Deflagration Parameters of Stoichiometric Propane-air Mixture During the Initial Stage of Gaseous Explosions in Closed Vessels

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1 Deflagration Parameters of Stoichiometric Propane-air Mixture During the Initial Stage of Gaseous Explosions in Closed Vessels VENERA BRINZEA 1, MARIA MITU 1, CODINA MOVILEANU 1, DOMNINA RAZUS 1 *, DUMITRU OANCEA 2 1 Romanian Academy, Institute of Physical Chemistry Ilie Murgulescu, 202 Spl. Independentei, , Bucharest, Romania 2 Department of Physical Chemistry, University of Bucharest, 4-12 Regina Elisabeta Blvd., , Bucharest, Romania The flame propagation during deflagration of the stoichiometric propane-air mixture ([C 3 ] = 4.02 vol.%), considered as a reference test mixture, in a spherical and two cylindrical closed vessels with central ignition was monitored by means of pressure measurements, in experiments performed at ambient initial temperature and various initial pressures within 0.3 and 1.3 bar. From pressure-time records during the early stage of the process, the constants of the cubic law of pressure increase in time and the corresponding burning velocities were computed by means of an isothermal compression model. The optimal duration of the early stage was discussed in correlation with the flame radius at the end of this stage, computed from burned mass fractions and with the fit parameters of pressure variation versus time correlations. Keywords: deflagration, propagation, closed vessel, flame radius, burning velocity The study of the early stage of flame propagation during closed vessel explosions as laminar deflagration provides useful information on flame initiation and growth, associated to unsteady heat generation and pressure increase. In particular, the pressure variation during this stage is important for vent design, required for mitigation of gaseous explosions in industrial reactors or storage tanks. Such devices work properly when the venting acts earlier than reaching the allowable pressure [1]. Examination of the early stage of flame development in a closed spherical vessel with central ignition revealed that the pressure variation at the end of this stage can be correlated with the time from ignition by a cubic law [2], as long as the flame propagates undisturbed and preserves its spherical shape. Based on this law, a simple method for burning velocity determination from pressure-time records during explosions of gaseous mixtures in closed vessels was recently developed [3] and the cubic law constants were used to compute the burning velocities of the examined systems according to isothermal or adiabatic compression models. Up to now, the early stage of flame development was empirically restricted to a pressure rise Δp less or equal to the total initial pressure p 0. Reliable values of burning velocities for various gaseous mixtures were obtained: propane-air, n-butane-air, ethylene-air and propylene-air [3-6], in very good agreement with data reported from other measurements [7-10]. However, the disturbing effects of energy input during initiation and of flame curvature and stretch after initiation may affect the accuracy of the results [11,12], especially when fuel-air mixtures far from stoichiometry are examined. Shorter durations of the early stage of explosion should be examined especially when near-limit flammable mixtures are studied or when non-spherical explosion vessels are used. The present paper reports the constants of the cubic law and the corresponding burning velocities of the stoichiometric propane-air mixture, considered as a reference test mixture for which many combustion data are available, at variable initial pressures within 0.3 and 1.3 bar, obtained from pressure-time records in a spherical and two cylindrical vessels, at various durations of the early stage of explosion propagation: Δp = f p 0, with f = 0.25, 0.50, 0.75 and The pressure-time records are used also for determination of the flame radius at the end of each early stage, computed from burned mass fractions by means of several specific equations (Manton-Lewisvon Elbe [13]; Grumer [14]; Oancea [15]) valid for this stage, as well. The analysis is necessary for finding the optimal duration of the early stage of propagation aiming at improvement of burning velocities determined by the mentioned method. Experimental part The experiments were made in three explosion vessels: a spherical vessel S (with radius R = 5 cm) and two cylindrical vessels (vessel C 1 with diameter Φ = 10 cm and height h = 15 cm and vessel C 2 with Φ = h = 6 cm). In all vessels the ignition was made with inductivecapacitive sparks produced between stainless steel electrodes. The ignition energy varied between 3 and 5 mj. The spark gap of constant width 3.5 mm was located in the geometrical centre of each vessel. The pressure variation during explosions was recorded with piezoelectric pressure transducers (Kistler 601A), connected to a Charge Amplifier (Kistler 5001SN) and an Acquisition Data System Tektronix TestLab 2505, at 5000 signals/s. Two ionisation probes mounted in each vessel, in equatorial position, with tips at various distances from the wall, allow the detection of the flame front. The test mixture is a stoichiometric propane-air mixture ([C 3 ] = 4.02 vol.%) at ambient initial temperature and various initial pressures between 0.3 and 1.3 bar. Propane (99.99%) (SIAD Italy) was used without further purification. Other details were given previously [3-6]. Data evaluation The normal burning velocity S u of a flammable mixture at total initial pressure p 0 was calculated by evaluation of p(t) diagrams in the early stage of flame propagation, according to [3]: * drazus@icf.ro REV. CHIM. (Bucharest) 62 No

