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Numerical flow simulation of dust deflagrations
163
Powder Technology, 71 (1992) 163-169
Numerical
flow simulation of dust deflagrations
L. Kjiildman Technical Research Centre of Finland, Nuclear Engineering Laboratory, P.O. Box 208, SF-02151 Espoo (Finland)
Abstract Computational fluid dynamics (cfd) has proven to be a powerful tool in the study of many complex flow systems. The paper presents an approach to applying cfd to dust deflagrations. The method used is intended for applications of practical interest rather than for -a detailed investigation of the basic explosion mechanisms. The gas-particle mixture is described as a continuous two-phase flow with interphasial transfer of mass, momentum and heat. Turbulence is calculated with the two equation (Jr, e)-model. The application of the model to peat dust deflagration experiments in a closed 20 dm3 vessel shows promising results.
Introduction During the last two decades computational fluid dynaniics (cfd) has become a useful tool in the study of complex flow systems in many areas of application including aerodynamics, gaseous deflagrations and detonations, and combustion in furnaces. The power of cfd lies in its ability to couple turbulent flow and physical subprocesses occurring in the flow and to calculate the local behaviour of the system in complicated geometries. Although the accuracy of the submodels of physical phenomena and especially the description of turbulence are at present not good enough for a detailed simulation of many processes, numerical simulation can often provide a qualitatively correct picture of the system of interest. Such a picture is usually difficult to obtain by other means. Dust deflagrations are complicated time dependent turbulent flow processes of reactive gas-particle mixtures with strong interphasial transfer of mass and heat. Turbulence is considered as the main mechanism of flame propagation in dust deflagrations [l, 2,3], although radiation can be important, too. The possibility of using numerical flow simulation to study dust deflagrations would be a clear advantage in the attempts to improve safety at power plants and in industry. This paper presents an approach to using cfd to study dust deflagrations. The method is based on a continuous two-phase flow description of the gas-particle mixture with the two equation (k, c)-model for turbulence. In spite of good results obtained with similar models for gaseous deflagrations [4] and pulverized fuel combustion in furnaces (e.g. [5, 6]), dust deflagrations seem to be a new application area of cfd.
0032-5910/92/$5.00
The only other application of multidimensional numerical flow simulation to dust explosions of which the author is aware is reported in [7]. Work in this field has recently started in the group of Prof. Markatos
PI. A two-phase flow description has been successfully applied to gas-particle flows, e.g., by Malin et al. [9], Markatos and Kirkcaldy [lo] and Ludwig et al. [ll]. The general basis of a multi-phase flow formulation is given by Ishii [12]. The purpose of the author’s work presented below was to get a view of the possibility of using cfd in the study of dust deflagrations at a level of practical interest. Peat dust deflagration experiments in a small scale 20 dm3 vessel formed the test cases. At this stage, the models of the physical subprocesses included a number of simplifying approximations. The computations should therefore be considered to represent a demonstration of the use of cfd to study dust deflagrations rather than a serious attempt to reproduce the experimental results. Unfortunately, no application to large scale cases could be done at this stage of the work. Peat dust is of special interest in Finland due to its increased use as pulverized fuel in power plants. Peat may be considered as geologically young coal with a high content of volatile substances, typically 70 wt.% of dry matter. About half of the heat of combustion of peat results from the combustion of volatile gases. In spite of the usually high moisture content of peat, pulverized peat forms a potential fire and explosion hazard at the power plants. In the next chapter, the model used by the author is presented, followed by the application of the model to experiments of peat dust explosions in a closed 20
0 1992 - Elsevier Sequoia. All rights reserved
164
dm3 spherical vessel and the simulation of an explosion in a vented 20 dm3 vessel. The article ends with a short summary. More details of the model and the applications can be found in [13].
