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Laser ignition of combustible gases by radiative heating of small particles
C O M B U S T I O N A N D F L A M E 91: 3 9 9 - 4 1 2 (1992)
399
Laser Ignition of Combustible Gases by Radiative Heating of Small Particles P. C. HILLS*'* D. K. ZHANG, P. J. SAMSON, and T. F. WALL BHP Research Newcastle Laboratories, P.O. Box 188, Wallsend,NSW 2287, Australia (P.C.H.;P.J.S.) Department of ChemicalEngineering, Universityof Newcastle, NS W 2308, Australia (D.K.Z.;T.F.W.) This article summarizes the ignition risks of laser power delivered by optical fiber to combustible atmospheres. Of six possible ignition mechanisms, the ignition of a combustible gas by a small optically heated body has been extensively investigated. Continuous-wave (CW) powers of 100 mW delivered by multimode optical fibers created explosion in combustible atmospheres. A numerical model of the ignition of a combustible gas by a small heated body on the exposed end of an optical fiber is developed. Important parameters include gas (type and concentration), particle (type, diameter, absorptivity, refractive index, reactivity, thermal capacity, density), optical fiber (core diameter and numerical aperture), and light (wavelength and power).
NOMENCLATURE a
ai Ag Ap Ci
Di Ei
k k' mi M N.A. n
effective absorption efficiency particle-light g e o m e t r i c overlap gas reaction rate preexponential factor, k g m -3 s I kPa -n particle reaction rate preexponential factor, kg m -2 s 1 kPa -n mass c o n c e n t r a t i o n of species i, kg m-3 thermal capacity, J k g - l K-1 mass diffusivity o f species i, m e s activation energy of species i, J kmol 1 reaction heat o f particle and gas respectively, J k g gas thermal conductivity, W m-~ K - J rate constant (coefficient) reaction o r d e r for 2 H 2 + 0 2 = 2 H 2 0 with respect to species i particle mass, kg numerical a p e r t u r e of optical fiber reaction o r d e r for C + O 2 = C O 2 with respect to oxygen c o n c e n t r a t i o n
P qrd
Qo f R
Ri t
L T(t, r)
optical power, W radiative heat flux, W m 2 particle spectral absorptivity radius, m universal gas constant, J kmol 1 K reaction rate, kg m -3 s 1 (gas), kg m 2 S-1 (particle surface) time, s ambient temperature, K particle temperature, K t e m p e r a t u r e at radius r from particle centroid at time t, K
Greek Symbols a~,j p o• A 0
stoichiometric factor, species i to j density, kg m -3 S t e f a n - B o l t z m a n n constant, W m -2 K-4 particle emissivity laser wavelength, /.tm m a x i m u m divergence angle of optical radiation f r o m fiber end (degrees)
Subscripts b * Present address: ICI Biospecialties, 57 Tourle Street, Mayfield, NSW 2304, Australia. * Please address further correspondence to Dong-ke Zhang at Department of Chemical Engineering, University of Newcastle, NSW 2308, Australia. Copyright © 1992 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc.
c C g
b o u n d a r y layer radius of the gas (from particle centroid) core radius of optical fiber carbon gas phase 0010-2180/92/$5.00
400
P
P. C. HILLS ET AL. gas species i = 1 for N2; i = 2 for 02; i = 3 for H2; i = 4 for H20; i = 5 for CO2 particle (surface)
INTRODUCTION Typical applications of optical sensors include safety systems in industries such as coal mining and petroleum production. The optical power is transmitted through optical fibers, avoiding the use of electricity in potentially explosive atmospheres. Continuous-wave (CW) powers of tens of watts can be transmitted over kilometer lengths of optical fiber. However, there has been little experimental [1-7] or theoretical [8-9] research on the safety of optical power delivered by optical fiber systems in combustible atmospheres. Furthermore, no regulations or standards currently address power limitations for optical fiber systems in potentially explosive atmospheres. A combustible atmosphere may be ignited by mechanical sparks, electrical sparks, or by thermal effects. Mechanical sparks are considered highly unlikely with optical systems as there are no moving parts, although the design and construction of transceivers, sensor heads, junction boxes, and connectors associated with a fiber optic system must be considered. The ignition capability of an electrical spark varies with gas concentration, humidity, oxygen content of the atmosphere, temperature, and turbulence, with as little as 0.02 mJ required [10]. In contrast, laser-induced explosions of particles, aerosols, gases, or explosives have typically used large amounts of energy in controlled environments [11-34]. Six possible ways in which light emerging from an optical fiber can cause gas/dust ignition have been identified: direct thermal ignition of gas, photochemical excitation of gas, dust or solid explosion by thermal ignition of a particle or explosive, direct laser spark ignition of gas, laser spark ignition of gas by small particles, and radiative heating of a small particle in a flammable atmosphere. Direct thermal ignition of gas by absorption of radiation causing a rapid increase in temperature has been demonstrated [11-16]. However, ignition at low power levels in a flammable
atmosphere is unlikely because even the most sensitive of gases has to be raised to at least 100°C throughout a volume of 100 ml or more for ignition to occur [1]. The low absorptivity of the absorption bands of flammable gases and vapors in air and the relatively wide spectral band width of sources other than lasers mean that a large proportion of the optical power will not be absorbed. Furthermore, the power required for ignition with this mechanism is wavelength dependent; the strongest absorption bands generally occur outside the silica optical fiber transmission window of 0.8-1.55 /xm. Photochemical ignition [17-20], in contrast to thermal ignition, occurs with photodissociation of molecular oxygen due to absorption of 130-175 nm ultraviolet radiation, which generates atomic oxygen and produces other reactive radicals via chain-branching. Subsequent reaction of the radicals with fuel molecules, as well as other intermediate species, release heat. Consequently, the temperature of the mixture rises, leading to ignition. Ignition requires high laser energies in the order of 350 mJ in a 20-ns pulse [20]. A dust or solids explosion could occur if a dust or solid exists in an explosive concentration and a small body or part of the solid is heated to supply enough energy to explode. This ignition mechanism includes laser initiation of explosives [21-25], a problem that has interested specialists from the time the first laser systems appeared and were introduced into laboratory research. Experiments have shown that the thermal theory of initiation explains the mechanism of initiation of condensed explosives by laser radiation. With this ignition mechanism absorption of light by a layer of explosive results in light energy being converted into shock-wave energy. Explosions have been reported with pulse energies as low as 5.4 mJ [22]. In direct laser-spark-initiated ignition of gases [26-30] optical breakdown of the gas occurs at the focal point of a laser beam. Ignition occurs with breakdown of the gas and plasma production at the focal point of a focused laser beam. Sufficient energy must be supplied to the gas mixture in a short time, the energy creating free radicals such that the
LASER IGNITION BY SMALL PARTICLES reaction between the flammable species and oxygen commences. Breakdown in gases can be achieved at the focal point of a laser beam when it is collimated by a simple convex lens. For example, a Q-switched ruby laser of 10 ns pulse width and maximum power of 120 MW (1.2 J) focused to a spot of 240 /xm created explosions at atmospheric pressure and room temperature [27]. Laser spark ignition of gases with small particles of the focal spot results in optical breakdown of the gas due to thermal explosion of small particles [31-34]. When small suspended particles are rapidly heated by absorbing highpower laser energy they change from a solid to a vapor, the explosion occurring if the vapor contains excess energy. Kingdon and Weinberg [34] demonstrated that normal critical minimum ignition energies govern the process by using Q-switched laser beams focused on small targets in flammable atmospheres. Laser spark ignition of gases occurs at lower power levels than direct thermal ignition and laser-sparkinitiated ignition of gases, as small particles are able to absorb laser power more efficiently than gases. For example, a Q-switched ruby laser of 40 ns pulse width and 0.5 mJ pulse energy focused to 80 /xm diameter and incident on a 12-/zm wire created explosions in 8.6% methane/air mixtures [34]. If sufficient optical power escapes from an optical fiber and illuminates a small particle, ignition is possible by heating the particle to ignite the surrounding atmosphere. This is the most likely mechanism for optical ignition with low CW power levels, the ignition hazard increasing if a reactive particle is illuminated. This situation could occur in a coal mine when an optical fiber cable is accidentally ruptured such that coal dust is illuminated in the presence of hydrogen- or methane-air mixtures. It has been demonstrated in the literature [1-9, 35-37] that it is possible to ignite flammable gases by CW laser illumination of particles that have similar dimensions to the core diameter of optical fibers (5-500 /zm). In one case several ignitions of free-falling carborundum (silicon carbide) particles within the range of 20-50 /xm diameter in di-ethyl gas occurred with greater than 2.8 W of optical power from an argon iron laser [2]. Moore and
401 Weinberg [35-37] used a focused laser beam to show that certain kinds of particles of approximately 1 mm diameter ignite with radiation fluxes of about 100 k W / m 2 in a variety of flammable atmospheres. Most notable were particles consisting of cotton wool, and Kaowool fiber, Kaowool being a nonflammable silica-alumina-based insulating wool that consists of fibers of 5 /zm diameter while cotton wool is a flammable material of 20 tzm diameter. Several laser ignition experiments have been performed with a quasi-CW laser. Homan and Sirignano [38] ignited flammable atmospheres with single aluminum particles of various diameters (20-80/~m) suspended on a glass fiber in a methane/air- or propane/air-combustible gas mixtures. The particle was heated and caused to burn by a 0.5-ms pulse from a neodymnium glass laser. The minimum diameter of single burning aluminum particles that ignite methane/air mixtures was determined experimentally to be between 20 and 30 /xm. In propane/air mixtures the minimum diameter is less than 20 /xm. If particles are small enough they can burn or vaporize in fuel/air mixtures and not obtain the critical amount of energy required to ignite the mixture [37, 38]. We have experimentally exploded/ignited over 300 gas/air mixtures. We have used optical fibers to deliver the laser beam to particles located in an explosion chamber rather than the focused laser beam experiments previously described. This allows the optical power emerging from the fiber end to be accurately measured and allows the light emerging from the fiber end to be directed onto a small particle with a high degree of accuracy. Furthermore, this is typical of industrial applications where laser light is delivered to combustible atmospheres via optical fibers. In this article a mathematical model is formulated to predict the minimum optical power carried by optical fibers that is required to ignite a combustible gas by heating a small reacting particle [8, 9]. A coal particle in a combustible mixture of hydrogen and air is considered. The effects of ignition delay, theoretical absorption efficiency, gas concentration, particle reaction, wavelength, and particle size are determined. Both gas-phase and particle