2 where R is the radius of the vessel, k is the coefficient of the cubic law of pressure rise and Δp max = p max - p 0 is the maximum (peak) pressure rise. The coefficient k, characteristic for the early stage of combustion, given originally by equation [2]: (2) was determined for each experiment by an improved method using a nonlinear regression, applied to an equation of the form: (3) where a and b are pressure and time corrections respectively, meant to eliminate the signal shift of pressure transducer and the possible delays in signal recording [3]. The normal burning velocities were calculated over a restricted range of transient pressures within the interval p p 0. At the evaluation of data recorded in cylindrical vessels, an apparent vessel radius (calculated from the volume of a sphere equivalent to the volume of the examined cylinder) was used instead of the geometrical radius. The flame radius at various moments of flame propagation was calculated as [13]: (1) well, limited only by the moment when the flame gets closer to the wall and the heat losses from the burned gas to the explosion vessel become important. Results and discussions A representative diagram of pressure variation in vessel S during the explosion of the test mixture at ambient initial pressure and temperature is given in figure 1, where the rate of pressure rise (dp/dt) and the transient signal of the ionization probe (U IP ) are also plotted. In the present experiments, the tip of the ionization probe was positioned 5 mm from the wall. On the diagram, the early stage defined by restriction Δp=p o = 1 bar was delimited. It can be seen that the early stage is much shorter than the time necessary to reach the maximum rate of pressure rise (in the present case, ms) when the heat losses become important. The peak value of the ionization probe signal, associated to a flame radius r b = 4.5 cm, is observed slightly later, at ms. Similar curves were recorded for all examined pressures, in the three explosion vessels. In cylindrical vessels C 1, the peak of the pressure rise is observed also later as compared to the end of early stage defined by restriction Δp =p o = 1 bar. where n is the burnt mass fraction; p is pressure at moment t; π = p/p 0, is the dimensionless transient pressure and γ u is the adiabatic compression coefficient of the unburnt gas. The burnt mass fraction, n, was calculated using several equations: Manton-Lewis-von Elbe [13]: (4) where p e is the end pressure of isochoric combustion and π e = p e /p 0. Grumer [14]: where E 0 is the expansion coefficient of gases, during the initial stage of flame propagation (cvasi-isobaric combustion). Oancea [15]: (5) (6) Fig. 1. Pressure-time history for explosion of a stoichiometric C 3 -air mixture in vessel S, at p 0 = 1.0 bar and T 0 = 298 K An enlarged diagram of the early stage period of explosions in the examined closed vessels is given in figure 2. On this diagram, several lines delimitate possible durations of the early stage : τ is the duration of a stage where Δp=p o (the relative pressure π varies between 1.00 and 2.00); 3/4. τ is the duration of a stage where Δp=3/4p o (1.00 π 1.75) and so on. For each duration (τ, 3τ/4, τ/2 and τ/4), eq. (3) was used to calculate the constants of the cubic law in vessels S, C 1. (7) where: and T f,v - the adiabatic flame temperature of isochoric combustion; T f,p - the adiabatic flame temperature of isobaric combustion. Equations (5) and (6) were developed only for the early stage of closed-vessel explosions, while equation (7) is valid also for later stages of explosions as Fig. 2 - Pressure variation during the early stage of explosion of the stoichiometric C 3 -air mixture in vessels S, C 1, at p 0 = 1.0 bar and ambient initial temperature REV. CHIM. (Bucharest) 62 No

