explosions in closed vessel, assuming spa-tially uniform pressure at any instant. Relation between particlescale surface burning rate and volumetric reaction rate at cloudscale was shown. However in this work particle scale modelingwas not attempted and surface reaction rate was assumed as ratecontrolling mechanism for aluminum particle combustion. Further,20 L spherical vessel was assumed as batch reactor for dust explo-sion reaction modeling. These simplified assumptions (may be dueto lack of computational power) resulted in disagreement betweenOgle’s [13] theoretical and experimental work. Nevertheless thiswork suggested an important methodology based on materialproperties of combustible mixture and cloud scale hydrodynamicsfor dust explosion prediction.

This contribution was motivated by the fact that proper under-standing of dust explosion phenomenon is necessary at ‘‘particlescale’’ as well as at ‘‘cloud scale’’. ‘‘Particle scale’’ deals with mech-anism of ignition, gas–solid non-catalytic reaction, all at the size orlength scale of the dust particles (which is usually a few microns).The transport phenomena at the ‘‘cloud scale’’ deals with flame andpressure propagation, which is actually in a two-phase gas–solidsmixture (referred to as the ‘‘cloud’’), even though for many pur-poses it may behave like a pure gas cloud. This overall vision ofthe dust explosion mechanism is reflected schematically in Fig. 1.This understanding and distinction of scale-wise transport shouldlead us to the formulation of a mathematical model to relate fac-tors, parameters and design variables. When coupled with compu-tational fluid dynamics (such as the work of Skjold et al. [8]), it is

Fig. 1. Proposed multi-scale approac

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possible to translate the particle-scale and cloud-scale physics tocomplex geometries.

In an earlier contribution [14], a CFD model has been presentedin which the dust-air mixture is viewed as an effective gas, and theexplosion was driven by an effective source term resulting fromparticle-scale combustion. In this contribution, we present thecombined model (involving particle-scale combustion and cloud-scale transport), show validation of this model and extend it tomodel a case study. Even with the assumption of quasi-homoge-neous dust cloud, the simulation for dust explosion in industrialsize of vessel �10.3 m3 presented in proposed manuscript takesconsiderable time of the order of month with IBM Server: 64 bitOperating System, Processor Intel(R) Xenon (R) CPU, 2.27 GHz,4.0 GB Memory. This is due to the fact that the time step used inproposed simulation is �10�5 s where as total time of combustionin the vessel is of the order of �1.0 s. The main advantage of pro-posed model compared with existing models is that it is basedon material properties of fuel and oxidizer at particle scale andat cloud scale CFD could be applied which will make it more gen-eralized and with lesser assumptions compared to existing models.This will also lead to fundamental understanding of dust explosionphenomenon. This model is versatile and could be applied for anygeometry.

2. Representing particle scale phenomena in dust cloud CFD

From our presentation of Fig. 1, it is clear that we intend to de-velop an ‘‘effective’’ description of particle scale phenomena andthen connect it to the cloud scale CFD model. Descriptions at par-ticle scale can be analytical, numerical or empirical (through corre-lations). Either of these descriptions are sensitive to the nature ofthe dust particles, the oxidizers, and most importantly, the averageinter-particle distance in the cloud. This factor actually determinesthe kind of combustion the dust particles would exhibit, and hencewhat role it would have in determining the overall explosionbehavior.

If these particles are separated by a large distance, single parti-cle combustion will define the combustion behavior of the cloud.However if the concentration of dust particle is high and particlesare in the vicinity, then the so-called Group Combustion or CloudCombustion modes is observed [15]. Therefore, the average inter-particle distance is an important factor in defining the cloud scaledust explosion phenomenon.

h for dust explosion modeling.




Fig. 3. Inter-particle distance as a function of volume fraction of particle phase.

V.K. Bind et al. / Chemical Engineering Journal xxx (2012) xxx–xxx 3

According to Eckhoff [1], typical dust concentration for whichexplosion can occur ranges from 10 to 1000 g/m3. Density of mostof the dust particles are of the order of 1000 kg/m3. Therefore, thetypical value of particle volume fraction is of the order of/P = 10�5 � 10�3. The average inter-particle distance between par-ticles as a function of volume fraction, in an assumed ‘‘particle-in-box’’ configuration shown in Fig. 2, is given by [16]:

/P ¼ðp=6Þd3

P

L3P

() LP

dP

� �¼ ðp=6/PÞ

1=3 ð1Þ

The relationship is shown in Fig. 3 as a ready reference. Natu-rally, the actual distribution of particles in a dust cloud need not fol-low the ‘‘particle-in-box’’ configuration (Fig. 2), but neverthelessthat configuration offers us a reference point to determine whatkind of combustion the cloud is experiencing. According to Annam-alai et al. [15], the individual particle combustion will take place ifthe inter-particle distance (Lp) is at-least twice the flame radius ofthe particle. In this case, the group combustion number dp/Lp� 1.0.

