Table Of ContentDust Explosion
Dynamics
Dust Explosion
Dynamics
Russell A. Ogle
Exponent, Inc.
Warrenville, IL, United States
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List of Figures
Figure1.1 Depiction ofthe structure of acombustion wave. 6
Figure1.2 Combustible dust pentagon. 9
Figure1.3 Schematic of the 20-L sphere explosiontestingdevice. 17
Figure1.4 Thesmoldering fire hazard ofcombustible dust. 19
Figure1.5 Theflash fire hazardof combustibledust. 20
Figure1.6 Thedust explosion hazard scenario. 21
Figure1.7 Thesecondary explosion hazard scenario. 22
Figure1.8 Theconfined accelerating flame hazardscenario. 23
Figure1.9 Thepressure piling hazard scenario. 24
Figure1.10 Totaluncertainty ofmodelpredictions asa function of 29
combustion model uncertainty and inputdatauncertainty.
Figure2.1 Equivalent spherical diameters. 38
Figure2.2 Discrete frequency distribution ofatomized aluminum 39
particle size measurements by light scattering.
Figure2.3 Continuous frequencydistributionof atomized aluminum 40
particle size measurements by light scattering.
Figure2.4 Cumulative distributionof atomized aluminum particle 40
sizemeasurements by light scattering.
Figure2.5 Continuous cumulative distributionof atomized 41
aluminum particle size measurements by light scattering.
Figure2.6 Subdivision ofsample sizes. 46
Figure2.7 Theeffect of dust concentration andparticle size onthe 48
dust explosbility parameters: (A)explosion pressure and
(B) maximum rate of pressure rise.
Figure2.8 Explosion parameters asa functionof polydispersity for 49
aluminum dust:(A) explosion pressure and(B) the
deflagration index, Kst.
Figure2.9 Ignitionproperties for Pittsburgh bituminouscoal as a 50
function ofparticle size: (A) minimum ignition
temperature and(B) minimum explosible concentration.
Figure3.1 Illustration ofclosedand open thermodynamic systems. 57
Figure3.2 Definition sketchfor a multiphasemixture. 62
Figure3.3 Illustration ofthe macroscale and microscaledimensions 69
for a dust flame burning at constant pressure.
Figure3.4 Definition sketchfor the adiabatic isobaric flame 70
temperature.
Figure3.5 Thermodynamicmodelfor constant volume combustion. 78
xvii
xviii List of Figures
Figure 3.6 Maximumpressure measurements asa function of dust 81
concentration: (A)cornstarch and(B) aluminum. The
solidlines indicate the chemical equilibrium calculation.
Figure 3.7 Definition sketch for the analysisof afractionalvolume 89
deflagration.
Figure 3.8 Fractional deflagration model for acombustible dust 92
with an isochoric combustion(explosion)pressure of
8bars at the stoichiometric condition.
Figure 3.9 Thermodynamic model for the secondary dust explosion 94
pressure.
Figure 3.10 Thermodynamic model for asecondary dust explosion 96
comparedwith the fractionaldeflagration model.
Figure 4.1 Illustration of one-dimensionalrectangularand spherical 103
coordinate systems.
Figure 4.2 Open tube ignition ofpremixed flammable gas mixture: 110
(A)the ignitionevent and (B) the propagationofthe
flame into the unburntmixture with the combustion
products flowing outofthe tube inthe opposite
direction.
Figure 4.3 Closed tube ignition of premixed flammable gas mixture: 111
(A)the ignitionevent,(B) the propagation of the flame
intothe unburnt mixture, (C) the formationofa shock
wave ahead ofthe combustionwave, and (D)the
merging of the shock and combustionwavesinto a
detonationwave.
Figure 4.4 Shock wave properties relative tolaboratory and shock- 112
fixed coordinate frames ofreference.
Figure 4.5 P2 diagramshowingthe Rayleigh line and the 115
Rankine(cid:1)Hugoniotcurve.
Figure 4.6 Rankine(cid:1)Hugoniotcurve with chemical energy addition 115
(Q.0).
Figure 4.7 Rankine(cid:1)Hugoniotdiagram divided intodifferent 116
regimes.
Figure 4.8 Temperature andfuel mass fraction profiles ina planar 123
premixed gas flame.
Figure 4.9 Definition sketch for Annamalaiand Puri’s energy 127
balance for apremixedflame.
Figure 4.10 Definition sketch for Spalding analysis ofpremixed 129
flame propagation.
Figure 4.11 Premixedflame thickness divided into a preheat zone 131
anda reaction zone.
