Influence of Gas Compression on the Process of an Accidental Methane/Air/Coal Dust Fire in a Coalmine

Transcription

1 4 th International Pittsburgh Coal Conerence, Pittsburgh, PA, Sept 5-8, 017 Inluence o Gas Compression on the Process o an Accidental Methane/Air/Coal Dust Fire in a Coalmine Elizabeth Ridgeway, Anish Raman Calavay, Sinan Demir and V yacheslav Akkerman* Center or Innovation in Gas Research and Utilization (CIGRU) Center or Alternative Fuels, Engines and Emissions (CAFEE) Department o Mechanical and Aerospace Engineering, West Virginia University Morgantown, WV , USA Abstract Coalmining keeps experiencing one the highest atality and injury rates or employees among the industries dealing with lammable gases and explosive dust. To reduce such a high level or risks, novel preventive mining/ire saety strategies have recently been developed by Demir et al. [ who has identiied and scrutinized the keys stages o the premixed lame ront evolution and quantiied its major characteristics such as the lame shape and its propagation velocity, acceleration rate, run-up distance and lamegenerated velocity proile. However, that analysis adopted the approach o incompressible lows, which made it a little ar rom the practical reality. To ix this discrepancy, in the presented study, the eect o gas compression is incorporated into Demir s predictive scenario o methane/air/coal dust ire in a coalmining passage, or a twodimensional geometry. Among various mechanisms responsible or the lame acceleration such as combustion instability, turbulence, acoustics, and wall riction, acceleration due to a inger-shaped lameront plays a dominant role in coalmines, because this mechanism is scale-invariant and, thereby, Reynolds-independent. This inger-lame acceleration is very powerul, promoting the lame speed by an order o magnitude. Starting with gaseous uels, the ormulation is then extended to gaseous-dusty lows, with combustible and inert dust as well as their mixture studied. Speciically, the eects o equivalence ratio on the lame evolution, as well as that o the size and concentration o the dust particles, are systematically investigated. It is shown that gas compression generally moderates lame acceleration, and its impact depends on various thermal-chemical parameters. While the eect o compression is minor (yielding -5% reduction) or lean and rich lames, thereby justiying the incompressible ormulation in that case, it appears signiicant (up to the reduction o %) or near-stoichiometric methane-air combustion, and thereore should be accounted in a rigorous ormulation. Furthermore, it is demonstrated that gas compression may control acceleration o slightly-reach lames. Keywords: gaseous and dusty explosions; expanding and inger lames; ire and mining saety; lame acceleration and delagration-to-detonation transition; the Darrieus-Landau instability. 1. Introduction Accidental gas/dust explosions constitute a tremendous hazard or personnel and equipment in industries dealing with lammable gases and explosive materials such as the coalmining industry. The latter has one o the highest occupational atality and injury rates, claiming hundreds o miners lives annually 1. Coalmining accidents are typically associated with spontaneous methane explosions in dusty mining passages, ollowed by the comprehensive methane/air/coal dust ires. Preventive mining ire saety strategies include: (i) prevention o the ire initiation (explosion); (ii) suppression/mitigation o ire spreading i it was nevertheless sparked; and (i a ire cannot be terminated) (iii) prevention o a delagration-to-detonation transition (DDT), because a shockwise nature o a detonation constitutes a huge disaster in mines even without combustion. These strategies require undamental understanding o all intermediate stages o the evolution o a methane/air/coal dust ire. Unortunately, in spite o some recent experimental, computational,4 and theoretical 5 studies shedding some light on gaseous-dusty burning, there is still much to be done to reduce a level o ire/explosion risk in coalmines and acilities handling lammable dust 1. 1

