BRHS /
DeflagrationDeflagration basicsEffect of obstacles on flame propagation and pressure build upFlame acceleration which is typically followed an ignition and laminar burning of hydrogen-air mixtures can have different origin. in fact, flame acceleration in all cases is connected with the presence and / or production of turbulence. One can distinguish at least three sources for turbulence production and therefore for flame acceleration: The particular process of the flame acceleration is a complex non-linear evolution of pressure perturbations linked to the combustion processes. However, generally it can be considered as a result of interaction of a series of relatively simple events. A flame during its propagation generates acoustic waves that can interact after reflections from the obstacles and channel walls with the flame front and develop flame perturbations through a variety of instability mechanisms. Such instabilities have been observed by Guenoche (1949) and Leyer & Manson (1971) in tubes, by Kogarko & Ryzkor (1992) in spherical chambers, and by van Wingerden & Zeeuwen (1983) and Tamanini & Chaffee (1992) in vented enclosures. Flame acoustic instabilities are usually associated with relatively slow flames in open atmosphere or enclosures that are free of obstacles. Turbulence inducing obstacles have shown to reduce relative contribution of acoustic instabilities on flame propagation and pressure build-up (Tamanini & Chaffee 1992). It has been also shown experimentally that such instabilities can be successfully eliminated by lining the enclosure or tube walls with materials that can absorb acoustic waves (TeodorczykA:1995a). The nature of the acoustic-flame instabilities have been reviewed by Oran & Gardner (1985) and Searby&Rochwerger (1991), Joulin (1994), Jackson et al.(1993) and Kansa&Perlee (1976) studied them in detail. These mechanisms cause flame distortion and wave amplification. Generally, if confinement and/or obstacles are present, several powerful instabilities may strongly influence flame propagation. These are Kelvin-Helmholtz (K-H) shear instability and Rayleigh-Tailor (R-T) density difference instability. In compressible flows the R-T instability is known as Richtmyer-Meshkov (R-M) instability. Both K-H and R-T instabilities are triggered when the flame is accelerated over an obstacle or through a vent. Detailed studies of flame propagation over single obstacle were performed by Wolanski&Wojcicki (1981) and Tsuruda&Hirano (1987). Finally, sufficient fast flames can produce a shock wave that can reflect off a wall and/or an obstacle and interact with the flame. As shown by Markstein&Somers (1953), Scarinci et al.(1993) and Thomas et al.(1997) this can result in severe flame distorsion and in extreme cases cause DDT. Gamezo et al.(2007) have studied flame acceleration in channels with obstacles using advanced 2D and 3D reactive Navier-Stokes numerical simulations. Computations have shown that during flame acceleration shock-flame interactions, R-T, R-M and K-H instabilities, and flame-vortex interactions in obstacle wakes are responsible for the increase of the flame surface area, the energy-release rate, and, eventually, the shock strength. As the flame passes obstacles (Fig. 1), it wrinkles due to R-T instability caused by the flow acceleration. The unreacted flow ahead of the flame becomes sonic. Noticeable shocks begin to form ahead of the flame and they reflect from obstacles and side walls, and interact with the flame triggering R-M instabilities. The K-H instabilities develop at the flame surface when a jet of hot burned material passes through a narrow part of the channel and a shear layer forms downstream of the obstacle. The elevated temperature behind shocks also contributes to the increased energy-release rate. Craven A.D. and Greig T.R. (1968) The development of detonation over-pressures in pipelines. IChemE Symposium Series, 25:41-50.(BibTeX) Effect of flow turbulenceLaminar flame propagation is intrinsically unstable. The nature of the flame instabilities is aerodynamic and possibly, dependent on the molecular weight of the fuel and the mixture composition, diffusional-thermal as well (MarksteinGH:1964). Flame instabilities give rise to flame-generated turbulence (SivashinskyGI:1979). In the most high-reactive fuel-oxygen mixtures such as stoichiometric hydrogen-oxygen and acetylene-oxygen these phenomena are the immediate cause of a run-up to detonation ((SokolikAS:1963) and (KogarkoSM:1965)). In relatively less-reactive fuel-air mixtures these phenomena seem to be controlled by the Huyghens principle owing to which waves tend to a plane geometry (KarlovitzB:1951). A further speed-up of the process is only possible under the appropriate boundary conditions. Rigid boundaries induce a structure in the expansion flow consisting of velocity gradients and turbulent mo-tion. When the flame contacts such a flow structure, the combustion rate is increased in several ways. The flame is stretched in the velocity gradients, thereby increasing its area and effective burning speed. Turbulence does not only speed up the transport processes of heat and species but, above all, turbulence increases the effective flame surface area i.e. the interface between flammable mixture and combustion products where the reaction takes place. Initially, when the turbulence is of low intensity, the eddies only wrinkle the flame surface and increase its effective area and burning speed. The conse-quence is a stronger expansion flow - flow velocities increase. Higher flow velocities go hand in hand with higher turbulence intensity levels. Under the influence of higher turbulence intensities, the flame front gradually looses its original smooth appearance. Its structure changes. Turbulent eddies tend to disintegrate the front leading to higher combustion rates. Higher combustion rates produce stronger expansion flow and higher intensity turbulence etc ... Turbulence generative boundary conditions trigger a positive feedback in the process of flame propagation by which it develops more or less exponentially both in speed and pressure (CCPS, 1994). The basic concept of a gas explosion can be summarised as a flame propagation process in a flamma-ble mixture, which is sped up by interaction with its self-induced expansion flow field. During this development, the process of turbulent mixing between flammable mixture and combustion products largely determines the combustion rate. The combustion front manifests itself as an extended mixing zone in which the internal interface between flammable mixture and combustion products can become very large. Turbulence generative (boundary) conditions are required for the development of high flame speeds and blast in deflagrative gas explosions. Markstein G.H. (1964) Nonsteady flame propagation. Pergamon Press.