Propagation of flames in dust clouds 387 Industrial and Engineering Chemistry. Process Design and Developm. 6 pp. 74-84 International Standardization Organization (1985) Explosion Protection Systems. Part I: Determi- nation of Explosion Indices of Combustible Dusts in Air. IS0 618411, ISO, Geneva Ishihama, W. (1961) Studies on the Critical Explosion Density of Coal Dust Clouds. Proc. of Ilth Internat. Conf. of Directors of Safety in Mines Research, (Oct.) Warsaw Ishihama, W., Enomoto, H., and Sekimoto, Y. (1982) Upper Explosion Limits of Coal Dust/ Methane/Air Mixtures. Journal of the Association of the Japanese Mining Industry (in Japanese) pp. 13-17 Ishii, R. (1983) Shock Waves in Gas-Particle Mixtures. Faculty of Engineering Memoirs 45 Kyoto University pp. 1-16. Jacobson, M., Cooper, A. R., and Nagy, J. (1964) Explosibility of Metal Powders. Rep. Inv. 6516, US Bureau of Mines, Washington Jaeckel, G. (1924) Die Staubexplosionen. Zeitschrift fiir technische Physik pp. 67-78 Jarosinski, J. (1984) The Thickness of Laminar Flames. Combustion and Flame 56 pp. 337-342 Jarosinski, J., Lee, J. H. S., Knystautas, R., et ai. (1987) Quenching Distance of Self-propagating Dust/Air Flames. Archivum Combustionis 7 pp. 267-278 Johnson, G. R., Murdoch, P., and Williams, A. (1988) A Study of the Mechanism of the Rapid Pyrolysis of Single Particles of Coal. Fuel 67 pp. 834-842 Jones, W. P., and Launder, B. E. (1972) The Prediction of Laminarization with a Two-Equation Model of Turbulence. Int. J. Heat Mass Transfer 15 pp. 301-314 Jones, W. P., and Launder, B. E. (1972) The Calculation of Low-Reynolds-Number Phenomena with a Two-Equation Model of Turbulence. Int. J. Heat Mass Transfer 16 pp. 11191130 Jouguet, M. (1905) Sur la propagation des reactions chimiques dans les gaz. Chapitre I et 11. Journal de Mathematiques pura et appliqutes 1 Series 61, pp. 347-425 Jouguet, M. (1906) Sur la propagation des reactions chimiques dans les gaz. Chapitre 111. Journal de Mathematiques pures et appliquees 2 Series 61, pp. 5-86 Kaesche-Krischer, B., and Zehr, J. (1958) Untersuchungen an StaublLuft-Flammen. Zeitschrift fiir Physikalische Chemie Neue Folge 14 5/6 Kaesche-Krischer, B. (1959) Untersuchungen an vorgemischten, laminar Staubkuft-Flammen. Staub 19 pp. 200-203 Kauffman, C. W., Ural, E., Nichols, J. A. et al. (1982) Detonation Waves in Confined Dust Clouds. Proc. of 3rd Internat. School of Explosibility of Dusts, (5-7 Nov.), Turawa, Poland Kauffman, C. W., Srinath, S. R., Tezok, F. I., et al. (1984) Turbulent and Accelerating Dust Flames. Proc. of 20th Symp. (Internat.) Combustion. The Combustion Institute pp. 1701-1708 Kauffman, C. W., Wolanski, P., Arisoy, A., et al. (1984a) Dust, Hybrid and Dusty Detonations. Progress in Astronautics and Aeronautics 94 pp. 221-240 Kawakami, T., Okajima, S., and Tinuma, K. (1988) Measurement of slow burning velocity by zero-gravity method. Proc. 22nd Symp. (Int.) on Combustion, The Comb. Inst. pp. 16091613 Khaikin, B. I., Bloshenko, V. N., and Merzhanov, A. G. (1970) Fizika Goreniya i Vzryva 5 No. 4 Kjaldman, L. (1987) Numerical Simulation of Peat Dust Explosions. Research Report No. 469, Technical Research Centre of Finland, Espoo Kjaldman, L. (1989) Modelling of peat dust combustion. Proc. of 3rd Internat. PHOENICS User Conference. (Aug./Sept .) Dubrovnik Klemens, R., and Wolanski, P. (1986) Flame Structure in Dust/Air and Hybrid/Air Mixtures near Lean Flammability Limits. Progr. Astronautics and Aeronautics 105 pp. 169-183 Klemens, R., Kotelecki, M., Malanovski, P., et al. (1988) An Investigation of the Mechanism of Turbulent Dust Combustion. Private communication to Eckhoff Kong Dehong (1986) Study of Flame Propagation in a Laminar Dust Cloud. M. Eng. Thesis. Dept. of Metallurgical and Physical Chemistry, Northeast University of Technology, Shenyang, P. R. China Krazinski, J. L., Backius, R. O., and Krier, H. (1977) Modelling Coal-Dust/Air Flames with 388 Dust Explosions in the Process Industries Radiative Tansport. Proc. Spring Meeting Central States Section. (March) The Combustion Institute, Cleveland, Ohio Krazinski, J. L., Backius, R. O., and Krier, H. (1978) A Model for Flame Propagation in Low Volatile Coal-Dust/Air Mixtures. J. Heat Transfer 100 pp. 105-111 