Statement of key research activities of Dr. Arief Dahoe 4 best journal publications: 2 reserve papers: 4 items of esteem:

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1 Statement of key research activities of Dr. Arief Dahoe Dr. Dahoe is researching hydrogen related problems on explosions and dispersion in cooperation with Prof. V.V. Molkov and Dr. D.V. Makarov from the University of Ulster (United Kingdom), and involved in research activities on dust explosions, explosion safety, the decay of turbulence, specific forms of turbulent combustion modelling for application to explosions, and least-squares gradient reconstruction in conjunction with stiff time integration with Mr. T. Skjold from the University of Bergen (Norway), Prof. R.S. Cant from the University of Cambridge (United Kingdom), and, Prof. H.J. Pasman, Prof. D.J.E.M. Roekaerts and Prof. M. Donze from Delft University of Technology (The Netherlands). Within the EC funded 'Network of Excellence Safety of Hydrogen as an Energy Carrier' (NoE HySafe), Dr. Dahoe is examining and reviewing the latest research in the field of hydrogen safety to aid the development of an International Curriculum on Hydrogen Safety Engineering ( and to identify knowledge gaps that require further research. 4 best journal publications: 1. Dahoe A.E., Cant R.S., and Scarlett B. On the decay of turbulence in the 20- liter explosion sphere. Flow, Turbulence and Combustion, 67: , Dahoe A.E., Hanjalic K., and Scarlett B. Determination of the laminar burning velocity and the Markstein length of powder-air flames. Powder Technology, 122: , Dahoe A.E. and de Goey L.P.H. On the determination of the laminar burning velocity of closed vessel explosions. Journal of Loss Prevention in the Process Industries, 16: , Dahoe A.E. Laminar burning velocities of hydrogen-air mixtures from closed vessel gas explosions. Journal of Loss Prevention in the Process Industries, 18: , reserve papers: 5. Dahoe A.E., Cant R.S., Pegg M.J., and Scarlett B. On the transient flow in the standard 20-liter explosion sphere. Journal of Loss Prevention in the Process Industries, 14: , Dahoe A.E., and Molkov V.V. On the development of an international curriculum on hydrogen safety engineering and its implementation into educational programmes. International Journal of Hydrogen Energy, 32: , items of esteem: Visiting scholar at the Division of Energy, Fluid Mechanics and Turbomachinery, Department of Engineering, University of Cambridge, Cambridge, United Kingdom ( ). Quotation by independent sources: Dr Dahoe's dust explosion work, the Dahoe equations for laminar flame propagation, the Dahoe equations of turbulent flame propagation, and the Dahoe equation for the explosion constant K. Prestigious award: CEC-funded project 'European Summer School on Hydrogen Safety' (Contract No. MSCF-CT , award: , ). Member of the European Network of Excellence 'Safety of Hydrogen as an Energy Carrier' (NoE HySafe).

2 Flow, Turbulence and Combustion 67: , Kluwer Academic Publishers. Printed in the Netherlands. 159 On the Decay of Turbulence in the 20-Liter Explosion Sphere A.E. DAHOE 1,2, R.S. CANT 2 and B. SCARLETT 1 1 Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands 2 Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom Received 10 October 2000; accepted in revised form 28 September 2001 Abstract. The transient flow field in the standard 20-liter explosion sphere was investigated by means of laser Doppler anemometry. Velocities were measured at various locations within the flow field, and this information was used to quantify the transient behavior of the root-mean-square of the velocity fluctuations and to investigate the spatial homogeneity and the directional isotropy of the turbulence. The investigation involved the transient flow fields generated by the three most widely used dust dispersion systems, namely, the Perforated Dispersion Ring, the Rebound Nozzle, and the Dahoe Nozzle. With all three dispersion dust devices, the decay of turbulence could be correlated by a decay law of the form v rms ( ) t n v rms =. t 0 It was found that no formal cube-root-law agreement exists between the 20-liter explosion sphere and the 1-m 3 vessel. The results of this work also call into question the widely held belief that the cube-root-law is a valid scaling relationship between dust explosion severities measured in laboratory test vessels and the severity of industrial dust explosions. Key words: cube-root-law, dust explosion, laser Doppler anemometry, turbulence decay. 1. Introduction The safe operation of chemical plants handling combustible particles requires characterization of the severity of an accidental dust explosion under actual process conditions of pressure, temperature and turbulence. In the absence of a comprehensive approach which is capable of predicting the transient combustion behavior of gas-particle flows in industrial plant units, researchers have adopted a practical methodology to assess the severity of an accidental dust explosion. In this methodology dust explosion severity parameters are measured using laboratory test vessels in order to estimate what would happen if the same mixture exploded in an industrial plant unit. Typical dust explosion severity parameters which form the design basis for a great deal of practical safety in industrial plants are the maximum explosion pressure, P max, and the maximum rate of pressure rise, (dp/dt) max. Their practical

3 160 A.E. DAHOE ET AL. Figure 1. Explosion curve of a 500 g m 3 cornstarch-air mixture in the standard 20-liter explosion sphere. relevance can be understood with the aid of the pressure-time curve of a cornstarchair dust explosion shown in Figure 1. At the beginning of the explosion the pressure is equal to the atmospheric pressure (1 bar) and increases up to a maximum value of about 7 bar, which marks the end of the explosion process. During the explosion the pressure increases progressively until the rate of pressure rise achieves a maximum, after which the pressure continues to increase with a progressively decreasing rate of pressure rise. The maximum explosion pressure and the maximum rate of pressure rise are both determined from the experimental pressure-time curve as shown by Figure 1. The reasons for choosing these quantities to characterize the severity of an industrial dust explosion are also evident from this figure. The maximum explosion pressure gives an indication of the magnitude of the damaging pressures that may be generated and the maximum rate of pressure rise indicates how fast these pressures can develop. From a practical point of view the maximum explosion pressure may be used to determine the design strength of industrial equipment so that it can withstand the violence of an explosion. The maximum rate of pressure rise may be used to dimension pressure relief systems which counteract the development of damaging pressures so that they do not exceed a particular design strength. Both the maximum explosion pressure and the maximum rate of pressure rise are known to be a function of the chemical composition, pressure, temperature and flow properties. In case of the maximum explosion pressure, the application of laboratory test data to industrial plant units appears to be straightforward, provided that similar conditions of pressure, temperature, and flow properties exist in the laboratory test vessels and the industrial equipment. The maximum explosion rate of pressure rise, however, requires the use of a scaling law which is known as the cube-root-law [1 3]. In other words, if chemically identical mixtures are ignited to deflagration in two differently sized vessels with identical conditions of pressure,

4 ON THE DECAY OF TURBULENCE IN THE 20-LITER EXPLOSION SPHERE 161 temperature and turbulence, and changes in these conditions would be the same during the course of an explosion in these vessels, one would measure identical maximum explosion pressures. At the same time, one would find a lower maximum rate of pressure rise in the larger vessel. As this is a consequence of the difference in size between the vessels, researchers have adopted the cube-root-law, K St = ( dp dt ) V 1/3, (1) which is to be applied as follows. The maximum rate of pressure rise measured in one vessel (i.e. the laboratory vessel) is multiplied by the cube root of its volume to yield a K St -value which is assumed to be a volume invariant dust explosion severity index. The maximum rate of pressure rise of the same mixture in the other vessel (i.e. plant unit) is obtained by dividing this K St -value by the cube root of its volume. The resulting dust explosion severity then forms the design basis for explosion protection (e.g. explosion relief venting, explosion suppression). This approach is known as the VDI-methodology and rests entirely on the validity of the cube-root-law. It is the purpose of this paper is to present experimental results which are relevant to two issues in the study and prediction of dust explosion behavior. The first issue concerns the formal cube-root-law agreement which is believed to exist between dust explosion severities measured in differently sized vessels, and hence between dust explosions in small laboratory test vessels and accidental dust explosions on an industrial scale. Bartknecht [3] presented research which showed that K St -values found using the 20-liter sphere were identical to those found using the 1-m 3 vessel (see Figure 2). This research was initially carried out because the 1-m 3 vessel, which was the only internationally accepted dust explosion testing device (ISO 6184/1 [4]), required much labor and large amounts of powder. With dust concentrations being typically between 0.1 and 1.5 kg m 3, the cost of dust explosion severity testing involving expensive powders (e.g. pharmaceutical compounds) would be greatly reduced by the use of a smaller explosion vessel. Therefore, Siwek [5] developed a 20- liter explosion sphere which requires much less labor and functions with 50 times less powder, and was hailed as a significant advance in powder safety testing. Its acceptance as a standardized dust explosion testing device, however, would depend on whether or not it would give the same K St -values as the 1-m 3 vessel. A particular problem which had to be overcome was that of the turbulence of the dust clouds which are ignited to deflagration in the test vessels. The origin of this problem stems from the fact that without some degree of fluid motion a dust cloud cannot exist because the particles have a tendency to settle out. With both test vessels an air blast is used to initially suspend the particles, and the turbulence which is generated by the air blast keeps the particles air-borne until ignition occurs. In order to clarify the difficulties posed by this problem it is necessary to consider the method by which the air blast is generated in some detail.

5 162 A.E. DAHOE ET AL. Figure 2. K St -values of various dusts measured in the 1 m 3 -vessel and the 20-liter sphere as reported by Bartknecht [3].

6 ON THE DECAY OF TURBULENCE IN THE 20-LITER EXPLOSION SPHERE 163 In case of the 1-m 3 vessel, two 5.4-liter pressure canisters are mounted on the explosion chamber. These are filled with the dust particles and with compressed air of 20 bar, after which their content is discharged into the explosion chamber. Before the air blast, the pressure in the explosion chamber is made equal to 1 bar and it is only slightly affected by the discharge because the volume of the canisters is comparatively small. The air blast, during which considerable turbulence is generated and a dust cloud is formed in the explosion chamber, lasts 600 ms. Since the burning rate is increased by turbulence, and due to the transient nature of the turbulence level, a practical test procedure was adopted which required that ignition must occur as soon as the air blast is completed. The time between the beginning of the air blast and the moment of ignition is known the ignition delay time. It was assumed that the turbulence level in the 1-m 3 vessel was the highest at an ignition delay time of 600 ms (after this time turbulence decay becomes larger than turbulence production) and that this significant, but unknown, turbulence level would never be exceeded by what might exist in industrial equipment. Dust explosion severity parameters, measured in the 1-m 3 vessel, were therefore believed to be a conservative estimate of what might happen when an accidental explosion occurs in industrial equipment. In case of the 20-liter sphere, the dust particles and compressed air are discharged into the explosion chamber from a pressure canister with a volume 0.4 liter. The explosion chamber is initially evacuated to a pressure of 0.4 bar and the pressure canister is filled with compressed air of 21 bar. The air blast lasts about 50 ms, after which the pressure in the explosion chamber becomes equal to 1 bar and turbulence starts to decay. As indicated by Figure 2, Bartknecht and Siwek observed that the 20-liter sphere produced K St -values that were in agreement those obtained with the 1-m 3 vessel when the ignition delay time in the former was set equal to 60 ms. This observation did not only give rise to the belief that the turbulence properties in the 20-liter sphere at an ignition delay time of 60 ms were equal to those in the 1-m 3 vessel at an ignition delay time of 600 ms. It also inspired the widespread belief that a formal cube-root-law agreement could exist between turbulent dust explosions in small laboratory test vessels and large scale dust explosions in industrial equipment. In addition to that, technical guidelines adopted the notion that powder safety testing of all types of combustible dusts can be performed using the 20-liter sphere by adhering to a single prescribed test procedure with a single, fixed ignition delay time of 60 ms, and that these results, in conjunction with the cube-root-law, can form the design basis of industrial safety. In spite of the experimental evidence presented by Bartknecht and Siwek, based on a variety of powders, other researchers questioned the generality of the observation of a formal cube-root-law agreement between the 20-liter sphere and the 1-m 3 vessel. Van der Wel et al. [6], measured the K St -value of potato starch, lycopodium, and activated carbon with both test vessels (see Figure 3), and found that the K St - value in the 20-liter sphere at an ignition delay time of 60 ms was not in agreement with that in the 1-m 3 vessel at an ignition delay time of 600 ms. Instead, they

7 164 A.E. DAHOE ET AL. Figure 3. K St -values of various dusts measured in the 1-m 3 vessel and the 20-liter sphere as reported by van der Wel et al. [6].

8 ON THE DECAY OF TURBULENCE IN THE 20-LITER EXPLOSION SPHERE 165 found that the K St -values in the 20-liter sphere were in agreement at ignition delay times of 80, 100, and 165 milliseconds. Apart from measuring K St -values in the 20-liter sphere at various ignition delay times, and hence different conditions of turbulence, van der Wel et al. used hot-wire anemometry to measure turbulence frequency spectra in both vessels [6]. Although these researchers did not measure the turbulence level in the 20-liter sphere explicitly, their research indicated that conditions of similar turbulence existed in the two vessels when the ignition delay time in the 20-liter sphere was equal to 165 ms, instead of the prescribed 60 ms. A similar observation was also made by Pu et al. [7], who performed explicit turbulence measurements inside the 20-liter sphere by means of hot-wire anemometry. A comparison of their results with those obtained in a 1-m 3 vessel (see Figure 13) indicates that equal turbulence levels exist in both test vessels when the ignition delay time of the 20-liter sphere is 200 ms. The work of van der Wel et al. and Pu et al. undermines the widespread belief that a formal cube-root-law agreement generally exists between the 20-liter sphere and the 1-m 3 vessel, and that dust clouds are ignited under similar conditions of turbulence when both vessels are operated according to prescribed test procedures. In fact, these observations undermine the entire notion that laboratory test results may be used to predict what would happen under industrial circumstances on the basis of the cube-root-law. The second issue concerns the abandonment of the VDI-methodology and its replacement by a more accurate and theoretically justified method of prediction. It was pointed out by various researchers [8 10] that the cube-root-law is no more than an approximation of a single realization of the explosion pressure curve and that it is only valid as a scaling relationship under hypothetical circumstances. First, the mass burning rate (i.e. the product of the burning velocity, the flame area, and the density of the unburnt mixture which is to be consumed by the flame) has to be the same in both the test vessel and the industrial vessel at the moment when the rate of pressure rise reaches its maximum value. This condition is only fulfilled when both vessels are spherical, ignition occurs at the center of both vessels, the flow properties are identical, and changes in pressure, temperature and turbulence of the unburnt mixture ahead of the flame have the same effect on the burning velocity. In reality none of these requirements are fulfilled. In addition to that, laboratory test results, obtained under particular conditions of turbulence, are applied to industrial circumstances where different conditions of turbulence exist. Since the effect of turbulence is not explicitly taken into account by the cuberoot-law, its application may lead to unacceptable over-estimations in situations where turbulence levels in industrial practice are much lower than those created in laboratory test vessels, but also to under estimations of the explosion severity under circumstances where additional turbulence is generated by the explosion itself. It was demonstrated by Tamanini [11] that worst case predictions by means of the VDI-methodology may underestimate the dust explosion severity when turbulence varies at the time of the explosion.

9 166 A.E. DAHOE ET AL. Secondly, the thickness of the flame must be negligible with respect to the radius of the vessel. It was demonstrated by Dahoe and co-workers [10, 12] that an inherent limitation of the cube-root-law is that it does not take the effect of flame thickness into account. When the flame thickness is significant with respect to the radius of a laboratory test vessel (i.e. > 1%), the cube-root-law no longer transforms the maximum rate of pressure rise into a volume invariant explosion severity index. Instead, it transforms a laboratory test result into an explosion severity index which systematically underestimates the maximum rate of pressure rise in a larger vessel. Since many powders have a flame thickness that is appreciable with respect to the radius of laboratory test vessels, the cube-root-law may not be considered as generally valid for the prediction of dust explosion severity. With some dusts, the flame thickness is so large that application the cube-root-law irrevocably leads to an underestimation of the maximum rate of pressure rise in larger vessels, even when laboratory testing is carried out at considerably higher turbulence levels. In order to overcome the limitations associated with the cube-root-law several models have been proposed by other researchers. Unlike the cube-root-law, which takes a single instant of the rate of pressure rise measured in a test vessel to predict a single instant of the rate of pressure rise during an industrial explosion, these so called integral balance models are capable of predicting the entire pressure evolution during an explosion. And, more importantly, since their derivation is based on fundamental relationships between the pressure development and the mass burning rate at any instant, the effect of mixture composition, pressure, temperature, and turbulence on the transient combustion process can be taken into account in an explicit manner. Existing models of this kind are those of Bradley and Mitcheson [13], Nagy and Verakis [14], Perlee et al. [15], and Chirila et al. [16], Bradley et al. [17], Tamanini [18] and Dahoe and co-workers [10, 12]. Ideally, these models enable the prediction of explosion behavior, and hence the explosion severity, under industrial circumstances when the mass burning rate is known from laboratory experiments and the (varying) turbulence parameters are known for industrial circumstances. In the case of premixed gases, the burning velocity and the flame thickness are recognized as fundamental measures of the driving force behind the combustion process and these quantities have been used with success to model the mass burning rate. It is believed that the same approach may be also applied to dust-air mixtures [9, 19]. When the burning velocity and flame thickness are used as key parameters in integral balance models, a distinction is made between a laminar burning velocity and a laminar flame thickness, on one hand, and a turbulent burning velocity and a turbulent flame thickness on the other hand. A great advantage of this distinction is that it separates the effect of mixture properties (chemical,thermodynamical) and the effect of flow properties (turbulence level,turbulence length scale) on the flame propagation process in a systematic way. When, for example, a flame is stabilized in a laminar flow of combustibles, it establishes itself at a fixed position in the flow field and its surface remains smooth. In other words, it inherits the laminar

10 ON THE DECAY OF TURBULENCE IN THE 20-LITER EXPLOSION SPHERE 167 behavior of the flow field. Moreover, the velocity at which the cold reactants enter the flame zone in the normal direction, the laminar burning velocity, and the width of the region in which reactants are converted into combustion products, the laminar flame thickness, appear to be a mixture specific properties. They reflect the sensitivity of the combustion process to changes in the chemical composition, fuel concentration, oxygen content, particle size, pressure and temperature of the approaching flow of reactants. By contrast, when a flame is trapped within a turbulent flow of combustibles, it inherits the turbulent nature of the flow field: the turbulence of the approaching flow continuously distorts the flame and ceaselessly shifts its position in space between certain geometrical boundaries. As a result, the surface area of the instantaneous laminar flame changes in a chaotic manner which is determined by the turbulence of the flow field. Owing to the fact that the relevant time scales of the fluid structures that compose the turbulent flow field are much larger than the the chemical time scale of the instantaneous combustion zone, the geometrical boundaries between which the instantaneous flame front shifts its position are identified as a turbulent flame thickness. Due to the enhancement of heat and mass transfer by turbulence, the turbulent flame zone propagates with a turbulent burning velocity which is greater than the laminar burning velocity. The local consumption of reactants at any particular portion of the flame surface, however, occurs within a zone whose width is equal to the local laminar flame thickness and at a rate which is determined by the local laminar burning velocity. With this picture in mind, various researchers have developed relationships which express the turbulent burning velocity and the turbulent flame thickness in terms of a combination of the laminar flame propagation parameters and the turbulence features of the flow field. It was mentioned earlier that integral balance models can be used to replace the VDI-methodology in the prediction of dust explosion behavior. Since integral balance models are capable of predicting the entire pressure development of an explosion, they can be used in conjunction with the above mentioned relationships to determine laminar burning velocity and the laminar flame thickness by regressing them to the pressure-time curve of laboratory experiments, as demonstrated by Dahoe and co-workers [10, 12], provided that the turbulence properties in the laboratory test vessels are known with sufficient accuracy. These fundamental flame propagation parameters can then be used to predict dust explosion behavior in plant units of a simple geometry by means of the same integral balance models, or, in complex geometries using CFD-codes. The success or failure of this approach, however, depends entirely upon our knowledge of the turbulence properties and how they may vary during the course of an explosion in both the laboratory test vessels as well as in industrial pant units. Based on the foregoing it is evident that quantitative knowledge of turbulence properties inside laboratory explosion test vessels is of critical importance to the modelling and the prediction of dust explosion behavior. Hence, it is the purpose of this paper to present experimental results on the transient turbulence levels in

11 168 A.E. DAHOE ET AL. the 20-liter sphere. Although turbulence in the 20-liter sphere was studied previously there are still a number of shortcomings. First of all, Pu et al. and van der Wel et al. used hot-wire anemometry to measure turbulence. While this technique enables one to quantify turbulence levels and to measure power density spectra, it is incapable of measuring independent velocity components simultaneously. As a result, it is not possible to investigate whether practically isotropic turbulence, or, a situation of highly non-isotropic turbulence exists in the 20-liter sphere. In order to overcome this limitation a two dimensional laser Doppler anemometer was used in this work. Secondly, previous research was limited to measurements at the geometric center of the 20-liter sphere and ignores the question of whether or not similar conditions of turbulence exist at other locations in the 20-liter sphere. In the present work turbulence measurements are performed at various locations in the flow field. Thirdly, the work by previous researchers is restricted to the investigation of the flow field generated by one specific dust dispersion device, namely, the Perforated Dispersion Ring. Since the dispersion behavior of particles differs from one powder to another, dust explosion severity testing involves the use of a variety of dust dispersion devices. In the present work, the flow fields of three of the most widely used dust dispersion devices, namely, the Perforated Dispersion Ring, the Rebound Nozzle and the Dahoe Nozzle, are investigated. Fourthly, there appears to be a discrepancy between the results of van der Wel et al. and Pu et al. It was observed by van der Wel et al. that conditions of turbulence, similar to those in the 1-m 3 vessel, exist in the 20-liter sphere when the ignition delay time is equal to 165 ms. A comparison between the results of Pu et al. and the turbulence level in the 1-m 3 vessel, however, shows that this ignition delay time should be equal to 200 ms. Since this discrepancy is significant in comparison with the prescribed ignition delay time of 60 ms, and knowing that turbulence decays rapidly after completion of the air blast, it would be interesting to measure turbulence levels in the 20-liter sphere with a technique which is different from the one used by Pu et al. and van der Wel et al., and to compare these results with the turbulence level in the 1-m 3 vessel. 2. Measurement of Turbulence Levels in the 20-Liter Sphere Due to the limited optical access of the actual explosion chamber, a plastic replica containing optical quality glass windows was constructed and mounted on the commercially available injection section. The transient flow fields were created by means of a blast of compressed air according to the prescribed test procedure for powder safety testing with the 20-liter sphere. This means that the pressure canister was pressurized up to 21 bar, the sphere was evacuated to a pressure of 0.4 bar, and the contents of the canister was subsequently discharged into the sphere. A two dimensional laser Doppler anemometer was used to measure the velocity at various locations in the transient flow field. The details of the laser Doppler anemometer and its implementation are omitted here and can be found in [12]. It is sufficient to

12 ON THE DECAY OF TURBULENCE IN THE 20-LITER EXPLOSION SPHERE 169 Figure 4. An overview of the measuring locations with (a) the Rebound Nozzle (perpendicular to optical axis), (b) the Rebound Nozzle (parallel to optical axis), (c) the Perforated Dispersion Ring, and (d) the Dahoe Nozzle. Figure 5. The Perforated Dispersion Ring (left), the Rebound Nozzle (middle) and the Dahoe Nozzle (right). mention here that the equipment was capable of measuring vertical and horizontal velocity components between 250 m s 1 and +250 m s 1, and that data rates of up to 25 khz were observed (i.e. time scales down to 0.02 ms could be resolved). The vertical and horizontal components of the instantaneous velocity were measured in the transient flow fields generated by three of the most widely used dust dispersion devices, namely, the Perforated Dispersion Ring, the Rebound Nozzle, and the Dahoe Nozzle (see Figure 5). Measurements were performed at six measurement locations and in order to have a sufficient amount of data for statistical averaging, at least ten time series were measured at each location. The measurement locations and the placement of the dust dispersion devices in the model sphere are shown in Figures 4 and 6. All dust dispersion devices are attached to the inlet through which compressed enters the model sphere and the shaded regions

13 170 A.E. DAHOE ET AL. Figure 6. Placement and initial flow patterns of the Perforated Dispersion Ring (left), Rebound Nozzle (middle) and the Dahoe Nozzle (right). in Figure 4 depict projections of these devices onto the equitorial plane of the model sphere. The six measurement locations, 3IL, 4IL, 5IL, 6IL, 7IL, and 8IL, are situated within the equitorial plane and along the optical axis of the beams emitted by the laser Doppler anemometer. Their relative position with respect to the dust dispersion devices is also indicated by Figure 4. A few examples of the instantaneous velocity components measured at the geometric center of the model sphere are shown in Figure 7. In the initial stage of the flow field generated by the Perforated Dispersion Ring, the vertical velocity component is seen to oscillate rapidly between 60 and 50 m s 1 with no systematic preference for a specific direction. At the same time the horizontal component varies between 50 and 40 m s 1, with a clear preference for the negative horizontal direction in the beginning, followed by a preference for the positive horizontal direction. Both velocity components are observed to decrease to a fraction of their initial magnitude within a period of about 60 milliseconds. With the Rebound Nozzle, the vertical velocity component is observed to vary between -60 and 100 m s 1 with a preference for the positive vertical direction. At the same time, the horizontal velocity component changes its magnitude between 45and40ms 1. During the injection process, the initial preference for the positive horizontal direction is seen to change into a preference for the negative horizontal direction. After a period of about 60 milliseconds, both velocity components exhibit a low frequency oscillatory behavior. The velocity components associated with the Dahoe Nozzle show a similar behavior, except that the vertical velocity component varies between 30 and 125 m s 1. The horizontal component lies between 60and30ms 1 with a systematic preference for the negative horizontal direction. In spite of the wild and spiky behavior of the instantaneous velocity, one may still discern a mean motion with relatively large time scales. With the Perforated Dispersion Ring, the mean motion appears to exist only during the first 60 milliseconds of the injection process, which is about equal to the time needed to discharge the contents of the storage vessel into the model sphere. With the Rebound Nozzle and the Dahoe Nozzle, there appears to be a sinusoidal mean motion with a decreasing amplitude and frequency, which persists beyond the discharge time. This is in spite of the fact that the driving force (i.e. the pressure difference

14 ON THE DECAY OF TURBULENCE IN THE 20-LITER EXPLOSION SPHERE 171 Figure 7. The vertical and horizontal component of the instantaneous velocity at the geometric center of the sphere (location 4IL). between the storage vessel and the model sphere) is no longer present after the first 60 milliseconds. According to Figure 6 this behavior must be attributed to the initial flow patterns of the dust dispersion devices. During the injection process, the Rebound Nozzle and the Dahoe Nozzle produce large jets which sustain their high velocity and preferential direction for a longer period of time. Since the Perforated Dispersion Ring consists of a metal tube with 112 holes of 3 mm diameter each, the fluid enters the model sphere in the form of a large number of thin jet streams that lose their initial velocity and preferential direction rapidly. Due to the presence of a mean motion, every realization of the instantaneous velocity had to be decomposed into a mean value and a fluctuation in order to quantify the transient turbulence level in the 20-liter sphere. The mean value was

15 172 A.E. DAHOE ET AL. Figure 8. Decomposition of the vertical velocity component into a mean value (top) and a fluctuation (bottom). The instantaneous value corresponds to the result presented in middle-left part of Figure 7. determined by means of a moving regression routine which fits a polynomial of a particular degree to a data window. The routine picks a sample record of a particular length, say (t 1,v 1 ),...,(t i,v i ),...,(t n,v n ), fits the polynomial to the data set, uses the regression coefficients to calculate the value of the polynomial at each t i, shifts the data window with one sample, and repeats the process all over with another sample, until all data are processed. The values of the fitted curve at the various values of t i are an estimation of the mean motion, and subtracting them from the instantaneous values, v i, yields the velocity fluctuations. The effect of this routine in decomposing a velocity data set into a mean value and a fluctuation is shown by Figure 8. In principle, the moving regression algorithm can be used with two kinds of data windows. The first, which is called here a point-window, consists of a fixed number of points. The second is called a time-window and consists of a number of samples contained within a fixed time interval. If the data rate would be constant, both windows would be identical with a fixed number of samples covering a fixed time duration. In the case of laser Doppler anemometry, however, where the data rate is not constant (it increases when the velocity increases and vice versa), a pointwindow covers a variable time interval, and a time-window includes a variable number of samples. Since the use of a time-window involves the risk of containing

16 ON THE DECAY OF TURBULENCE IN THE 20-LITER EXPLOSION SPHERE 173 Figure 9. Behavior of the pressure in the model sphere (with the Rebound Nozzle) and the canister during the air blast. too few points to compute the average, a point-window was used. In this way the algorithm adapted itself to the behavior of the flow: if the velocity decreased, samples were taken from a larger time interval so that the averaging was always performed with a large number of samples. The size of the point-window, as well as the degree of the polynomial, are of great importance. If the point-window is too small, the mean motion can not be resolved because the moving regression will follow the fluctuations. A point-window which is too large will lead to a flattened-out average, and the mean motion will appear in the fluctuation. When the degree of the fitting polynomial is too high, it tends to follow behavior of the fluctuations instead of the trend of the mean motion. This results in an underestimation of the fluctuations. The optimal choice was found to be a point-window with 71 points (35 points to the left and 35 points to the right of the point where the mean motion is to be estimated) and a second degree polynomial. All velocity-time recordings, similar to the ones presented in Figure 7, were processed with these settings. After subtraction of the mean motion from the instantaneous velocity, the fluctuation of the latter (see the lower part of Figure 8) was used to quantify and compare the turbulent flow fields generated by the different dust dispersion devices. The behavior of the root-mean-square value of the vertical and the horizontal velocity component at the six different measuring locations is shown in Figure 10. Each data point in this figure is the result of at least ten measurements and was determined as follows. The fluctuation of each velocity-time recording was calculated as described above and the time axis was subdivided into equal time slices of 4 ms. The root-mean-square value associated with each time slice was subsequently calculated by combining the corresponding data of all velocity fluctuations at a particular location and by applying v rms = 1 N N i=1 v 2 i. (2)

17 174 A.E. DAHOE ET AL. Figure 10. Root-mean-square values of the velocity fluctuations at the various measuring locations ( 8IL, 7IL, 6IL, 5IL, 4IL, + 3IL) in the 20-liter sphere.