leading to CO, and H,O. The reaction rate is assumed to be limited by turbulent diffusion and is given by the expression [18] Rt, = 4p, ; rnin(mrU, mO,s - ‘)
A two-phase flow model of a gas-particle mixture The dust-gas flow with interfacial and energy transfer. The model includes drying, and heterogenous combustion of particles. The burn in phase. For the present application, radiation particles has assumed the particle surfaces. The the particle with shadow method
[141. For lack of more detailed experimental data, the composition of the devolatilized gases is taken as independent of temperature and from experiments with a low heating rate. The composition of the pyrolysis products used in the simulations is given in Table 1. The given amount of methane in Table 1 also contains higher hydrocarbons, whose reported amount was 2.4 vol.% [15]. ’ Experiments with high heating rates indicate that the pyrolysis rate follows the Arrhenius law [16]. The values of the parameters were, however, questionable [17]. Therefore, the pre-exponential factor of the Arrhenius law was used as a free parameter, whose value was chosen to get approximately the experimentally found maximum rate of pressure rise for one experimental case. This is the only parameter in the model, whose value was fitted. The values of the parameters of the pyrolysis rate used are A, = 3 - lo4 1 s-’ and E, = 26 kJ mol-‘. This pre-exponential factor is nine times the measured value of [16]. Typical values of the amount of volatile matter (70% in weight of dry peat) and that of ash (3% in weight of dry peat) and total heat of combustion (20 MJ kg-l of dry peat) were used in the simulations. The combustible devolatilized gases are treated as a single gaseous fuel with a one step combustion reaction TABLE 1. F’yrolysis products of peat [15] Substance (gaseous)
Volume percent
co2 NZ
20 10 17 20 33
& HZ
(1)
where s is the stoichiometric amount of oxygen needed to burn 1 kg of fuel. For the present application s = 2.41. Devolatilization and drying are assumed to occur with reducing particle density but constant size, whereas during char burning the density is constant and the particle shrinks. The particles are considered to be spherical, although peat particles have mostly an elongated shape. The heterogenous char combustion is assumed to take place at the particle surface above surface temperature T,=600 K according to the reaction C + 0, + CO,. The reaction rate is determined by chemical kinetics or diffusion of oxygen to the surface. Values for brown coal [19] are used for the chemical kinetics part of the reaction rate. In the present two-phase flow formulation the initial size distribution of the particles is represented by a single mass average value. This will affect the predicted development of the explosion. To account for a size distribution of the particles a continuous multi-phase flow or a discrete Lagrangian description could be used. These may, however, lead to substantial computer time requirements in applications of practical interest. A reasonable extension of the present treatment could be a two-phase flow formulation with concentrations to represent the size distribution of the particles. In this way the difference in interphasial heat and mass transfer rates of particles of different sizes could be modeled, but not the difference in local particle velocities. The variables to be solved in the present model are the volume fractions of gas (r,) and particles (rp), the shadow volume fraction (t-J, the concentrations of the gas phase of the devolatilized combustible gases (m,,), oxygen (m,,) and combustion products (M,-~ and mHzosg, the concentrations of the particle phase of moisture content (mH2& and volatile matter (m,,,), the velocities of both phases (Iz,, a,), the enthalpies of the phases (h, and h,) and turbulence variables (k and l ). The equations are of the form given by eqn. (2) with the source terms in Table 2. The equations are solved with the commercial PHOENICS81code of CHAM Ltd using the IPSA algorithm [20]. y
+ V(r&)
- V(r& Vff~)= S, .
(2)
In Table 2 the mass transfer terms are due to drying (&,) and devolatilization (niWl) of the particles, char combustion (ti,,) and ignition source (&,). The en-
165 TABLE 2. Source tern for variable 4 in eqn. (2)
1 (eqn. for rg)
ljl** + t&l+
1 (eqn. for rp)
-rirdr-rfljl,,-rilch
ti& +
?flign
1 (eqn. for rr)
-&-f&l
%J
0.427&,, - R fu
mo2
- 2.67tiCh- 2.41Rh,
mCO2
0.436&,, + 3.67&
mH~O.
g
nh0.
p
+ 1.89Rfu
riz&+ 1.52Rf, -mdr -md
mm1
-rg
$7 +(~~~~+nivo~+~~~)(u&.+up,,)~+F~(up,,-u,,)~-Ug,~)+~ignUg.r.ign
ap . - -(m~,+~,~+~~h)(~g.,+~p.3/2+Fgp(Ug,~-~p,~) p au,
-r
h, + lrig12/2
h, +
lLzp12/2
~~ps+nichHch+Fgp(Up_LZg)(~p+~gig)/2+~jl,lHfu-~w+4ign_qrad,g
ap
pat -(ti&-&,l
r -
-ti&)(hp+
; tigtip)+~rp+Fg&g-tip)(tig++p)/2
thalpy equation of the gas phase includes convective heat transfer (4,) to the particle source, heat from the ignition source (&.,), heat loss through radiation (&& and convection to the wall of the vessel (4,)* The ‘standard’ (k, l )-model was used for turbulence [21]. It should be noticed that in the simulation of gas deflagration an additional term due to compression or expansion of the gas [4] or a different term involving pressure and density gradients [22] have been found to be of importance. Such a term could be significant in large scale dust deflagrations, too. The surface temperature T, of the particles is determined from the heat balance at the surface: & - 4, +&z&h
+ 4rad.p - tirad.s= 0 ,
(3)
which include the convective heat transfer rates between the particle surface and particle and gas phases (4, and qgs), the heat of combustion of char (&,) and the radiation heat loss (&,,& and gain (Qradss) on the surface. The interphase friction force is given by
(4) where d is the diameter of the particle and C,, is the drag coefficient.
Simulation of peat dust experiments in a closed vessel Peat dust explosion experiments done in a closed 20 dm3 spherical vessel at the Fire Technology Laboratory of the Technical Research Centre of Finland formed the test cases for the present model development [23]. In this apparatus the dust is blown into the vessel through small holes on a ring-shaped pipe to form a uniformly dispersed dust-air mixture. After about 60 ms the mixture is ignited with two chemical ignitors of 5 kJ each. The pressure is measured at two locations at the wall of the vessel. The additional pressure increase due to the ignitors is subtracted from the measured values. An ignitor of 5 kJ produces in air an N 10 cm long elongated flame for about 10 ms [24, 251. The effective energy of one ignitor in the flame region is 2.12 kJ, the rest of the energy being released as radiation or dissipated [26]. The material released from the ignitors was modelled to be gaseous although it is known that most of the material is particulate [26]. In the experiments peat dusts of various particle size distributions and moisture content were studied. The cases chosen for the present simulations are defined in Table 3. The explosions were assumed to be cylindrically symmetric. Consequently, the flow geometry to be con-
166
PRESSURE/bar
1
P max -
Fig. 1. Definition of times I~,tr and ts of the pressure development of a dust explosion in a closed vessel. Ignition starts at time r,; schematically only.
