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Vented explosion overpressures from combustion of hydrogen and hydrocarbon mixtures
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 2 3 2 9 e2 3 3 6
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Vented explosion overpressures from combustion of hydrogen and hydrocarbon mixtures C.R. Bauwens, J. Chaffee, S.B. Dorofeev* FM Global, Research Division, 1151 Boston-Providence Turnpike, Norwood, MA 02061, USA
article info
abstract
Article history:
Experimental data obtained for hydrogen mixtures in a room-size enclosure are presented
Received 1 February 2010
and compared with data for propane and methane mixtures. This set of data was also used
Received in revised form
to develop a three-dimensional gasdynamic model for the simulation of gaseous
30 March 2010
combustion in vented enclosures. The experiments were performed in a 64 m3 chamber
Accepted 1 April 2010
with dimensions of 4.6 4.6 3.0 m and a vent opening on one side and vent areas of
Available online 21 May 2010
either 2.7 or 5.4 m2 were used. Tests were performed for three ignition locations, at the wall opposite the vent, at the center of the chamber or at the center of the wall containing the
Keywords:
vent. Hydrogeneair mixtures with concentrations close 18% vol. were compared with
Explosions
stoichiometric propaneeair and methaneeair mixtures. Pressure data, as function of time,
Hydrogen
and flame time-of-arrival data were obtained both inside and outside the chamber near the
Venting
vent. Modeling was based on a Large Eddy Simulation (LES) solver created using the
Modeling
OpenFOAM CFD toolbox using sub-grid turbulence and flame wrinkling models. A comparison of these simulations with experimental data is discussed. ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Explosion venting can be used to prevent or minimize damage to an enclosure by relieving the pressure generated within the volume and is an important engineering loss prevention solution. Experimentally, the subject of vented explosions has been widely studied with research performed over a range of scales, from laboratory scale tests (see, e.g., [1]) to large-scale tests (see, e.g., Refs. [2e4]). Factors contributing to the pressure build-up in vented explosions have been extensively studied [1e8]. Analytical models and empirical correlations have also been developed (see, e.g., Refs. [8e11]), a number of which have been included in engineering guidelines [12,13]. These correlations, however, often have conflicting recommendations. This is due to the complex nature of the process itself, as mentioned above, and the influence of other factors that can
affect the peak overpressure, such as size and shape of the enclosure, the mixture being burned, the type of vent and vent deployment pressure, congestion or obstacles inside the chamber and the ignition location. Computational Fluid Dynamics (CFD) simulations of vented explosions, and the comparison of these simulations with experimental data [4,14,15], have shown some of the challenges in adequately modeling the major physical phenomena. Although there are a few examples of successful CFD applications for several selected tests, such as [15], it is not unusual to find CFD predictions that are off the test results by more than an order of magnitude. Because of the limited reliability of the current methods for the prediction of pressure generation during a vented explosion, a research project was initiated with the goals of generating a parametric set of experimental data as well as developing and validating a computational code and new
* Corresponding author. E-mail address: [email protected] (S.B. Dorofeev). 0360-3199/$ e see front matter ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.04.005
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engineering tools. The first part was performed for low reactivity stoichiometric methaneeair mixtures [16]. Another study examined the effect of the RayleigheTaylor instability on flame propagation [17]. The lean hydrogen mixtures used in the present study, however, present additional challenges. This is mainly due to two factors. First, that the DarrieuseLandau (DL) flame instability is enhanced by thermal diffusion effects, which results in a significant increase in the flame surface for lean hydrogen mixtures. The second challenge is the effect of the Lewis number on the rate of change of the turbulent burning velocity with respect to the turbulent intensity. Currently, the strength of these effects is not known well enough to be reliably modeled. Comparisons with stoichiometric methaneeair and propaneeair mixtures illustrate the significant differences caused by these instabilities and yield some insight on how to model them. The objectives of the present work are to (i) examine the similarities and differences between three mixtures of similar laminar flame speed, 18% hydrogeneair, 9.5% methaneeair and 4.0% propaneeair; and (ii) test an extension to the numerical CFD model developed in the previous study and identify its capabilities and deficiencies to describe the physics responsible for the pressure build-up.
2.
Experiments
The data presented here were obtained from experiments performed in a 64 m3 explosion test chamber. The overall dimensions of the chamber were 4.6 3.0 4.6 m with a square vent of either 5.4 m2, or 2.7 m2 located on one of the vertical walls. Four chamber pressure transducers were mounted to the chamber, one at the center of the wall opposite the vent, one on the wall containing the vent, and two on a wall perpendicular to the vent (one on-axis with the center of the chamber, one off-axis), (see Fig. 1). Twenty flame time-ofarrival thermocouples, at a height of 1.4 m above the floor of the chamber, were placed at 0.5 m intervals inside the chamber
along two axes and at 1 m intervals outside of the chamber. Two blast-wave pressure transducers were installed in a concrete slab outside of the chamber, below the line of thermocouples at a height of 0.3 m above the ground, 1.17 m and 3.45 m from the vent. One high speed and four low speed cameras were used to observe the tests, either directed into the chamber or directed outside to capture the external explosion. Data was collected using a 32 channel high speed data acquisition system sampling at a rate of 25,000 scans/s. The initial mixture was supplied by injecting the pure fuel through an inlet at the floor of the chamber while mixing fans within the chamber were used to create a uniform mixture. The concentration of gas inside the chamber was controlled using a Cirrus mass spectrometer. The unburned mixture was contained within the chamber (prior to ignition) using a 0.02 mm thin sheet of polypropylene. Ignition was supplied using a carbon rod igniter at one of three locations, either at the center of the chamber, 0.25 m from the center of the wall opposite the vent (back ignition) or 0.25 m from the center of the wall containing the vent (front ignition). The time between when the mixing fans were stopped and ignition was controlled to ensure a consistent initial turbulent intensity (u0 z 0.1 m/s), which was determined in a series of preliminary tests using measurements from a bi-directional velocity probe. In this study three mixture compositions were examined: 18% vol. hydrogeneair, 9.5% methaneeair and 4.0% propaneeair. For each of mixtures experiments were performed for the three ignition locations, center, back and front, and two vent sizes 2.7 m2 and 5.4 m2.
3.
Numerical simulations
3.1.
Solver details
Numerical simulations were performed using a custom solver built using the OpenFOAM CFD toolbox [18]. The code is based
Fig. 1 e Chamber geometry and instrumentation, showing: pressure transducers (rectangles), thermocouples (circles) and blast-wave transducers (triangles).