Kuchta, J. M. (1985) Investigation of Fire and Explosion Accidents in the Chemical, Mining and Fuel-Related Industries - A Manual. Bulletin 680, US Bureau of Mines, Washington Kulikovskii, V. A. (1987) Existence of convergent Chapman-Jouguet Detonation Waves in Dust-Laden Gas. Fizika Goreniya i Vzryva 23 pp. 3541 (Translated by Plenum Publishing Corporation) Launder, B. E., and Spalding, D. B. (1972) Mathematical Models of Turbulence. Academic Press Lee, J. H. S. (1987) Dust Explosions: An Overview. Proc. Internat. Symp. Shock Tubes and Waves, Lee, J. H. S., Yi Kang Pu, and Knystautas, R. (1987) Influence of Turbulence in Closed Volume Lee, J. H. S. (1988) Dust Explosion Parameters, their Measurement and Use. VDZ-Berichte 701 Leuschke, G. (1965) Beitrage zur Erforschung des Mechanismus der Flammenausbreitung in Staubwolken. Staub 25 pp. 180-186 Levendis, Y. A., Flagan, R. C., and Gavals, G. R. (1989) Oxidation Kinetics of Monodisperse Spherical Carbonaceous Particles of Variable Properties. Combustion and Flame 76 pp. 221-241 Lewis, B., and von Elbe, G. (1961) Combustion, Flames and Explosion of Gases. 2nd Ed., Academic Press Liebman, I., Cony, J., and Perlee, H. E. (1972) Ignition and Incendivity of Laser Irradiated Single Micron-Size Magnesium Particles. Combustion Science and Technology 5 pp. 21-30 Lindstedt, R. P., and Michels, H. J. (1989) Deflagration to Detonation Transitions and Strong Deflagrations in Alkane and AlkaneIAir Mixtures. Combustion and Flame 76 pp. 169-181 Ma, A. S. C., Spalding, D. B., and Sun, L. T. (1982) Application of ‘Escimo’ to Turbulent HydrogedAir Diffusion flame. Proc. of 19th Symp. (Internat.) on Combustion. The Combustion Institute pp. 393402 Magnussen, B. F., and Hjertager, B. H. (1976) On Mathematical Modelling of Turbulent Com- bustion with Special Emphasis on Soot Formation and Combustion. Proc. of 16th Symp. (Internat.) on Combustion. The Combustion Institute, Pittsburgh pp. 719-729 Mallard, E., and le Chatelier, H. L. (1883) Recherches Experimentales et Theoretiques sur la Combustion des MClanges Gazeux Explosifs. Annales des Mines 4 p. 379 Malte, P. C., and Dorri, B. (1981) The Behaviour of Fuel Particles in Wood-Waste Furnaces. Proc. of Spring Meeting, Western States Section, (April), Combustion Institute, Washington State University Mason, W. E., and Wilson, M. J. G. (1967) Laminar Flames of Lycopodium Dust in Air. Combustion and Flame 11 pp. 195-200 Matalon, M. (1982) The Steady Burning of a Solid Particle. SIAM J. Appl. Math. 42 pp. 787-803 Mitsui, R., and Tanaka, T. (1973) Simple Models of Dust Explosion. Predicting Ignition Temperature and Minimum Explosive Limit in Terms of Particle Size. Ind. Eng. Chem. Process Des. Develop. 12 pp. 384-389 Moen, I., Lee, J. H. S., and Hjertager, B. H. (1982) Pressure Development due to Turbulent Flame Propagation in Large-Scale MethaneIAir Explosions. Combustion and Flame 47 pp. 31-52 Moore, P. E. (1979) Characterization of Dust Explosibility: Comparative Study of Test Methods. Chemistry and Industry 7 p. 430 Nagy, J., Seiler, E. C., Conn, J. W., et al. (1971) Explosion Development in Closed Vessels. Rep. Inv. No. 7507, US Bureau of Mines, Washington Nagy, J., Conn, J. W., and Verakis, H. C. (1969) Explosion Development in a Spherical Vessel. Rep. Inv. 7279, US Bureau of Mines, US Dept. Interior, Washington Aachen, F. R. Germany, 16: pp. 21-38 Explosion of Dust/Air Mixtures. Archivum Combustionis 7 pp. 279-297 pp. 113-122 Propagation of flames in dust clouds 389 Nagy, J., and Verakis, H. C. (1983) Development and Control of Dust Explosions. Marcel Dekker, Nelson, L. S., and Richardson, N. L. (1964) The Use of Flash Heating to Study the Combustion of Nelson, L. S. (1965) Combustion of Zirconium Droplets Ignited by Flash Heating. Pyrodynamics 3 Nettleton, M. A. (1987) Gaseous Detonations: Their Nature, Effects and Control, Chapman and Hall, London Neumann, J. von (1942) Progress Report on the Theory of Detonation Waves. Report No. 549, OSRD Nomura, S I., and Tanaka, T. (1978) Theoretical Discussion of the Flame Propagation Velocity of a Dust Explosion. The Case of Uniform Dispersion of Monosized Particles. Heat Transfer. Japanese Research 7 pp. 79-86 Nomura, S I., and Tanaka, T. (1980) Prediction