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Study of interaction of entrained coal dust particles in lean methane–air premixed flames
Combustion and Flame 159 (2012) 2449–2456
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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e
Study of interaction of entrained coal dust particles in lean methane–air premixed flames Yanxuan Xie a, Vasudevan Raghavan b, Ali S. Rangwala a,⇑ a b
Department of Fire Protection Engineering, Worcester Polytechnic Institute, Worcester, MA 01609, USA Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India
a r t i c l e
i n f o
Article history: Received 19 October 2011 Received in revised form 3 January 2012 Accepted 8 February 2012 Available online 12 March 2012 Keywords: Coal dust interaction Laminar premixed flame Equivalence ratio Laminar burning velocity Shadowgraph image Cone angle method
a b s t r a c t This study investigates the interaction of micron-sized coal particles entrained into lean methane–air premixed flames. In a typical axisymmetric burner, coal particles are made to naturally entrain into a stream of the premixed reactants using an orifice plate and a conical feeder setup. Pittsburgh seam coal dust, with particle sizes in the ranges of 0–25 lm, 53–63 lm, and 75–90 lm, is used. The effects of different coal dust concentrations (10–300 g/m3) entrained into the mixture of methane–air at three lean equivalence ratios, /, of 0.75, 0.80 and 0.85, on the laminar burning velocity are studied experimentally. The laminar burning velocity of the coal dust–methane–air mixture is determined by taking high quality shadowgraph images of the resulting flames and processing them using the cone-angle method. The results show that the laminar burning velocity reduces with the addition of coal dust having particle sizes in the ranges of 53–63 lm and 75–90 lm, irrespective of the equivalence ratio values. However, burning velocity promotion is observed for one case with particle size in the range of 0–25 lm at an equivalence ratio of 0.75. Two competing effects are considered to explain these trends. The first effect is due to volatile release, which increases the overall equivalence ratio and thus, the flame temperature and burning velocity. The second is the heat sink effect that the coal particles take up to release the volatiles. This process reduces the flame temperature and accordingly the burning velocity also. A mathematical model is developed considering these effects and it is seen to successfully predict the change of laminar burning velocity for various cases with different dust concentrations and equivalence ratios of the gas mixture. Furthermore, the implication of this study to coal mine safety is discussed. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction Many materials, which are virtually non-flammable in their bulk form, become highly reactive and even explosive, if dispersed as a cloud of fine particles in air, due to significant increase in the surface area for enhancing heat and mass transfer processes. From a combustion viewpoint, this can be treated as both a benefit and a hazard. In industries that manufacture, transport, process and/or use combustible dusts, accidental dust deflagrations represent a real hazard to both personnel and equipment. An example is the recent coal mine explosion in West Virginia (April 5, 2010), which resulted in the killing of 29 miners and considered as one of the most disastrous mining accidents in US history. Interestingly, most coal mine explosions often involve both a methane deflagration combined with fugitive coal dust that is collected by the combustion wave as it progresses through the mine. The physical and chemical processes involved during the travel of a combustion wave through a flammable gas–dust–air mixture
⇑ Corresponding author. Fax: +1 508 831 5862. E-mail address: [email protected] (A.S. Rangwala).
are shown in Fig. 1. Three distinct steps are identified in Fig. 1. First, the dust deposited on the floor, walls, and ceiling can be lifted up by the pressure blast of the initial methane explosion causing a cloud of dust to be suspended in the air. When the gaseous flame front meets the combustible dust/particle cloud, the particles pyrolyze and contribute volatile vapor to the fuel–air mixture. Also, condensed fuel particles in a gas flow can cause instabilities, which could potentially alter the structure of the premixed flame. Greenberg et al. [1] have shown that adding combustible liquid droplets to a gas flame can increase the burning velocity under certain conditions. Based on droplet concentration and size, Suard et al. [2] identified different spreading regimes for such fuel droplet–gas– air flames. Wendt and Graves [3] studied the flammability of coal dust in a laminar opposed jet diffusion flame. Numerical models related to the propagation of a flame in a homogeneous mixture of coal-dust–air have been developed by Smoot and Horton [4], Krazinski et al. [5], and Slezak et al. [6]. An interested reader is directed to the comprehensive reviews related to this topic by Eckhoff [7] and Cashdollar [8]. However, the interaction between solid combustible dust particles and a gaseous premixed flame have been rarely investigated in combustion literature and is the main focus of the current study.
0010-2180/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2012.02.013
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Nomenclature A B b Cp Cs Ctotal cs E h k Lv M m000 CH4 m000 air m000 fuel m000 v n ns P n_ air Q_ q_ 00 R r Su Tb
parameter characterizing rate of vaporization of particles, Eq. (2) frequency factor characterizing rate of gas phase oxidation of gaseous fuel burner diameter heat capacity of gas mixture heat capacity of solid particle heat capacity of particle-gas mixture concentration of particles activation energy characterizing the gas phase reaction height of the flame cone thermal conductivity of air heat of gasification molecular weight mass of methane present in 1 m3 mass of air present in 1 m3 mass of fuel present in 1 m3 rate of devolatilization temperature exponent characterizing rate of vaporization of coal particles in Eq. (2) number of particles pressure moles of air per unit time heat release rate heat flux to particles in Fig. 5 gas constant mean radius of particle burning velocity flame temperature based on original premixture
2. Experimental apparatus Figure 2a presents the schematic of the experiment setup used for the measurement of laminar burning velocity and dust entrainment rate. The design is based on the concept of a Bunsen burner having side openings to entrain coal dust particles into the flow of the reactant mixture. Specific details of the dust injector in such a burner are discussed by Xie et al. [9]. The burner is made of a steel tube with an inner diameter of 10.2 mm and wall thickness of 1.2 mm. A 1 mm thick acrylic plate with a 1 mm diameter orifice
Tf T 0f T 00f tr U V_ air V_ CH
4
V x Ze
flame temperature with particles promoted flame temperature due to locally increased equivalence ratio reduced flame temperature due to heat sink effect of particles residence time average flow velocity at burner nozzle volumetric flow rate of air volumetric flow rate of methane volume spatial coordinate zeldovich number
Greek symbols a cone angle q density of the mixture qs density of the particle d thickness of devolatilization zone U original gaseous mixture equivalence ratio /s equivalence ratio of coal particles and air assuming complete gasification Subscripts b adiabatic condition based on original gas phase condition f flame s solid particle u conditions in the ambient condition v vapor
is installed inside the steel tube, 150 mm away from the burner exit, to allow the flow streamlines to become parallel well before the burner exit. Dust is fed to the orifice plate through three openings of dimensions 7.5 mm wide and 9 mm long, located on the tube in an axisymmetric fashion above the orifice plate as shown in Fig. 2b. A brass jacket tube of inner diameter 0.1 mm larger than the outer diameter of the steel tube is secured by two socket head screws. This is used to adjust the opening size and therefore the dust entrainment. Pittsburgh seam coal dust (with no additives) is used in the present study. Few separate experiments have been
Fig. 1. Schematic of dust deflagration process.
