Effect of the concentration distribution on the gaseous deflagration propagation in the case of hydrogen/oxygen mixture

Transcription

1 Effet of the onentration distribution on the gaseous deflagration propagation in the ase of hydrogen/oxygen mixture Isabelle Sohet, Philippe Gillard, Florent Guelon To ite this version: Isabelle Sohet, Philippe Gillard, Florent Guelon. Effet of the onentration distribution on the gaseous deflagration propagation in the ase of hydrogen/oxygen mixture. Journal of Loss Prevention in the Proess Industries, Elsevier, 26, 19, pp <hal > HAL Id: hal Submitted on 9 De 211 HAL is a multi-disiplinary open aess arhive for the deposit and dissemination of sientifi researh douments, whether they are published or not. The douments may ome from teahing and researh institutions in Frane or abroad, or from publi or private researh enters. L arhive ouverte pluridisiplinaire HAL, est destinée au dépôt et à la diffusion de douments sientifiques de niveau reherhe, publiés ou non, émanant des établissements d enseignement et de reherhe français ou étrangers, des laboratoires publis ou privés.

2 Effet of the onentration distribution on the gaseous deflagration propagation in the ase of H 2 /O 2 mixture I. Sohet + - P. Gillard * - F.Guélon + Laboratoire Energétique Explosions Strutures - EA125 - Université d Orléans + ENSIB 1 boulevard Lahitolle BOUGES edex Frane isabelle.sohet@ensi-bourges.fr Fax : * IUT 63 avenue De Lattre de Tassigny BOUGES edex Frane Abstrat The investigation of flame propagation aompanying the explosions of unonfined gaseous reative louds whih are diluted in atmosphere ambient is a fundamental interest in the analysis of industrial risk assessment. Following the previous work Sohet, Guelon, & Gillard (22), an experimental study is onduted on a deflagration of a hydrogen/oxygen gaseous loud whih is released in air. The burning veloity is diretly or indiretly measured. The flammability limits of the non homogeneous loud has been as well investigated. Key words : deflagration, explosion, hydrogen, non uniform reative mixture Introdution During an explosion, one knows that two modes of explosion are possible: the deflagration and the detonation. However, the deflagration proess is that probable during an aidental explosion. Indeed, an analysis of 1 major aidents made by Gujan (1978) over one period going from 1921 to 1977 did not reveal any mode of detonation. The deflagration proess study in a ontext of industrial safety is thus of a apital interest. The hoie of an H 2 /O 2 ombustible mixture presents a real interest. Indeed, hydrogen is strongly present in industry and its development as a fuel of the future is very probable following eologial onsiderations ("lean" ombustion), geopolitial onsiderations (researh of an energy independene to the Middle East) and the probable end of the hydroarbon reserves within one entury. Following an industrial aident where there is a gas leakage in surrounding air, the gas loud obtained is not uniform. However it is known that the presene of onentration gradients in a gas mixture has a strong impat on flame propagation during the ombustion of this mixture. It is thus essential to have a better knowledge of the flame propagation in non-uniform mixtures for a better understanding of aidental vapour loud explosion. From a theoretial point of view [Cambray, & Deshaies, 1978; Deshaies, & Clavin, 1979; Deshaies, & Leyer, 198], it appears that the overpressure generated by a divergent spherial unonfined deflagration depends on the flame aeleration. However, flame aeleration depends on the onentration gradient of the gas mixture in whih it is propagated. With a seurity aim, study of pressure profile onseutive to a non-uniform gas loud deflagration thus represents a first approah for a better omprehension of deflagration proess in non-uniform mixture. From an experimental point of view, several studies were undertaken. Most of the work performed with non-uniform mixtures deals with the propagation of flames in diretions normal to the gradient (Phillips (1965), Hirano, Suzuki, Mashiko, &.Iwai (1977), Girard, Huneau, abasse, & Leyer (1978), Badr & Karim (1984), Karim & Lam (1986), Whitehouse, Greig & Koroll (1996)). Most of this work was performed in losed apparatus, a part from the analysis of Girard et al whih has been onduted in ambient air. In the latter ase, the gradients were obtained with onentri soap bubble ontaining fuel and oxidizer. A signifiant work was arried out by Whitehouse, Greig & Koroll (1996) on the ombustion of non-uniform mixtures hydrogen-air. The tests were arried out in a vertial ylinder of 1.7 m 3 (radius of 1.5 m, height of 5.7 m). The hydrogen gradient was suh as the weakest hydrogen onentrations were in the low part of the ylinder and strongest ones in the high part. For an ignition at the top of the ylinder, the differenes between ombustion pressures of gradient and well-mixed gases are most signifiant when the average onentration of hydrogen is less than 1%. This limit oinides with the downward propagation limit for hydrogen (mixtures ontaining between 4% and 9% hydrogen will only propagate in the bouyany assisted upward diretion). In a onentration gradient, even though the average hydrogen onentration was below the downward propagation limit, the loal onentration at the igniter position was well above this limit. This allowed a large fration of the hydrogen to be burned, resulting in higher ombustion pressures. For the same reason, the flame veloities and the rising rate of pressure observed in gradients were muh higher than in well-mixed gases having similar average 1