18 ON THE DECAY OF TURBULENCE IN THE 20-LITER EXPLOSION SPHERE 175 In this equation, v rms denotes the root-mean-square value, N the total number of samples in each time slice and v i stands for the fluctuation of the instantaneous velocity. The resulting v rms -value was finally assigned to the center of each corresponding time slice. The spatial homogeneity and directional isotropy of the turbulent flow fields generated by the injection process may be considered by means of Figures 10 and 11. According to Figure 10 the root-mean-square value of both the vertical and the horizontal velocity component, measured at various locations in the model sphere have converged towards each other with all three dust dispersion devices at 60 ms. This implies that homogeneous turbulence exists in the 20-liter sphere at the prescribed ignition delay time of 60 ms, and thereafter. Figure 11 shows the behavior of the space averaged root-mean-square value of the vertical and horizontal velocity fluctuations. Each point of this figure belongs to a time slice of 4 ms and was calculated by superimposing all the corresponding velocity fluctuations, measured at all six locations, and by applying Equation (2). It is seen that the initially different v rms -values of the vertical and the horizontal velocity components have converged to more or less the same value at the prescribed 60 ms. Hence, conditions of practically isotropic turbulence exist in the 20-liter sphere with all three dust dispersion devices. The associated turbulence level at the prescribed ignition delay time of 60 ms is respectively equal to 2.68 m s 1,3.75ms 1 and 2.79 m s 1 in case of the Perforated Dispersion Ring, the Rebound Nozzle and the Dahoe Nozzle. 3. Decay of Turbulence in the 20-Liter Sphere In order to correlate the transient turbulence level in the 20-liter sphere it is helpful to consider the decay of grid generated turbulence, of which the earliest extensive measurements were made by Batchelor and Townsend [20 22]. These researchers passed a stream of air with a uniform velocity profile through a regular grid of bars and studied the behavior of the velocity fluctuations at the downstream side of the grid. They observed that within a region of up to ten times the mesh spacing, the magnitude of the velocity fluctuations at the downstream side of the grid was increasing to a maximum. It was also observed that within this region, the rootmean-square value of the individual velocity components became independent of position across the stream, and approximately equal to each other. After this region, the magnitude of the velocity fluctuations was found to decay with distance while the turbulence remained homogeneous and isotropic. Batchelor and Townsend distinguished various stages of the decay process and classified them as the initial period of decay, the transition period of decay, and the final period of decay. In all cases the decay of turbulence could be generalized and correlated by means of an equation of the form v rms ( ) t n v rms =, (3) t 0

19 176 A.E. DAHOE ET AL. Figure 11. Space averaged root-mean-square values.

20 ON THE DECAY OF TURBULENCE IN THE 20-LITER EXPLOSION SPHERE 177 where the distance from the grid at the downstream side is represented by a time coordinate, t (this was accomplished by dividing distance by the mean velocity of the flow). In the initial and final period of decay the exponent, n, was observed to have a constant value of respectively 1.0 and In the transition period of decay the exponent, n, was found to change gradually from 1.0 to The turbulent flow field in the 20-liter sphere appears to behave in a similar way. Figure 10 shows that with all three dust dispersion devices the prescribed ignition delay time of 60 ms is preceded by an initial period of turbulence buildup, followed by a period of turbulence decay. According to Figures 10 and 11, a strongly nonhomogeneous and anisotropic turbulent flow field is produced in an initial period of about 10 ms. In this period the scatter in the v rms -value measured at different locations is in the order of 10 m s 1, and a difference of the same order of magnitude can be observed in the v rms -value of the independent velocity components. As time elapses the turbulent flow field becomes more and more homogeneous and isotropic. At 60 ms both the scatter and the difference between the v rms -value of the independent velocity components are in the order of 1 m s 1, and this decreases further to 0.1 m s 1 at 1000 ms. Although the injection process lasts about 50 ms (Figure 9 shows that the pressure in the model sphere and the canister become equal at about 50 ms), it is seen that turbulence buildup occurs only in an initial period of about 10 ms, and that the decay of turbulence begins to occur while there is still an injection flow of compressed air. In order to understand why the buildup of turbulence is restricted to the first 10 ms, and why turbulence starts to decay while the injection flow is still active, it is helpful to consider the various mechanisms of turbulence generation which are active during the air blast. The first mechanism may be inferred from the vorticity equation, ω t + v ω = ω v + ν 2 ω ω v + ρ p ρ 2, (4) where ω = (1/2) v denotes the vorticity, v the velocity vector, ρ the density, p the pressure, and ν the kinematic viscosity. Prior to the injection process, the storage canister is filled with compressed air of 21 bar (this has a density of about 27 kg m 3 ), and the model sphere is evacuated to a pressure of 0.4 bar (and the air inside the sphere has a density of about 0.5 kg m 3 ). When these values are taken into consideration, it is evident that the baroclinic term in the vorticity equation, ( ρ p)/ρ 2, must be regarded as a very strong source of vorticity during the injection process. If the length of the duct (which is about 10 cm) that separates the contents of the pressure canister from the contents of the model sphere is taken as a measure of the distance across which the pressure gradient and density gradient exist, and the gradients are assumed to be perpendicular to each other at every fluid element present inside the duct, one finds a vorticity production rate, ω/ t, of about s 2 at the very beginning of the injection process. If this situation were to last for only a millisecond, then the initially static state of each fluid element would change into a rotating state of about 3000 cycles per second. In practice, of

21 178 A.E. DAHOE ET AL. Figure 12. Decay of the root-mean-square velocity from 60 to 200 milliseconds in the 20-liter sphere. course, the pressure gradient and density gradient are not always perpendicular to one another at every fluid element, and decrease rapidly. This estimate nevertheless gives a reasonable impression of the vigorousness associated with the discharge of the contents of the pressure canister into the model sphere. The second mechanism of turbulence generation during the injection process is by wall friction. On its passage from the canister to the model sphere, the air flows at almost sonic velocities through the duct and subsequently past the dispersion device, and turbulence is generated by friction with the wall. The third mechanism is that of shear turbulence. The air streams emerging from the dust dispersion devices enter the model sphere with a preferential direction and at high velocities, and the associated sliding and shearing of fluid layers is a source of turbulence. Of all three mechanisms, the baroclinic effect in the region where high pressure and low pressure air are initially separated is considered to be the most important because it constitutes a source of turbulence which is much stronger than wall friction or the shearing of fluid layers. In the first 10 ms the baroclinic effect produces a large amount of turbulence which starts to decay when the pressure and density gradient have decreased. During this decay process, the mechanisms of turbulence generation by wall friction and sliding fluid streams continue to produce turbulence. This additional turbulence, however, is insufficient to counteract and to overcome the decay of the turbulence produced by the baroclinic effect. After the first 50 ms, turbulence generation by wall friction is practically absent because there is no longer a flow from the pressure canister to the sphere. The contribution of shear turbulence is also small after this time because the fluid streams that emerge from the dust dispersion devices lose their initial velocity rapidly. When the decay of turbulence in the 20-liter sphere (i.e. Figure 11) is compared with the decay of grid generated turbulence, as observed by Batchelor and

22 ON THE DECAY OF TURBULENCE IN THE 20-LITER EXPLOSION SPHERE 179 Figure 13. Decay of the root-mean-square velocity in the 20-liter sphere with the Perforated Dispersion Ring ( our measurements, Pu et al. [7], dashed line: 1-m 3 vessel at the prescribed ignition delay time of 600 milliseconds [23]). Townsend, it is seen that in the period of 10 ms to 50 ms the exponent, n, in Equation (3) gradually decreases to a constant value, as indicated by Figure 12, and that it remains at this constant value until 200 ms. After this time, the exponent increases gradually and tends to become equal to zero. Both behavior and the value of the exponent, n, appear to be different from what has been observed during the decay of grid generated turbulence. The most striking difference is that the decay process of grid generated turbulence consists of two periods in which the exponent, n, assumes a constant value, while the decay of turbulence in the 20-liter sphere involves only one such period. Moreover, the decay exponent in case of the 20-liter sphere assumes a systematically larger (negative) value than the ones observed during the initial and final period of the decay of grid generated turbulence. The reasons for this discrepancy must be sought in the fact that the turbulent fluctuations in the 20-liter sphere are generated by a different mechanism, namely, the baroclinic effect, as described earlier. In the case of grid generated turbulence, friction between the fluid and the grid is the predominant mechanism of turbulence. In order to have a quantitative description of the behavior of the turbulence level in the 20-liter sphere, our results in the period of 60 to 200 ms were correlated by means of Equation (3). The reason for choosing this time interval was that the decay exponent assumes a constant value and that the explosion times of dust-air mixtures in the 20-liter sphere, ignited at an ignition delay time of 60 ms, rarely exceed 100 ms. According to Figure 12, the constants v rms and n in Equation (3) assume the values of 2.68 m s 1 and 1.49 with the Perforated Dispersion Ring, 3.75 m s 1 and 1.61 with the Rebound Nozzle, and 2.79 m s 1 and 1.52 with the Dahoe Nozzle. In all cases the constant t 0 has a value of 60 ms. The data points associated with the Rebound Nozzle were calculated in the same manner as those

23 180 A.E. DAHOE ET AL. in Figure 11, except that the measurements with the Rebound Nozzle parallel and perpendicular to the optical axis were combined. Apart from reducing the volume of the explosion chamber, the development of the 20-liter sphere also involved the development of a dust dispersion device that was to be used in the new vessel. Since the 1-m 3 vessel uses a perforated half-ring with 13 holes of 6 mm diameter each to disperse the dust, a Perforated Dispersion Ring was designed for the 20-liter sphere which consists of a perforated half-ring with 112 holes of 3 mm diameter each. As this device did not work well with a large number of dusts, an alternative device was developed, namely, the Rebound Nozzle, which gave the same K St -value as the Perforated Dispersion Ring. The results presented in Figure 12, however, show that these identical K St -values were measured under significantly different conditions of turbulence using the two dust dispersion devices. At the prescribed ignition delay time of 60 ms, the turbulence level generated by the Rebound Nozzle is a factor 1.4 larger than that generated by the Perforated Dispersion Ring. The turbulence levels produced by the Dahoe Nozzle, on the other hand, are in close agreement with those produced by the Perforated Dispersion Ring. Figure 12 shows a comparison between our turbulence measurements in the 20- liter sphere with the Perforated Dispersion Ring and the turbulence measurements reported by Pu et al. It is seen that our results, obtained by means of laser Doppler anemometry, are in agreement with those obtained by Pu et al., who used hotwire anemometry to measure turbulence. The turbulence level in the 20-liter is also compared with the turbulence level in the 1-m 3 vessel at the prescribed ignition delay time of 600 ms. According to this comparison, the turbulence level in the 20- liter sphere is equal to that in the 1-m 3 vessel when the ignition delay time is equal to 200 ms, instead of the prescribed 60 ms. This result contradicts the observation made by van der Wel et al., namely, that similar conditions of turbulence exist in both vessels when the ignition delay time in the 20-liter sphere is equal to 165 ms. It was mentioned in the Introduction that the 20-liter explosion sphere would only be accepted by technical guidelines for powder safety testing if it would produce the same K St -values as the 1-m 3 vessel. Hence, Barknecht and Siwek performed extensive measurements, involving a variety of powders, and found that this was indeed the case when the 20-liter sphere was operated with an ignition delay time of 60 ms. According to our turbulence measurements, these K St -values were produced at a turbulence level in the 20-liter sphere which is significantly different from that in the 1-m 3 vessel. In other words, the 20-liter sphere was used to produce K St -values that were equal to those measured in the 1-m 3 vessel by varying the ignition delay time and by making use of the fact that the combustion rate changes with turbulence.

24 ON THE DECAY OF TURBULENCE IN THE 20-LITER EXPLOSION SPHERE Conclusions Laser Doppler anemometry was used to measure the turbulence level in the 20-liter explosion sphere. Two independent velocity components were measured simultaneously at six different locations in the flow fields generated by the three most widely used dust dispersion devices, namely, the Perforated Dispersion Ring, the Rebound Nozzle and the Dahoe Nozzle. A moving regression algorithm was used to decompose the instantaneous velocity components into a mean value and a fluctuation, and the latter was used to quantify the turbulence level. Our results on the turbulence level in the flow field generated by the Perforated Dispersion Ring are in agreement with the results reported by Pu et al., who used hot-wire anemometry to measure turbulence in the 20-liter sphere. During the injection process with the Perforated Dispersion Ring the instantaneous vertical velocity component varies between 60 and 50 m s 1,andthe instantaneous horizontal velocity component lies between 50 and 40 m s 1. With the Rebound Nozzle, the vertical velocity component is observed to vary between 60 and 100 m s 1, and the horizontal velocity component changes its magnitude between 45 and 40 m s 1. The highest instantaneous velocity components were found with the Dahoe Nozzle. In this case the vertical velocity component was found to range from 30 to 125 m s 1, and the horizontal velocity component was between 60 and 30 m s 1. The lower instantaneous velocities associated with the Perforated Dispersion Ring and the higher velocities observed with the other two dispersion systems can be ascribed to the different geometries and the consequential difference in the fluid streams that emerge from them. The turbulent flow fields generated with all three dust dispersion devices were found to be spatially homogeneous and directionally isotropic at the prescribed ignition delay time of 60 milliseconds, as well as thereafter. The spatial homogeneity follows from the fact that the root-mean-square values of the velocity fluctuations measured at different locations converge towards each other. The establishment of directional isotropy follows from the observation that the root-mean-square values of the horizontal and vertical velocity fluctuations converge to each other. At the prescribed ignition delay time of 60 ms, the turbulence level in the 20-liter sphere has a root-mean-square value which depends on the dust dispersion device. In case of the perforated Dispersion Ring, v rms is equal to 2.68 m s 1. With the Rebound Nozzle and the Dahoe Nozzle v rms is respectively equal to 3.75 and 2.79 m s 1. When the standard 20-liter explosion sphere is operated according to the prescribed injection procedure for dust explosion testing, the turbulence intensity in the period from 60 to 200 ms after the very beginning of the air blast can be correlated by means of Equation (3), where the constant t 0 hasavalueof60ms for all three dust dispersion devices. The constants v rms and n assume respective values of 2.68 m s 1 and 1.49 for the Perforated Dispersion Ring, 3.75 m s 1 and 1.61 for the Rebound Nozzle, and 2.79 m s 1 and 1.52 for the Dahoe Nozzle.

25 182 A.E. DAHOE ET AL. The decay of turbulence in the 20-liter sphere was compared with the decay of grid generated turbulence and observed to behave in a distinct manner. While the decay of grid generated turbulence consists of two stages where the exponent, n,in Equation (3) assumes a constant value, namely, the initial and final period of decay, the decay of turbulence in the 20-liter sphere appears to have only one stage with a constant exponent. The value of this exponent is systematically different from those in the initial and final period of the decay of grid generated turbulence. The reason for this disparate behavior is ascribed to the fact that the turbulent fluctuations in the 20-liter sphere are created by a different mechanism (the baroclinic effect) than in the case of grid generated turbulence (friction). It was mentioned in the Introduction that various researchers discussed the limitations of the cube-root-law and advocated its replacement by a more fundamental approach which takes the effect of turbulence explicitly into account. Since this approach involves the use integral balance models in conjunction with relationships that describe the turbulent flame propagation process in terms of laminar flame propagation parameters and the turbulence properties of the unburnt mixture ahead of the flame, accurate knowledge of both becomes of crucial importance. In practice, it is very difficult to stabilize a laminar dust flame in order to measure the laminar burning velocity and the laminar flame thickness. It is comparatively easy, however, to create turbulent dust explosions in laboratory test vessels, such as the 20-liter sphere, and to measure the behavior of the pressure as a function of time. When the turbulence properties in the test vessels are known at the moment of ignition, as well as during the course of the explosion, integral balance models can be fitted to the pressure-time recordings in order to determine the laminar burning velocity and the laminar flame thickness. In this respect, the decay law expression (3), with its parameters characterized for the three most widely used dust dispersion devices, will contribute to the establishment of a more fundamental approach to dust explosion severity prediction. Since correlations for the turbulent burning velocity and the turbulent flame thickness also involve the turbulence length scale, it is also important to investigate the behavior of this quantity in laboratory explosion vessels. A comparison between the turbulence levels in the 20-liter sphere and the 1- m 3 vessel, based on our measurements, shows that equal turbulence levels exist in both vessels when the ignition delay time in the 20-liter sphere is equal to 200 ms. This result is consistent with the implication of the observations made by Pu et al., namely, that equal turbulence levels exist in both vessels when the ignition delay time in the 20-liter sphere is equal 200 ms. At the same time the result of this comparison contradicts van der Wel et al., who claim that similar conditions of turbulence exist in the two test vessels when the ignition delay time in the 20-liter sphere is equal to 165 ms. As mentioned in the Introduction, Bartknecht and Siwek measured equal K St - values in the 20-liter sphere and the 1-m 3 vessel. Apart from giving rise to the notion that equal turbulence levels exist in both test vessels at the prescribed igni-

26 ON THE DECAY OF TURBULENCE IN THE 20-LITER EXPLOSION SPHERE 183 tion delay times of 60 ms and 600 ms, their research also inspired the widespread belief that a formal cube-root-law agreement exists between dust explosion severities measured in the two test vessels. In addition to that, their research stimulated the use of the cube-root-law as a predictive tool which enables engineers to assess the severity of an industrial dust explosion on the basis of dust explosion severities measured in laboratory test vessels. Our measurements show that significantly different turbulence levels exist in the two test vessels at the prescribed ignition delay times. Hence, the results of Bartknecht and Siwek, which form the experimental basis of the cube-root-law, were obtained by igniting dust clouds under significantly different conditions of turbulence in the two test vessels. As a result the cube-root-law may not be considered as a generally valid. In fact, its use in the practice of scaling laboratory test results into what might happen during accidental industrial dust explosions must be regarded as fundamentally wrong. This conclusion supports the idea of abandoning the cube-root-law and replacing it with a more fundamental approach. References 1. Venting of Deflagrations. NFPA 68, National Fire Protection Association (NFPA) (1988). 2. Pressure Venting of Dust Explosions. VDI 3673, Verein Deutscher Ingenieure (VDI), Düsseldorf (1995). 3. Bartknecht, W., Dust Explosions: Course, Prevention, Protection. Springer-Verlag, Berlin (1989). [Translation of Staubexplosionen, by R.E. Bruderer, G.N. Kirby and R. Siwek.] 4. International Standardization Organization (ISO), Explosion protection systems Part 1: Determination of explosion indices of combustible dusts in air. ISO 6184/1 (1985). 5. Siwek, R., 20-l Laborapparatur für die Bestimmung der Explosionskenngrößen brennbarer Stäube. Ph.D. Thesis, Technical University of Winterthur, Winterthur, Switzerland (1977). 6. Van der Wel, P.G.J., van Veen, J.P.W., Lemkowitz, S.M., Scarlett, B. and van Wingerden, C.J.M., An interpretation of dust explosion phenomena on the basis of time scales. Powder Technology 71(2) (1992) Pu, Y.K., Jarosinski, J., Johnson, V.G. and Kauffman, C.W., Turbulence effects on dust explosions in the 20-liter spherical vessel. In: Proceedings of the Twenty-Third Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA (1990) pp Eckhoff, R.K., Dust Explosions in the Process Industries, 2nd edn. Butterworth and Heinemann (1996). 9. Bradley, D., Chen, Z. and Swithenbank, J.R., Burning rates in turbulent fine dust-air explosions. In: Proceedings of the Twenty-Second Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA (1988) pp Dahoe, A.E., Zevenbergen, J.F., Lemkowitz, S.M. and Scarlett, B., Dust explosions in spherical vessels: The role of flame thickness in the validity of the cube-root-law. Journal of Loss Prevention in the Process Industries 9(1) (1996) Tamanini, F., Turbulence effects on dust explosion venting. Plant/Operations Progress 9(1) (1990) Dahoe, A.E., Dust explosions: A study of flame propagation. Ph.D. Thesis, Delft University of Technology (2000). 13. Bradley, D. and Mitcheson, A., Mathematical solutions for explosions in spherical vessels. Combustion and Flame 26 (1976)

27 184 A.E. DAHOE ET AL. 14. Nagy, J. and Verakis, H.C., Development and Control of Dust Explosions. Marcel Dekker, New York (1983). 15. Perlee, H.E., Fuller, F.N. and Saul, C.H., Constant-volume flame propagation. Report of Investigations 7839, United States Department of the Interior, Bureau of Mines, Washington, DC (1974). 16. Chirila, F., Oancea, D., Razus, D. and Ionescu, N.I., Pressure and temperature dependence of normal burning velocity for propylene-air mixtures from pressure-time curves in a spherical vessel. Revue Roumaine de Chimie 40(2) (1995). 17. Bradley, D., Lawes, M., Scott, M.J. and Mushi, E.M.J., Afterburning in spherical premixed turbulence explosions. Combustion and Flame 99 (1994) Tamanini, F., Modeling of turbulent unvented gas/air explosions. Progress in Aeronautics and Astronautics 154 (1993) Bradley, D. and Lee, J.H.S., In: Proceedings of the First International Colloquium on the Explosibility of Industrial Dusts, Volume 2 (1984) pp Batchelor, G.K. and Townsend, A.A., Decay of vorticity in the isotropic turbulence. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences 190 (1947) Batchelor, G.K. and Townsend, A.A., Decay of isotropic turbulence in the initial period. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences 193 (1948) Batchelor, G.K. and Townsend, A.A., Decay of isotropic turbulence in the final period. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences 194 (1948) Van der Wel, P.G.J., Ignition and propagation of dust explosions. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands (1993).

28 Ž. Powder Technology Determination of the laminar burning velocity and the Markstein length of powder air flames A.E. Dahoe a,b,), K. Hanjalic c, B. Scarlett a a Department of Chemical Engineering, Delft UniÕersity of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands b Department of Engineering, UniÕersity of Cambridge, Cambridge, United Kingdom c Department of Applied Physics, Delft UniÕersity of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands Received 11 August 2000; accepted 2 October 2000 Abstract This work deals with the determination of the laminar burning velocity and introduces the Markstein length of powder air mixtures. A powder burner was used to stabilize laminar cornstarch air dust flames and the laminar burning velocity was determined by means of laser Doppler anemometry. The dust concentration was varied from 0.26 to 0.38 kg m y3. The measured laminar burning velocities were found to be sensitive to the shape of the flame. With the same dust concentration, parabolic flames were found to have a laminar burning Ž y1 y1 velocity, which was almost twice that of a planar flame ca. 30 cm s for the latter as compared with ca. 54 cm s for the former.. From this discrepancy and the flame curvature, the Markstein length could be determined. It was found to have a value of 11.0 mm. This Markstein length was subsequently used to correct the measured laminar burning velocities at various dust concentrations in order to obtain the unstretched laminar burning velocity. The unstretched laminar burning velocity lies between 15 and 30 cm s y1 and is thought to be a property of the dust and of the concentration. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Dust explosion; Burning velocity; Markstein length; Flame propagation; Laser Doppler anemometry 1. Introduction The severity of a dust explosion is a function of a wide variety of parameters. Some of these parameters represent properties that are specific to the chemical properties of the exploding dust air mixture, while others reflect the sensitivity of the explosion to the flow properties of the dust cloud. Due to the absence of a comprehensive description of the transient combustion behavior of any particular dust air mixture under arbitrary conditions Žpressure, temperature, flow properties., it is common practice to mea- Ž 3 sure the explosion severity in laboratory test vessels 1-m vessel, 20-l sphere. and to predict what would happen if the same mixture exploded in an industrial plant unit. This is currently done by means of the well-known cube-rootw1 3 x. The maximum rate of pressure rise measured in law the test vessel is multiplied by the cube root of the test volume to yield a K St value, which is assumed to be a volume invariant dust explosion severity index. The dust explosion severity of the same mixture in a plant unit is ) Corresponding author. Tel.: q ; fax: q address: aed23@eng.cam.ac.uk Ž A.E. Dahoe.. predicted by dividing this K St value by the cube root of the volume of the plant unit. The resulting dust explosion severity dictates the design basis for safety protection Že.g. explosion relief venting, explosion suppression.. In this approach, known as the VDI methodology, it is assumed that laboratory test data can be considered to be applicable to accidental explosions in plant units and to represent a conservative case even when the actual industrial circumstances are not reproduced in the laboratory experiments. Already from the beginning, the VDI methodology was questioned by a number of researchers. Eckhoff wx 4 pointed out that the cube-root-law was no more than an approximation of a single realization of the explosion pressure curve. Based on earlier work by Nagy et al. wx 5 on the pressure development during the course of explosions in spherical vessels, he discussed the conditions under which the cuberoot-law is a valid approximation of the dust explosion severity, and the conditions under which the cube-root-law may be used to scale dust explosion severities, measured in laboratory test vessels, into dust explosion severities that one might expect in larger industrial vessels. First, the mass burning rate Ži.e. the product of the burning velocity, the flame area, and the density of the unburnt mixture which is to be consumed by the flame r02r$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. Ž. PII: S

29 ( ) A.E. Dahoe et al.rpowder Technology has to be the same in both the test vessel and the industrial vessel at the moment when the rate of pressure rise reaches its maximum value. This condition is only fulfilled when both vessels are spherical, ignition occurs at the center of both vessels, changes in the pressure and temperature of the unburnt mixture ahead of the flame have the same effect on the burning velocity, and the turbulent flow fields, as well as changes in the flow fields during the course of an explosion, are identical in both vessels. In practice none of these requirements are fulfilled because the changes in the pressure and temperature of the unburnt mixture are not the same in differently sized vessels containing identical mixtures, and dust explosion severity testing is done in laboratory vessels under conditions of significant but unknown turbulence. Moreover, test results from laboratory vessels are applied to industrial situations with unknown turbulence. Based upon the fact that dust explosion severity increases with increasing turbulence intensity, it is presently assumed that if the turbulence intensity in the laboratory test vessels is made high enough, laboratory test results yield conservative estimates of what may happen during an explosion in a plant unit. This, however, may lead to unacceptable over-estimations in situations where the turbulence levels in industrial practice are much lower than those created in laboratory test vessels, but also to under estimations of the explosion severity under circumstances where additional turbulence is generwx 6 demon- ated by the explosion itself. Tamanini et al. strated that worst case predictions by means of the VDI methodology may underestimate the dust explosion severity when the turbulence varies at the time of the explosion. Secondly, the thickness of the flame must be negligible with respect to the radius of the vessel. An inherent flaw of the cube-root-law is that it does not take the phenomenon of flame thickness into account. As the flame thickness becomes appreciable with respect to the apparatus radius Ž i.e. ) 1%., the cube-root-law becomes increasingly inacwx 7. curate in predicting the maximum rate of pressure rise If for example chemically identical mixtures, under physically identical conditions, are ignited to deflagration in two differently sized vessels, application of the cube-root-law to the maximum rate of pressure rise, measured in the two vessels yields different K St values. Since many powders have a flame thickness that is appreciable with respect to the radius of the 20-l sphere, and even with respect to the radius of the 1-m 3 vessel, the cube-root-law may not be considered as generally valid for the prediction of dust explosion severity. In order to overcome the limitations associated with the cube-root-law, several models have been proposed by other researchers. Unlike the cube-root-law, which takes the single instant of the rate of pressure rise measured in a test vessel to predict a single instant of the rate of pressure rise during an industrial explosion, these so-called integral balance models are capable of predicting the entire pressure evolution during an explosion. More importantly, since their derivation is based on fundamental relationships between the pressure development and the mass burning rate at any instant, the effect of mixture composition, pressure, temperature, and turbulence on the transient combustion process can be taken into account explicitly. Existing models of this kind are those of Bradley and Mitchewx 8, Nagy and Verakis wx 9, Perlee et al. w10 x, and son Chirila et al. w11 x, Bradley et al. w12 x, Tamanini w13x and Dahoe et al. wx 7. Ideally, these models enable engineers to predict the behavior of explosions, and hence the explosion severity, under industrial circumstances when the behavior of the mass burning rate is known from laboratory experiments and the Ž varying. turbulent aerodynamic parameters are known for the industrial circumstances. In the case of premixed gases, the burning velocity and the flame thickness are recognized as fundamental measures of the driving force behind the combustion process and these quantities have been used with success to model the mass burning rate. When burning velocities and flame thickness are used as key parameters in integral balance models, a distinction is made between a laminar burning velocity and a laminar flame thickness, on the one hand, and a turbulent burning velocity and a turbulent flame thickness on the other. The reason for making this distinction is that, when a flame is stabilized in a laminar flow of combustibles, it establishes itself at a fixed position in the flow field and its surface remains smooth. In other words, it inherits the laminar behavior of the flow field. Moreover, the velocity at which the cold reactants enter the flame zone in the normal direction, the laminar burning velocity, appears to be a mixture specific property. It reflects the sensitivity of the combustion process to changes in the chemical composition, fuel concentration, oxygen content, particle size, pressure and temperature of the approaching flow of reactants. By contrast, when a flame is trapped within a turbulent flow of combustibles, it inherits the turbulent nature of the flow field: the turbulence of the approaching flow continuously distorts the flame and ceaselessly shifts its position in space between certain geometrical boundaries. As a result, the surface area of the instantaneous laminar flame changes in a chaotic manner, which is determined by the turbulence of the flow field. Owing to the fact that the relevant time scales of the fluid structures that compose the turbulent flow field are much larger than the chemical time scale of the instantaneous combustion zone, the geometrical boundaries between which the instantaneous flame front shifts its position are identified as a turbulent flame thickness. Due to the enhancement of heat and mass transfer by turbulence, the turbulent flame zone propagates with a turbulent burning velocity which is greater than the laminar burning velocity. The local consumption of reactants at any particular portion of the flame surface, however, occurs within a zone whose width is equal to the local laminar flame thickness and at a rate which is determined by the local laminar burning velocity. It is for