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Fig. 2. Schematic of the experimental apparatus: (a) dust burner and the weighing assembly; (b) dust entrainment assembly.
carried out with sand particles as well. The sand–dust particles are used to analyze the influence of an inert on the burning velocity. The coal dust is filled in an inverted cone-shaped acrylic container, which is also attached to the steel tube. The cone angle of the container is equal to 60°, which represent the critical angle of repose of dust particle size ranges used in this study. The repose angle is determined using an experimental method discussed by Botz et al. [10]. The adjustable burner and its attachments are secured in a support frame and the entire assembly is kept over a Cole-Palmer Symmetry PR 4200 load cell. The load cell has a total weighing capacity of 4.2 kg with a sensitivity of 0.01 g. The factory specified uncertainty in the mass measurement is ±0.03 g. A ring stand is kept outside the load cell to support a collection pan as shown in Fig. 2. Pittsburgh seam bituminous coal dust with particle sizes in the range of 0–25 lm, 53–63 lm, and 75–90 lm are used in the experiment. The size ranges are obtained by Retsch AS 300 sieve shaker. Compressed air and methane (99.99% purity) cylinders are used to supply the burner with an upstream pressure of 0.5 bar. Each gas flow is controlled by a SIERRA Model 100 mass flow controller, which has an accuracy of ±1% of its maximum flow capacity. Direct shadowgraph technique is used to capture the flame cone with or without coal dust injection. The schematic of the shadowgraph setup is shown in Fig. 3. A projector lamp of capacity 420 W is converted into a point light source and placed at a distance of one focal length from a double convex lens. A Canon EOS 5D single-lens reflex (SLR) camera with a macro-lens (Canon EF100/2.8 Macro USM) with a minimum focal length of 31 mm is placed be-
hind the flame along the center axis of the parallel light beam. The camera is manually adjusted (shutter speed of 1/4000 s, ISO of 1600, and aperture of 2.8) to obtain the sharpest image for post processing.
3. Experimental results A sample image of the actual flame and the shadowgraph image obtained by the macro-lens are shown in Fig. 4. The main advantage of the shadowgraph is that it can capture clearly the flame cone even when the flame is loaded with high concentration of burning particles. As shown in Fig. 4a, it is hard to locate the edge of the flame cone using conventional direct photograph technique, while the flame cone is easily identified in the shadowgraph (Fig. 4b). For each dust concentration and equivalence ratio of the reactant mixture, a minimum of 15 images are captured and processed by an image process algorithm programed in MATLAB. The corresponding average cone angle is used to estimate the laminar burning velocity. A sample of the processed image is shown in Fig. 4c. The algorithm converts the shadowgraph into a gray-scale image and detects the cone edge where a significant change in the normalized intensity (a value from 0 to 1) is observed on each row within the preselected boundary of the flame cone. The detected cone edge is shown as two clusters of dots in Fig. 4c. Slopes that connect each dot on one side of the cone are calculated. Then a
Fig. 3. Schematic for shadowgraph setup.
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Fig. 4. Photographs of (a) actual flame, (b) shadowgraph and (c) processed image.
larger than 25 lm. It is clear that with 0–25 lm coal particles, Su is promoted as shown by the solid gray triangular symbols, connected by solid line in Fig. 5. It is shown in Fig. 5 that the decreasing trend in the slope of Su for 53–63 lm coal particles is lesser than that with 75–95 lm particles. This indicates that the particle size plays an important role in the problem. To further analyze the results a mathematical model is developed based on the reasoning that two competing effects of a heat sink and an increase in the effective equivalence ratio (due to coal volatilization) causes Su to change, and is discussed subsequently.
Fig. 5. Experimental laminar burning velocity of methane–air flame with different concentrations and particle size ranges of coal particles.
best-fit line for all the detected dots, shown as black solid line in Fig. 4c, is used to obtain the averaged cone half angle (a). The standard deviation of the angle experimentally measured is within ±1.5°. The laminar burning velocity is obtained by using cone angle method as follows:
Su ¼ U sinðaÞ;
ð1Þ
where Su represents the laminar burning velocity, U is the average velocity of the mixture and a is the cone half-angle as shown in Fig. 4. It should be noted here that this method is not the most accurate method to calculate laminar burning velocity. This method is used to provide only the trend of variation of laminar burning velocity with equivalence ratio. Since the same method is used to evaluate the laminar burning velocity for all the cases with or without dust injection, the comparison of the trends is expected to be reasonable. Figure 5 shows the laminar burning velocity determined from shadowgraph images as a function of the concentration of coal dust. Experiments were conducted for three coal particle size ranges: 75–90 lm, 53–63 lm, and 0–25 lm and three methane– air equivalence ratios of / = 0.75, 0.8, and 0.85. Due to the strong cohesive forces, the dust entrainment rate is unsteady when smaller particles are employed at low concentrations. Therefore only one data point is obtained using the coal particles in the size range of 0–25 lm, at a higher concentration of around 290 g/m3. Figure 5 shows that the interaction of the coal particles with a laminar premixed methane–air flame reduces Su when the particle sizes are
4. Mathematical model As mentioned earlier, a mathematical model is developed to explain the observation made in the experiments and to carry out parametric studies to predict Su for particles of sizes not included in the experiments. Figure 6 illustrates the interaction of the particles with the premixed flame and is used as a basis to develop a model to estimate Su. The path of a coal particle, assumed to be along a flow streamline, is shown in Fig. 6. The particle absorbs the heat from the flame while it travels though the devolatilization zone as illustrated by q_ 00 in the inset to Fig. 6. The initial temperature of the particle is assumed to be equal to the mixture temperature. Due to heat transfer from the flame, once the temperature of the particle reaches a va-
Fig. 6. Illustration of parameters involved in a typical dust–flame interaction (q_ 00 is _ 000 the heat flux from flame to the particle; m v represents volatization rate unit volume of the mixture; Tf is flame temperature; Tv is initiation temperature for coal devolatilization; d is the thickness of devolatilization zone; a is the cone half angle; b is the burner diameter; h is the cone height).
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lue of Tv, the gasification process is initiated, thereby releasing gas_ 000 eous volatiles at the rate of m v (Fig. 6). In this study, for simplicity, the volatiles are assumed to be constituted by methane only as suggested by Seshadri et al. [12]. This additional fuel released from the coal particle can increase the equivalence ratio of the reactant mixture locally in the devolatilization zone. For a lean mixture flame, increased equivalence ratio promotes Su. This is the first effect of the particle interaction. In Fig. 6, Tf is the temperature of the flame and the thickness of the zone within which the temperature increases from Tv to Tf is denoted by d. It is assumed in this study that coal particles will pyrolize and release volatiles when it traverses this distance d. The height and the width of the flame cone are represented by h and b, respectively. The cone half angle is designated as a. In addition, the particle also acts as a heat sink, since it takes heat from the flame. As a result, the flame temperature and thus Su is reduced. This is the second effect of particle interaction in premixed flames. These two effects are competing in nature and affect the flame speed simultaneously; based on the combined effect the flame speed will either increase or decrease due to particle injection. To simplify the theoretical model, the two processes are analyzed initially in a decoupled manner, and then re-coupled later. The change in the flame temperature due to each effect is calculated separately and then superimposed to obtain the estimated correct flame temperature.
The duration of devolatilization needs to be determined in order to use Eq. (2) and estimate the total amount of vaporized fuel. As shown in Fig. 6 the devolatilization process is limited to a narrow band with thickness of d, in a region close to the reaction zone on the unburned side, where the temperature increases from Tv to Tb. The thickness of this zone is estimated by applying an energy balance: 2
k
d T dx
2
qUC total
d¼
kðT b T v Þ
qUC total ðT b T u Þ
qair V_ air þ qCH4 V_ CH4 V_ air þ V_ CH4
þ cs ;
and the averaged flow velocity is given by
, _ _ U ¼ V air þ V CH4
pb2 4
! :
The volumetric flow rate of the coal dust is very small (around three orders of magnitude lesser than the gas-mixture flow rate), therefore, its contribution to the average velocity is negligible. The time of devolatilization or the residence time of particles is then given as:
d sinðaÞ
tr ¼
U:
ð5Þ
The devolatilization time is used to estimate the total mass of volatiles released per unit volume during the passage of dust particles through a distance d and is given by:
_ 000 m000 v ¼m v tr :
ð6Þ
With this amount of fuel added to the supplied reactant mixture, the new equivalence ratio can be calculated. The consolidated amount of the gaseous fuel per unit volume in the mixture, de000 000 000 noted by m000 fuel , can be estimated as: mfuel ¼ mCH4 þ mv , where 000 mCH4 is mass of the original methane present per unit volume of the mixture. Accordingly the new equivalence ratio is calculated as,
ð2Þ
_ 000 where m v is mass of gaseous fuel evolved per unit volume per second (g/m3s). The quantities A and n are constants for a given coal type. The particle temperature is denoted as Ts and it is assumed that Ts = 0.5(Tb + Tv), where Tb is the adiabatic flame temperature based on the methane–air equivalence ratio. For coal particles, devolatilization initiates at a temperature (Tv) of around 600 K [13]. The value of Tb is calculated using an equilibrium solver, based on the minimization of free energy (GASEQ) [14]. The total volume of particles present per unit volume of the reactant mixture is estimated by dividing the dust concentration cs (g/m3) by the particle density qs (g/m3). The number of particles per unit volume (ns) is then equal to ns = (cs/qs)/Vs, where Vs is the volume of a single particle, assumed to be spherical.