(BibTeX) Fast deflagrationsThe studies of deflagration in very rough, obstacle-filled tubes have demonstrated that the flame speed in a given combustible mixture can be varied continuously over three orders of magnitude between the slow limit of a laminar flame to the fast limit of a CJ detonation. The steady flame speed is governed by the boundary conditions in the tube: i.e. geometry and obstacle configurations. It should be noted that the so-called steady flame speed is an averaged value in the direction of propagation over a distance at least of the order of several obstacle spacings or tube diameters, whichever is greater. Large fluctuations are observed locally in the highly three-dimensional transient structure of the flame front. For the so-called quasi-detonation regime (i.e. flame speeds between 1200 m/s and the normal C-J value of about 2500 m/s for fuel-oxygen mixtures) the studies by Teodorczyk et al. and Chan have conclusively demonstrated that the mechanism of propagation is due to auto-ignition via shock reflections. These studies show that normal shock reflections from the obstacle, Mach reflection of the diffracted shock on the bottom wall and Mach reflection of the reflected shock from the top wall can lead to auto-ignition. The role of the obstacle is to promote strong shock reflections leading to high local temperatures for auto-ignition. Detonations are initiated from these local "hot spots" but are later destroyed by diffraction quenching around the obstacles themselves. Hence for quasi-detonations, the diffraction around the obstacles destroys the initiated detonation while shock reflections resulting from the interactions of the decoupled shock with the obstacle and the tube will give rise to local hot spots and re-initiation of the detonation. Experimentally, it has also been observed that there exists a fast deflagration regime (flame speeds between 400 m/s to 1200 m/s) in which the shock reflections are observed to be not strong enough to result in auto-ignition. A decoupled shock and reaction zone complex which propagates at an averaged steady speed is observed. The studies by Teodorczyk have shown that in the fast deflagration regime, shock reflections do not lead to auto-ignition as in the case of quasi-detonations. The mechanism for sustaining the fast propagation speed is intense combustion via flame turbulization by
The importance of transverse waves (and their interaction with the flame) was clearly demonstrated since their elimination results in a significant decrease in the combustion intensity (and hence the deflagration speed). The elimination of the transverse waves also greatly delays the onset of transition from the deflagration to the detonation regime indicating that the transverse waves not only provide a mechanism to promote intense combustion via interface instability, but also a feedback mechanism where the energy released can be coupled to the leading shock front. In a one-dimensional flow the feedback must proceed via the pressure waves generated. Near the sound speed these pressure waves no longer provide the transfer of energy to the front. The structure of a turbulent high speed deflagration consists of a series of compression waves in the front followed by a highly turbulent reaction zone. Lee J.H., Knystautas R., Chan C.K. (1984) Proc.Combust.Inst., Vol.20, p.1663 Deflagrations in a system of connected vesselsFast deflagrationsThe studies of deflagration in very rough, obstacle-filled tubes have demonstrated that the flame speed in a given combustible mixture can be varied continuously over three orders of magnitude between the slow limit of a laminar flame to the fast limit of a CJ detonation. The steady flame speed is governed by the boundary conditions in the tube: i.e. geometry and obstacle configurations. It should be noted that the so-called steady flame speed is an averaged value in the direction of propagation over a distance at least of the order of several obstacle spacings or tube diameters, whichever is greater. Large fluctuations are observed locally in the highly three-dimensional transient structure of the flame front. For the so-called quasi-detonation regime (i.e. flame speeds between 1200 m/s and the normal C-J value of about 2500 m/s for fuel-oxygen mixtures) the studies by Teodorczyk et al. and Chan have conclusively demonstrated that the mechanism of propagation is due to auto-ignition via shock reflections. These studies show that normal shock reflections from the obstacle, Mach reflection of the diffracted shock on the bottom wall and Mach reflection of the reflected shock from the top wall can lead to auto-ignition. The role of the obstacle is to promote strong shock reflections leading to high local temperatures for auto-ignition. Detonations are initiated from these local "hot spots" but are later destroyed by diffraction quenching around the obstacles themselves. Hence for quasi-detonations, the diffraction around the obstacles destroys the initiated detonation while shock reflections resulting from the interactions of the decoupled shock with the obstacle and the tube will give rise to local hot spots and re-initiation of the detonation. Experimentally, it has also been observed that there exists a fast deflagration regime (flame speeds between 400 m/s to 1200 m/s) in which the shock reflections are observed to be not strong enough to result in auto-ignition. A decoupled shock and reaction zone complex which propagates at an averaged steady speed is observed. The studies by Teodorczyk have shown that in the fast deflagration regime, shock reflections do not lead to auto-ignition as in the case of quasi-detonations. The mechanism for sustaining the fast propagation speed is intense combustion via flame turbulization by