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 2 3 2 9 e2 3 3 6
on a Large Eddy Simulation (LES) solver of the NaviereStokes conservation equations for mass, momentum and energy using a robust, implicit, pressureevelocity, iterative solution framework, with a fully compressible Pressure-Implicit Split Operator (PISO) solution method [19]. Sub-grid scale turbulence was modeled using a one-equation eddy viscosity model [20]. An unstructured grid was used for the current study. Second order schemes were used in space and time, central differencing for velocity, a bounded TVD scheme for scalars, and second order backward differencing for time. The combustion model is based on a transport equation for a regress combustion variable b [21]. The transport of the regress variable is governed by a laminar burning velocity, SL and a flame surface wrinkling factor, X. The scalar flame surface wrinkling factor, X, was transported to take into account the effect of flame wrinkling on the burning velocity. Flame instabilities in a lean hydrogeneair mixture can produce a significant increase in the flame’s surface area and propagation speed. This effect was incorporated into the model using Eq. (1) below, X ¼ XI XT XRT ;
(1)
where XI is the surface wrinkling factor due to the DL flame instability, XT is the surface wrinkling factor due to turbulence and XRT is the surface wrinkling factor due to the RayleigheTaylor instability, whose role in vented explosions is described in [17] and is summarized in the following section. The form of Eq. (1) suggests that the characteristic length scales of the three types of wrinkling are different. The XI term in Eq. (1) may be expressed as [22]: XI ¼
1=3 lm ; lc
(2)
where lm is the maximum unstable scale and lc is the cutoff wavelength. In a sub-grid model lm D, where D is the filter size. Experimentally, the onset of instability is observed for sufficiently large Peclet numbers, Pe ¼ r/d > Pecl, where r is the flame radius, d is the flame thickness, and Pecl is the critical Pe number [23,24]. The cutoff scale is given by: lc =d ¼ 2pPecl =ncl ;
(3)
where ncl is the critical wave number and is of the order of 10. This yields the following equation for XI: 1=3 D XI ¼ max 1; aI lc
(4)
where aI is a coefficient to account for the uncertainty in lc. In cases when aI(D/lc)1/3 < 1, flame instabilities are expected to be resolved on the grid scale and XI ¼ 1. This was the case in [16] where methaneeair mixtures were used. For an 18% hydrogeneair mixture at 365 K the cutoff scale has been estimated as lc ¼ 7 mm [24]. The value of lc for normal initial temperature, however, is unknown. In the current study the values of lc ¼ 7 mm and aI ¼ 1.2 were used, and were found to produce agreement with the initial flame propagation velocity. The surface wrinkling factor due to turbulence, XT was computed using a transport equation taking into account the
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generation and removal of flame surface wrinkling. The equilibrium XT, Xeq* is given by the following turbulent burning velocity correlation [25]: 1
1
Xeq ¼ 1:04$ðu0 =SL Þ2 ðLT =dÞ6 ;
(5)
where u0 is the turbulent intensity, LT is the integral turbulent length scale and d is the flame thickness. The coefficient of 1.04 in the correlation was determined in the previous study using methane [17] and is used because the value of the burning velocity predicted by Bradley’s correlation is only estimated within a factor of 2. A decrease of the Lewis number may increase the rate of change of the turbulent burning velocity with turbulence intensity as suggested in [25,26]. In the current model, however, this effect was not considered, and was not observed in the experimental results presented below. The effect of the Lewis number was solely attributed to the changes of burning velocity due to the flame instabilities.
3.1.1. Model for flame surface wrinkling due to the RayleigheTaylor instability The basic approach taken to model the flame surface wrinkling due to the RT instability is to solve an additional transport equation for XRT [17]. The development of the transport equation requires the specification of generation and removal rates for the sub-grid wrinkling. Although the process through which the RT instability grows on a surface with acceleration is highly non-linear, one can use a linearized theory to estimate the growth and removal rates. The parameters of these estimates are then adjusted to compensate for non-linear effects through comparison with experimental data. A general expression for the linearized growth rate of flame instabilities is given in [27] includes terms describing the baseline DL instability with thermal diffusion effects and the RT instability. To simplify the problem, we assume the DL and RT instabilities occur at significantly different wavelengths, this allows the component of the generation rate that varies with acceleration to be separated: 1=2 s * 1* a$ n ; GRT ¼ 2 kRT sþ1
(7)
where kRT is the unstable wave number associated with the RT instability, a is acceleration and s is the expansion ratio. Considering that the removal of flame wrinkling is due to flame propagation and annihilation of the flame surface at cusps yields a transport equation for XRT: dXRT ¼ GRT ðXRT 1Þ RRT ðXRT 1Þ; dt
(8)
where RRT is the removal rate of the RT flame surface wrinkling given by: RRT ¼ 8sSL kRT =p:
(9)
Initial estimates for the constant kRT were obtained using high-resolution 2D simulations. However, due to the limitations of the linear model, which is only applicable for small amplitude disturbances, as well as uncertainties in the calculation of the flame surface acceleration, the values of GRT and RRT were considered to be constants for a given mixture.
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Their values were then calibrated using experimental data for propane, namely two back wall ignition tests. The values of GRT and RRT were then computed for the 18 vol. % hydrogen mixture in accordance with Eqs. (7) and (9) assuming a constant kRT.
3.2.
Mesh geometry, initial and boundary conditions
An unstructured computational mesh was generated for the 64 m3 explosion test chamber geometry matching the major significant features of the experimental setup (Fig. 2). An external volume of 50.0 32.0 40 m was also meshed to capture the venting of burned gas, the external explosions and to reduce the effect of non-ideal boundary conditions. A cell size of 5 cm was used in the region inside the chamber and the area immediately outside the chamber to resolve the external explosion. This yielded a computational mesh of approximately 106 cells, the limit for a reasonable study. Simulations were also performed on a coarser mesh with cell sizes of 10 cm inside the chamber. Flame speeds and maximum overpressures were found to be within 10% between simulations performed on the two meshes, and grid convergence was found to be acceptable. The boundary conditions applied to the geometry were non-slip adiabatic walls for the chamber walls and ground, and wave transmissive pressure boundary conditions were used for the free boundaries to minimize reflections. An unrestricted open vent was used in the simulations. The initial level of turbulence u0 z 0.1 m/s was imposed to match the initial conditions observed in the experiments.
overpressures acting at a sufficiently low frequency to present potentially damaging pressure loads. Multiple pressure peaks and high-frequency oscillations are clearly visible in Fig. 3. These peaks originate from the interactions between various effects such as Helmholtz oscillations and the external explosion that can result in the Taylor instabilities that have been previously observed [1,16]. It can also be seen that, immediately following the first peak related to the external explosion, high frequency acoustics centered about 700 Hz with a range of 100 Hz, corresponding to the natural frequencies of major structural components of the chamber, are also excited.
4.2.