ð4Þ
:
The density of the mixture, q, is calculated by the following expression,
4.1. Effect of equivalence ratio promotion
2 n _ 000 m v ¼ Ans 4pr T s ;
ð3Þ
along with boundary conditions that at x = 0, T = Tv, at x = d, T = Tb, and at x = 1 T = Tu. dT/dx is assumed to be a constant in the dev3 olatilization zone and C total ¼ C P þ 4pr 3Cqs qs ns [12]. In Eq. (3), U is the average velocity, q is the density of the unburned mixture, and k is the thermal conductivity, assumed to be as same as that of air (0.052 W/m K), calculated at 400 °C, approximately equal to the average temperature in the devolatilization zone. Integrating Eq. (3) the thickness of the devolatilization zone can be obtained as,
q¼ Volatiles are released from the coal particles into the gaseous mixture as the result of heat transfer from the reaction zone into the devolatilization zone. In order to estimate the amount of volatiles present in the gaseous mixture, it is necessary to explore the rate of the volatile release and quantify the same as a function of heat transfer. There are four possible methods to estimate devolatilization. The first method is based on a much simplified assumption that all volatiles are released when the particle reach a certain temperature. However, such a method excludes the fact that devolatilization is a transient process. The second method is to treat the particles as liquid droplets and the gasification rate can be estimated as discussed by Suard et al. [2]. This method, however, does not capture the non-linear behavior of devolatilization of a solid particle such as coal, since the droplet evaporation is fairly first order and linear. In the other two methods, devolatilization can be solved by a set of equations based on Arrhenius rate law as described by Solomon and Colket [11], or it can also be estimated based on a temperature dependent power-law relation as proposed by Seshadri et al. [12]. The last method is employed in this study as it is simplified yet an accurate method. Seshadri et al. [12] used the expression given below to predict devolatilization rate of coal particles,
dT ¼ 0; dx
/ ¼ 9:52
m000 fuel
M CH4
m000 air ; M air
where the coefficient 9.52 is the ratio of numbers of moles of methane to air when / equals 1. For the supplied mixture, the mass of methane and air present per unit volume are given as,
0
m000 CH4
1 _ CH P V M CH 4 4 A; ¼@ Ru T u V_ air þ V_ CH
ð7Þ
4
0
m000 air
1 _ air P V M air A; ¼@ Ru T u V_ air þ V_ CH4
ð8Þ
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where P is the atmospheric pressure (101,325 Pa), Tu is the unburned gas temperature (293 K) and Ru is the universal gas constant. M denotes the molecular weight of each species and V_ air and V_ CH4 are the supply volumetric flow rates of air and methane respectively. With the new equivalence ratio, the new flame temperature T 0f is estimated by using the equilibrium solver [14]. The calculated results are shown in Fig. 7 for coal particles having sizes in the range of 75–90 lm, with supply methane–air equivalence ratios of 0.75, 0.80, and 0.85. As shown in Fig. 7, the flame temperature increases with increased dust concentration as it results in more volatiles to be released and a higher effective equivalence ratio obtained. 4.2. Heat sink effect of coal particles In addition to a local increase in equivalence ratio, a coal particle will also act as a heat sink as it absorbs the heat from flame for devolatilization. Two aspects are considered for modeling the heat sink effect; (1) the heat used to raise the temperature of coal particles from ambient condition to the flame temperature and (2) the heat used to gasify the coal particles. Three assumptions have been made; (1) the heat release rate from the flame is assumed to remain constant, (2) the coal particles simply act as inert particles, which are also able to devolatilize by absorbing energy from the flame and (3) coal particles reach the flame temperature when they reach the flame sheet. Based on these assumptions, the heat released to raise the gas temperature per unit time for flame without dust will be equal to the sum of heat release required to raise the temperature of gas and particles and the heat of gasification per unit time. Therefore, each term should be determined to estimate the flame temperature after accounting for the heat sink effect. First, the heat released from flame without dust is calculated. For a lean methane–air mixture, the global chemical reaction is given by,
/ / CH4 þ ðO2 þ 3:76N2 Þ ! CO2 þ /H2 O þ 3:76N2 þ 2ð1 /ÞO2 2 2
mixed flame without coal dust for a given flow rate of air and /, can be calculated as:
h i n_ X air Q_ ¼ ðT b T u Þ C p nproduct ; 4:76
ð10Þ
where n_ air is the number of moles of air supplied per unit time. For the flame with coal dust particles, the same heat is released; however, it is also affected by the energy requirement for volatile gasification and for rising the temperature of the particles. Therefore, the corrected flame temperature T 00f can be estimated using energy conservation as shown in Eq. (11).
h i n_ X air þ n_ s C s ðT 00f T u Þ þ Lv =t; C p nproduct Q_ ¼ ðT 00f T u Þ 4:76
ð11Þ
where n_ s represents the number of coal particles per unit volume per unit time, passing through the flame, given by,
n_ s ¼ ðV_ air þ V_ CH4 Þns qs V particle =M c ;
ð12Þ
where Mc is the molecular weight of carbon. Similarly Lv in Eq. (11) represents the heat of gasification, which is assumed to be a fraction of the heat produced during the reaction and is given by,
Lv ¼ vðm000 v V d DhCH4 Þ;
ð13Þ
where the fraction, v, is assumed to be 0.01, as suggested by Seshadri et al. [12], DhCH4 is the heat of combustion of methane, and Vd represents the volume of the devolatilization zone (conical space with a thickness of d as shown in Fig. 6), given by,
Vd ¼
2 2 1 b 1 d b d ph þ p h : 3 sinðaÞ 2 cosðaÞ 4 3
ð14Þ
The term, Lv/tr, represents the heat consumed by the gasification process for the time the particle spends in the devolatilization zone. This is estimated by Eq. (5). Rearranging Eq. (11), the corrected flame temperature T 00f that takes into account of the heatsink effects is obtained as,
ð9Þ The total heat released during the complete combustion, for (// 2) mole of methane or 4.76 mol of air, is solved by energy conservation as follows:
½ðT b T u Þ
P
C p nproduct ;
where Tb is the adiabatic flame temperature, estimated using the equilibrium solver [14]. Therefore, the heat release rate of the pre-
Fig. 7. Adiabatic flame temperature calculated as a function of / due to addition of coal dust particles in the size range of 75–90 lm.
T 00f ¼
n_ air 4:76
P
Q_ Lv =t r C p nproduct þ n_ s C s
þ Tu:
ð15Þ
Using Eq. (15), T 00f is calculated for several cases and is plotted in Fig. 8. As observed in Fig. 8, the flame temperature reduces due to heat sink effects, as the concentration of dust increases for all three equivalence ratios.
Fig. 8. Corrected flame temperature considering the heat sink effect by coal particles.
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4.3. Combined effects The combined effects of increase in the flame temperature due to equivalence ratio promotion and decrease in the flame temperature due to heat sink effects are accounted for, by calculating an average flame temperature,
T f ¼ ðT 0f þ T 00f Þ=2: The corresponding flame temperature is then used to estimate Su using the model developed by Seshadri et al. [12].