402
P. C. HILLS ET AL.
surface reactions are considered. The radial and temporal variation of temperature and species concentration in the boundary layer are predicted and the effects of various parameters on the ignition characteristics are examined. There are many parameters that influence whether ignition will occur, including particle reactivity (inert or reactive), activation energy, and reaction enthalpy for the oxygen reaction, size, porosity, spectral absorptivity, thermal conductivity, density, initial temperature, and heat capacity. Properties of importance for the light source include the pulse duration (continuous wave or pulsed at a certain duty cycle), peak power, power density, pulse shape, and wavelength. As light is transmitted through optical fibers their properties must also be considered. Optical fibers consist of single-mode and multimode types. Single-mode optical fibers have core diameters in the range of 2-10 txm while multimode fibers typically have core diameters greater than 50 /xm. The light diverging from both multimode and single-mode optical fibers has been approximated by a uniform irradiance, the angle of divergence being determined by the sine of the fiber numerical aperture (N.A.). EXPERIMENTAL
The apparatus shown in Fig. 1 simulated the accidental rupturing of an optical fiber cable where the exposed end of an optical fiber illuminated dust particles in a combustible atmosphere. The optical source was a CW Nd:YAG laser operating at 1.06 /xm with adjustable output power, the laser radiation being launched into the fiber with a microscope
Launching l
objective. Explosion tests were performed with lengths of greater than 100 m of single mode (r c = 10 mm, N.A.= 0.1) and multimode [50/125 /xm (N.A.= 0.2), 62.5/125 /xm (N.A. = 0.29), 100/140/xm (N.A. = 0.29)] optical fibers. The optical power was measured at the output end of the cleaved fiber with a surface absorbing optical power meter. A 2-L combustion vessel of sacrificial plastic structure allowed positioning of the optical fiber and viewing of particles contained in a glass dish. Steps of 20 mW optical power were used to determine the critical optical power for explosions with particles of the following size ranges: 0-38, 38-45, 45-63, 63-75, 75-90, 90-125, 125-250, and 250-500 /xm. Particles of Appin coal were primarily used for ignition testing, the proximate analysis being shown in Table 1. Particles of cotton wool, manganese dioxide, steel wool, coal, and rock (shale) ignited hydrogen/air mixtures with optical powers of less than 400 mW, delivered by a 100/140 /xm multimode optical fiber. Coal particles illuminated by optical power glowed bright red and fused to the end of the optical fiber and continued glowing for up to 30 rain. When such a particle was surrounded by combustible gas the glowing increased until the gas ignited and consequently exploded, typically within 100 ms of particle illumination, or the glowing decreased as the oxygen was locally depleted. The maximum laser power that could be delivered through 100 m of 10/125-/xm single-mode optical fiber was 30 mW, limited by the available laser power and the smallcore size of the optical fiber. Particles were observed to heat up and glow red with 30 mW of optical power delivered by single-mode optical fiber. However, no explosions occurred in the
optics
Laser
I
Opfica[ fibre
I
Eoil
ooo ~I
particles
Gas mixer Laser power supp(y
Explosion chamber
Fig. 1. Apparatus for gas/dust ignition testing with optical fiber to deliver optical power.
LASER IGNITION BY SMALL PARTICLES TABLE 1
Proximate Analysis of Appin Coal Volatile matter (%) Ash (%) Fixed carbon (%)
22.20 12.63 67.17
Combustion kinetics estimated by ignition technique
[49l: Ap = 6 8 4 0 0 . 0 k g m 2 s-1 kPa n, Ep ~ 90.8 MJ/kmol, n = 1.0
hydrogen/air mixtures with these power levels. Photographic evidence of several explosions was obtained to investigate the ignition mechanism. A 40-/zm-diameter coal particle was illuminated by optical power delivered by a 100/140-/~m multimode optical fiber and observed to heat up and consequently explode both hydrogen/air and m e t h a n e / a i r mixtures. Figure 2a shows the sequence of events for an explosion recorded with a 12% hydrogen/air
403 mixture, taking 80 ms to explode with an incident optical power of 120 mW. Initially the fiber can be seen (jacketed on the left side and stripped on the right side), the black coal particle on the end of the stripped section of fiber not being visible. The particle heats up in the second photo (t = 30 ms), however, and flame that may be present is not visible (hydrogen has an invisible flame). At t = 75 ms the particle is glowing red. At t = 80 ms the explosion has occurred. Similarly, a 40-tzm particle was heated up by 360 mW in an 8% m e t h a n e / a i r mixture, as shown in Fig. 2(b). The flame is clearly visible in this case. After 35 ms an ignited jet of volatile matter was emitted during particle heating on the side of the particle remote from the heat source, the gas mixture exploding after 45 ms. These observations confirm that CW optical heating was the ignition mechanism being observed throughout the experiments.
t=Oms t=Oms
t = 30 ms
t= 75ms
t = 80 ms
t=2Om$
t=35ms
t = 45 ms
(a) (b) Fig. 2. Explosion of combustible mixtures by heating a 40-/xm-diameter coal particle with CW laser power delivered by 100/140-/xm multimode optical fiber for (a) 12% H 2 / a i r and 120 mW and (b) 8% CH4/air and 360 roW.
404
P. C. HILLS ET AL.
Utilizing standard gas/air mixtures for the intrinsic safety testing of electrical equipment [39] the minimum optical power delivered by a 50/125-pm multimode optical fiber to ignite coal dust of 38-45 /.~m diameter was determined for fuel/air mixtures of hydrogen, ethylene, propane, and methane (Table 2). Of the four gas groupings hydrogen/air mixtures ignited with the the lowest optical powers. Experiments were performed in 21% hydrogen/air mixtures to determine the most hazardous particle size range. Figure 3 shows the minimum optical power as the function of median coal particle size for three different core sizes of multimode of optical fibers. The higher power density of smaller core optical fibers results in a higher probability of light being absorbed by a small particle. The minimum optical power occurred for particles in the size range of 0.38 /zm with the 50/125-/xm multimode optical fiber. The minimum optical power as a function of hydrogen/air concentration was determined as shown in Fig. 4 for ignition with 50/125-/xm multimode optical fiber for a fixed particle size of 38-45/xm. Explosions occurred with a critical optical power (i.e., minimum ignition power for all particle radii) of as small as 100 mW for hydrogen/air mixtures of 10%-15%; the minimum optical power for ignition of hydrogen/air mixtures rapidly increasing when the lower flammability limit of 4% was approached.
3
300
2
260 1 o
~220 o°-i ~,0 E
•E lz, O 100
1
i
I
,
I
200
I00
i
300
400
Particte Diameter {~m)
Fig. 3. Minimum optical power as a function of coal particle size to ignite 21% H 2 / a i r mixture with (1) 50/125 /xm (2) 62.5/125 ~ m and (3)100/140-/xm multimode optical fibers.
combustible mixture by an isothermal body. Ignition was always possible given sufficient time. This was useful for highly reactive systems in which ignition occurred fairly rapidly. For less reactive systems in which the ignition source is only moderately hot a n d / o r the reactant concentrations are low, then at least two other limitations need to be considered. The first is the substantial amount of reactant consumption needed to initiate thermal runaway. The second is the particle's finite size and thereby heat capacity. Ignition may not occur with these extra constraints. In a recent study, Xiong and Law [41] removed these two limitations by extending the transient gas-phase ignition analysis to include reactant consumption
THEORETICAL 280
Su and Sirignano [40] have used matched asymptotic analysis in the realistic limit of large activation energy for gas-phase reactions involved in the transient ignition process of a
Stoichiom efric composition: 29.6 %
2l+0
~o z00
-~
TABLE 2
160
o
Standard Gas Mixtures and Minimum Optical Power to Ignite 38-45-/xm Coal Particles Gas
Percentage Gas
Minimum Power (mW)
Methane Propane Ethylene Hydrogen
8 5 8 21
300 240 200
140
120 E ~-"
80
~
I 9
,
Percentage
I 13
=
1 17
hydrogen
,
I 21
I
I 25
in air
Fig. 4. M i n i m u m optical p o w e r d e l i v e r e d by 50/125 I.Lm optical fiber as a f u n c t i o n o f H 2 / a i r c o n c e n t r a t i o n to heat a coal particle o f 3 8 - 4 5 - / ~ m f r a c t i o n to ignition.
LASER IGNITION BY SMALL PARTICLES [42]; the gas-phase results were then coupled to the heat transfer process in the particle. In this study, ignition of a combustible gas by a single, stationary, optically heated and reacting spherical coal particle was analyzed by predicting the radial and temporal variations of temperature and species concentration in the gas as well as the particle surface temperature-time histories. A transient model and a numerical approach were developed that accounted for mass and heat diffusion, heterogeneous and homogeneous reactions, and reactant depletion. A range of conditions that resulted in ignition of the combustible mixture was sought. The initial conditions were the particle and environmental temperature and hydrogen concentration in air. The following conditions were assumed: the particle was a sphere of constant size (density varied); the gas was ideal; pressure was constant; momentum equations were excluded; the convection term of Stefan flow from the particle due to the surface reaction was also neglected, this was justified on the basis of the low gasification rate predicted; the gas-phase reaction was represented by a one-step irreversible overall process; viscous dissipation and natural convection of the gas due to temperature variations were negligible; the particle was isothermal, but there was temporal variation of temperature due to heat exchange; the values characteristic of a chemical reaction (activation energy, preexponential factor, heat of reaction) and of heating conditions were constant throughout the process; except for chemical reaction there was no volume heat source within the particle, which was heated only through the surface; the particle was immobile in the heating area and no phase transformations occurred. The emission of volatiles from coal particles and their combustion was not considered.