3 quantities of hydrogen and arrival times of wave pressure were muh shorter. For an ignition at the bottom of the ylinder, the ombustion pressures were about the same for gradient and well-mixed tests exhibiting average hydrogen ontentrations below 14%. Above this value, the gradients produed lower ombustion pressures than well-mixed gases having similar quantities of hydrogen. This was attributed to a higher burning fration in the wellmixed gases. Arrival times of pressure wave were muh shorter in the homogeneous mixtures than in the stratified mixtures. Indeed, most of the time to peak pressure in the gradient burn was the time that the flame kernel took to travel from the ignition point to the hydrogen rih mixtures at the top of ylinder. In this paper, we analyse the pressure wave propagation resulting from a non-uniform gas mixture deflagration, the burning veloity and the flammability limits. The experimental results are given in terms of the diffusion of the gas mixture for different initial harges and different ignition loations. The present investigation is onduted at a small sale. The interest of a small sale experimental analysis is to attain an understanding of the phenomena, to isolate more easily the governing parameters and to reprodue a great number of times the experiments ontrary to the tests onduted at large sales. Experiments 2.1 Experimental setup The experimental method used in this study to simulate the diffusion and the explosion of a gas loud is that of the soap bubble. The omplet experimental setup was already presented in a previous paper in ase of the detonation proess (Sohet, Lamy, & Brossard (2). The hemispherial harges (aqueous onfinement) are formed on a horizontal plate ( m) using metal rings (radius.3 < <.8 m). In this study, the gas mixture used is a stoehiometri hydrogen-oxygen mixture. The non-uniform louds are obtained by the rupture of aqueous onfinement: the diffusion of the gas mixture in surrounding air an then be arried out and the onentration gradient is diretly related to the diffusion time noted by t. In experiments (fig. 1) the aqueous onfinement is broken by an eletromagneti striker and the diffusion time (i.e. time between the rupture of aqueous onfinement and gas loud ignition) is fixed by a time delay line and ontrolled by a stop wath. The ignition of the gas mixtures is obtained by means of an eletri spark. The two brass eletrodes are separated from 4 mm (inter-axial distane of 6 mm) and the eletri power neessary to obtain the spark is stored in a 2 µf ondenser under a voltage of 35 V. The nominal energy then delivered during the ignition is mj. The density of the hydrogen-oxygen gas loud is lower than that of the air, its diffusion in the surrounding atmosphere is thus asending. To take speifiity into aount, an altitude ignition devie was thus manufatured (fig. 1). Thus, the ignition of the gas loud an be arried out at any point of spae within the explosion limits. The ignition loation is referened by i, Z i, where i is the radial distane starting from the enter of the plate and Z i the altitude level from the plane surfae. A pressure gage equipment allows to haraterize the shok wave generated by the explosion of the gas loud: five piezoeletri pressure gauges are laid out radially, along the same diretion, on the plane surfae ( =.117,.191,.29,.491 and.692 m measured starting from the enter of the plate). Numerial osillosopes allow to visualize and aquire the pressure profiles amplified by the harge amplifiers onneted to the sensors. We use an optial system to measure the flame veloity. It ontains an interferential filter at 75 nm with a bandwidth of 1 nm orresponding to an OH band, and holds a fousing lens. This system allows to determine a fast signal (~1µs) at a preise point of the dispersion of the H 2 /air mixture Pressure waves profiles The evolution of the pressure indued by the deflagration of a stoehiometri hydrogen-oxygen mixture initially onfined in a hemispherial volume of initial radius.7 m is represented for various diffusion times of the loud in the air (fig. 2). The pressure profiles were reorded by a pressure sensor loated to.117 m of the enter of the explosion. The evolution of the pressure wave aording to the diffusion time has been desribed in a previous paper [Sohet, Guelon, & Gillard, 22]. In the present study, we will study more preisely a speifi phenomenon that has been 2