30 224 ( ) A.E. Dahoe et al.rpowder Technology this reason that the turbulent burning velocity and the turbulent flame thickness are always expressed in terms of a combination of the laminar flame propagation parameters and the turbulence features of the flow field Ži.e. rootmean-square velocity and length scale.. While the laminar burning velocity and the laminar flame thickness of a premixed gas are considered as fundamental mixture properties, their application to dust clouds appears to be controversial. This controversy stems from the fact that, while on a macroscopic scale, a dust cloud may seem like a homogeneous mixture of fuel and oxidizer, on a microscopic scale it consists of a number of discrete particles immersed in a continuum of the oxidizer. With solid fuel particles of a density of 1000 kg m y3, and a particle size of 15 mm, one finds an interparticle spacing of about 150 mm when the solid fuel concentration is equal to 500 g m y3. With the interparticle spacing being 5 10 times the particle size Ždust explosions typically y3 involve dust concentrations between 125 and 1000 g m., a combustible dust cloud consists of a number of discrete particles that are separated by a distance, which are orders of magnitude larger than the molecular mean-free path. As a result, physical and chemical properties that determine the magnitude of the laminar burning velocity may not be considered as volume average mixture properties. Bradley and Lee w14x pointed out that dust clouds do possess a laminar burning velocity and a laminar flame thickness similar to the ones used in the modeling of gas flames if the fuel particles emit appreciable amounts of volatile components. As the particle temperature increases in the preheat zone of the flame, volatile components begin to be emitted and mix with the surrounding oxidizer. This leads to the formation of a primary reaction zone that is largely sustained by gaseous combustion. There are the heat release in the primary reaction zone and the subsequent conduction of heat into the unburnt mixture that determine the magnitude of the laminar flame propagation parameters. In comparison with premixed gases, the laminar burning velocity and the laminar flame thickness of a dust cloud additionally depend on the rate of evolution of volatile components, the mixing of these volatile components with the oxidizer that surrounds the particles, the coupling of the particle and gas phase oxidation and the radiative energy exchange between the flame and the unburnt mixture. The emission of volatile components and the mixing process continues into the reaction zone and is largely completed before the end of the reaction zone. With lignites, bituminous coals, vegetable grains and powdered foodstuffs, the remaining char burns in the hot oxygen beyond the preheat zone. Particles of less than 1 mm can be oxidized entirely in the primary reaction zone and the effect of the chemical heat release of the oxidation of these particles on the laminar burning velocity is additive to that of the volatile species. For particle sizes greater than 10 mm, the oxidation of char in the primary reaction zone is slow in comparison with the gaseous combustion process. In this case, the oxidation of char within the primary reaction zone hardly affects the laminar burning velocity. However, when the oxygen concentration beyond the primary reaction zone is high enough, the subsequent oxidation of the char particles may result in the formation of a secondary reaction zone. The presence of a secondary reaction zone where the combustion of char occurs may increase the laminar burning velocity because of the additional heat release. When gas phase reactions have such a predominant influence on the laminar flame propagation of dust clouds, then it is furthermore anticipated that the enhancement of this burning velocity due to the effects of turbulence is similar to what occurs with entirely gaseous premixed flames w15 x. In spite of the similarity with the combustion of premixed gases and the importance of laminar flame propagation parameters in the modeling of dust explosions, our knowledge of these flame characteristics lags behind in what is already known for gas flames. It is the purpose of this paper to demonstrate that the same approach which has been successful in the study of gas flames can also be applied to gas solid mixtures. Hence, the present study deals with the determination of the laminar burning velocity of dust air mixtures. Cornstarch was chosen as the model material because of its consistent composition and particle size, its high volatile content, and its use by previous researchers w15,16 x. In this experimental work, laminar cornstarch flames were stabilized by means of a powder burner and the laminar burning velocity at the center of the flame surfaces was determined by performing velocity measurements in the flow field along the symmetry axis. The velocity measurements were achieved by means of laser Doppler anemometry. The laminar burning velocity of cornstarch air mixtures was determined with dust concentrations from 0.26 to 0.38 kg m y3. The determination of the unstretched laminar burning velocities from the measured laminar burning velocities requires the use of an additional parameter, namely, the Markstein length. The role and significance of this quantity will be clarified in the next section. The laminar burning velocity of cornstarch air mixtures was measured by previous researchers by means of other methods. The results obtained in this work are compared with the results obtained by two previous investigations namely, those of Proust and Veyssiere w16x and Bradley et al. w15 x. 2. The laminar burning velocity and the Markstein length In order to clarify the aim and structure of the present study of cornstarch air mixtures, it is helpful to consider the determination of the laminar burning velocity of premixed gases. A common way to measure the laminar burning velocity of premixed gases is by means of a Bunsen burner Žsee

31 ( ) A.E. Dahoe et al.rpowder Technology Fig. 1.. The device essentially consists of a tube that serves as a mixing chamber for the fuel and the oxidizer. When the combustible mixture is ignited, a stationary flame surface establishes itself at a small distance above the tube. The detachment of the flame is caused by the fact that the heat losses to the rim sustain a narrow region where the temperature is so low that combustion cannot occur. The flame anchors itself in that position by adapting its shape to changes in the velocity of the oncoming mixture. Depending on the magnitude and the spatial distribution of the exit velocity of the unburnt mixture, the flame may assume a variety of shapes Ž see Fig. 1.. If the exit velocity, z, is less than twice the laminar burning velocity, the flame will have a parabolic shape. At greater exit velocities, the flame assumes a conical shape and at still higher velocities Že.g. five times the laminar burning velocity. the shape becomes hyperbolical and tipblowthrough may occur. Burning velocity measurements with the Bunsen burner are often conducted with conical flames. The method relies on a relationship between the laminar burning velocity of a conical flame and the flow speed at the burner exit. Strictly speaking, each point of the flame surface has a radius of curvature in the direction normal to the unburnt mixture. However, if the conical flame is sufficiently large, a surface element of the cone mantle may be regarded locally as an oblique planar combustion wave as depicted by Fig. 2. The dashed line represents a surface element of the boundary where the temperature rises just above the initial temperature of the unburnt mixture, T, due to heat u conduction from the combustion wave. The associated density change beyond the dashed line is indicated by the deflected streamlines. In the case of a planar flame the streamlines intersect the flame perpendicularly and the separation between any two adjacent streamlines remains constant along the flame surface provided that the increment of the corresponding stream function is the same. In other words, the tangential velocity to the surface element, Fig. 1. Bunsen burner with different flame shapes: Ž. a conical flame, Ž. b parabolic flame, Ž. c low velocity button shaped flame, Ž. d hyperbolic flame with tip-blowtrough. Fig. 2. Decomposition of the velocity of the unburnt mixture. z t,f, is zero and does not change along the flame surface, and the unburnt mixture enters the flame perpendicularly with a uniform velocity z f,n. The laminar burning velocity of the surface element may therefore be related to the velocity at the tube exit by measuring the cone angle a and by decomposing the exit velocity z along the dashed line into a normal and a tangential component Ž z and z. n t. Then, rus ul'ruznsruzsinasru,fzf Ž 1. and hence SuL szsina. Ž 2. However, when this methodology is applied to the center of the flame tip, and there is nothing wrong in doing so, it is found that SuL sz because as90 8. Thus, the laminar burning velocity at the center of the flame tip is found to be a factor 1rsina greater than that of the cone mantle and it is evident that different laminar burning velocities exist within the same combustible mixture. This implies that the laminar burning velocity may not be regarded as a fundamental mixture property unless it is normalized with respect to flame shape in some way. This issue has been addressed by a number of researchers w17 31 x. The increased laminar burning velocity at the center of the flame tip is associated with two phenomena namely, flame stretch and flame curvature. The flame tip is a narrow region where the cone mantle develops curvature. As the oncoming unburnt mixture reaches the flame tip, it is heated by the lateral parts of the flame, and the uniform velocity profile is therefore distorted. The unburnt mixture no longer enters the flame perpendicularly and has a tangential velocity component. The tangential velocity also

32 226 ( ) A.E. Dahoe et al.rpowder Technology has a gradient along the flame surface. A laminar flame within a nonuniform flow field with a sufficiently strong velocity gradient along its surface is subjected to tangential strain and therefore develops curvature. If a curved flame is concave with respect to the unburnt mixture Župper part of Fig. 3., adjacent points traveling along the flame surface move closer together Ž negative flame stretch. in the tangential direction. Conversely, if the flame is convex towards the unburnt mixture Ž lower part of Fig. 3., adjacent points on the flame surface move further apart Žflame stretch. in the tangential direction. The convergence and the divergence of the streamlines along the flame surface in Fig. 3 illustrate how the local flame structure is being modified by the strain. It is evident that the mass flow per unit area of a concave flame exceeds that of a planar flame and for a convex flame it becomes less. Although flame curvature is invariably coupled to nonuniformities of the velocity field, it must be realized that even in the absence of strain, it may significantly alter the local laminar burning velocity. A flame surface serves as a local sink for reactants and a local source for heat. Increasing the diffusion rate of the reactants to the flame increases the rate of heat release and hence, tends to increase the flame temperature. An increase of the conduction heat flux from the flame sheet into the oncoming unburnt mixture tends to reduce the flame temperature. However, changes in the conductive heat flux are coupled to changes in the diffusive flux of the reactants towards the flame surface. When a planar flame develops curvature, the heat conducted from one location is convected to another location at the flame surface. A convex bulge conducts heat into the oncoming unburnt mixture, as shown in the lower part of Fig. 4, and this heat is convected towards parts of the bulge away from the center. This leads to an increased laminar burning velocity at the lateral parts of the flame and to a lower laminar burning velocity at the center. In the case of concavity, shown in the upper part of Fig. 4, the heat conducted by the lateral parts of the bulge is convected towards the center and the effect on the laminar burning velocity is reversed. In the case of weakly strained flames, the influence of flame stretch on the laminar burning velocity of a curved Ž w x. Fig. 3. Flame stretch in a nonuniform flow field after Ref. 21. Fig. 4. Heat conduction, reactant diffusion and convective heat transfer in Ž w x. the preheat zone of a curved flame after Ref. 32, p flame is taken into account by expressing the latter as follows w17,p,22,32,p,357 x, L S s 1q S o ul ul. Ž 3. R Here SuL o denotes the laminar burning velocity of an unstretched flame and the quantity L is known as the Markstein length. R is the radius of curvature of the flame sheet, defined as the reciprocal of the mean curvature w33,p,136 x. It is taken to be positive for convexity towards the burnt mixture and negative for convexity towards the unburnt mixture. The Markstein length, L, introduced by Clavin w21x for gaseous fuels, is a mixture specific constant with a magnitude of the order of the flame thickness and serves as a measure of the sensitivity of the laminar burning velocity to the influence of flame shape modifications. Neither its theoretical nor its experimental evaluation is easy, and much remains to be learned about its precise functional dependence on the chemical and transport properties of a specific mixture. It is for this reason that the Williams Clavin formula is currently accepted as an adequate relationship to be used in conjunction with Eq. Ž. 3 in order to describe the response of the laminar burning velocity to changes of the flame shape. The Williams Clavin formula w20,23,34x is given by, / L 1 1 ZeŽ Ley1.Ž 1yg. Mk' s ln q o d g ž 1yg 2g = L H grž 1yg. lnž 1qx. 0 x d x. Ž 4. This formula was derived for a two reactant mixture with a single-step overall reaction rate, a large activation energy, a constant thermal conductivity, a constant kinematic viscosity, and a constant specific heat. In this equation Mk' o Lrd denotes the Markstein number, Ze' Ž E s RT 2.Ž L a f Tf y T. the Zeldovich number, Le' lrc ID the Lewis u P

33 ( ) A.E. Dahoe et al.rpowder Technology number and gsž T yt. f u rt f. With g typically lying be- tween 0.8 and 0.9, this formula predicts that L is times the thickness of an unstretched laminar flame, d L o,if Le s 1. More sophisticated expressions have also been developed. Clavin and Garcia w28,35x for example, extended Eq. Ž. 4 to include the temperature dependence of the thermal and molecular diffusivity. Rogg and Peters w31x derived an analytical expression similar to Eq. Ž. 4 by performing a theoretical analysis on a weakly strained stoichiometric methane air flame using a reduced threestep mechanism with six reactants. They rejected the simplification of a global single step reaction involving only two reactants, but retained the assumption that the diffusivities are independent of the temperature. When laminar flames are subjected to severe stretch, Eq. Ž. 3 is no longer valid and one must resort to an equation that invokes two Markstein lengths: one for strain, Ls and one for curvature effects, L c. The stretch rate, s, of a surface element, A, in a strained fluid is defined as, 1 da ss. Ž 5. A dt It consists of two additive contributions, s s and s c. The first includes the influence of strain and the second involves the effect of curvature. At any point of a flame surface, these contributions are related to the velocity of the flow field, z, and the normal unit vector of the surface in the direction of the unburnt mixture by the universal expression, ss ynn:=zq=pz q S o =Pn. Ž 6. ^ ` _ ul ^`_ ṡ s ṡc Here SuL o is the magnitude of the unstretched laminar burning velocity vector. Clavin w21x has shown that when a planar laminar flame with a thickness d L o is distorted into a bulge of a size L4d L o, then the local laminar burning Ž w x. Fig. 6. Wrinkled flame burner after Ref. 28. velocity at each point can be related to the local stretch rate as, SuL o ysul L 1 da 2 s qo Ž e.. Ž 7 o o ž. S S A dt ul ul / Here sd L o rl is a small number. This equation can be rewritten into, 1 da o 2 SuL ysul slž / qo Ž e. Ž 8. A dt S o ys sl sqo Ž e 2.. Ž 9. ul ul It is then obvious that the Markstein length is intended to serve as a proportionality ratio between the change of the laminar burning velocity and the stretch rate. In order to reconcile this result with the general expression for the stretch rate Eq. Ž. 6, researchers have decided to express L s as a linear combination of quantities that account for Fig. 5. Experimental Markstein numbers measured by Quinard taken from Ref. w21 x.. Ždata Fig. 7. Markstein lengths of methane air mixtures from numerical experi- Ž w x. ments from Bradley et al. 24.

34 228 ( ) A.E. Dahoe et al.rpowder Technology Ž 12. to Eq. Ž 13., use has been made of the relationship Žsee Equations Ž and Ž of Ref. w36 x., =PnsyŽ k1qk 2.. Ž 14. Fig. 8. Markstein numbers of methane air mixtures from numerical Ž w x. experiments from Bradley et al. 24. the separate effect of variables such as strain rate, flame curvature, and pressure, each having its own Markstein length. Thus, L s was replaced by Lss sql cs cq... and hence, S o ys s L s ql s q... qo Ž e 2.. Ž 10. Ž. ul ul s s c c Combination of Eqs. Ž.Ž. 6, 8 and Ž 10. leads to the equation which is to be used in case of severe flame stretching, o S sl wnn:=zy=pzxq w1yl =PnxS Ž 11. ul s c ul ms sl wnn:=zy=pzxq 1q Ž k qk. L S o ul s 1 2 c ul L c o ul sw x ul Ž 12. ms sl nn:=zy=pz q 1q S. Ž 13. R Ž. Ž. It is seen that Eq. 13 may be simplified to Eq. 3 when the influence of strain is negligible. In the step from Eq. Here k1 and k2 denote the minimum and maximum curvature of an arbitrary surface. The mean curvature is defined as the sum of these quantities and its reciprocal value is considered to be the radius of curvature, R, ofa flame surface. The Markstein length of several gaseous fuels was investigated by a number of researchers and the most illustrative of these investigations will be mentioned here. Quinard w21,28x used a wrinkled flame burner to experimentally determine the Markstein length. The study involved hydrogen, methane, ethylene, and propane air mixtures as seen in Fig. 5. The measurement technique will be described here to illustrate how the Markstein length was determined. The wrinkled flame burner, shown in Fig. 6, consists of three sections: a settling chamber, a convergent section and a rectangular burner head. The combustible mixture is made laminar in the settling chamber, and an initial uniform velocity profile at the entrance of the convergent section is ensured by grids. At the exit of the convergent section there is an array of water cooled tubes. These tubes cause laminar perturbations in the velocity profile and as a result, the flame takes the form of a two-dimensional sinusoidal sheet. At the exit of the burner, a water-cooled grid decouples the hot combustion products from the cold ambient air. The curvature of the flame front was obtained by means of a photo-diode array and by fitting a portion of the digitized picture to a sinusoid of an appropriate wavelength. The local burning velocity was measured by means of laser doppler anemometry. The curvature and velocity measurements were performed at Fig. 9. The powder burner set-up used to measure the laminar burning velocity of cornstarch air mixtures by means of laser Doppler anemometry.

35 ( ) A.E. Dahoe et al.rpowder Technology Experimental set-up Fig. 10. Positioning of the measurement location. the minima and maxima of the flame surface where the strain and curvature systematically have opposite signs and equal magnitudes. Here, also the tangential component of the flow velocity is zero and practically no horizontal velocity gradient exists. Bradley et al. w24x solved the conservation equations for mass, momentum, species and energy for inwardly oriented spherical laminar methane air flames, initiated by an instantaneous ignition around an outer spherical boundary. The reduced kinetic mechanism adopted was that of Mauss and Peters Ž C. 1 with 18 species and 40 reactions, in which OP, HOP, HOP, 2 HO,PCH, 2 2 PCH 2, PCHO, PCH 2O, and PCH 3 are steady-state species. As these numerical implosion experiments resolved the details of the flow field and the curvature at any particular location of the flame front, the separate Markstein lengths, Ls and L c, could be determined over a wide range of equivalence ratios. These quantities and the associated Markstein numbers are shown in Figs. 7 and 8. The experimental set-up is shown in Fig. 9 and consists of two main parts: a powder burner to create stabilized dust flames and a laser Doppler anemometer for measuring the flow velocity at various locations inside the flame zone. The powder burner consists of a glass tube in which the combustible particles are fluidized together with a certain amount of glass beads. Before each experiment the tube was filled with a mixture of approximately 100 g of mm glass beads and about 300 g of cornstarch. The tube has a length of 51.5 cm, an internal diameter of 4.8 cm and a burner head, with a 28.5-mm internal diameter burner rim, is mounted onto the tube exit. The distributor is a porous plate and the flow rate is regulated by means of a flow meter. Since the pressure drop across the fluidized bed is impossible to predict exactly, and since the flow meter is calibrated at atmospheric pressure, it cannot be used to control the flow rate. Hence, the exact flow rate had to be calculated for each flame from the velocities at the tube exit as measured with the laser Doppler anemometer Ž see Fig Figs. 11 and 12 show the radial profile of the measured vertical velocity component at two different heights above the burner head, namely, at a distance of 2.5 and 6.3 mm. Unlike the parabolic profiles commonly observed at the exit of the Bunsen burner, the velocity profiles at the powder burner exit were observed to be flat. The reason for this is that the dust cloud enters the burner head as a laminar, plug flow Ždue to the uniform velocity distribution created by the fluid bed. and the length to diameter ratio of the burner head is too small Ždiameter 28.5 mm, length 55 mm. for a parabolic profile to be formed. In the case of the Bunsen burner, the length to diameter ratio is sufficiently large to allow the development of Poiseuille flow. At greater heights, there is a zone where the initially uniform velocity distribution shows a change that makes it Fig. 11. Radial profile of the vertical velocity component at 2.5 mm above the burner head.

36 230 ( ) A.E. Dahoe et al.rpowder Technology Fig. 12. Radial profile of the vertical velocity component at 6.3 mm above the burner head. necessary to consider two possible causes. The first possible cause is the behavior of a pressure gradient. Inside the burner head, the pressure gradient is oriented along the symmetry axis. As soon as the fluid exits the burner head, it expands and the pressure gradient points away from center line. As a result, the flow changes its direction in the outer parts of the jet, and the vertical velocity component becomes smaller. The second possible cause may be sought in the momentum diffusion, away from the laminar jet and into the ambient air due to the shear forces. The distance across which this alters the velocity profile can be estimated by means of, ' ds p Õt, 15 Ž. where d denotes the penetration depth, Õ the kinematic viscosity and t the time during which the momentum transfer occurs. At an exit velocity of 30 cm s y1, a stationary fluid element needs about 0.02 s to cross a distance of 6.3 mm. With these values and a kinematic viscosity of 10 y5 m 2 s y1, one finds a penetration depth of 0.8 mm, which does not account for the observed distortion of the velocity profile at a height of 6.3 mm. At larger heights, however, this effect would become an important factor and, together with the effect of the pressure gradient, the laminar jet may entrain ambient air into the flame. The laser Doppler anemometer used in this work measures only one velocity component and consists of the following components: a laser, a beam splitter, a photomultiplier tube, a high voltage power supply and a correlator. The laser, the beam splitter and the photomultiplier tube are mounted on a type RF 340 optical bench, supplied by Malvern Intruments. The laser is a Melles Griot type 05-LHP-927 He Ne laser with an output power of 50 mw. It emits a light beam with a wavelength of nm and obtains its energy from a Melles Griot 05-LPL power supply. Fig. 13. The autocorrelation function.

37 ( ) A.E. Dahoe et al.rpowder Technology Table 1 Optimal values of the parameters of Eq. Ž 16. Parameter Value"S.E. Ž. y1 a1 11.5"2.0 =10 Ž. y3 Õ 970.1"3.8 =10 Ž. y3 sõ 20.6"7.5 =10 Ž. y2 m 23.8"2.5 =10 Ž. y6 r 92.9"9.8 =10 y6 s 7.919=10 Ž fixed. Ž. y1 b y1.8"2.0 =10 1 For a 95% confidence interval, multiply S.E. by The primary laser beam is divided into two equal intensity beams by means of the beam splitter, which can be rotated around an axis that coincides with the center line of the primary beam. The separation between the two new beams can be varied by adjusting the position and the orientation of the optical crystals inside the beam splitter. In this work, the separation between the two beams was set to 20 mm and a converging lens with a focal length of 250 mm was used to cross the beams in order to form the probe volume. Hence, the fringe spacing was equal to 7.919=10 y6 m. When a particle crosses the probe volume, it scatters the light of both incident beams, and the scattered light is collected in the backscatter mode by an EMI 9863 KBr100 photomultiplier. Before reaching the photomultiplier, the scattered light passes through a zoomlens, a 200-mm pinhole and an optical filter that admits light of narrow range around nm. The high voltage Žoptimal signals were obtained in the voltage range between 1.2 and 2.5 kv. was supplied by an EMI PM 28B power supply. The photomultiplier tube converts the optical signal into a time series of TTL signals with a repetitive pattern of which the cycle time corresponds to the modulation frequency of the optical signal. The electrical signals given off by the photomultiplier are subsequently processed by a 64-channel Malvern K7025 correlator, which computes the autocorrelation function of the received electrical signals. It can be derived w37x that the autocorrelation function, GŽ t., has the following form, ž / 2 2 Ž Õ. ž 2 s / ž s Õ t m GŽ t. sa1exp y 1q 2 r / 2 ps t 2p Õt = exp y cos qb. Ž 16. In this equation: a1 denotes a scaling factor; Õ denotes the velocity component of the scattering particle, perpendicular to the bisection of the angle formed by the crossing laser beams; sõ denotes the standard deviation of Õ; t denotes the separation time; m denotes the fringe visibility; r denotes the effective radius of the measuring volume; s 1 denotes the fringe spacing; and b1 denotes the contribution of the background signal. The correlator was continuously operated in a specific program, ldamenu. This program collects the autocorrelation functions and performs a rudimentary form of data validation before storage in a digital computer. v The program normalizes the autocorrelation function on the basis of the highest recorded value and checks whether the highest normalized value occurs in the first few channels of the correlator. v The program verifies that the normalized autocorrelation function has a decreasing trend. At each measuring location in the flow field, at least six valid autocorrelation functions were gathered, and the velocity was determined by fitting Eq. Ž 16. to these data sets. Fig. 13 shows an example of a fitted autocorrelation function, and the optimal values of the parameters of Eq. Ž 16. are shown in Table Determination of the laminar burning velocity and the Markstein length Deshaies and Cambray w38x performed an experimental study on the laminar burning velocity of propane oxygen nitrogen mixtures with a nonuniform flow field. The experimental set-up used by these authors is shown in Fig. 14. The reactive mixtures flowed from a cylindrical tube, where different kinds of honeycomb structures and damping grids are positioned and impinges on a flat stagnation surface. After ignition, axi-symmetric flames with a positive, negative and zero curvature were seen to stabilize below the stagnation plate. Laser Doppler velocimetry was used to measure the local velocity of the fluid and laser tomography to visualize the shape of a meredian section of the flame front. The visualization of the flame front was Fig. 14. Schematic diagram of the experimental set-up used by Deshaies and Cambray w38 x.

38 232 ( ) A.E. Dahoe et al.rpowder Technology Fig. 15. Structure of the flow field measured by Deshaies and Cambray w38 x. accomplished by seeding the reactive mixture with small oil droplets that evaporate upon entering the hot zones of the flame. Prior to entering the flame zone, these droplets serve as scatterers of the laser sheet light, and after evaporation there are no scatterers present. The meridian section of the flame, which appears as a transition region between the bright unburnt mixture and the dark flame zone, was recorded by means of a video camera and the pictures were digitized and stored as grayscale images. Deshaies and Cambray distinguished four zones in the flow field of the flames Ž Fig. 15.: the flow field of the unburnt mixture which is not influenced by the heat of the flame, the preheat zone of the flame, the reaction zone, and a final zone with the combustion products. In the first zone, the vertical velocity component was found to decrease owing to the presence of the stagnation plate at a downstream position in the flow field. The decrease of the vertical velocity component continues until the heat of the Fig. 16. Mass throughput of the fluidized bed as a function of the velocity at the center at the lowest measuring location above the burner head.

39 ( ) A.E. Dahoe et al.rpowder Technology Ž. Fig. 17. The height of the flame tip in case of planar flames, the center of the flame surface relative to the burner head for the flames investigated in this work. flame accelerates the fluid. This minimum velocity marks the upstream boundary of the preheat zone. Deshaies and Cambray fitted a straight line to the velocity profile in the first zone and extrapolated this information to what the velocity would be, in the absence of heat effects, at the position where the flame temperature attains its highest value. This velocity was taken as the laminar burning velocity by these authors. In the present work, eight cornstarch dust flames were investigated and these are specified here as flames Ž A H.. At low flow rates Ž flames A C., the dust flames were observed to stabilize as a flat flame, very close to the burner rim. At higher flow rates Ž flames E H. the flame was found to stabilize further away from the burner rim and its shape changed into a parabola. Between these extremes there seems to be more than one stable situation Ž flame D.: the flame showed a tendency to change its shape continually between the parabolic shape and the planar shape, with a preference for the former Žmoderately curved.. The associated mass throughput and particle velocities measured with the laser Doppler anemometer are shown in Fig. 16, and it is seen that this transitional behavior of the flame occurs when the exit velocity at the burner head is equal to approximately m s y1. Fig. 17 shows the height of the flame tip above the burner head of the flames investigated. Figs. 18 and 19 show the profiles of the vertical velocity component measured in flames Ž C. and Ž D.. With the dust flames it is also possible to discern a flow field structure as depicted by Fig. 17, and it is interesting to see that the flow velocity increases further in the after-burning zone. This indicates that the laminar combustion process of cornstarch air mixtures may involve multiple flame zones. Only the first combustion zone, the actual flame, is the truly premixed flame. The after-burning zone is considered to be a diffusion flame where the burning of char takes place, as mentioned in the introduction of this paper and pointed out by Bradley and Lee w14 x. The laminar burning velocity of the dust flames was taken to be equal to the minimum velocity that marks the upstream boundary of the preheat zone for two reasons. The first reason is that an extrapolation like the one applied by Deshaies and Cambray would lead to unacceptably low and even negative values. The second reason is Fig. 18. Vertical velocity component at the center line of flame C.