Reaction K i n e t i c s
The quantitative behavior of a chemical reaction is described by a rate law that specifies the time rate of change of the concentration of chemical species in terms of a product of concentration terms and a rate constant (or rate
405 coefficient). The rate constant is independent of concentration but is dependent on temperature. For the reaction represented by the stoichiometric equation (1)
2H 2 + 02 = 2 H 2 0 , the rate law takes the form [13]: 1 d[H2] 2
dt
d[O2]
1 d[H20 ]
dt
2
dt
= k'[H211"7[O2 ]°8.
(2)
This is not two hydrogen molecules colliding with a single oxygen molecule to form water; the global process is an abbreviation of a complex sequence of many reactions, consisting of elementary steps. The rate law is valid over a wide range of temperature and pressure. The temperature variation of rate data was expressed in a modified Arrhenius form [43]: k' = A g e x p ( - ~-~ ).
(3)
The M o d e l E q u a t i o n s
The temperature at which ignition occurred could not be regarded as a physical or chemical constant. Ignition was defined to occur when the gas temperature gradient near the particle surface becomes positive (i.e., the gas temperature exceeded the particle temperature) such that a runaway reaction occurred. The temporal temperature profile of the coal particle during optical heating was determined from the energy balance equation for the particle. The thermal energy accumulated by the particle depends on the laser energy absorbed by the particle, the energy generated from particle surface reaction, the energy conducted to the gas and the radiation loss from the particle such that
(
MCp 0-~'- = aP + 47rrp 2 HpAp
exp
-
)
XC2, p "~- k dr + qm •
(4)
406
P . C . HILLS E T AL.
The term on the LHS is the thermal energy accumulated by the particle. The first term on the RHS is the laser energy absorbed by the particle. The second term on the RHS is the energy generated from the particle surface reaction C + 0 2 = CO 2. The third term on the RHS is the energy conducted between the particle and gas. The fourth term on the RHS is the grey body radiation loss determined by the Stefan-Boltzmann law to be
qr,,
=
(5)
--
where
R i = aijA ~ e x p , -
Eg ) C~,,2C~3,
(9)
such that R 1 = 0,
for all r,
(10)
R2 = Cea,2Ag e x p ( - ~ g
)C2'2C"f 3, forrp < r < G ,
The mass balance equation for the particle depends on the particle reaction kinetics such that
"-~ - 4rrr,,2Apexp - ~
C;.,,.
u,,
R 2 = c%,2Ai, e x p ( - -~-f£ )C2"
(6)
Eg ) c~n2C.~,3'
+ OQ.2 Ag e x p ( -
at r = rp, The temperature profile in the gas was determined from the energy balance equation for the gas. The thermal energy accumulated in the gas depends on the energy from heat conduction and the energy from gas-phase reaction such that
at
(12)
Eg ]ICm2crn3 2 3 ,
R 3 = oe4,3Mg exp - ~
for rp < r < r b, R4
(~pCgTg -- 1 (~ (r2k cgZg)
(11)
(13)
= Zg exp [__ Eg )cm2c;n3 ' k
r z Or ~
forrp < r
(14)
q- Hg Agexp ( - ~g-g Eg )C2n2C~3' R5
= O¢c,5A p
exp - ~
2,
for r = rp,
(7) (15) where the gas is assumed to be ideal. The term on the LHS of Eq. 7 is the thermal energy accumulated in the gas per unit volume. The first term on the RHS is the energy from heat conduction. The second term on the RHS is the energy from gas-phase reactions. The gas concentration near the particle surface depends on the gas diffusivity and reaction rate. The species equations are
3C i 1 (~ [ 2 ()Ci 1 . . . . [r D i ] = Ri, at r 2 Or \ Or
(8)
R 5 = 0,
f o r r p < r < r b.
(16)
Initial conditions Tp = Tg = T, at t = 0: initially the particle temperature was equal to the ambient temperature. If a hot particle was considered, then the critical optical power required for ignition would decrease. M = M 0 at t = 0: initially the mass of the particle was M 0. The mass of a reactive particle decreases during heating because of the reaction of carbon with oxygen.
LASER IGNITION BY SMALL PARTICLES
407
C i = C~,0 at t = 0: the mass concentration of gas species N2, 02, H2, H 2 0 , and CO 2 were initially known constant. Boundary conditions Tg = Tp at r = rp: the gas temperature was
equal to the particle temperature at the particle surface at all times. O T g / O r = O at r = r b : the change in gas temperature at the outer boundary gas layer, sufficiently far from the particle (r b ~. rp), was zero at all times. C i = C i . o at r = r b for i = 1,2,3,4,5: the species N2, 02, H2, H 2 0 , and CO 2 concentrations at the outer boundary gas layer, sufficiently far from the particle were constant. c~Ci/Or = 0 at r = rp for i = 1, 3, 4: there was no mass transfer of gas species N2, H z, and H 2 0 concentrations at the particle surface (as surface reaction involves C and 02) at all times. The model requires the simultaneous solution of eight nonlinear differential equations, which can only be performed numerically. A Package for Analogue Modelling (PAM) with special numerical treatment was used to solve these equations [44].
Effective Absorption Efficiency "a" The effective absorption efficiency of optical power by a particle is defined as
Fig. 5. Particle absorption of light diverging from the end of an optical fiber.
is approximated by
rp2 a i =
a i =
( r c + rptan 0) 2 1
for rp < r~
(18)
for rp >_ r 1
The particle spectral absorption efficiency Qa can be determined from Mie theory [45] if the particle size, complex refractive index, and incident wavelength of light are known. This theory has been used to predict the light scattering and absorption by small particles [45-48]. The input data for Mie theory and the model are tabulated in Table 3. Figure 6 shows the effective absorption of a coal particle as a function of particle size for optical power at a wavelength of 1.06 /zm for different types of optical fiber. The optical power was less efficiently absorbed as particle size approached the wavelength of the incident radiation.
Ignition Delay Time a = aiQ ~,
(17)
where a t is the geometric overlap of the optical power emerging from the optical fiber with the particle cross-section and Qa is the particle spectral absorption efficiency at the laser wavelength. As the particle size reduces below the core diameter of the optical fiber it is not possible for the particle to absorb all the incident optical radiation such that the divergence of the optical beam had to be considered. Figure 5 shows a schematic of a particle illuminated by light delivered by optical fiber. If we assume optical power has a uniform distribution on the particle for multimode and single model optical fibers then the geometric factor
Ignition occurred when the temperature gradient of the gas near the particle surface became positive (i.e., the boundary gas layer temperature exceeded the particle temperature), as shown in Fig. 7a. After ignition the gas temperature in the boundary layer rapidly increased due to the reaction between hydrogen and oxygen. When ignition failed the ignition delay time approached infinity because the power loss equaled the supplied optical power, resulting in a steady-state temperature profile as shown in Fig. 7b. In the nonignition case hydrogen and oxygen were consumed beyond the flammability limits as shown in Fig. 8. The ignition delay time varied with the incident optical power, requiring longer heating
408
P. C. HILLS ET AL. TABLE 3
Summary of the Model Inputs
Particle:
Density: 1500 kg m 3, heat capacity: 1243 J kg- 1 K 1 Surface Reaction: C + O 2 = CO 2 Heating value: 30 MJ kg- 1 Complex refractive index at the 1,064-#m laser wavelength [46]: N = 1.3 + 0.01i for coal particle Effective absorption efficiency: Fig. 6 Gas phase," Density: 0.60 kg m -3, heat capacity: 1000 J kg- 1 K 1 Gas-phase reaction: 2H 2 + O e = 2 H 2 0 Kinetics: Ag 3.88 × 10 s kg m - 3 s Reaction orders m2 = 0.8 ( 0 2) and m3 = 1.7 (H 2) Heating value: 120 MJ kg 1 Boundary layer thickness: 50 times particle diameter =
for smaller optical power. Figure 9 shows the critical optical power required to heat 10-/~m and 40-/zm particles to ignite 12.5% hydrogen/air mixture with increasing ignition delay time for light from a 50/125-/zm multimode optical fiber. It was generally found that after 50 ms a steady-state solution (i.e., ignition or nonignition) existed. In this model the CW heating time was limited to 100 ms, although this could be increased.
1050 900 750
600 m ~SO
300
1I I
~parficle~rface
RESULTS I 5o
The minimum optical power as a function of coal particle size for ignition of a 12.5% hydrogen/air mixture (ignition delay time of 40 ms) for single-mode (r C = 10 /xm, N.A. = 0.1) and multimode [50/125 /~m (N.A. = 0.2), 62.5/125
B0
60
{
i
i
1oo
200
300
400
3'00
~-00
Radius(pro) (a) 1100
~
1°°t
I
5k,.
700
500
21
30o
i,, L I
~'---Pa r ficte surface t'O
100
I
100
2;0 Radius (pro 1
20
(b) 0
i 0
40
80
120
160
200
PacticLe diameter (IJm)
Fig. 6. Theoretical absorption efficiency " a " as a function of particle diameter for 1.064-/zm radiation from (1) 10/125-ttm (2) 50/125-/zm (3) 62.5/125-/zm and (4) 100/140-~m optical fibers.
Fig. 7. Predicted boundary layer temperature profiles for (a) ignition in a 12.5% H 2 / a i r mixture and (b) nonignition in 25% H 2 / a i r mixture while heating a 50-/xm particle with 100 mW power delivered by 50/125-/xm multimode optical fiber at specific illumination times of (1) 0, (2) 30, (3) 60, (4) 80, and (5) 85 ms.
L A S E R I G N I T I O N BY S M A L L P A R T I C L E S 2~
409
r I I I
1000
E ~
15
100 m
7.5
E c
I*-P~ r tid.e surf a~ l 100
0 0
I ZOO
I 300
1
0
tOO
I 20
I
I 60
t,O
I
I
f
80
100
120
I
1L,O
160
Particte diameter {pm)
Radius (~m)
Fig. 8. 0 2 concentration profile for non-ignition case of Fig. 7(b).