2.1. Metallic particles

Consider the dust explosion of aluminum-air mixture withaverage concentration of aluminum of 0.35 kg/m3, which corre-sponds to a concentration that is somewhat higher than the stoi-chiometric concentration required for aluminum combustion. Forthis concentration, the inter-particle distance is approximately 32times the particle radius. The flame radius for aluminum particleis of the order of 2–5 times the particle diameter [17], hence thereis little probability that group combustion will occur in case of alu-minum particle combustion. Eckhoff [1] has reported on Leuschke’sclassical experiment which demonstrated the relative importanceof radiative heat transfer in dust explosion flame propagation. Inthis experiment, on two sides of a double glass window, two dustclouds were simultaneously generated. Immediately after that oneof the dust clouds was ignited using gas flame. It was observedfrom study that metallic (Zr, Ti, Al and Mg) flames produced suffi-cient radiation to ignite the cloud on the other side of the doublewalled glass window. Thus, it may be safely assumed during deri-vation of cloud scale energy and species source term that any sin-gle particle in the cloud will not ‘‘feel’’ the presence of otherparticles, however the flame will still be propagated primarily byradiation. This reasoning may be true for most of the metallic par-ticles which have similar density as aluminum and lower volatilityas compared to organic particles. Therefore the rate of consump-tion of particle phase (including radiation effects) could be trans-formed into quasi-homogeneous reaction rate for metallicparticles according to following equation:

R000 ¼ a� 6dp� R00ðdp; T; P;CO2 Þ ð2Þ

where a represents volume fraction of fuel, R00ðdp; T; P;CO2 Þ repre-sents the surface reaction rate, R000 represents the volumetric reac-

Fig. 2. Assumed ‘‘particle-in-box’’ configuration of dust (spherical) cloud in air.


tion rate, dP is the particle diameter. Hence, in case of metallicdust explosion, surface reaction rate can be averaged over volumearound particle and obtained volumetric reaction rate could be usedin cloud scale CFD model. This will be the case, for instance, whenthe case of Al-air dust explosion would be considered.

For the case of metallic particles, then, the problem of connect-ing it to the dust cloud CFD model, as described in Fig. 1, would be todevelop an appropriate mathematical description of the R000 term inEq. (2) above, and then use it as a volumetric reaction rate term in agas-phase CFD to describe the explosion in a ‘‘dust cloud’’ gas. Ofcourse it will be assumed that the particles are in the micron range,and hence in Stokes’ regime of settling with a small particle relax-ation time, so that the particles actually follow the gas with fidelity.

As described earlier, the R000 term in Eq. (2) could be either esti-mated through a detailed analytical model incorporating the parti-cle scale heat and mass transport, and reaction chemistry. Indeedsuch an exercise has been accomplished by the authors but is beingcommunicated through a different paper which will be dedicatedto that model alone. Here, we use the alternate approach, whichis to incorporate the particle scale dynamics though an appropriatecorrelation which models the particle scale combustion. Such acorrelation, widely applied for aluminum dust particle combustionis the Beckstead combustion time correlation [18]. The authors ofthe current contribution has shown elsewhere the Beckstead’s cor-relation [18] also agrees very well with the single particle combus-tion model developed by them.

2.1.1. Use of Beckstead’s correlation for aluminum combustionAccording to Beckstead [18], a correlation could be developed

for combustion time of single Aluminum particle in various oxidiz-ing environments based on combustion data from more than tensources with 400 data points. The correlated expression is given as:

sc ¼adn

p0

Xeff T0:2P0:1 where Xeff ¼ yO2þ 0:6yH2O þ 0:22yCO2

ð3Þ

where a = 0.0244 for n = 1.5 and a = 0.00735 for n = 1.8, pressure isin atmospheres, temperature in K, diameter in lm, and time in ms.Estimation of volumetric reaction rate based on Beckstead’s correla-tion [18] involves assumption of the volumetric reaction rate andsurface reaction rate in following forms respectively:

R000 ¼ Ae�E=RT CxAlC

yO2

ð4Þ

R00 ¼ 1

pd2p0

dðp6 d3p0qAl=MAlÞ

dtð5Þ





For CFD modeling of Al-air dust explosion using Arrheniuskinetics, therefore four volumetric reaction rate coefficients (A, E,x and y) needs to be estimated.

Ae�E=RT CxAlC

yO2¼ a

MAld3p0

dðqAld3p0Þ

dt� a

Md3p0

qAld3p0

scð6Þ

Applying Beckstead’s combustion time correlation [18]

Ae�E=RT CxAlC

yO2¼ aqAl

MAl

� �Xeff T

0:2P0:1

adnp0

ð7Þ

In the right hand side the term inside parentheses represents effec-tive aluminum concentration i.e. CAl = aqAl/MAl. Mole fraction ofoxidizer species (Xeff) in the ambient will be independent of temper-ature and pressure (for the closed system) and will be proportionalto oxygen concentration (Xeff / CO2 ) in case of Al-air dust explosion.Pressure of the closed system will be proportional to temperature:P / T. Applying the above three conditions:

Ae�E=RT CxAlC

yO2¼ CAlCO2 T0:3uðdp0Þ ð8Þ

) �E=RT ¼ 0:3 ln T þ lnðuðdp0Þ=AÞ ð9Þ

Assuming the reaction of aluminum-air is first order with re-spect to both the components (in absence of any better informa-tion) and the second term in RHS of Eq. (9) is independent oftemperature, the activation energy could be evaluated from theslope of plot of (0.3 lnT) v/s. 1/T. Hence,