2 Figure 1: Consecutive stages o the mining ire scenario: (a) ignition o an expanding lame; (b) ormation o a cellular lame structure; (c) inger-lame acceleration; (d) lame propagation driven by wall-riction; and (e) lame spreading through obstacles. To provide guidance or preventing and controlling the ire disasters in mines, Demir et al 6 have developed a predictive quantitative scenario o a methane-air-dust mining ire, as illustrated in Fig. 1. As any premixed lame, the ire spreading is characterized by the unstretched laminar lame velocity S L ; i a lameront was planar, it would propagate with this speed with respect to the uel mixture. However, the lameront is not planar, but strongly corrugated such that it consumes more uel per unit time and propagates aster. Further, the experiments by Rockwell & Rangwala 7 have shown that the lame corrugations increase in the presence o dust particles. The ire scenario includes several conceptually distinctive stages 6. First, an initially smooth lameront, Fig. 1a, experiences a cellular Darrieus-Landau () instability that may ampliy the lame velocity by an order o magnitude in a space o a human height size, Fig. 1b 8. Second, when a lameront starts approaching the tunnel wall, it slows down in the radial direction but accelerates in the axial one, thereby acquiring a inger-like shape, Fig. 1c Overall, the ingerlame surace area grows very ast, which promotes the lame velocity by one more order o magnitude by the time when the lameront contacts a wall 10. This inger-shape acceleration is Reynolds-independent, being equally strong in micro-pipes and mining passages. Third, ingerlike acceleration stops ater a lameront contacts a wall. Then the lame may urther accelerate due to wall riction, Fig. 1d 1, and/or in-built obstacles, Fig. 1e 1. However, while both these acceleration mechanisms are o primary importance oome conigurations, their role is minor in a mining passage 6. Consequently, inger acceleration is the dominant mechanism in a mining ire, and thereby this was a ocus o Re. 6. Speciically, the and inger acceleration stages in gaseous and gaseous-dusty environments were combined into a uniied analytical ormulation. The input parameters or this ormulation include the geometry o a mining passage, the methane/air equivalence ratio as well as the size, concentration and other properties o the inert and combustible dust. It is noted that the pilot ormulation 6 did not account or certain actors rom the practical reality o a coalmine such as turbulence and spatial/temporal variations o the premixture, but what is more important it was derived within the approach o incompressible lows. While this is acceptable or the initial (almost isobaric) stage o combustion, the role o gas compression certainly becomes substantial by the end o the inger stage, Fig. 1c, when lame propagation may attain near-sonic velocities. Since gas compression moderates lame acceleration in various

3 conigurations 11-14, the same eect is anticipated in the coalmining geometry, and veriying this statement constitutes the ocus o the present work. Namely, we quantiy the role o gas compression in inger lame acceleration in a mining passage, thereby validating the incompressible ormulation 6. Foimplicity, here we deal with a two-dimensional (D) geometry, which is however acceptable to relate the incompressible and compressible analyses; a realistic (D) coniguration will be considered elsewhere. Speciically, the theory 6 is extended it to account and identiy the relative contribution o gas compression. Starting with gaseous combustion, the ormulation is then extended to gaseous-dusty lows. The eects o equivalence ratio and o the size and concentration o the dust particles on the lame evolution are systematically investigated. It is shown that gas compression moderates lame acceleration, and its impact depends on various thermochemical parameters. While the eect is minor (-5% reduction) or lean and rich methane-air premixtures, thus justiying the incompressible ormulation in that case, it appears signiicant (with the reduction o up to %) or near-stoichiometric methane-air combustion, and thereore should be accounted in a rigorous ormulation. II. Formulation We consider an accidental ignition o a methane-air premixture occurring at a distance h rom a side wall o a D tunnel, as illustrated in Fig. 1a. At the early stage o burning, the lame expands outwardly rom the ignition point, as a circle, Fig. 1a, with a constant velocity dr / dt S with respect to the ignition point, where R is the lame radius, u / b the thermal expansion ratio, which is coupled to the equivalence ratio, and S L the unstretched laminar lame speed. Table 1 relates, and S L or methane-air combustion 15. ϕ Θ S L (m/s) Table 1: Methane-air lame parameters [15]. As the lame circle grows, the instability eventually develops, continuously generating new cells over the lame surace, and thereby increasing its area 8. As a result, an expanding lameront accelerates in a sel-similar manner, Fig. 1b. According to numerous experimental and computational studies, a reasonable itting law ouch acceleration is 8 R where n n 1n R 0 Ct Ct, C n / S L / n n, and, L, (1) is the cuto wavelength, which is proportional to the thermal lame thickness conventionally deined as L Dth / SL, where D th is the thermal diusivity. Similar to Re. 6, here we employ the ormula 16 1 ln 1 L 1 () such that 5L, though any other ormulation or can readily be employed. With the power-law lame acceleration, Eq. (1), the instantaneous global (radial) lame speed with respect to the uel mixture is not a constant S, but a time-dependent quantity L L