4 observed in the previous paper: the appearane of a seond peak in the inreasing front of the positive phase of pressure wave. In this ase ( =.7 m, fig. 2), this seondary peak of overpressure appears in the inreasing front of the positive phase for a diffusion time t of 14 ms. Then, as the diffusion time inreases, seondary peak is more detahed from the prinipal peak of overpressure. Thus, between the profile of appearane of this seondary peak ( t = 14 ms) and the signal taken to t = 22 ms, one notes that the seondary peak moved 3 ms away from the main peak. This phenomenon is explained by the division of the gas harge in two louds aused, after a ertain time, by the diffusion of the loud in the surrounding air (mushroom shape loud). The seondary peak omes from the explosion of the low part of the loud. Then, when the diffusion time inreases, the distane between the two gas harges (high part and low part of the loud) inreases and the seondary peak is detahed, then moves away from the prinipal peak of overpressure (fig. 2). The overall study of the pressure waves as a funtion of time of diffusion (profiles not represented), for various initial radius of onfinement of the loud and various ignition loation, shows diffusion times where a seondary peak of overpressure is observed. These results are synthesized in the table 1. The results of the table onfirm the division of the initial harge in two frations related to the diffusion: diffusion time orresponding to the appearane of the seondary peak inreases with the initial radius of onfinement and no appearane of the seondary peak is noted for an altitude ignition higher than.3 m and for a radial ignition higher than.3 m ( =.7 m). For result analysis, the following terms are defined: edued radial distane (m.mj -1/3 ) : = ; 3 E edued positive impulse (bar.ms. MJ -1/3 I+ ) : 3 E ; P+ elative positive peak overpressure : ; P edued arrival time (ms. MJ -1/3 ) : Adimensional number D ta E ; 3 who represents ratio of the distane between ignition soure and the sensor (D ) on the initial radius of onfinement ( ). The distane D in the ase of a radial ignition, is then equal to and, in the ase of an altitude ignition to 2.3. Uniform loud Volume influene +Z. 2 2 i elative positive peak overpressure (fig. 3a), redued positive impulse (fig. 3b) and redued arrival time (fig. 3) are plotted versus for various radial distanes from the sensor ( =.117,.191,.29,.491 and.692 m). The urves show that the inrease of the initial radius of onfinement yields an inrease of the relative positive peak overpressure and the redued positive impulse, and a derease of the redued arrival time. Based on the experimental results obtained, it is possible to provide an empirial orrelation of eah parameter observed aording to the radial oordinate (m) and of the initial radius of onfinement (m) : For relative positive peak overpressure : + P = for.1 ( m).7 P and ( ).4 m.8 3

5 For redued positive impulse : + I = E For redued arrival time : ta = E for.1 ( m).7 and ( ).4 m.8 for.1 ( m).7 and ( ).4 m.8 It is signifiant to note that these orrelations were given, and thus are valid only for the radial oordinates ( ) and the initial radius of onfinement mentioned Loation ignition influene adial ignition elative positive peak overpressure (fig. 4a), redued positive impulse (fig. 4b) and redued arrival time (fig. 4) are presented aording to the non-dimensional number D / for various radial ignition ( i =.,.1,.3,.5,.7 m, Z i =. m). The observation of the figures shows that the inrease of the radial oordinate ignition i yields a redution of the relative positive peak overpressure and of the redued positive impulse. However, the redued arrival time does not vary muh with the inrease of the radial oordinate ignition exept for ignition at the periphery of the hemispherial onfinement ( =.7 m) whih seems onsistent with the explosibility limit of the loud. The analysis of the experimental points, enables to assoiate empirial orrelations that show the evolution of relative positive peak overpressure and redued positive impulse as a funtion of the non-dimensional number D / and ignition radius i (m): For relative positive peak overpressure : + P =.2982 e i P D For redued positive impulse : + I =.7671 e 3 E i D D and for i ( m).7 D and for i ( m).7 Keeping away the urve that exhibits the redued arrival time as a funtion of the non-dimensional number D / for the ignition radial oordinate i =.7 m, one obtains a simple empirial orrelation between the redued arrival time and the adimensional number D / : Altitude ignition t a D =.845 E D for The evolution of relative positive peak overpressure (fig. 5a), redued positive impulse (fig. 5b) and redued arrival time (fig. 5) are represented versus the adimensional number D / for various altitude ignition ( i =. m, Z i =.,.1,.3,.5,.7 m). The experimental results show two phases for relative positive peak overpressure : in the first plae we note : P P P (Z i =. m) < (Z i =.1 m) < (Z i =.3 m) P P P It is explained by an ignition whih is more entered on the volume of gas. The ignition soure approahes the entre of gravity of the hemispherial loud. The flame propagation an be arried out either in the all spae and or in half spae as in the ase of the entered ignition ( i =. m, Z i =. m). 4