of Maximum Rate of Pressure Rise due to Dust Explosion in Closed Spherical and Non-Spherical Vessels. Ind. Eng. Chem. Process Des. Dev. 19 pp. 451459 Nomura, S I., Torimoto, M., and Tanaka, T. (1984) Theoretical Upper Limit of Dust Explosions in Relation to Oxygen Concentration. Ind. Eng. Chem. Process Des. Dev. 23 pp. 42W23 Nordtest (1989) Dust Clouds: Minimum Explosible Dust Concentration. NT Fire 011, Nordtest, Helsinki Nusselt , W. (1924) Der Verbrennungsvorgang in der Kohlenstaubfeuerung. Zeitschrift Ver. Deutscher Ingenieure 68 pp. 124-128 Ogle, R. A., Beddow, J. K., and Vetter, A. F. (1983) Numerical Modelling of Dust Explosions: The Influence of Particle Shape on Explosion Intensity. Powder and Bulk Solids Handling and Processing, Technol. Progr., Internat. Powder Science Institute Ogle, R. A., Beddow, J. K., Vetter, A. F. (1984) A Thermal Theory of Laminar Premixed Dust Flame Propagation. Combustion and Flame 58 pp. 77-79 Ogle, R. A., Beddow, J. K., Chen, L. D. (1988) An Investigation of Aluminium Dust Explosions. Combustion Science and Technology 61 pp. 75-99 Palmer, K. N., and Tonkin, P. S. (1971) Coal Dust Explosions in a Large-Scale Vertical Tube Apparatus. Combustion and Flame 17 pp. 159-170 Pineau, J. P., and Ronchail, G. (1982) Propagation of Dust Explosions in Ducts. Proc. of International Symposium: The Control and Prevention of Dust Explosions, (November) Orga- nized by Oyes/IBC, Bade Pineau, J. P. (1987) Dust Explosions in Pipes, Ducts and Galleries. A State-of-the-Art Report with Criteria for Industrial Design. Proceedings of Shenyang International Symposium on Dust Explosions, Sept. 14-16, NEUT, Shenyang, P. R. China Prentice, J. L. (1970) Combustion of Pulse-Heated Single Particles of Aluminium and Beryllium Cornbustion Science and Technology 1 pp. 385-398 Proust, C., and Veyssiere, B. (1988) Fundamental Properties of Flames Propagating in Starch DustlAir Mixtures. Combustion Science and Technology 62 pp. 149-172 Radandt, S. (1989) Explosionsablaufe in Abhangigkeit von Betriebsparametern. VDZ-Berichte 701, Volume 2. VDI-Verlag, Dusseldorf pp. 801-817 Rae, D. (1971) Coal Dust Explosions in Large Tubes. Proc. of 8th International Shock Tube Symposium, (July), London Razdobreev, A. A., Skorik, A. I., and Frolov, Yu.V. (1976) Ignition and Combustion Mechanism of Aluminium Particles. Fizika Goreniya i Vzryva 12 No. 2 pp. 203-208 (Translated by Plenum Publishing Corporation) Richmond, J. K., and Liebman, I. (1975) A Physical Description of Coal Mine Explosions. Proc. of 15th Symp. (Internat.) on Combustion. The Combustion Institute, Pittsburgh, USA pp. 115-126 Richmond, J. K., Liebman, I., Bruszak, A. E., et al. (1978) A Physical Description of Coal Mine Inc. Liquid Metal Droplets. The Journal of Physical Chemistry 68 No. 5 pp. 1269-1270 pp. 121-134 390 Dust Explosions in the Process Industries Explosions. Part 11. Proc. of 17th Symp. (Internat.) on Combustion. The Combustion Institute, Pittsburgh, USA pp. 1257-1268 Samsonov, V. P. (1984) Flame Propagation in an Impulsive Acceleration Field. Fizika Goreniya i Vzryva 20 No. 6 pp. 58-61 (Translated by Plenum Publishing Corporation) Schlapfer, P. (1951) Ueber Staubflammen und Staubexplosionen. Schweiz. Verein von Gas- und Wasserfachmannern Monatsbulletin No. 3, 31 pp. 69-82 Scholl, E. W. (1981) Brenn- und Explosionsverhalten von Kohlenstaub. Zement-Kalk-Gips No. 5 Schuber, G. (1988) Zunddurchschlagverhalten von Staub-Luft-Gemischen und Hybriden- Gemischen. Publication Series: Humanisierung des Arbeitslebens, Vol. 72 VDI-Verlag, Dusseldorf Schuber, G. (1989) Ignition Breakthrough Behaviour of Dust/Air and Hybrid Mixtures through Narrow Gaps. Proc. of 6th Internat. Symp. Loss Prev. Safety Prom. Proc. Ind., Oslo Schonewald, I. (1971) Vereinfachte Methode zur Berechnung der unteren Zundgrenze von StaubLuft-Gemischen. Staub-Reinhalt. Luft 31 pp. 376-378 Selle, H., and Zehr, J. (1957) Experimentaluntersuchungen von Staubverbrannungsvorgangen und ihre Betrachtung von reaktionsdynamischen Standpunkt. VDZ-Berichte 19 pp. 73-87 Semenov, E. S. (1965) Measurement of Turbulence Characteristics in a Closed Volume with Artificial Turbulence. Combustion, Explosion and Shock Waves 1 No. 2 pp. 57-62 Semenov, N. N. (1951) Tech. Memo. No. 