The importance of transverse waves (and their interaction with the flame) was clearly demonstrated since their elimination results in a significant decrease in the combustion intensity (and hence the deflagration speed). The elimination of the transverse waves also greatly delays the onset of transition from the deflagration to the detonation regime indicating that the transverse waves not only provide a mechanism to promote intense combustion via interface instability, but also a feedback mechanism where the energy released can be coupled to the leading shock front. In a one-dimensional flow the feedback must proceed via the pressure waves generated. Near the sound speed these pressure waves no longer provide the transfer of energy to the front. The structure of a turbulent high speed deflagration consists of a series of compression waves in the front followed by a highly turbulent reaction zone. Lee J.H., Knystautas R., Chan C.K. (1984) Proc.Combust.Inst., Vol.20, p.1663 Non-uniform mixtures deflagrationsDeflagration in open atmosphereAccelerated flame propagationC. Chan, P. Thibault cited by OECD-SOAR „Flame Acceleration and DDT“ (Breitung, 2000) A freely expanding flame is intrinsically unstable. It has been demonstrated, both in laboratory-scale experiments (Wagner, 1982, Moen, 1982, Lee, 1985, Chan, 1981) and large-scale experiments (Hjertager, 1983, Moen, 1982, Van Wingerden, 1986, Cummings, 1987), that obstacles located along the path of an ex-panding flame can cause rapid flame acceleration. Qualitatively, the mechanism for this flame accel-eration is well understood. Thermal expansion of the hot combustion products produces movement in the unburned gas. If obstacles are present, turbulence can be generated in the combustion-induced flow. Turbulence increases the local burning rate by increasing both the flame surface area and the local mass and energy transport. An overall higher burning rate, in turn, produces a higher flow veloc-ity in the unburned gas. This feedback loop results in a continuous acceleration of the propagating flame. Under appropriate conditions, this can lead to transition to detonation. Turbulence induced by obstacles in the displacement flow does not always enhance the burning rate. Depending on the mixture sensitivity, high-intensity turbulence can lower the overall burning rate by excessive flame stretching and by rapid mixing of the burned products and the cold unburned mixture. If the temperature of the reaction zone is lowered to a level that can no longer sustain continuous propagation of the flame, a flame can be extinguished locally. The quenching by turbulence becomes more significant as the velocity of the unburned gas increases. For some insensitive mixtures, this can set a limit to the positive feedback mechanism and, in some cases, lead to the total extinction of the flame. Hence, both the rate of flame acceleration and the eventual outcome (maximum flame speed attained) depend on the competing effects of turbulence on combustion. Depending on the fuel concentration and the flow geometry, flame acceleration may be expected to progress through a series of regimes as depicted in Figure 1. For the case of mild ignition, the first phase involves a laminar flame that propagates at a ve-locity determined by the laminar burning velocity and the density ratio across the flame front. This phase of the flame propagation is very well understood and data is available for a wide range of hydrogen-air mixtures. The laminar flame propagation regime is relatively short-lived and is soon replaced by a "wrinkled" flame regime. For most accidental explosions, this regime can persist over relatively large flame propagation distances. For this reason, it is therefore far more important than the initial laminar regime. Due to the increase in flame area, the burning rate, and hence the flame propagation velocity for the wrinkled flame, can be sev-eral times higher than for the laminar flame. Due to turbulence generated by obstacles or boundary layers, the wrinkled flame eventually transforms into a turbulent flame brush. This results in further flame acceleration due to the increase in surface area of the laminar flamelets inside the flame brush. For sufficiently high levels of turbulence, the flamelet structure may be destroyed and then replaced by a distrib-uted reaction zone structure. The flame acceleration process can eventually lead to DDT. For configurations involving re-peated obstacles, the turbulent flame propagation regime is self-accelerating due to the feed-back mechanism between the flame velocity and the level of turbulence ahead of the flame front. The final flame velocity produced by the turbulent flame acceleration process depends on a variety of parameters including the mixture composition, the dimensions of the enclo-sure, and the size, shape and distribution of the obstacles. Figure 2 shows the maximum flame speed achievable in tubes of various diameters. Various turbulent flame and detonation propagation regimes have been identified for hydrogen-air mixtures in obstacle-filled tubes. These regimes include: - A quenching regime where the flame fails to propagate;
- A subsonic regime where the flame is travelling at a speed that is slower than the sound speed of the combustion products;
- A choked regime where the flame speed is comparable to the sound speed of the combus-tion products;
- A quasi-detonation regime with a velocity between the sonic and Chapman-Jouguet (C-J) velocity;
- A C-J detonation regime where the propagation velocity is equal to the CJ detonation ve-locity.