Effect of mixture composition
A filtered and unfiltered pressure time history of a 18% hydrogeneair mixture with center ignition and a 5.4 m2 vent is shown below in Fig. 3 as an example of a typical pressure time history for a vented explosion of a hydrogen mixture. An 80 Hz low pass filter was used to remove the higher frequency component of the pressure signal and isolate the
Table 1 gives a summary of flame speed parameters for the mixtures studied. It is important to note that all three mixtures have similar values of laminar flame speed, which typically corresponds to the propagation speed of the flame observed in the laboratory frame. Despite having similar flame speeds however, lean hydrogen mixtures have a Lewis number less than unity and the increased thermal diffusion amplify the DL flame instability causing lean hydrogen mixtures to propagate faster. The final column of the table shows the average speed for the flame front to reach the thermocouple closest to ignition. While the data in this column shows that the propane and methane mixtures initially propagated at their laminar flame speeds it also shows that hydrogen propagated almost twice as fast as it laminar flame speed. This result illustrates the need for a treatment of flame instabilities in modeling hydrogen deflagrations and provided a value to use in the development of the model. The pressure data presented in this section were all taken from readings of transducer P1 using an 80 Hz low pass filter. No significant differences were found in the readings between transducers. Flame velocities were calculated using flame time-of-arrival data from the line of thermocouples, with the positive direction toward the vent and negative direction toward the back wall. Figs. 4e6 below summarize the results of different mixtures. The pressure time histories seen in Fig. 4 show
Fig. 2 e The geometry of the computational domain used in the numerical simulations.
Fig. 3 e Filtered and unfiltered pressure time history for an 18% hydrogeneair mixture ignited with central ignition and a 5.4 m2 vent.
4.
Results
4.1.
Experimental results
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Table 1 e Summary of flame speed parameters for mixtures studied. Mixture
Laminar burning velocity, SL (m/s)
Expansion ratio, s
Flame speed, (s SL) (m/s)
Average measured initial flame speed, U0 (m/s)
0.40 0.38 0.64
8.0 7.5 5.2
3.2 2.9 3.3
3.31 0.06 2.90 0.14 6.47 0.16
4.0% Propane 9.5% Methane 18% Hydrogen
similar behavior between the propane and methane mixtures with the main difference that the propane peaks occur slightly earlier due to propane’s higher laminar flame speed. While the hydrogen mixtures had the same laminar flame speed as the propane mixtures, the pressure plots show the hydrogen mixtures produced much earlier pressure peaks and achieved significantly higher overall pressures than the propane or methane mixtures. The reason for this can be seen in Figs. 5a and 6a where the flame velocity as a function of position is normalized by the theoretical laminar flame speed of the mixture. In this plot it can be seen that while methane and propane velocities converge to a single curve the hydrogen mixtures exhibited a significantly higher flame propagation speed. It is important to note, however, that when the hydrogen velocity is normalized by its initial measured flame speed, shown in Figs. 5b and 6b, the overall hydrogen velocity curve matches the methane and propane velocity curves. This implies that the enhancement of the hydrogen propagation speed caused by flame instabilities remains more or less constant throughout the combustion process and the increase
4.3.
Experimental results of hydrogen tests
Fig. 7 shows the pressure time history for an 18% hydrogeneair mixture with back ignition, for a 2.7 m2 vent (top) and 5.4 m2 vent (bottom). For both vent sizes a strong pressure transient is generated by the external explosion which is immediately followed by Helmholtz oscillations. The pressure time history for the central ignition tests is shown in Fig. 8. Compared to back-wall ignition, the center ignition tests show the formation of two distinct pressure peaks which are separated by approximately 0.2 s. For the large vent case the pressure within the chamber drops to atmospheric between the two peaks, however with the small vent the pressure does not. For front ignition, shown in Fig. 9, it is clearly seen that the second peak dominates. This is due to the fact that igniting the mixture near the vent prevents the formation of an unburned cloud outside the chamber and virtually eliminates
Hydrogen Methane Propane
0.25
Overpres s u re (bar)
in observed burning velocity can be modeled as a constant factor.
0.20 0.15 0.10 0.05 0.00 -0.05 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
T i me (s)
Overpres s u re (bar)
0.15 Hydrogen Methane Propane
0.10 0.05 0.00 -0.05 0.0
0.2
0.4
0.6
0.8
1.0
Time (s) Fig. 4 e Pressure time history plots comparing hydrogen, methane and propane mixtures for center ignition with a 2.7 m2 vent (top) and back-wall ignition with a 5.4 m2 vent (bottom).
Fig. 5 e Velocity normalized by laminar flame speed (top) and initial flame speed (bottom) for hydrogen, methane and propane mixtures for center ignition with a 2.7 m2 vent.
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40
0.25
U/F S
30
Overpressure (bar)
Hydrogen Methane Propane
20
10
Experiment Simulation
0.20 0.15 0.10 0.05 0.00
0
Overpressure (bar)
20
U/U0
15 10 5 0
0.04
0.02
0.00 0
1
2
3
4
5
6
7
0.0
Distance from Ignition (m)
the pressure transient associated with the external explosion. However, this ignition location appears to amplify the effect of acoustics on the second pressure transient. This is likely due to the larger flame area in the chamber at the time acoustics
Experiment Simulation
0.3
0.2
0.4
0.6
Time ( s )
Fig. 6 e Velocity normalized by laminar flame speed (top) and initial flame speed (bottom) for hydrogen, methane and propane mixtures for back ignition with a 5.4 m2 vent.
Overpressure (bar)
0.06
0.2
0.1
0.0
Fig. 8 e Pressure time history plots for lean hydrogeneair mixtures for center ignition with a 2.7 m2 vent (top) and a 5.4 m2 vent (bottom).
develop as well as the increased the amount of unburned gas which is consumed inside the chamber as opposed to outside. The effect of ignition location for both large and small vents can readily be seen in the results above. Two different peaks developed in the tests and their intensities varied depending on the ignition location. As the ignition takes place farther from the vent the pressure transient associated with the external explosion increased in amplitude due to a larger cloud of unburned gas outside of the chamber as well as a larger flame surface area at the time of the external explosion. As the ignition location moved towards the vent the amplitude of the second peak increased due to an increased amount of gas remaining inside the chamber and larger flame surface area at the time acoustics develop.
Overpressure (bar)
0.15
4.4.
Performance of CFD model
0.10 0.05 0.00 -0.05 0.0
0.2
0.4
0.6
Time (s)
Fig. 7 e Pressure time history plots for lean hydrogeneair mixtures for back-wall ignition with a 2.7 m2 vent (top) and a 5.4 m2 vent (bottom).