Fig. 10. Minimum optical power as a function of coal particle size to ignite 21% H J a i r mixture with (1) 100/140-/zm 0 multimode optical fibers, (2) 62.5/125-/zm 0, (3) 50/125-/xm 0, and (4) 10/t25-/xm single mode.
tzm and 100/140 /xm ( N . A . = 0.29)] optical fibers was determined as shown in Fig. 10. A coal particle of 12 /xm diameter provided optim u m heat transfer to the boundary gas layers for single-mode optical fiber. For smaller particle size absorption efficiency of the incident light decreased and radiative losses increased. For larger particles m o r e optical power was required to heat the particles to a high enough t e m p e r a t u r e to ignite the combustible gas. The model predicts that the minimum optical power required for ignition rapidly increases for particles of less than 10 ~ m and greater than 6 0 / x m . Figure 10 compares calculated and experimental results of minimum
optical power as a function of coal particle size for ignition of 21% h y d r o g e n / a i r mixture with 5 0 / 1 2 5 /xm multimode optical fiber. Experimental results indicate that the minimum optical power does not increase rapidly for larger particles. This occurs because large coal particles melt to form a thin disk over the end of the optical fiber. Such particles ignited gases at lower optical powers because they absorbed much of the incident power. The critical optical power for ignition (i.e., occurred at approximately 13% hydrogen), in-
300
600 3=
500 I ~
200
~oo 2 m
300 ..-
1oo
200
&
c
loo 0
I
0
20
40
60
80
100
Ignition delay time(ms)
Fig. 9. Predicted optical power for ignition as a function of particle illumination time for (1) 10-/xm and (2) 40-/xm coal particles in 12.5% H2/air mixture with 50/125-/zm multimode optical fiber.
0
i
0
I
,
10 Percentage hydrogen
I
20
,
30
in air ( % )
Fig. 11. Minimum optical power as a function of H2/air concentration for heating a 40-/xm coal particle to ignition with 50/125-/~m multimode optical fiber (experimental data for 38-45-/xm fraction).
410 fluenced mainly by the kinetic data of Eq. 2 for the hydrogen/oxygen reaction. Figure 11 compares calculated results of critical optical power as a function of hydrogen/air concentration for heating a 40 /zm coal particle to experimental results of ignition by heating 38-45 ~m coal particles with power delivered by 50/125 gm multimode optical fiber. DISCUSSION The present study offers additional insights into the ignition mechanism that occurs when optical power heats a small particle in a combustible gas and offers certain limiting conditions. The observed decrease in optical power with decreasing particle size to 38 #m is predicted. Similarly, the optimum hydrogen/air concentration of approximately 13% for ignition agrees with the experimentally determined value of 10%-15%. Furthermore, this value is different for inert and reactive particles due to particle surface reaction. The experimentally observed hydrogen concentration of 10%-15% for which minimum optical power is required is less than the stoichiometric combustion of 29.6% hydrogen/air (by volume). The hydrogen concentration at which the flame propagation speed is maximum is 16.3%, much less than the stoichiometric ratio [20]. In this case, coal particle reaction locally consumes oxygen, resulting in a minimum optical power occurring at 13% hydrogen/air. The experimentally observed methane concentration of 9.5% and the concentration for the fastest flame speed (9.96%) [50] due to oxygen consumption by coal combustion. The effective absorption efficiency of optical power by a particle decreases with particle size such that particles of a similar size to the wavelength of the incident light absorb very little power. However, small particles (10-40 /zm) require much less optical power for ignition as they heat up much faster than larger particles and have smaller thermal losses. Such particles are often airborne and are typical of the particle sizes found in underground coal mines. The high power density and the small core diameter of single-mode optical fiber results in a high probability of light being absorbed by a
P . C . HILLS ET AL. small particle. The model predicts that optical powers of 1 mW delivered by single-mode optical fibers at a wavelength of 0.8 p~m and incident on a small blackbody (a = 1) of 8 /xm diameter can create explosions in 12.5% hydrogen/air mixtures. Small-core multimode optical fibers carrying the same amount of optical power as large-core optical fibers have a higher ignition risk due to the higher power density. In general, the wavelength of operation in optical fibers is 0.5-1.5/xm. The optical wavelength has less than 2% effect on the minimum optical power for ignition with particles of greater than 15 p~m. For smaller particles up to 40% less power may be required for ignition at a wavelength of 0.5 /zm compared with 1.06 /xm. Although we have only considered CW optical sources, pulsed optical sources are also prevalent in communication and sensing systems. As the particle illumination time reduces to less than the minimum ignition delay time, such as with a pulse optical source or by a particle falling through an optical beam, the minimum optical power for ignition increases. A preliminary experimental investigation of pulsed optical sources was performed. The minimum optical power from a 1.06-/zm Nd:Yag laser delivered by a 100/140-/xm optical fiber to exploded a 12% hydrogen/air mixture was 9 W peak power for 1 100-~s pulse of 10 Hz repetition rate. This is equivalent to an average power of 9 roW--an order of magnitude less than the CW optical source. This reduction in energy occurs because the particle obtains sufficient energy during the single pulse to ignite the gas. As the pulse repetition rate is increased the effects of repetitive heating must be considered. For extremely fast repetition rates CW heating is approached. SUMMARY
This work numerically and experimentally studies the ignition of a hydrogen/air mixture by a laser-heated coal particle. Careful and elaborate experiments were performed to investigate the minimum CW laser powers delivered by multimode optical fibers that can cause an explosion. CW powers of 100 mW delivered by 50/125-p.m graded index multimode optical
LASER IGNITION BY SMALL PARTICLES fibers, and incident on coal dust particles of 0-38 /xm diameter, create explosions in combustible hydrogen/air mixtures. A numerical model was developed to determine the hazardous power levels for CW optical systems in potentially explosive atmospheres. The important ignition parameters and their effects on the minimum optical power for ignition were predicted. Although the model does not agree exactly with the experimental results there is a definite correlation between the theory and experiment. The decrease in optical power with particle size to less than 38 /~m is predicted. Similarly the optimum hydrogen/air concentration of approximately 13% for ignition agrees with the experimentally determined value of 10%-15%, this being less than the ratio for measured maximum flame speed, due to oxygen consumption near the coal particle surface. The high power density and small core diameter of single-mode optical fibers results in a high probability of light being absorbed by a small particle. Similarly, small-core optical fibers carrying the same amount of power as large-core optical fibers, have a higher ignition risk in explosive atmospheres. This work thus demonstrates the need for further research and experimental work to develop standards that allow safe operating conditions for optical systems in potentially explosive or flammable atmospheres.
411 7.
8.
9. 10. 11. 12. 13. 14. 15. 16. 17.
18.
19. 20. 21. 22. 23.
24.
The authors thank BlIP Co. Ltd. for funding and permission to publish and Chuguang Zheng for prouiding data on the spectral absorptivity of coal. REFERENCES 1. Tortoishell, G., Proceedings, SPIE, Vol. 522, Fibre Optics '85, 1985, pp. 132-139. 2. Tortoishell, G., Process Optical Measurements and Industrial Methods, The Hague, Netherlands, SPIE Vol. 1266, March 1990, Paper 14. 3. Carleton, F. B., and Weinberg, F. J., Fibre Optics '90, London, SPIE Vol. 1314, 1990. 4. Hills, P. C., Samson, P. J., and Webster, I., J. Electric. Electron. Eng. Australia 10:207-220 (1990). 5. Hills, P. C., Elect. Lett. 26:1982-1983 (1990). 6. Hills, P. C., Samson, P. J., and Webster, I., Proceedings 7th International Conference on Optical Fibre Sensors, IREE, Sydney, Australia, 1990, pp. 63-66.
25.
26. 27. 28. 29. 30.
31. 32. 33. 34.
Hills, P. C., and Samson, P. J., Proceedings 16th Australian Conference on Optical Fibre Technology, IREE, Adelaide, Australia, 1991, pp. 258-261. Zhang, D. K., Wall, T. F., and Hills, P. C., Proceedings 7th International Conference on Optical Fibre Sensors, IREE, Sydney, Australia, 1990, pp. AI-4. Hills, P. C, and Samson, P. J., SPIE OE/Fibres '91, Boston, September, 1991 (in press). Lewis, B., and von Elbe, G., Combustion Flames and Explosions of Gases, Academic, London, 1961. Lyman, J. L., and Jensen, R. J., J. Phys. Chem. 77:883 (1973). Bauer, S. H., Bar-Ziv, E., and Haberman, J. A., 1EEE J. Quant. Elect., QE-14:237-245 (1978). Hill, R. A., and Laguna, G. A., Opt. Commun. 32:435-439 (1980). Hill, R. A., Appl. Opt. 20:2239 (1981). Trott, W. M., J. Appl. Phys. 54:118 (1983). Raffel, B., Warnatz, J., and Wolfrum, J., Appl. Phys. B37:189 (1985). Norrish, R. G. W., Tenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1985. p. 1. Lucas, D., Peterson, R., Brown, N. J., and Oppenhelm, A. K., Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1985, p. 1205. Lavid, M., and Stevens, J. G , Combust. Flame 60:195-202 (1985). Lucas, D., Dunn-Rankin, D., Horn, K., and Brown, N. J., Combust. Flame 69:171 (1987). Menichelli, V. J., and Yang, L. C., Appl. Phys. Lett. 19:473 (1971). Mizuchuima, Y., and Nishiyama, J., J. Indus. Explos. Japan 35(4): 169-176 (1974). Cook, J. R., and Habersat, J. D., Proceedings of the Eleventh Symposium on Explosives and l~,rotechnics, Philadelphia, 1981, pp. 50.1-8. loffe, V. B., Dolgolaptev, A. V., Aleksandrov, V. E., and Obraztsov, A. P., Combust. Explos. Shock Wat,es 21:316-320 (1985). Ostmark, H., International Congress of the Pyrotechnical Society, Juan-Les-Pins, France, 1987, pp. 241-245. Meyerand, R. G., AIAA J. 5:1730 (1967). Lee, J. H., and Knystautas, R., AIAA J. 7:312-317 (1969). Weinberg, F. J., and Wilson, J. R., Proc. R. Soc. Lond. A 321:41 52 (1971). Dale, J. D., Smy, P. R., Way-Nee, D., and Clements, R. M., Combust. Flame 30:319 (1977). Wilson, C. W., Proceedings 13th AL4A Fluid and Plasma Dynamics Conference, AIAA, Colorado, 1980, pp. 1-6. Schmieder, R. W., Appl. Phys. 52:3000 (1981). Bunkin, F. V., and Savranskii, V. V., Sot,. Phys. JETP 38:1091 1096 (1974). Boddington, T., Feng, C., and Gray, P., Proc. R. Soc. Lond. A 390:265 (1983). Kingdon, R. G., and Weinberg, F. J., Sixteenth Sympo-
412
35. 36. 37. 38.