It should be noted that the above regimes are geometry-dependent for a given mixture. Con-sequently, the concentration range for each regime in Figure 2 may differ for circular tubes and rectangular channels. Breitung W., Eder A., Chan C.K. e.a. SOAR on flame acceleration and DDT in nuclear safety, O-ECD/NEA/CSNI/R (2000) 7, 2000. Pressure waves from deflagrations: dependence on flame velocity and accelerationDeflagration processes produce pressure waves ranging from extremely weak acoustic waves, which man can only hear, to extremely strong shock waves in case of detonation, which can produce consid-erable damages. The intensity of pressure wave resulted from deflagration is defined by the intensity of the combustion process. In case of slow subsonic flames the pressure wave typically has gradually growing front with the typical peak overpressure less than 1 bar and duration of several seconds. In case of fast supersonic flames (which are usually fast turbulent flames) the pressure wave transforms into shock (which is characterized by abrupt step-wise changes in media characteristics) with typical overpressures of order of magnitude of 10 bar and its duration of 200 - 500 ms. In the limiting case of detonation a shock wave is also formed but with higher peak values and shorter duration. For example, in case of detona-tion of stoichiometric hydrogen-air mixture at normal conditions an amplitude of detonation wave reaches 17 bar with duration of less than 100 ms. Pressure waves generated by combustion process decay while they propagate from their source. In far zone the amplitude of such pressure wave is defined only by the chemical energy released during com-bustion. This means that for the same amount of hydrogen independently on the intensity and charac-teristics of the combustion process, the overpressure value will be the same. On the other hand (see e.g., Figure 1), in the near zone the observed peak overpressure strongly depends on the speed of combustion. Dorofeev S.B. (2002) Flame acceleration and DDT in gas explosions. Journal de Physique de France IV, 12(7):3-10.(BibTeX) Confined deflagrationsDynamics of flame propagation and pressure build up in closed spaceFlame and pressure dynamics in a closed vessel has been studied best in the simplest case of a spherical vessel with central ignition and spherical flame propagation. At the initial stage of combustion the spherical flame front expands similar to that one in unbounded space – the pressure rise is negligible, vessel walls are relatively far from the flame front to affect the combustion process and the flame front velocity is equal to V_{ff} = s_u E_i , where s_u - burning velocity of the mixture, E_i = \rho _i / \rho _b - expansion coefficient of the combustion products. As the flame propagates closer to the walls the flame front velocity slows down due to compression of the unburnt (fresh) gas. In vicinity of walls the unburnt gas doesn’t expand any more and the flame front velocity equals simply to the burning velocity V_{ff} = s_u . In spite of decelerating flame velocity, the speed of pressure built up is rising owing to the increasing with radius flame front area and, thus, mass burning rate. The most of pressure rise occurs at the final stage of combustion when the flame front is close to the vessel wall. According to the model developed in (DB, Ya. Zeldovich, 1985), for a mixture with expansion coefficient , only 20% of pressure rise occurs during flame propagation over 80% of vessel radius. The pressure during combustion in a closed vessel may be assumed constant across a vessel as the sound speed is much faster than the flame front velocity and pressure equilibration time is much shorter than the combustion time. Combustion process in a closed vessel implies there is no overall gas expansion and the process is accompanied by a pressure rise in a vessel. As the heat of reaction is not spent on work of expansion, but goes solely into raising the internal energy of the gas, the combustion products in a closed vessel have larger temperature compare to combustion of the same fuel-oxidiser composition at a constant pressure. Pressure dynamics with time may be found starting from the balance equation for the burnt mixture mass fraction (Ya.Zeldovich, 1985): m{{d\eta } / {dt}} = \rho \left( {p,\,T_u } \right)\,s_u \left( {p,\,T_u } \right)\,A\left( t \right),
where m - mass of gas in the vessel, \eta - fraction of burnt mixture, t - time, \rho \left( {p,\,T_u } \right) - density of unburnt mixture as a function of pressure P in vessel and temperature of unburnt mixture T_u , s_u \left( {p,\,T_u } \right) - burning velocity, A\left( t \right) - flame area. The flame and pressure dynamics with time may be obtained provided the dependence of the burning velocity with temperature and pressure for a particular mixture and a flame shape are known. Different integral balance models are available from literature, e.g. (BradleyD:1976), (Ya.Zeldovich, 1985), (MolkovVV:1981), (A.Dahoe, 2005). One may use an integral balance model together with inverse problem method to obtain burning velocity of mixture from deflagration pressure dynamics in a closed vessel. Burning velocity and baric index for stoichiometric hydrogen-air deflagration in a large-scale vessel were obtained in (MolkovVV:2000); burning velocity of unstretched hydrogen-air flame was obtained in (A.Dahoe, 2005) in a range of equivalence ratios \Phi = 0.5 - 3.0 from a small-scale closed vessel experiments. More versatile method of modelling flame and pressure dynamics in closed vessels may be computational fluid dynamics (CFD) methods, which don’t require assumption about the shape of a flame front, but, instead, model its development from first principles. For example, a stoichiometric hydrogen-air deflagration in a closed vessel was modelled in (MolkovVV:2004f). There the application of large-eddy simulation (LES) method, which is an advanced method of modelling turbulent and reacting flows, allowed to resolve development of the flame front including the effect of hydrodynamic instabilities. Zeldovich Ya.B., Barenblatt G.I., Librovich V.B., Makhviladze G.M. The