The results of the simulations are shown in Figs. 7e9 in comparison with the test data. For all vent sizes and ignition locations the initial pressure build-up and general shape of the pressure time history, outside of the pressure transients, was captured well by the model. For the back-wall ignition tests for the both small vent as well as large vent the CFD model performs well, showing good agreement with the general shape and maximum pressures observed. The pressure peaks generated by the external explosion are captured due to the implementation of the RayleigheTaylor instability model as seen in back ignition propane tests in a previous study [17].
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 2 3 2 9 e2 3 3 6
Overpressure (bar)
0.20 Experiment Simulation 0.15 0.10 0.05 0.00
Overpressure (bar)
0.04
0.02
0.00
-0.02 0.0
0.2
0.4
0.6
0.8
1.0
1.2
Time ( s )
Fig. 9 e Pressure time history plots for lean hydrogeneair mixtures for front ignition with a 2.7 m2 vent (top) and a 5.4 m2 vent (bottom).
For the center ignition tests, particularly for the large vent case, the CFD simulation produces the two distinct pressure peaks seen in the experiments. In fact, for the large vent, the simulation reproduces all of the main features of the pressure trace as well as some small details. This is different from the performance of the same model for propane tests in the previous study. It is possible that the values of GRT and kRT, which were obtained from back ignition propane tests, perform better for the higher magnitude of acceleration generated in center ignition, hydrogen cases but not propane. With the smaller vent the agreement was not as good, particularly after the external explosion where the simulation significantly over-predicts the pressure prior to the second peak. With front ignition it is seen that, while the simulations reproduce the overall shape of the pressureetime history, the model does not capture the pressure transient associated with acoustics in the chamber. This is likely due to the inability of the model to predict the structural response of the chamber; no structural response model was used in the simulations so the walls of the chamber responded as fixed ridged walls. This prevents a coupling to develop between acoustics and the structure, which wrinkles the flame surface, causing it to consume the remaining gas faster, creating the pressure transient. It should be noted that a physics-based model was used in this study. For methaneeair [16] and propaneeair [17] mixtures, one coefficient was needed to calibrate the turbulent burning velocity correlation and another two were needed for the generation and removal rates in the
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RayleigheTaylor model [17]. These underlying coefficients, however, were not changed for the current study. The lean hydrogen mixtures used in this study presented an additional challenge. In lean hydrogen, the DL instability is enhanced by thermal diffusion effects which result in a significant increase of the flame surface. The governing parameter for this instability, such as the cutoff scale, was not known for the mixture tested. Thus, the corresponding XI ¼ 2 was estimated from experimental data for the initial flame speed. The effect of the Lewis number on the rate of change of the turbulent burning velocity with turbulent intensity posed another problem. However, for the test conditions and hydrogen mixture used this effect was not present. It may, however, play a role for other conditions and mixture compositions. This emphasizes that more detailed data on basic properties of lean hydrogen flames are required for the development and validation of numerical models for the description of hydrogen flames in general and in vented explosions in particular.
5.
Conclusions
Experiments were performed in FM Global’s 64 m3 chamber for 18% vol. hydrogeneair, 9.5% methaneeair and 4.0% propaneeair mixtures for two ignition locations and two vent sizes. These experiments showed that, despite having similar laminar flame speeds, the hydrogen mixtures propagated at flame speeds significantly higher than the methane and propane mixtures. Due to the higher propagation speeds of the hydrogen flames, significantly higher pressures were generated during the vented explosions when compared to the methane and propane mixtures. Using the results of the hydrogen experiments, a numerical CFD model was tested and its capabilities and deficiencies were identified. It was found that the model gave a good prediction of initial pressure build-up for all ignition locations and vent sizes and predicted maximum overpressures well for back and center ignition tests. The primary difference seen between experiments and simulations for front ignition was likely due to the structural response of the chamber itself and would require further modeling to capture. It was also shown that there is a need for more detailed information on basic properties of lean hydrogen flames to be used for predictive explosion simulations, particularly at different concentrations. Further studies are necessary to explore improvements of the model and to validate the model over a wide representative range of test conditions.
Acknowledgements The work presented in this paper was funded by FM Global and performed within the framework of the FM Global Strategic Research Program on Explosions and Material Reactivity. The authors are thankful to Franco Tamanini for many helpful discussions of the measurement techniques and test results. The technical assistance of Mike Gravel and Kevin Mullins in preparing and conducting the tests is greatly appreciated.
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[1] Cooper MG, Fairweather M, Tite JP. On the mechanisms of pressure generation in vented explosions. Combust Flame 1986;65:1e14. [2] Zalosh RG. Gas explosion tests in room-size vented enclosures. Proceedings of the 13th loss prevention symposium, Houston; 1979, pp. 98e108. [3] van Wingerden CJM. On the venting of large-scale methaneeair explosions. In: Sixth international symposium of loss prevention and safety promotion in the process industries, 19e22, June 1989, Oslo. [4] Bimson SJ, Bull DC, Cresswell TM, Marks PR, Masters AP, Prothero A, et al. An experimental study of the physics of gaseous deflagration in a very large enclosure.In: Fourteenth international colloquium on the dynamics of explosions and reactive systems, 1ste6th, August 1993, Coimbra, Portugal. [5] Harrison AJ, Eyre JA. External explosions as a result of explosion venting. Combust Sci Technol 1987;52:91e106. [6] Solberg DM, Papas JA, Skramstadt E. Observations of flame instabilities in large scale vented gas explosions. In: 18th International symposium on combustion. Waterloo, ON: The Combustion Institute; 1980. p. 1607e14. [7] Tamanini F, Chaffee JL. Combined turbulence and flame instability effects in vented explosions. In: Seventh international symposium on loss prevention and safety promotion in the process industries, 1992, Taormina, pp. 3811/38-19. [8] Tamanini F. Characterization of mixture reactivity in vented explosions. In: Fourteenth international colloquium on the dynamics of explosions and reactive systems, 1ste6th, August 1993, Coimbra, Portugal. [9] Bradley D, Mitcheson A. The venting of gaseous explosions in spherical vessels. Combust Flame 1978;32:221e55. [10] Molkov VV. Innovative vent sizing technology for gaseous deflagrations. In: Sixth international symposium on fire safety science, July, 1999, France. [11] Molkov VV, Dobashi R, Suzuki M, Hirano T. Modeling of vented hydrogen-air deflagrations and correlations for vent sizing. J Loss Prevent Process Ind 1999;12:147e56. [12] VDI 3673. Pressure venting of dust explosions. Verein Deutcher Ingenieure; 1995. [13] NFPA 68. Standard on explosion protection by deflagration venting. 2007 edn. Quincy, MA 02269: National Fire Protection Association; 2007.