1282, NACA Shevchuk, V. G., Kondrat’ev, E. N., Zolotko, A. N., et al. (1979) Effect of the Structure of a Gas Suspension on the Process of Flame Propagation. Fizika Goreniya i Vzryva 15 No. 6 pp. 4145 (Translated by Plenum Publishing Corporation) Shevchuk, V. G., Bezrodnykh, A. K., Kondrat’ev, E. N., et al. (1986) Combustion of Airborne Aluminium Particles in Free Space. Fizika Goreniya i Vzryva 22 No. 5 pp. 40-43 (Translated by Plenum Publishing Corporation) Siwek, R. (1977) 20 Liter Laborapparatur fur die Bestimmung der Explosionskennzahlen brenn- barer Staube. MSc. Thesis, Winterthur Engineering College, Wintherthur Slezak, S. E., Buckius, R. O., and Krier, H. (1986) Evidence of the Rich Flammability Limit for Pulverized Pittsburgh Seam CoaYAir Mixtures. Combustion and Flame 63 pp. 209-215 Smith, I. W. (1971) Kinetics of Combustion of Size-Graded Pulverized Fuels in the Temperature Range 1200-2270 K. Combustion and Flame 17 pp. 303-4 Smoot, L. D., and Horton, M. D. (1977) Propagation of Laminar Coal-Air Flames. Progr. Energy Combust. Sci. 3 pp. 235-258 Smoot, L. D., Horton, M. D., and Williams, G. A. (1977) Propagation of Laminar Pulverized Coal-Air Flames. Proc. of 16th Symp. (Internat.) on Combustion. The Combustion Institute, pp. 375-387 Spalding, D. B. (1957) Predicting the Laminar Flame Speed in Gases with Temperature-explicit Reaction Rates. Combustion and Flame 1 pp. 287-295 Spalding, D. B., Stephenson, P. L., and Taylor, R. G. (1971) A Calculation Procedure for the Prediction of Laminar Flame Speeds. Combustion and Flame 17 p. 55 Spalding, D. B. (1982) Representations of Combustion in Computer Models of Spark Ignition. Report CFD/82/18, Computational Fluid Dynamic Unit, Imperial College of Science and Technology, London Specht, E., and Jeschar, R. (1987) Ermittlung der geschwindigkeitsbestimmenden Mechanismen bei der Verbrennung von dichten Kohleteilchen. VDZ-Berichte 645 pp. 45-56 Srinath, R. S., Kauffman, C. W., Nicholls, J. A., et al. Flame Propagation due to Layered Combustible Dusts. Proc. of 10th International Colloquium on Dynamics of Explosions and Reactive Systems, (August), Berkeley, USA Taffanel, M. J. (1907) Premiers Essais sur 1’InflammabilitC des Poussieres, Rapport publique par la ComitC Central des Houill2res de France, Aout Tai, C. S., Kauffman, C. W., Sichel, M., et al. (1988) Turbulent Dust Combustion in a Jet-Stirred pp. 227-233 Propagation of flames in dust clouds 39 1 Reactor. Progress in Astronautics and Aeronautics, 113 pp. 62-86 Tamanini, F. (1983) Dust Explosion Propagation in Simulated Grain Conveyor Galleries, Technical Report FMRC J.I. OFIW.RK, (July), Prepared for National Grain and Feed Association, Washington DC Tamanini, F. (1989) Turbulence Effects on Dust Explosion Venting. Proc. of AZChF LOSS Prevention Symposium, (April 24), Session 8, Plant Layout, Houston Tamanini, F., and Chaffee, J. L. (1989) Large-Scale Vented Dust Explosions - Effect of Turbu- lence on Explosion Severity. Technical Report FMRC J.I. OQ2E2.RK, (April), Factory Mutual Research Tanford, C., and Pease, R. N. (1947) Theory of Burning Velocity. 11. The Square Root Law for Burning Velocity. J. Chemical Physics 15 pp. 861-865 Tulis, A. J., and Selman, J. R. (1984) Unconfined Aluminium Particle Two-Phase Detonation in Air. Progress in Astronautics and Aeronautics 94 pp. 277-292 Tulis, A. J. (1984) Initiation and Propagation of Detonation in Unconfined Clouds of Aluminium Powder in Air. Proc. of 9th Int. Semin. Pyrotechnics Ubhayakar, S. K., and Williams, F. A. (1976) Burning and Extinction of a Laser-Ignited Carbon Particle in Quiescent Mixtures of Oxygen and Nitrogen. Journ. Electrochem. Society 123 Vareide, D., and Sonju, 0. K. (1987) Theoretical Predictions of Char Burn-Off. Report No. STF15 A87044 SINTEF, Trondheim, Norway Wagner, R., Schulte, A., Miihlen, H J., et al. (1987) Laboratoriumsuntersuchungen zum Zunden und Abbrandgeschwindigkeit bei der Verbrennung einzelner Kohlekorner. VDZ-Berichte 645 Weber, R. 0. (1989) Thermal Theory for Determining the Burning Velocity of a Laminar Flame, Using the Inflection Point in the Temperature Profile. Combust. Sci. and Tech. 64 pp. 135-139 Weckman, H. (1986) Safe Production and Use of Domestic Fuels. Part 4. Fire