E ¼ �0:3Rdðln TÞdð1=TÞ ð10Þ

Applying Eq. (10), the ‘‘effective’’ activation energy of 8.55 kJ/mol is obtained at 3400 K (approximate of Al-air flame tempera-ture). The activation energy for Al particle surface reaction is re-ported as 73.6 kJ/mol [19]. The low value of activation energyseems to indicate that combustion is diffusion limited in this case,with a certain degree of falsification of the intrinsic kinetics. Con-sequently, the validity of Beckstead’s correlation [18] is limitedto large scale aluminum particles (particle size range of 15–760 lm) only from which it is derived.

2.2. Organic particles

Eckhoff [1] in his book referred to the work of Gieras et al. [20],and reported that the maximum flame radius of coal particle is ofthe order of 3–6 times the radius of the particle. The result alsoshows that flame radius increase with increasing in volatile compo-sition of the coal particle. Law [21] reported the maximum ratio offlame radius to radius of heptane droplet is approximately 15.Therefore, this can be argued that the ratio of flame radius to parti-cle radius increases with increase in volatile content or the particle.

Organic particles mainly consist of volatiles including water va-por, fixed carbon and ash. Along with these components pores maybe also present in the particles. Therefore organic particles are hav-ing bulk density which is lower than the true density of the fixedcarbon and ash. The bulk density is defined as:

qbulk ¼ eFC qFC þ eAsh qAsh þ evolatile qvolatile þ epore qgas ð11Þ

1 ¼ eFC þ eAsh þ evolatile þ epore ) eFC þ eAsh

¼ ð1� eporeÞ � evolatile ð12Þ

Here ei and qi represents volume fraction and true density of com-ponent ‘i’: fixed carbon, ash content, volatile, pores and gas. The truedensity of fixed carbon (high strength graphite) and the ash content(mineral such as alumina, silica and magnesia.) is reported as1500 kg/m3 and 2600–3900 kg/m3 respectively [22]. The absolute


density of most of the organic liquids/volatile lies between 800and 1000 kg/m3 [23] much lower than the fixed carbon and ashcontent. Therefore assuming the volume fraction of pore (epore) con-stant, if low density volatile is present in the organic particle it willreduce the volume of higher density fixed carbon and ash contentand hence the presence of volatiles reduces the bulk density ofthe particle. If all the volatiles are removed by heating from the par-ticle, the pore volume fraction of the particle will increase. As thedensity of gases is order of magnitude lower than the fixed carbonand ash content the bulk density of particle will reduce in this case.According to Fig. 3, the inter-particle distance reduces with de-crease in density, therefore for very volatile particles, the individualparticle combustion mode may not be observed. It is probable thatin many cases burning of individual particle will be felt by neigh-boring particles. Therefore in case of organic particle combustion,estimation of quasi-homogeneous reaction rate similar to metallicdust cloud will give erroneous result and hence should not be ap-plied. For organic particle combustion reaction rate will be deter-mined from one set of cloud combustion and thereafter itspredictability validated for other set of conditions.

3. CFD model for dust explosion and parameter estimation

3.1. CFD model formulation

The model formulation has been discussed and the methodol-ogy has been demonstrated using hydrogen-air mixture combus-tion by Bind et al. [14]. As mentioned by Bind et al. [14], thedensity-based solver of commercial CFD software Fluent 6.3.26has been used for modeling dust explosion. For modeling chemis-try during dust explosion species transport and finite-rate chemis-try model has been used. A dust-air mixture approach, which isbest suited for very small particles with a small particle relaxationtime, is applied in present study. Accordingly kinetic parametersand physical properties are modified to account for combustiblesolid particles in the dust cloud. The density-based solver of com-mercial CFD software Fluent 6.3.26 has been used for modelingdust explosion which solves the governing equations of continuity,momentum, energy, and species transport simultaneously:

Continuity :@q@tþr:ðq~vÞ¼0 ð13Þ

Momentum :@

@tðq~vÞþr:ðq~v~vÞ¼�rpþr:ðseff Þþq~g ð14Þ

Energy :@

@tðqEÞþr:ðq~vEþp~vÞ¼r:ðkeffrT�

Xj

hj~Jjþseff~vÞþSh ð15Þ

Species :@

@tðqYiÞþr:ðq~vYiÞ¼�r:ððqDi;eff þlt=SctÞrYiÞþR000i ð16Þ

The following equation for turbulent kinetic energy (k) and turbu-lence dissipation (e) are solved after Eqs. (13)–(16) at each step.