List of Figures xix
Figure4.12 Definition sketchfor criticalradiusof ignition. 134
Figure4.13 Definition sketchfor flame quenching ina tube. 136
Figure4.14 Isolatedliquidfuel droplet surrounded by aflame sheet. 139
Figure4.15 Heatfluxes for asingle burning particle. 140
Figure4.16 Sketch showing relationship ofspecies flux directions 140
with respect tothe flame sheet (Fis fuel, OX is oxidizer,
and P is products).
Figure4.17 Temperatureand mass fraction profiles for aburning 146
liquid droplet.
Figure4.18 Diagram of arepresentativeelementary volume for a 149
combustible dust deposit.
Figure4.19 Effective thermal conductivity ofa porous medium with 153
parallel structure.
Figure4.20 Effective thermal conductivity ofa porous medium with 154
series structure.
Figure4.21 Flow regimesfor dispersed multiphase flow. 157
Figure4.22 Controlvolume sketch for the radiative transfer equation. 166
Figure4.23 Definition of the solid angle ω. 167
Figure4.24 Surface energy balance for thermalradiationon asolid 168
surface.
Figure4.25 Spectrum ofelectromagnetic waves in comparison with 169
the potential particle size range ofcombustible dusts.
Figure4.26 Absorption and scattering ofincidentthermal radiation 170
by a spherical particle.
Figure5.1 Thermal structure ofa smolder wave. 184
Figure5.2 Depiction ofa self-heating depositofcombustible dust. 186
Figure5.3 Temperatureprofilesforaself-heatingbodyinsubcritical 187
andsupercriticalstates.Thecriticaltemperatureoccurs
betweenthesubcriticalandsupercriticalstates.
Figure5.4 Heatgenerationand heat loss rate for the Semenov 189
analysis.
Figure5.5 Rectangular slab geometryfor a self-heatingporous 192
medium.
Figure5.6 Definition sketchfor Williams’s scale analysis of 199
smolder wave propagation.
Figure5.7 Reverse smolder wave propagation. 201
Figure5.8 Ohlemiller’s diagram showing the influxofoxygeninto 202
a two-dimensional smolder front.
Figure5.9 Definition sketchfor the diffusion analysis ofthe vertical 203
profileof the smolderfront.
xx List of Figures
Figure 5.10 Verticalprofile ofthe smolder wave front. 204
Figure 6.1 Sequenceof diffusion, adsorption, and chemical reaction 215
stepsin agas(cid:1)solidcombustion process.
Figure 6.2 Theshrinking particle model. 226
Figure 6.3 Concentration profile for species Awhen the gas film 227
resistanceis controlling.
Figure 6.4 Concentration profile ofspecies Awhenthe chemical 230
reaction is the rate-determining step.
Figure 6.5 Theshrinking unreactedcore model with constant 233
particle diameter.
Figure 6.6 Concentration profile for species Afor the shrinking 234
unreactedcore modelwhen the gas film resistanceis
controlling.
Figure 6.7 Concentration profile for species Afor the shrinking 236
unreactedcore modelwhen the productlayerdiffusion
resistanceis controlling.
Figure 6.8 Concentration profile for species Afor the shrinking 237
unreactedcore modelwhen the chemical reactionrate is
the controllingstep.
Figure 6.9 Relative importance ofthe rates ofgas film diffusion, 239
product layer (ash)diffusion,and chemical reaction on
the overall reaction rate asa functionof temperature.
Figure 6.10 Theprogressive conversionmodelfor a particle of 241
constant diameter.
Figure 6.11 Photographs ofsingle droplet diffusion flamesfor four 246
different hydrocarbon liquids.
Figure 6.12 Silhouette photograph ofburning petroleum ether 246
droplet, originaldiameter 1.5mm.
Figure 6.13 Godsave’splot ofdroplet diameter-squared versus time 247
for three liquid fuels.
Figure 6.14 Typical unburnt polymer particlesused ina single 252
particle combustion study byPanagiotou and Levendis.
Figure 6.15 High-speed video framesof aburningpolystyrene 252
particle.Thetime between two consecutive frames is
1ms (left toright).
Figure 6.16 Variation inthe particle sizes andshapes ofa Pittsburgh 257
coal dust sample beforeand after combustion.
Figure 6.17 Sections of a30-mmbituminous particle at various 260
stages of conversionfrom 0% to100% (fromleft to
right) ina combustionfurnace at 1000(cid:3)C.