Su ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2Bke2 E ; exp RT f qC total
ð16Þ
where
e ¼ 1=Z e ; and Z e ¼
EðT f T u Þ RT 2f
:
The values of B and E are chosen as 3.5 106 mol1 s1 and 88,800 kJ mol1 respectively to match the calculated burning velocity with burning velocity obtained by experiments for flames without dust. The constants, A = 0.034 g/m2K s and n = 1.1, were introduced in eq. (2) and used to evaluate T 0f . 5. Results and discussion 5.1. Validation The calculated burning velocities are compared with the experiment data in Fig. 9. Overall, the model captures the measured experimental trends reasonably well. Considering the simplifications in the model, an exact agreement is impossible, however, a good qualitative agreement has been obtained. Further, for 0– 25 lm coal particles the model predicts Su is promoted as shown by the dotted line (theory) that intersects the solid gray triangular symbol (experimental data point) in Fig. 9. Further, it should be noted that for the same size range of 75–95 lm, the reduction in Su by injecting the coal particles is lesser than the case where sand particles are injected. This observation demonstrates that the heat sink effect is partially compensated by the increase in the overall equivalence ratio due to gasification. However, in the case of the sand particles only the heat sink effect plays a role. It is shown in Fig. 9 that the decreasing trend in the slope of Su for 53–63 lm coal particles is lesser than that with the particles in the size range of 75–95 lm. It indicates that as the size of coal par-
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ticle reduces, the equivalence ratio increase is significant when compared to the heat sink effect. When the size of coal particles are as small as 0–25 lm, the influence of heat sink plays a minor role and the increase in the effective equivalence ratio causes Su to increase. However, it should be noted that the present experiments provide only one data point for this smallest size range and shows increasing trend of Su. Specifically, more experiments have to be carried out by designing a better feeding system for the coal dust capable of handling very small particle sizes to confirm the increasing trend of Su. 5.2. Parametric study The theoretical model is used to calculate Su for wide range of parameters such as different dust concentrations, at various equivalence ratios of methane–air mixture and coal particle sizes. The results are plotted in Fig. 10. As shown in Fig. 10, the slope of the Su vs. dust concentration curve is negative in most cases, however, it gets flatter as the particle size decreases at a given lean equivalence ratio. For the lowest / value of 0.70, when particles in the size range of 0–25 lm are injected, there is an increasing trend for Su. This is due to faster pyrolysis of smaller particles causing an increase of overall equivalence ratio (Fig. 11) as well as an increase in the flame temperature (Fig. 12) with dust injection. For / = 0.85, for the smallest particle size range, Su remains almost invariant with dust concentration; there is a small increase in its value initially and as the dust concentration increases beyond approximately 180 g/m3, Su suffers a slight decrease. Even though the overall equivalence ratio increases for this case (Fig. 11) and the flame temperature also shows an increasing trend (Fig. 12), Su remains almost flat because of increase in the Ctotal, the specific heat of the gas–solid mixture, with increasing concentration. As / is increased to 1, there is a steeper decreasing trend for Su, when the particle size is the smallest. For this case, the overall equivalence ratio increases as in the previous cases, especially for
Fig. 10. Burning velocity with coal particles of different sizes at different supply equivalence ratios.
Fig. 9. Burning velocity of a methane–air premixed flame with injected coal particles and sand particles at lean conditions; experimental data are represented by symbols and theoretical prediction is shown by lines.
Fig. 11. Change of overall / due to particle injection calculated for three supply equivalence ratios and different particle sizes.
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and heat transfer processes in the turbulent regime. The devolatilization process will also be enhanced due to the increased residence time for the particle present within the turbulent eddies. As a result, the flame velocity will be further promoted. A deflagration to detonation transition will become likely. 6. Conclusions
Fig. 12. Average flame temperature calculated using combined effects of increase in flame temperature due to increase in overall equivalence ratio and decrease in temperature due to heat loss to coal particles as a function of dust concentration.
the smallest particle size range (Fig. 11). However, there is a notable decrease in the average flame temperature as shown in Fig. 12. In general, higher gasification from smaller particles leads to an increase in the overall equivalence ratio. Based on the particle size and the dust concentration, which affects the mixture specific heat value, if the increase in the overall equivalence ratio is such that it remains less than the slightly rich value where Su is the maximum for gaseous flames, then the increasing trend in the Su can be preserved. However, for the supply equivalence ratio of unity, increase in the overall equivalence ratio due to the injection of smaller particles is such that its value goes to the richer side, where the heat release, the flame temperature, and hence, the laminar flame speed show a decreasing trend. This is shown in Fig. 11, for / = 1 case having smallest particle dust injected, where the overall equivalence ratio shoots up beyond 1.05 (approximate / at which Su is the maximum for gaseous flames), around the dust concentration of approximately 100 g/m3 and a notable decrease in flame temperature is also observed in Fig. 12 beyond this concentration. Apart from this, the value of the mixture specific heat, which depends on particle size and dust concentration, also plays a vital role. The explosion in coal mine tunnels evolves through three stages: laminar flame, turbulent flame and detonation. The Bunsen burner type experiment setup in this study facilitates a better understanding of interaction of coal particles and flame at the first stage of the explosion. As shown in this study, small coal particles (0–25 lm) have the ability to enhance the laminar burning velocity of methane–air mixture under certain conditions. The initial pressure blast of methane–air explosion (fire-damp) in a coal mine can activate the coal dust deposited over various surfaces. Small particles can be easily suspended in air as compare to the larger ones. Therefore, a flame initiated due to hot spots will first interact with smaller particles coarsely suspended. This study shows that if the flame interacting with these particles has been initiated by a lean fuel–air mixture, then there is a good possibility for the flame velocity to be enhanced by the interaction of small coal particles. This initial enhancement in the burning velocity could grow to a turbulent condition. At this stage, more dust particles of various sizes can be drawn into the flame due to enhanced mixing, mass
In this study, a lab scale experiment has been conducted to understand the effects of the coal dust injection into a lean methane–air premixed flame. The laminar burning velocity, Su, of the coal dust–methane–air flame is determined by capturing a shadowgraph image of the laminar flame and evaluating using the cone-angle method. Experimental results show that the presence of coal dust of sizes in the ranges 53–63 lm and 75–90 lm decreases Su, irrespective of the supply equivalence ratio (0.75, 0.80, and 0.85) and the dust concentration (10–300 g/m3). However, the particles having size in the range of 0–25 lm promotes Su, at lower supply equivalence ratios. The promotion in Su is apparent from experiments at a supply equivalence ratio of 0.75. However, more experiments have to be carried out by designing better feeder for the coal dust having very small particle sizes in this range to completely confirm the increasing trend of Su. The mathematical model includes the effect of increase in the equivalence ratio due to volatilizing coal particle and the effect of heat transfer from the flame to volatilize. The model is able to predict the burning velocity of premixed gas-methane flame with coal dust at various dust concentrations performed in this study. For three supply equivalence ratio values, the laminar burning velocity has been plotted as a function of coal dust concentration, where it is clearly illustrated that the average flame temperature that takes into account enhancement of heat release due to increased equivalence ratio as well as the heat sink effects, dictates the variation of laminar burning velocity. Acknowledgment This work is funded by NSF Award #0846764 and the authors like to give our special thanks to National Science Foundation (NSF). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