4 1 n1 nc / t U dr / dt. () Equations (1) () describe the accelerative lame expansion in an opening. However, when a lameront starts approaching a tunnel wall (even not contacting ye, the dierence between the radial and axial lows modiies the lame shape, orming two outwardly propagating ingerlike ronts, Fig. 1c. In act, the expansion o the burning matter leads to a strong low in the axial direction, which drits the o a inger-shaped lame. Because o the elongated shape, the lameront surace area is much larger than the passage cross section. As a result, the lame accelerates. However, this acceleration stops when the lameront contacts the passage wall. Similar to Re. 6, we next combine the above expanding lame analysis with a inger-lame ormulation 11 by employing Eq. () instead o S L. Then, with the approach o a potential low, the D incompressible continuity equation, u 0, has the solution u z, 1 A 1 t z, u x, 1 A 1 t h x, u z, A t z, u x, A t x (4) or the z- and x-velocities ahead (index 1 ) and behind (index ) the lameront. The matching conditions at the ront, x R, are dr / dt u U t, u u U t x, 1 x, 1 x, 1, z, 1 z, Equations () (5) provide the evolution equation or the lame skirt dr / dt 11 R / h1u 11 R / h with h n1 1 nc / t u u. (5), (6) A A 1U t R (, the initial condition R 0, and the solution 1 / h 1 n R t 1 exp Ct. (7) 1 h A characteristic time instant devoted to the transition rom a globally-spherical to a inger-like lame shape, t sph, as well as the corresponding lame velocity U ( t sph ) and radius R ( t sph ) are evaluated: 1/ t h 1 C, (8) U sph n n1 1/ n ( n1) / n t sph nc / tsph nc / h ( 1) 1 t 1 e h 1 0.6h 1 t0, (9) R. (10) sph The evolution equation or the lame reads dz dt u U t dz z, / => dt 1 Z / hu t U t /, (11) with the solution n h ( 1) Ct Z t exp 1. (1) 1 h Thereore, the lame velocity in the laboratory reerence rame is dz n n1 ( 1) Ct U t nc t exp. (1) dt h The lame skirt contacts the tunnel wall when t wall 1/ n R h, i.e. at the time instant hln 1 C (14) 4

5 n such that twall / t sph ln. The quantities t sph, Eq. (8), and t wall, Eq. (14), determine the limits o inger lame acceleration. They are presented in Fig. versus the methane-air equivalence ratio or n 1. 4 and h 1m, with the relation between and rom Table 1. Obviously, near-stoichiometric combustion corresponds to the largest and thereby astest lame spreading and the lowest t sph and t wall, while very lean or reach combustion spreads much slower, making these timings an order o magnitude larger. Again, the inger-lame acceleration terminates at Z t h, and the lame t, with the lame position, Eq. (1), at this instant being wall ( n1) / wall n velocity, Eq. (1), being U t nct wall. wall Figure : The time limitations o the inger lame acceleration, t sph, Eq. (8), and t wall, Eq. (14), versus the equivalence ratio ϕ or methane-air lames with h 1m, n The analysis above is a D part o the ormulation 6. We next extend it to account omall but inite Mach number associated with the lame propagation based on the methodology 11. However, while such a Mach number was constant, Ma S L / c0, in Re. 11, with c 0 being the initial sound speed in the resh mixture, here n1 Mat U t c0 nc / t c0, (15) where U ( is given by Eq. (). As soon as combustion is substantially subsonic, Ma 1, the low in the unburnt gas can be treated as isentropic, with the instantaneous density, pressure and temperature given by (see Re. 11 or more details) /( 1) ( u ( 1 uz,1( 1 0 c0 P ( 1 uz,1( 1 P 0 c0 1 Ma( 1 Ma( Z 1 1 h /( 1) ( u Z 1 1 h, (16), (17) T u t Z t u ( 1 z,1( ) ( ) 1 1 1Ma( 1 1 T, (18) 0 c0 h where c p / c 1. 4 is the adiabatic index and 0, P0, T0 the initial values in the unburnt gas. v 5