@

@tðqkÞ þ r:ðq~vkÞ ¼ r: lþ lt

rk

� �rk

� �þ Gk þ Gb � qe� YM þ Sk

ð17Þ

@

@tðqeÞ þ r:ðq~veÞ ¼ r: lþ lt

re

� �re

� �þ C1e

ekðGk þ C3eGbÞ

� C2eqe2

kþ Se ð18Þ

The equations mentioned above contain effective physical prop-erties and kinetic parameters. These effective properties dependupon physical properties of each phase, components and dust load-ing in combustible dust cloud. Equation for estimation of some ofthe effective physical properties and kinetic parameters are men-tioned in Table 1. Cloud density and pressure are related using a





modified equation of state [24]. The reason for this modification isdue to the presence of solid particles which does not exert anypressure on the enclosure containing dust cloud at steady state.Another main modification required is estimation of volumetricreaction rate from single particle combustion which is mentionedin previous section. In the proposed model stoichiometric combus-tion has been applied as it is intended to model the worst conse-quence of dust explosion for risk and hazard analysis applicationpurpose. Although the stoichiometric combustion conditions maynot be always achieved in actual practice, it does provide worseconsequence prediction and hence a limiting envelope for differentnon-stoichiometric conditions leading to different levels of incom-plete combustion.

The estimated effective physical properties and kinetic parame-ters are applied in CFD model as if the dust cloud is an ‘‘effective’’gas phase. In the earlier work of Bind et al. [14], the methodologyhas been demonstrated using gaseous mixture combustion in 20 LSiwek apparatus. In present study the model has been extended toinclude dust combustion (explosion) in the similar apparatus,treating the gas–solid mixture as a quasi-homogeneous phase.

As pointed out in Section 2, depending on whether the dustexplosion is for a metallic powder or organic powder, the way inwhich the particle-scale events are incorporated in the CFD modelwould be different. In fact, a somewhat different algorithm needsto be utilized in each case. Fig. 4 summarizes this approach, andin fact is an algorithmic representation of the overall modeling ap-proach shown in Fig. 1. In the rest of this contribution, the centralidea shown in Fig. 4 has been detailed in specific cases of alumi-num and starch powder explosion.

3.2. Observed kinetic parameter estimation based on experimentaldata

The actual dust explosion is a complex phenomenon, spatialand temporal variations of most of the parameters (pressure, tem-perature, etc.) are nonlinear. Therefore there was a need of stan-dard experimental apparatus whose data could be used topredict the real dust explosion. 20 L dust characterization appara-tus emerged as standard apparatus worldwide due to lower capitaland operating cost and consistency of result with larger apparatus[25]. In this standardized setup, the pressure history of the vessel isobtained as an output. Three dimensional symmetry of sphericalgeometry reduces the requirement of modeling it completely (ow-ing to symmetry considerations), therefore only one-eighth of the20 L sphere has been modeled in current studies. As representativesamples for metallic and organic dust, aluminum and starch parti-cles has been chosen, respectively.

3.2.1. Parameter estimation for aluminum dust explosionExperimental data provided in Ogle’s Ph.D. thesis [13] has been

principally considered for estimation of kinetic parameter usingCFD model and model validation purposes. The paper publishedby Dufaud et al. [5] has been also considered to verify the applica-bility of estimated parameters from particle scale model in differ-

Table 1Effective physical properties and kinetic parameters for CFD Model.

Reference Physical properties and kinetic parameters

Wallis [24] Cloud density (q)

Einstein’s equation Cloud viscosity (l)Maxwell’s equation Cloud thermal conductivity (k)

Wallis [24] Cloud ratio of specific heat (c)– Cloud volumetric reaction rate (R000)


ent sets of experimental results of various researchers. The worksmentioned above are in 20 L apparatus only. Few large scale dustexplosions are also mentioned in literature; however enough datais not provided in them to carry out validation of CFD model. In thecurrent CFD approach, the kinetic expression has been assumedsimilar to Ogle’s model [13]. However in this case activation energyestimated from particle scale model has been used, as per the dis-cussion around Beckstead’s correlation in Section 2.1.1.

In the context of metallic dust particles, it is important to men-tion the parallel approach (to our work) that has been followed byGoroshin et al. [26–28]. Goroshin et al. [27] has stressed that rep-resentation of polydisperse dust by some average particle size isnot adequate due to variation of particle combustion rate with par-ticle size. Discrete combustion has been suggested for aluminumdust explosion by Goroshin et al. [28] as it was observed that forlean dust mixtures, the flame width is comparable to or even less(in average) than the distance between particles. However, in ouropinion modeling of all the underlying mechanisms (kinetics ver-sus transport) at the same time and considering discrete modelingwill make it a complex and, computationally costly. Besides, suchdetailed turbulence-chemistry interactions may not be neededfor modeling dust explosions for most safety applications. This isparticularly relevant in view of the uncertainties in the experimen-tal data as there is no data available at present that correlates par-ticle scale combustion with distribution in particle size, and thevariation in controlling mechanism (kinetics or heat and masstransport) of combustion.

Thus, in the present study, the entire particle size range hasbeen modeled assuming the mean particle size as the representa-tive size of the particle. It is assumed that the particles with samemechanism of combustion have equal observed activation energyand could be directly incorporated from particle scale combustionmodel. However the observed Arrhenius pre-exponential factor,needs to be estimated from one set of experimental data (pressureversus time in a closed vessel) for that sample only, to account forthe effect of polydisperse dust.