39.
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41. 42.
P . C . H I L L S E T AL. sium (International) on Combustion, The Combustion Institute, Pittsburgh, 1977, pp.747-756. Moore, S. R., and Weinberg, F. J., Nature 240:39 40 (1981). Moore, S. R., and Weinberg, F. J., Proc. R. Soc. Lond. ,4 385:373-387 (1983). Moore, S. R., and Weinberg, F. J., Proc. R. Soc. Lond. A 409:1-20 (1987). Homan, H. S., and Sirignano, W. A., Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1981, pp. 1709-1717. International Standard: Electrical Apparatus for Explosive Gas Atmospheres: Construction and Testing of Intrinsically Safe and Associated Apparatus, IEC 79-11. Su, Y. P. and Sirignano, W. A., Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1981, pp. 1719-1728. Xiong, T., and Law, C. K., ,4/AA J. 23:889-892 (1985). Law, C. K. and Chung, S. H., Combust. Sci. Technol. 32:307 (1983).
43. Glassman, I., Combustion, 2nd ed., Academic Press, London, 1987, p. 38. 44. Zhang, D. K., Technical Bulletin, University of Newcastle, Australia, 1990. 45. van der Hulst, H. C., Light Scattering by Small Particles, Wiley, New York, 1957. 46. Goodwin, D. G., and Mitchner, M., J. Thermophys. 3:53-60 (1989). 47. Toon, O. B., Pollack, J. B., and Sagan, C., ICARUS 31:663-696 (1977). 48. Zhang, D. K., Gupta, R. P., and Wall, T. F., Proceedings of The First Australian Flame Days, Australian Flame Research, Brisbane, Australia, 1990, paper 9. 49. Zhang, D. K., Wall, T. F., Harris, D. J., Smith, I. W., Chen, J. Y, and Stanmore, B. R., Fuel, (in press). 50. Gaydon, A. G., and Wolfhard, H. G., Flames: Their Structure, Radiation and Temperature, 3rd ed., Chapman & Hall, London, 1970. Received 23 August 1991; revised 25 July 1992
399
Laser Ignition of Combustible Gases by Radiative Heating of Small Particles P. C. HILLS*'* D. K. ZHANG, P. J. SAMSON, and T. F. WALL BHP Research Newcastle Laboratories, P.O. Box 188, Wallsend,NSW 2287, Australia (P.C.H.;P.J.S.) Department of ChemicalEngineering, Universityof Newcastle, NS W 2308, Australia (D.K.Z.;T.F.W.) This article summarizes the ignition risks of laser power delivered by optical fiber to combustible atmospheres. Of six possible ignition mechanisms, the ignition of a combustible gas by a small optically heated body has been extensively investigated. Continuous-wave (CW) powers of 100 mW delivered by multimode optical fibers created explosion in combustible atmospheres. A numerical model of the ignition of a combustible gas by a small heated body on the exposed end of an optical fiber is developed. Important parameters include gas (type and concentration), particle (type, diameter, absorptivity, refractive index, reactivity, thermal capacity, density), optical fiber (core diameter and numerical aperture), and light (wavelength and power).
NOMENCLATURE a
ai Ag Ap Ci
Di Ei
k k' mi M N.A. n
effective absorption efficiency particle-light g e o m e t r i c overlap gas reaction rate preexponential factor, k g m -3 s I kPa -n particle reaction rate preexponential factor, kg m -2 s 1 kPa -n mass c o n c e n t r a t i o n of species i, kg m-3 thermal capacity, J k g - l K-1 mass diffusivity o f species i, m e s activation energy of species i, J kmol 1 reaction heat o f particle and gas respectively, J k g gas thermal conductivity, W m-~ K - J rate constant (coefficient) reaction o r d e r for 2 H 2 + 0 2 = 2 H 2 0 with respect to species i particle mass, kg numerical a p e r t u r e of optical fiber reaction o r d e r for C + O 2 = C O 2 with respect to oxygen c o n c e n t r a t i o n
P qrd
Qo f R
Ri t
L T(t, r)
optical power, W radiative heat flux, W m 2 particle spectral absorptivity radius, m universal gas constant, J kmol 1 K reaction rate, kg m -3 s 1 (gas), kg m 2 S-1 (particle surface) time, s ambient temperature, K particle temperature, K t e m p e r a t u r e at radius r from particle centroid at time t, K
Greek Symbols a~,j p o• A 0
stoichiometric factor, species i to j density, kg m -3 S t e f a n - B o l t z m a n n constant, W m -2 K-4 particle emissivity laser wavelength, /.tm m a x i m u m divergence angle of optical radiation f r o m fiber end (degrees)
Subscripts b * Present address: ICI Biospecialties, 57 Tourle Street, Mayfield, NSW 2304, Australia. * Please address further correspondence to Dong-ke Zhang at Department of Chemical Engineering, University of Newcastle, NSW 2308, Australia. Copyright © 1992 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc.
c C g
b o u n d a r y layer radius of the gas (from particle centroid) core radius of optical fiber carbon gas phase 0010-2180/92/$5.00
400
P
P. C. HILLS ET AL. gas species i = 1 for N2; i = 2 for 02; i = 3 for H2; i = 4 for H20; i = 5 for CO2 particle (surface)
INTRODUCTION Typical applications of optical sensors include safety systems in industries such as coal mining and petroleum production. The optical power is transmitted through optical fibers, avoiding the use of electricity in potentially explosive atmospheres. Continuous-wave (CW) powers of tens of watts can be transmitted over kilometer lengths of optical fiber. However, there has been little experimental [1-7] or theoretical [8-9] research on the safety of optical power delivered by optical fiber systems in combustible atmospheres. Furthermore, no regulations or standards currently address power limitations for optical fiber systems in potentially explosive atmospheres. A combustible atmosphere may be ignited by mechanical sparks, electrical sparks, or by thermal effects. Mechanical sparks are considered highly unlikely with optical systems as there are no moving parts, although the design and construction of transceivers, sensor heads, junction boxes, and connectors associated with a fiber optic system must be considered. The ignition capability of an electrical spark varies with gas concentration, humidity, oxygen content of the atmosphere, temperature, and turbulence, with as little as 0.02 mJ required [10]. In contrast, laser-induced explosions of particles, aerosols, gases, or explosives have typically used large amounts of energy in controlled environments [11-34]. Six possible ways in which light emerging from an optical fiber can cause gas/dust ignition have been identified: direct thermal ignition of gas, photochemical excitation of gas, dust or solid explosion by thermal ignition of a particle or explosive, direct laser spark ignition of gas, laser spark ignition of gas by small particles, and radiative heating of a small particle in a flammable atmosphere. Direct thermal ignition of gas by absorption of radiation causing a rapid increase in temperature has been demonstrated [11-16]. However, ignition at low power levels in a flammable
atmosphere is unlikely because even the most sensitive of gases has to be raised to at least 100°C throughout a volume of 100 ml or more for ignition to occur [1]. The low absorptivity of the absorption bands of flammable gases and vapors in air and the relatively wide spectral band width of sources other than lasers mean that a large proportion of the optical power will not be absorbed. Furthermore, the power required for ignition with this mechanism is wavelength dependent; the strongest absorption bands generally occur outside the silica optical fiber transmission window of 0.8-1.55 /xm. Photochemical ignition [17-20], in contrast to thermal ignition, occurs with photodissociation of molecular oxygen due to absorption of 130-175 nm ultraviolet radiation, which generates atomic oxygen and produces other reactive radicals via chain-branching. Subsequent reaction of the radicals with fuel molecules, as well as other intermediate species, release heat. Consequently, the temperature of the mixture rises, leading to ignition. Ignition requires high laser energies in the order of 350 mJ in a 20-ns pulse [20]. A dust or solids explosion could occur if a dust or solid exists in an explosive concentration and a small body or part of the solid is heated to supply enough energy to explode. This ignition mechanism includes laser initiation of explosives [21-25], a problem that has interested specialists from the time the first laser systems appeared and were introduced into laboratory research. Experiments have shown that the thermal theory of initiation explains the mechanism of initiation of condensed explosives by laser radiation. With this ignition mechanism absorption of light by a layer of explosive results in light energy being converted into shock-wave energy. Explosions have been reported with pulse energies as low as 5.4 mJ [22]. In direct laser-spark-initiated ignition of gases [26-30] optical breakdown of the gas occurs at the focal point of a laser beam. Ignition occurs with breakdown of the gas and plasma production at the focal point of a focused laser beam. Sufficient energy must be supplied to the gas mixture in a short time, the energy creating free radicals such that the
LASER IGNITION BY SMALL PARTICLES reaction between the flammable species and oxygen commences. Breakdown in gases can be achieved at the focal point of a laser beam when it is collimated by a simple convex lens. For example, a Q-switched ruby laser of 10 ns pulse width and maximum power of 120 MW (1.2 J) focused to a spot of 240 /xm created explosions at atmospheric pressure and room temperature [27]. Laser spark ignition of gases with small particles of the focal spot results in optical breakdown of the gas due to thermal explosion of small particles [31-34]. When small suspended particles are rapidly heated by absorbing highpower laser energy they change from a solid to a vapor, the explosion occurring if the vapor contains excess energy. Kingdon and Weinberg [34] demonstrated that normal critical minimum ignition energies govern the process by using Q-switched laser beams focused on small targets in flammable atmospheres. Laser spark ignition of gases occurs at lower power levels than direct thermal ignition and laser-sparkinitiated ignition of gases, as small particles are able to absorb laser power more efficiently than gases. For example, a Q-switched ruby laser of 40 ns pulse width and 0.5 mJ pulse energy focused to 80 /xm diameter and incident on a 12-/zm wire created explosions in 8.6% methane/air mixtures [34]. If sufficient optical power escapes from an optical fiber and illuminates a small particle, ignition is possible by heating the particle to ignite the surrounding atmosphere. This is the most likely mechanism for optical ignition with low CW power levels, the ignition hazard increasing if a reactive particle is illuminated. This situation could occur in a coal mine when an optical fiber cable is accidentally ruptured such that coal dust is illuminated in the presence of hydrogen- or methane-air mixtures. It has been demonstrated in the literature [1-9, 35-37] that it is possible to ignite flammable gases by CW laser illumination of particles that have similar dimensions to the core diameter of optical fibers (5-500 /zm). In one case several ignitions of free-falling carborundum (silicon carbide) particles within the range of 20-50 /xm diameter in di-ethyl gas occurred with greater than 2.8 W of optical power from an argon iron laser [2]. Moore and
401 Weinberg [35-37] used a focused laser beam to show that certain kinds of particles of approximately 1 mm diameter ignite with radiation fluxes of about 100 k W / m 2 in a variety of flammable atmospheres. Most notable were particles consisting of cotton wool, and Kaowool fiber, Kaowool being a nonflammable silica-alumina-based insulating wool that consists of fibers of 5 /zm diameter while cotton wool is a flammable material of 20 tzm diameter. Several laser ignition experiments have been performed with a quasi-CW laser. Homan and Sirignano [38] ignited flammable atmospheres with single aluminum particles of various diameters (20-80/~m) suspended on a glass fiber in a methane/air- or propane/air-combustible gas mixtures. The particle was heated and caused to burn by a 0.5-ms pulse from a neodymnium glass laser. The minimum diameter of single burning aluminum particles that ignite methane/air mixtures was determined experimentally to be between 20 and 30 /xm. In propane/air mixtures the minimum diameter is less than 20 /xm. If particles are small enough they can burn or vaporize in fuel/air mixtures and not obtain the critical amount of energy required to ignite the mixture [37, 38]. We have experimentally exploded/ignited over 300 gas/air mixtures. We have used optical fibers to deliver the laser beam to particles located in an explosion chamber rather than the focused laser beam experiments previously described. This allows the optical power emerging from the fiber end to be accurately measured and allows the light emerging from the fiber end to be directed onto a small particle with a high degree of accuracy. Furthermore, this is typical of industrial applications where laser light is delivered to combustible atmospheres via optical fibers. In this article a mathematical model is formulated to predict the minimum optical power carried by optical fibers that is required to ignite a combustible gas by heating a small reacting particle [8, 9]. A coal particle in a combustible mixture of hydrogen and air is considered. The effects of ignition delay, theoretical absorption efficiency, gas concentration, particle reaction, wavelength, and particle size are determined. Both gas-phase and particle