sidered consists of only a slice of an eighth of the spherical vessel. In the computation a coarse grid of 10 x 10 cells in a cylindrical coordinate system was used. Initially, the dust was assumed to’ be uniformly distributed and at rest. The initial turbulence was determined by the values k = 0.01 (m s-l)2 and e=2 (m s-l)2 s-’ [13]. The results of the simulations are given in Table 4. Considering the approximations and uncertainties in the physical description of the peat particles and the expected scattering of the experimental .results, the overall agreement between the simulations and experiments is promising. The simulated explosions are faster than the real cases. This is believed to be mainly due to the modelling of the ignition mechanism and the pyrolysis. The experimental peak pressure for dry dust decreases with increasing particle size, whereas the computed pressures increase. This seems to result from the treatment of radiation heat transfer. With increasing particle size and constant concentration a larger amount of radiation reaches the wall of the vessel. In the simulation all heat radiated was assumed to be absorbed uniformly back on the particle surfaces.
The lack of radiative heat loss to the wall could partly explain the overpredicted value of the peak pressure for dust with high moisture content (33.6%). In this case almost all devolatilized gases and a considerable amount of char has burned according to the model. The difference between the experimental and computed values for this case could also be affected by the possible agglomeration of moist particles in the experiment. The maximum rate of pressure rise is of greater interest than the peak pressure or duration of the explosion. The values obtained for the maximum rate of pressure rise differ from the experimental values, but the qualitative behaviour is mostly correct. The predicted value of dust with high moisture content (33.6%) is higher than that of the case with denser dust and moderate moisture content (bulk density 1 kg me3, moisture 13.0%) whereas the measured values are in the opposite order. Typical computing times with a Cyber 180/840 computer were 1 h 16 min for dry dust and 2 h 9 min for moist dust.
Simulation of an explosion in a vented vessel As an application of the developed model the explosion of dry fine peat dust in the 20 dm3 spherical vessel with venting was simulated. Initially the diameter of the particles was 54 pm and the concentration of the dust 0.5 kg mm3. The vent area was chosen to be 3.28. 10m3 m’. Due to the symmetrical treatment of the geometry, there are two holes of circular cross section with a radius of 2.28 cm on the opposite sides of the vessel. The venting was assumed to start at zero overpressure. The computational region was extended outside the vessel to ensure correct boundary condition at the vent hole. The simulated pressure development is shown in Fig. 2. These values include the effect of the ignitor. The pressure distribution within the vessel is spatially nearly uniform with lower values only close to the hole. The
TABLE 3. Peat dust experiments [23]. The times ti, tz and r, are defined in Fig. 1
mass average
Bulk density of dust (kg mm3)
Moisture content (wt.%)
t1 (ms)
54 96 165 38 100 72
0.5 0.5 0.5 0.5 1.0 0.5
0 0 0 14.1 13.0 33.6
35 47 4.5 46 59 60
Diameter of particles range <74 74...125 125...250 <74 74...125 <74
(w@
t2
b
(ms)
(ms)
Pm=
(bar)
dp ( dr 1 max
(bar/s) 16 15 12 19 22 17
62 63 62 62 62 63
8.4 7.8 7.7 a.4 7.8 7.2
610 413 395 513 350 248
167
TABLE 4. Results from simulations of peat dust explosion in a closed vessel. The definitions of the times tr and tz are given in Fig. 1 Diameter of particles (pm)
Bulk density of dust (kg mm3)
Moisture content (wt.%)
54 96 165 38 100 72
0.5 0.5 0.5 0.5 1.0 0.5
0 0 0 14.1 13.0 33.6
t, (ms)
tz (ms)
PIIUX
(bar)
!!?
(1dt rnax
(bar/s) 18 22 29 21 34 35
7.2 6.7 5.5 8.4 8.6 9.4
8.1 8.6 9.1 8.1 7.2 9.0
700 570 390 670 280 370
Char combusted at time t,
Gaseous fuel combusted at tl
(wt.%)
(wt.%)P
11 13 17 17 18 24
54 59 63 61 31 89
“Weight percent from devolatilized matter.
4--
0
5
10
15
TIME
20
2.5
30
(ms)
Fig. 2. Computed pressure development in the explosion of dry fine (d = 54 pm) peat dust in a vented 20 dm3 vessel; (1) pressure inside the vessel; (2) pressure close to the vent bole inside the vessel.