6 Instead o the initial thermal expansion ratio, we now deal with an instantaneous (reduced) expansion ratio ( 1 Ma( 1 1 Z ( / h. (19) The D continuity equation omall but inite compressibility, u ( Pu / / Pu, has the solution in the burnt gas in the orm 1 Pu x 1 Pu U ( ux, u z z Pu t h 1 Pu t h. (0) Substituting Eqs. (15) (0) into a modiied Eq. (11), Z u ( ( U ( ), and urther z, t neglecting second and higher order terms in Ma, we eventually arrive to the inal evolution equation or the lame n1 n1 dz nct Z nct ( 1) 1 1 dt c0 h Z n1 n1 nct Z nct 1 ( 1) 1 1 c0 h h n n Z n( n 1) Ct 1 n C t 1 1 Z h c h hc 0 0. (1) III. Results and Discussion Equation (1) describes the eect o gas compression on inger lame acceleration in a mining passage. It has been solved numerically and compared to the incompressible ormulation (1), (1) or a variety o methane-air parameters. Speciically, Fig. presents the methane-air lame evolution or various 0.6 ~ 1. 4, between the instants t sph and t wall, i.e. during the entire inger lame scenario. Figure a shows the lame position, while its velocity is shown in Fig. b. In both igures, the compressible, Eq. (1), and incompressible, Eqs. (1), (1), ormulations are shown by the solid and dashed lines, respectively. It is seen that gas compression moderates the acceleration process, which agrees with our anticipation. Still, the eect is minor or the lean and rich mixtures, whereas it is substantial or near-stoichiometric combustion associated with strongest acceleration. (a) (b) Figure. : Comparison o the incompressible (dashed) and compressible (solid) ormulations: evolution o the lame position Z (a) and its velocity U (b) or methane-air lames o various equivalence ratios:. 0.6; 0.8; 1.0; 1.4 6

7 The same result is also justiied in Fig. 4, where the maximal lame position, Z ), Fig. 4a, and velocity U ), Fig. 4b, are presented versus. Figure 4a is probably the most interesting result o this work as it shows a qualitative dierence between the incompressible and compressible approaches. Indeed, while the incompressible analysis anticipatively yields the maximal Z ) or near-stoichiometric burning, 1. 1, with the reductions in Z ) or leaner and richer lames, Eq. (1) shows a monotonic increase in Z ) with within the entire range. Speciically, it grows noticeably in the lean branch ( ) and the rich branch ( ), being near-constant or Opposite trends that the curves in Fig. 4a exhibit or 1. 1 justiy the role o gas compression that may control the acceleration process or reach lames. However, this is not the case or Fig. 4b, where both approaches show qualitatively the same trends or the maximal lame velocity U ). Nevertheless, a noticeably quantitative dierence is also seen in Fig. 4b: the reduction in U ) due to gas compression varies rom -5 % or lean/rich mixtures till the maximum o % or Such a reduction o the maximal velocity attained by a lame during the inger acceleration scenario certainly diminishes the risk o DDT as compared to incompressible predictions 6. Nevertheless, even the result (1) exceeds the nominal value S L by 1- orders o magnitude. As a result, we have validated the incompressible ormulation 6 or various equivalence ratios as shown in Figs. and 4. To be rigorous, Eq. (14) or t wall should also be extended to account or gas compression: moderation o acceleration makes a lameront contacting the tunnel wall later. However, t wall depends on gas compression very slightly 11, so this eect is neglected here. (a) (b) Figure. 4: Comparison o the incompressible (dashed) and compressible (solid) ormulations: maximal coordinate Z ) (a) and velocity U ) (b), attained by a methane-air lame during the inger lame acceleration, versus the equivalence ratio. IV. Extension to Dusty-Gaseous Combustion We next extend the analysis to gaseous-dusty combustion, since the presence o dust otentimes plays a key role or the ire saety in coalmines 7,17. In particular, combustible (say, coal) dust may spark a lame, promote its acceleration and even trigger DDT. On the other hand, inert dust particles (say, sand) may appear a certain remedy to prevent/mitigate a ire. The laminar lame velocity may either increase or decrease in the presence o dust. On the one hand, it is promoted by the eect o volatiles released rom coal particles through the gaseous mixture, which appears 7