A particle size dependent ‘‘effective’’ Arrhenius pre-exponentialfactor (A) has been estimated for Al-air using experimental dataavailable in literature. Variation of this parameter does not changethe combustion mechanism of combustion, only time of combus-tion is altered. The value of A has been evaluated by random searchof pre-exponential factor (A) in a large domain followed by selec-tion of value of ‘A’ based on value of coefficient of correlation(CoC) and visual inspection of curves. The CFD modeling of Al-airdust explosion has been carried out using activation energy ofE = 8.55 � 1003 kJ/kmol (approximately 316 kJ/kg) obtained fromparticle scale model in previous section. The mixture was ignitedby patching temperature of 3500 K in sphere (radius 3.0 cm) atthe center. The model setting and initial condition mentioned inTable 2 were used for simulation.

3.2.2. Parameter estimation for starch dust explosionStarch is an organic material and hence undergoes Group

Combustion, as explained in Section 2.2. The experimental data

Relationship

q ¼ 1þ a½qsqg� 1�

� �p

RTP

iðYi=Mw;iÞ

Yi ? mass fraction of vapor phase of species ‘i’

l = lg(1 + 2.5a)k

kg¼ 1þ 3a

ðksþ2kg Þ=ðks�kg Þ�a

c = (Cpg + YsCps)/(Cvg + YsCvs)

R000 ¼ Ae�E=RT CmFuelC

nO2¼ a� ð6=dpÞ � R00 (Heterogeneous/homogeneous single

particle reaction rate ? quasi homogeneous reaction rate)




Fig. 4. Solution algorithm for dust cloud kinetic parameter estimation.


provided in Ph.D. thesis of Dahoe [29], for 15 lm particle diametercorn starch in a 20 L apparatus, has been used for estimation ofkinetic parameters and validation of CFD model in present work.Large scale experimental work, in a 10.3 m3 cylindrical vessel, car-ried out by Kumar et al. [6] has been considered in next section.

For the cases where group combustion of particles occurs in-stead of single particle combustion, particle scale models are notavailable or not reliable due to complexity involved with combus-tion mechanism. Also in such cases, the material characterizationor data used in model is not available. However, for purposes ofmodeling, the observed kinetic parameters could be estimatedfor particular dust-air system based on experimental data on theoverall combustion characteristics. To extract the effective kineticsvia numerical regression of the experimental data, two parameters(effective Arrhenius pre-exponential factor, A, and effective Activa-tion Energy, E) has been selected for analysis.

The method of evaluation of observed kinetic parameters hasbeen mentioned in Fig. 4. Note that in this case, the regression pro-cess itself involved a complete CFD calculation with Fluent 6.3.26

Table 2Model settings and initial parameters for Al-air simulation.

Model settings Initial con

Space 3DTime Unsteady, 1st-Order Implicit Mass fracViscous k–e turbulence model Mass fracHeat transfer Enabled Mass fracSpecies-transport Reacting (Al, Al2O3, O2, N2) Mass fracTime step (s) 10�5 s TemperatMax. iterations per time step 100

Reaction rate term for species:Al: �rAl = A � exp(�8.55e + 06(J/kmol)/RT) � CAl � CO2 .O2 : �rO2 = 0.75 � A�exp(�8.55e + 06(J/kmol)/RT) � CAl � CO2 .Al2O3: rAl2O3

= 0.5 � A � exp(�8.55e + 06(J/kmol)/RT) � CAl � CO2 .N2 : rN2 ¼ 0.


in the 20 L spherical geometry, to simulate the experiments of Da-hoe [29]. Essentially, by this process one is claiming that whateveruncertainties exist between the model and real experiment, are alllumped into the two unknown parameters (A and E). The model,initial condition, and reaction kinetics were used for testing thefeasibility of simulation is presented in Table 3. Subsequently,these parameters were used to simulate other cases of starch dustexplosions, as discussed later.

4. Results and discussion

4.1. Simulation of aluminum dust explosion

For simulating the case of Aluminum dust explosion, incorpo-rating the particle scale information in the dust-gas CFD simula-tion, the results were compared with Ogle et al.’s [30]experimental data and simulation work. Ogle [13] in his Ph.D. workdeveloped a one-dimensional model based on spherical symmetry.

dition in vessel (corresponding to 500 g/m3 aluminum suspension in air)

tion of Al 0.2797tion of Al2O3 0tion of O2 0.189tion of N2 0.5313ure 300 K




Table 3Model settings and initial parameters for starch-air simulation.

Model settings Initial condition in vessel (this corresponds to cornstarch concentration of 429 g/m3 orequivalence ratio 1.876)

Space 3D Mass fraction of starch 0.25Time Unsteady, 1st-order implicit Mass fraction of H2O 0Viscous k–e turbulence model Mass fraction of CO2 0Heat transfer Enabled Mass fraction of O2 0.15Species-transport Reacting (5 species: starch, H2O,CO2, O2, N2) Mass fraction of N2 0.6Time step (s) 5.0 � 10�5 s Temperature 300 KMax. Iterations per time step 100

Reaction rate term for species:starch: �rStarch = 1.8e+08(m3/(kmol s)) � exp(�100 (kJ/mol)/RT) � CStarch � CO2 .O2: �rStarch = 6 � 1.8e+08(m3/(kmol s)) � exp(�100(kJ/mol)/RT) � CStarch � CO2 .H2O: rH2O = 5 � 1.8e+08(m3/(kmol s)) � exp(�100(kJ/mol)/RT) � CStarch � CO2 .CO2: rCO2 = 6 � 1.8e+08(m3/(kmol s)) � exp(�100(kJ/mol)/RT) � CStarch � CO2 .N2 : rN2 ¼ 0.