J.B. Greenberg, A.C. McIntosh, J. Brind, Proc. Roy. Soc. 457 (2001) 1–31. S. Suard, P. Haldenwang, C. Nicoli, C.R. Mec. 332 (2004) 387–396. D.B. Graves, J.O.L. Wendt, Proc. Combust. Inst. 19 (1982) 1189–1196. L.D. Smoot, M.D. Horton, Prog. Energy Comb. Sci. 3 (1977) 235–258. J.L. Krazinski, R.O. Buckius, H. Krier, Prog. Energy Comb. Sci. 5 (1979) 31–71. S.E. Slezak, R.O. Buckius, H. Krier, Combust. Flame 59 (1985) 251–265. R.K. Eckhoff, Dust Explosions in the Process Industries, third ed., Gulf Professional Publishing, Boston, 2003. K.L. Cashdollar, J. Loss Prev, Proc. Ind. 13 (2000) 183–199. Y. Xie, V. Raghavan, A.S. Rangwala, Powder Technol. 213 (2011) 199–201. J.T. Botz, C. Loudon, J.B. Barger, J.S. Olafsen, D.W. Steeples, J. Kansas Entomol. Soc. 76 (2003) 426–435. P.R. Solomon, M.B. Colket, Proc. Combust. Inst. 17 (1979) 131–143. K. Seshadri, A.L. Berlad, V. Tangirala, Combust. Flame 89 (1992) 333–342. L.D. Smoot, P.J. Smith, Coal Combustion and Gasification, Plenum Press, New York, 1985. C. Morley, 2005, Gaseq
Contents lists available at SciVerse ScienceDirect
Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e
Study of interaction of entrained coal dust particles in lean methane–air premixed flames Yanxuan Xie a, Vasudevan Raghavan b, Ali S. Rangwala a,⇑ a b
Department of Fire Protection Engineering, Worcester Polytechnic Institute, Worcester, MA 01609, USA Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India
a r t i c l e
i n f o
Article history: Received 19 October 2011 Received in revised form 3 January 2012 Accepted 8 February 2012 Available online 12 March 2012 Keywords: Coal dust interaction Laminar premixed flame Equivalence ratio Laminar burning velocity Shadowgraph image Cone angle method
a b s t r a c t This study investigates the interaction of micron-sized coal particles entrained into lean methane–air premixed flames. In a typical axisymmetric burner, coal particles are made to naturally entrain into a stream of the premixed reactants using an orifice plate and a conical feeder setup. Pittsburgh seam coal dust, with particle sizes in the ranges of 0–25 lm, 53–63 lm, and 75–90 lm, is used. The effects of different coal dust concentrations (10–300 g/m3) entrained into the mixture of methane–air at three lean equivalence ratios, /, of 0.75, 0.80 and 0.85, on the laminar burning velocity are studied experimentally. The laminar burning velocity of the coal dust–methane–air mixture is determined by taking high quality shadowgraph images of the resulting flames and processing them using the cone-angle method. The results show that the laminar burning velocity reduces with the addition of coal dust having particle sizes in the ranges of 53–63 lm and 75–90 lm, irrespective of the equivalence ratio values. However, burning velocity promotion is observed for one case with particle size in the range of 0–25 lm at an equivalence ratio of 0.75. Two competing effects are considered to explain these trends. The first effect is due to volatile release, which increases the overall equivalence ratio and thus, the flame temperature and burning velocity. The second is the heat sink effect that the coal particles take up to release the volatiles. This process reduces the flame temperature and accordingly the burning velocity also. A mathematical model is developed considering these effects and it is seen to successfully predict the change of laminar burning velocity for various cases with different dust concentrations and equivalence ratios of the gas mixture. Furthermore, the implication of this study to coal mine safety is discussed. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction Many materials, which are virtually non-flammable in their bulk form, become highly reactive and even explosive, if dispersed as a cloud of fine particles in air, due to significant increase in the surface area for enhancing heat and mass transfer processes. From a combustion viewpoint, this can be treated as both a benefit and a hazard. In industries that manufacture, transport, process and/or use combustible dusts, accidental dust deflagrations represent a real hazard to both personnel and equipment. An example is the recent coal mine explosion in West Virginia (April 5, 2010), which resulted in the killing of 29 miners and considered as one of the most disastrous mining accidents in US history. Interestingly, most coal mine explosions often involve both a methane deflagration combined with fugitive coal dust that is collected by the combustion wave as it progresses through the mine. The physical and chemical processes involved during the travel of a combustion wave through a flammable gas–dust–air mixture
⇑ Corresponding author. Fax: +1 508 831 5862. E-mail address: [email protected] (A.S. Rangwala).
are shown in Fig. 1. Three distinct steps are identified in Fig. 1. First, the dust deposited on the floor, walls, and ceiling can be lifted up by the pressure blast of the initial methane explosion causing a cloud of dust to be suspended in the air. When the gaseous flame front meets the combustible dust/particle cloud, the particles pyrolyze and contribute volatile vapor to the fuel–air mixture. Also, condensed fuel particles in a gas flow can cause instabilities, which could potentially alter the structure of the premixed flame. Greenberg et al. [1] have shown that adding combustible liquid droplets to a gas flame can increase the burning velocity under certain conditions. Based on droplet concentration and size, Suard et al. [2] identified different spreading regimes for such fuel droplet–gas– air flames. Wendt and Graves [3] studied the flammability of coal dust in a laminar opposed jet diffusion flame. Numerical models related to the propagation of a flame in a homogeneous mixture of coal-dust–air have been developed by Smoot and Horton [4], Krazinski et al. [5], and Slezak et al. [6]. An interested reader is directed to the comprehensive reviews related to this topic by Eckhoff [7] and Cashdollar [8]. However, the interaction between solid combustible dust particles and a gaseous premixed flame have been rarely investigated in combustion literature and is the main focus of the current study.
0010-2180/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2012.02.013
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Nomenclature A B b Cp Cs Ctotal cs E h k Lv M m000 CH4 m000 air m000 fuel m000 v n ns P n_ air Q_ q_ 00 R r Su Tb
parameter characterizing rate of vaporization of particles, Eq. (2) frequency factor characterizing rate of gas phase oxidation of gaseous fuel burner diameter heat capacity of gas mixture heat capacity of solid particle heat capacity of particle-gas mixture concentration of particles activation energy characterizing the gas phase reaction height of the flame cone thermal conductivity of air heat of gasification molecular weight mass of methane present in 1 m3 mass of air present in 1 m3 mass of fuel present in 1 m3 rate of devolatilization temperature exponent characterizing rate of vaporization of coal particles in Eq. (2) number of particles pressure moles of air per unit time heat release rate heat flux to particles in Fig. 5 gas constant mean radius of particle burning velocity flame temperature based on original premixture
2. Experimental apparatus Figure 2a presents the schematic of the experiment setup used for the measurement of laminar burning velocity and dust entrainment rate. The design is based on the concept of a Bunsen burner having side openings to entrain coal dust particles into the flow of the reactant mixture. Specific details of the dust injector in such a burner are discussed by Xie et al. [9]. The burner is made of a steel tube with an inner diameter of 10.2 mm and wall thickness of 1.2 mm. A 1 mm thick acrylic plate with a 1 mm diameter orifice
Tf T 0f T 00f tr U V_ air V_ CH
4
V x Ze
flame temperature with particles promoted flame temperature due to locally increased equivalence ratio reduced flame temperature due to heat sink effect of particles residence time average flow velocity at burner nozzle volumetric flow rate of air volumetric flow rate of methane volume spatial coordinate zeldovich number
Greek symbols a cone angle q density of the mixture qs density of the particle d thickness of devolatilization zone U original gaseous mixture equivalence ratio /s equivalence ratio of coal particles and air assuming complete gasification Subscripts b adiabatic condition based on original gas phase condition f flame s solid particle u conditions in the ambient condition v vapor
is installed inside the steel tube, 150 mm away from the burner exit, to allow the flow streamlines to become parallel well before the burner exit. Dust is fed to the orifice plate through three openings of dimensions 7.5 mm wide and 9 mm long, located on the tube in an axisymmetric fashion above the orifice plate as shown in Fig. 2b. A brass jacket tube of inner diameter 0.1 mm larger than the outer diameter of the steel tube is secured by two socket head screws. This is used to adjust the opening size and therefore the dust entrainment. Pittsburgh seam coal dust (with no additives) is used in the present study. Few separate experiments have been
Fig. 1. Schematic of dust deflagration process.