[14] Watterson JK, Connel IJ, Savill AM, Dawes WN. A solution adaptive mesh procedure for predicting confined explosions. Int J Numer Methods Fluids 1998;26:235e47. [15] Molkov V, Makarov D, Puttock J. The nature and large eddy simulation of coherent deflagrations in a vented enclosureatmosphere system. J Loss Prevent Process Ind 2006;19:121e9. [16] Bauwens CR, Chaffee J, Dorofeev S. Experimental and numerical study of methaneeair deflagrations in a vented enclosure. In: Sixth international symposium on fire safety science, September, 2008, Germany. [17] Bauwens CR, Chaffee J, Dorofeev SB. Effect of instabilities and acoustics on pressure generated in vented propaneeair explosions. In: 22nd international colloquium on the dynamics of explosions and reactive systems, 2009, Minsk, Belarus. [18] Weller HG, Tabor G. A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput Phys 1998;12(No. 6):620e31. [19] Issa RI. Solution of the implicitly discretised fluid flow equations by operator-splitting. J Computat Phys 1986;62: 40e65. [20] Fureby C, Tabor G, Weller HG, Gosman AD. A comparative study of subgrid scale models in homogeneous isotropic turbulence. Phys Fluids 1997;9(No. 5):1416e29. [21] Weller HG, Tabor G, Gosman AD, Fureby C. Application of a flame-wrinkling LES combustion model to a turbulent mixing layer. In: 27th International symposium on combustion. Boulder, CO: The Combustion Institute; 1998. p. 899e907. [22] Bychkov V. Importance of the Darrieus-Landau instability for strongly corrugated turbulent flames. Phys Rev E 2003;68. [23] Bradley D, Sheppard CGW, Woolley R, Greenhalgh DA, Lockett RD. The development and structure of flame instabilities and cellularity at low Markstein numbers in explosions. Combust Flame 2000;122:195e209. [24] Bradley D, Lawes M, Liu K, Verhelst S, Woolley R. Laminar burning velocities of lean hydrogeneair mixtures at pressures up to 1.0 MPa. Combust Flame 2007;149:162e72. [25] Bradley D, Lau AKC, Lawes M. Flame stretch rate as a determinant of turbulent burning velocity. Philos Trans Roy Soc Lond Ser A 1992;338:359e87. [26] Driscoll JF. Turbulent premixed combustion: flamelet structure and its effect on turbulent burning velocities. Prog Energy Combust Sci 2008;34:91e134. [27] Zeldovich YB, Barenblatt GI, Librovich VB, Makhviladze GM. Mathematical theory of combustion and explosion. New York: Consultants Bureau; 1985.
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Vented explosion overpressures from combustion of hydrogen and hydrocarbon mixtures C.R. Bauwens, J. Chaffee, S.B. Dorofeev* FM Global, Research Division, 1151 Boston-Providence Turnpike, Norwood, MA 02061, USA
article info
abstract
Article history:
Experimental data obtained for hydrogen mixtures in a room-size enclosure are presented
Received 1 February 2010
and compared with data for propane and methane mixtures. This set of data was also used
Received in revised form
to develop a three-dimensional gasdynamic model for the simulation of gaseous
30 March 2010
combustion in vented enclosures. The experiments were performed in a 64 m3 chamber
Accepted 1 April 2010
with dimensions of 4.6 4.6 3.0 m and a vent opening on one side and vent areas of
Available online 21 May 2010
either 2.7 or 5.4 m2 were used. Tests were performed for three ignition locations, at the wall opposite the vent, at the center of the chamber or at the center of the wall containing the
Keywords:
vent. Hydrogeneair mixtures with concentrations close 18% vol. were compared with
Explosions
stoichiometric propaneeair and methaneeair mixtures. Pressure data, as function of time,
Hydrogen
and flame time-of-arrival data were obtained both inside and outside the chamber near the
Venting
vent. Modeling was based on a Large Eddy Simulation (LES) solver created using the
Modeling
OpenFOAM CFD toolbox using sub-grid turbulence and flame wrinkling models. A comparison of these simulations with experimental data is discussed. ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Explosion venting can be used to prevent or minimize damage to an enclosure by relieving the pressure generated within the volume and is an important engineering loss prevention solution. Experimentally, the subject of vented explosions has been widely studied with research performed over a range of scales, from laboratory scale tests (see, e.g., [1]) to large-scale tests (see, e.g., Refs. [2e4]). Factors contributing to the pressure build-up in vented explosions have been extensively studied [1e8]. Analytical models and empirical correlations have also been developed (see, e.g., Refs. [8e11]), a number of which have been included in engineering guidelines [12,13]. These correlations, however, often have conflicting recommendations. This is due to the complex nature of the process itself, as mentioned above, and the influence of other factors that can
affect the peak overpressure, such as size and shape of the enclosure, the mixture being burned, the type of vent and vent deployment pressure, congestion or obstacles inside the chamber and the ignition location. Computational Fluid Dynamics (CFD) simulations of vented explosions, and the comparison of these simulations with experimental data [4,14,15], have shown some of the challenges in adequately modeling the major physical phenomena. Although there are a few examples of successful CFD applications for several selected tests, such as [15], it is not unusual to find CFD predictions that are off the test results by more than an order of magnitude. Because of the limited reliability of the current methods for the prediction of pressure generation during a vented explosion, a research project was initiated with the goals of generating a parametric set of experimental data as well as developing and validating a computational code and new
* Corresponding author. E-mail address: [email protected] (S.B. Dorofeev). 0360-3199/$ e see front matter ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.04.005
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engineering tools. The first part was performed for low reactivity stoichiometric methaneeair mixtures [16]. Another study examined the effect of the RayleigheTaylor instability on flame propagation [17]. The lean hydrogen mixtures used in the present study, however, present additional challenges. This is mainly due to two factors. First, that the DarrieuseLandau (DL) flame instability is enhanced by thermal diffusion effects, which results in a significant increase in the flame surface for lean hydrogen mixtures. The second challenge is the effect of the Lewis number on the rate of change of the turbulent burning velocity with respect to the turbulent intensity. Currently, the strength of these effects is not known well enough to be reliably modeled. Comparisons with stoichiometric methaneeair and propaneeair mixtures illustrate the significant differences caused by these instabilities and yield some insight on how to model them. The objectives of the present work are to (i) examine the similarities and differences between three mixtures of similar laminar flame speed, 18% hydrogeneair, 9.5% methaneeair and 4.0% propaneeair; and (ii) test an extension to the numerical CFD model developed in the previous study and identify its capabilities and deficiencies to describe the physics responsible for the pressure build-up.
2.