Fig. 5. Experimental data and theoretical model comparison for Al (dP = 12.1 lmand CAl = 300 g/m3) combustion in 20 L apparatus, as reported by Ogle et al. ([30]).

Fig. 6. Comparison of CFD simulation with Ogle’s [13] and Dufaud et al. [5]experimental work.


Fig. 5 shows the experimental and theoretical work of Ogle [13],wherein the two show clearly very different trends. We believe thisdiscrepancy emanates from the inadequacy in description of parti-cle-scale effects in that original work [13]. Following kinetics wasused in the two models:

Ogle’s model [13]:

�rAl ¼ 1:4eþ 05ððm3=gÞ1=2 s�1Þ � expð�24ðkcal=molÞ=RTÞ

� q3=2YAl � Y1=2O2

ð19Þ

Current CFD simulation :

� rAl ¼ A � expð�8:55eþ 06ðJ=kmolÞ=RTÞ � CAl � CO2 ð20Þ

where A ¼ 3200 m3=ðkmol sÞfor particle size of 6:69 1:1 lm¼ 1600 m3=ðkmol sÞfor particle size of 12:1 lm¼ 800 m3=ðkmol sÞfor particle size ðdP;50Þ of 11 lm

In our case, the ‘‘effective’’ Arrhenius factor ‘‘captures’’ the particlescale effects, through the treatment described in Section 2.1.1.

As shown in Fig. 6, CFD results are qualitatively and quantita-tively similar to experimental results, and remarkably capturethe experimentally observed trends of Ogle [13]. Fig. 6 also showsa comparison of CFD simulation result with recently publishedexperimental data of Dufaud et al. [5]. Again, our CFD simulationresults (incorporating the particle scale effects) closely tracks the


experimental trends, in contrast to the prediction of Ogle et al.[30] where the trends could not be captured. It is noteworthy thatin both the cases it was assumed that all the aluminum particleparticles in the 20 L apparatus start burning at the same time. Ogle[13] considers heterogeneous surface reaction (activation energy�100 kJ/mol) as the rate determining step whereas Dufaud et al.[5] considers both heterogeneous surface reaction (activation en-ergy �12 kJ/mol) as well as species diffusion limitation for singleparticle combustion. It is worth noting that in the present CFD sim-ulations, the effective observed activation energy of E = 8.55 kJ/molwas considered whereas Dufaud et al. [5] considers activation en-ergy �12 kJ/mol for modeling heterogeneous surface reaction ofaluminum particles. It is clear that these two values are of the sameorder of magnitude, indicating strong mass transfer limitations(and the same underlying physics) in both the cases. Naturally,our model is general enough to capture whatever controlling re-gime may exist in the combustion process.

4.2. Simulation of starch dust explosion

In this case, CFD simulations were performed without using anexplicit particle scale description, as outlined in Sections 2.2 and3.2.2. For these cases, determination of effective kinetics has beencarried out using one set of experimental data, whereas validationhas been done for different sets of experimental data of 20 L dustexplosion apparatus available in literature. Value of coefficient of




Fig. 7. Comparison of simulation results with experimental data of Dahoe [29].

Fig. 8. Schematic of the experimental apparatus (Kumar et al. [6]).


correlations (CoCs) and visual inspection of curves are the basis ofvalidation study. For validation purposes, two different studies

Fig. 9. Average pressure history for cornstarch (291 g/m3)/air mixture dust explo


were undertaken: one for the trend analysis and another for themaximum pressure achieved. As shown in Fig. 7, the CFD resultsare qualitatively and quantitatively similar to experimental resultsreported in the doctoral thesis of Dahoe [29]. However, the pre-dicted final overpressure is slightly higher than the experimentaldata. This is expected since the actual experiments in 20 L standardSiwek apparatus involve unaccounted heat loss, incomplete com-bustion etc. which is not considered in simulation. The experimen-tal results were provided in Dahoe’s thesis [29] only for 15 lmstarch particle size therefore only one value for effective Arrheniuspre-exponential factor, A, could be obtained. The final effectivereaction rate expression used in the CFD simulations is:

�rStarch ¼ 1:8eþ08ðm3=ðkmol sÞÞ � expð�100ðkJ=molÞ=RTÞ � CStarch � CO2

ð21Þ

The estimated observed activation energy for starch-air explo-sion in 20 L apparatus is of the same order of magnitude as thatfor H2-air estimated by Bind et al. [14]. The same order of magni-tude for observed activation energy suggests homogeneous com-bustion for dust explosion phenomenon of starch-air mixture.The reason for homogeneous-gaseous type combustion of starch-air mixture might be due to requirement of much lower gasifica-tion temperature for starch compared to flame temperature ofstarch-air mixture during dust explosion phenomenon. Therefore,before the actual burning of starch, it is decomposed into smallergaseous molecules, mixing of gaseous fuel and oxidizer takes place,and finally homogeneous combustion takes place; although someminor amount of char is also present during combustion process.In case of aluminum-air dust explosion presented in current studysuch homogeneous combustion is not observed. The reason for thisis relatively larger particle combustion duration of micron size alu-minum solid dust particles compared to gaseous fuel moleculesformed during starch combustion. The composition of aluminumreduces slowly with reduction of mass of aluminum during particleburning process.