mathematical theory of combustion and explosions. Consultants Bureau, New-York, 1985. Mache effectThe temperature gradient exists in the gas burnt in a closed vessel, rising from the gas burnt last to the gas burnt first (B.Lewis, 1961). The temperature gradient is known as “Mache effect” (Ya.Zeldovich, 1985) and was theoretically estimated in a paper (L.Flamm, 1917). In a closed vessel combustion the gas temperature changes due to the heat release and due to adiabatic compression. Generally, an intermediate portion of unburnt gas in a closed vessel may be pre-compressed due to combustion of initial portions of gas, then it burns, producing burnt mixture with a higher temperature, and then these combustion products are compressed again due to combustion of following portions of gas. At initial stage of process (close to ignition point) combustion occurs at initial pressure and temperature and then the combustion products undergo adiabatic compression with corresponding temperature rise. A volume of gas, which burns last, has been pre-compressed initially, and doesn’t undergo future compression and temperature rise after burning. Thus, these gas portions will have different initial conditions, different combustion products temperature and different composition. The Mache effect is known to reduce the explosion pressure below the one for uniform temperature distribution. The Mache effect is strongly pronounced for combustion in a closed spherical vessel with a central ignition, where the gas motion doesn’t cause mixing (Ya.Zeldovich, 1985). Lewis B., von Elbe G. Combustion, Flames and Explosion of Gases. Academic Press, London, 1961. Vented deflagrationsMulti-peaks structure of pressure transients and underlying physical phenomenaVented deflagration pressure dynamics has multi-peak structure. The number of peaks and their magnitude depend on various explosion conditions. Detailed analysis of this peak structure was performed in paper [1]. Vented deflagration of 10% natural gas-air mixture in a vessel of volume V=0.76 m3 with venting area F=V2/3/9.2 and low vent release pressure panel (inertia 3.3 kg/m2) was analysed. Four distinct pressure peaks were registered for the case of vented deflagration in low-strength enclosures (Figure 1). The following deflagration phenomena and pressure peak are identified for vented deflagration with initially closed vent cover. After ignition deflagration develops in closed vessel until moment (a) when vent cover is released. So, pressure peak P1 is associated with vent release. At moment (b), when time derivative of pressure is equal to zero, the volume of gases produced by combustion inside the vessel is equal to volume of gases flowing out of the vessel, i.e. \DeltaVdefl=\DeltaVoutflow. It is known that venting of combustion products is more efficient for reducing explosion pressure compared to flammable mixture as for the same pressure drop at the vent a velocity of flow is proportional to square root of temperature. This explains that moment (c) on pressure transient corresponds to the beginning of burnt gas outflow. After it the combustion products “flow through” flammable mixture, which just escaped the vessel, and external explosion occurs at moment (d) with corresponding peak pressure P2. Helmholz oscillations could be generated after external explosion with characteristic wave length longer than resonator (vessel) size. The Helmholz oscillations can induce Rayleigh-Taylor instability [2]. Increase of mass burning rate due to increase of flame front area implies growth of pressure with time. At moment (e) the contact of flame front with walls of the vessel is sufficient for the heat losses to compensate the heat release by combustion and pressure peak P3 is formed. At final stage of the explosion when combustion proceed mainly close to walls and in corners high-frequency oscillations may be generated. Rayleigh criterion is applied in this case: "If heat be given to the air at the moment of greatest condensation, or taken from it at the moment of greatest rarefaction, the vibration is encouraged" [3]. Oscillations of peak P4 can be eliminated by taking adequate measures, such as lining the interior of the vessel to be protected with damping material. It is important to note that when the vent cover failure pressure is increased to 7.5 kPa the second and third peaks practically can no longer be seen on the pressure transient. For relatively high vent release pressures, which are characteristic for process equipment, only two pressure peaks (one - vent release, another - mixture burnout) can be observed. 1.Cooper M.G., Fairweather M., Tite J.P., On the mechanisms of pressure generation in vented explosions, Combustion and Flame, 1986, Vol. 65, Issue 1, pp.1-14. Turbulence generated by venting processFor gaseous explosions the venting process itself is known to cause the flame to accelerate [1]. Gov-erning equations for turbulent vented gaseous deflagrations were derived from the first principles in paper [2]. The inverse problem method for vented gaseous deflagrations has been developed [3] and efficiently used over the years of research allowing to gather unique data on venting generated turbu-lence. For example, an analogue to the Le Chatelier-Brown principle for vented gaseous deflagrations [3] was revealed by this method. The universal correlation for vented deflagrations was developed for the first time in 1995 [4] followed by the closure of this fundamentally new vent sizing approach with the correlation for venting generated turbulence, presented for the first time two years later in 1997 [5]. Two of our previous articles were devoted to the problem of inertial vent covers in explosion protection [6-7]. Recently our original correlations for vent sizing were developed further to include experimental data on fast burning mixtures, such as near stoichiometric and rich hydrogen-air mixtures, and test data on elevated initial pressures [8-11]. The attempts to produce any reasonable correlations for venting generated turbulence have failed for another reason as well – due to a neglect of the role of the generalised discharge