8 an additional uel source or the combustion process. On the other hand, dust particles gain heat rom the lame during the devolatilization process, thereby acting as a heat sink 18. Similar to Re. 6, here we employ the Seshadri ormulation 18, or the gaseous-dusty laminar burning velocity 1 Bk u E E a a T Tu S d, L exp, Ze, () Ze uct RuT RuT where B is the requency actor, k u the thermal conductivity, E a the activation energy, Ze the Zeldovich number, CT CP CsVsns d / the total heat capacity o the mixture, with C p and C s associated with the gas and dust, and d their densities, Vs 4 / the volume o a single particle o radius, n s ( cd / d ) / Vs the number o particles per unit volume, and c d the concentration o particles. More details o the ormulation are presented in Res. 6, 7, 17, 18. (a) (b) Figure 5: Comparison o the incompressible (dashed) and compressible (solid) ormulations: evolution o the lame position U (b) or methane-air lames o equivalence ratio 0. 7 in the presence Z (a) and its velocity o combustible dust o concentration c d 10g / cm and mean particle radii 10m, 75m. Figure 5 demonstrates the eect o gas compression on lame acceleration in the presence o combustible dust particles. Speciically, small, 10 m, and relatively larger, 75 m, particles are considered, with 0. 7 and c d 10g / cm in both cases. The event o no particles is also presented and compared. Combustible dust promotes the lame velocity, and the smaller the particles the stronger acceleration is. According to Fig. 5a, the relative reduction in Z ) due to gas compression is 8% or 10 m, 5% or 75 m and 4% or the event o no dust. As or the lame velocity, Fig. 5b, the relative reduction in U ) constitutes 19% or 10 m, 1 % or 75 m and 11% or no dust. Consequently, gas compression moderates methane-air-dust lame acceleration, and the eect appears even stronger than that or gaseous combustion. The dependences o Z ) and U ) on the particle concentration are presented in Fig. 6 or 75m and various. Here, Figs. 6 (a, b) are devoted to combustible dust, while inert dust is shown in Figs. 6 (c, d). In is seen that unlike the particle size, the concentration inluences the lame dynamics much weaker: the eect is really minor or combustible dust, and it is moderate or inert particles. 8

9 (a) (b) (c) (d) Figure 6: Comparison o the incompressible (dashed) and compressible (solid) ormulations: maximal coordinate Z ) (a, c) and velocity U ) (b, d), attained by the o methane-air-dust lames o various 0.7, 0.8, 1. equivalence ratios 0 during the inger acceleration, versus the concentration c d o combustible (a, b) and inert (c, d) dust o particle radius 75m. (a) (b) Figure 7: Comparison o the incompressible (dashed) and compressible (solid) ormulations: evolution o the lame position U (b) or methane-air lames o equivalence ratio 0. 7 or no dust as well Z (a) and velocity as in the presence o combustible/inert dust o concentration c d 10g / cm and particle radius 10 m. Finally, lame evolutions in the situations o no dust, combustible dust, inert dust, and their combination are compared in Fig. 7 or 0. 7, c d 10g / cm, and 10m. It is observed that both combustible and inert particles provide noticeable deviations rom the no-dust curves by promoting/moderating lame acceleration, respectively. When both combustible and inert dust present in the mixture, their impacts oppose each otheuch that their net eect resembles that o 9