Figure 6.18 Fourexamples ofbiomass material. 263
List of Figures xxi
Figure6.19 SEM micrographsof beech wood char particlesafter fast 265
pyrolysis at atemperature of950(cid:3)C: (A) 350μm, (B)
500μm,(C) 700μm,and (D)800μm.
Figure6.20 Burnouttime for volatiles combustion ofcorncob 266
particles asa functionof particle diameter.
Figure6.21 Burnouttime for char combustion ofcorncob particles as 267
a functionof particle diameter.
Figure6.22 Spherical diffusion flame surrounding burning particle at 268
threedifferent oxygen concentrations. Volatile
combustion infirst three frames followed bychar
oxidation. Numbers underneath each photograph
represents the burning time inmilliseconds.
Figure6.23 Typical char formationon aflat slab ofDouglas fir 270
wood. Top andside views ofchar fissures andcracks;
box denotesthe terminationof afissure.Scaleis in
inches.
Figure6.24 Conceptual modelofwood char development. 271
Figure6.25 Charpatterndevelopment in 50mmdiameter rosewood 272
sphereswith the formationof characteristic cracks and
fissures.
Figure6.26 Parentpine sawdust particle (A)and charred particles 273
caused bylow (B), high (C), andextremely high heating
rates (D).
Figure6.27 Carboncombustion models:(A)the heterogeneous 277
chemical reactionsinvolved inoxidation, (B)
concentration profiles for the one-film model, and(C)
concentration profiles for the two-film model.
Figure6.28 Surface control volume at the particle surface showing 278
reactionratesfor the one-film carbon particle
combustion model.
Figure6.29 Surface control volumes at the particle surface andthe 280
flame sheet showingthe reactionratesfor the two-film
modelof carbon combustion.
Figure6.30 Aluminum particle diameter-squaredversusburnout 288
time.
Figure6.31 Luminosity images for four burning aluminum particles 289
(210μmdiameter)in freefall.Scale on the left indicates
distance frompoint of ignition bylaser. Images show the
fullrange ofcombustion behavior.
Figure6.32 Shrinking unreacted core model for iron particle 291
combustion.
xxii List of Figures
Figure 6.33 Flame propagation ina cloud ofiron dust.Iron dust 292
concentration of 1.05kg/m3;time is the burning time
since ignition.
Figure 7.1 Schematic oftypical dust flame burner. 310
Figure 7.2 Homogeneous flame behavior in adispersed phase fuel 319
cloud. The flame preheatsand vaporizesthe fuel
particlescreating a premixed fuel vapor(cid:1)air mixture.
Figure 7.3 Heterogeneous flame behavior inadispersed phase fuel 320
cloud. The individual burning particlespreheats and
ignites their nearestneighbors with each particle burning
essentiallyindependently.
Figure 7.4 Mallard(cid:1)LeChatelier modelfor a dust flame. 330
Figure 7.5 Burning velocityof dust flame for aluminum (left side) 339
andmagnesium (right side) as afunction ofdust
concentration. Families ofcurvesrepresent different
mean particle diameters. Symbols are measured
velocitiesand solidlines are the modelpredictions.
Figure 7.6 Burning velocityof coal dust flames asa functionof 340
equivalence factor (dust concentration).(A)Comparison
ofBersham(▲), Beynon (x), andAnnesley (’) coals.
Influenceofvolatile matter (v.m.) and particle size (p.s.)
indicated byarrows. (B) Annesley coal: Theory versus
experiment.(C) Bershamcoal: Theory versus
experiment.
Figure 7.7 Dimensionless flame thicknessfor different fuels as a 341
function of the equivalence ratio.
Figure 7.8 Burning velocityversusthe Spalding transfer number B. 341
Thetypesoffuel depicted inthisfigure range from
propane vapor (g.f.,gaseous fuel) to iso-octane liquid
mist (l.m.), and fromvolatile solid fuels (s.f.)to
nonvolatilesolids. Calculations based on the
stoichiometric concentration of fuel, aparticle diameter
of30μm,atmospheric pressure,and ambient
temperature. Fuel abbreviations: k, kerosene; d.f.,diesel
fuel; h.f.o., heavy fuel oil; p.f., prevaporized fuel; and
f.l., flammability limit.
Figure 7.9 Laminar burning velocityfor iso-octane mist flames at 354
different Sautermean diameters (SMD) and fuel vapor
fractions (Ω)for two different equivalence ratios.
Figure 7.10 Plot ofmaximum flame temperature and mean flame 358
speed asa functionofdust concentration for three fatty
alcohols.