10-2
lYY 2.10-2
3.10-2
.5 3 t=14ms, 1aTgest
TIME fms)
Fig. 3. Computed mass outflow rate from a vented 20 dm3 vessel; (1) Outflow rate of particles; (2) Outflow rate of gas; (3) Total outflow rate.
maximum rate of pressure rise is 340 bar s-’ and peak pressure is 3.6 bar. An extrapolation of the VDInomograms [27] for this case gives a peak pressure between 3.5 bar and 4 bar. The outflow rate from the vessel is shown in Fig. 3. The total outfiow rate has two maxima. The outfiow until the first maximum consists of unreacted matter and is due to the expansion of the gas after ignition
value
3.5
t=2hns, largest value 0.039
Fig. 4. Reaction rate (normalized units) of gaseous volatile combustion in a vented explosion of dry peat dust in a 20 dm3 vessel.
and the subsequent combustion in the central region of the vessel. The development of the explosion inside the vessel is shown in Figs. 4 to 6. The non-spherical behaviour is due to the effects of the ignitor and the venting. The computing time with a Cyber 180/840 computer with a time step of 0.1 ms (300 time steps) was 3 h 42 min.
t=Fas,
3arge.evalue smllest
1709 K
t=7.%,
largest value 1786 K sllal1estva.lue 383 K
EkLue 343 K
'.24 1600
t=,ms,
hryest
value 2.9
el2.W.
lacqestvalue wal1est
value
3.24
t=,Cms, laqest
0.05
value 1835 K
sndlestvalue468K
t=12.%s,
Lxqest smllest
value 1773 K value 646 K
0.8
0.8
0.6
0.4 0.2 t=l4m,
kqest mallest
value 2.73 value 0.07
t=2hs.
larqest value 0.95 sm11est
t=,4m,
value 0.09
Fig. 5. Volume fraction of particles in a vented explosion of dry peat dust in a 20 dm3 vessel. Values normalized with the initial value.
An approach to using cfd to study dust deflagrations was presented. The method is based on a continuous two-phase flow description of the gas-particle mixture. The application of the numerical model was demonstrated by simulating peat dust explosions in a small scale 20 dm3 vessel. Although the behaviour of the fuel, especially the pyrolysis of peat, was inadequately known, promising results were obtained. The trends of the maximum rate of pressure rise as obtained experimentally could mostly be predicted.
Acknowledgement The author is grateful to the Technology Development Centre of Finland for financing the project in 1985436, during which time the work was done.
List of symbols
t=20ms. largest value
1548 K
srallast value 964 K
Fig. 6. Temperature of gas (K) in a vented explosion of dry peat dust in a 20 dm3 vessel.
A
Conclusions
largest value 1749 K smallest value 819 K
CD d E FI, H h k m r?i min P 4 R r s, s T t 4 u, x
pre-exponential factor, s-’ drag coefficient, particle diameter, m activation energy, J mol-l friction coefficient between phase 1 and 2, kg m-3
s-l
heat of combustion, J kg-’ enthalpy, J kg-l kinetic energy of turbulence, (m s-l)* mass fraction, mass transfer rate per unit volume, kg mW3 s-l minimum value, pressure, Pa heat transfer rate per unit volume, J mW3 s-l reaction rate (with subscript), kg mm3 s-l volume fraction, source term for quantity 4, [4] kg mW3 s- ’ coefficient of stoichiometry, temperature, K time, s velocity, r-component of velocity, m s-l space coordinate, m
Greek letters r effective diffusion coefficient, kg m-l
s-l
169
E
P
dissipation rate of kinetic energy of turbulence, (m s-l)’ s-l density, kg
Subscripts ch char dr drying fu fuel ( = combustible g gas ignition ign particle P ;a5 PyrolYsis radiation S shadow (volume W
volatile gases)
wall T-coordinate
References J. H. S. Lee, Proc. Znt. Symp. Shock Waves and Shock Tubes, Aachen, Germany, 1987, p. 18. P. R. Amyotte, S. Chippett and M. J. Pegg, Prog. Energy Cornbust Sci., 14 (1988) 293. I. Swift, Proc. Znt. Con$ Fuel-Air Explosions, University of Waterloo Press, Waterloo, Canada, 1982, p. 375. B. H. Hjertager, SZMS’89-Conf on Simulation and Scientijic Computation, Bergen, Norway, 1989, p. 34. L. D. Smoot, P. 0. Hedman and P. J. Smith, Prog Energy Cornbust. Sci., 10 (1984) 359. F. C. Lockwood et al., 20th Symp. (Znt.) Cornbust., The Combustion Institute, Pittsburgh, PA, 1984, p. 513. V. P. Korobeinicov, V. V. Markov and I. S. Menshov, Proc. 1st Znt. Colloq. Explosibili@ of Industrial Dusts, I, Baranov, Poland, 1984, p. 191.