6 furthermore we note : P P P (Z i =. m) > (Z i =.5 m) > (Z i =.7 m) P P P On the top of the hemispherial harge, the radial distribution of gas beomes less signifiant and, as in the ase of a radial ignition, it is logial that the relative positive peak overpressure dereases ompared to a entered ignition ( i =. m, Z i =. m). The experimental data related to the redued positive impulse are less ontrasted than those of the relative positive peak overpressure. The values of the redued positive impulse observed for altitude ignition of.,.1 and.3 m are nearly idential and one finds a derease of these values for Z i =.5 et.7 m. Thus, it seems that the entring of the ignition to the gas harge has a signifiant impat on relative positive peak overpressure as opposite to the redued positive impulse. The redued arrival time versus to the adimensional number D / is independent of altitude ignition. As in the ase of a radial ignition, the experimental points lead to a simple empirial orrelation between the redued arrival time and the adimensional number D / : 2.4. Non-uniform loud Centered ignition t D =.7584 E a D for The evolution of relative positive peak overpressure (fig. 6a), redued positive impulse (fig. 6b) and redued arrival time (fig. 6) are presented as a funtion of the adimensional number D / for a entered ignition of non-uniform (diffusion timet = 2, 4, 6, 8, 1, 14, 18 and 2 ms). For diffusion times of 4 and 6 ms, a signifiant inrease in relative positive peak overpressure ompared to that obtained in the ase of a uniform loud is noted. This disturbane is probably due to the rupture mode of the soap bubble onfinement. Under these onditions while urve obtained for diffusion times of gas of 4 and 6 ms, one observes a derease in relative positive peak overpressure as a funtion of diffusion time. An empirial orrelation an be dedued between relative positive peak overpressure, the adimensional number D / and the diffusion time t (ms): + P =.2935 e -.42t P D D for and t(ms) 2 The redued positive impulse also dereases with the inrease of the diffusion time of gas in surrounding atmosphere. At this point, still negleting the two unmathed diffusion times, it is possible to define an empirial orrelation between the redued positive impulse, the adimensional number D / and the diffusion timet (ms): + I =.8326 e 3 E -.33t D D for and t(ms) 2 The redued arrival time as a funtion of the adimensional number D / is independent of diffusion time. The examination of the experimental points leads to a simple empirial orrelation between the redued arrival time and the adimensional number D / : t a D =.7166 E D for

7 Influene of the ignition loation adial ignition The experimental urves obtained for a radial ignition of non-uniform loud (diffusion time t = 4, 8, 1, 14, 18 and 2 ms) are presented as a funtion of the adimensional number D / for two radial ignitions ( i =.3 and.5 m, fig. 7-8). The relative positive peak overpressure ( i =.3 m fig. 7a, i =.5 m fig. 8a), redued positive impulse ( i =.3 m Fig. 7b, i =.5 m Fig. 8b) and redued arrival time ( i =.3 m fig. 7, i =.5 m fig. 8) are study. At a radial ignition of.3 m, the relative positive peak overpressure and redued positive impulse do not flutuate strongly as the diffusion time inrease ontrary to the study related to the entered ignition of non-uniform loud. However, one finds the phenomenon observed at t = 4 ms for a entered ignition and allotted to the impat of the rupture of onfinement : a signifiant inreaseof the relative positive peak overpressure and redued positive impulse ompared to those obtained in the ase of a uniform loud. In the ase of a radial ignition of.5 m, it is interesting to note that the relative positive peak overpressure is maximum for diffusion time of 14 and 2 ms whereas for these same time the redued positive impulse is minimum. The redued arrival time aording to the adimensional number D / is independent of the diffusion time of gas in the surrounding air to t = 14 ms for i =.3 m, and to t = 8 ms for i =.5 m. For these two radial ignitions and within their limits of diffusion time, it is still possible to dedue a simple empirial relation between redued arrival time and the adimensional number D / : For i =.3 m : t a D =.8231 E D for and t 14 ms For i =.5 m : t a D =.9285 E D for and t 8 ms Altitude ignition The experimental results obtained for an altitude ignition of non-uniform loud (diffusion time t = 2, 4, 6, 8, 1, 14, 18 et 2 ms) are presented as a funtion of the adimensional number D / for two altitude ignitions (Z i =.5 et.7 m, fig. 9-1). The relative positive overpressure peaks (Z i =.5 m fig. 9a, Z i =.7 m fig. 1a), redued positive impulse (Z i =.5 m fig. 9b, Z i =.7 m fig. 1b) and redued arrival time (Z i =.5 m fig. 9, Z i =.7 m fig. 1) are studied. The urves of relative positive overpressure peak show the existene of the non-uniform loud envelope that is more favorable to the explosion. This area moves vertially with the diffusion time t : for Z i =.5 m, relative positive peak overpressure and reahes a maximum when the diffusion time t is of the order of 6 and 8 ms and for Z i =.7 m, it is maximum to t = 14 and 18 ms. The importane and dangerosity of the asending diffusion harater of the hydrogen-oxygen stoehiometri mixture in the air then is well highlighted: the safety dereases with the inrease of the diffusion time of the loud in the air if there is a potential risk of altitude ignition of the loud. The experimental results for redued positive impulse (fig. 9b and 1b) are less ontrasted than for relative positive peak overpressure, but they follow the same tendeny: redued positive impulse values for Z i =.5 m are maximum to t = 8 and 6 ms, and, for Z i =.7 m, they are slightly similar and independent of diffusion time. There still, for the altitude ignition used, that is being the redued arrival time aording to the adimensional number D / is independent of the diffusion time of gas in surrounding air. An empirial relation between redued arrival time of arrival and adimensional number D / is then obtained for eah altitude ignition: For Z i =.5 m : t a D =.7218 E D for