10 no dust. Still, the relative eect o combustible dust exceeds that o inert one. The inluence o gas compression is also seen. Qualitatively, Fig. 7a shows the relative reduction in Z ) due to gas compression to be 4% or the case o no dust, also 4% or inert dust, 8% or combustible dust and 6% or their combination. As or the lame velocity, Fig. 6b, gas compression provides the relative reduction in U ) o 11% or the case o no dust, o 10% or inert particles, o 18% or combustible particles, and o 14% or their combination. V. Conclusions In this study, the incompressible theory o methane/air/coal dust lame acceleration in a mining passage 6 is validated by incorporating the eect o gas compression into the analysis. It is shown that gas compression moderates lame acceleration, and its impact depends on various thermalchemical parameters. The relative role o gas compression (as compared to the predictions 6 ) is quantiied or a variety o parameters such as,, c d, and it appeared to be stronger or the gaseous-dusty environments as compared to purely gaseous combustion. As a result, the intrinsic accuracy o the ormulation 6 is ound or a given set o parameters. While the eect o compressibility is minor or the lean and rich lames (yielding a -5% reduction), thus justiying the incompressible ormulation in that case, it is signiicant (with the reduction o up to %) or near-stoichiometric, methane-air lames. Furthermore, in contrast to incompressible predictions, the solution to Eq. (1) or Z ) exhibits a qualitatively dierent monotonic dependence on, Fig. 4a, thus yielding that gas compression may actually control acceleration o a reach lame. Acknowledgements This work is supported by the West Virginia University s Summer Undergraduate Research Experience (SURE) Program (E.R.) as well as by the NSF, through the CAREER Award # (V.A.), prior to which it was sponsored by the Alpha Foundation or the Improvement o Mine Saety and Health, Inc (ALPHA FOUNDATION). The views, opinions and recommendations expressed herein are solely those o the authors and do not imply any endorsement by the ALPHA FOUNDATION, its Directors and sta. Reerences 1. K.L. Cashdollar, M.J. Sapko, E.S. Weiss, M.L. Harris, C.K. Man, S.P. Harteis, G.M. Green, Report o Investigations NIOSH, Pittsburgh, (010) K. Chatrathi, J. E. Going, B. Grandesta, Process Saety Progress 0(4) (001) 86.. M. Bi, C. Dong, Y. Zhou, Appl. Therm. Eng. 40 (01) R.W. Houim, E.S. Oran, J. Loss Prev. Process Ind. 6 (015) X. Chen, Y. Zhang, Y. Zhang, Energies 5 (01) S. Demir, V. Bychkov, S.H.R. Chalagalla, V. Akkerman, Combust. Theor. Model. (017) S. Rockwell, A. Rangwala, Combust. Flame 160 (01) V. Akkerman, C.K. Law, V. Bychkov, Phys. Rev. E 8 (011) C. Clanet, G. Searby, Combust. Flame 105 (1996) V. Bychkov, V. Akkerman, G. Fru, A. Petchenko, L.-E. Eriksson, Combust. Flame 150 (007) D. Valiev, V. Akkerman, M. Kuznetsov, L.-E. Eriksson, C.K. Law, V. Bychkov, Comb. Flame 160 (01) V. Akkerman, V. Bychkov, A. Petchenko, L.-E. Eriksson, Combust. Flame 145 (006) D. Valiev, V. Bychkov, V. Akkerman, C.K. Law, L.-E. Eriksson, Combust. Flame 157 (010) D. Valiev, V. Bychkov, V. Akkerman, L.-E. Eriksson, Phys. Rev. E 80 (009) S.G. Davis, J. Quinard, G. Searby, Combust. Flame 10 (00) V. Akkerman, V. Bychkov, Combust. Theory Modelling 7 (00) Y. Xie, V. Raghavan, A.S. Rangwala, Combust. Flame 159 (01) K. Seshadri, A.L. Berlad, V. Tangirala, Combust. Flame 89 (199). 10