8 N. C. Markatos, National Techn. Univ. of Athens, Greece, private communication, 1990. 9 M. R. Malin, N. C. Markatos, D. G. Tatchell and D. B. Spalding, A.S.M.E. Paper No. 82-FE-8, 1982, p. 18. 10 N. C. Markatos and D. Kirkcaldy, Znt. J. Heat Mass Transfeer, 26 (1983) 1037. 11 J. Ludwig, N. Rhodes and D. G. Tatchell, Proc. 7th Znt. Ballistics Symp., 1983, p. 37. 12 M. Ishii, Thermo-fluid dynamic theov of two-phase flow, Eyrolles, Paris, 1975, p. 248. 13 L. Kjlldman, Research Report No 469, Technical Research Centre of Finland, Helsinki, 1987, p. 85. 14 D. B. Spalding, 19th Symp. (Znt.) Cornbust, The Combustion Institute, Pittsburgh, PA, 1983, 941. 15 A. Sundgren and E. Ekman, Sue, I1 (1960) 96. (In Finnish.) 16 B. Blomqvist, Proc. of Bio Energi -86, ZI, Stockholm, 1986, p. 139. 17 G. Eklund, private communication, Stud&k Energiteknik Ab, Nykijping, Sweden, 1986. 18 B. F. Magnussen and B. H. Hjertager, 16th Symp. (Znt.) Combust., The Combustion Institute, Pittsburgh, PA, 1976, p. 719. 19 R. J. Hamor, J. W. Smith and R. J. Tyler, Cornbust. Flame, 21 (1973) 153. 20 D. B. Spalding, Recent Advances in Numerical Methods in Fluids, Pineridge Press, Swansea, UK, 1980, p. 139. 21 B. E. Launder and D. B. Spalding, Computer Methods in Appl. Me& Eng., 3 (1974) 269. 22 A. C. van den Berg, TNO-Report PML 1980-ZN48, TN0 Prins Maurits Laboratory, Rijswijk, The Netherlands, 1989, p. 42. 23 H. We&man, Fire Safety J., 12 No 2 (1987) 97. 24 M. Hertzberg, private communication, U.S. Bureau of Mines, Pittsburgh, USA (1986). 25 J. Kaikkonen, private communication, Technical Inspection Centre of Finland, Helsinki, Finland (1986). 26 M. Hertzberg, K. L. Cashdollar and I. Zlochover, 2Zst Symp. (Znt.) Cornbust., The Combustion Institute, Pittsburgh, PA, 1986, p. 303. 27 mZ3673,VereinDeutscherIngenieure,Diisseldorf, Germany, 1979, p. 51.
Powder Technology, 71 (1992) 163-169
Numerical
flow simulation of dust deflagrations
L. Kjiildman Technical Research Centre of Finland, Nuclear Engineering Laboratory, P.O. Box 208, SF-02151 Espoo (Finland)
Abstract Computational fluid dynamics (cfd) has proven to be a powerful tool in the study of many complex flow systems. The paper presents an approach to applying cfd to dust deflagrations. The method used is intended for applications of practical interest rather than for -a detailed investigation of the basic explosion mechanisms. The gas-particle mixture is described as a continuous two-phase flow with interphasial transfer of mass, momentum and heat. Turbulence is calculated with the two equation (Jr, e)-model. The application of the model to peat dust deflagration experiments in a closed 20 dm3 vessel shows promising results.
Introduction During the last two decades computational fluid dynaniics (cfd) has become a useful tool in the study of complex flow systems in many areas of application including aerodynamics, gaseous deflagrations and detonations, and combustion in furnaces. The power of cfd lies in its ability to couple turbulent flow and physical subprocesses occurring in the flow and to calculate the local behaviour of the system in complicated geometries. Although the accuracy of the submodels of physical phenomena and especially the description of turbulence are at present not good enough for a detailed simulation of many processes, numerical simulation can often provide a qualitatively correct picture of the system of interest. Such a picture is usually difficult to obtain by other means. Dust deflagrations are complicated time dependent turbulent flow processes of reactive gas-particle mixtures with strong interphasial transfer of mass and heat. Turbulence is considered as the main mechanism of flame propagation in dust deflagrations [l, 2,3], although radiation can be important, too. The possibility of using numerical flow simulation to study dust deflagrations would be a clear advantage in the attempts to improve safety at power plants and in industry. This paper presents an approach to using cfd to study dust deflagrations. The method is based on a continuous two-phase flow description of the gas-particle mixture with the two equation (k, c)-model for turbulence. In spite of good results obtained with similar models for gaseous deflagrations [4] and pulverized fuel combustion in furnaces (e.g. [5, 6]), dust deflagrations seem to be a new application area of cfd.
0032-5910/92/$5.00
The only other application of multidimensional numerical flow simulation to dust explosions of which the author is aware is reported in [7]. Work in this field has recently started in the group of Prof. Markatos
PI. A two-phase flow description has been successfully applied to gas-particle flows, e.g., by Malin et al. [9], Markatos and Kirkcaldy [lo] and Ludwig et al. [ll]. The general basis of a multi-phase flow formulation is given by Ishii [12]. The purpose of the author’s work presented below was to get a view of the possibility of using cfd in the study of dust deflagrations at a level of practical interest. Peat dust deflagration experiments in a small scale 20 dm3 vessel formed the test cases. At this stage, the models of the physical subprocesses included a number of simplifying approximations. The computations should therefore be considered to represent a demonstration of the use of cfd to study dust deflagrations rather than a serious attempt to reproduce the experimental results. Unfortunately, no application to large scale cases could be done at this stage of the work. Peat dust is of special interest in Finland due to its increased use as pulverized fuel in power plants. Peat may be considered as geologically young coal with a high content of volatile substances, typically 70 wt.% of dry matter. About half of the heat of combustion of peat results from the combustion of volatile gases. In spite of the usually high moisture content of peat, pulverized peat forms a potential fire and explosion hazard at the power plants. In the next chapter, the model used by the author is presented, followed by the application of the model to experiments of peat dust explosions in a closed 20
0 1992 - Elsevier Sequoia. All rights reserved
164
dm3 spherical vessel and the simulation of an explosion in a vented 20 dm3 vessel. The article ends with a short summary. More details of the model and the applications can be found in [13].