coefficient, \mu, which is dependent on vented deflagration conditions. This fact of discharge coefficient dependence on con-ditions was recognised already about 20 years ago by various authors, e.g. [12]. It has been demon-strated in a series of studies that reduced explosion pressure correlates with the deflagration-outflow interaction (DOI) number, that is the ratio of the turbulence factor, \chi, to the discharge coefficient, \mu, rather than with the turbulence factor alone. The following correlation for venting generated turbulence has been obtained by processing a wide range of experimental data on vented gaseous deflagration [11, 13] \chi / \mu = \alpha {\left[ \frac(1 + 10V{_{\#}}{^{1/3}} )(1 + 0.5 Br{^{\beta}}) {1 + \pi{_{\nu}} } \right]}^{0.4} \pi{_{i\#}}^{0.6} where the empirical coefficients \alpha and \beta are equal for hydrogen-air mixtures to \alpha=1.00 and \beta=0.8 and for hydrocarbon-air mixtures to \alpha=1.75 and \beta=0.5; V_\# - dimensionless volume (numerically equal to enclosure volume in m3), V{_\#} = V / V{_{1 m^3}} ; \pi{_{i\#}} - dimensionless initial pressure, ; \pi{_{\nu}} - dimensionless vent closure release pressure, \pi{_{\nu}} = P{_\nu} / P{_i} = (P{_{stat}} / P{_i} + 1) with P_\nu - vent closure release pressure, bar abs., P_{stat} - vent closure release pressure used in the NFPA 68, bar gauge, and P_i - initial pressure, bar abs.; and the Bradley number is Br = \frac {F} {V^{2/3}} \frac {c_{ui}} {S_{ui} (E{_i} - 1)} , where F – vent area, m2; V – enclosure volume, m3; c_{ui} – speed of sound, m/s; S_{ui} – burning velocity at initial conditions, m/s; Ei – combustion products expansion coefficient. The empirical correlation for the DOI number gives the dependence of turbulence level as enclosure scale in power 0.4. This is in agreement with conclusions of fractal theory with corresponding fractal dimension 2.4 for turbulent premixed flame characteristic for vented deflagrations. The turbulent combustion intensifies with increase of the Bradley number as follows from the correla-tion. It means that an increase of venting area F will be accompanied by an increase of turbulence factor. The increase of burning velocity has opposite effect, i.e. a growth of laminar burning velocity will decrease turbulent factor at other conditions being conserved. The DOI number is increasing with increase of initial pressure in enclosure. The turbulence level for vented deflagration in conditions of experiments [14] increased from 4-6 at initial atmospheric pres-sure to 15-20 at initial pressure 7 atmospheres. Hence the increase of initial pressure from 1 to 7 at-mospheres leads to about four-fold increase of the turbulence level. It has been found that there is only 20% increase of the turbulence factor for the stage of deflagration in closed vessel for the same in-crease of initial pressure [13]. This result demonstrates explicitly that it is venting that is responsible for a substantial increase in the turbulence level, but not just an elevated initial pressure itself. 1. Tamanini, F., 1996, Modelling of panel inertia effects in vented dust explosions, Process safety Progress, 15: 247-257. Coherent deflagrations in a system enclosure-atmosphere and the role of external explosionsApparently, Swedish scientists were the first to undertake an experimental investigation in 1957 that emphasised the importance of the external explosion during a vented deflagration [1]. They found that in some cases the maximum explosion overpressure outside a 203 m3 enclosure exceeded the maxi-mum overpressure inside of the enclosure. In 1980 Solberg et al further highlighted the danger of ex-ternal explosions [2]. They found that during vented deflagrations in a 35-mm3 vessel, the flame front propagation velocity could reach 100 m/s in a lateral direction outside the vent. In their experiments the flame propagated up to 30 m outside the enclosure though the vessel was only 4 m long. Harrison and Eyre [3] came to conclusion that for “large vents, where the internally generated pressures are low, the external explosion can be the dominating influence on the internal pressure” and that this influence “could be very important for large volume, low strength structures such as buildings or off-shore modules”. In 1987 Harrison and Eyre [3], and Swift and Epstein [4], independently suggested that the mechanism of external explosion influence on the internal pressure dynamics is contained in the decrease of the mass flow rate through the vent. Theoretical analysis performed by Molkov in 1997 [5], based on the processing of experimental data by Harrison and Eyre [3] confirmed that the turbulence factor inside the enclosure was practically unaffected by the occurrence of the external explosion. Instead, a substantial decrease of the generalised discharge coefficient, i.e. mass outflow, was found for tests with pronounced external combustion. It was concluded that the decrease of the pressure drop on the vent due to combustion outside the enclosure was the main reason for reduced venting of gas outside the enclosure. In 1991 Catlin [6] studied the scaling of external explosions. He found that the external overpressure grows proportionally to the velocity of the flow and flame emerging from the vent. The physics of the phenomenon of coherent deflagrations, i.e. coupled internal and external explo-sions, has been recently clarified [7-9] through application of the large eddy simulation (LES) model developed at the University of Ulster to experiments in 547 mm3 SOLVEX facility [10]. The comparison between experimental and LES pressure transients inside and outside the enclosure and external flame shape led to some important conclusions on the nature of coherent deflagrations. The formation of the turbulent starting vortex in the flammable mixture pushed out of the enclosure during the internal deflagration is a prerequisite for a subsequent intense combustion outside the enclosure. The rapid acceleration of combustion outside the enclosure commences not at the moment when the flame front emerges from the vent, but after the flame front “touches” the edges of the vent. At this point the flame reaches the region of strong turbulence generated in the shear layers at the perimeter of the external jet. There is consequently a rapid increase in the rate of combustion and a coherent steep pressure rise is observed both inside and outside the enclosure. The external pressure rise in the atmosphere is a direct consequence of the highly turbulent deflagration there, but there is no increase of the burning rate inside the enclosure. The pressure rise inside the enclosure is caused by the decrease of mass flow rate from the enclosure to the atmosphere due to the high pressure just outside the vent. In such scenarios the mitigation strategy should aim primarily at the suppression of combustion outside the enclosure. 1. Report of Committee for Explosion Testing, Stockholm, 1957, Kommitten for Explosions Forsok,