Experiments
The data presented here were obtained from experiments performed in a 64 m3 explosion test chamber. The overall dimensions of the chamber were 4.6 3.0 4.6 m with a square vent of either 5.4 m2, or 2.7 m2 located on one of the vertical walls. Four chamber pressure transducers were mounted to the chamber, one at the center of the wall opposite the vent, one on the wall containing the vent, and two on a wall perpendicular to the vent (one on-axis with the center of the chamber, one off-axis), (see Fig. 1). Twenty flame time-ofarrival thermocouples, at a height of 1.4 m above the floor of the chamber, were placed at 0.5 m intervals inside the chamber
along two axes and at 1 m intervals outside of the chamber. Two blast-wave pressure transducers were installed in a concrete slab outside of the chamber, below the line of thermocouples at a height of 0.3 m above the ground, 1.17 m and 3.45 m from the vent. One high speed and four low speed cameras were used to observe the tests, either directed into the chamber or directed outside to capture the external explosion. Data was collected using a 32 channel high speed data acquisition system sampling at a rate of 25,000 scans/s. The initial mixture was supplied by injecting the pure fuel through an inlet at the floor of the chamber while mixing fans within the chamber were used to create a uniform mixture. The concentration of gas inside the chamber was controlled using a Cirrus mass spectrometer. The unburned mixture was contained within the chamber (prior to ignition) using a 0.02 mm thin sheet of polypropylene. Ignition was supplied using a carbon rod igniter at one of three locations, either at the center of the chamber, 0.25 m from the center of the wall opposite the vent (back ignition) or 0.25 m from the center of the wall containing the vent (front ignition). The time between when the mixing fans were stopped and ignition was controlled to ensure a consistent initial turbulent intensity (u0 z 0.1 m/s), which was determined in a series of preliminary tests using measurements from a bi-directional velocity probe. In this study three mixture compositions were examined: 18% vol. hydrogeneair, 9.5% methaneeair and 4.0% propaneeair. For each of mixtures experiments were performed for the three ignition locations, center, back and front, and two vent sizes 2.7 m2 and 5.4 m2.
3.
Numerical simulations
3.1.
Solver details
Numerical simulations were performed using a custom solver built using the OpenFOAM CFD toolbox [18]. The code is based
Fig. 1 e Chamber geometry and instrumentation, showing: pressure transducers (rectangles), thermocouples (circles) and blast-wave transducers (triangles).
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 2 3 2 9 e2 3 3 6
on a Large Eddy Simulation (LES) solver of the NaviereStokes conservation equations for mass, momentum and energy using a robust, implicit, pressureevelocity, iterative solution framework, with a fully compressible Pressure-Implicit Split Operator (PISO) solution method [19]. Sub-grid scale turbulence was modeled using a one-equation eddy viscosity model [20]. An unstructured grid was used for the current study. Second order schemes were used in space and time, central differencing for velocity, a bounded TVD scheme for scalars, and second order backward differencing for time. The combustion model is based on a transport equation for a regress combustion variable b [21]. The transport of the regress variable is governed by a laminar burning velocity, SL and a flame surface wrinkling factor, X. The scalar flame surface wrinkling factor, X, was transported to take into account the effect of flame wrinkling on the burning velocity. Flame instabilities in a lean hydrogeneair mixture can produce a significant increase in the flame’s surface area and propagation speed. This effect was incorporated into the model using Eq. (1) below, X ¼ XI XT XRT ;
(1)
where XI is the surface wrinkling factor due to the DL flame instability, XT is the surface wrinkling factor due to turbulence and XRT is the surface wrinkling factor due to the RayleigheTaylor instability, whose role in vented explosions is described in [17] and is summarized in the following section. The form of Eq. (1) suggests that the characteristic length scales of the three types of wrinkling are different. The XI term in Eq. (1) may be expressed as [22]: XI ¼
1=3 lm ; lc
(2)
where lm is the maximum unstable scale and lc is the cutoff wavelength. In a sub-grid model lm D, where D is the filter size. Experimentally, the onset of instability is observed for sufficiently large Peclet numbers, Pe ¼ r/d > Pecl, where r is the flame radius, d is the flame thickness, and Pecl is the critical Pe number [23,24]. The cutoff scale is given by: lc =d ¼ 2pPecl =ncl ;
(3)
where ncl is the critical wave number and is of the order of 10. This yields the following equation for XI: 1=3 D XI ¼ max 1; aI lc
(4)
where aI is a coefficient to account for the uncertainty in lc. In cases when aI(D/lc)1/3 < 1, flame instabilities are expected to be resolved on the grid scale and XI ¼ 1. This was the case in [16] where methaneeair mixtures were used. For an 18% hydrogeneair mixture at 365 K the cutoff scale has been estimated as lc ¼ 7 mm [24]. The value of lc for normal initial temperature, however, is unknown. In the current study the values of lc ¼ 7 mm and aI ¼ 1.2 were used, and were found to produce agreement with the initial flame propagation velocity. The surface wrinkling factor due to turbulence, XT was computed using a transport equation taking into account the
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generation and removal of flame surface wrinkling. The equilibrium XT, Xeq* is given by the following turbulent burning velocity correlation [25]: 1
1
Xeq ¼ 1:04$ðu0 =SL Þ2 ðLT =dÞ6 ;
(5)
where u0 is the turbulent intensity, LT is the integral turbulent length scale and d is the flame thickness. The coefficient of 1.04 in the correlation was determined in the previous study using methane [17] and is used because the value of the burning velocity predicted by Bradley’s correlation is only estimated within a factor of 2. A decrease of the Lewis number may increase the rate of change of the turbulent burning velocity with turbulence intensity as suggested in [25,26]. In the current model, however, this effect was not considered, and was not observed in the experimental results presented below. The effect of the Lewis number was solely attributed to the changes of burning velocity due to the flame instabilities.
3.1.1. Model for flame surface wrinkling due to the RayleigheTaylor instability The basic approach taken to model the flame surface wrinkling due to the RT instability is to solve an additional transport equation for XRT [17]. The development of the transport equation requires the specification of generation and removal rates for the sub-grid wrinkling. Although the process through which the RT instability grows on a surface with acceleration is highly non-linear, one can use a linearized theory to estimate the growth and removal rates. The parameters of these estimates are then adjusted to compensate for non-linear effects through comparison with experimental data. A general expression for the linearized growth rate of flame instabilities is given in [27] includes terms describing the baseline DL instability with thermal diffusion effects and the RT instability. To simplify the problem, we assume the DL and RT instabilities occur at significantly different wavelengths, this allows the component of the generation rate that varies with acceleration to be separated: 1=2 s * 1* a$ n ; GRT ¼ 2 kRT sþ1
(7)
where kRT is the unstable wave number associated with the RT instability, a is acceleration and s is the expansion ratio. Considering that the removal of flame wrinkling is due to flame propagation and annihilation of the flame surface at cusps yields a transport equation for XRT: dXRT ¼ GRT ðXRT 1Þ RRT ðXRT 1Þ; dt
(8)
where RRT is the removal rate of the RT flame surface wrinkling given by: RRT ¼ 8sSL kRT =p:
(9)
Initial estimates for the constant kRT were obtained using high-resolution 2D simulations. However, due to the limitations of the linear model, which is only applicable for small amplitude disturbances, as well as uncertainties in the calculation of the flame surface acceleration, the values of GRT and RRT were considered to be constants for a given mixture.