leading to CO, and H,O. The reaction rate is assumed to be limited by turbulent diffusion and is given by the expression [18] Rt, = 4p, ; rnin(mrU, mO,s - ‘)
A two-phase flow model of a gas-particle mixture The dust-gas flow with interfacial and energy transfer. The model includes drying, and heterogenous combustion of particles. The burn in phase. For the present application, radiation particles has assumed the particle surfaces. The the particle with shadow method
[141. For lack of more detailed experimental data, the composition of the devolatilized gases is taken as independent of temperature and from experiments with a low heating rate. The composition of the pyrolysis products used in the simulations is given in Table 1. The given amount of methane in Table 1 also contains higher hydrocarbons, whose reported amount was 2.4 vol.% [15]. ’ Experiments with high heating rates indicate that the pyrolysis rate follows the Arrhenius law [16]. The values of the parameters were, however, questionable [17]. Therefore, the pre-exponential factor of the Arrhenius law was used as a free parameter, whose value was chosen to get approximately the experimentally found maximum rate of pressure rise for one experimental case. This is the only parameter in the model, whose value was fitted. The values of the parameters of the pyrolysis rate used are A, = 3 - lo4 1 s-’ and E, = 26 kJ mol-‘. This pre-exponential factor is nine times the measured value of [16]. Typical values of the amount of volatile matter (70% in weight of dry peat) and that of ash (3% in weight of dry peat) and total heat of combustion (20 MJ kg-l of dry peat) were used in the simulations. The combustible devolatilized gases are treated as a single gaseous fuel with a one step combustion reaction TABLE 1. F’yrolysis products of peat [15] Substance (gaseous)
Volume percent
co2 NZ
20 10 17 20 33
& HZ
(1)
where s is the stoichiometric amount of oxygen needed to burn 1 kg of fuel. For the present application s = 2.41. Devolatilization and drying are assumed to occur with reducing particle density but constant size, whereas during char burning the density is constant and the particle shrinks. The particles are considered to be spherical, although peat particles have mostly an elongated shape. The heterogenous char combustion is assumed to take place at the particle surface above surface temperature T,=600 K according to the reaction C + 0, + CO,. The reaction rate is determined by chemical kinetics or diffusion of oxygen to the surface. Values for brown coal [19] are used for the chemical kinetics part of the reaction rate. In the present two-phase flow formulation the initial size distribution of the particles is represented by a single mass average value. This will affect the predicted development of the explosion. To account for a size distribution of the particles a continuous multi-phase flow or a discrete Lagrangian description could be used. These may, however, lead to substantial computer time requirements in applications of practical interest. A reasonable extension of the present treatment could be a two-phase flow formulation with concentrations to represent the size distribution of the particles. In this way the difference in interphasial heat and mass transfer rates of particles of different sizes could be modeled, but not the difference in local particle velocities. The variables to be solved in the present model are the volume fractions of gas (r,) and particles (rp), the shadow volume fraction (t-J, the concentrations of the gas phase of the devolatilized combustible gases (m,,), oxygen (m,,) and combustion products (M,-~ and mHzosg, the concentrations of the particle phase of moisture content (mH2& and volatile matter (m,,,), the velocities of both phases (Iz,, a,), the enthalpies of the phases (h, and h,) and turbulence variables (k and l ). The equations are of the form given by eqn. (2) with the source terms in Table 2. The equations are solved with the commercial PHOENICS81code of CHAM Ltd using the IPSA algorithm [20]. y
+ V(r&)
- V(r& Vff~)= S, .
(2)
In Table 2 the mass transfer terms are due to drying (&,) and devolatilization (niWl) of the particles, char combustion (ti,,) and ignition source (&,). The en-
165 TABLE 2. Source tern for variable 4 in eqn. (2)
1 (eqn. for rg)
ljl** + t&l+
1 (eqn. for rp)
-rirdr-rfljl,,-rilch
ti& +
?flign
1 (eqn. for rr)
-&-f&l
%J
0.427&,, - R fu
mo2
- 2.67tiCh- 2.41Rh,
mCO2
0.436&,, + 3.67&
mH~O.
g
nh0.