40 234 ( ) A.E. Dahoe et al.rpowder Technology Fig. 19. Vertical velocity component at the center line of flame D. that it is desirable to relate the propagation velocity of the flame to known properties of the combustible mixture involved. Since the mixture properties undergo changes in the preheat zone that cannot be described by means of a simple extrapolation from the mixture properties prior to the preheat zone, such an extrapolation leads to an undefined, and perhaps nonexistent, frame of reference. In order to find the minimum value of the vertical velocity component and to overcome the errors introduced by the scatter in the measured data, a third order polynomial was fitted to the initial part of the velocity profiles w39x and the resulting laminar burning velocities are shown in Fig. 20. The laminar burning velocities shown in Fig. 20 appear to be clustered according to the shape of the flame front. The more the shape deviates from a planar flame towards a parabolic flame, the higher the experimental burning velocity becomes. At a dust concentration of 0.33 kg m y3 the laminar burning velocity is observed to increase by a factor of about two when the flame shape changes from planar to parabolic. The reasons for this behavior are the flame curvature and strain due to nonuniformities in the velocity field which were discussed in Section 2. Eq. Ž 13. was used to find the value of the unstretched laminar burning velocity. Since the pressure gradient at the burner exit is small and there is no stagnation point in the flow field, the contribution of the first term on the right hand side of the above equation is considered to make a negligible contribution to the experimental value of the laminar burning velocity. Hence, the equation may be simplified to Eq. Ž. 3, taking only the effect of the flame curvature into account. The first step in using Eq. Ž 17. to find the unstretched laminar burning velocity is to find the Markstein length, L c, from the experimental data at a dust concentration of 0.33 kg m y3 in Fig. 20. The idea behind this correction is that, since the dust concentration is the same in flames Ž B., Ž C. and Ž G., there is a Markstein length such that Eq. Ž 17. must give the same unstretched laminar burning velocity Fig. 20. The laminar burning velocity, S ul, of flames A H.

41 ( ) A.E. Dahoe et al.rpowder Technology Table 2 The laminar burning velocity S ul, the radius of curvature R and the unstretched laminar burning velocity S o of flames A H Ž. o Flame Dust conc. SuL R m SuL Ž y3. Ž y1. Ž y1 kg m cm s cm s. A B C y2 D = y2 E = y3 F = y2 G = H y3 7.3= for all three flames. The radii of curvature Ž see Table 2. were determined by fitting a parabola, až s. sw xž s., yž s.x, to a few points of the flame profile which was obtained by photographing the flame and by employing the parametric form of the parabola as 1 1 y Y Ž s. s. Ž 17 3r2. R X 2 1qy Ž s. Application of this procedure and Eq. Ž 17. to obtain the same unstretched laminar burning velocity, SuL o, for flames Ž B. and Ž G. resulted in a Markstein length, L c, of 11.0 mm. Although the Markstein length is known to depend on the composition of the combustible mixture, the latter value was subsequently used to calculate the unstretched laminar burning velocity of all flames, and the results are plotted in Fig. 21. The unstretched laminar burning velocities are between 15 and 30 cm s y1. Fig. 22 shows a comparison between the unstretched laminar burning velocities obtained by means of the poww16 x. The data band reported by these authors was obtained by der burner and the results of Proust and Veyssiere observing the motion of upwardly propagating laminar cornstarch air flames in a tube. The parabolic dust flames were allowed to propagate from the open end of the tube Ž at the bottom. up to the closed end Ž at the top. in quiescent cornstarch air mixtures of various dust concentrations. The laminar burning velocity was taken as the difference between the velocity of the flame contour and the velocity of the unburnt mixture ahead of it, obtained from photographic records of the moving flame. None of 1 2 If a is a regular curve in R with a Ž s. sw xž s., yž s.x, then the curvature, kž s.,ofa is given by w40 x, p. 11 x X Ž s. y Y Ž s. y x Y Ž s. y X Ž s. k Ž s. s. X 2 X 2 3r2 x Ž s. q y Ž s. In the present work the flame profile was parametrized as xž s. s s a Ž s. 2. ½ yž s. s b 0 q b 2 s ul the resulting laminar burning velocities was corrected for flame stretch and flame curvature. Although our results and those of Proust and Veyssiere appear to be of the same magnitude, an interpretation of Fig. 22 in terms of flame stretch and flame curvature puts things in a different perspective. It was mentioned in Section 2 that when a flame front bulges convexly with respect to the unburnt mixture, it propagates with a lower burning velocity than that of a planar flame. The moving flames studied by Proust and Veyssiere were parabolic and convex with respect to the unburnt mixture Žsee the phow16 x.. A correction of tographs presented by these authors the laminar burning velocity of a parabolic flame by means of the radius of curvature and the Markstein length according to Eq. Ž. 3 changes the measured laminar burning velocity by a factor of 1.5 to 2 Žsee flames Ž D H. in Table 2.. In their case the associated unstretched laminar burning velocities would be between 40 and 50 cm s y1. This is about twice the unstretched laminar burning velocities obtained in our experiments using the powder burner. The reason for this discrepancy must be sought in the fact that buoyancy may have a different effect on moving flames in a tube than in the case of a stationary flame. When a flame propagates in the upward direction from the open end of a tube, the flame enters the unburnt mixture at the downstream side with a velocity that is assisted by the buoyancy force. As a result, the velocity difference between the moving flame and the moving reactants ahead of it, which is the measured burning velocity, may be larger than in the case of the powder burner, where the unburnt mixture enters a stationary flame from the downstream side. Bradley et al. w15x determined the laminar burning velocity of a kg m y3 cornstarch air mixture by igniting turbulent dust clouds to deflagration in a fan-stirred bomb and found a laminar burning velocity of 12 cm s y1. The turbulent burning velocity was determined at various, known, turbulence levels. Next, the ratio between the turbulent burning velocity and the laminar burning velocity, SuTrS ul, was plotted against the ratio between the root-mean-square value of the turbulent velocity fluctuations and the laminar burning velocity, Õ X rmsrs ul. From this plot, the laminar burning velocity could be determined by means of extrapolation to a zero turbulence level Ži.e. X Õ 0. rms. This extrapolation is based on the assumption that the generalized correlation for the turbulent burning velocity of gaseous fuels, S S ut ul X n Õrms ž S / ul s1qc, Ž 18. is also applicable to the turbulent burning velocity of dust clouds. In this equation, C is a parameter that depends on the length scale of the turbulence and n is known as the bending exponent. For stoichiometric propane air mix-

42 236 ( ) A.E. Dahoe et al.rpowder Technology Fig. 21. The unstretched laminar burning velocity, S o, of flames A to H. ul tures for example, Trautwein et al. w41x observed that Cs3.31 and ns0.48. At a dust concentration of kg m y3, Bradley et al. Ž y1 found a laminar burning velocity 12 cm s. which is about half the unstretched laminar burning velocity ob- Ž y1 tained by means of the powder burner 22 cm s ; see Table 2.. This difference can be attributed to the fact that the results obtained by means of the fan-stirred bomb were not corrected for the effect of flame stretch and flame curvature. The turbulent burning velocities used in the extrapolation were obtained at a flame radii of 20, 25, 30 and 35 mm. As the flames grow in the outward direction after point ignition, they are convex with respect to the unburnt mixture and, as discussed in Section 2, the laminar burning velocity is less than that of a planar flame. When these flame radii are compared with the radii of curvature in Table 2, it is seen that a correction by means of the Markstein length leads to an unstretched laminar burning velocities of about 1.5 times the measured laminar burning velocity. With this correction, one obtains an unstretched laminar burning velocity of 18 cm s y1 which is closer to the value of 22 cm s y1 found with the powder burner. Fig. 22. A comparison between the unstretched laminar burning velocity, SuL o, of flames A H and laminar burning velocities measured by Proust and Veyssiere w16 x.

43 ( ) A.E. Dahoe et al.rpowder Technology Conclusions v Laminar burning velocities of cornstarch air mixtures Ž y3 of various dust concentrations kg m. have been measured by stabilizing laminar dust flames on a powder burner. The measured laminar burning velocity was found to be sensitive to the shape of the flame. When the dust concentration was kept the same, parabolic flames were found to have a laminar burning velocity which was almost twice the laminar burning velocity of a planar Ž y1 flame ca. 30 cm s for the latter as compared with ca. 54 y1 cm s for the former; see Fig. 20 and Table 2.. v From the discrepancy mentioned under the previous item the flame curvature Mark Stein length, L c, of lami- nar cornstarch air flames could be determined, and it was found to have a value of 11.0 mm. With this Markstein length, the measured laminar burning velocities at various dust concentrations could be corrected in order to obtain the unstretched laminar burning velocity of cornstarch air mixtures as a function of the dust concentration Žsee Fig The unstretched laminar burning velocities are between 15 and 30 cm s y1. v The development of damaging pressures due to explosions are predicted by means of integral balance models. With gas explosions in particular, the turbulent burning rate is commonly incorporated by means of Eq. Ž 18. or a similar expression and it is evident that inaccuracies in the laminar burning velocity invariably result in large errors. Since the Markstein length of cornstarch air mixtures is much larger than the Markstein length of methane air mixtures Ž11.0 mm for the former as compared with 0.1, 0.2 mm for the latter; see Fig. 7. errors due to the use of laminar burning velocities which are not corrected by means of the Markstein length are more severe for dust air mixtures than for purely gaseous premixtures. Hence, knowledge of the Markstein length is of crucial importance in the modeling of dust explosions. List of symbols A Flame area Žm 2. C P Ž y1 y1 Constant pressure specific heat J mol K. E a Ž y1 Activation energy J mol. K St Volume normalized maximum rate of pressure Ž y1 rise of a dust explosion Pa m s. n Bending exponent in generalized turbulent burning velocity correlation Ž. R Ž y1 y1 Universal gas constant J mol K. ṡ Stretch rate Žs y1. ṡ s Stretch rate due to strain Žs y1. ṡ c Stretch rate due to curvature Žs y1. S ul Ž y1 Laminar burning velocity m s. S ut Ž y1 Turbulent burning velocity m s. T Absolute temperature Ž K. T f Flame temperature Ž K. T u Temperature of the unburnt mixture Ž K. z Ž y1 Velocity vector m s. Õ X rms Root-mean-square value of the velocity fluctua- Ž y1. tions m s Greek letters g Heat capacity ratio Ž. d Penetration depth Ž m. d L Laminar flame thickness Ž m. Õ Ž 2 y1 Kinematic viscosity m s. l Ž y1 y1 Thermal conductivity W m K. r Ž y3 Density kg m. Other symbols ID Ž 2 y1 Diffusion coefficient m s. L Markstein length Ž m. L s Strain Markstein length Ž m. L c Curvature Markstein length Ž m. R Radius of flame curvature Ž m. Dimensionless groups Le Lewis number Ž. Mk Markstein number Ž. Ze Zeldovich number Ž. References wx 1 National Fire Protection Association Ž NFPA., Venting of deflagrations, 1988, NFPA 68, 1988 edition. wx 2 Verein Deutcher Ingenieure Ž VDI., Pressure venting of dust explosions, 1995, VDI wx 3 W. Bartknecht, Dust Explosions: Course, Prevention, Protection, Springer, 1989, Translation of Staubexplosionen by R.E. Bruderer, G.N. Kirby and R. Siwek. wx 4 R.K. Eckhoff, Dust Explosions in the Process Industries, 2nd edn., Butterworth and Heinemann, wx 5 J. Nagy, E.C. Conn, H.C. Verakis, Explosion development in a spherical vessel, Report of investigations 7279, United States Department of the Interior, Bureau of Mines, Washington, wx 6 F. Tamanini, Turbulence effects on dust explosion venting, Plantr Operations Progress 9 Ž.Ž wx 7 A.E. Dahoe, J.F. Zevenbergen, S.M. Lemkowitz, B. Scarlett, Dust explosions in spherical vessels: the role of flame thickness in the validity of the cube-root-law, Journal of Loss Prevention in the Process Industries 9 Ž.Ž , March. wx 8 D. Bradley, A. Mitcheson, Mathematical solutions for explosions in spherical vessels, Combustion and Flame 26 Ž wx 9 J. Nagy, H.C. Verakis, Development and Control of Dust Explosions, Marcel Dekker, New York, w10x H.E. Perlee, F.N. Fuller, C.H. Saul, Constant-volume flame propagation, Report of investigations 7839, United States Department of the Interior, Bureau of Mines, Washington, w11x F. Chirila, D. Oancea, D. Razus, N.I. Ionescu, Pressure and temperature dependence of normal burning velocity for propylene air mixtures from pressure time curves in a spherical vessel, Revue Roumaine de Chimie 40 Ž.Ž

44 238 ( ) A.E. Dahoe et al.rpowder Technology w12x D. Bradley, M. Lawes, M.J. Scott, E.M.J. Mushi, Afterburning in spherical premixed turbulent explosions, Combustion and Flame 99 Ž w13x F. Tamanini, Modeling of turbulent unvented gasrair explosions, Progress in Aeronautics and Astronautics 154 Ž w14x D. Bradley, J.H.S. Lee, Proceedings of the First International Colloquium on the Explosibility of Industrial Dusts, vol. 2, 1984, pp w15x D. Bradley, Z. Chen, J.R. Swithenbank, Burning rates in turbulent fine dust air explosions, Proceedings of the 22nd Symposium ŽInter- national. on Combustion, The Combustion Institute, 1988, pp w16x C. Proust, B. Veyssiere, Fundamental properties of flames propagating in starch dust air mixtures, Combustion Science and Technology 62 Ž w17x G.H. Markstein, Nonsteady Flame Propagation, Pergamon, w18x S.H. Chung, C.K. Law, An invariant derivation of flame stretch, Combustion and Flame 55 Ž w19x P. Clavin, F.A. Williams, Theory of premixed-flame propagation in large-scale turbulence, Journal of Fluid Mechanics 90 Ž w20x P. Clavin, F.A. Williams, Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low turbulence, Journal of Fluid Mechanics 116 Ž w21x P. Clavin, Dynamic behavior of premixed flame fronts in laminar and turbulent flows, Progress in Energy and Combustion Science 11 Ž w22x M. Matalon, On flame stretch, Combustion Science and Technology 31 Ž w23x D. Bradley, A.K.C. Lau, M. Lawes, Flame stretch as a determinant of turbulent burning velocity, Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences 338 Ž w24x D. Bradley, P.H. Gaskell, X.J. Gu, Burning velocities, Markstein lengths, and flame quenching for spherical methane air flames: a computational study, Combustion and Flame 104 Ž w25x S.M. Candel, T.J. Poinsot, Flame stretch and the balance equation for the flame area, Combustion Science and Technology 70 Ž w26x C.K. Law, Dynamics of stretched flames, Proceedings of the 22nd Symposium Ž International. on Combustion, The Combustion Institute, 1988, pp w27x G.I. Sivashinsky, Instabilities, pattern formation, and turbulence in flames, Annual Reviews on Fluid Mechanics 15 Ž w28x G. Searby, J. Quinard, Direct and indirect measurements of Mark- stein numbers of premixed flames. Combustion and Flame 82 Ž w29x V.P. Karpov, A.N. Lipatnikov, V.L. Zimont, Flame curvature as a determinant of preferential diffusion effects in premixed turbulent combustion, Progress in Astronautics and Aeronautics 173 Ž , Chap. 14. w30x V.P. Karpov, A.N. Lipatnikov, P. Wolanski, Finding the Markstein number using the measurements expanding spherical laminar flames, Combustion and Flame 109 Ž w31x B. Rogg, N. Peters, The asymptotic structure of weakly strained stoichiometric methane air flames, Combustion and Flame 79 Ž w32x F.A. Williams, Combustion Theory, 2nd edn., Addison-Wesley Publishing, w33x D.C. Kay, Theory and Problems of Tensor Calculus, Schaum s Outline Series, McGraw-Hill, w34x K.N.C. Bray, N. Peters, Laminar flamelets in turbulent flames, in: P.A. Libby, F.A. Williams Ž Eds.., Turbulent Reacting Flows, Academic Press, 1994, pp , Chap. 2. w35x P. Clavin, P. Garcia, The influence of the temperature dependence of diffusivities on the dynamics of flame fronts. J. de Mec. Theoretique et Appliquee 2 Ž w36x R. Aris, Vectors, Tensors, and the Basic Equations of Fluid Mechanics, Dover Publications, New York, w37x C.A.P. Zevenhoven, Particle Charging and Granular Bed Filtration for High Temperature Application, PhD thesis, Delft University of Technology, Delft, The Netherlands, December 1992, Delft Univ. Press. w38x B. Deshaies, P. Cambray, The velocity of a premixed flame as a function of the flame stretch: an experimental study, Combustion and Flame 82 Ž w39x A. Vleeshouwers, The propagation of gas and dust flames, Part A: The experimental determination of the laminar burning velocity of cornstarch by means of laser doppler anemometry. Part B: Evaluation of density profiles in propagating methane air flames in a constant volume vessel by means of interferometry. Master s thesis, Delft University of Technology, Division of Particle Technology, February w40x A. Gray, Modern Differential Geometry of Curves and Surfaces, Studies in Advanced Mathematics, CRC Press, w41x S.E. Trautwein, A. Grudno, G. Adomeit, The influence of turbulence intensity and laminar flame speed on turbulent flame propagation under engine like conditions, Proceedings of the 23rd Symposium Ž International. on Combustion, The Combustion Institute, 1990, pp

45 Journal of Loss Prevention in the Process Industries 18 (2005) Laminar burning velocities of hydrogen air mixtures from closed vessel gas explosions A.E. Dahoe* Faculty of Engineering, University of Ulster, FireSERT (Block 27), Co. Antrim, Shore Road, Newtownabbey BT37 0QB, Northern Ireland, UK Received 31 January 2005; received in revised form 24 March 2005; accepted 29 March 2005 Abstract The laminar burning velocity of hydrogen air mixtures was determined from pressure variations in a windowless explosion vessel. Initially, quiescent hydrogen air mixtures of an equivalence ratio of were ignited to deflagration in a 169 ml cylindrical vessel at initial conditions of 1 bar and 293 K. The behavior of the pressure was measured as a function of time and this information was subsequently exploited by fitting an integral balance model to it. The resulting laminar burning velocities are seen to fall within the band of experimental data reported by previous researchers and to be close to values computed with a detailed kinetics model. With mixtures of an equivalence ratio larger than 0.75, it was observed that more advanced methods that take flame stretch effects into account have no significant advantage over the methodology followed in the present work. At an equivalence ratio of less than 0.75, the laminar burning velocity obtained by the latter was found to be higher than that produced by the former, but at the same time close enough to the unstretched laminar burning velocity to be considered as an acceptable conservative estimate for purposes related to fire and explosion safety. It was furthermore observed that the experimental pressure time curves of deflagrating hydrogen air mixtures contained pressure oscillations of a magnitude in the order of 0.25 bar. This phenomenon is explained by considering the velocity of the burnt mixture induced by the expansion of combusting fluid layers adjacent to the wall. q 2005 Elsevier Ltd. All rights reserved. Keywords: Explosion; Burning velocity; Hydrogen 1. Introduction The present paper describes the determination of the laminar burning velocity of hydrogen air mixtures from closed vessel gas explosions. Available methods to determine the laminar burning velocity rely on measurements of the flow structure of stabilized flames, the observation of moving flames in the course of confined deflagrations in an optically accessible explosion vessel, or the measurement of pressure variations caused by confined deflagrations in a windowless explosion chamber. The last method, which is the one adopted in the present work and called the traditional approach (Tse, Zhu, & Law, 2000), allows experimentation at initial conditions of very high pressure and temperature. It was demonstrated by various * Tel.: C ; fax: C address: ae.dahoe@ulster.ac.uk /$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi: /j.jlp authors that laminar burning velocities of air mixed with hydrogen (Iijima & Takeno, 1986; Milton & Keck, 1984), methane (Agnew & Graiff, 1961; Iijima & Takeno, 1986), propane (Agnew & Graiff, 1961; Babkin, Bukharov, & Molkov, 1989; Metghalchi & Keck, 1980), n-butane (Clarke, Stone, & Beckwith, 2001), iso-butane (Clarke et al., 2001), 2-methyl-pentane (Halstead, Pyle, & Quinn, 1974), n-heptane (Babkin, Vyun, & Kozachenko, 1967), iso-octane (Babkin et al., 1967; Metghalchi & Keck, 1982), ethylene (Agnew & Graiff, 1961; Halstead et al., 1974), acetylene (Agnew & Graiff, 1961; Rallis, Garforth, & Steinz, 1965), benzene (Babkin et al., 1967), toluene (Agnew & Graiff, 1961; Halstead et al., 1974), indolene (Metghalchi & Keck, 1982), methanol (Metghalchi & Keck, 1982), and acetone (Molkov & Nekrasov, 1981), could be determined by this method. In some cases, the initial conditions were varied up to 50 bar and 700 K. Because of the growing interest in the use of hydrogen as an energy carrier, it seemed worthwhile to investigate whether the same approach could also be applied to hydrogen air mixtures. A particular concern was that

46 A.E. Dahoe / Journal of Loss Prevention in the Process Industries 18 (2005) Nomenclature Latin symbols K G gas explosion severity index bar (m s K1 ) m u mass of unburnt mixture (kg) n unit normal (m) n 0 moles of gas present before explosion (mol) n e moles of gas present after explosion (mol) P macroscopic pressure (Pa) P 0 initial pressure (Pa), reference pressure (Pa) P max maximum explosion pressure (Pa) r f flame radius (m) R specific gas constant (J kg K1 K K1 ) S ul laminar burning velocity (m s K1 ) S o ul laminar burning velocity at reference conditions (m s K1 ) S ul unstretched laminar burning velocity (m s K1 ) t time (s) T temperature (K) T 0 reference temperature (K) temperature of the unburnt mixture (K) T u T u0 initial temperature of the unburnt mixture (K) v velocity vector (m s K1 ) V v volume explosion vessel (m 3 ) Greek symbols g specific heat ratio ( ) ni 0 stoichiometric coefficient of the ith species on the reactant side ( ) ni 00 stoichiometric coefficient of the ith species on the product side ( ) r density (kg m K3 ) r b density of the burnt mixture (kg m K3 ) r u density of the unburnt mixture (kg m K3 ) f equivalence ratio ( ) Other symbols (dp/dt) max maximum rate of pressure rise (Pa s K1 ) L c curvature Markstein length (m) L s stretch Markstein length (m) R radius of curvature (m) the tendency of laminar hydrogen air flames to develop into wrinkled structures (Aung, Hassan, & Faeth, 1997; Aung, Hassan, & Faeth, 1998; Tse et al., 2000) might render this methodology useless for the experimental determination of the laminar burning velocity. This concern stems from the fact that the use of windowless explosion vessels appears to be unacceptable to some researchers (Tse et al., 2000) because influences of stretch intensity and flame shape, which are inherently coupled to the development of flames into wrinkled structures, are not taken into account. Measurements of the laminar burning velocity that do not take contemporary insights in stretch and curvature effects into account are even considered to be flawed by other researchers (Dowdy, Smith, Taylor, & Williams, 1990). Wu and Law (1984) were the first who measured stretchfree laminar burning velocities by introducing a methodology to subtract stretch effects out from experimental laminar burning velocities of flames in stagnation flows. This work inspired the subsequent use of counter-flow flames for the determination of stretch-free laminar burning velocities (Law, Zhu, & Yu, 1988; Yu, Law, & Wu, 1986; Zhu, Egolfopoulos, Cho, & Law, 1989; Zhu, Egolfopoulos, & Law, 1989) and attempts to compensate stretch effects on spherically propagating flames in optically accessible explosion vessels (Aung et al., 1997, 1998; Brown, McLean, Smith, & Taylor, 1996; Dowdy et al., 1990; Hassan, Aung, & Faeth, 1997; Hassan, Aung, & Faeth, 1998; Kwon, Tseng, & Faeth, 1992; Tse et al., 2000; Tseng, Ismail, & Faeth, 1993). However, when stretched and unstretched laminar burning velocities are plotted together (see the upper part of Fig. 5), it is seen that laminar burning velocities of fuel-rich mixtures obtained from a windowless vessel (e.g. the data of Iijima & Takeno, 1986) fall within the scatter of the data obtained by more advanced methods that take stretch effects into account. It is also seen that laminar burning velocities of fuel-lean mixtures obtained from a windowless vessel are consistently larger than stretch-free data. With this being the case, laminar burning velocities from windowless explosion vessels are to be considered valuable for the assessment of accidental combustion hazards, even when they are unacceptable or flawed in the light of more advanced methods. Conversely, if the laminar burning velocities of fuel-lean mixtures had been consistently lower that the stretch-free values, their use as a quick estimate for the assessment of accidental combustion hazards would have been unacceptable. With the foregoing in mind, it was decided to apply the methodology by Dahoe and de Goey (2003) and Dahoe, Zevenbergen, Lemkowitz, and Scarlett (1996) to the pressure time curves of hydrogen air explosions in a closed vessel. It was demonstrated earlier by Dahoe et al. (1996) that this methodology could be applied to turbulent dust explosions in closed vessels to find an estimate of the turbulent burning velocity of a dust air mixture. In a later contribution, Dahoe and de Goey (2003) demonstrated that it could also be applied to closed vessel gas explosions to find an estimate of the laminar burning velocity of methane air mixtures. Although it is shown further in this paper that the laminar burning velocities of hydrogen air mixtures obtained by this approach fall within the scatter of data produced by more advanced methods, it is emphasized that this method should only be applied when the application of more advanced ones becomes impractical.

47 154 A.E. Dahoe / Journal of Loss Prevention in the Process Industries 18 (2005) Fig. 1. The experimental setup. Upper-left part: a schematic overview in the equatorial plane. Lower-left part: a schematic overview in the meridian plane. Right part: a photograph of the explosion vessel. The shaded region in the upper-left and lower-left parts indicates the trajectory of the flame that corresponds with the pressure data shown in middle-left and lower-left part of Fig. 6. The latter are used to determine the laminar burning velocity. 2. Explosion behavior of hydrogen air mixtures in a 169 ml vessel A cylindrical explosion vessel with a diameter of 70 mm and a length of 44 mm, and hence, a volume of 169 ml, was used in the present work. The reason for choosing such a small volume was to achieve a significant amount of pressure buildup before buoyancy effects would manifest themselves, as discussed by Dahoe and de Goey (2003). A photograph of the explosion vessel is shown in the right part of Fig. 1. Its dimensions on an equatorial and a meridian intersecting plane are given in the left part of the same figure. The vessel is constructed from stainless steel, with quartz windows mounted on its end caps. The cylinder mantle houses a piezo-electric pressure sensor, an inlet port to admit gases, and an outlet port to dispose combustion products. Tungsten electrodes with a diameter of 1 mm, entering through the cylinder mantle, were used to enable spark ignition within a gap of 2 mm at the center of the vessel. The sparks used in the present work had a duration of less than 25 ms and an energy of about 100 mj. To prevent spark discharges from the electrodes to the vessel wall, the electrical insulation of a diameter of 17 mm, was extended into the interior of the vessel over a length of 12 mm, thereby reducing the effective volume to 165 ml. A series of experiments was conducted with initially quiescent hydrogen air mixtures at an initial pressure of 1 bar and an initial temperature of K. Hydrogen air mixtures of an equivalence ratio of 0.5, 0.75, 1.0, 1.25, 1.5, 2.0, and 3.0 were ignited to deflagration at the center of the vessel, and the behavior of the pressure was measured at a sample-rate of 64 khz. The pressure time curves are shown in Fig. 2. Each curve exhibits a similar behavior: after ignition, the pressure in the explosion vessel increases progressively until the rate of pressure rise achieves a maximum, (dp/dt) max, and continues to increase with a progressively decreasing rate of pressure rise towards a maximum, P max. Once P max is reached, the pressure in the vessel begins to decrease. In this respect, the behavior of these pressure time curves is similar to that of methane air mixtures in a 20-l explosion sphere (see Fig. 6 of pressure (bar) pressure (bar) 8 1bar bar time (ms) Fig. 2. Measured explosion pressure curves of stoichiometric and fuel-lean hydrogen air mixtures (top), and fuel-rich hydrogen air mixtures (bottom).

48 A.E. Dahoe / Journal of Loss Prevention in the Process Industries 18 (2005) Dahoe & de Goey, 2003). Despite this similarity the inflection point occurs for a different reason in the 169 ml vessel used in the present work. As discussed previously by Dahoe and de Goey (2003), the duration of an explosion in a 20-l sphere is long enough to allow the flame ball to rise in the vessel due to buoyancy. As a result, there is still a layer of unburnt mixture present below the lower hemispherical part of the flame, after all reactants ahead of the upper hemispherical part of the flame have been consumed. Because the surface area of the lower hemispherical part of the flame decreases progressively during the consumption of the remaining part of the reactants in the final stage of the explosion, the accompanying rate of pressure rise also decreases progressively. Although the role of buoyancy is negligible in the 169 ml vessel, there is still the effect of a progressively decreasing flame surface area in the final stage of the explosion. Initially, the flame ball grows with a progressively increasing flame surface area, until it reaches the wall of the vessel. From that moment onwards, the flame surface area, and hence the rate of pressure rise, decreases progressively as the reactants in the corners of the vessel are being consumed. It may also be observed from Fig. 2 that, unlike with methane air mixtures, the pressure time curves of hydrogen air mixtures exhibit oscillations whose magnitude may vary up to about 0.25 bar. These oscillations arise with both fuel-lean and fuel-rich mixtures, and tend to become zero when the mixture strength approaches the flammability limits. Their onset occurs before the maximum explosion pressure is reached, after an initial period of smooth pressure buildup, and their presence continues after the explosion has completed. The cause of this phenomenon is described by Garforth and Rallis (1976) and Lewis and von Elbe (1961), Chapter 15, and will be discussed in Section 3. To enable a comparison with results presented by other researchers, the maximum explosion pressure, P max, and the maximum rate of pressure rise, (dp/dt) max,weredeterminedas illustrated by the upper part of Fig. 3. Since the experimental Fig. 3. An illustration of the determination of the maximum explosion pressure, P max, and the maximum rate of pressure rise, (dp/dt), from the measured explosion curve (top), theoretical values of the maximum explosion pressure (middle), and the behavior of the maximum explosion pressure and the maximum rate of pressure rise as a function of the equivalence ratio (bottom).