and Explosion Properties of Peat. Research Report No. 448. Technical Research Centre of Finland, Espoo Wolanski, P. (1977) Numerical Analysis of the Coal Dust/Air Mixtures Combustion. Archivum Termodynamiki i Spalania 8 pp. 451458 Wolanski, P., Lee, D., Sichel, M., et al. (1984) The Structure of Dust Detonations. Progress in Astronautics and Aeronautics 94 pp. 242-263 Wolanski, P. (1987) Detonation in Dust Mixtures, Proc. Shenyang Internat. Symp. Dust Expl. NEUT, Shenyang, P. R. China, pp. 568-598 Wolanski, P. (1988) Oral Statement made at 3rd Internat. Coll. on Dust Explosions, (Oct. 24-28) Szczyrk, Poland Yi Kang Pu: (1988) Fundamental Characteristics of Laminar and Turbulent Flames in Cornstarch Dust/Air Mixtures. (January), Ph.D. Thesis, Dept. Mech. Eng., McGill University Yi Kang Pu, Mazurkiewicz, J., Jarosinski, J. et al. (1988) Comparative Study of the Influence of Obstacles on the Propagation of Dust and Gas Flames. Proc. 22nd Symp. (Znt.) on Combustion The Combustion Institute pp. 1789-1797 Pittsburgh, USA Zabetakis, M. G. (1965) Flammability Characteristics of Combustible Gases and Vapors. Bulletin 627, US Bureau of Mines, Washington Zehr, J. (1957) Anleitung zu den Berechnungen uber die Ziindgrenzwerte und die maximalen Explosionsdriicke. VDI-Berichte 19 pp. 63-68 Zehr, J. (1959) Die Experimentelle Bestimmung der oberen Ziindgrenze von StaubLuft- Gemischen als Beitrag zur Beurteilung der Staubexplosionsgefahren. Staub 19 pp. 204-214 Zeldovich, Ya.B. (1940) On the Theory of the Propagation of Detonation in Gaseous Systems. J. Exp. Theor. Phys. USSR 10 p. 524. (Translation: NACA Tech. Memo No. 1261, (1950) pp. 1-50) Zeldovich, Ya.B., Istratov, A. G., Kidin, N. I., et al. (1980) Flame Propagation in Tubes: Hydrodynamics and Stability. Combustion Science and Technology 24 pp. 1-13 pp. 747-756 pp. 33-43 Chapter 5 Ignition of dust clouds and dust deposits: further consideration of some selected aspects 5.1 WHAT IS IGNITION? The word ‘ignition’ is only meaningful when applied to substances that are able to propagate a self-sustained combustion or exothermal decomposition wave. Ignition may then be defined as the process by which such propagation is initiated. Ignition occurs when the heat generation rate in some volume of the substance exceeds the rate of heat dissipation from the volume and continues to do so as the temperature rises further. Eventually a temperature is reached at which diffusion of reactants controls the rate of heat generation, and a characteristic stable state of combustion or decomposi- tion is established. The characteristic dimension of the volume within which ignitionho ignition is decided, is of the order of the thickness of the front of a self-sustained flame though the mixture. This is because self-sustained flame propagation can be regarded as a continuing ignition wave exposing progressively new parts of the cloud to conditions where the heat generation rate exceeds the rate of heat dissipation. A similar line of thought applies to propagation of smouldering fires in powder deposits and layers, as discussed in Section 5.2.2.4. In the ignition process the concepts of stability and instability play a key role. Thorne (1985) gave an instructive simplified outline of some basic features of the instability theory of ignition, which will be rendered in the following. In most situations diffusion, molecular as well as convective, plays a decisive role in the ignition process. Systems that can ignite, may be characterized by a dimensionless number D,, the Damkohler number, which is the ratio of the rate of heat production within the system due to exothermic chemical reactions, to the rate of heat loss from the system by conduction, convection and radiation. Often D, is expressed as the ratio of two characteristic time constants, one for the heat loss and one for the heat generation: D, = TLITG (5.1) The influence of temperature on the rate of chemical reactions is normally described by the exponential Arrhenius law: k = fexp(- EIRT) (5.2) where k is the rate constant, f the pre-exponential factor or frequency factor, E the activation energy, R the gas constant and T the absolute temperature. Ignition of dust clouds and dust deposits 393 In general the