p
+ 1.89Rfu
riz&+ 1.52Rf, -mdr -md
mm1
-rg
$7 +(~~~~+nivo~+~~~)(u&.+up,,)~+F~(up,,-u,,)~-Ug,~)+~ignUg.r.ign
ap . - -(m~,+~,~+~~h)(~g.,+~p.3/2+Fgp(Ug,~-~p,~) p au,
-r
h, + lrig12/2
h, +
lLzp12/2
~~ps+nichHch+Fgp(Up_LZg)(~p+~gig)/2+~jl,lHfu-~w+4ign_qrad,g
ap
pat -(ti&-&,l
r -
-ti&)(hp+
; tigtip)+~rp+Fg&g-tip)(tig++p)/2
thalpy equation of the gas phase includes convective heat transfer (4,) to the particle source, heat from the ignition source (&.,), heat loss through radiation (&& and convection to the wall of the vessel (4,)* The ‘standard’ (k, l )-model was used for turbulence [21]. It should be noticed that in the simulation of gas deflagration an additional term due to compression or expansion of the gas [4] or a different term involving pressure and density gradients [22] have been found to be of importance. Such a term could be significant in large scale dust deflagrations, too. The surface temperature T, of the particles is determined from the heat balance at the surface: & - 4, +&z&h
+ 4rad.p - tirad.s= 0 ,
(3)
which include the convective heat transfer rates between the particle surface and particle and gas phases (4, and qgs), the heat of combustion of char (&,) and the radiation heat loss (&,,& and gain (Qradss) on the surface. The interphase friction force is given by
(4) where d is the diameter of the particle and C,, is the drag coefficient.
Simulation of peat dust experiments in a closed vessel Peat dust explosion experiments done in a closed 20 dm3 spherical vessel at the Fire Technology Laboratory of the Technical Research Centre of Finland formed the test cases for the present model development [23]. In this apparatus the dust is blown into the vessel through small holes on a ring-shaped pipe to form a uniformly dispersed dust-air mixture. After about 60 ms the mixture is ignited with two chemical ignitors of 5 kJ each. The pressure is measured at two locations at the wall of the vessel. The additional pressure increase due to the ignitors is subtracted from the measured values. An ignitor of 5 kJ produces in air an N 10 cm long elongated flame for about 10 ms [24, 251. The effective energy of one ignitor in the flame region is 2.12 kJ, the rest of the energy being released as radiation or dissipated [26]. The material released from the ignitors was modelled to be gaseous although it is known that most of the material is particulate [26]. In the experiments peat dusts of various particle size distributions and moisture content were studied. The cases chosen for the present simulations are defined in Table 3. The explosions were assumed to be cylindrically symmetric. Consequently, the flow geometry to be con-
166
PRESSURE/bar
1
P max -
Fig. 1. Definition of times I~,tr and ts of the pressure development of a dust explosion in a closed vessel. Ignition starts at time r,; schematically only.
sidered consists of only a slice of an eighth of the spherical vessel. In the computation a coarse grid of 10 x 10 cells in a cylindrical coordinate system was used. Initially, the dust was assumed to’ be uniformly distributed and at rest. The initial turbulence was determined by the values k = 0.01 (m s-l)2 and e=2 (m s-l)2 s-’ [13]. The results of the simulations are given in Table 4. Considering the approximations and uncertainties in the physical description of the peat particles and the expected scattering of the experimental .results, the overall agreement between the simulations and experiments is promising. The simulated explosions are faster than the real cases. This is believed to be mainly due to the modelling of the ignition mechanism and the pyrolysis. The experimental peak pressure for dry dust decreases with increasing particle size, whereas the computed pressures increase. This seems to result from the treatment of radiation heat transfer. With increasing particle size and constant concentration a larger amount of radiation reaches the wall of the vessel. In the simulation all heat radiated was assumed to be absorbed uniformly back on the particle surfaces.
The lack of radiative heat loss to the wall could partly explain the overpredicted value of the peak pressure for dust with high moisture content (33.6%). In this case almost all devolatilized gases and a considerable amount of char has burned according to the model. The difference between the experimental and computed values for this case could also be affected by the possible agglomeration of moist particles in the experiment. The maximum rate of pressure rise is of greater interest than the peak pressure or duration of the explosion. The values obtained for the maximum rate of pressure rise differ from the experimental values, but the qualitative behaviour is mostly correct. The predicted value of dust with high moisture content (33.6%) is higher than that of the case with denser dust and moderate moisture content (bulk density 1 kg me3, moisture 13.0%) whereas the measured values are in the opposite order. Typical computing times with a Cyber 180/840 computer were 1 h 16 min for dry dust and 2 h 9 min for moist dust.
Simulation of an explosion in a vented vessel As an application of the developed model the explosion of dry fine peat dust in the 20 dm3 spherical vessel with venting was simulated. Initially the diameter of the particles was 54 pm and the concentration of the dust 0.5 kg mm3. The vent area was chosen to be 3.28. 10m3 m’. Due to the symmetrical treatment of the geometry, there are two holes of circular cross section with a radius of 2.28 cm on the opposite sides of the vessel. The venting was assumed to start at zero overpressure. The computational region was extended outside the vessel to ensure correct boundary condition at the vent hole. The simulated pressure development is shown in Fig. 2. These values include the effect of the ignitor. The pressure distribution within the vessel is spatially nearly uniform with lower values only close to the hole. The
TABLE 3. Peat dust experiments [23]. The times ti, tz and r, are defined in Fig. 1
mass average
Bulk density of dust (kg mm3)
Moisture content (wt.%)
t1 (ms)
54 96 165 38 100 72
0.5 0.5 0.5 0.5 1.0 0.5
0 0 0 14.1 13.0 33.6
35 47 4.5 46 59 60
Diameter of particles range <74 74...125 125...250 <74 74...125 <74
(w@
t2
b
(ms)
(ms)
Pm=
(bar)
dp ( dr 1 max
(bar/s) 16 15 12 19 22 17
62 63 62 62 62 63
8.4 7.8 7.7 a.4 7.8 7.2
610 413 395 513 350 248
167
TABLE 4. Results from simulations of peat dust explosion in a closed vessel. The definitions of the times tr and tz are given in Fig. 1 Diameter of particles (pm)
Bulk density of dust (kg mm3)
Moisture content (wt.%)
54 96 165 38 100 72
0.5 0.5 0.5 0.5 1.0 0.5
0 0 0 14.1 13.0 33.6
t, (ms)
tz (ms)
PIIUX
(bar)
!!?