Bromma 1957, Slutrapport, Stockholm, April 1958. Le Chatelier-Brown principle analogue for vented deflagrationsThe following relationship could be extracted from a conservative form of the universal correlation for vented gaseous deflagrations [1] and will be used to discuss the Le Chatelier-Brown principle analogue for vented gaseous deflagrations [2] \pi_{red} \sim \left[ S_{ui} \frac{\chi}{\mu} \frac{1}{F} \right]^{25} where \pi_{red} – reduced explosion pressure; S_{ui} – burning velocity, m/s; \chi – turbulence factor; \mu – generalized discharge coefficient; F – vent area, m2. The Le Chatelier-Brown principle analogue states that gasdynamics of premixed turbulent combustion in vented vessel responds to external changes in the process conditions in such a way as to weaken the effect of external influence. Response action is always weaker than primary one. Let us say one would like to reduce explosion pressure \pi_{red} simply through an increase of the venting area F. However, an increase of the vent area F is always (!) accompanied by increase of deflagration-outflow-interaction number \chi/\mu. For example, in experiments on hydrogen-air deflagration [3] 1.5 increase of F is accompanied by 1.25 increase of \chi/\mu. In experiments on 10-20% hydrogen-air defla-grations in spherical vessel of 2.3-m diameter [4] ninefold growth of vent area F was accompanied by 2.79 increase of \chi/\mu for 10% hydrogen-air and 2.93 increase for 20% hydrogen-air mixture. Thus effective increase of venting area for this case is about 3 rather than 9. The same manifestation of the Le Chatelier-Brown principle analogue was observed for hydrocarbon-air mixtures. For propane-air deflagration [3] twofold increase of F is accompanied by 1.57 times increase of \chi/\mu. In experiments by Harrison and Eyre in 30.4 m3 vessel with natural gas-air mixture 2.06 times increase in F was practi-cally compensated by 1.87 increase of \chi/\mu. As a result an effective increase of vent area, i.e. F/(\chi/\mu) is often much less than expected. In the last case the effective increase of vent area is just 2.06/1.87=1.1 (10% only), but not as much as 2.06. Sixfold increase of initial burning velocity Sui, when hydrogen concentration in air increased from 10% to 20% [4], is accompanied by slight, but nevertheless 1.15 decrease of urbulence factor \chi. The significant decrease of the discharge coefficient \mu at the same series of experiments on vented hydrogen-air deflagrations [4] in 2.25 times, when vent diameter changed from 15 to 45 cm due to duct effect, is accompanied by 1.12 decrease of the turbulence factor \chi. Another demonstration of this principle: 1.5 times increase of the turbulence factor \chi in FM Global experiments [5] was compensated partially by 1.25 increase of the discharge coefficient \mu. The Le Chatelier-Brown principle analogue explains why, for example, an increase of venting area is not always so efficient in engineering practice to mitigate explosions to safe level as expected. 1. Molkov V.V., Accidental gaseous deflagrations: modelling, scaling and mitigation, Journal de Physique IV, 2002, Vol.12, pp.7-19 – 7-30. Venting of hydrogen deflagrations through ductsThe discharge of hot combustion products and blast waves from vent devices is often ducted to safe locations to avoid damage to surrounding equipment and buildings. The presence of a duct, however, is likely to increase the severity of an explosion compared to simply vented enclosures. For instance, with stoichiometric acetone-air mixtures it was observed that connecting a duct of 5 cm diameter and a length of 183 cm to a 5 cm diameter vent opening in a 27 liter sphere, increased the reduced pres-sure from 0.7 atm to 4.7 atm [1]. Various authors [2,3,4,5,6] have identified the phenomena that lead to an enhanced explosion severity when a vent device is equipped with a duct: a secondary explosion in the duct due to ‘burn-up’ of reactants emerging from the enclosure, frictional drag, inertia of the gas column in the duct, acoustic interactions, and, Rayleigh-Taylor instability induced by Helmholtz oscillations. The increased explosion severity due to the presence of a duct may be mitigated by three dif-ferent methods: the application of a diaphragm to the vent opening, increasing the discharge pressure, and suppression of combustion in the duct by injecting an extinguishing agent at the onset of the vent-ing process. An interesting study of the venting of hydrocarbon-air (methane and propane) and hydrogen-air defla-grations through ducts is described in ref. [8]. These authors investigated the pressure development in a 200-litre cylindrical vessel (length: 1.0m, diameter: 0.5m, see Figure 1). A vent pipe (length: 1.0m, diameter: 0.162m) was fitted to the explosion vessel. The behaviour of the pressure in the explosion vessel and the vent duct is shown in Figures 2 and 3. It is seen that, while the pressure in the explosion vessel with propane-air mixtures remains in the deflagration mode during the ‘burn-up’ in the vent duct, hydrogen-air mixtures exhibit a sudden detonation-like spike. This happens well after the flame has passed the vessel-duct assembly. This phenomenon has been ascribed to the effect of flow reversal across the vessel-duct assembly due to the secondary explosion, and the consequential enhancement of the burning rate of remaining reactants in the explosion vessel. 