3 Fig. 3. The cubic law coefficients of pressure rise for the test mixture, at various initial pressures and ambient initial temperature A set of illustrative results obtained by using the restriction Δp = p o is given in figure 3, where the cubic law coefficients k obtained in the three explosion vessels, in experiments made at various initial pressures, are plotted. From these data, the normal burning velocities S u were calculated with equation (1). Results obtained for the three explosion vessels, at several initial pressures, are listed in table 1. At ambient initial pressure, the normal burning velocity obtained from experiments in vessel S is 41.1 cm/ s, in good agreement with reference data from literature [7-10]. Higher burning velocities were obtained from data measured in vessels C 1 in comparison to those measured in vessel S, at all initial pressures. In order to ascertain these systematic differences, it is useful to examine the flame dimension at the end of an early stage with various durations: τ, 3/4. τ, 1/2. τ, 1/4. τ). The results are given in table 2, where the flame radii in vessel S were obtained from the burnt mass fraction calculated by means of equations (5), (6) and (7). The three models give close values of the flame radius, for all time intervals considered in data evaluation. It is worth to mention that flame reaches a radius r b = 3.85 cm at the end of the early stage period defined by condition:δp = p o. In terms of relative values, the dimensionless flame radius defined as R b = r b /R = 0.77 at π = p 0 /p = 2.0. At this flame dimension, only the model developed by Oancea should be applied for a further examination of results, especially for those obtained in vessels C 1. A set of data are given in table 3, for measurements made at ambient initial pressure and temperature. In all explosion vessels, the flame reaches a radius R b = at the end of an early stage with the duration 1/4. τ and a radius R b = at the end of an early stage with the duration τ. For none of these cases, the stretch effect and the flame curvature (important at R b 0.1) should influence the value of normal burning velocity. It appears that any duration between 1/4. τ and τ is adequate for application of equation (1). The selection of the optimal duration of the early stage can be made after examination of the fit parameters obtained for regressions of Δp versus time t. Data referring to tests at various initial pressures and durations of the early stage, are given in tables 4 (vessel S) and 5 (vessel C 1 ). It can be observed that, for a certain burnt mass fraction during the early stage of the process, the dimensionless flame radius is much greater than the relative pressure increase (p/p e ), indicating its usefulness in the early detection of the deflagration initiation. For both closed vessels S and C 1, the cubic law coefficients k (and the corresponding burning velocities S u ) decrease when shorter ranges of data are examined i.e. 290 points (for Δp = 0.75 p 0 ) as compared to 315 (for Δp = p 0 ) at 1 bar initial pressure, in vessel S or 416 points (for Δp = 0.75 p 0 ) as compared to 454 (for Δp = p 0 ) at 0.6 bar initial pressure, in vessel C 1. For all examined systems, the standard deviation of k increases up to 25% at τ/4, due to a large noise of pressure measurements immediately after explosion ignition i.e. when 1.0 π 1.2. According to F-values, the best correlations are obtained when the condition Δp = p o is fulfilled. Table 1 NORMAL BURNING VELOCITIES OF THE TEST MIXTURE, AT VARIOUS INITIAL PRESSURES AND AMBIENT TEMPERATURE, FROM CUBIC LAW EQUATION. RESTRICTION: 1.0 π 2.0 Table 2 THE FLAME RADIUS OF C 3 -AIR COMBUSTION IN SPHERICAL VESSEL S, FOR VARIOUS DURATIONS OF THE INITIAL STAGE OF FLAME PROPAGATION, AT p 0 = 1 bar REV. CHIM. (Bucharest) 62 No

4 Table 3 THE DIMENSIONLESS FLAME RADIUS R b CALCULATED BY MEANS OF OANCEA EQUATION, FOR VARIOUS DURATIONS OF THE INITIAL STAGE OF FLAME PROPAGATION AT p 0 = 1 BAR, IN VESSELS S, C 1 Table 4 THE CUBIC LAW CONSTANT OF PRESSURE RISE, k, AND NORMAL BURNING VELOCITY, S u, FOR COMBUSTION OF THE TEST MIXTURE IN SPHERICAL VESSEL S, AT VARIOUS DURATIONS OF THE EARLY STAGE Table 5 THE CUBIC LAW CONSTANT OF PRESSURE RISE, k, AND NORMAL BURNING VELOCITY, S U, FOR COMBUSTION OF THE TEST MIXTURE IN CYLINDRICAL VESSEL C 1, AT VARIOUS DURATIONS OF THE EARLY STAGE Conclusions Examination of transient values of pressure during the initial stage of gaseous explosions, in three closed vessels, afforded calculation of several deflagration parameters: the burnt mass fraction, the flame radius and the burning velocity, with high relevance towards the design of active protection devices and for safety recommendations REV. CHIM. (Bucharest) 62 No