8 For Z i =.7 m : t a D =.7476 E D for emark onerning the arrival time In the ase of the redued arrival time, we obtained empirial laws whih were independent of the ignition loation (uniform loud), and of the diffusion time of the loud (non-uniform loud) of the following form: t a 3 E a b D = The values of the oeffiients a and b an be ompared aording to the onfiguration of the experiment. Table 2 summarizes the various experimental onfigurations for whih an empirial orrelation an be obtained, by speifying the values of a and b dedued and the range of validity they are based on. Data analysis of table 2 enables to dedue a single empirial law making that yields the redued arrival time as a funtion of the adimensional number D / in the ase of a uniform or non-uniform loud ( t (ms) 2 ) ignited in any point of its vertial axis ( i =. m, t a D =.736 E Z i (m).7 ). It an be in the form: for t (ms) 2 and i =. m,. Z i (m).7 The fator.736 has been obtained by arrying out an average of the a values of lines 2, 3, 4 and 5 of table 2. The standard deviation assoiated to this average represents 2.73 % of this latter. The exponent value has been obtained by arrying out an average of the b values of lines 2, 3, 4 and 5 of table 2. The standard deviation assoiated to this average represents 1.81 % of this latter. 2.6 Experimental burning veloity The burning veloity D an be alulated in two ways: a diret or an indiret method. The diret method is based on the use of the optial transduer. The burning veloity is then simply given by d/t ratio where d is the optial transduer-ignition distane and t the arrival time of flame front to the optial transduer (fig.11). The indiret method is based on the analogy of piston proposed by Deshaies, & Clavin (1979). This model onsists in splitting the flow field of a deflagration in two zones: inompressible and aousti. The solution gives the pressure P at the radius and time t as a funtion of flame propagation F (t), the expansion elerity of flame front and its aeleration. By two suessive integrations of the pressure signal, the history of flame is dedued. The burning veloity is then defined by the ratio of the expansion elerity of flame front over the expansion ratio (fig.12). Atually, the real limitations of this model are not known, a priori. However, this model is based on the uniform gaseous loud. Therefore, we use it only for uniform H 2 /O 2 mixture (i.e. with no diffusion time delay). 3 Burning veloity 3.1. Uniform gaseous loud The burning veloity D, regarded as onstant, of a laminar spherial flame being propagated in a hemispherial uniform gas mixture an be alulated from the fundamental flame veloity and the ratio of expansion (ratio of the density of the burned gases to that of fresh gases) by using the relation: D = α F For a stoehiometri hydrogen-oxygen mixture, the fundamental flame veloity is of 1.73 m.s -1 (Chemkin ode), the density of fresh gases is of.493 kg.m -3 to T = 298 K and the density of the burned gases is of.58 kg.m -3 to 376 K. One then obtains a burning veloity D onstant of 91.2 m.s -1. The burning veloity measured using the optial transduer, for a uniform loud ignited in its enter, are onstant but have a dissymmetry with respet of the axis of measurement : m.s -1 along to the radial axis and 73.1 m.s -1 along to the vertial axis. However, one an notie a good adequay of the value of the speed as a funtion of the radial axis with the theoretial value of the burning veloity D onstant. 1 V 7