chemical rate of a combustion reaction may be written: Rc = kCf C%R (5.3) where p + q = m is the order of the reaction, and Cf and COR the concentration of fuel and oxygen in the reaction zone. In the case where the fuel is non-depleting and q = 1, one gets: Rc = kCoR (5.4) RD = D(C0S - COR) (5.5) The rate of diffusion of oxygen from the surroundings into the reaction zone is: where D is the thermal diffusion rate constant and Cos the oxygen concentration in the surroundings. As the temperature in the reaction zone increases, the thermal reaction rate increases according to Equations (5.2) and (5.4), and a point is reached where the rate is ccntrolled by the diffusional supply of oxygen to the reaction zone. Then Rc = RD and the right-hand sides of Equations (5.4) and (5.5) are equal. kCOR = D(cOS - COR) = p (5-6) p = kD/(k + 0) (5.7) where is called the Frank-Kamenetskii's overall rate constant, and k is as defined in Equation (5.2). By introducing the heat of reaction Q, the rate of heat generation can, according to Equation (5.6), be expressed as: RG = Q X cos X (5.8) By inserting Equation (5.2) into (5.7) and substituting for p in (5.8), one gets: The general expression for the heat loss from the system considered is: RL = U(T - To)", n 2 1 (5.10) where U and n are characteristic constants for the system, T the temperature in the reaction zone and TO the ambient temperature. Figure 5.1 illustrates the stability/instability conditions in a system that behaves according to Equations (5.9) and (5.10). Figure 5.1 reveals three intersections between the S-shaped RG curve and the heat loss curve RL. In the figure, RL is a straight line, corresponding to n = 1, which applies to heat loss by conduction only. For convection, n is 514 and for radiation 4. The upper (3) and lower (1) intersections are stable, whereas the intermediate one (2) is unstable. A perturbation in Tat this point either leads to cooling to the lower intersection (l), or to a temperature rise to the upper intersection (3). If the heat loss decreases due to changes of the constants in Equation (5.10), the heat loss curve RL shifts to the right, and the intersection points (1) and (2) approach each other and finally merge at the critical point of tangency (4). At the same time intersection point (3), which determines the stable state of combustion, moves to higher temperatures. 394 Dust Explosions in the Process Industries Figure 5.1 Heat generation and heat loss as functions of temperature in the reaction zone. Explanation of the various features (lH5) are given in the text (From Thorne, 1985) If U in Equation (5.10) increases, another critical point of tangency (5) is reached. If U increases further, ignition becomes impossible. If the temperature rise AT of the system described by Figure 5.1 is plotted as a function of the Damkohler number as defined in Equation (5.1), a stabilityhstability diagram as illustrated in Figure 5.2 is obtained. The intersection and tangency points (1) to (5) in Figure 5.1 are indicated. The lower branch in Figure 5.2 is stable and corresponds to a slow, non-flaming reaction. The upper branch is also stable and corresponds to steady propagation of the combustion or decomposition wave. The intermediate branch is unstable. The system temperature can be raised from ambient temperature without significant increase in the reaction rate until the ignition point (2) has been passed. Then the system jumps to the Figure 5.2 Stability/instability diagram for a com- bustible system. The features of the points (lH5) are explained in the text (From Thorne, 1985) Ignition of dust clouds and dust deposits 395 upper stable flame propagation branch. Upon cooling, i.e. increasing U or n or both in Equation (5.10), the rate of reaction is reduced. However, the reaction continues right down to (5) in Figure 5.2, from which the system temperature drops to a stable condition in the extinguished regime. The scheme illustrated in Figures 5.1 and 5.2 is quite general and applicable to different types of systems. More extensive treatments of general ignitiodcombustion-stability theory were given for example by Gray and Lee (1967), Gray and Sherrington (1977) and Bowes (1981). The classical basis for this type of analysis was established by Semenov (1959) and Frank-Kamenetzkii (1969). The book by Bowes (1984) provides a unique, comprehensive overview of the field of self-heating and ignition, not least in solid materials including dust layers and heaps. Although the basic considerations implied in Figures 5.1 and 5.2 to some extent provide a satisfactory general definition of ignition, the precise theoretical definition has remained a topic of scientific discussion. One example is the dialogue between Lermant and Yip (1984, 1986) and Essenhigh (1986). 