402
P. C. HILLS ET AL.
surface reactions are considered. The radial and temporal variation of temperature and species concentration in the boundary layer are predicted and the effects of various parameters on the ignition characteristics are examined. There are many parameters that influence whether ignition will occur, including particle reactivity (inert or reactive), activation energy, and reaction enthalpy for the oxygen reaction, size, porosity, spectral absorptivity, thermal conductivity, density, initial temperature, and heat capacity. Properties of importance for the light source include the pulse duration (continuous wave or pulsed at a certain duty cycle), peak power, power density, pulse shape, and wavelength. As light is transmitted through optical fibers their properties must also be considered. Optical fibers consist of single-mode and multimode types. Single-mode optical fibers have core diameters in the range of 2-10 txm while multimode fibers typically have core diameters greater than 50 /xm. The light diverging from both multimode and single-mode optical fibers has been approximated by a uniform irradiance, the angle of divergence being determined by the sine of the fiber numerical aperture (N.A.). EXPERIMENTAL
The apparatus shown in Fig. 1 simulated the accidental rupturing of an optical fiber cable where the exposed end of an optical fiber illuminated dust particles in a combustible atmosphere. The optical source was a CW Nd:YAG laser operating at 1.06 /xm with adjustable output power, the laser radiation being launched into the fiber with a microscope
Launching l
objective. Explosion tests were performed with lengths of greater than 100 m of single mode (r c = 10 mm, N.A.= 0.1) and multimode [50/125 /xm (N.A.= 0.2), 62.5/125 /xm (N.A. = 0.29), 100/140/xm (N.A. = 0.29)] optical fibers. The optical power was measured at the output end of the cleaved fiber with a surface absorbing optical power meter. A 2-L combustion vessel of sacrificial plastic structure allowed positioning of the optical fiber and viewing of particles contained in a glass dish. Steps of 20 mW optical power were used to determine the critical optical power for explosions with particles of the following size ranges: 0-38, 38-45, 45-63, 63-75, 75-90, 90-125, 125-250, and 250-500 /xm. Particles of Appin coal were primarily used for ignition testing, the proximate analysis being shown in Table 1. Particles of cotton wool, manganese dioxide, steel wool, coal, and rock (shale) ignited hydrogen/air mixtures with optical powers of less than 400 mW, delivered by a 100/140 /xm multimode optical fiber. Coal particles illuminated by optical power glowed bright red and fused to the end of the optical fiber and continued glowing for up to 30 rain. When such a particle was surrounded by combustible gas the glowing increased until the gas ignited and consequently exploded, typically within 100 ms of particle illumination, or the glowing decreased as the oxygen was locally depleted. The maximum laser power that could be delivered through 100 m of 10/125-/xm single-mode optical fiber was 30 mW, limited by the available laser power and the smallcore size of the optical fiber. Particles were observed to heat up and glow red with 30 mW of optical power delivered by single-mode optical fiber. However, no explosions occurred in the
optics
Laser
I
Opfica[ fibre
I
Eoil
ooo ~I
particles
Gas mixer Laser power supp(y
Explosion chamber
Fig. 1. Apparatus for gas/dust ignition testing with optical fiber to deliver optical power.
LASER IGNITION BY SMALL PARTICLES TABLE 1
Proximate Analysis of Appin Coal Volatile matter (%) Ash (%) Fixed carbon (%)
22.20 12.63 67.17
Combustion kinetics estimated by ignition technique
[49l: Ap = 6 8 4 0 0 . 0 k g m 2 s-1 kPa n, Ep ~ 90.8 MJ/kmol, n = 1.0
hydrogen/air mixtures with these power levels. Photographic evidence of several explosions was obtained to investigate the ignition mechanism. A 40-/zm-diameter coal particle was illuminated by optical power delivered by a 100/140-/~m multimode optical fiber and observed to heat up and consequently explode both hydrogen/air and m e t h a n e / a i r mixtures. Figure 2a shows the sequence of events for an explosion recorded with a 12% hydrogen/air
403 mixture, taking 80 ms to explode with an incident optical power of 120 mW. Initially the fiber can be seen (jacketed on the left side and stripped on the right side), the black coal particle on the end of the stripped section of fiber not being visible. The particle heats up in the second photo (t = 30 ms), however, and flame that may be present is not visible (hydrogen has an invisible flame). At t = 75 ms the particle is glowing red. At t = 80 ms the explosion has occurred. Similarly, a 40-tzm particle was heated up by 360 mW in an 8% m e t h a n e / a i r mixture, as shown in Fig. 2(b). The flame is clearly visible in this case. After 35 ms an ignited jet of volatile matter was emitted during particle heating on the side of the particle remote from the heat source, the gas mixture exploding after 45 ms. These observations confirm that CW optical heating was the ignition mechanism being observed throughout the experiments.
t=Oms t=Oms
t = 30 ms
t= 75ms
t = 80 ms
t=2Om$
t=35ms
t = 45 ms
(a) (b) Fig. 2. Explosion of combustible mixtures by heating a 40-/xm-diameter coal particle with CW laser power delivered by 100/140-/xm multimode optical fiber for (a) 12% H 2 / a i r and 120 mW and (b) 8% CH4/air and 360 roW.
404
P. C. HILLS ET AL.
Utilizing standard gas/air mixtures for the intrinsic safety testing of electrical equipment [39] the minimum optical power delivered by a 50/125-pm multimode optical fiber to ignite coal dust of 38-45 /.~m diameter was determined for fuel/air mixtures of hydrogen, ethylene, propane, and methane (Table 2). Of the four gas groupings hydrogen/air mixtures ignited with the the lowest optical powers. Experiments were performed in 21% hydrogen/air mixtures to determine the most hazardous particle size range. Figure 3 shows the minimum optical power as the function of median coal particle size for three different core sizes of multimode of optical fibers. The higher power density of smaller core optical fibers results in a higher probability of light being absorbed by a small particle. The minimum optical power occurred for particles in the size range of 0.38 /zm with the 50/125-/xm multimode optical fiber. The minimum optical power as a function of hydrogen/air concentration was determined as shown in Fig. 4 for ignition with 50/125-/xm multimode optical fiber for a fixed particle size of 38-45/xm. Explosions occurred with a critical optical power (i.e., minimum ignition power for all particle radii) of as small as 100 mW for hydrogen/air mixtures of 10%-15%; the minimum optical power for ignition of hydrogen/air mixtures rapidly increasing when the lower flammability limit of 4% was approached.