1. Nekrasov, V.P., Meshman, L.M., and Molkov, V.V., The Influence of Exhaust Ducts on Reduced Explosion Pressure, Loss Prevention in Industry, 5:38-39, 1983 (in Russian). Venting of hydrogen deflagrations with inertial vent covers, jet effectExisting standards, e.g. NFPA 68, address mainly the issue of vent sizing for non-inertial vent covers. However, in various applications only heavy inertial vent closures can be used for technological rea-sons. Most buildings will suffer appreciable structural damage from an internal pressure less than 7 kPa [1]. Deflagration of a hydrogen-air mixture in only 1-2% of an enclosure volume would cause substantial damage. Recent gaseous explosions in domestic structures have shown that new products, such as double glassed windows, can increase the severity of the explosion consequences, up to demolition of most of the building. Most vented deflagrations can be characterised by two pressure peaks. Previous studies have demon-strated that the inertia of the vent cover does influence the value of the first peak, but does not practi-cally influence the second. However, this may not be always the case. An inertial vent cover can affect the second pressure peak in some “implicit” ways. For example, it could happen because of changes in venting generated turbulence, e.g. decrease of turbulence by the gradual opening of the venting area by use of an inertial device. It has been proven that inertial vent covers decrease the maximum turbulence generated during venting, by 20% on average, and by 55% in some experiments with hydrocarbon-air mixtures. This effect could be even more essential for more “sensitive” hydrogen-air mixtures (ex-perimental data are absent at the moment). From another point of view an increase of turbulence could be caused by an increase of vent cover deployment pressure. Indeed, a stronger initial rarefaction wave and consequent pressure oscillations could have a larger effect on the development of flame front wrinkling and hence increase of the burning rate. As another example, it could happen because of changes in the development of “external” explosion during deployment of the inertial vent cover. The jetting of a high-speed flammable mixture into the atmosphere by significantly narrower streams in case of inertial cover deployment contributes to a consequently stronger mixture dilution by air during outflow. This definitely mitigates the external deflagration or could halt it altogether for lean or stoichiometric mixtures of hydrogen with air. Besides, external combustion decreases the pressure drop at the vent and thereby reduces the venting discharge from the enclosure. This in turn causes a higher pressure build up inside the enclosure. Characteristic experimental and simulated (CYNDY code of the University of Ulster) results are pre-sented in the figures below. Figure 1 shows a comparison between theory and experiment [2] for trans-lating vent covers with initially quiescent (test 3-A with a surface density of the vent cover of w=89 kg/m2) and initially agitated by fan (test 3-C, w=42 kg/m2) methane-air mixtures in a 50-m3 enclosure with one 2.45-m2 vent. Two displacement curves for test 3-A are related to two different edges of the vent cover in this particular experiment. The simulated transients are very close to experimental except for the pressure at the final stages of deflagration when the heat losses to the walls reduce the experi-mental pressure.
Results for experiments with “butterfly” style hinged vent covers [2] are presented in Fig.2 for a 50-m3 enclosure with two 0.957-m2 vents. The comparison with experiments was performed for quiescent (test 3-B, surface density of w=124 kg/m2) and initially turbulent (3-D, w=73 kg/m2) mixtures.
A comparison between theory and experiment (pentane-air) with a spring-loaded vent cover [3] is shown in Fig.3, which refers to the case of a 1.72-m3 enclosure with a 0.164-m2 vent. The mixture was initially quiescent. The surface density of the vent cover was 245 kg/m2. The stepped change of the turbulence factor at the start of vent cover opening can be explained by the high pressure of vent cover deployment (1.55 bar).
The maximum value of the turbulence factor at the end of the period of its gradual growth in experi-ments with initially turbulent hydrocarbon-mixtures is 70-80% higher than the maximum value for initially quiescent mixtures. It is notable that this difference is larger than the 25-50% initial difference in turbulence factor values due to fan agitation. For the investigated configurations, hinged vent covers result in lower levels of venting generated turbulence than translating vent covers. Vent cover jet effect. This phenomenon was unknown until recently. It significantly affects explosion dynamics in enclosure with inertial vent covers. Several phenomena affecting inertial vent cover dis-placement were examined. The results of the analysis of the drag effect and the air cushioning effect between the moving vent cover and its constraints suggested that these two phenomena were insuffi-cient to account for the experimentally observed displacement of the vent cover. It has been demon-strated that the formation of a jet of flowing out of an enclosure gases on an “internal” surface of the inertial vent cover drastically influences the movement of the cover and hence affects the transient explosion pressure. Mathematical modelling of the pressure distribution, including the jetting flow of explosion products, resulted in a pressure force on the vent cover half that predicted by traditional modelling for translating covers. It was determined by comparison with experiments that the change from full to reduced pressure due to this jet effect becomes significant when the virtual venting area reaches 5-10% of the nominal venting area. The jet effect is crucial to simulating explosion dynamics for all types of venting devices: moving in translation, rotation or spring-loaded [4-7]. References 15. Howard W.B., Karabinis A.H., Tests of explosion venting of buildings, Plant/Operations Progress, 1982, Vol.1, No.1, pp.51-65. |