9 From these results, three onlusions an be drawn: 1. The good agreement between the values of the burning veloities obtained diretly or indiretly. 2. The veloity burning in a uniform loud ignited in its entre (initial of ontainment of.7 m) is onstant. 1 V 3. The relation ( D = α F ) provides a good approximation of the veloity burning, but it does not desribe the dissymmetry observed in the experiments along the and Z axes whih may be explained by the effet of gravity for the vertial omponent of the veloity and to roughness of the surfae for the radial omponent veloity Non-uniform gaseous loud The experimental results onerning the speeds of flame measured in experiments using the optial transduer yield the following remarks 1. For a entered ignition soure, the flame aelerates aording in the asending diretion of the loud. The length rossed by the flame inside the fresh gas is more signifiant along Z (.12 m) that is along to (.25 m): the maximum flame veloity along to is about 3-4 m.s -1 and about 5-6 m.s -1 along Z. 2. For a non-entered ignition soure in height, the measured radial flame veloity (optial transduer in Z = m, moved along to ) inreases by 4 to 7 m/s. The veloity also doubles when it is measured vertially (optial transduer in =. m, moved along to Z) between Z =.4 m and.8 m. Nevertheless, this veloity measurement is about twie smaller than the measured radial flame veloity: V Z =.5V. Along axis Z, with an ignition soure in height (Z i =.4 m), the flame rosses a homogeneous zone. The mixture is poor at the point of ignition, the flame veloity (V Z remains lower than the veloity obtained in a stoehiometri mixture. V is then definitely higher than V Z beause the flame is aelerated by the presene of a gradient of reativity whih, although negative, plays a role similar to that a turbulene zone. 4 Flammability limits In the industrial safety ontext, we have experimentally investigated the explosion limits of a given non-uniform gas loud in order to know the real zones of ignition of a loud whih diffused in the air. It is a apital interest in this ontext. For a fixed ignition (entered, radial and in height), we investigated the time of diffusion orresponding to the point where an ignition of the loud beomes impossible (fig ). Taking into aount the operating onditions, it is signifiant to note that the explosion limits measured in these experiments an vary. In order to express the results we systematially defined an explosion limit with a probability equals to and a limit of inflammability with a probability equals to 1. Beyond the first limit, the ignition of the loud is impossible, below the seond one it systemati and between these two, it is random. The observation of the temporal explosion limits yields the following remarks: 1. When the initial radius of onfinement inreases, the temporal explosion limits inrease. The larger the initial radius of onfinement, the greater amount of gas loated around soure of ignition seems to stagnate. Therefore, more time is required to reah the lower onentration limits hydrogen of the explosion of hydrogen (4%). 2. In the ase of an ignition soure elevation, the temporal explosion limits inreases with the height of ignition of the loud, but it is not the ase for a height of ignition lower than.5 m. One an suppose a ground effet (roughness of the table of experiments), whih ould be have an effet on the diffusion of the loud in the surrounding air. 3. When the radius of ignition inreases, the temporal explosion limits derease. 5 Disussion - Conlusion The present experiments, onduted at laboratory s sale, for uniform and non-uniform 2H 2 + O 2 mixtures allow to haraterize the pressure wave onseutive to the deflagration as a funtion of the diffusion time and the ignition loation. In uniform mixtures, the analysis of the pressure profiles enables to provide empiri laws on the redued arrival time, relative positive peak overpressure and the redued positive impulse aording to the sensor loation and to the initial radius of the gas load. In non-uniform mixtures the pressure profiles highlighted the appearane of a seondary peak in the inreasing front of the positive phase. This seondary peak is detahed from the prinipal peak of pressure as the diffusion time 8