Y. Xie et al. / Combustion and Flame 159 (2012) 2449–2456
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Fig. 2. Schematic of the experimental apparatus: (a) dust burner and the weighing assembly; (b) dust entrainment assembly.
carried out with sand particles as well. The sand–dust particles are used to analyze the influence of an inert on the burning velocity. The coal dust is filled in an inverted cone-shaped acrylic container, which is also attached to the steel tube. The cone angle of the container is equal to 60°, which represent the critical angle of repose of dust particle size ranges used in this study. The repose angle is determined using an experimental method discussed by Botz et al. [10]. The adjustable burner and its attachments are secured in a support frame and the entire assembly is kept over a Cole-Palmer Symmetry PR 4200 load cell. The load cell has a total weighing capacity of 4.2 kg with a sensitivity of 0.01 g. The factory specified uncertainty in the mass measurement is ±0.03 g. A ring stand is kept outside the load cell to support a collection pan as shown in Fig. 2. Pittsburgh seam bituminous coal dust with particle sizes in the range of 0–25 lm, 53–63 lm, and 75–90 lm are used in the experiment. The size ranges are obtained by Retsch AS 300 sieve shaker. Compressed air and methane (99.99% purity) cylinders are used to supply the burner with an upstream pressure of 0.5 bar. Each gas flow is controlled by a SIERRA Model 100 mass flow controller, which has an accuracy of ±1% of its maximum flow capacity. Direct shadowgraph technique is used to capture the flame cone with or without coal dust injection. The schematic of the shadowgraph setup is shown in Fig. 3. A projector lamp of capacity 420 W is converted into a point light source and placed at a distance of one focal length from a double convex lens. A Canon EOS 5D single-lens reflex (SLR) camera with a macro-lens (Canon EF100/2.8 Macro USM) with a minimum focal length of 31 mm is placed be-
hind the flame along the center axis of the parallel light beam. The camera is manually adjusted (shutter speed of 1/4000 s, ISO of 1600, and aperture of 2.8) to obtain the sharpest image for post processing.
3. Experimental results A sample image of the actual flame and the shadowgraph image obtained by the macro-lens are shown in Fig. 4. The main advantage of the shadowgraph is that it can capture clearly the flame cone even when the flame is loaded with high concentration of burning particles. As shown in Fig. 4a, it is hard to locate the edge of the flame cone using conventional direct photograph technique, while the flame cone is easily identified in the shadowgraph (Fig. 4b). For each dust concentration and equivalence ratio of the reactant mixture, a minimum of 15 images are captured and processed by an image process algorithm programed in MATLAB. The corresponding average cone angle is used to estimate the laminar burning velocity. A sample of the processed image is shown in Fig. 4c. The algorithm converts the shadowgraph into a gray-scale image and detects the cone edge where a significant change in the normalized intensity (a value from 0 to 1) is observed on each row within the preselected boundary of the flame cone. The detected cone edge is shown as two clusters of dots in Fig. 4c. Slopes that connect each dot on one side of the cone are calculated. Then a
Fig. 3. Schematic for shadowgraph setup.
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Fig. 4. Photographs of (a) actual flame, (b) shadowgraph and (c) processed image.
larger than 25 lm. It is clear that with 0–25 lm coal particles, Su is promoted as shown by the solid gray triangular symbols, connected by solid line in Fig. 5. It is shown in Fig. 5 that the decreasing trend in the slope of Su for 53–63 lm coal particles is lesser than that with 75–95 lm particles. This indicates that the particle size plays an important role in the problem. To further analyze the results a mathematical model is developed based on the reasoning that two competing effects of a heat sink and an increase in the effective equivalence ratio (due to coal volatilization) causes Su to change, and is discussed subsequently.
Fig. 5. Experimental laminar burning velocity of methane–air flame with different concentrations and particle size ranges of coal particles.
best-fit line for all the detected dots, shown as black solid line in Fig. 4c, is used to obtain the averaged cone half angle (a). The standard deviation of the angle experimentally measured is within ±1.5°. The laminar burning velocity is obtained by using cone angle method as follows:
Su ¼ U sinðaÞ;
ð1Þ
where Su represents the laminar burning velocity, U is the average velocity of the mixture and a is the cone half-angle as shown in Fig. 4. It should be noted here that this method is not the most accurate method to calculate laminar burning velocity. This method is used to provide only the trend of variation of laminar burning velocity with equivalence ratio. Since the same method is used to evaluate the laminar burning velocity for all the cases with or without dust injection, the comparison of the trends is expected to be reasonable. Figure 5 shows the laminar burning velocity determined from shadowgraph images as a function of the concentration of coal dust. Experiments were conducted for three coal particle size ranges: 75–90 lm, 53–63 lm, and 0–25 lm and three methane– air equivalence ratios of / = 0.75, 0.8, and 0.85. Due to the strong cohesive forces, the dust entrainment rate is unsteady when smaller particles are employed at low concentrations. Therefore only one data point is obtained using the coal particles in the size range of 0–25 lm, at a higher concentration of around 290 g/m3. Figure 5 shows that the interaction of the coal particles with a laminar premixed methane–air flame reduces Su when the particle sizes are
4. Mathematical model As mentioned earlier, a mathematical model is developed to explain the observation made in the experiments and to carry out parametric studies to predict Su for particles of sizes not included in the experiments. Figure 6 illustrates the interaction of the particles with the premixed flame and is used as a basis to develop a model to estimate Su. The path of a coal particle, assumed to be along a flow streamline, is shown in Fig. 6. The particle absorbs the heat from the flame while it travels though the devolatilization zone as illustrated by q_ 00 in the inset to Fig. 6. The initial temperature of the particle is assumed to be equal to the mixture temperature. Due to heat transfer from the flame, once the temperature of the particle reaches a va-
Fig. 6. Illustration of parameters involved in a typical dust–flame interaction (q_ 00 is _ 000 the heat flux from flame to the particle; m v represents volatization rate unit volume of the mixture; Tf is flame temperature; Tv is initiation temperature for coal devolatilization; d is the thickness of devolatilization zone; a is the cone half angle; b is the burner diameter; h is the cone height).
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lue of Tv, the gasification process is initiated, thereby releasing gas_ 000 eous volatiles at the rate of m v (Fig. 6). In this study, for simplicity, the volatiles are assumed to be constituted by methane only as suggested by Seshadri et al. [12]. This additional fuel released from the coal particle can increase the equivalence ratio of the reactant mixture locally in the devolatilization zone. For a lean mixture flame, increased equivalence ratio promotes Su. This is the first effect of the particle interaction. In Fig. 6, Tf is the temperature of the flame and the thickness of the zone within which the temperature increases from Tv to Tf is denoted by d. It is assumed in this study that coal particles will pyrolize and release volatiles when it traverses this distance d. The height and the width of the flame cone are represented by h and b, respectively. The cone half angle is designated as a. In addition, the particle also acts as a heat sink, since it takes heat from the flame. As a result, the flame temperature and thus Su is reduced. This is the second effect of particle interaction in premixed flames. These two effects are competing in nature and affect the flame speed simultaneously; based on the combined effect the flame speed will either increase or decrease due to particle injection. To simplify the theoretical model, the two processes are analyzed initially in a decoupled manner, and then re-coupled later. The change in the flame temperature due to each effect is calculated separately and then superimposed to obtain the estimated correct flame temperature.