49 156 A.E. Dahoe / Journal of Loss Prevention in the Process Industries 18 (2005) pressure time curve contained pressure oscillations, the mean underlying curve and its derivative had to be determined by a smoothing filter. This was accomplished by means of the Savitzky Golay method (Savitzky & Golay, 1964), using the algorithm savgol by Press, Teukolsky, Vetterling, and Flannery (1992) with a second degree polynomial and a data window involving 21 points, namely, 10 on the left, and 10 on the right of the point where the mean value and its first derivative are to be evaluated. The dark curve in the upper-left part of Fig. 3 denotes the filtered pressure time curve, and the filtered derivative is denoted by the dark curve in the upperright part. The upper-right part of Fig. 3 also shows the behavior of the time-derivative as obtained from central differencing. It is seen that the points are so heavily scattered around the mean underlying value that the determination of (dp/dt) max becomes meaningless without the application of a smoothing filter. The lower part of Fig. 3 shows a comparison between the values of P max and (dp/dt) max obtained with the 169 ml vessel, and those measured in a 120 l vessel by Cashdollar, Zlochower, Green, Thomas, and Hertzberg (2000). Theoretical 1 estimates of P max, whose numerical values are tabulated in the middle of the figure, are also plotted in the lower-left part of Fig. 3. A comparison between the maximum explosion pressures shows that practically no difference exists between the values measured by Cashdollar et al. (2000) and the theoretical values. At the same time it may be observed that the maximum explosion pressure in the 169 ml vessel may be up to 10% lower than the theoretical values. This discrepancy may be attributed, to the larger surface to volume ratio, and the consequential larger heat losses in the final stage of the explosion. The lower-right part of Fig. 3 indicates that the maximum rate of pressure rise increases by a factor of about 1.4 when the effective volume of the explosion vessel increases by a factor of about 700. The scales on the left axis of the figure indicate that no formal cube-root-law 2 agreement exists between the maximum rates of pressure rise in the two vessels. The existence of a cube-root-law agreement between the maximum rates of pressure rise in both vessels would cause the scales on the left axis to be identical. 1 These calculations were performed with GASEQ for the reaction given in footnote 3. GASEQ is a program for computation of chemical equilibria for perfect gasses, written by Chris Morley. 2 The K G -value, also known as the gas explosion severity index, is a quantity which forms the design basis of a great deal of practical safety measures. It is defined as the product of the maximum rate of pressure rise and the cube-root of the volume of the explosion vessel, K G Z (dp/dt) max V 1/3, and believed to be a mixture specific explosion severity index. The K G -value was defined in this way because it was believed that maximum rates of pressure rise measured in differently sized vessels would become volume-invariant when multiplied by the cube-root of the volume. The practical significance of this quantity rests on the assumption that once it is known for a particular mixture from an experiment in a small laboratory test vessel, the maximum rate of pressure rise in a larger industrial vessel is predicted correctly by dividing it by the cube-root of the larger volume. 3. Oscillations in the pressure time curve of hydrogen air deflagrations Prior to addressing the mechanism behind the pressure oscillations, it is helpful to consider the behavior of the gas contained within a small volume, located around the center of the vessel. At the moment of ignition, the gas contained within this volume burns at constant pressure, which is equal to the initial pressure. After an initial period of expansion, the gas is subsequently compressed to nearly the initial volume it occupied before ignition occurred. The size of a fluid pocket, as well as the temperature of the burnt gases contained within it during the successive stages of expansion and compression may be estimated by means of the adiabatic compression laws: r Z P Kð1=gÞ ; r 0 P 0 r Z T Kð1=gK1Þ ; and (1) r 0 T 0 T Z P ðgk1þ=g : T 0 P 0 For a stoichiometric hydrogen air mixture for example, knowing 3 that the constant pressure and constant volume adiabatic flame temperature are 2386 and 2766 K, and that the maximum explosion pressure after constant volume combustion equals bar, the third expression in (1) reveals that the temperature of a fluid pocket at the center rises from 2386 to 4324 K in the course of the explosion. This is more than 1500 K above the constant volume adiabatic flame temperature. At the same time, a fluid pocket of a radius of 1 mm, located at the center of the vessel and containing reactants only, initially expands to spherical region of a radius of 5.7 mm containing only combustion products, and is subsequently compressed to a radius of 1.3 mm. Thus, a fluid particle residing at the boundary of the spherical region undergoes an oscillatory motion: first it moves 4.7 mm away from the center of the vessel, and then it travels 4.4 mm back towards the center. 3 These flame temperatures and maximum explosion pressure were calculated with GASEQ. The initial temperature was K and the chemical reaction n 0 H 2 H 2 Cn 0 O 2 O 2 Cn 0 N 2 N 2 /n 00 H 2 OH 2 O Cn 00 O 2 O 2 Cn 00 N 2 N 2 Cn 00 H 2 H 2 Cn 00 HO,HO, Cn 00 H,H, Cn 00 O,O, ; with n 0 H 2 Z0:42, n 0 O 2 Z0:21, and n 0 N 2 Z0:79 for the reactants. The stoichiometric coefficients of the product mixture after combustion at constant pressure were calculated to be n 00 H 2 OZ0:39668, n 00 O 2 Z0:00679, n 00 N 2 Z0:79, n 00 H 2 Z0:01772, n 00 HO,Z0:009, n 00 H,Z0:00218, n 00 O,Z7:227!10 K4, and after constant volume combustion, n 00 H 2 OZ 0:3806, n 00 O 2 Z0:00997, n 00 N 2 Z0:79, n 00 H 2 Z0:02824, n 00 HO,Z0:01764, n 00 H,Z0:0047, n 00 O,Z0: The total number of moles before and after the reaction, n 0 and n e, is not being conserved: the ratio n e /n 0 is

50 A.E. Dahoe / Journal of Loss Prevention in the Process Industries 18 (2005) Similarly, a fluid pocket of a radius of 3 mm, containing only reactants, expands to a spherical region of a radius of 17.1 mm consisting of combustion products only, and is subsequently compressed to a radius of 3.9 mm. Moreover, according to the third expression in (1), a temperature gradient that establishes itself within the burnt mixture, such that the temperature is the highest at the point where ignition occurred, and the lowest at the flame surface. The role of this oscillatory motion as the cause of the pressure oscillations may be assessed by considering what happens to a fluid particle residing between the boundary that separates the burnt mixture from the unburnt mixture, r b (t), and the vessel wall, R v (see the upper-left part of Fig. 4). Initially, the fluid particle is being pushed away from the center by the expansion flow. This process continues until it has been consumed by the flame. Next, the fluid particle continues to move away from the center while being part of the expansion flow until its motion is reversed by the expansion of combusting layers closer to the vessel wall. To facilitate the derivation of an expression for its velocity, the shape of the vessel is idealized to a sphere (with an effective volume of 165 ml, its radius, R v, becomes 34 mm) and the boundary separating the burnt and unburnt mixture, r b (t), is viewed upon as if it is an impermeable wall that expands like soap bubble from the center towards the wall with a velocity _r b ðtþ. When the location of a fluid particle residing on an arbitrary spherical surface between r b (t) and the vessel wall is denoted by r(t) (see the upper-left part of Fig. 4), it becomes evident that the ratio of the mass contained between r b (t) and r(t), and the mass contained between r b (t) and the vessel wall Fig. 4. Effect of compression on the position and velocity of fluid elements. The upper-left part illustrates the compression of the unburnt mixture ahead of an expanding flame. The upper-right part illustrates the compression of the burnt mixture caused by the expansion of combusting layers close to the wall. The middle part shows the behavior of five fluid particles in the unburnt mixture at initial positions, r 1 (0)Z3 mm, r 2 (0)Z6 mm, r 3 (0)Z10 mm, r 4 (0)Z15 mm, and r 5 (0)Z20 mm from the center. The lower part shows the behavior of the velocity of fluid particles within the burnt mixture when they are being compressed by an expanding layer close to the wall.

51 158 A.E. Dahoe / Journal of Loss Prevention in the Process Industries 18 (2005) remains constant: 4 3 pr u½r 3 ðtþ KrbðtÞŠ pr u½r 3 v Krb 3 Z constant: (2) ðtþš When this expression is differentiated with respect to time ½R 3 v Kr 3 bðtþš½r 3 ðtþkr 3 bðtþš 0 K½r 3 ðtþkr 3 bðtþš½r 3 v Kr 3 bðtþš 0 ½R 3 v Kr 3 b ðtþš2 Z0; only the nominator needs to be evaluated ½R 3 v KrbðtÞŠ½3r 3 2 ðtþ_rðtþk3r bðtþ_r 2 b ðtþš C½r 3 ðtþkrbðtþš½3r 3 bðtþ_r 2 b ðtþš Z0 5R 3 vr 2 ðtþ_rðtþkr 3 vrbðtþ_r 2 b ðtþkrbðtþr 3 2 ðtþ_rðtþ Cr 3 ðtþrbðtþ_r 2 b ðtþ Z0 5r 2 ðtþ½r 3 v Kr 3 bðtþš_rðtþ Zr 2 bðtþ½r 3 v Kr 3 ðtþš_r b ðtþ; (6) to obtain the following expression for the velocity of the fluid particle, _rðtþ: _rðtþ Z r2 bðtþ R 3 v Kr 3 ðtþ r 2 ðtþ R 3 v Krb 3ðtÞ _r bðtþ: (7) Since r b (t)%r(t)%r v, it is evident that the velocity of the fluid particle, r(t), cannot exceed _r b ðtþ. It is furthermore seen that the fluid particle attains a maximum speed, equal to _r b ðtþ (i.e. the flame speed minus the burning velocity), at the moment when it is being consumed by the flame. Its subsequent motion as a constituent of the burnt mixture is continued with a velocity smaller than _r b ðtþ. The behavior of r(t) and _rðtþ of five fluid particles, initially at a distance of r 1 (0)Z3 mm, r 2 (0)Z6 mm, r 3 (0)Z 10 mm, r 4 (0)Z15 mm, and r 5 (0)Z20 mm from the center, along with the behavior of r b (t) and _r b ðtþ, are shown in the middle-part of Fig. 4. The position and velocity of each particle were computed from Eq. (7) and rðt nc1 Þ Z rðt n Þ C _rðt n ÞDt; (8) where r(t nc1 ) denotes the position at a next time, r(t n ) the position at a previous time, and Dt the time increment between two consecutive times. The values of r b and _r b,as needed by Eq. (7) were obtained from the filtered pressure time curve and filtered (dp/dt)-curve shown in Fig. 3 by means of r b Z 3V 1=3 v 1 K P 1=g 1=3 0 P max KP ; (9) 4p P P max KP 0 which is identical to Eq. (18) for the position of the flame, and its derivative with respect to time _r b Z d_r b dt Z v_r b dp (10) vp dt (3) ð4þ ð5þ 1 3V 1=3 _r b Z v 1K P 1=g Kð2=3Þ 0 P max KP 3ðP max KP 0 Þ 4p P P max KP 0! 1C 1 1=g P0 dp gp P dt : ð11þ The time increment in Eq. (8) was equal to the reciprocal value of the sample-rate (64 khz) used to measure the experimental pressure curve. If these fluid particles would suddenly lose their motion to become static, the result would be a pressure disturbance of a magnitude of at most ð1=2þr u _r 2 bðtþ. However, with an assumed value of 1 kg m K3 for r u, and the velocities shown in the right-middle part of Fig. 4 the resulting pressure oscillations are negligible. This situation becomes different when particle velocities are induced by the combustion of fluid layers closer to the wall. Combusting fluid layers closer to wall induce a displacement velocity in the burnt mixture, directed towards the center. This reversal of the particle velocity within the burnt mixture is caused by the fact that the gas adjacent to the wall expands by a factor of nearly six into the direction of the center. The magnitude of this velocity may be estimated from the observation that, when the flame surface is idealized to an impermeable wall that compresses the burnt mixture with a certain velocity, the ratio of the mass contained between the flame front and the surface where a fluid particle resides, and the mass contained between the latter and the vessel wall (see the upper-right part of Fig. 4) remains constant: 4 3 pr b½rbðtþ 3 Kr 3 ðtþš 4 3 pr u½r 3 v Krb 3ðtÞŠ C 4 3 pr b½rb 3ðtÞ Z constant: (12) Kr3 ðtþš Differentiation with respect to time, and repeating the steps shown by Eqs. (3) (6) ½ðr u =r b Þ½R 3 v KrbðtÞŠ 3 C½rbðtÞ 3 Kr 3 ðtþšš½rbðtþ 3 Kr 3 ðtþš 0 K½rbðtÞ 3 Kr 3 ðtþš½ðr u =r b Þ½R 3 v KrbðtÞŠ 3 C½rbðtÞ 3 Kr 3 ðtþšš 0 Z 0 5½ðr u =r b Þ½R 3 v KrbðtÞŠ 3 C½rbðtÞ 3 Kr 3 ðtþšš½3rbðtþ_r 2 b ðtþ K3r 2 ðtþ_rðtþš K½rbðtÞ 3 Kr 3 ðtþš½k3ðr u =r b ÞrbðtÞ_r 2 b ðtþ C3rbðtÞ_r 2 b ðtþ K3r 2 ðtþ_rðtþš Z 0 5R 3 vr 2 ðtþ_rðtþ KR 3 vr 2 bðtþ_r b ðtþ Kr 3 bðtþr 2 ðtþ_rðtþ ð13þ ð14þ Cr 3 ðtþr 2 bðtþ_r b ðtþ Z 0 (15) 5r 2 ðtþ½r 3 v Kr 3 bðtþš_rðtþ Z r 2 bðtþ½r 3 v Kr 3 ðtþš_r b ðtþ; (16) again leads to Eq. (7). According to this result, the displacement velocity of a fluid particle increases progressively as the distance from the center becomes less, and would become infinitely large for a fluid particle residing at the center. The solution of Eq. (7) for the situation depicted by the upper-right part of Fig. 4, with r b (t)z33.0 mm

52 A.E. Dahoe / Journal of Loss Prevention in the Process Industries 18 (2005) and _r b ðtþzk1:5 ms K1 is shown in the lower part of Fig. 4. At a distance of 3 mm from the center, for example, the particle velocity is seen to increase to about 2000 m s K1. With an assumed value of 0.1 kg m K3 for r b, the expression for the dynamic pressure, ð1=2þr b r 2 ðtþ this velocity implies that pressure disturbances of about 2.0 bar are generated when the fluid particles lose their motion instantaneously. The reason for the smaller oscillations in the upper-left part of Fig. 3 must be sought in the fact that upon arrival at the sensor, the pressure waves are partly being absorbed and partly being reflected. It is the reflected part, which determines the magnitude of the experimentally observed pressure disturbances. Knowing that pressure disturbances scale quadratically with _r b ðtþ, their absence at fz0.5 in Fig. 2 may also be explained by Eq. (7). With the laminar burning velocity, and hence the flame speed, being three times smaller than in the case of stoichiometric mixtures, the pressure disturbances become nine times smaller, i.e. about bar. This is close to the detection limit of the pressure sensor (0.2% of 10 bar). 4. Adapting the thin-flame model to the geometry of the 169 ml explosion vessel A thin-flame model will now be derived for the explosion vessel shown in Fig. 1. This derivation is analogous to the one derived by Dahoe et al. (1996) and the resulting model is only valid while the radius of the flame is less than 20 mm (i.e. before the shape of the flame becomes distorted by interaction with the windows at a distance of 22 mm, or with the electrical insulation at a distance of 23 mm from the center). Following the derivation by Dahoe et al. (1996), the expression relating the rate of pressure rise to the mass burning rate (obtained from Eqs. (6) and (7) of Dahoe et al., 1996) dp dt Z ðp 4p P 1=g max KP 0 Þ rf 2 S V v P ul (17) 0 is combined with the expression that relates the flame radius to the instantaneous pressure (obtained from Eqs. (8) and (9) of Dahoe et al., 1996) r f Z 3V 1=3 v 1 K P 1=g 1=3 0 P max KP (18) 4p P P max KP 0 to give: dp dt Z 3ðP 4p 1=3 max KP 0 Þ 1 K P 1=g 2=3 0 P max KP 3V v P P max KP 0! P 1=g S P ul: ð19þ 0 This expression, together with a correlation to incorporate the effect of changes in the pressure and temperature on the laminar burning velocity, as discussed in Section 5, will be fitted to the initial part of the experimental pressure time curve. Note that Eqs. (17) (19) are independent of the shape of the vessel, as long as there is no interaction between the flame and the wall. Moreover, as long as the radius of the flame does not exceed 20 mm, the problem may be idealized to a situation in which the flame propagates in a spherical vessel of the same volume. 5. The laminar burning velocity of hydrogen air mixtures The laminar burning velocity of hydrogen air mixtures is known to depend on the chemical composition, the pressure, and the temperature. This sensitivity is commonly described by a power law expression of the form S ul S o Z T b1 u P b2; (20) ul T u0 P 0 where S o ul denotes the laminar burning velocity at reference conditions of pressure and temperature, and S ul the laminar burning velocity at arbitrary conditions of pressure and temperature. The dependence of S o ul on the equivalence ratio is shown in the upper part of Fig. 5. It is seen to assume a maximum value at an equivalence ratio of 1.6 and to decrease as the flammability limits are approached. The middle and lower part of Fig. 5 indicate that the laminar burning velocity of hydrogen air mixtures increases with pressure and temperature. The linear dependence in the right part of these sub-figures implies that this behavior may be described by Eq. (20) and that the influence of temperature and pressure may be incorporated by the exponents b 1 and b 2. The latter are known to be a weak function of the equivalence ratio. Iijima and Takeno (1986) observed that b 1 Z1:54C 0:026ðfK1Þ and b 2 Z0:43C0:003ðfK1Þ. These authors determined the value of b 1 and b 2 as a function of the equivalence ratio by assuming that S ul S o Z T b1 u 1 Cb ul T 2 ln P u0 P 0 : (21) Note that because this expression follows from Eq. (20) by the series expansion a b 2 Z 1 C b 2 ln a C ðb 2 ln aþ 2 C ðb 2 ln aþ 3 C/ 1! 2! 3! C ðb 2 ln aþ n ; (22) n! b 2 in Eq. (20) will also exhibit a similar weak dependence. With this in mind, b 1 and b 2 were taken to be constant and equal to (140.0G3.7)!10 K2 and (194.0G4.4)!10 K3 in the present work. These values were determined from the experimental results reported by Iijima and Takeno (1986) on the influence of pressure and temperature on the laminar

53 160 A.E. Dahoe / Journal of Loss Prevention in the Process Industries 18 (2005) Fig. 5. Effect of equivalence ratio (upper part), pressure (middle-left part), and temperature (lower-left) on the laminar burning velocity of hydrogen air mixtures (!: Takahashi, Mizomoto, & Ikai, 1983;,: Dowdy et al., 1990; %: Koroll, Kumar, & Bowles, 1993; $: Vagelopoulos, Egolfopoulos, & Law, 1995; : Iijima & Takeno, 1986;?: Wu & Law, 1984; 6: Egolfopoulos & Law, 1990; B: Lamoureux, Djebaili-Chaumeix, & Paillard, 2002, stretched; :: Lamoureux et al., 2002, unstretched; ;: Kwon & Faeth, 2001; 0: Law, Aung et al., 1997; 4: Tse et al., 2000; solid line: Marinov et al., 1996). burning velocity of hydrogen air mixtures (see the middle and lower part of Fig. 5). Because of adiabatic compression of the unburnt mixture, the pressure and the temperature in Eq. (20) do not behave independently, but change simultaneously. This simultaneous change in pressure and temperature is taken into account by substituting the third expression of Eq. (1) into Eq. (20) so that S ul S o Z P b2 Cb 1 ððgk1þ=gþ Z P b : (23) ul P 0 P 0 With b 1 Z1.4, b 2 Z0.194, and gz1.4, it is seen that bz0.6. Eq. (23) was incorporated into Eq. (19) and the laminar burning velocity was determined by fitting the latter by means of the Levenberg Marquardt method (Marquardt, 1963; Press et al., 1992) to the initial part of the pressure time curves shown in Fig. 2 with S o ul as the only degree of freedom. This was accomplished by modifying the routine mrqmin by Press et al., such, that it enabled the fitting of a differential equation by its numerical solution to a set of discrete data points. The numerical solution of Eq. (19) was calculated by means of a fourth order Runge Kutta method, using the routine rkdumb by the same authors. Owing to the lower experimental maximum explosion pressures due to the size of the vessel, as discussed in Section 2,

54 A.E. Dahoe / Journal of Loss Prevention in the Process Industries 18 (2005) and the uncertainty introduced by the oscillations in the experimental pressure time curve, the theoretical values shown in the middle of Fig. 2 have been used for P max in Eq. (19). To minimize modification of the laminar burning velocity by flame curvature and flame acceleration due to excessive spark ignition energies in the initial stage of the explosions, and to avoid flame wall interaction, Eq. (19) was fitted to the early part of the pressure time curves where the pressure changed from 1.15 to 1.3 bar. It may be verified by means of Eq. (18) that with all equivalence ratios, the flame radius varies between 15 and 20 mm when the pressure changes between 1.15 and 1.3 bar. This is indicated by the shaded region in the left part of Fig. 1. The correspondence between the solution of Eq. (19) and the experimental data is illustrated by the middle-left and lower-left part of Fig. 6. The upper part of Fig. 6 shows a comparison between the optimal values of the laminar burning velocity, S o ul, obtained by fitting Eq. (19), and values reported by other researchers. The shaded region in the upper-left part denotes the band of data shown in Fig. 5. It is seen that the laminar burning velocities obtained in this work fall within the band of data reported by other researchers. The upper-right part shows a comparison with laminar burning velocities computed by Marinov, Westbrook, and Pitz (1996) by means of a detailed kinetic scheme, and experimental data that was obtained by more advanced methods (Dowdy et al., 1990; Kwon & Faeth, 2001; Tse et al., 2000). This comparison indicates that laminar burning velocities at equivalence ratios greater than 0.75, obtained by fitting an integral balance model to the pressure curve fall within the scatter of those produced by more advanced methods. Therefore, more advanced methods that take stretch effects into account have little or no advantage over the traditional method. This conclusion is in agreement with an earlier observation involving the data by Iijima and Takeno (1986), Fig. 6. Upper part: a comparison between laminar burning velocities obtained by fitting the thin-flame model to experimental pressure time curves and values reported by other researchers (shaded region: data band shown in the upper part of Fig. 5; solid line: computed data by Marinov et al., 1996;,: Dowdy et al., 1990; ;: Kwon & Faeth, 2001; 4: Tse et al., 2000; : this work). Middle-left and lower-left part: comparison between the model curves and measured data.

55 162 A.E. Dahoe / Journal of Loss Prevention in the Process Industries 18 (2005) as discussed in Section 1. The laminar burning velocity at an equivalence ratio of 0.5 is larger than the stretch-corrected ones, but still close enough to the latter to be suitable as a conservative input for the assessment of accidental combustion hazards. The absence of a significant advantage by more advanced methods that take flame stretch into account over the traditional method employed in the present work with fuelrich mixtures, and the consistently higher laminar burning velocities produced by the latter with fuel-lean mixtures, deserve some further clarification. It has been observed experimentally that flames develop into wrinkled structures when the limiting reactant in a combustible mixture is also the more mobile constituent. This phenomenon is known to begin with flame cracking, followed by a further development into a cellular structure (Bradley, 1999; Bradley, Cresswell, & Puttock, 2001; Bradley & Harper, 1994; Bradley, Hicks, Lawes, Sheppard, & Woolley, 1998; Bradley, Sheppard, Woolley, Greenhalgh, & Lockett, 2000; Groff, 1982; Gu, Haq, Lawes, & Woolley, 2000; Haq, Sheppard, Woolley, Greenhalgh, & Lockett, 2002). The role of the limiting reactant in cell formation is clearly demonstrated by the work of Tse et al. (2000). These authors presented Schlieren photographs of spark ignited spherically propagating flames in H 2 /O 2 /N 2 - and H 2 /O 2 /Hemixtures, at initial conditions of 298 K and 3, 5, 20, 40, and 60 atm. Some of these photographs are included in the upper part of Fig. 7 to support the present discussion. Pictures of H 2 /O 2 /N 2 -flames at equivalence ratios of 0.70 and 2.25 (ignited at 3 and 5 atm), 0.85 and 1.50 (ignited at 20 atm), and 3.5 (ignited at 40 and 60 atm), and of H 2 /O 2 / He-flames, at equivalence ratios of 0.70 and 2.25 (ignited at 3 and 5 atm), 0.85 and 1.50 (ignited at 20 atm), and 0.70 (ignited at 40 and 60 atm), were presented. With H 2 /O 2 / N 2 -flames, it may be observed that, when the equivalence ratio is less than unity, and hence the more mobile constituent becomes the limiting reactant, the flame surface is initially distorted by large-scale wrinkles that originate from system perturbations, and subsequently by wrinkles of an ever decreasing size, down to a magnitude in the order of the laminar flame thickness (see the lower-right part of Fig. 7). When the equivalence ratio is greater than unity, H 2 / O 2 /N 2 -flames appear to be free of wrinkles at low pressure (e.g. at 3 atm), and contain only large-scale wrinkles arising from system perturbations at higher pressures (e.g. 5, 20, 40, and 60 atm). No cascade of wrinkles from large to smallscale appears to be present during the growth of the flame. With H 2 /O 2 /He-flames (i.e. with N 2 being replaced by He, the limiting reactant can no longer be the more mobile one), this cascade of wrinkles turns out to be absent for all equivalence ratios and only large-scale wrinkles are seen to evolve at higher pressures (e.g. 20, 40, and 60 atm). The development of a flame surface into a wrinkled structure causes the true laminar burning velocity, S ul,to deviate from the unstretched laminar burning velocity, S * ul, i.e. the magnitude it would have if the flame were planar. This modification is caused by two distinct, but invariably coupled effects, namely, the effect of flame curvature (see the middle-right part of Fig. 7) and the effect of flame stretch (see the lower-left part of Fig. 7). When a flame is bulged into concavity with respect to the unburnt mixture, heat which is initially conducted into the unburnt mixture, is subsequently convected to parts of the flame closer to the center. This process enhances the laminar burning velocity at the center and reduces the laminar burning velocity at the lateral parts of the flame. When the flame is convex with respect to the unburnt mixture, the opposite happens: heat is conducted into the unburnt mixture and convected away from the center. This reduces the laminar burning velocity at the center and increases the laminar burning velocity of the lateral parts. The presence of a wrinkled flame causes the flow-field of the approaching unburnt mixture to become non-uniform. Because of the non-zero velocity gradients in the unburnt mixture, fluid elements approaching a wrinkled flame are no longer the same as those approaching a planar flame. As illustrated by lower-left part of Fig. 5, fluid elements, respectively, undergo compression or stretch, prior to being consumed by a concave or convex flame surface. The compression of fluid elements enhances the laminar burning velocity due to the increase in the mass flow of reactants entering the flame per unit area. The stretching of fluid elements reduces the mass flow of reactants into the flame, and hence the laminar burning velocity. To cope with this situation, various researchers have attempted to establish relationships between the true laminar burning velocity of a wrinkled flame and the unstretched laminar burning velocity. To support the present discussion, Eq. (13) by Dahoe, Hanjalic, and Scarlett (2002) is quoted here as an example: S ul Z L s ½nn : Vv KV$vŠ C½1 KL c V$nŠS ul * Z L s ½nn : Vv KV,vŠ C 1 C L c S ul * (24) R The reader may consult Dahoe et al. (2002) and references cited therein for further information on its origin and motivation. In this equation, nn: VvKV$v denotes the stretch intensity, R the local radius of curvature, L s the stretch Markstein length and L c the curvature Markstein length. The latter are proportionality constants between the laminar burning velocity and effects due to stretch and curvature. Eq. (24) may be used to compare the laminar burning velocities obtained by the traditional method, with those obtained by more advanced methods shown in the upperright part of Fig. 6. When fr1.0, the more mobile constituent of the mixture is no longer the limiting reactant, and the flame surface remains smooth. With stretch effects due to velocity gradients being small, and the radius of curvature (i.e. 15 mm%r%20 mm) being much larger than the curvature Markstein length (this is known to be in