4.3. Case study: modeling practical process plant situation

This case study deals with validation of dust explosion modelfor organic particle dust explosion frequently occurring in agricul-ture sector. In this study, experimental work of Kumar et al. [6]involving corn starch dust explosion experiments in a 10.3 m3

sion in 10.3 m3 experimental setup (Kumar et al. [6]) and simulation results.





cylindrical vessel, has been simulated using the developed model.The experiment was performed in a 1.5 m diameter and 5.7 m high(H/D = 3.8) cylindrical vessel whose schematic is shown in Fig. 8.For details of experimental setup and procedure Kumar et al. [6]work could be referred.

The experiments in the paper of Kumar et al. [6] were per-formed at ambient conditions: �25 �C (298 K) and �100 kPa atthe time of ignition of dust cloud. The approximate average sizeof starch particles were 20 lm. Pressure histories was recordedfor varying degrees of turbulence. Maximum pressure and rate ofpressure rise for corn starch-air dust explosion was claimed to beconsistent with literature in this study. The experimental resultof the Kumar et al.’s [6] describing average pressure history inthe vessel with and without fan generated turbulence for cornstarch- air mixture is given in Fig. 9. As expected, in the vessel,the rate of pressure rise increases with increased turbulence gener-ated due to fans compared to condition when fan is off.

The model, initial condition, and reaction kinetics were used fortesting the feasibility of simulation is presented in Table 4. Themixture was ignited by patching temperature of 3500 K in sphere(radius 25.0 cm) at the bottom of the vessel and kept at mid-dis-tance between axis and wall of the cylinder. Dynamic grid adapta-tion technique based on gradient of temperature has been used forsimulation. Same kinetics, as reported in Section 4.2 (Eq. (21)),were used for these simulations. No other parameters were arbi-trarily set. However, it may be noted that in Dahoe [29], the datais reported for 15 lm starch particles whereas in Kumar et al.’s[6] experimental data is for 20 lm starch particles. In the absenceof available kinetic parameters for 20 lm starch particles, kineticdata for 15 lm starch particles evaluated in previous section wereapplied in present study without any further changes.

One of the main observed differences between experimentaldata and simulation is total combustion time of starch-air mixturein cylinder. According to the simulation results shown in Fig. 9, theflame reaches upper wall of the cylinder in approximately 800 ms.This combustion time is lower than the experimentally predictedvalue of combustion time by Kumar et al. [6]. One of the main rea-sons for reduction in predicted combustion time is use of effectivekinetic parameters of 15 lm starch particles instead of 20 lm usedin experiments. The combustion kinetics for 15 lm starch particlesin air is expected to be markedly faster than that of 20 lm starchparticles. Fig. 9 shows the contours of temperature for starch-airdust explosion, obtained using CFD modeling in cylinder represent-ing experimental setup. After ignition near the bottom of cylinder,the flame moves rapidly towards the unreacted starch-air mixture.The movement of flame is due to reaction as well as due to expan-sion of burned section caused by increased temperature and in-crease in the number of moles of gases.

Table 4Model settings and initial parameters for case study simulation.

Model settings Initialor equ

Space 3DTime Unsteady, 1st-Order implicit MassViscous k–e turbulence model MassHeat transfer Enabled MassSpecies-transport Reacting (5 species: starch, H2O,CO2, O2, N2) Mass

MassTime step (s) 1.0 � 10�5 s TempeMax. iterations per time step 100

Reaction rate term for species:Starch: �rStarch = 1.8e+08 (m3/(kmol s)) � exp(�100(kJ/mol)/RT) � CStarch � CO2

O2: �rStarch = 6 � 1.8e+08(m3/(kmol s)) � exp(�100(kJ/mol)/RT) � CStarch � CO2 .H2O: rH2O = 5 � 1.8e+08(m3/(kmol s)) � exp(�100(kJ/mol)/RT) � CStarch � CO2 .CO2: rCO2 = 6 � 1.8e+08(m3/(kmol s)) � exp(�100(kJ/mol)/RT) � CStarch � CO2 .N2 : rN2 ¼ 0.