3
300
2
260 1 o
~220 o°-i ~,0 E
•E lz, O 100
1
i
I
,
I
200
I00
i
300
400
Particte Diameter {~m)
Fig. 3. Minimum optical power as a function of coal particle size to ignite 21% H 2 / a i r mixture with (1) 50/125 /xm (2) 62.5/125 ~ m and (3)100/140-/xm multimode optical fibers.
combustible mixture by an isothermal body. Ignition was always possible given sufficient time. This was useful for highly reactive systems in which ignition occurred fairly rapidly. For less reactive systems in which the ignition source is only moderately hot a n d / o r the reactant concentrations are low, then at least two other limitations need to be considered. The first is the substantial amount of reactant consumption needed to initiate thermal runaway. The second is the particle's finite size and thereby heat capacity. Ignition may not occur with these extra constraints. In a recent study, Xiong and Law [41] removed these two limitations by extending the transient gas-phase ignition analysis to include reactant consumption
THEORETICAL 280
Su and Sirignano [40] have used matched asymptotic analysis in the realistic limit of large activation energy for gas-phase reactions involved in the transient ignition process of a
Stoichiom efric composition: 29.6 %
2l+0
~o z00
-~
TABLE 2
160
o
Standard Gas Mixtures and Minimum Optical Power to Ignite 38-45-/xm Coal Particles Gas
Percentage Gas
Minimum Power (mW)
Methane Propane Ethylene Hydrogen
8 5 8 21
300 240 200
140
120 E ~-"
80
~
I 9
,
Percentage
I 13
=
1 17
hydrogen
,
I 21
I
I 25
in air
Fig. 4. M i n i m u m optical p o w e r d e l i v e r e d by 50/125 I.Lm optical fiber as a f u n c t i o n o f H 2 / a i r c o n c e n t r a t i o n to heat a coal particle o f 3 8 - 4 5 - / ~ m f r a c t i o n to ignition.
LASER IGNITION BY SMALL PARTICLES [42]; the gas-phase results were then coupled to the heat transfer process in the particle. In this study, ignition of a combustible gas by a single, stationary, optically heated and reacting spherical coal particle was analyzed by predicting the radial and temporal variations of temperature and species concentration in the gas as well as the particle surface temperature-time histories. A transient model and a numerical approach were developed that accounted for mass and heat diffusion, heterogeneous and homogeneous reactions, and reactant depletion. A range of conditions that resulted in ignition of the combustible mixture was sought. The initial conditions were the particle and environmental temperature and hydrogen concentration in air. The following conditions were assumed: the particle was a sphere of constant size (density varied); the gas was ideal; pressure was constant; momentum equations were excluded; the convection term of Stefan flow from the particle due to the surface reaction was also neglected, this was justified on the basis of the low gasification rate predicted; the gas-phase reaction was represented by a one-step irreversible overall process; viscous dissipation and natural convection of the gas due to temperature variations were negligible; the particle was isothermal, but there was temporal variation of temperature due to heat exchange; the values characteristic of a chemical reaction (activation energy, preexponential factor, heat of reaction) and of heating conditions were constant throughout the process; except for chemical reaction there was no volume heat source within the particle, which was heated only through the surface; the particle was immobile in the heating area and no phase transformations occurred. The emission of volatiles from coal particles and their combustion was not considered.
Reaction K i n e t i c s
The quantitative behavior of a chemical reaction is described by a rate law that specifies the time rate of change of the concentration of chemical species in terms of a product of concentration terms and a rate constant (or rate
405 coefficient). The rate constant is independent of concentration but is dependent on temperature. For the reaction represented by the stoichiometric equation (1)
2H 2 + 02 = 2 H 2 0 , the rate law takes the form [13]: 1 d[H2] 2
dt
d[O2]
1 d[H20 ]
dt
2
dt
= k'[H211"7[O2 ]°8.
(2)
This is not two hydrogen molecules colliding with a single oxygen molecule to form water; the global process is an abbreviation of a complex sequence of many reactions, consisting of elementary steps. The rate law is valid over a wide range of temperature and pressure. The temperature variation of rate data was expressed in a modified Arrhenius form [43]: k' = A g e x p ( - ~-~ ).
(3)
The M o d e l E q u a t i o n s
The temperature at which ignition occurred could not be regarded as a physical or chemical constant. Ignition was defined to occur when the gas temperature gradient near the particle surface becomes positive (i.e., the gas temperature exceeded the particle temperature) such that a runaway reaction occurred. The temporal temperature profile of the coal particle during optical heating was determined from the energy balance equation for the particle. The thermal energy accumulated by the particle depends on the laser energy absorbed by the particle, the energy generated from particle surface reaction, the energy conducted to the gas and the radiation loss from the particle such that
(
MCp 0-~'- = aP + 47rrp 2 HpAp
exp
-
)
XC2, p "~- k dr + qm •
(4)
406
P . C . HILLS E T AL.
The term on the LHS is the thermal energy accumulated by the particle. The first term on the RHS is the laser energy absorbed by the particle. The second term on the RHS is the energy generated from the particle surface reaction C + 0 2 = CO 2. The third term on the RHS is the energy conducted between the particle and gas. The fourth term on the RHS is the grey body radiation loss determined by the Stefan-Boltzmann law to be
qr,,
=
(5)
--
where
R i = aijA ~ e x p , -
Eg ) C~,,2C~3,
(9)
such that R 1 = 0,
for all r,
(10)
R2 = Cea,2Ag e x p ( - ~ g
)C2'2C"f 3, forrp < r < G ,
The mass balance equation for the particle depends on the particle reaction kinetics such that
"-~ - 4rrr,,2Apexp - ~
C;.,,.
u,,
R 2 = c%,2Ai, e x p ( - -~-f£ )C2"
(6)
Eg ) c~n2C.~,3'
+ OQ.2 Ag e x p ( -
at r = rp, The temperature profile in the gas was determined from the energy balance equation for the gas. The thermal energy accumulated in the gas depends on the energy from heat conduction and the energy from gas-phase reaction such that
at
(12)
Eg ]ICm2crn3 2 3 ,
R 3 = oe4,3Mg exp - ~
for rp < r < r b, R4
(~pCgTg -- 1 (~ (r2k cgZg)
(11)
(13)
= Zg exp [__ Eg )cm2c;n3 ' k
r z Or ~
forrp < r
(14)
q- Hg Agexp ( - ~g-g Eg )C2n2C~3' R5
= O¢c,5A p
exp - ~
2,
for r = rp,
(7) (15) where the gas is assumed to be ideal. The term on the LHS of Eq. 7 is the thermal energy accumulated in the gas per unit volume. The first term on the RHS is the energy from heat conduction. The second term on the RHS is the energy from gas-phase reactions. The gas concentration near the particle surface depends on the gas diffusivity and reaction rate. The species equations are
3C i 1 (~ [ 2 ()Ci 1 . . . . [r D i ] = Ri, at r 2 Or \ Or
(8)
R 5 = 0,
f o r r p < r < r b.
(16)
Initial conditions Tp = Tg = T, at t = 0: initially the particle temperature was equal to the ambient temperature. If a hot particle was considered, then the critical optical power required for ignition would decrease. M = M 0 at t = 0: initially the mass of the particle was M 0. The mass of a reactive particle decreases during heating because of the reaction of carbon with oxygen.
LASER IGNITION BY SMALL PARTICLES
407
C i = C~,0 at t = 0: the mass concentration of gas species N2, 02, H2, H 2 0 , and CO 2 were initially known constant. Boundary conditions Tg = Tp at r = rp: the gas temperature was
equal to the particle temperature at the particle surface at all times. O T g / O r = O at r = r b : the change in gas temperature at the outer boundary gas layer, sufficiently far from the particle (r b ~. rp), was zero at all times. C i = C i . o at r = r b for i = 1,2,3,4,5: the species N2, 02, H2, H 2 0 , and CO 2 concentrations at the outer boundary gas layer, sufficiently far from the particle were constant. c~Ci/Or = 0 at r = rp for i = 1, 3, 4: there was no mass transfer of gas species N2, H z, and H 2 0 concentrations at the particle surface (as surface reaction involves C and 02) at all times. The model requires the simultaneous solution of eight nonlinear differential equations, which can only be performed numerically. A Package for Analogue Modelling (PAM) with special numerical treatment was used to solve these equations [44].
Effective Absorption Efficiency "a" The effective absorption efficiency of optical power by a particle is defined as
Fig. 5. Particle absorption of light diverging from the end of an optical fiber.
is approximated by
rp2 a i =
a i =
( r c + rptan 0) 2 1
for rp < r~
(18)
for rp >_ r 1
The particle spectral absorption efficiency Qa can be determined from Mie theory [45] if the particle size, complex refractive index, and incident wavelength of light are known. This theory has been used to predict the light scattering and absorption by small particles [45-48]. The input data for Mie theory and the model are tabulated in Table 3. Figure 6 shows the effective absorption of a coal particle as a function of particle size for optical power at a wavelength of 1.06 /zm for different types of optical fiber. The optical power was less efficiently absorbed as particle size approached the wavelength of the incident radiation.
Ignition Delay Time a = aiQ ~,
(17)
where a t is the geometric overlap of the optical power emerging from the optical fiber with the particle cross-section and Qa is the particle spectral absorption efficiency at the laser wavelength. As the particle size reduces below the core diameter of the optical fiber it is not possible for the particle to absorb all the incident optical radiation such that the divergence of the optical beam had to be considered. Figure 5 shows a schematic of a particle illuminated by light delivered by optical fiber. If we assume optical power has a uniform distribution on the particle for multimode and single model optical fibers then the geometric factor
Ignition occurred when the temperature gradient of the gas near the particle surface became positive (i.e., the boundary gas layer temperature exceeded the particle temperature), as shown in Fig. 7a. After ignition the gas temperature in the boundary layer rapidly increased due to the reaction between hydrogen and oxygen. When ignition failed the ignition delay time approached infinity because the power loss equaled the supplied optical power, resulting in a steady-state temperature profile as shown in Fig. 7b. In the nonignition case hydrogen and oxygen were consumed beyond the flammability limits as shown in Fig. 8. The ignition delay time varied with the incident optical power, requiring longer heating
408
P. C. HILLS ET AL. TABLE 3
Summary of the Model Inputs
Particle:
Density: 1500 kg m 3, heat capacity: 1243 J kg- 1 K 1 Surface Reaction: C + O 2 = CO 2 Heating value: 30 MJ kg- 1 Complex refractive index at the 1,064-#m laser wavelength [46]: N = 1.3 + 0.01i for coal particle Effective absorption efficiency: Fig. 6 Gas phase," Density: 0.60 kg m -3, heat capacity: 1000 J kg- 1 K 1 Gas-phase reaction: 2H 2 + O e = 2 H 2 0 Kinetics: Ag 3.88 × 10 s kg m - 3 s Reaction orders m2 = 0.8 ( 0 2) and m3 = 1.7 (H 2) Heating value: 120 MJ kg 1 Boundary layer thickness: 50 times particle diameter =
for smaller optical power. Figure 9 shows the critical optical power required to heat 10-/~m and 40-/zm particles to ignite 12.5% hydrogen/air mixture with increasing ignition delay time for light from a 50/125-/zm multimode optical fiber. It was generally found that after 50 ms a steady-state solution (i.e., ignition or nonignition) existed. In this model the CW heating time was limited to 100 ms, although this could be increased.