56 A.E. Dahoe / Journal of Loss Prevention in the Process Industries 18 (2005) Fig. 7. Upper part: pictures by Tse et al. (2000) showing the development of small-scale wrinkles when the limiting reactant is also the more mobile constituent of a combustible mixture. Middle-left part: modification of the laminar burning velocity by the development of flame curvature. Middle-right part: the role of heat conduction and convective heat transfer in the modification of the laminar burning velocity of curved flames. Lower-left part: the role of flame stretch in the modification of the laminar burning velocity. Lower-right part: the cascading of large-scale wrinkles to small-scale wrinkles during flame growth. the order of the laminar flame thickness which is less than 0.5 mm for hydrogen air mixtures), it becomes obvious that the performance of the more advanced methods will not differ significantly from the method applied in the present work. This situation becomes different when f!1.0. As discussed previously, laminar flames develop into wrinkled flames when the limiting reactant is also the more mobile constituent. The photographs by Tse et al. (2000) in the upper part of Fig. 7 (the frame diagonal is 74 mm) show that an initially smooth hydrogen air flame at fz0.7 contains only large-scale wrinkles when its radius has grown to 8 mm at 4 ms, the cascade process to small-scale wrinkles is well underway at 5 ms when the radius is 11.5 mm, and that this cascade process has reached an equilibrium when the flame radius has become 17 mm at 6 ms. With this in mind, the agreement between the laminar burning velocity at fz0.75 obtained by the methodology applied in the present work and that from more advanced methods may be explained by

57 164 A.E. Dahoe / Journal of Loss Prevention in the Process Industries 18 (2005) arguing that the flame surface does not contain sufficient small-scale wrinkles when the flame radius is between 15 and 20 mm. It is emphasized, however, that photographs of the flame morphology at fz0.75 are needed to verify this argument. Following the same reasoning, the higher laminar burning velocity at fz0.5 is easily explained. Based on the observations by Tse et al. (2000), it is obvious that the flame surface at fz0.5 consists of small-scale wrinkles when the flame radius is between 15 and 20 mm. In this situation, the application of Eq. (19) boils down to evaluating the product of a wrinkled flame surface and the true laminar burning velocity as the product of a smooth spherical flame surface area coinciding with the global flame curvature (see the lower-right part of Fig. 7) and a surface averaged laminar burning velocity. While a surface averaged laminar burning velocity would make sense because crests in the flame surface are compensated by troughs, this idealization does not take the increase in flame surface area due to flame wrinkling into account. This deficiency leads to a higher laminar burning velocity. 6. Conclusions Laminar burning velocities of hydrogen air mixtures were determined from closed vessel gas explosions. Initially quiescent mixtures were ignited in a 169 ml vessel, the pressure was measured as a function of time, and an integral balance model (i.e. Eq. (19)) was fitted to the experimental pressure time curve to extract the laminar burning velocity. The equivalence ratio varied from 0.5 to 3.0, and all experiments were conducted at initial conditions of 1 bar and 293 K. Inaccuracies due to the flame curvature and flame acceleration caused by excessive spark ignition energies in the initial stage of the explosions, as well as those arising from flame wall interaction, were avoided by using only the part of the pressure time curves between 1.15 and 1.3 bar (see the middle-left and lower-left part of Fig. 6). A correlation for the effect of pressure and temperature on the laminar burning velocity (i.e. Eq. (20)) was incorporated into the integral balance model to avoid further inaccuracies caused by changes in the thermodynamic of the unburnt mixture in the course of the explosions. The resulting laminar burning velocities were subsequently compared with those reported in the literature. The conclusions arising from this comparison are as follows: Laminar burning velocities of fuel-rich mixtures obtained by the methodology followed in the present paper are seen to fall within the scatter of data obtained by more advanced methods that take the influence of flame stretch into account (see the upper-right part of Fig. 6. This observation implies that, with fuel-rich mixtures, more advanced methods have no significant advantage over methodologies that rely only on pressure variations from windowless explosion vessels for the determination of the laminar burning velocity. Moreover, with fuel-rich mixtures, the cost-benefit balance is in favor of the latter. Laminar burning velocities of fuel-lean mixtures are seen to be consistently higher, but at the same time close enough to the ones obtained by more advanced methods. Because of this, they may be considered as acceptable conservative estimates of the laminar burning velocity for engineering calculations that form the design basis for fire and explosion safety. The pressure time curves of hydrogen air mixtures are seen to exhibit pressure oscillations (see Fig. 2), which are absent when methane air mixtures for example (see Fig. 6 by Dahoe & de Goey, 2003), are ignited to deflagration at the same initial conditions. These oscillations were considered in Section 3, and an Eq. (7) was derived to describe their cause. The implications of this equation are that combusting fluid layers adjacent to the wall are inducing particle velocities in the order of kilometers per second which in turn give rise to pressure spikes. The magnitude of these particle velocities is directly proportional to the flame speed, quadratically proportional to r b (t) the vessel radius, and inversely proportional to the distance from the wall where flow reversal occurs R 3 nðtþkr 3 bðtþ. Of these three proportionalities, the last one is the subject of most concern. For combustible mixtures such as hydrogen air and hydrogen oxygen mixtures, this last proportionality may give rise to high-pressure spikes because of the small flame thickness. It is easy to see that the distance from the vessel wall where flow reversal occurs, and hence R 3 nðtþkr 3 bðtþ, decreases when the flame thickness becomes smaller. As a result, the handling of such mixtures involves an additional safety problem which is absent with hydrocarbon air mixtures. This may impose a limitation on the use of hydrogen as an energy carrier with at least the same level of safety and comfort as with today s fossil fuel energy carriers. Acknowledgements The experiments described in this paper were conducted by a group of undergraduate students at the Department of Mechanical Engineering of Eindhoven University of Technology, namely, Bram van Benthum, Jean-Pierre Thoolen, Harrie Smetsers and Joris Wismans. The contribution and the support of Philip de Goey to this work are gratefully acknowledged. References Agnew, J. T., & Graiff, L. B. (1961). The pressure dependence of laminar burning velocity by the spherical bomb method. Combustion and Flame, 5,

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60 Journal of Loss Prevention in the Process Industries 14 (2001) On the transient flow in the 20-liter explosion sphere A.E. Dahoe a, b,*, R.S. Cant b, M.J. Pegg c, B. Scarlett a a Department of Chemical Engineering, Delft University of Technology, Delft, The Netherlands b University of Cambridge, Department of Engineering, CFD-Lab, Trumpington Street, Cambridge CB2 1PZ, UK c Department of Chemical Engineering, Dalhousie University, Nova Scotia, Canada Abstract The turbulence level in the 20-l explosion sphere, equipped with the Perforated Dispersion Ring, was measured by means of laser Doppler anemometry. The spatial homogeneity of the turbulence was investigated by performing velocity measurements at various locations in the transient flow field. Directional isotropy was investigated by measuring two independent components of the instantaneous velocity. The transient turbulence level could be correlated by a decay law of the form v rms v o rms t n t 0, in which the exponent, n, assumes a constant value of 1.49±0.02 in the period between 60 and 200 ms after the start of the injection process. In this time interval the turbulence was also observed to be homogeneous and practically isotropic. The results of this investigation imply that the turbulence level in the 20-l explosion sphere at the prescribed ignition delay time of ms is not equal to the turbulence level in the 1 m 3 -vessel. Hence, these results call into question the widely held belief that the cube-root-law may be used to predict the severity of industrial dust explosions on the basis of dust explosion severities measured in laboratory test vessels Elsevier Science Ltd. All rights reserved. Keywords: Cube-root-law; Dust explosion; Laser Doppler anemometry; Turbulence decay 1. Introduction A great deal of practical safety in industrial plants handling combustible particles is based on two dust explosion severity parameters, namely, the maximum explosion pressure, P max, and the maximum rate of pressure rise, (dp/dt) max. Both quantities are known to be a function of the chemical composition, pressure, temperature and flow properties, and their practical relevance can be understood with the aid of Fig. 1. This figure shows the pressure development of a cornstarch air explosion in a 20-l explosion sphere. At the beginning of the explosion the pressure is equal to the atmospheric pressure (1 bar) and increases up to a maximum value of about 7 bar, which marks the end of the explosion process. During the explosion the pressure * Corresponding author. Address for correespondence: University of Cambridge, Department of Engineering, CFD-Lab, Trumpington Street, Cambridge CB2 1PZ, UK. Tel.: ; fax: address: aed23@eng.cam.ac.uk (A.E. Dahoe). increases progressively until the rate of pressure rise achieves a maximum, after which the pressure continues to increase with a progressively decreasing rate of pressure rise. The maximum explosion pressure and the maximum rate of pressure rise are determined as indicated in Fig. 1: the former is equal to the maximum value of the pressure curve and the latter is equal to the maximum slope. The practical significance of these quantities is also evident from this figure: the maximum explosion pressure gives an indication of the magnitude of the damaging pressures that may be generated and the maximum rate of pressure rise indicates how fast these pressures can develop. Currently, it is common practice to measure dust explosion severity parameters of a specific mixture in laboratory test vessels and to predict what would happen if the same mixture exploded in a plant unit. In case of the maximum explosion pressure, the application of laboratory test data to industrial plant units appears to be straightforward, provided that similar conditions of pressure, temperature and turbulence exist in the laboratory test vessels and the industrial equipment. The appli /01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S (01)

61 476 A.E. Dahoe et al. / Journal of Loss Prevention in the Process Industries 14 (2001) Fig. 1. Explosion curve of a 500 g m 3 cornstarch air mixture in the standard 20-l explosion sphere. cation of the maximum rate of pressure rise, however, involves the use of a scaling law which is known as the cube-root-law (NFPA 68, 1988; VDI 3673, 1995; Bartknecht, 1989), because this quantity is not volumeinvariant. Ideally, the cube-root-law, K St dp dt V 1 3 (1) transforms the maximum rate of pressure rise into a volume-invariant dust explosion severity index which is applied as follows. The maximum rate of pressure rise of a specific mixture, measured in a laboratory test vessel, is multiplied by the cube root of the volume of the test vessel to yield a volume-invariant K St -value. The maximum rate of pressure rise of the same mixture in an industrial plant unit is subsequently predicted by dividing the K St -value by its volume, and forms the design basis for explosion protection and mitigation. This approach is known as the VDI-methodology and rests entirely on the validity of the cube-root-law. Bartknecht (1989) presented experimental results which indicated that the cube-root-law could indeed be regarded as a valid scaling relationship between maximum rates of pressure rise measured in differently sized vessels. It was shown that K St -values measured in the 20-l sphere were equal to those measured in the 1 m 3 -vessel (see Fig. 2). In fact, this research was carried out because the 1 m 3 -vessel, which was the only internationally accepted dust explosion testing device (ISO 6184/1, 1985), required much labor and large amounts of powder. With dust concentrations being typically between 0.1 and 1.5 kg m 3, the cost of dust explosion severity testing involving expensive powders (e.g. pharmaceutical compounds) would be greatly reduced by the use of a smaller explosion vessel. Therefore, Siwek (1977) developed a 20-l explosion sphere which requires much less labor and functions with 50 times less powder, and was hailed as a significant advance in powder safety testing. Its acceptance as a standardized dust explosion testing device, however, would depend on whether or not it would give the same K St -values as the 1 m 3 -vessel. A particular problem which had to be overcome was that of the turbulence of the dust clouds which are ignited to deflagration in the test vessels. The origin of this problem stems from the fact that without some degree of fluid motion a dust cloud cannot exist because the particles have a tendency to settle out. With both test vessels an air blast is used to initially suspend the particles, and the turbulence which is generated by the air blast keeps the particles air-borne until ignition occurs. In order to clarify the difficulties posed by this problem it is necessary to consider the method by which the air blast is generated in some detail. In case of the 1 m 3 -vessel, two 5.4 l pressure canisters are mounted on the explosion chamber. These are filled with the dust particles and with compressed air of 20 bar, after which their content is discharged into the explosion chamber. Before the air blast, the pressure in the explosion chamber is made equal to 1 bar and it is only slightly affected by the discharge because the volume of the canisters is comparatively small. The air blast, during which considerable turbulence is generated and a dust cloud is formed in the explosion chamber, lasts 600 ms. Since the burning rate is increased by turbulence, and due to the transient nature of the turbulence level, a practical test procedure was adopted which required that ignition must occur as soon as the air blast is completed. The time between the beginning of the air blast and the moment of ignition is known the ignition delay time. It was assumed that the turbulence level in the 1 m 3 -vessel was the highest at an ignition delay time of 600 ms (after this time turbulence decay becomes larger than turbulence production) and that this significant, but unknown, turbulence level would never be exceeded by what might exist in industrial equipment. Dust explosion severity parameters, measured in the 1 m 3 -vessel, were therefore

62 A.E. Dahoe et al. / Journal of Loss Prevention in the Process Industries 14 (2001) Fig. 2. K St -values of various dusts measured in the 1 m 3 -vessel and the 20-l sphere as reported by Bartknecht (1989). believed to be a conservative estimate of what might happen when an accidental explosion occurs in industrial equipment. In case of the 20-l sphere, the dust particles and compressed air are discharged into the explosion chamber from a pressure canister with a volume 0.4 l. The explosion chamber is initially evacuated to a pressure of 0.4 bar and the pressure canister is filled with compressed air of 21 bar. The air blast lasts about 50 ms, after which the pressure in the explosion chamber becomes equal to 1 bar and turbulence starts to decay. As indicated by Fig. 2, Bartknecht (1989) and Siwek (1977) observed that the 20-l sphere produced K St -values that were in agreement those obtained with the 1 m 3 - vessel when the ignition delay time in the former was set equal to 60 ms. This observation did not only give rise to the belief that the turbulence properties in the 20- l sphere at an ignition delay time of 60 ms were equal to those in the 1 m 3 -vessel at an ignition delay time of 600 ms. It also inspired the widespread belief that a formal cube-root-law agreement could exist between turbulent dust explosions in small laboratory test vessels and large scale dust explosions in industrial equipment. In addition to that, technical guidelines adopted the notion that powder safety testing of all types of combustible dusts can be performed using the 20-l sphere by adhering to a single prescribed test procedure with a single, fixed ignition delay time of 60 ms, and that these results, in conjunction with the cube-root-law, can form the design basis of industrial safety. In spite of the experimental evidence presented by Bartknecht (1989) and Siwek (1977), based on a variety of powders, other researchers questioned the generality of the observation of a formal cube-root-law agreement between the 20-l sphere and the 1 m 3 -vessel. van der Wel, van Veen, Lemkowitz, Scarlett, and van Wingerden (1992), measured the K St -value of potato starch, lycopodium, and activated carbon with both test vessels (see Fig. 3), and found that the K St -value in the 20-l sphere at an ignition delay time of 60 ms was not in agreement with that in the 1 m 3 -vessel at an ignition delay time of 600 ms. Instead, they found that the K St -values in the 20-l sphere were in agreement at ignition delay times of 80, 100, and 165 ms. Apart from measuring K St -values in the 20-l sphere at various ignition delay times, and hence different conditions of turbulence, van der Wel et al. (1992) used hot-wire anemometry to measure turbulence frequency spectra in both vessels. Although these researchers did not measure the turbulence level in the 20-l sphere explicitly, their research indicated that conditions of similar turbulence existed in the two vessels when the ignition delay time in the 20-l sphere was equal to 165 ms, instead of the prescribed 60 ms. A similar observation was also made by Pu, Jarosinski, Johnson, & Kauffman (1990), who performed explicit turbulence measurements inside the 20-l sphere by means of hotwire anemometry. A comparison of their results with those obtained in a 1 m 3 -vessel (see Fig. 11) indicates that equal turbulence levels exist in both test vessels when the ignition delay time of the 20-l sphere is 200 ms. The work of van der Wel et al. (1992) and Pu et al. (1990) undermines the widespread belief that a formal cube-root-law agreement generally exists between the 20-l sphere and the 1 m 3 -vessel, and that dust clouds are ignited under similar conditions of turbulence when both vessels are operated according to prescribed test procedures. In fact, these observations undermine the entire notion that laboratory test results may be used to predict what would happen under industrial circumstances on the basis of the cube-root-law. Taking this into consideration, it is the purpose of the present paper to present experimental results on the transient turbulence levels in the 20-l explosion sphere.

63 478 A.E. Dahoe et al. / Journal of Loss Prevention in the Process Industries 14 (2001) Fig. 3. K St values of various dusts measured in the 1 m 3 -vessel and the 20-l sphere as reported by van der Wel et al. (1992). Although turbulence in the 20-l sphere was studied previously there are still a number of shortcomings. First of all, van der Wel et al. (1992) and Pu et al. (1990) used hot-wire anemometry to measure turbulence. While this technique enables one to quantify turbulence levels and to measure power density spectra, it is incapable of measuring independent velocity components simultaneously. As a result, it is not possible to investigate whether practically isotropic turbulence, or, a situation of highly non-isotropic turbulence exists in the 20-l sphere. In order to overcome this limitation a two dimensional laser Doppler anemometer was used in this work. Secondly, previous research was limited to measurements at the geometric center of the 20-l sphere and ignores the question of whether or not similar conditions of turbulence exist at other locations in the 20-l sphere. In the present work turbulence measurements are performed at various locations in the flow field. Thirdly, there appears to be a discrepancy between the results of van der Wel et al. (1992) and Pu et al. (1990). It was observed by van der Wel et al. (1992) that conditions of turbulence, similar to those in the 1 m 3 -vessel, exist in the 20-l sphere when the ignition delay time is equal to 165 ms. A comparison between the results of Pu et al. (1990) and the turbulence level in the 1 m 3 -vessel, however, shows that this ignition delay time should be equal to 200 ms. Since this discrepancy is significant in comparison with the prescribed ignition delay time of 60 ms, and knowing that turbulence decays rapidly after completion of the air blast, it would be interesting to measure turbulence levels in the 20-l sphere with a technique which is different from the one used by Pu et al. (1990) and van der Wel et al. (1992), and to compare these results with the turbulence level in the 1 m 3 -vessel. 2. The experimental setup and the measurement of turbulence in the 20-l sphere The experimental setup, shown in Fig. 4, essentially consists of two major parts: a 20-l plastic model sphere and a laser Doppler anemometer. Due to the limited optical access of the actual explosion chamber, a plastic replica containing optical quality glass windows was constructed. The plastic model sphere was mounted on the commercially available injection equipment (i.e. pressure canister, injection valve and tubing). Like the standard 20-l sphere, the model sphere houses a vacuum port to enable partial evacuation of the chamber prior to a test, a pressure transducer port to enable dynamic pressure measurements during the air blast, and two 178 mm diameter optical quality glass windows to permit the use of laser Doppler anemometry. The laser Doppler anemometer was supplied by TSI- Aerometrics and consists of a number of components: a laser, a fiber drive, a transceiver, a receiver, a photomultiplier box and two real-time signal analyzers. It is important to mention here that the equipment was capable of measuring vertical and horizontal velocity components between 250 and +250 m s 1, and that data rates of up to 25 khz were observed (i.e. time scales down to 0.02 ms could be resolved). The laser is a water cooled Spectra Physics stabilite s, argon-ion laser with an output power of 6 W and is equipped with a Spectra Physics 2550 power supply. The light beam produced by the laser is emitted into an Aerometrics FBD 240-R fiber drive. This unit splits the incoming beam into three separate beams of different wavelengths, 514.5, 4880 and nm, by means of a prism and a turning mirror. The LDA configuration in this work is two-dimensional and employs only the first two wavelengths. Each of these two beams is subsequently split into two equal intensity beams by means of a Bragg cell, which is also housed by the fiber drive. The Bragg cell imposes a frequency shift of 40 MHz on one of the new beams and leaves the other unshifted. The shifted and unshifted beams are transmitted to an optical probe, the transceiver, which is connected to the fiber drive by means of optical fibers. The transceiver (Aerometrics XRV ) is a portable device which contains all necessary optics to form the probe volume

64 A.E. Dahoe et al. / Journal of Loss Prevention in the Process Industries 14 (2001) Fig. 4. An overview of the experimental setup. at the location where the velocity is to be measured. The laser beams emitted by the transceiver are focused to intersect by means a lens with a focal length of 250 mm. This leads to the formation of two coinciding probe volumes at the point where the beams intersect: one with a fringe spacing of µm for the vertical velocity component (514.5 nm) and one with a fringe spacing of µm for the horizontal velocity component (4880 nm). The light scattered by the tracer particles on their passage through these probe volumes is collected by a receiver. The receiver (Aerometrics RCV ) is another portable instrument designed to collect scattered laser light. The input end of the receiver consists of a multi-element lens system and has a focal length of 250 mm. The scattered light is focused onto a spatial filter behind a slit. After the slit, a collimating lens directs the light into an optical fiber. This light beam is then split into a blue and green component by means of beam splitter cubes and line filters, and the resulting light beams are transmitted to a photomultiplier box by means of optical fibers for photo-detection. The photomultiplier box (RCM 200 LPS) converts the scattered light into electronic signals by means of photomultiplier tubes and their output is subsequently passed to the real-time signal analyzers. These real-time signal analyzers (RSA P) simultaneously and continuously detect, process and validate the signals coming from the photomultiplier tubes. They determine the frequency of the Doppler bursts and pass this information on to the computer with the RSA-interface board which computes the velocity components of the tracer particles. In order to fix the measuring location in a rigid and accurate manner, it was decided to restrict the movement of the transmitting optics to the vertical direction and to perform the alignment in the horizontal plane by shifting the model sphere. This was accomplished by mounting the former on an elevation table and by clamping the model sphere and the injection section to a rig that only permits discrete displacements of 15 mm in the horizontal plane. The receiving optics were also mounted on an elevation table, but can be traversed and tilted in all three directions. This freedom of positioning and orienting was necessary in order to get the probe volume into the focus of the receiving optics and to fix the optimal collection angle. The laser Doppler anemometer and the injection valve of the model sphere were synchronized by means of a trigger box. This device emits two simultaneous electrical signals. The first signal activates the injection valve and the second signal triggers the data acquisition process on the computer containing the data acquisition board. As soon as the data acquisition board was triggered, this computer started to record the pressure in the sphere and the canister, and signaled the computer containing the RSA-interface board to measure the velocity inside the sphere. Pressure was measured (see Fig. 5) by means of two piezo-electric transducers. When these devices sense a differential change in the pressure they emit a proportional amount of charge which is converted into voltage by means of charge amplifiers. This voltage was recorded by the computer containing the data acquisition board. The transient flow fields of interest were created by means of a blast of compressed air according to the prescribed test procedure for powder safety testing with the standard 20-l sphere. This means that the canister was

65 480 A.E. Dahoe et al. / Journal of Loss Prevention in the Process Industries 14 (2001) Fig. 5. The measuring locations in the model sphere. The shaded region denotes the projection of the perforated dispersion ring on the equitorial plane of the sphere. pressurized up to 21 bar, the sphere was evacuated to a pressure of 0.4 bar, and the injection valve was subsequently opened so that the contents of the canister was discharged into the sphere until the pressure in both vessels reached equilibrium. The gas flow was seeded with 0.3 µm alumina (Al 2 O 3 ) particles which were capable of following the turbulent fluctuations since they have a relaxation time of about 5 µs. The vertical and horizontal components of the instantaneous velocity were measured at six locations in the flow field and in order to have a sufficient amount of data for statistical averaging, at least ten time series were measured at each location. The six measurement locations (see Fig. 5), 3IL, 4IL, 5IL, 6IL, 7IL, and 8IL, were situated within the equitorial plane and along the optical axis of the beams emitted by the transceiver. An example of the instantaneous velocity components measured at the geometric center of the model sphere is shown in Figs. 6 and 7. In the initial stage of the flow field, the vertical velocity component is seen to oscillate rapidly between 60 and 50 m s 1 with no systematic preference for a specific direction. At the same time the horizontal component varies between 50 and 40 m s 1, with a clear preference for the negative horizontal direction in the beginning, followed by a preference for the positive horizontal direction. Both velocity components are observed to decrease to a fraction of their initial magnitude within a period of about 60 ms. In spite of the wild and spiky behavior of the instantaneous velocity, one may still discern a mean motion with relatively large time scales. Due to the presence of this mean motion, every realization of the instantaneous velocity had to be decomposed into a mean value and a fluctuation in order to quantify the transient turbulence level in the 20-l sphere. The mean value was determined by means of a moving regression routine which fits a polynomial of a particular degree to a data window. The routine picks a sample record of a particular length, say (t 1,v 1 ),,(t i,v i ),,(t n,v n ), fits the polynomial to the data set, uses the regression coefficients to calculate the value of the polynomial at each t i, shifts the data window with one sample, and repeats the process all over with another sample, until all data are processed. The values of the fitted curve at the various values of t i are an estimation Fig. 6. The vertical and horizontal component of the instantaneous velocity at the geometric center of the sphere (location 4IL).

66 A.E. Dahoe et al. / Journal of Loss Prevention in the Process Industries 14 (2001) Fig. 7. Behavior of the pressure in the model sphere (with the rebound nozzle) and the canister during the air blast. of the mean motion, and subtracting them from the instantaneous values, v i, yields the velocity fluctuations. The effect of this routine in decomposing a velocity data set into a mean value and a fluctuation is shown by Fig. 8. In principle, the moving regression algorithm can be used with two kinds of data windows. The first, which is called here a point-window, consists of a fixed number of points. The second is called a time-window and consists of a number of samples contained within a fixed time interval. If the data rate would be constant, both windows would be identical with a fixed number of samples covering a fixed time duration. In the case of laser Doppler anemometry, however, where the data rate is not constant (it increases when the velocity increases and vice versa), a point-window covers a variable time interval, and a time-window includes a variable number of samples. Since the use of a time-window involves the risk of containing too few points to compute the average, a point-window was used. In this way the algorithm adapted itself to the behavior of the flow: if the velocity decreased, samples were taken from a larger time interval so that the averaging was always performed with a large number of samples. The size of the point-window, as well as the degree of the polynomial, are of great importance. If the pointwindow is too small, the mean motion can not be resolved because the moving regression will follow the fluctuations. A point-window which is too large will lead to a flattened-out average, and the mean motion will appear in the fluctuation. When the degree of the fitting polynomial is too high, it tends to follow behavior of the fluctuations instead of the trend of the mean motion. This results in an underestimation of the fluctuations. The optimal choice was found to be a point-window with 71 points (35 points to the left and 35 points to the right of the point where the mean motion is to be estimated) and a second degree polynomial. All velocity time recordings, similar to the ones presented in Fig. 6, were processed with these settings. After subtraction of the mean motion from the instantaneous velocity, the fluctuation of the latter (see the lower part of Fig. 8) was used to quantify and compare the turbulent flow fields generated by the different dust dispersion devices. The behavior of the root-mean-square value of the vertical and the horizontal velocity component at the six different measuring locations is shown in Fig. 9. Each data point in this figure is the result of at least ten measurements and was determined as follows. The fluctuation of each velocity time recording was calculated as described above and the time axis was subdivided into equal time slices of 4 ms. The root-mean-square value associated with each time slice was subsequently calculated by combining the corresponding data of all velocity fluctuations at a particular location and by applying v rms 1 N N i 1 In this equation, v rms v 2 i. (2) denotes the root-mean-square Fig. 8. Decomposition of the vertical velocity component into a mean value (top) and a fluctuation (bottom).

67 482 A.E. Dahoe et al. / Journal of Loss Prevention in the Process Industries 14 (2001) Fig. 9. Root-mean-square values of the velocity fluctuations at the various measuring locations ( 8IL, 7IL, 6IL, 5IL, 4IL, + 3IL) in the 20-l sphere. value, N the total number of samples in each time slice and v i stands for the fluctuation of the instantaneous velocity. The resulting v rms -value was finally assigned to the center of each corresponding time slice. The spatial homogeneity and directional isotropy of the turbulent flow fields generated by the injection process may be considered by means of Figs. 9 and 10. According to Fig. 9 the root-mean-square value of both the vertical and the horizontal velocity component, measured at various locations in the model sphere have converged towards each other with all three dust dispersion devices at 60 ms. This implies that homogeneous turbulence exists in the 20-l sphere at the prescribed ignition delay time of 60 ms, and thereafter. Fig. 10 shows the behavior of the space averaged root-mean-square value of the vertical and horizontal velocity fluctuations. Each point of this figure belongs to a time slice of 4 ms and was calculated by superimposing all the corresponding velocity fluctuations, measured at all six locations, and by applying Eq. (2). It is seen that the initially different v rms -values of the vertical and the horizontal velocity components have converged to more or less the same value at the prescribed 60 ms. Hence, conditions of practically isotropic turbulence exist in the 20-l sphere with all three dust dispersion devices. The associated turbulence level at the prescribed ignition delay time of 60 ms is equal to 2.68 m s A correlation for the turbulence level in the 20-l sphere In order to correlate the transient turbulence level in the 20-l sphere it is helpful to consider the decay of grid generated turbulence, of which the earliest extensive measurements were made by Batchelor & Townsend Fig. 10. Space averaged root-mean-square values.