10 inreases. For suffiiently long diffusion times, the loud adopts a mushroom shape. The seondary peak orresponds to a weak primary explosion before the main explosion of the rest of the loud. This primary explosion an be defined as the explosion of an under-load of very low volume loated at the base of mushroom. The division of the initial harge in two frations is onfirmed for entered, eentred ignition (on and Z), and is validated as a funtion of the volume of the initial harge. The harateristis of pressure profiles (arrival time, positive overpressure, positive impulse) ould be expressed in terms of redued variables aording to the diffusion time and the ignition loation. An empirial relation between redued arrival time of pressure wave and adimensional number D/ is obtained independently of the diffusion time.conerning the burning veloity the orrelation obtained for a uniform gaseous loud between experiments and numerial results are in a good agreement. Hene, the burning veloity is equal to m.s -1 by using the optial transduer, is m.s -1 by applying the piston model (Deshaies, & Leyer 198), and is 96.2 m.s -1 with the modelling. In ase of the non uniform gaseous loud, the experimental results show that the flame veloity depends on the reativity gradient, on the omponents V and V Z. The investigation of temporal inflammability limits show that an explosion an be obtained: i) even though the ignition soure is not at the enter of the explosive loud ; ii) even though the gaseous mixture is dispersed into surrounding air. Hene, the importane and dangerosity of the asending harater diffusion of the hydrogen-oxygen stoehiometri mixture in the air is well highlighted. The safety dereases as the diffusion time of the loud in the air inreases. There is a potential risk of altitude ignition of the loud. The authors are very muh aware that this study was arried out at a laboratory sale and should now be extended to large sale tests oupled to a modelling. Furthermore, the empirial relations whih are defined versus the diffusion time ould be expressed as a funtion of the evolution of the onentration. This point will be onduted as soon as possible. eferenes Badr, O., & Karim, G.A (1984), Flame propagation in stratified methane-air mixtures, J.Fire Si.2, Cambray, P., & Deshaies, B. (1978). Eoulement engendré par un piston sphérique : solution analytique approhée, Ata Astronautia, vol.5, Deshaies, B., & Clavin, P. (197). Effets dynamiques engendrés par une flamme sphérique à vitesse onstante, Journal de méanique, vol. 18, n 2, 213. Deshaies, B., & Leyer, J.C. (198), Flow field indued by unonfined spherial aelerating flames, Comb. and Flame,. Vol. 4, Gillard P., & oux M. (22) Study of the radiation emitted during the ombustion of pyrotehni harges. Part I: Non stationary measurement of the temperature by means of a two-olor pyrometer, Propellants, Explosives, Pyrotehnis vol. 27, Girard, P., Huneau, M., abasse, C., & Leyer, J.C. (1978), Flame propagation through unonfined and onfined hemispherial stratified gaseous mixtures. Pro. 17 th Symp. on ombustion, Combustion Institute, Combustion Institute, Gujan, K. (1978). Unonfined Vapor Cloud Explosions, Gulf Publishing Company, Hirano, H., Suzuki, T., Mashiko, I. & Iwai, K. (1977), Flame propagation through mixtures with onentration gradients. Pro. 16 th Symp. on ombustion, Combustion Institute, Karim G.A., & Lam, H.T. (1986), Ignition and flame propagation within stratified methane-air formed by onvetive diffusion, Pro. 21 st Symp. on ombustion., Combustion Institute, Magnussen, B.F., & Hjertager, B.H. (1976), On mathematial models of turbulent ombustion with speial emphasis on soot formation and ombustion, Pro. 16 th Symp. on ombustion, Combustion Institute, Marinov, N.M., Westbrook, C.K. & Pitz, W.J. (1999). Detailed and global hemial kinetis model for hydrogen, Contrat No. W-745-ENG-48, Lawrene Livermore National Laboratory, P.O. Box 88,L 298, Livermore, CA , USA, Phillips, H. (1965), Flame in a buoyant methane layer, Pro. 1 th Symp. On ombustion, Combustion Institute, Sohet, I., Guelon F., & Gillard, P. (22). Deflagrations of non-uniform mixtures : A first experimental approah, Journal of physis, vol. 12, 7-273, Sohet, I., Lamy T. and Brossard J. (2), Experimental investigation on the detonability of non-uniform gaseous mixtures, Journal Shok Waves, vol. 1, 363, 2. 9

11 Whitehouse, D.., Greig, D.., & Koroll G.W (1996). Combustion of stratified hydrogen-air mixtures in the 1.7 m 3 Combustion Test Faility Cylinder, Nulear Engineering and Design,

12 Symbols D : burning veloity (m.s -1 ) D : distane between ignition soure and the pressure gauge (m) E : energy released by the explosion of gaseous harge (MJ) I + : positive impulse (bar.ms) P : atmospheri pressure (bar) : distane, on the plane surfae, of the pressure gauge from the enter of the plate (m) i : radial distane of the ignition loation from the enter of the plate (m) : radius of initial harge (m) t a : arrival time (ms) V F : fundamental flame veloity (m.s -1 ) V : radial flame veloity (m.s -1 ) V Z : vertial flame veloity (m.s -1 ) Z i : altitude level of the ignition loation from the enter of the plate (m) P + : positive overpressure (bar) t : diffusion time (ms) 11

13 (m) Time delay of diffusion for seondary peak appearane (ms) Z i (m) Time delay of diffusion for seondary peak appearane (ms) i (m) Time delay of diffusion for seondary peak appearane (ms) i =. m Z i =. m i =. m =.7 m Z i =. m =.7 m none.4 none none.5 none.6 none.6 none.7 none.7 none Table 1: Diffusion time where the appearane of a seondary peak of overpressure is observed for various sizes of initial loud in entered ignition, and for louds with a onfinement of radius equal to.7 m in eentri ignition. 12