Another major difference between experimental observationand simulation result is the trend of the average pressure historycurve which could be observed in Fig. 9. Since dust explosion isdeflagration phenomenon therefore the pressure in the vesselcould be considered uniform for all practical purposes, hence aver-age pressure is compared with the experimental data. Fig. 9 showsthat according to experimental data, during initial stages of dustexplosion, pressure and rate of pressure rise in the cylinder in-creases smoothly with time and in final stage of combustion, max-ima is observed for pressure and rate of pressure rise startsdecreasing and reaches to zero value when pressure becomes max-imum. Simulation results also confirm a similar trend as shown,except for the reduction in the rate of pressure rise in betweenignition and the instant of combustion completion in the cylinder.The reason for this discrepancy is evident from the contour plots inFig. 9, which show that the incipient flame rapidly moves in bothdirections until it reaches the bottom. Therefore the initial rate ofpressure rise in cylinder is due to combustion in two differentplanes. The combustion in lower direction stops at a time of about200–300 ms due to consumption reactant exhaustion in the lowerportion. The period 200–300 ms is also the time after ignition atwhich a decrease in rate of pressure rise is observed for the firsttime.

The third difference in predicted value and simulation results ismaximum pressure reached in cylinder during dust explosion. Inthe present simulation, the peak pressure observed is of the orderof 10.0 bar whereas Kumar et al. [6] reported a value of approxi-mately 7.0 bar. The possible reason for difference might be use ofdifferent starch dust particle (15 lm instead of 20 lm used inexperiment) combustion kinetics in simulation and use of adia-batic boundary condition at the vessel wall. Further, 15 lm starchparticle might be more efficient for combustion compared to20 lm starch particles which is used by Kumar et al. [6] for exper-imental study. It was reported by Kumar et al. [6] that incompletecombustion was observed during starch-air dust explosion. In ananother experimental data of corn starch-air dust explosions, Rad-andt et al. [31] has reported maximum pressure of 10.47 bar for H/D ratio of 4 where corn starch median size was 15 lm. H/D ratio of4 by Radandt et al. [31] is close to the geometry of experimentalvessel used by Kumar et al. [6] for which H/D ratio is 3.8. Thus,our results are in reasonable agreement with that data as well.

The present case study suggests that pressure in the processvessel rises in finite time for starch-air dust explosions. Therefore,with the application of developed CFD tool various mitigation mea-sures, such as suppression, venting and partial inerting, could bedesigned and optimized. Apart from designing one mitigation mea-sure at a time, a combination of above mentioned techniques couldbe designed and optimized with the application of CFD.

condition in vessel (This corresponds to cornstarch concentration of 0.429 kg/m3

ivalence ratio 1.876)

fraction of starch 0.25fraction of H2O 0fraction of CO2 0fraction of O2 0.15fraction of N2 0.6rature 300 K





5. Summary and conclusions

The present study was concerned with modeling of dust explo-sions in a 20 L spherical apparatus (the so-called ‘‘Siwek 20 Lapparatus), which is most widely used for dust explosion charac-terization as per international standards. The well defined exper-imental procedure and sufficient data available in literature for20 L spherical apparatus makes it appropriate for validation ofdeveloped CFD model for dust explosions. Due to complexityand computational costs involved with combined turbulent mul-tiphase flow and combustion during dust explosion, a dust-gasmixture approach has been used to model the cloud scale phe-nomena in present study. This assumption have helped in obtain-ing better prediction of dust explosion compared to existingoptions at the same time keeping the scope for futureimprovements.

The density based solver of the commercial Finite Volume basedCFD software, Fluent 6.3.26, was used for CFD modeling of combus-tion/dust explosion in 20 L apparatus. In this model, the ‘‘dustcloud’’ is assumed as homogeneous mixture which comprises ofsolid dust particles and gaseous oxidizers. Therefore, the CFD mod-el mentioned above incorporates effective physical properties andkinetic parameters which depend upon physical properties of eachphase, components and dust loading in combustible dust cloud.The equation for estimation of some of the effective physical prop-erties and kinetic parameters are presented. Algorithm for estima-tion of observed kinetic parameters for dust explosion has beenpresented for two different types of dust particles explosions:metallic dust particle explosion, and organic dust particle explo-sion. The variation of approach for observed kinetic parameter esti-mation helps in avoiding the complexity and computational costarises due to group combustion of organic particles and helps inestablishing a practical approach for using CFD in dust explosionconsequence prediction. The CFD modeling using particle scalemodel has been demonstrated for aluminum dust explosion,whereas for organic particle combustion CFD modeling of dustexplosion is carried out for starch without using particle scalemodel. In both the cases, either using, or without using particlescale model for CFD simulation, model has been validated againstexperimental data. Qualitatively and quantitatively similar resultswere obtained compared to experimental results for both alumi-num and starch combustion.

The estimated observed kinetic parameters for starch-air dustexplosion has been applied for modeling of dust explosions in real-istic conditions. Case study dedicated to organic dust explosion hasbeen presented. The CFD simulation of starch-air dust explosion isvalidated with experimental data and it was demonstrated that theusing same physics and estimated kinetic parameters using 20 Lapparatus, fairly satisfactory prediction in real geometries couldbe obtained. Thus, the numerical challenge here is no longer tomodel the transport-chemistry, but ability to mesh large volumesand complex geometries. This has been successfully shown byCFD modeling of case study. Therefore, the developed CFD modelcould effectively utilized for design of safety systems and riskassessment of real dust explosions.


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