(1dt rnax
(bar/s) 18 22 29 21 34 35
7.2 6.7 5.5 8.4 8.6 9.4
8.1 8.6 9.1 8.1 7.2 9.0
700 570 390 670 280 370
Char combusted at time t,
Gaseous fuel combusted at tl
(wt.%)
(wt.%)P
11 13 17 17 18 24
54 59 63 61 31 89
“Weight percent from devolatilized matter.
4--
0
5
10
15
TIME
20
2.5
30
(ms)
Fig. 2. Computed pressure development in the explosion of dry fine (d = 54 pm) peat dust in a vented 20 dm3 vessel; (1) pressure inside the vessel; (2) pressure close to the vent bole inside the vessel.
10-2
lYY 2.10-2
3.10-2
.5 3 t=14ms, 1aTgest
TIME fms)
Fig. 3. Computed mass outflow rate from a vented 20 dm3 vessel; (1) Outflow rate of particles; (2) Outflow rate of gas; (3) Total outflow rate.
maximum rate of pressure rise is 340 bar s-’ and peak pressure is 3.6 bar. An extrapolation of the VDInomograms [27] for this case gives a peak pressure between 3.5 bar and 4 bar. The outflow rate from the vessel is shown in Fig. 3. The total outfiow rate has two maxima. The outfiow until the first maximum consists of unreacted matter and is due to the expansion of the gas after ignition
value
3.5
t=2hns, largest value 0.039
Fig. 4. Reaction rate (normalized units) of gaseous volatile combustion in a vented explosion of dry peat dust in a 20 dm3 vessel.
and the subsequent combustion in the central region of the vessel. The development of the explosion inside the vessel is shown in Figs. 4 to 6. The non-spherical behaviour is due to the effects of the ignitor and the venting. The computing time with a Cyber 180/840 computer with a time step of 0.1 ms (300 time steps) was 3 h 42 min.
t=Fas,
3arge.evalue smllest
1709 K
t=7.%,
largest value 1786 K sllal1estva.lue 383 K
EkLue 343 K
'.24 1600
t=,ms,
hryest
value 2.9
el2.W.
lacqestvalue wal1est
value
3.24
t=,Cms, laqest
0.05
value 1835 K
sndlestvalue468K
t=12.%s,
Lxqest smllest
value 1773 K value 646 K
0.8
0.8
0.6
0.4 0.2 t=l4m,
kqest mallest
value 2.73 value 0.07
t=2hs.
larqest value 0.95 sm11est
t=,4m,
value 0.09
Fig. 5. Volume fraction of particles in a vented explosion of dry peat dust in a 20 dm3 vessel. Values normalized with the initial value.
An approach to using cfd to study dust deflagrations was presented. The method is based on a continuous two-phase flow description of the gas-particle mixture. The application of the numerical model was demonstrated by simulating peat dust explosions in a small scale 20 dm3 vessel. Although the behaviour of the fuel, especially the pyrolysis of peat, was inadequately known, promising results were obtained. The trends of the maximum rate of pressure rise as obtained experimentally could mostly be predicted.
Acknowledgement The author is grateful to the Technology Development Centre of Finland for financing the project in 1985436, during which time the work was done.
List of symbols
t=20ms. largest value
1548 K
srallast value 964 K
Fig. 6. Temperature of gas (K) in a vented explosion of dry peat dust in a 20 dm3 vessel.
A
Conclusions
largest value 1749 K smallest value 819 K
CD d E FI, H h k m r?i min P 4 R r s, s T t 4 u, x
pre-exponential factor, s-’ drag coefficient, particle diameter, m activation energy, J mol-l friction coefficient between phase 1 and 2, kg m-3
s-l
heat of combustion, J kg-’ enthalpy, J kg-l kinetic energy of turbulence, (m s-l)* mass fraction, mass transfer rate per unit volume, kg mW3 s-l minimum value, pressure, Pa heat transfer rate per unit volume, J mW3 s-l reaction rate (with subscript), kg mm3 s-l volume fraction, source term for quantity 4, [4] kg mW3 s- ’ coefficient of stoichiometry, temperature, K time, s velocity, r-component of velocity, m s-l space coordinate, m
Greek letters r effective diffusion coefficient, kg m-l
s-l
169
E
P
dissipation rate of kinetic energy of turbulence, (m s-l)’ s-l density, kg
Subscripts ch char dr drying fu fuel ( = combustible g gas ignition ign particle P ;a5 PyrolYsis radiation S shadow (volume W
volatile gases)
wall T-coordinate
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