14 Test parameters ( =.7 m). i(m).7, Z i =. m Uniform loud (t = ms ) i =. m,. Z i(m).7 Uniform loud (t = ms ) i =. m, Z i =. m Non-uniform loud ( t (ms) 2 ) i =. m, Z i =.5 m Non-uniform loud ( t (ms) 2 ) i =. m, Z i =.7 m Non-uniform loud ( t (ms) 2 ) i =.3 m, Z i =. m Non-uniform loud ( t (ms) 2 ) i =.5 m, Z i =. m Non-uniform loud ( t (ms) 2 ) a b Validity range i(m) Z i(m) t (ms) t (ms) t (ms) t (ms) t (ms) 8 Table 2 : Empiri laws for redued arrival time. 13

15 Altitude ignition ( i, Z i ) Z Pressure wave upture of onfinement Pressure sensors O Figure 1: Experimental setup Initial gaseous harge Centered ignition ( i =. m, Z i =. m) 14

16 Seondary peak Prinipal peak Seondary peak Seondary peak Prinipal peak Prinipal peak Seondary peak Prinipal peak Prinipal peak Seondary peak Figure 2: Pressure profile ( =.117 m) resulting of a 2H 2 +O 2 mixture deflagration ( =.7 m) for different time delay of diffusion t. Centered ignition (, ). 15

17 a b Figure 3 : Uniform mixtures - elative positive peak overpressure (a), redued positive impulse (b) and redued arrival time () of pressure wave as a funtion of the adimensional number D / for various initial radius of onfinement. 16

18 a b Figure 4 : Uniform mixtures - elative positive peak overpressure (a), redued positive impulse (b) and redued arrival time () of pressure wave as a funtion of the adimensional number D / for various radial ignition. Initial radius of onfinement:.7 m. 17

19 a b Figure 5 : Uniform mixtures - elative positive peak overpressure (a), redued positive impulse (b) and redued arrival time () of pressure wave as a funtion of the adimensional number D / for various altitude ignition. Initial radius of onfinement :.7 m 18

20 a b Figure 6: elative positive peak overpressure (a), redued positive impulse (b) and redued arrival time () of pressure wave as a funtion of the adimensional number D / for various diffusion time. Initial radius of onfinement:.7 m. Centered ignition (, ). 19

21 a b Figure 7 : elative positive peak overpressure (a), redued positive impulse (b) and redued arrival time () of pressure wave as a funtion of the adimensional number D / for various diffusion time. Initial radius of onfinement :.7 m. adial ignition ( i =.3 m, Z i =. m). 2

22 Figure 1 : elative positive peak overpressure (a), redued positive impulse (b) and redued arrival a b Figure 8 : elative positive peak overpressure (a), redued positive impulse (b) and redued arrival time () of pressure wave as a funtion of the adimensional number D / for various diffusion time. Initial radius of onfinement :.7 m. adial ignition ( i =.5 m, Z i =. m). 21

23 a b Figure 9 : elative positive peak overpressure (a), redued positive impulse (b) and redued arrival time () of pressure wave as a funtion of the adimensional number D / for various diffusion time. Initial radius of onfinement :.7 m. Altitude ignition ( i =. m, Z i =.5 m). 22

24 a b Figure 1 : elative positive peak overpressure (a), redued positive impulse (b) and redued arrival time () of pressure wave as a funtion of the adimensional number D / for various diffusion time. Initial radius of onfinement:.7 m. Altitude ignition ( i =. m, Z i =.7 m). 23

25 Optial tranduer signal, V,6,4,2 -,2 -,4 -,6 -,8 t,5 1 1,5 Time, ms Figure 11: Optial transduer signal versus time 24

26 Burning veloity, m/s 14, 12, 1, 8, 6, 4, 2,, Time, ms Figure 12: Burning veloity alulated from pressure reord (at.692 m)- 2 H 2 +O 2-1 atm K 25

27 Diffusion time limit (ms) No inflammation P 1 Inflammability limit Probability P = Inflammability limit Probability P = 1 Initial radius (m) Figure 13 : Experimental temporal explosion limits of a non-uniform hydrogen-oxygen loud versus the initial radius of onfinement. Centered ignition ( i = m, Z i = m) 26

28 No inflammation Diffusion time limits (ms) P 1 Inflammability limit Probability P = Inflammability limit Probability P = 1 Altitude ignition (m) Figure 14 : Experimental temporal explosion limits of a non-uniform hydrogen-oxygen loud versus the altitude position of ignition soure. Deentered ignition ( i = m, Z i > m) 27

29 Inflammability limit Probability P = Inflammability limit Probability P = 1 Diffusion time limits (ms) No inflammation P 1 adial ignition (m) Figure 15 : Experimental temporal explosion limits of a non-uniform hydrogen-oxygen loud versus the radial position of ignition soure. Deentered ignition ( i > m, Z i = m) 28