The duration of devolatilization needs to be determined in order to use Eq. (2) and estimate the total amount of vaporized fuel. As shown in Fig. 6 the devolatilization process is limited to a narrow band with thickness of d, in a region close to the reaction zone on the unburned side, where the temperature increases from Tv to Tb. The thickness of this zone is estimated by applying an energy balance: 2
k
d T dx
2
qUC total
d¼
kðT b T v Þ
qUC total ðT b T u Þ
qair V_ air þ qCH4 V_ CH4 V_ air þ V_ CH4
þ cs ;
and the averaged flow velocity is given by
, _ _ U ¼ V air þ V CH4
pb2 4
! :
The volumetric flow rate of the coal dust is very small (around three orders of magnitude lesser than the gas-mixture flow rate), therefore, its contribution to the average velocity is negligible. The time of devolatilization or the residence time of particles is then given as:
d sinðaÞ
tr ¼
U:
ð5Þ
The devolatilization time is used to estimate the total mass of volatiles released per unit volume during the passage of dust particles through a distance d and is given by:
_ 000 m000 v ¼m v tr :
ð6Þ
With this amount of fuel added to the supplied reactant mixture, the new equivalence ratio can be calculated. The consolidated amount of the gaseous fuel per unit volume in the mixture, de000 000 000 noted by m000 fuel , can be estimated as: mfuel ¼ mCH4 þ mv , where 000 mCH4 is mass of the original methane present per unit volume of the mixture. Accordingly the new equivalence ratio is calculated as,
ð2Þ
_ 000 where m v is mass of gaseous fuel evolved per unit volume per second (g/m3s). The quantities A and n are constants for a given coal type. The particle temperature is denoted as Ts and it is assumed that Ts = 0.5(Tb + Tv), where Tb is the adiabatic flame temperature based on the methane–air equivalence ratio. For coal particles, devolatilization initiates at a temperature (Tv) of around 600 K [13]. The value of Tb is calculated using an equilibrium solver, based on the minimization of free energy (GASEQ) [14]. The total volume of particles present per unit volume of the reactant mixture is estimated by dividing the dust concentration cs (g/m3) by the particle density qs (g/m3). The number of particles per unit volume (ns) is then equal to ns = (cs/qs)/Vs, where Vs is the volume of a single particle, assumed to be spherical.
ð4Þ
:
The density of the mixture, q, is calculated by the following expression,
4.1. Effect of equivalence ratio promotion
2 n _ 000 m v ¼ Ans 4pr T s ;
ð3Þ
along with boundary conditions that at x = 0, T = Tv, at x = d, T = Tb, and at x = 1 T = Tu. dT/dx is assumed to be a constant in the dev3 olatilization zone and C total ¼ C P þ 4pr 3Cqs qs ns [12]. In Eq. (3), U is the average velocity, q is the density of the unburned mixture, and k is the thermal conductivity, assumed to be as same as that of air (0.052 W/m K), calculated at 400 °C, approximately equal to the average temperature in the devolatilization zone. Integrating Eq. (3) the thickness of the devolatilization zone can be obtained as,
q¼ Volatiles are released from the coal particles into the gaseous mixture as the result of heat transfer from the reaction zone into the devolatilization zone. In order to estimate the amount of volatiles present in the gaseous mixture, it is necessary to explore the rate of the volatile release and quantify the same as a function of heat transfer. There are four possible methods to estimate devolatilization. The first method is based on a much simplified assumption that all volatiles are released when the particle reach a certain temperature. However, such a method excludes the fact that devolatilization is a transient process. The second method is to treat the particles as liquid droplets and the gasification rate can be estimated as discussed by Suard et al. [2]. This method, however, does not capture the non-linear behavior of devolatilization of a solid particle such as coal, since the droplet evaporation is fairly first order and linear. In the other two methods, devolatilization can be solved by a set of equations based on Arrhenius rate law as described by Solomon and Colket [11], or it can also be estimated based on a temperature dependent power-law relation as proposed by Seshadri et al. [12]. The last method is employed in this study as it is simplified yet an accurate method. Seshadri et al. [12] used the expression given below to predict devolatilization rate of coal particles,
dT ¼ 0; dx
/ ¼ 9:52
m000 fuel
M CH4
m000 air ; M air
where the coefficient 9.52 is the ratio of numbers of moles of methane to air when / equals 1. For the supplied mixture, the mass of methane and air present per unit volume are given as,
0
m000 CH4
1 _ CH P V M CH 4 4 A; ¼@ Ru T u V_ air þ V_ CH
ð7Þ
4
0
m000 air
1 _ air P V M air A; ¼@ Ru T u V_ air þ V_ CH4
ð8Þ
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where P is the atmospheric pressure (101,325 Pa), Tu is the unburned gas temperature (293 K) and Ru is the universal gas constant. M denotes the molecular weight of each species and V_ air and V_ CH4 are the supply volumetric flow rates of air and methane respectively. With the new equivalence ratio, the new flame temperature T 0f is estimated by using the equilibrium solver [14]. The calculated results are shown in Fig. 7 for coal particles having sizes in the range of 75–90 lm, with supply methane–air equivalence ratios of 0.75, 0.80, and 0.85. As shown in Fig. 7, the flame temperature increases with increased dust concentration as it results in more volatiles to be released and a higher effective equivalence ratio obtained. 4.2. Heat sink effect of coal particles In addition to a local increase in equivalence ratio, a coal particle will also act as a heat sink as it absorbs the heat from flame for devolatilization. Two aspects are considered for modeling the heat sink effect; (1) the heat used to raise the temperature of coal particles from ambient condition to the flame temperature and (2) the heat used to gasify the coal particles. Three assumptions have been made; (1) the heat release rate from the flame is assumed to remain constant, (2) the coal particles simply act as inert particles, which are also able to devolatilize by absorbing energy from the flame and (3) coal particles reach the flame temperature when they reach the flame sheet. Based on these assumptions, the heat released to raise the gas temperature per unit time for flame without dust will be equal to the sum of heat release required to raise the temperature of gas and particles and the heat of gasification per unit time. Therefore, each term should be determined to estimate the flame temperature after accounting for the heat sink effect. First, the heat released from flame without dust is calculated. For a lean methane–air mixture, the global chemical reaction is given by,
/ / CH4 þ ðO2 þ 3:76N2 Þ ! CO2 þ /H2 O þ 3:76N2 þ 2ð1 /ÞO2 2 2
mixed flame without coal dust for a given flow rate of air and /, can be calculated as:
h i n_ X air Q_ ¼ ðT b T u Þ C p nproduct ; 4:76
ð10Þ
where n_ air is the number of moles of air supplied per unit time. For the flame with coal dust particles, the same heat is released; however, it is also affected by the energy requirement for volatile gasification and for rising the temperature of the particles. Therefore, the corrected flame temperature T 00f can be estimated using energy conservation as shown in Eq. (11).
h i n_ X air þ n_ s C s ðT 00f T u Þ þ Lv =t; C p nproduct Q_ ¼ ðT 00f T u Þ 4:76
ð11Þ
where n_ s represents the number of coal particles per unit volume per unit time, passing through the flame, given by,
n_ s ¼ ðV_ air þ V_ CH4 Þns qs V particle =M c ;
ð12Þ
where Mc is the molecular weight of carbon. Similarly Lv in Eq. (11) represents the heat of gasification, which is assumed to be a fraction of the heat produced during the reaction and is given by,
Lv ¼ vðm000 v V d DhCH4 Þ;
ð13Þ
where the fraction, v, is assumed to be 0.01, as suggested by Seshadri et al. [12], DhCH4 is the heat of combustion of methane, and Vd represents the volume of the devolatilization zone (conical space with a thickness of d as shown in Fig. 6), given by,
Vd ¼
2 2 1 b 1 d b d ph þ p h : 3 sinðaÞ 2 cosðaÞ 4 3
ð14Þ
The term, Lv/tr, represents the heat consumed by the gasification process for the time the particle spends in the devolatilization zone. This is estimated by Eq. (5). Rearranging Eq. (11), the corrected flame temperature T 00f that takes into account of the heatsink effects is obtained as,
ð9Þ The total heat released during the complete combustion, for (// 2) mole of methane or 4.76 mol of air, is solved by energy conservation as follows:
½ðT b T u Þ
P
C p nproduct ;
where Tb is the adiabatic flame temperature, estimated using the equilibrium solver [14]. Therefore, the heat release rate of the pre-
Fig. 7. Adiabatic flame temperature calculated as a function of / due to addition of coal dust particles in the size range of 75–90 lm.
T 00f ¼
n_ air 4:76
P
Q_ Lv =t r C p nproduct þ n_ s C s
þ Tu:
ð15Þ
Using Eq. (15), T 00f is calculated for several cases and is plotted in Fig. 8. As observed in Fig. 8, the flame temperature reduces due to heat sink effects, as the concentration of dust increases for all three equivalence ratios.