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Their values were then calibrated using experimental data for propane, namely two back wall ignition tests. The values of GRT and RRT were then computed for the 18 vol. % hydrogen mixture in accordance with Eqs. (7) and (9) assuming a constant kRT.
3.2.
Mesh geometry, initial and boundary conditions
An unstructured computational mesh was generated for the 64 m3 explosion test chamber geometry matching the major significant features of the experimental setup (Fig. 2). An external volume of 50.0 32.0 40 m was also meshed to capture the venting of burned gas, the external explosions and to reduce the effect of non-ideal boundary conditions. A cell size of 5 cm was used in the region inside the chamber and the area immediately outside the chamber to resolve the external explosion. This yielded a computational mesh of approximately 106 cells, the limit for a reasonable study. Simulations were also performed on a coarser mesh with cell sizes of 10 cm inside the chamber. Flame speeds and maximum overpressures were found to be within 10% between simulations performed on the two meshes, and grid convergence was found to be acceptable. The boundary conditions applied to the geometry were non-slip adiabatic walls for the chamber walls and ground, and wave transmissive pressure boundary conditions were used for the free boundaries to minimize reflections. An unrestricted open vent was used in the simulations. The initial level of turbulence u0 z 0.1 m/s was imposed to match the initial conditions observed in the experiments.
overpressures acting at a sufficiently low frequency to present potentially damaging pressure loads. Multiple pressure peaks and high-frequency oscillations are clearly visible in Fig. 3. These peaks originate from the interactions between various effects such as Helmholtz oscillations and the external explosion that can result in the Taylor instabilities that have been previously observed [1,16]. It can also be seen that, immediately following the first peak related to the external explosion, high frequency acoustics centered about 700 Hz with a range of 100 Hz, corresponding to the natural frequencies of major structural components of the chamber, are also excited.
4.2.
Effect of mixture composition
A filtered and unfiltered pressure time history of a 18% hydrogeneair mixture with center ignition and a 5.4 m2 vent is shown below in Fig. 3 as an example of a typical pressure time history for a vented explosion of a hydrogen mixture. An 80 Hz low pass filter was used to remove the higher frequency component of the pressure signal and isolate the
Table 1 gives a summary of flame speed parameters for the mixtures studied. It is important to note that all three mixtures have similar values of laminar flame speed, which typically corresponds to the propagation speed of the flame observed in the laboratory frame. Despite having similar flame speeds however, lean hydrogen mixtures have a Lewis number less than unity and the increased thermal diffusion amplify the DL flame instability causing lean hydrogen mixtures to propagate faster. The final column of the table shows the average speed for the flame front to reach the thermocouple closest to ignition. While the data in this column shows that the propane and methane mixtures initially propagated at their laminar flame speeds it also shows that hydrogen propagated almost twice as fast as it laminar flame speed. This result illustrates the need for a treatment of flame instabilities in modeling hydrogen deflagrations and provided a value to use in the development of the model. The pressure data presented in this section were all taken from readings of transducer P1 using an 80 Hz low pass filter. No significant differences were found in the readings between transducers. Flame velocities were calculated using flame time-of-arrival data from the line of thermocouples, with the positive direction toward the vent and negative direction toward the back wall. Figs. 4e6 below summarize the results of different mixtures. The pressure time histories seen in Fig. 4 show
Fig. 2 e The geometry of the computational domain used in the numerical simulations.
Fig. 3 e Filtered and unfiltered pressure time history for an 18% hydrogeneair mixture ignited with central ignition and a 5.4 m2 vent.
4.
Results
4.1.
Experimental results
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Table 1 e Summary of flame speed parameters for mixtures studied. Mixture
Laminar burning velocity, SL (m/s)
Expansion ratio, s
Flame speed, (s SL) (m/s)
Average measured initial flame speed, U0 (m/s)
0.40 0.38 0.64
8.0 7.5 5.2
3.2 2.9 3.3
3.31 0.06 2.90 0.14 6.47 0.16
4.0% Propane 9.5% Methane 18% Hydrogen
similar behavior between the propane and methane mixtures with the main difference that the propane peaks occur slightly earlier due to propane’s higher laminar flame speed. While the hydrogen mixtures had the same laminar flame speed as the propane mixtures, the pressure plots show the hydrogen mixtures produced much earlier pressure peaks and achieved significantly higher overall pressures than the propane or methane mixtures. The reason for this can be seen in Figs. 5a and 6a where the flame velocity as a function of position is normalized by the theoretical laminar flame speed of the mixture. In this plot it can be seen that while methane and propane velocities converge to a single curve the hydrogen mixtures exhibited a significantly higher flame propagation speed. It is important to note, however, that when the hydrogen velocity is normalized by its initial measured flame speed, shown in Figs. 5b and 6b, the overall hydrogen velocity curve matches the methane and propane velocity curves. This implies that the enhancement of the hydrogen propagation speed caused by flame instabilities remains more or less constant throughout the combustion process and the increase
4.3.
Experimental results of hydrogen tests
Fig. 7 shows the pressure time history for an 18% hydrogeneair mixture with back ignition, for a 2.7 m2 vent (top) and 5.4 m2 vent (bottom). For both vent sizes a strong pressure transient is generated by the external explosion which is immediately followed by Helmholtz oscillations. The pressure time history for the central ignition tests is shown in Fig. 8. Compared to back-wall ignition, the center ignition tests show the formation of two distinct pressure peaks which are separated by approximately 0.2 s. For the large vent case the pressure within the chamber drops to atmospheric between the two peaks, however with the small vent the pressure does not. For front ignition, shown in Fig. 9, it is clearly seen that the second peak dominates. This is due to the fact that igniting the mixture near the vent prevents the formation of an unburned cloud outside the chamber and virtually eliminates
Hydrogen Methane Propane
0.25
Overpres s u re (bar)
in observed burning velocity can be modeled as a constant factor.
0.20 0.15 0.10 0.05 0.00 -0.05 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
T i me (s)
Overpres s u re (bar)
0.15 Hydrogen Methane Propane
0.10 0.05 0.00 -0.05 0.0
0.2
0.4
0.6
0.8
1.0
Time (s) Fig. 4 e Pressure time history plots comparing hydrogen, methane and propane mixtures for center ignition with a 2.7 m2 vent (top) and back-wall ignition with a 5.4 m2 vent (bottom).