5.2 SELF-HEATING AND SELF-IGNITION IN POWDER DEPOSITS 5.2.1 OVERVIEWS Bowes (1984) gave the state of the art of experimental evidence and theory up to the beginning of the 1980s. Considerable information was available, and theory for predicting self-heating properties of powders and dusts under various conditions of storage had been developed. There were nevertheless some gaps in the quantitative knowledge, one of which is biological heating. In vegetable and animal materials such as feed stuffs and natural fibres, self-heating may be initiated by biological activity, in particular if the volume of material is large, its moisture content high and the period of storage long. However, because the micro organisms responsible for the biological activity cannot survive at temperatures above about 75"C, biological heating terminates at this temperature level. Further heating to ignition, therefore, must be due to non-biological exothermic oxidation, for which theory exists. It is possible, however, that the long-term biological activity in a real industrial situation may generate chemically different starting conditions for further self-heating than the conditions established in laboratory test samples heated artificially to 75°C by supply of heat from the outside. Further research seems required in this area. Starting with the extensive account by Bowes (1984), Beever (1988) highlighted the theoretical developments that she considered most useful for assessing the self-heating and ignition hazards in industrial situations. In spite of many simplifying assumptions, the models available appeared to agree well with experimental evidence. However, extrapo- lating over orders of magnitude, from laboratory scale data to industrial scale, was not recommended. Biological activity was not involved in the self-heating processes considered. 396 Dust Explosions in the Process Industries 5.2.2 SOME EX PE RI MENTAL I NVESTl GAT1 ON S 5.2.2.1 lsoperibolic experiments In the isoperibolic configuration, the outside of the dust deposits is kept at a constant temperature while the temperature development at one or more points inside the deposit is monitored. The dust sample may either be mechanically sealed from the surroundings, or air may be allowed to penetrate it, driven by the buoyancy of heated gases inside the dust sample or by external over-pressure or suction. Leuschke (1980, 1981) conducted extensive experimental studies of the critical para- meters for ignition of deposits of various combustible dusts under isoperibolic conditions, with natural air draught through the sample, driven by buoyancy. Figure 5.3 shows a plot of the minimum ambient air temperature for self-ignition of deposits of cork dust samples of various shapes and sizes as a function of the volume-to-surface ratio of the sample. This correlation can be interpreted in terms of the critical Frank-Kamenetzkii para- meter for self-ignition (Equation (5.11) below), which was discussed extensively by Bowes (1984). Note that the abscissa scale in Figure 5.3 is linear with the logarithm of the Figure 5.3 and shapes as a function of the volume/surface area ratio (From Leuschke, 1981) Minimum ambient air temperature for self-ignition of cork dust deposits of various sizes [...]