Fig. 8. Corrected flame temperature considering the heat sink effect by coal particles.
Y. Xie et al. / Combustion and Flame 159 (2012) 2449–2456
4.3. Combined effects The combined effects of increase in the flame temperature due to equivalence ratio promotion and decrease in the flame temperature due to heat sink effects are accounted for, by calculating an average flame temperature,
T f ¼ ðT 0f þ T 00f Þ=2: The corresponding flame temperature is then used to estimate Su using the model developed by Seshadri et al. [12].
Su ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2Bke2 E ; exp RT f qC total
ð16Þ
where
e ¼ 1=Z e ; and Z e ¼
EðT f T u Þ RT 2f
:
The values of B and E are chosen as 3.5 106 mol1 s1 and 88,800 kJ mol1 respectively to match the calculated burning velocity with burning velocity obtained by experiments for flames without dust. The constants, A = 0.034 g/m2K s and n = 1.1, were introduced in eq. (2) and used to evaluate T 0f . 5. Results and discussion 5.1. Validation The calculated burning velocities are compared with the experiment data in Fig. 9. Overall, the model captures the measured experimental trends reasonably well. Considering the simplifications in the model, an exact agreement is impossible, however, a good qualitative agreement has been obtained. Further, for 0– 25 lm coal particles the model predicts Su is promoted as shown by the dotted line (theory) that intersects the solid gray triangular symbol (experimental data point) in Fig. 9. Further, it should be noted that for the same size range of 75–95 lm, the reduction in Su by injecting the coal particles is lesser than the case where sand particles are injected. This observation demonstrates that the heat sink effect is partially compensated by the increase in the overall equivalence ratio due to gasification. However, in the case of the sand particles only the heat sink effect plays a role. It is shown in Fig. 9 that the decreasing trend in the slope of Su for 53–63 lm coal particles is lesser than that with the particles in the size range of 75–95 lm. It indicates that as the size of coal par-
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ticle reduces, the equivalence ratio increase is significant when compared to the heat sink effect. When the size of coal particles are as small as 0–25 lm, the influence of heat sink plays a minor role and the increase in the effective equivalence ratio causes Su to increase. However, it should be noted that the present experiments provide only one data point for this smallest size range and shows increasing trend of Su. Specifically, more experiments have to be carried out by designing a better feeding system for the coal dust capable of handling very small particle sizes to confirm the increasing trend of Su. 5.2. Parametric study The theoretical model is used to calculate Su for wide range of parameters such as different dust concentrations, at various equivalence ratios of methane–air mixture and coal particle sizes. The results are plotted in Fig. 10. As shown in Fig. 10, the slope of the Su vs. dust concentration curve is negative in most cases, however, it gets flatter as the particle size decreases at a given lean equivalence ratio. For the lowest / value of 0.70, when particles in the size range of 0–25 lm are injected, there is an increasing trend for Su. This is due to faster pyrolysis of smaller particles causing an increase of overall equivalence ratio (Fig. 11) as well as an increase in the flame temperature (Fig. 12) with dust injection. For / = 0.85, for the smallest particle size range, Su remains almost invariant with dust concentration; there is a small increase in its value initially and as the dust concentration increases beyond approximately 180 g/m3, Su suffers a slight decrease. Even though the overall equivalence ratio increases for this case (Fig. 11) and the flame temperature also shows an increasing trend (Fig. 12), Su remains almost flat because of increase in the Ctotal, the specific heat of the gas–solid mixture, with increasing concentration. As / is increased to 1, there is a steeper decreasing trend for Su, when the particle size is the smallest. For this case, the overall equivalence ratio increases as in the previous cases, especially for
Fig. 10. Burning velocity with coal particles of different sizes at different supply equivalence ratios.
Fig. 9. Burning velocity of a methane–air premixed flame with injected coal particles and sand particles at lean conditions; experimental data are represented by symbols and theoretical prediction is shown by lines.
Fig. 11. Change of overall / due to particle injection calculated for three supply equivalence ratios and different particle sizes.
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and heat transfer processes in the turbulent regime. The devolatilization process will also be enhanced due to the increased residence time for the particle present within the turbulent eddies. As a result, the flame velocity will be further promoted. A deflagration to detonation transition will become likely. 6. Conclusions
Fig. 12. Average flame temperature calculated using combined effects of increase in flame temperature due to increase in overall equivalence ratio and decrease in temperature due to heat loss to coal particles as a function of dust concentration.
the smallest particle size range (Fig. 11). However, there is a notable decrease in the average flame temperature as shown in Fig. 12. In general, higher gasification from smaller particles leads to an increase in the overall equivalence ratio. Based on the particle size and the dust concentration, which affects the mixture specific heat value, if the increase in the overall equivalence ratio is such that it remains less than the slightly rich value where Su is the maximum for gaseous flames, then the increasing trend in the Su can be preserved. However, for the supply equivalence ratio of unity, increase in the overall equivalence ratio due to the injection of smaller particles is such that its value goes to the richer side, where the heat release, the flame temperature, and hence, the laminar flame speed show a decreasing trend. This is shown in Fig. 11, for / = 1 case having smallest particle dust injected, where the overall equivalence ratio shoots up beyond 1.05 (approximate / at which Su is the maximum for gaseous flames), around the dust concentration of approximately 100 g/m3 and a notable decrease in flame temperature is also observed in Fig. 12 beyond this concentration. Apart from this, the value of the mixture specific heat, which depends on particle size and dust concentration, also plays a vital role. The explosion in coal mine tunnels evolves through three stages: laminar flame, turbulent flame and detonation. The Bunsen burner type experiment setup in this study facilitates a better understanding of interaction of coal particles and flame at the first stage of the explosion. As shown in this study, small coal particles (0–25 lm) have the ability to enhance the laminar burning velocity of methane–air mixture under certain conditions. The initial pressure blast of methane–air explosion (fire-damp) in a coal mine can activate the coal dust deposited over various surfaces. Small particles can be easily suspended in air as compare to the larger ones. Therefore, a flame initiated due to hot spots will first interact with smaller particles coarsely suspended. This study shows that if the flame interacting with these particles has been initiated by a lean fuel–air mixture, then there is a good possibility for the flame velocity to be enhanced by the interaction of small coal particles. This initial enhancement in the burning velocity could grow to a turbulent condition. At this stage, more dust particles of various sizes can be drawn into the flame due to enhanced mixing, mass
In this study, a lab scale experiment has been conducted to understand the effects of the coal dust injection into a lean methane–air premixed flame. The laminar burning velocity, Su, of the coal dust–methane–air flame is determined by capturing a shadowgraph image of the laminar flame and evaluating using the cone-angle method. Experimental results show that the presence of coal dust of sizes in the ranges 53–63 lm and 75–90 lm decreases Su, irrespective of the supply equivalence ratio (0.75, 0.80, and 0.85) and the dust concentration (10–300 g/m3). However, the particles having size in the range of 0–25 lm promotes Su, at lower supply equivalence ratios. The promotion in Su is apparent from experiments at a supply equivalence ratio of 0.75. However, more experiments have to be carried out by designing better feeder for the coal dust having very small particle sizes in this range to completely confirm the increasing trend of Su. The mathematical model includes the effect of increase in the equivalence ratio due to volatilizing coal particle and the effect of heat transfer from the flame to volatilize. The model is able to predict the burning velocity of premixed gas-methane flame with coal dust at various dust concentrations performed in this study. For three supply equivalence ratio values, the laminar burning velocity has been plotted as a function of coal dust concentration, where it is clearly illustrated that the average flame temperature that takes into account enhancement of heat release due to increased equivalence ratio as well as the heat sink effects, dictates the variation of laminar burning velocity. Acknowledgment This work is funded by NSF Award #0846764 and the authors like to give our special thanks to National Science Foundation (NSF). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
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