Fig. 5 e Velocity normalized by laminar flame speed (top) and initial flame speed (bottom) for hydrogen, methane and propane mixtures for center ignition with a 2.7 m2 vent.
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40
0.25
U/F S
30
Overpressure (bar)
Hydrogen Methane Propane
20
10
Experiment Simulation
0.20 0.15 0.10 0.05 0.00
0
Overpressure (bar)
20
U/U0
15 10 5 0
0.04
0.02
0.00 0
1
2
3
4
5
6
7
0.0
Distance from Ignition (m)
the pressure transient associated with the external explosion. However, this ignition location appears to amplify the effect of acoustics on the second pressure transient. This is likely due to the larger flame area in the chamber at the time acoustics
Experiment Simulation
0.3
0.2
0.4
0.6
Time ( s )
Fig. 6 e Velocity normalized by laminar flame speed (top) and initial flame speed (bottom) for hydrogen, methane and propane mixtures for back ignition with a 5.4 m2 vent.
Overpressure (bar)
0.06
0.2
0.1
0.0
Fig. 8 e Pressure time history plots for lean hydrogeneair mixtures for center ignition with a 2.7 m2 vent (top) and a 5.4 m2 vent (bottom).
develop as well as the increased the amount of unburned gas which is consumed inside the chamber as opposed to outside. The effect of ignition location for both large and small vents can readily be seen in the results above. Two different peaks developed in the tests and their intensities varied depending on the ignition location. As the ignition takes place farther from the vent the pressure transient associated with the external explosion increased in amplitude due to a larger cloud of unburned gas outside of the chamber as well as a larger flame surface area at the time of the external explosion. As the ignition location moved towards the vent the amplitude of the second peak increased due to an increased amount of gas remaining inside the chamber and larger flame surface area at the time acoustics develop.
Overpressure (bar)
0.15
4.4.
Performance of CFD model
0.10 0.05 0.00 -0.05 0.0
0.2
0.4
0.6
Time (s)
Fig. 7 e Pressure time history plots for lean hydrogeneair mixtures for back-wall ignition with a 2.7 m2 vent (top) and a 5.4 m2 vent (bottom).
The results of the simulations are shown in Figs. 7e9 in comparison with the test data. For all vent sizes and ignition locations the initial pressure build-up and general shape of the pressure time history, outside of the pressure transients, was captured well by the model. For the back-wall ignition tests for the both small vent as well as large vent the CFD model performs well, showing good agreement with the general shape and maximum pressures observed. The pressure peaks generated by the external explosion are captured due to the implementation of the RayleigheTaylor instability model as seen in back ignition propane tests in a previous study [17].
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 2 3 2 9 e2 3 3 6
Overpressure (bar)
0.20 Experiment Simulation 0.15 0.10 0.05 0.00
Overpressure (bar)
0.04
0.02
0.00
-0.02 0.0
0.2
0.4
0.6
0.8
1.0
1.2
Time ( s )
Fig. 9 e Pressure time history plots for lean hydrogeneair mixtures for front ignition with a 2.7 m2 vent (top) and a 5.4 m2 vent (bottom).
For the center ignition tests, particularly for the large vent case, the CFD simulation produces the two distinct pressure peaks seen in the experiments. In fact, for the large vent, the simulation reproduces all of the main features of the pressure trace as well as some small details. This is different from the performance of the same model for propane tests in the previous study. It is possible that the values of GRT and kRT, which were obtained from back ignition propane tests, perform better for the higher magnitude of acceleration generated in center ignition, hydrogen cases but not propane. With the smaller vent the agreement was not as good, particularly after the external explosion where the simulation significantly over-predicts the pressure prior to the second peak. With front ignition it is seen that, while the simulations reproduce the overall shape of the pressureetime history, the model does not capture the pressure transient associated with acoustics in the chamber. This is likely due to the inability of the model to predict the structural response of the chamber; no structural response model was used in the simulations so the walls of the chamber responded as fixed ridged walls. This prevents a coupling to develop between acoustics and the structure, which wrinkles the flame surface, causing it to consume the remaining gas faster, creating the pressure transient. It should be noted that a physics-based model was used in this study. For methaneeair [16] and propaneeair [17] mixtures, one coefficient was needed to calibrate the turbulent burning velocity correlation and another two were needed for the generation and removal rates in the
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RayleigheTaylor model [17]. These underlying coefficients, however, were not changed for the current study. The lean hydrogen mixtures used in this study presented an additional challenge. In lean hydrogen, the DL instability is enhanced by thermal diffusion effects which result in a significant increase of the flame surface. The governing parameter for this instability, such as the cutoff scale, was not known for the mixture tested. Thus, the corresponding XI ¼ 2 was estimated from experimental data for the initial flame speed. The effect of the Lewis number on the rate of change of the turbulent burning velocity with turbulent intensity posed another problem. However, for the test conditions and hydrogen mixture used this effect was not present. It may, however, play a role for other conditions and mixture compositions. This emphasizes that more detailed data on basic properties of lean hydrogen flames are required for the development and validation of numerical models for the description of hydrogen flames in general and in vented explosions in particular.
5.
Conclusions
Experiments were performed in FM Global’s 64 m3 chamber for 18% vol. hydrogeneair, 9.5% methaneeair and 4.0% propaneeair mixtures for two ignition locations and two vent sizes. These experiments showed that, despite having similar laminar flame speeds, the hydrogen mixtures propagated at flame speeds significantly higher than the methane and propane mixtures. Due to the higher propagation speeds of the hydrogen flames, significantly higher pressures were generated during the vented explosions when compared to the methane and propane mixtures. Using the results of the hydrogen experiments, a numerical CFD model was tested and its capabilities and deficiencies were identified. It was found that the model gave a good prediction of initial pressure build-up for all ignition locations and vent sizes and predicted maximum overpressures well for back and center ignition tests. The primary difference seen between experiments and simulations for front ignition was likely due to the structural response of the chamber itself and would require further modeling to capture. It was also shown that there is a need for more detailed information on basic properties of lean hydrogen flames to be used for predictive explosion simulations, particularly at different concentrations. Further studies are necessary to explore improvements of the model and to validate the model over a wide representative range of test conditions.
Acknowledgements The work presented in this paper was funded by FM Global and performed within the framework of the FM Global Strategic Research Program on Explosions and Material Reactivity. The authors are thankful to Franco Tamanini for many helpful discussions of the measurement techniques and test results. The technical assistance of Mike Gravel and Kevin Mullins in preparing and conducting the tests is greatly appreciated.
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 2 3 2 9 e2 3 3 6
references
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