1050 900 750
600 m ~SO
300
1I I
~parficle~rface
RESULTS I 5o
The minimum optical power as a function of coal particle size for ignition of a 12.5% hydrogen/air mixture (ignition delay time of 40 ms) for single-mode (r C = 10 /xm, N.A. = 0.1) and multimode [50/125 /~m (N.A. = 0.2), 62.5/125
B0
60
{
i
i
1oo
200
300
400
3'00
~-00
Radius(pro) (a) 1100
~
1°°t
I
5k,.
700
500
21
30o
i,, L I
~'---Pa r ficte surface t'O
100
I
100
2;0 Radius (pro 1
20
(b) 0
i 0
40
80
120
160
200
PacticLe diameter (IJm)
Fig. 6. Theoretical absorption efficiency " a " as a function of particle diameter for 1.064-/zm radiation from (1) 10/125-ttm (2) 50/125-/zm (3) 62.5/125-/zm and (4) 100/140-~m optical fibers.
Fig. 7. Predicted boundary layer temperature profiles for (a) ignition in a 12.5% H 2 / a i r mixture and (b) nonignition in 25% H 2 / a i r mixture while heating a 50-/xm particle with 100 mW power delivered by 50/125-/xm multimode optical fiber at specific illumination times of (1) 0, (2) 30, (3) 60, (4) 80, and (5) 85 ms.
L A S E R I G N I T I O N BY S M A L L P A R T I C L E S 2~
409
r I I I
1000
E ~
15
100 m
7.5
E c
I*-P~ r tid.e surf a~ l 100
0 0
I ZOO
I 300
1
0
tOO
I 20
I
I 60
t,O
I
I
f
80
100
120
I
1L,O
160
Particte diameter {pm)
Radius (~m)
Fig. 8. 0 2 concentration profile for non-ignition case of Fig. 7(b).
Fig. 10. Minimum optical power as a function of coal particle size to ignite 21% H J a i r mixture with (1) 100/140-/zm 0 multimode optical fibers, (2) 62.5/125-/zm 0, (3) 50/125-/xm 0, and (4) 10/t25-/xm single mode.
tzm and 100/140 /xm ( N . A . = 0.29)] optical fibers was determined as shown in Fig. 10. A coal particle of 12 /xm diameter provided optim u m heat transfer to the boundary gas layers for single-mode optical fiber. For smaller particle size absorption efficiency of the incident light decreased and radiative losses increased. For larger particles m o r e optical power was required to heat the particles to a high enough t e m p e r a t u r e to ignite the combustible gas. The model predicts that the minimum optical power required for ignition rapidly increases for particles of less than 10 ~ m and greater than 6 0 / x m . Figure 10 compares calculated and experimental results of minimum
optical power as a function of coal particle size for ignition of 21% h y d r o g e n / a i r mixture with 5 0 / 1 2 5 /xm multimode optical fiber. Experimental results indicate that the minimum optical power does not increase rapidly for larger particles. This occurs because large coal particles melt to form a thin disk over the end of the optical fiber. Such particles ignited gases at lower optical powers because they absorbed much of the incident power. The critical optical power for ignition (i.e., occurred at approximately 13% hydrogen), in-
300
600 3=
500 I ~
200
~oo 2 m
300 ..-
1oo
200
&
c
loo 0
I
0
20
40
60
80
100
Ignition delay time(ms)
Fig. 9. Predicted optical power for ignition as a function of particle illumination time for (1) 10-/xm and (2) 40-/xm coal particles in 12.5% H2/air mixture with 50/125-/zm multimode optical fiber.
0
i
0
I
,
10 Percentage hydrogen
I
20
,
30
in air ( % )
Fig. 11. Minimum optical power as a function of H2/air concentration for heating a 40-/xm coal particle to ignition with 50/125-/~m multimode optical fiber (experimental data for 38-45-/xm fraction).
410 fluenced mainly by the kinetic data of Eq. 2 for the hydrogen/oxygen reaction. Figure 11 compares calculated results of critical optical power as a function of hydrogen/air concentration for heating a 40 /zm coal particle to experimental results of ignition by heating 38-45 ~m coal particles with power delivered by 50/125 gm multimode optical fiber. DISCUSSION The present study offers additional insights into the ignition mechanism that occurs when optical power heats a small particle in a combustible gas and offers certain limiting conditions. The observed decrease in optical power with decreasing particle size to 38 #m is predicted. Similarly, the optimum hydrogen/air concentration of approximately 13% for ignition agrees with the experimentally determined value of 10%-15%. Furthermore, this value is different for inert and reactive particles due to particle surface reaction. The experimentally observed hydrogen concentration of 10%-15% for which minimum optical power is required is less than the stoichiometric combustion of 29.6% hydrogen/air (by volume). The hydrogen concentration at which the flame propagation speed is maximum is 16.3%, much less than the stoichiometric ratio [20]. In this case, coal particle reaction locally consumes oxygen, resulting in a minimum optical power occurring at 13% hydrogen/air. The experimentally observed methane concentration of 9.5% and the concentration for the fastest flame speed (9.96%) [50] due to oxygen consumption by coal combustion. The effective absorption efficiency of optical power by a particle decreases with particle size such that particles of a similar size to the wavelength of the incident light absorb very little power. However, small particles (10-40 /zm) require much less optical power for ignition as they heat up much faster than larger particles and have smaller thermal losses. Such particles are often airborne and are typical of the particle sizes found in underground coal mines. The high power density and the small core diameter of single-mode optical fiber results in a high probability of light being absorbed by a
P . C . HILLS ET AL. small particle. The model predicts that optical powers of 1 mW delivered by single-mode optical fibers at a wavelength of 0.8 p~m and incident on a small blackbody (a = 1) of 8 /xm diameter can create explosions in 12.5% hydrogen/air mixtures. Small-core multimode optical fibers carrying the same amount of optical power as large-core optical fibers have a higher ignition risk due to the higher power density. In general, the wavelength of operation in optical fibers is 0.5-1.5/xm. The optical wavelength has less than 2% effect on the minimum optical power for ignition with particles of greater than 15 p~m. For smaller particles up to 40% less power may be required for ignition at a wavelength of 0.5 /zm compared with 1.06 /xm. Although we have only considered CW optical sources, pulsed optical sources are also prevalent in communication and sensing systems. As the particle illumination time reduces to less than the minimum ignition delay time, such as with a pulse optical source or by a particle falling through an optical beam, the minimum optical power for ignition increases. A preliminary experimental investigation of pulsed optical sources was performed. The minimum optical power from a 1.06-/zm Nd:Yag laser delivered by a 100/140-/xm optical fiber to exploded a 12% hydrogen/air mixture was 9 W peak power for 1 100-~s pulse of 10 Hz repetition rate. This is equivalent to an average power of 9 roW--an order of magnitude less than the CW optical source. This reduction in energy occurs because the particle obtains sufficient energy during the single pulse to ignite the gas. As the pulse repetition rate is increased the effects of repetitive heating must be considered. For extremely fast repetition rates CW heating is approached. SUMMARY
This work numerically and experimentally studies the ignition of a hydrogen/air mixture by a laser-heated coal particle. Careful and elaborate experiments were performed to investigate the minimum CW laser powers delivered by multimode optical fibers that can cause an explosion. CW powers of 100 mW delivered by 50/125-p.m graded index multimode optical
LASER IGNITION BY SMALL PARTICLES fibers, and incident on coal dust particles of 0-38 /xm diameter, create explosions in combustible hydrogen/air mixtures. A numerical model was developed to determine the hazardous power levels for CW optical systems in potentially explosive atmospheres. The important ignition parameters and their effects on the minimum optical power for ignition were predicted. Although the model does not agree exactly with the experimental results there is a definite correlation between the theory and experiment. The decrease in optical power with particle size to less than 38 /~m is predicted. Similarly the optimum hydrogen/air concentration of approximately 13% for ignition agrees with the experimentally determined value of 10%-15%, this being less than the ratio for measured maximum flame speed, due to oxygen consumption near the coal particle surface. The high power density and small core diameter of single-mode optical fibers results in a high probability of light being absorbed by a small particle. Similarly, small-core optical fibers carrying the same amount of power as large-core optical fibers, have a higher ignition risk in explosive atmospheres. This work thus demonstrates the need for further research and experimental work to develop standards that allow safe operating conditions for optical systems in potentially explosive or flammable atmospheres.
411 7.
8.
9. 10. 11. 12. 13. 14. 15. 16. 17.
18.
19. 20. 21. 22. 23.
24.
The authors thank BlIP Co. Ltd. for funding and permission to publish and Chuguang Zheng for prouiding data on the spectral absorptivity of coal. REFERENCES 1. Tortoishell, G., Proceedings, SPIE, Vol. 522, Fibre Optics '85, 1985, pp. 132-139. 2. Tortoishell, G., Process Optical Measurements and Industrial Methods, The Hague, Netherlands, SPIE Vol. 1266, March 1990, Paper 14. 3. Carleton, F. B., and Weinberg, F. J., Fibre Optics '90, London, SPIE Vol. 1314, 1990. 4. Hills, P. C., Samson, P. J., and Webster, I., J. Electric. Electron. Eng. Australia 10:207-220 (1990). 5. Hills, P. C., Elect. Lett. 26:1982-1983 (1990). 6. Hills, P. C., Samson, P. J., and Webster, I., Proceedings 7th International Conference on Optical Fibre Sensors, IREE, Sydney, Australia, 1990, pp. 63-66.
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