... contributions to the published literature on the spark ignition of dust clouds have been produced Indeed they have confirmed that ignition of dust clouds by electric discharges is a real possibility and the cause of many severe dust explosions during the years, in mines as well as in industrial plants 4 12 Dust Explosions in the Process Industries 5.3.2 THE OHMIC RESISTANCE OF A SPARK CHANNEL BETWEEN... well as the order of magnitude of the series 4 16 Dust Explosions in the Process industries resistance giving this maximum decrease, agree with the corresponding figures found by Boyle and Llewellyn for other powders Line et al attributed the dramatic influence of spark discharge time to decreasing disturbance of the dust cloud by the blast wave from the spark discharge as the discharge time increased... encountered with the maize starch and grain dusts During heating, the starch charred and expanded, whereas the grain dust swelled and distorted The test was found acceptable for the purpose of determining the minimum layer ignition temperature of a variety of dusts Tyler and Henderson (19 87) conducted a laboratory-scale study in which the minimum hot-plate temperatures for inducing self-ignition in 5 4 0 mm... was termed the ‘cavity’ Only gases (air plus combustion products) were present in this region However, Ignition of dust clouds and dust deposits 40 1 Figure 5.6 Influence of dissipated power in a hot platinum wire coil, embedded in a layer of grain dust, per unit area of the dust in contact with the coil, on the minimum dissipated energy required for initiating smouldering combustion in the dust layer... Formation of a second diffusion flame zone between the burning premixed zone and the hot surface, receiving fuel via further pyrolysis caused by the rich primary burning zone 4 Extinction of diffusion flame due to lack of oxidizer Drop in pyrolysis rate due to cooling by extinguishing gas 5 Stabilization of premixed flame close to d u d g a s interface 408 Dust Explosions in the Process industries Figure...Ignition of dust clouds and dust deposits 3 97 volume-ro-surface area, whereas the ordinate axis is linear with the reciprocal of the temperature [K] Some further experimental results produced by Leuschke (1980,1981) are mentioned in Section 5.2.3.2 Hensel (19 87) , continuing the line of research initiated by Leuschke, investigated the influence of the particle size of coal on the minimum self-ignition... shown in Figure 5.6 The points in Figure 5.6 are experimental results, whereas the dotted curve is the expected trend in the low power end The vertical dashed line indicates the value of powedarea at which the rate of energy input is equal to the rate of heat loss from the layer The experimental data in Figure 5.6 indicate that for the higher values of powedarea, more energy was needed to ignite the dust. .. of the air surrounding the dust sample in the furnace), Q heat of reaction per unit mass, p bulk density of the dust sample, and A the thermal conductivity of the dust sample In a further contribution Hensel(l989) confirmed that data of the type shown in Figure 5 3 , for various sample shapes, could in fact be correlated with a good fit using the Frank-Kamenetzkii parameter (Equation (5.11)) The linear... when the temperature of the unburnt material reached a minimum value characteristic of that particular material The pyrolysis products were gaseous volatiles and solid char The volatiles escaped to the surroundings while the char remained in the layer, forming the second region of the combustion wave, the combustion zone Oxygen from the atmosphere diffused into this zone, oxidizing the hot char, thereby... Movementhurbulence of dust cloud The marked increase of the minimum ignition energy for premixed gases with the turbulence intensity of the gas mixture has been demonstrated by various workers, including Ballal and Lefebvre (1 977 ), and Bradley and Lung (19 87) One would expect a similar influence of the turbulence intensity of dust clouds on their minimum ignition energies, as indicated by Figure 1.40 in Chapter . Northeast University of Technology, Shenyang, P. R. China Krazinski, J. L., Backius, R. O., and Krier, H. (1 977 ) Modelling Coal -Dust/ Air Flames with 388 Dust Explosions in the Process Industries. (1987a, 1988). A = thermal conductivity of the sample [J m-' h-' K-' 1 406 Dust Explosions in the Process Industries Figure 5 .7 Temperature distributions in a cylindrical. surroundings into the reaction zone is: where D is the thermal diffusion rate constant and Cos the oxygen concentration in the surroundings. As the temperature in the reaction zone increases,