68 A.E. Dahoe et al. / Journal of Loss Prevention in the Process Industries 14 (2001) (1947, 1948a,b). These researchers passed a stream of air with a uniform velocity profile through a regular grid of bars and studied the behavior of the velocity fluctuations at the downstream side of the grid. They observed that within a region of up to ten times the mesh spacing, the magnitude of the velocity fluctuations at the downstream side of the grid was increasing to a maximum. It was also observed that within this region, the root-meansquare value of the individual velocity components became independent of position across the stream, and approximately equal to each other. After this region, the magnitude of the velocity fluctuations was found to decay with distance while the turbulence remained homogeneous and isotropic. Batchelor and Townsend (1947, 1948a,b) distinguished various stages of the decay process and classified them as the initial period of decay, the transition period of decay, and the final period of decay. In all cases the decay of turbulence could be generalized and correlated by means of an equation of the form v rms v o rms t n t 0, (3) where the distance from the grid at the downstream side is represented by a time coordinate, t (this was accomplished by dividing distance by the mean velocity of the flow). In the initial and final period of decay the exponent, n, was observed to have a constant value of respectively 1.0 and In the transition period of decay the exponent, n, was found to change gradually from 1.0 to The turbulent flow field in the 20-l sphere appears to behave in a similar way. Fig. 9 shows that the prescribed ignition delay time of 60 ms is preceded by an initial period of turbulence buildup, followed by a period of turbulence decay. According to Figs. 9 and 10, a strongly non-homogeneous and anisotropic turbulent flow field is produced in an initial period of about 10 ms. In this period the scatter in the v rms -value measured at different locations is in the order of 10 m s 1, and a difference of the same order of magnitude can be observed in the v rms -value of the independent velocity components. As time elapses the turbulent flow field becomes more and more homogeneous and isotropic. At 60 ms both the scatter and the difference between the v rms -value of the independent velocity components are in the order of 1 ms 1, and this decreases further to 0.1 m s 1 at 1000 ms. Although the injection process lasts about 50 ms (Fig. 7 shows that the pressure in the model sphere and the canister become equal at about 50 ms), it is seen that turbulence buildup occurs only in an initial period of about 10 ms, and that the decay of turbulence begins to occur while there is still an injection flow of compressed air. In order to understand why the buildup of turbulence is restricted to the first 10 ms, and why turbulence starts to decay while the injection flow is still active, it is helpful to consider the various mechanisms of turbulence generation which are active during the air blast. The first mechanism may be inferred from the vorticity equation, w t v w w v n 2 w w v r p, (4) r 2 where w= 1 2 v denotes the vorticity, v the velocity vector, r the density, p the pressure, and n the kinematic viscosity. Prior to the injection process, the storage canister is filled with compressed air of 21 bar (this has a density of about 27 kg m 3 ), and the model sphere is evacuated to a pressure of 0.4 bar (and the air inside the sphere has a density of about 0.5 kg m 3 ). When these values are taken into consideration, it is evident that the baroclinic term in the vorticity equation, ( r p)/r 2, must be regarded as a very strong source of vorticity during the injection process. If the length of the duct (which is about 10 cm) that separates the contents of the pressure canister from the contents of the model sphere is taken as a measure of the distance across which the pressure gradient and density gradient exist, and the gradients are assumed to be perpendicular to each other at every fluid element present inside the duct, one finds a vorticity production rate, w/ t, of about s 2 at the very beginning of the injection process. If this situation were to last for only a millisecond, then the initially static state of each fluid element would change into a rotating state of about 3000 cycles per second. In practice, of course, the pressure gradient and density gradient are not always perpendicular to one another at every fluid element, and decrease rapidly. This estimate nevertheless gives a reasonable impression of the vigorousness associated with the discharge of the contents of the pressure canister into the model sphere. The second mechanism of turbulence generation during the injection process is by wall friction. On its passage from the canister to the model sphere, the air flows at almost sonic velocities through the duct and subsequently past the dispersion device, and turbulence is generated by friction with the wall. The third mechanism is that of shear turbulence. The air streams emerging from the dust dispersion devices enter the model sphere with a preferential direction and at high velocities, and the associated sliding and shearing of fluid layers is a source of turbulence. Of all three mechanisms, the baroclinic effect in the region where high pressure and low pressure air are initially separated is considered to be the most important because it constitutes a source of turbulence which is much stronger than wall friction or the shearing of fluid layers. In the first 10 ms the baroclinic effect produces a large amount of turbulence which starts to decay when the pressure and density gradient have decreased. During this decay process, the mechanisms of turbulence generation by wall friction and sliding fluid streams continue

69 484 A.E. Dahoe et al. / Journal of Loss Prevention in the Process Industries 14 (2001) to produce turbulence. This additional turbulence, however, is insufficient to counteract and to overcome the decay of the turbulence produced by the baroclinic effect. After the first 50 ms, turbulence generation by wall friction is practically absent because there is no longer a flow from the pressure canister to the sphere. The contribution of shear turbulence is also small after this time because the fluid streams that emerge from the dust dispersion devices lose their initial velocity rapidly. When the decay of turbulence in the 20-l sphere (i.e Fig. 10) is compared with the decay of grid generated turbulence, as observed by Batchelor and Townsend (1947, 1948a,b), it is seen that in the period of ms the exponent, n, in Eq. (3) gradually decreases to a constant value, as indicated by Fig. 11, and that it remains at this constant value until 200 ms. After this time, the exponent increases gradually and tends to become equal to zero. Both behavior and the value of the exponent, n, appear to be different from what has been observed during the decay of grid generated turbulence. The most striking difference is that the decay process of grid generated turbulence consists of two periods in which the exponent, n, assumes a constant value, while the decay of turbulence in the 20-l sphere involves only one such period. Moreover, the decay exponent in case of the 20-l sphere assumes a systematically larger (negative) value than the ones observed during the initial and final period of the decay of grid generated turbulence. The reasons for this discrepancy must be sought in the fact that the turbulent fluctuations in the 20-l sphere are generated by a different mechanism, namely, the baroclinic effect, as described earlier. In the case of grid generated turbulence, friction between the fluid and the grid is the predominant mechanism of turbulence. In order to have a quantitative description of the behavior of the turbulence level in the 20-l sphere, our results in the period of ms were correlated by means of Eq. (3). The reason for choosing this time interval was that the decay exponent assumes a constant value and that the explosion times of dust air mixtures Fig. 11. Decay of the root-mean-square velocity in the 20-l sphere with the Perforated Dispersion Ring ( our measurements, Pu et al. (1990), dashed line: 1 m 3 -vessel at the prescribed ignition delay time of 600 ms (van der Wel, 1993). in the 20-l sphere, ignited at an ignition delay time of 60 ms, rarely exceed 100 ms. According to Fig. 11, the constants v rmso, and n in Eq. (3) assume the values of 2.68 m s 1 and 1.49±0.02. Fig. 11 shows a comparison between our turbulence measurements in the 20-l sphere with the Perforated Dispersion Ring and the turbulence measurements reported by Pu et al. (1990). It is seen that our results, obtained by means of laser Doppler anemometry, are in agreement with those obtained by Pu et al. (1990), who used hot-wire anemometry to measure turbulence. The turbulence level in the 20-l is also compared with the turbulence level in the 1 m 3 -vessel at the prescribed ignition delay time of 600 ms. According to this comparison, the turbulence level in the 20-l sphere is equal to that in the 1m 3 -vessel when the ignition delay time is equal to 200 ms, instead of the prescribed 60 ms. This result contradicts the observation made by van der Wel et al. (1992), namely, that similar conditions of turbulence exist in both vessels when the ignition delay time in the 20-l sphere is equal to 165 ms. It was mentioned in the Introduction that the 20-l explosion sphere would only be accepted by technical guidelines for powder safety testing if it would produce the same K St -values as the 1 m 3 -vessel. Hence, Bartknecht (1989) and Siwek (1977) performed extensive measurements, involving a variety of powders, and found that this was indeed the case when the 20-l sphere was operated with an ignition delay time of 60 ms. According to our turbulence measurements, these K St - values were produced at a turbulence level in the 20-l sphere which is significantly different from that in the 1 m 3 -vessel. In other words, the 20-l sphere was used to produce K St -values that were equal to those measured in the 1 m 3 -vessel by tuning the turbulence of the dust cloud and by making use of the fact that the combustion rate changes with turbulence. 4. Conclusions The turbulence level in the 20-l explosion sphere, equipped with the Perforated Dispersion Ring, was measured by means of laser Doppler anemometry. The instantaneous velocity was measured at six different locations in the transient flow field, and two independent velocity components were measured simultaneously. The turbulence level was determined from the instantaneous velocity by decomposing it into a mean value and a fluctuation using a moving regression algorithm, and by calculating the root-mean-square value of the latter. The results of this work are in agreement with the turbulence levels reported by Pu et al. (1990), who used hot wire anemometry to measure turbulence in the 20- l sphere. The turbulence in the 20-l sphere was found to

70 A.E. Dahoe et al. / Journal of Loss Prevention in the Process Industries 14 (2001) become spatially homogeneous and directionally isotropic at the prescribed ignition delay time of 60 ms and this continues to be so after this period. The spatial homogeneity follows from the fact that the root-mean-square values of the velocity fluctuations measured at different locations converge towards each other. The establishment of directional isotropy follows from the observation that the root-mean-square values of the horizontal and vertical velocity fluctuations converge to each other. At the prescribed ignition delay time of 60 ms, the turbulence level in the 20-l sphere is found to be equal to 2.68 m s 1. The behavior of the turbulence level in the period of ms after the beginning of the air blast could be correlated by a decay law expression Eq. (3) in which the constants t 0, v rmso, and n assume values of respectively 60 ms, 2.68 m s 1 and 1.49±0.02. The decay of turbulence in the 20-l sphere was compared with the decay of grid generated turbulence and observed to behave in a distinct manner. While the decay of grid generated turbulence consists of two stages where the exponent, n, in Eq. (3) assumes a constant value, namely, the initial and final period of decay, the decay of turbulence in the 20-l sphere appears to have only one stage with a constant exponent. The value of this exponent is systematically different from those in the initial and final period of the decay of grid generated turbulence. The reason for this disparate behavior is ascribed to the fact that the turbulent fluctuations in the 20-l sphere are created by a different mechanism (the baroclinic effect) than in the case of grid generated turbulence (friction). A comparison between the turbulence levels in the 20- l sphere and the 1 m 3 -vessel, based on our measurements, shows that equal turbulence levels exist in both vessels when the ignition delay time in the 20-l sphere is equal to 200 ms. This result is consistent with the implication of the observations made by Pu et al. (1990), namely, that equal turbulence levels exist in both vessels when the ignition delay time in the 20-l sphere is equal to 200 ms. At the same time the result of this comparison contradicts van der Wel et al. (1992), who claim that similar conditions of turbulence exist in the two test vessels when the ignition delay time in the 20-l sphere is equal to 165 ms. As mentioned in the Introduction, Bartknecht (1989) and Siwek (1977) measured equal K St -values in the 20- l sphere and the 1 m 3 -vessel. Apart from giving rise to the notion that equal turbulence levels exist in both test vessels at the prescribed ignition delay times of 60 and 600 ms, their research also inspired the widespread belief that a formal cube-root-law agreement exists between dust explosion severities measured in the two test vessels. In addition to that, their research stimulated the use of the cube-root-law as a predictive tool which enables engineers to assess the severity of an industrial dust explosion on the basis of dust explosion severities measured in laboratory test vessels. Our measurements show that significantly different turbulence levels exist in the two test vessels at the prescribed ignition delay times. Hence, the results of Bartknecht (1989) and Siwek (1977), which form the experimental basis of the cuberoot-law, were obtained by igniting dust clouds under significantly different conditions of turbulence in the two test vessels. As a result the cube-root-law may not be considered as a generally valid. In fact, its use in the practice of scaling laboratory test results into what might happen during accidental industrial dust explosions must be regarded as fundamentally wrong. This conclusion supports various researchers who advocate the abandonment of the cube-root-law and its replacement by a more fundamental approach. It was pointed out by various researchers (Eckhoff, 1996; Bradley, Chen, & Swithenbank, 1988; Dahoe, Zevenbergen, Lemkowitz, & Scarlett, 1996) that the cube-root-law is no more than an approximation of a single realization of the explosion pressure curve and that it is only valid as a scaling relationship under hypothetical circumstances. First, the mass burning rate (i.e. the product of the burning velocity, the flame area, and the density of the unburnt mixture which is to be consumed by the flame) has to be the same in both the test vessel and the industrial vessel at the moment when the rate of pressure rise reaches its maximum value. This condition is only fulfilled when both vessels are spherical, ignition occurs at the center of both vessels, the flow properties are identical, and changes in pressure, temperature and turbulence of the unburnt mixture ahead of the flame have the same effect on the burning velocity. In reality none of these requirements are fulfilled. In addition to that, laboratory test results, obtained under particular conditions of turbulence, are applied to industrial circumstances where different conditions of turbulence exist. Since the effect of turbulence is not explicitly taken into account by the cube-root-law, its application may lead to unacceptable over-estimations in situations where turbulence levels in industrial practice are much lower than those created in laboratory test vessels, but also to under estimations of the explosion severity under circumstances where additional turbulence is generated by the explosion itself. It was demonstrated by Tamanini (1990) that worst case predictions by means of the VDI-methodology may underestimate the dust explosion severity when turbulence varies at the time of the explosion. Secondly, the thickness of the flame must be negligible with respect to the radius of the vessel. It was demonstrated (Dahoe et al., 1996; Dahoe, 2000) that an inherent limitation of the cube-root-law is that it does not take the effect of flame thickness into account. When the flame thickness is significant with respect to the radius of a laboratory test vessel (i.e. 1%), the cuberoot-law no longer transforms the maximum rate of pressure rise into a volume invariant explosion severity

71 486 A.E. Dahoe et al. / Journal of Loss Prevention in the Process Industries 14 (2001) index. Instead, it transforms a laboratory test result into an explosion severity index which systematically underestimates the maximum rate of pressure rise in a larger vessel. Since many powders have a flame thickness that is appreciable with respect to the radius of laboratory test vessels, the cube-root-law may not be considered as generally valid for the prediction of dust explosion severity. With some dusts, the flame thickness is so large that application the cube-root-law irrevocably leads to an underestimation of the maximum rate of pressure rise in larger vessels, even when laboratory testing is carried out at considerably higher turbulence levels. In order to overcome the limitations associated with the cube-root-law several models have been proposed. Unlike the cube-root-law, which takes a single instant of the rate of pressure rise measured in a test vessel to predict a single instant of the rate of pressure rise during an industrial explosion, these so called integral balance models are capable of predicting the entire pressure evolution during an explosion. And, more importantly, since their derivation is based on fundamental relationships between the pressure development and the mass burning rate at any instant, the effect of mixture composition, pressure, temperature, and turbulence on the transient combustion process can be taken into account in an explicit manner. Existing models of this kind are those of Bradley and Mitcheson (1976), Nagy and Verakis (1983), Perlee, Fuller, and Saul (1974), Chirila, Oancea, Razus, and Ioenscu (1995), Bradley, Lawes, Scott, and Mushi (1994), Tamanini (1993), Dahoe et al. (1996) and Dahoe (2000). Since integral balance models make use of relationships which express the mass burning rate in terms of laminar flame propagation parameters (i.e. laminar burning velocity, laminar flame thickness) and the turbulence properties, quantitative knowledge of the former quantities becomes of crucial importance. In practice it is very difficult to stabilize a laminar dust flame in order to measure the laminar burning velocity and the laminar flame thickness. It is comparatively easy, however, to create turbulent dust explosions in laboratory test vessels, such as the 20-l sphere, and to measure the behavior of the pressure as a function of time. When the turbulence properties in the test vessels are known at the moment of ignition, as well as during the course of the explosion, integral balance models can be fitted to the pressure time recordings in order to determine the laminar burning velocity and the laminar flame thickness, as demonstrated by Dahoe et al. (1996) and Dahoe (2000). In this respect, the decay law expression Eq. (3), with its parameters characterized, will contribute to the establishment of a more fundamental approach to dust explosion severity prediction. Acknowledgements The authors wish to express their gratitude to Dr S.M. Lemkowitz for presenting part of the material described in this work at the Third International Symposium on Hazards, Prevention, and Mitigation of Industrial Explosions, held in October 2000, in Tsukuba, Japan. References Bartknecht, W. (1989). Dust explosions: course, prevention, protection. Berlin: Springer. Batchelor, G. K., & Townsend, A. A. (1947). Decay of vorticity in the isotropic turbulence. In (pp ). Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 190. London: Royal Society of London. Batchelor, G. K., & Townsend, A. A. (1948a). Decay of isotropic turbulence in the initial period. In (pp ). Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 193. London: Royal Society of London. Batchelor, G. K., & Townsend, A. A. (1948b). Decay of isotropic turbulence in the final period. In (pp ). Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 194. London: Royal Society of London. Bradley, D., & Mitcheson, A. (1976). Mathematical solutions for explosions in spherical vessels. Combustion and Flame, 26, Bradley, D., Chen, Z., & Swithenbank, J. R. (1988). Burning rates in turbulent dust air explosions. In 22nd Symposium (International) on Combustion (pp ). Pittsburgh: The Combusion Institute. Bradley, D., Lawes, M., Scott, M. J., & Mushi, E. M. J. (1994). Afterburning in spherical premixed turbulent explosions. Combustion and Flame, 99, Chirila, F., Oancea, D., Razus, D., & Ionescu, N. I. (1995). Pressure and temperature dependence of normal burning velocity for propylene air mixtures from pressure time curves in a spherical vessel. Revue Roumaine de Chimie, 40 (2), Dahoe, A. E., Zevenbergen, J. F., Lemkowitz, S. M., & Scarlett, B. (1996). Dust explosions in spherical vessels: the role of flame thickness in the validity of the cube-root-law. Journal of Loss Prevention in the Process Industries, 9, Dahoe, A. E. (2000). Dust explosions: a study of flame propagation. Ph.D. thesis, Delft University of Technology, Delft, The Netherlands. Eckhoff, R. K. (1996). Dust explosions in the process industries. Oxford: Butterworth and Heinemann. ISO 6184/1. (1985). Explosion protection systems part 1: determination of explosion indices of combustible dusts in air. International Standardization Organization. Nagy, J., & Verakis, H. C. (1983). Development and control of dust explosions. New York: Marcel Dekker. NFPA 68. (1988). Venting of deflagrations. National Fire Protection Association. VDI (1995). Pressure venting of dust explosions. Verein Deutscher Ingenieure. Perlee, H. E., Fuller, F. N., & Saul, C. H. (1974). Constant-volume flame propagation. Bureau of Mines, report of investigations Washington: United States Department of the Interior. Pu, Y. K., Jarosinski, J., Johnson, V. G., & Kauffman, C. W. (1990). Turbulence effects on dust explosions in the 20-l spherical vessel. In 23rd Symposium (International) on Combustion (pp ). Pittsburgh: The Combustion Institute. Siwek, R. (1977) Laborapparatur für die Bestimmung der

72 A.E. Dahoe et al. / Journal of Loss Prevention in the Process Industries 14 (2001) Explosionskenngrößen brennbarer Stäube. Ph.D. thesis, Technical University of Winterthur, Winterthur, Switzerland. Tamanini, F. (1990). Turbulence effects on dust explosion venting. Plant/Operations Progress, 9 (1), Tamanini, F. (1993). Modeling of turbulent unvented gas/air explosions. Progress in Aeronautics and Astronautics, 9 (1), van der Wel, P. G. J., van Veen, J. P. W., Lemkowitz, S. M., Scarlett, B., & van Wingerden, C. J. M. (1992). An interpretation of dust explosion phenomena on the basis of time scales. Powder Technology, 71, van der Wel, P. G. J., (1993). Ignition and propagation of dust explosions. Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.

73 Journal of Loss Prevention in the Process Industries 16 (2003) On the determination of the laminar burning velocity from closed vessel gas explosions A.E. Dahoe, L.P.H. de Goey Department of Mechanical Engineering, Eindhoven University of Technology, Den Dolech 2, Postbus 513, 5600 MB Eindhoven, The Netherlands Abstract A methodology to determine the laminar burning velocity from closed vessel gas explosions is explored. Unlike other methods which have been used to measure burning velocities from closed vessel explosions, this approach belongs to the category which does not involve observation of a rapidly moving flame front. Only the pressure time curve is required as experimental input. To verify the methodology, initially quiescent methane air mixtures were ignited in a 20-l explosion sphere and the equivalence ratio was varied from 0.67 to The behavior of the pressure in the vessel was measured as a function of time and two integral balance models, namely, the thin-flame and the three-zone model, were fitted to determine the laminar burning velocity. Data on the laminar burning velocity as a function of equivalence ratio, pressure and temperature, measured by a variety of other methods have been collected from the literature to enable a comparison. Empirical correlations for the effect of pressure and temperature on the laminar burning velocity have been reviewed and two were selected to be used in conjunction with the thin-flame model. For the three-zone model, a set of coupled correlations has been derived to describe the effect of pressure and temperature on the laminar burning velocity and the laminar flame thickness. Our laminar burning velocities are seen to fall within the band of data from the period A comparison with recent data from the period shows that our results are 5 10% higher than the laminar burning velocities which are currently believed to be the correct ones for methane air mixtures. Based on this observation it is concluded that the methodology described in this work should only be used under circumstances where more accurate methods can not be applied Elsevier Ltd. All rights reserved. Keywords: Deflagration; Burning velocity; Flame thickness 1. Introduction In an earlier paper (Dahoe, Zevenbergen, Lemkowitz, & Scarlett, 1996; hereafter referred to as DZLS) two integral balance models have been presented as an alternative to the well-known cube-root-law and it was demonstrated that they can be applied in two distinct ways. Firstly, they can be used to predict the pressure development of a deflagration in an enclosure when the burning velocity and the flame thickness of a particular combust- Corresponding author. Tel.: ; fax: address: a.e.dahoe@tue.nl (A.E. Dahoe). 1 The symbols used throughout this work are explained below. When a symbol represents something else than stated here, or when a symbol in the text is not explained here, or when a symbol represents more than one quantity, its precise meaning is clarified by the text. ible mixture are known in advance. Secondly, they can be fitted to the experimental pressure time curve of a deflagration in a laboratory test vessel to find an estimate of the burning velocity and the flame thickness. Although the possibility of finding the burning velocity and flame thickness has indeed been demonstrated in DZLS by fitting the three-zone model to the pressure curve of a turbulent cornstarch-air explosion, little was done to explore the true potential of this approach. This was partly due to the absence of reference data on the burning velocity and the flame thickness of dust air mixtures, partly to a deficiency in our knowledge of how these quantities behave as a function of turbulence, and partly to a lack in our understanding of how turbulent flow properties are being modified in the course of an explosion. Since laminar gas explosions present a much simpler case, it was decided to apply the thin-flame model and /$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi: /s (03)

74 458 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Nomenclature Ĉ P constant pressure specific heat per unit mass (J kg 1 K 1 ) 1 Ĉ V constant volume specific heat per unit mass (J kg 1 K 1 ) E a activation energy (J mol 1 ) f i sum of body forces per unit mass acting on the ith species (N kg 1 ) j h enthalpy flux vector (W m 2 ) h microscopic enthalpy per unit mass (J kg 1 ) h f i heat of formation of the ith species at reference conditions (J kg 1 ) K G gas explosion severity index (bar m s 1 ) m u mass of unburnt mixture (kg) n 0 moles of gas present before explosion (mol) n e moles of gas present after explosion (mol) q radiant flux (W m 2 ) p microscopic pressure (Pa) P macroscopic pressure (Pa) P max maximum explosion pressure (Pa) r flame flame radius (m) location of front edge of the flame zone (m) r front r rear location of rear edge of the flame zone (m) R universal gas constant (J mol 1 K 1 )specific gas constant (J kg 1 K 1 ) S fl surface enclosing the flame zone (m 2 ) S ul laminar burning velocity (m s 1 ) t times T temperature (K) T reference temperature (K) T f flame temperature (K) T u temperature of the unburnt mixture (K) T u0 initial temperature of the unburnt mixture (K) v velocity vector (m s 1 ) V i diffusion velocity vector of the ith species (m s 1 ) V fl volume occupied by the flame zone (m 3 ) V vessel volume explosion vessel (m 3 ) ẇ i source term of the ith species (kg m 3 s 1 ) w F average fuel consumption rate (kg m 3 s 1 ) X i ith species mole fraction ( ) Y i ith species mass fraction ( ) Greek symbols a i interaction parameter of the ith species (kg m 2 s 1 ) g heat capacity ratio, Ĉ P /Ĉ V ( ) d L laminar flame thickness (m) c H heat of combustion (J kg 1 ) R H heat of reaction (J kg 1 ) l thermal conductivity (W m 1 K 1 ) n i stoichiometric coefficient of the ith species on the reactant side ( ) n i stoichiometric coefficient of the ith species on the product side ( ) r density (kg m 3 ) r u density of the unburnt mixture (kg m 3 ) t shear stress tensor (N m 2 ) f equivalence ratio ( )

75 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Other symbols D i diffusion coefficient of the ith species (m 2 s 1 ) D ij binary diffusion coefficient between the ith and the jth species (m 2 s 1 ) (dp=dt) max maximum rate of pressure rise (Pa s 1 ) M i molecular mass of the ith species (kg mol 1 ) Dimensionless groups Le Lewis number ( ) the three-zone model to deflagrating gas mixtures in a closed vessel with no turbulence present. Methane was chosen as the fuel because of the wide availability of experimental laminar burning velocities, air was chosen as the oxidizer, and the equivalence ratio was varied from fuel-lean (f = 0.67) to fuel-rich (f = 1.36). Quiescent methane air mixtures at initial conditions of atmospheric pressure and room temperature were centrally ignited to deflagration in a 20-l sphere, the pressure in the explosion chamber was measured as function of time, and the two integral balance models were fitted to these pressure time curves. The resulting laminar burning velocities are compared with literature data and the relative importance of this approach with respect to existing methods to determine the laminar burning velocity is taken into consideration. Despite the apparent simplicity in the absence of initial turbulence there are still a number of pitfalls that require some further clarification. Firstly, there is the influence of continually varying conditions of pressure and temperature in the vessel during an explosion. After ignition, a small spherical laminar flame is formed around the ignition point. The flame propagates away from its origin by consuming reactants at the downstream side, leaving hot combustion products behind in its wake. The sudden temperature rise of the gasses passing through the flame is accompanied by a rise in the local pressure, which generates an expansion flow and causes the unburnt mixture between the flame surface and the vessel wall to be compressed. As a result, the unburnt mixture consumed by the flame at each instant of time has different pressure and temperature. The influence of varying pressure and temperature on the laminar burning velocity and the laminar flame thickness is taken into account by means of correlations. Secondly, there is the effect of buoyancy. The buoyancy force comes into play when hot combustion products and cold reactants coexist. It becomes increasingly important during the growth of the flame and causes its shape to change from spherical to more of a mushroom shape. The influence of buoyancy was reduced to a minimum by limiting the analysis to the early part of the pressure time curve, based on considerations described in Section 6. Thirdly, there is the effect of baroclinic distortion of the flame which may be understood by inspecting the source term, r p/r 2, of the vorticity equation (e.g. Eq. (5) of Dahoe, Cant, Pegg, & Scarlett, 2001). Because the flame zone is a region where the density decreases rapidly in the direction towards the ignition point and the pressure is known to decrease in the opposite direction, r and p are non-zero, and it is only under the hypothetical circumstance of perfect alignment of these gradients over the entire flame surface that no vorticity will be produced. However, the slightest misalignment between these to gradients will cause the baroclinic term to act as a source of vorticity and lead to flame wrinkling. This implies that an initially spherical laminar flame has a tendency to evolve into a wrinkled flame, even in the absence of turbulence in the flow field of the unburnt mixture ahead of the flame. The onset of such instability in closed vessels, freely propagating laminar flames and vented enclosures, first as flame cracking and then as a developed cellular structures discussed by Bradley and Harper (1994), Bradley, Hicks, Lawes, Sheppard, and Woolley (1998), Gu, Haq, Lawes, and Woolley (2000), Bradley, Cresswell, and Puttock (2001), Bradley, Sheppard, Woolley, Greenhalgh, and Lockett (2000) and Haq, Sheppard, Woolley, Greenhalgh, and Lockett (2002). With stoichiometric methane air mixtures, ignited to deflagration in a 380 mm diameter sphere, it was observed that the onset of the instability occurred when the flame reached a radius of about 20 mm (see Fig. 1 of Gu et al.). When the flame surface becomes distorted by instability, it is subjected to a stretch rate which alters the local laminar burning velocity. Additional information from photographic observation of the propagating flame is required to find the unstretched laminar burning velocity. Since this information is absent in the methodology explored in the present paper, it is reason-