5 The early stage, defined in previous papers by the condition Δp = p o (duration =τ), was further divided into shorter time intervals (durations: 3 τ/4; τ/2 and τ/4) and for each duration, the burnt mass fractions and the flame radius were calculated. The three models used for this purpose provide close values of the flame radius in spherical vessel S, for any time interval taken into account. The validity of the cubic law was also examined at various fractions from the early stage (τ; 3 τ/4; τ/2 and τ/4). The best agreement of burning velocity from cubic law coefficients (present results) with literature data was obtained by using the restricting condition, Δp = p o, for data obtained in the spherical explosion vessel. Acknowledgement: This work was supported by CNCSIS UEFISCSU, project number PNII IDEI code 458/2008. References 1.BABKIN, V.S., BABUSHOK, V.I., Combustion, Explosion and Shock Waves, 13, nr.1, 1977, p ZABETAKIS, M.G., U.S. Departament of Interior, Bureau of Mines, Bulletin 627, RAZUS, D., MOVILEANU, C., OANCEA, D., J.Loss Prev. Process Ind., 19, 2006, p RAZUS, D., MOVILEANU, C., OANCEA, D., Burning velocity evaluation from pressure evolution during the early stage of closed-vessel explosions, Proc. 19-th Intern. Symp. Comb. Proc., Beskidy, Poland, 2005, p RAZUS, D., BRINZEA, V., MITU, M., OANCEA, D., Energy & Fuels, 24, 2010, p BRINZEA, V., MITU, M., RAZUS, D., OANCEA, D., Rev. Roum. Chim, 55, 2010, p GIBBS, G., CALCOTE, H., J.Chem. Eng. Data, 4, 1959, p GUNTHER, R., JANISCH, G., Chemie-Ing. Techn., 43, nr. 17, 1971, p TSENG, L., ISMAIL, M., FAETH, G., Combust. Flame, 95, 1993, p BOSSCHAART, K.J., DE GOEY, L.P.H., BURGERS, J.M., Combust. Flame, 136, 2004, p ZHANG, Z., HUANG, Z., WANG, X., XIANG, J. WANG, X., MIAO, H., Combust. Flame, 155, 2008, p BRADLEY, D., GASKELL, P.H., GU, X.J., Combust. Flame, 104, 1996, p LEWIS, B., VON ELBE, G., Combustion, Flames and Explosion of Gases, 3-rd. Ed., Acad. Press, New York and London, 1987, Chap GRUMER, J., COOK, E.B., KUBALA, T.A., Combust. Flame, 3, 1959, p OANCEA, D., RAZUS, D., IONESCU, N.I., Rev. Roum. Chim., 39, 1994, p RAZUS, D., BRINZEA, V., MITU, M., OANCEA, D., Rev. Chim.(Bucharest), 60, nr. 8, 2009, p RAZUS, D., MOVILEANU, C., BRINZEA, V., OANCEA, D., J.Hazard. Mater., 135, 2006, p. 58 Manuscript received: REV. CHIM. (Bucharest) 62 No

EXPLOSION PRESSURES OF CONFINED DEFLAGRATIONS PROPAGATING IN STOICHIOMETRIC GASEOUS MIXTURES OF LOWER ALKANES WITH AIR

EXPLOSION PRESSURES OF CONFINED DEFLAGRATIONS PROPAGATING IN STOICHIOMETRIC GASEOUS MIXTURES OF LOWER ALKANES WITH AIR Department of Physical Chemistry 4-12 Regina Elisabeta Blvd, District 3, Bucharest phone: +40-21-3143508; fax: +40-21-3159249 ISSN: 1844-0401 ARS DOCENDI PUBLISHING HOUSE Sos. Panduri 90, District 5 Bucharest