76 460 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) able to expect a systematic difference between our laminar burning velocities and those corrected for flame stretch. It is worthwhile to mention that various other models have been proposed which enable the determination of the burning velocity from pressure data. A comprehensive review of these models may be found in Chapter 17 of Lees (1996). Their derivation aims at the establishment of relationships between the pressure in a closed vessel, the rate of change of the pressure, the radius of the burnt gas core in the wake of the flame, the rate of change of this radius, and the burning velocity. Our thinflame and three-zone model may be considered as an addition to this list. Another recent model by Senecal and Beaulieu (1998) also deserves to be added to the list. It is remarkable that, following a different derivation, the final expression obtained by these authors (Eq. A-16 of Senecal and Beaulieu) to calculate the value of the burning velocity from the maximum rate of pressure rise is identical to the differential equation which constitutes the thin-flame model (i.e. Eq. (1) of the present paper). An important advantage of their approach is that it gives an estimate of the turbulent burning when the maximum explosion pressure of combustible mixture is independent of turbulence. The reader may consult Dahoe, van der Nat, Braithwaite, and Scarlett (2001) for a detailed account on the sensitivity of the maximum explosion pressure to turbulence. This paper is organized as follows. Section 2 contains a brief description of the thin-flame model and a revision of the three-zone model. A variety of correlations for the dependence of the laminar burning velocity on pressure and temperature are reviewed in Section 3. Two of these correlations, Eqs. (19) and (20), were selected and incorporated into the thin-flame model. The reasons for choosing these particular correlations are explained. Since the three-zone model involves the laminar flame thickness as well, Section 4 is devoted to the derivation of a complementary set of correlations; one for the laminar burning velocity (76) and one for the laminar flame thickness (77). A general set of correlations, (72) and (73), is first derived from the governing equations for a multi-component reactive mixture. It is subsequently shown how these correlations are constrained to avoid redundancy before their incorporation into the three-zone model. Although parts of this derivation and methodology can be found in reference works (Williams, 1985; Kuo, 1986; Turns, 1996) it was decided to include it in a comprehensive manner. The alternative, namely, to state Eqs. (72) and (73), and to leave their verification to the self-motivation of the reader would obscure the assumptions and simplifications made to arrive at the result. Section 5 contains a review of the literature data on the dependence of the laminar burning velocity of methane air mixtures on equivalence ratio, pressure, and temperature. The correlations of the previous two sections are fitted to these data to find an estimate of their parameters for the purpose of comparison. Section 6 describes the application of the integral balance models to experimental pressure time curves. Laminar burning velocities obtained in this manner, as well as the optimal values of the parameters contained in the correlations from Sections 3 and 4, are compared with reference material presented in Section 5. The conclusions arising from this investigation are summarized in Section The thin-flame model and the three-zone model The thin-flame model, described by DZLS, is only mentioned briefly here, Its derivation results in a dynamic relationship between the pressure and the burning velocity (DZLS, Eq. (11)), based on the assumption that the flame zone is a surface where a sudden transition occurs from unburnt into burnt mixture, and that the consumption rate of unburnt mixture equals the product of the unburnt mixture density, the flame area and the burning velocity (DZLS, Eq. (5)). For the present work it is sufficient to reproduce the final result only: dp dt 3(P max P 0 ) R vessel 1 P 1/g 2/3 0 P P max P P max P 0 P 1/g P 0 S ul. (1) The three-zone model is described more extensively because it has undergone a revision after its first publication. The principal reason for reformulating the threezone model was that it did not become identical to the thin-flame model in the limit case of zero flame thickness. The derivation of the revised model is entirely analogous to that presented in DZLS and only the modifications are presented here. Like in the earlier version, the flame zone is a region of finite width where a gradual transition occurs from unburnt to burnt mixture, which is described by expressing the fraction of unburnt mixture as a linear function of radial coordinate. Again, two cases, each consisting of three phases are distinguished during the flame propagation process. The criteria separating the cases and governing the boundaries between the various phases remain the same. What becomes different is the manner in which the consumption rate of unburnt mixture is used to establish a relationship between the pressure development and the burning velocity (compare Eqs. (2) (8) below with Eqs. (13) (18) of DZLS. The consumption of unburnt mixture within the moving flame region may be expressed as dm u dt d r u f(r)dv (2) dt V fl Because f is formally a scalar function of location r and time t, application of the Leibnitz formula to the total time derivative of the integral lead to

77 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) dm u dt V fl [r u f(r)] dr r dt dv S fl r u f(r)(v s n)ds. (3) When this equation is applied to the flame region only, it states that the accumulation of unburnt mixture equals the sum of the consumption rate within the flame zone, and the influx and efflux of unburnt mixture through the flame boundaries. For the entire volume, however, one should only take the first term on the right hand side into account because the fluxes of unburnt mixture through the flame boundaries do not affect the overall amount of unburnt mixture. Hence, substitution of Eq. (3) into (DZLS, Eq. (4)) yields the following expression for the pressure evolution: dp dt P max P 0 m u0 V fl [r u f(r)] dr dv. (4) r dt Relative to a fixed observer, the integration limits, i.e. the rear and front boundaries of the flame, are propagating with the flame speed. Of course, no unburnt mixture would be consumed by the flame unless we postulate the integrand of the above equation as an explicit rate of consumption. Taking notice of the fact that the cold unburnt mixture enters the flame zone from the downstream side with a velocity equal to the burning velocity and that the consumption rate of unburnt mixture scales with this velocity, it is postulated here that the rate of disappearance of reactants in the flame zone equals the product of the gradient of the fraction of unburnt mixture and the burning velocity. In terms of Eq. (4) it simply means that the integral is evaluated by an observer standing on the combustion wave and consequently dr/dt must be set equal to S ul. Then, Eq. (4) becomes dp dt P max P 0 m u0 P max P 0 m u0 r u f(r) t P max P 0 m u0 r r front f(r) 4πr 2 S ul r u r rear r f(r) front 4πr 2 S ul r u r rear r f(r) r u r u f(r) dr r f(r) front 4πr 2 r u S ul r rear which may be rewritten into dp dt P max P 0 V vessel P 1/g P 0 front 4πS ul r f(r) r u r dr (5) (6) r 1 lnr u (7) lnf(r) dr, r 2 f(r) r rear r 1 (8) lnr u lnf(r) dr, after application of the adiabatic compression law (DZLS, Eq. (7)). Although the density of the unburnt mixture is known to change within the flame zone, it is assumed in the present work that lnr u / lnf(r) = 0. With this assumption it is seen that Eq. (7) reduces to (DZLS, Eq. (6)) when the flame thickness becomes zero, and it is obvious that the three-zone model becomes identical to the thinflame model. Expressions for the pressure evolution can be obtained by substituting Eqs. (20), (24), (28) and (32) of DZLS into Eq. (8). These are given in Table 1 and their solution is illustrated by Fig. 1. Expressions for the calculation of the flame boundaries during the various phases remain the same as those described in DZLS. 3. Empirical correlations for the effect of pressure and temperature on the laminar burning velocity The simultaneous change in the pressure and temperature of the unburnt mixture during a closed vessel explosion makes it necessary to rely on correlations which take these effects into account. While correlations for the laminar flame thickness are scarce, many have been proposed to describe the behavior of the laminar burning velocity. Because of their simplicity and the minimal computational burden they impose, this section is restricted to correlations which express the laminar burning velocity in terms of properties of the unburnt mixture only (i.e. S ul = f(t u,p,f)). These relationships may be classified as follows: Equations that separately describe the influence of pressure and temperature on the laminar burning velocity of stoichiometric methane air mixtures. Correlations describing the simultaneous influence of pressure and temperature on the burning velocity of stoichiometric methane air mixtures. Correlations describing the simultaneous influence of pressure, temperature and equivalence ratio. For stoichiometric methane air mixtures, Andrews and Bradley (1972), proposed two separate equations, namely, S ul 43P 0.5 cm s 1 (9) and S ul T 2.31 u cm s 1. (10) These relationships are recommended for the pressure range from 5 to 100 atm at room temperature and for the temperature range from 100 to 1000 K at atmospheric pressure. Smith and Agnew (1951) correlated the behavior of the burning velocity as a function of pressure with an equation of an entirely different form: S ul exp(0.3(1 P S 0.54 )). (11) ul

78 462 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Table 1 Differential equations of the three-zone model for the pressure development Case 1 Phase 1a Equation Phase 1b Equation Phase 1c Equation Case 2 Phase 2a Equation Phase 2b Equation Phase 2c Equation d L R vessel r rear = 0.0, r front d L dp dt = P max P 0 V vessel P 1/g P 0 4πS ul r 3 front d L r rear = r front d L, d L r front R vessel dp dt = P max P 0 V vessel P 1/g P 0 4πS ul r3 front r 3 rear d L R vessel d L r rear R vessel, r front = R vessel dp dt = P max P 0 V vessel P 1/g P 0 4πS ul R3 vessel r 3 rear d L d L R vessel r rear = 0.0, r front R vessel Same as phase 1a r rear = 0.0, r front = R vessel dp dt = P max P 0 V vessel P 1/g R P 0 3 vessel 4πS ul d L 0.0 r rear R vessel, r front = R vessel Same as phase 1c pressure(bar) (a) mm 2cm 2 5cm 10cm 20cm time (milliseconds) (dp/d t) (bar/s) (b) mm 2cm 5cm 10cm 20cm time (milliseconds) Fig. 1. Predicted pressure evolution and rate of pressure rise in a 20- l sphere and different flame thicknesses with the three-zone model. P 0 = 1 bar; P max = 8 bar; g = 1.4, S ul = 0.6 m s 1. This equation is supposed to hold for the pressure range from 0.1 to 20 atm at room temperature. Another expression for the pressure dependence of the burning velocity, valid for pressure from 0.5 to 20 atm, was given by Agnew and Graiff (1961): S ul lnP cm s 1. (12) Barassin, Lisbet, Combourieu, and Laffitte (1967) correlated their experimental results on the effect of temperature on the burning velocity of stoichiometric methane air mixtures as S ul T 2.11 u cm s 1. (13) The temperature of the unburnt mixture was varied from 293 to 532 K at atmospheric pressure. Dugger (1952) investigated the effect of initial mixture temperature of stoichiometric methane air in the temperature range from 141 to 615 K at atmosphere pressure and correlated their results as S ul T 2.11 u cm s 1. (14) When applied to closed vessel explosions, the aforementioned relationships have the disadvantage that not all combinations of pressure and temperature, as these occur in the course of the combustion process, are covered. Clearly, correlations are needed which describe the simultaneous influence of pressure and temperature on the burning velocity. For stoichiometric methane air mixtures at temperatures from 323 to 473 K, Babkin and Kozachenko (1966) proposed an equation, S ul T 2 u ( logp) cm s 1, (15) for the pressure range from 1 to 23 atm and an equation, S ul 9.06 T 1.47 u P (T u /1000) cm s 1, (16) for the pressure range from 23 to 70 atm. Perlee, Fuller, and Saul (1974) suggested that S ul T u T u ln P P 0 cm s 1. (17) for stoichiometric methane air mixtures. There are correlations which, in addition to describing the simultaneous effect of pressure and temperature on the burning velocity, also include the influence of equivalence ratio. A system of equations for predicting the laminar burning velocity (in cm s 1 ) for pressures from 1 to 8 atm, temperatures from 300 to 600 K, and equivalence ratios from 0.8 to 1.2 was given by Sharma, Agrawal, and Gupta (1981):

79 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) S ul C(T u/300) 1.68/ f if f 1.0 C(T u /300) 1.68 f if f 1.0 with C f 1196 f f 3 15f10 logp. Iijima and Takeno (1986) proposed a correlation, (18) S ul S T u b ul T 2 u0 b1 1 ln P (19) P 0, which expresses the laminar burning velocity, S ul (P, T u ), at an arbitrary pressure and temperature, in terms of the laminar burning velocity at reference conditions, S 0 ul(p 0,T u0 ). The reference temperature, T u0, must be set equal to 291 K and the reference pressure, P 0, is 1 atm. The model is valid in the pressure range from 0.3 to 30 atm in combination with a temperature range from 291 to 500 K, and for an equivalence ratio in the range from 0.8 to 1.3. The dependence of the laminar burning velocity on the equivalence ratio is incorporated by means of expressions for the reference burning velocity, S 0 ul, and the pressure exponents, b 1 and b 2, which are specific to the fuel. For methane air mixtures: b (f 1) (20) b (f 1) (21) S ul (f 1.12) 2 335(f 1.12) 3 cm s 1 (22) Based on experimental observations of the combustion behavior of methanol air, iso-octane air, and indolene air mixtures, Metghalchi and Keck (1982) found that 2 S ul S T u ul T u0 b1 P P 0 b2 (23) for a pressure range from 0.4 to 5.0 atm, temperatures between 298 and 700 K and equivalence ratios from 0.8 to 1.5. The reference temperature and pressure are 298 K and 1 atm. The influence of the equivalence ratio was incorporated through the temperature and pressure exponents, and through the reference burning velocity: b (f 1) (24) b (f 1) (25) S ul B m B 2 (f f m ) 2 cm s 1 (26) Unlike Iijima and Takeno (1986), these authors observed that the pressure and temperature exponents are 2 Notice that Eqs. (19) and (23) are related through the following series expansion: a x 1 xlna 1! (xlna)2 2! (xlna)3 3! % (xlna)n. n! independent of the fuel type (within the estimated experimental error as the authors state). The reference burning velocity, however, is known to be a function of fuel type and this dependency was incorporated through the constants B m, B 2 and f m, which are specific to fuel type. Of all correlations reviewed in this section, Eqs. (19) and (23) are chosen to describe the influence of pressure and temperature on the laminar burning velocity. The reasons for this choice are twofold. First of all, these equations may be regarded as valid simplifications of a more general expression (see Eq. (69)) which can be derived from first principles. The second reason is that, unlike the other equations presented here, these correlations are particularly suitable for the methodology proposed in this paper because the laminar burning velocity at an arbitrary set of experimental conditions is expressed as a function of the laminar burning velocity at a particular set of reference conditions. When the latter is taken into account as a degree of freedom in an integral balance model, its magnitude can be determined by fitting the model to the pressure time curve of a closed vessel explosion. 4. Derivation of a set of correlations for the pressure and temperature dependence of the laminar burning velocity and the laminar flame thickness A set of correlations will now be derived for the effect of pressure and temperature on the laminar burning velocity and the laminar flame thickness by considering the Shvab Zeldovich energy equation. This form of the energy equation can be obtained by combining the species and energy conservation equations of a multi-component reactive mixture, (ry i ) (rvy t i ) j si ẇ i (27) (rh) t (rvh) p t v p t: v j h (28) N ry i f i V i, i 1 into a single expression. The flux of the ith species, j si ry i V i, (29) is stated in terms of a diffusion velocity, V i, and the heat flux vector, N j h l T q ry i h i V i (30) i 1 N RT N i 1 j 1 X ja i M i D i V j ), ij (V

80 464 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) is the sum of four contributions: thermal diffusion, the radiant energy flux, the Soret flux and a Dufour flux. Although both effects constitute small contributions to the overall heat balance, the Soret effect is kept in the expression for the total heat flux in order to facilitate the derivation of the Shvab Zeldovich form of the energy equation. For a steady laminar flame, when the body forces, f i, the pressure gradient, p, the viscous dissipation, t: v, and the radiant flux, q, are neglected, and, by making use of the fact that h = Y i h i, Eqs. (27) and (28) may be simplified to [ry i (v V i )] ẇ i (31) N ry i h i (v V i ) l T 0. (32) i 1 Since h i h f i T Ĉ Pi dt, (33) T Eq. (32) may be rewritten into N N ry i (v V i )h f i ry i (v V i ) T Ĉ Pi dt (34) i 1 i 1 T l T 0, which upon application of Eq. (31) to the first term on the left hand side becomes N T N rv Y i V i T i 1 N l T T Y i Ĉ Pi dt r i 1 h f i ẇ i. i 1 T Ĉ Pi dt (35) When air is used as the oxidizer, it is as if the combustion reactions occur in nitrogen as a background fluid and hence the diffusion velocity may be described by Fick s law: ry i V i rd Y i. (36) Application of Fick s law to Eq. (35), and use of the fact that Ĉ P =ΣY i Ĉ P, leads rv T N Ĉ P dt rd T i 1 N h f i ẇ i, i 1 ( Y i ) T T Ĉ Pi dt l T (37) which can be rewritten into T rv T Ĉ P dt rd Ĉ Pi dt rĉ P D T (38) T T N l T or equivalently, i 1 h f i ẇ i, T rv T Ĉ P dt rd Ĉ Pi dt rĉ P D[1 (39) T T N Le] T h f i ẇ i, because T N Ĉ P dt T i 1 N ( Y i ) T i 1 N ( Y i ) T i 1 i 1 Y i T T Ĉ Pi dt N Ĉ Pi dt T i 1 N Ĉ Pi dt T i 1 Y i T Y i Ĉ Pi T T Ĉ Pi dt (40) N ( Y i ) T Ĉ Pi dt Ĉ P T. i 1 T Up to Eq. (39) none of the physical properties were assumed constant and no simplifying assumptions have been made regarding the specific heats of the individual species. The so-called Shvab Zeldovich energy equation is obtained by setting the Lewis number, Le, in Eq. (39) equal to unity: T N rv T Ĉ P dt rd Ĉ P dt h T T f i ẇ i. (41) i 1 Since the specific heat is known to be a weak function of temperature, it may be treated as a constant. An immediate consequence of the unity Lewis number assumption is that rd may be replaced by l/ĉ P. The continuity equation (see Fig. 2), r u v r u S ul, (42) Fig. 2. Simplified structure of a premixed laminar flame.

81 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) then implies that Eq. (41) may be simplified to N r u Ĉ P S ul T [l T] h f i ẇ i. (43) i 1 If the overall combustion reaction is represented by 1 kg Fuel n kg Oxidizer (n (44) 1) kg Products, then ẇ F 1 n ẇ O 1 n 1 ẇ Pr (45) and hence, N h f i ẇ i h f F ẇ F h f O ẇ O h f Pr ẇ Pr (46) i 1 (h f F nh f O (n 1)h f Pr )ẇ F (47) c Hẇ F, (48) where c H denotes the fuel s heat of combustion. For the laminar flame under consideration, Eq. (43) then simplifies to dt r u Ĉ P S ul dx dx l d dt dx c Hẇ F. (49) Following the procedure described by Turns (1996) and Spalding (1979) the above differential equation may be integrated twice with the boundary conditions as dictated by the assumed temperature profile shown in Fig. 2. The first integration is performed over the entire physical domain with the boundary conditions, dt x : T T u 0 (50) dx dt x : T T f 0, (51) dx and gives: r u Ĉ P S ul T T f T u l T dt/dx=0 x dt/dx=0 c H ẇ F dx. (52) When the assumed temperature profile is used to apply a change of variables, T x T f T u dx d L dt, (53) d L T f T u Eq. (52) transforms into r u Ĉ P S ul (T f T u ) d T L c H T f T u f ẇ F dt (54) T u d L c w F where w F denotes the average fuel consumption rate. This results in a single algebraic equation, r u Ĉ P S ul (T f T u ) d L c Hw F 0 (55) with two unknowns, namely, the laminar burning velocity, S ul, and the laminar flame thickness, d L. Notice that this equation requires that the heat production in the reaction zone is balanced by the heat absorption of the incoming unburnt mixture. In order to obtain explicit expressions for S ul and d L, it is necessary to find a second equation. This is done by repeating the integration procedure with the following boundary conditions: dt x : T T u 0 (56) dx x d L 2 : T T u T f dt 2 dx T f T u. (57) d L This leads to the following integrated form of Eq. (49): r u Ĉ P S ul T (T u +T f )/2 T u /2 L c H d ẇ F dx, l T (T f T u )/d L x dt/dx=0 (58) which simplifies into 1 2 r uĉ P S ul (T f T u ) l T f T u 0, (59) d L since ẇ F is practically zero in the preheat zone. This equation state that the required energy flux for heating the unburnt mixture to the flame temperature is controlled by the conduction of heat through the preheat zone. The desired expressions for S ul and d L can then be obtained by solving Eqs. (55) and (59): S ul 2 l 1/2 c H w F r u Ĉ P Ĉ P (T f T u ) r u (60) d L 2 l 1/2 Ĉ P (T f T u ) r u r u Ĉ P c H w F. (61) Since the heat of combustion of the fuel relates to the temperature of the product mixture as c H = (n + 1)Ĉ P (T f T u ), these relationships may also be stated as S ul 2 l r u Ĉ P (n 1) w F d L 2 l 1 r u Ĉ P n 1 1/2 r u 1/2 r u w F (62). (63) Notice that the factor 2 in these equations results from the choice of the width of the preheat zone. A wider or

82 466 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) thinner preheat zone would have resulted in a different value. It is assumed that this arbitrariness is largely canceled in the establishment of Eqs. (72) and (73). The effect of pressure and temperature can now be incorporated as follows. With an assumed generalized reaction, N i 1 N n i M i i 1 n i M i, (64) and an overall reaction order of n =Σ N i = 1n i, the mass consumption rate of each individual species may be stated as: d(ry i /M i ) (n dt i n i )BT m exp E a RT N j 1 ry j (65) M j n j, where the constants m and E a, respectively, denote the temperature exponent of the pre-exponential factor and the activation energy. Hence, w F r n BT m exp E a RT N (Y j /M j ) n j, (66) j 1 and since r u T 1 u P, (67) while most of the combustion occurs in the reaction zone, the average fuel consumption rate is found to scale as follows: w F T n f P n T m f exp E a (68) RT f. Substitution of the two preceding relationships into Eqs. (62) and (63) gives the following scalings for the laminar burning velocity and the laminar flame thickness: T u T u0 P P 0 2R 1 1 T f T f S ul l(t S ul u ) l(t u0 ) d L d L E a l(t u ) l(t u0 ) P P 0 E a 2R 1 1 T f T f, (n/2) T f (n 2)/2 T f T f T f n/2 T f (n/2) T f T f (m/2) T f m/2 exp (69) exp (70) where S ul, d L and T f are the laminar burning velocity, the laminar flame thickness and the flame temperature of the unburnt mixture at a reference state P 0 and T u0. The thermal conductivity is a function of the temperature of the preheat zone and should in fact be expressed as a function of the average preheat zone temperature, T u + 1/2(T f T u ). Since the flame temperature is hardly affected by the temperature of the unburnt mixture, the thermal conductivity is expressed here as a function of the temperature of the unburnt mixture only. Owing to the fact that the unburnt mixture at the downstream side of the flame undergoes adiabatic compression during an explosion in a closed vessel, the pressure and temperature of the unburnt mixture do not behave independently from each other. Instead, they are correlated according to the adiabatic compression law, T u T u0 P P 0 (g 1)/g, (71) where g denotes the specific heat ratio. When Eqs. (69) and (70) are rewritten as S ul l(t S ul u ) T u l(t u0 ) T u0 P P 0 1 T (n m)/2 f T f P n/2 P 0 exp (72) d L d L 2R 1 T f 1 T f E a l(t u ) l(t u0 ) 1 T f, (n m)/2 T f P P 0 T f (n/2) exp E a 2R 1 (73) T f substitution of the adiabatic compression law (71) and the following assumptions 3, l(t u) l(t u0 ) T u T u0 a1 (74) T f leads to (n m)/2 T f exp E a P P 0 c+(g 1)/g 1+a 2R 1 T f 1 T f P P 0 a2, (75) S ul (76) S ul d L P (77) P 0 c a, d L where c denotes a mixture specific constant. These are the correlations for the effect of pressure and temperature on the laminar burning velocity and the laminar flame thickness to be used in conjunction with the threezone model. 3 The temperature dependence of the thermal conductivity is described by the Sutherland equation (Vasserman, Kazavchinskii, & Rabinovich, 1971: p. 311), l(t) l(t 0 ) T 0 C T C T 3/2 T 0 where C denotes the Sutherland constant which must be determined experimentally for each substance. It is assumed that this relationship may be approximated by Eq. (74).

83 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Assumption (75) requires some further clarification. For a constant-pressure flame, for example, the law of conservation of energy requires the total enthalpy per unit mass of mixture to remain constant throughout the flame zone. This may be expressed by N ui h i 1 Y f i Y ui T N u Ĉ Pi dt bi h T i 1 Y fi (78) Y bi T f T Ĉ Pi dt, where Y ui and Y bi denote the mass fractions of the species that, respectively, constitute the unburnt and the burnt mixture. When this equation is rewritten as N i 1 N Y ui Ĉ Pi (T u T ) R H i 1 Y bi Ĉ Pi (T f T ), (79) where N R H (Y bi Y ui )h f i (80) i 1 denotes the heat of reaction per mass unit, it is obvious that an increase in T u will have little effect on T f since ΣY ui Ĉ Pi (T u T ) R H. Eq. (79) also clarifies the influence of pressure on the flame temperature. If dissociation occurs to a significant degree within the reaction zone, a chemical equilibrium exists between the reaction products and their subsequent dissociation products. Changes in the system pressure will alter the mass fractions of the burnt mixture, Y bi, and since the left hand side of Eq. (79) is practically independent of pressure, a change in the species mass fractions can only be balanced by a change of T f. It is known that, the hotter the flame, the larger the degree of dissociation, and the more sensitive the flame temperature becomes to variations in the system pressure. Due to the comparatively low flame temperature of methane air mixtures 4 dissociation, and hence the effect of pressure on the flame temperature, is considered to be of minor importance. It is nevertheless assumed that the effect of pressure on the flame temperature must be taken into account by Eq. (75). 5. Literature data on the effect of equivalence ratio, pressure and temperature on the laminar burning velocity The aim of this section is to find estimates for the effect of equivalence ratio, pressure and temperature on 4 The final temperature of the burnt mixture can be estimated from the explosion pressure since P e /P 0 = (n e /n 0 )/(T f /T 0 ) where n 0 and n e denote the total number of moles of gas present, before and after the explosion. Stoichiometric methane air mixtures gave an explosion pressure of 8.7 bar (see Fig. 6). Air consists for 79% of inert nitrogen and the stoichiometric methane oxygen reaction, CH 4 +2O 2 CO 2 the laminar burning velocity. Experimental and calculated burning velocities reported by other researchers are interpreted here on the basis of correlations presented in the previous two sections. Fig. 3 shows the variation of the laminar burning velocity as a function of the equivalence ratio. One may observe a variation of about 10 cm s 1 between the 16 different data sets when the equivalence ratio ranges from the lower flammability limit to the stoichiometric concentration, and this discrepancy increases as the upper flammability limit is approached. This large factor of uncertainty may be ascribed to the variety of methods that have been used to determine the magnitude of this quantity. The laminar burning velocities obtained in our work will be compared with these results. The literature data on the effect of pressure on the laminar burning velocity of stoichiometric methane air mixtures (see Fig. 4) imply a weak dependence as a function of pressure. The laminar burning velocity changes by a factor of 20 (from 100 to 5 cm s 1 ) when the pressure is changed by a factor of 1000 (from 0.1 to 100 bar). The experimental results from 14 different data sets in Fig. 4 also indicate that the overall reaction order does not remain constant over the entire pressure range and that there are discrepancies between the results obtained by different experimental methods. These discrepancies are more pronounced for pressures lower than Fig. 3. Effect of equivalence ratio on the laminar burning velocity of methane air mixtures, P = 1 bar, T = K. Clingman, Brokaw, and Pease (1953), Karpov and Sokolik (1961), Barassin et al. (1967), Lindow (1968), Edmondson and Heap (1969), Edmondson and Heap (1970), Reed, Mineur, and McNaughton (1971), Andrews and Bradley (1972), Günther and Janisch (1972), van Maaren et al. (1994), Clarke, Stone, and Beckwith (1995), Wu and Law (1984), Iijima and Takeno (1986), Kawakami, Okajima, and Iinuma (1988), Egolfopoulos, Cho, and Law (1989), Flamelet Library, curve 1: Scholte and Vaags (1959), curve 2: Gibbs and Calcote (1959), curve 3: Egerton and Lefebvre (1954), curve 4: Warnatz (1981), curve 5: Tsatsaronis (1978). +2H 2 O, conserves the amount of gas. Therefore, n e = n 0 and the temperature of the burnt mixture is found to be 2610 K.

84 468 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Fig. 4. Effect of pressure on the laminar burning velocity of stoichiometric methane air mixtures, T = K. Egerton and Lefebvre (1954), Diederichsen and Wolfhard (1956), Clingman and Pease (1956), Manton and Milliken (1956), Singer, Grumer, and Cook (1956), Gilbert (1957) (luminous zone), Gilbert (1957) (wire shadow), Strauss and Edse (1959), Agnew and Graiff (1961), Babkin and Kozachenko (1966), Bradley and Hundy (1971), Babkin, Kozachenko, and Kuznetsov (1964), Egolfopoulos et al. (1989), Flamelet Library, curve 1: Tsatsaronis (1978), model 1: Eq. (9) by Andrews and Bradley (1972), model 2: Eq. (18) by Sharma et al. (1981). 1 bar. To minimize these inaccuracies only literature data in the pressure range of 1 10 bar are used. Each data set was re-scaled by dividing it by the value of the laminar burning velocity at reference conditions, and this ratio is plotted in accordance with Eqs. (19) and (23), as shown in the lower part of Fig. 4, so that the slope of these data corresponds to the pressure exponent, b 2, in these equations. The value of b 2 found by means of fitting the thin-flame model and the three-zone model can then be compared with the value of the slope. The solid line in the lower-left part of Fig. 4 indicates that the pressure exponent of Eq. (19) has a value of 0.28, but the dashed lines indicate that this pressure exponent may vary between 0.15 and 0.4 from one method of determination to another. The lower-right part of the figure indicates that the pressure exponent of Eq. (23) has a value of 0.41, but that it can vary between 0.2 and 0.6. With hydrocarbon air mixtures, it is generally observed that S ul T b 1 where the exponent b1 ranges between 1.5 and 2. The temperature exponent in Eqs. (19) and (23) can be determined by re-scaling the literature data in the upper part of Fig. 5 as shown by the lower part of the same figure. From the latter, one may deduce a value of 1.89 (the slope of the solid line) for the temperature exponent. The dashed lines, with slopes of 1.5 and 2.2, reflect the considerable scatter in both the magnitude of the laminar burning velocities, as well as in their rate of increase with temperature. The lower-right part of Fig. 5 may also be used to estimate the values of c and a in Eqs. (76) and (77). From the slope of these data and Eq. (69) one may conclude that P 1 P 0 (b 1)((g 1)/g) P (81) P 0 c. l(t u) l(t u0 ) T b 1 1 u T u0 When the value of g is taken to be 1.4, one finds that c = 0.25 with b 1 = 1.89, and that c varies between 0.14 and 0.34 on the basis of the slopes of the dashed lines. An estimation of the value of a can be obtained as follows. Dryer and Glassman (1972) proposed the following expression (which is considered to be outdated by some researchers but nevertheless suitable for our

85 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Fig. 5. Effect of temperature on the laminar burning velocity of stoichiometric methane air mixtures, P = 1 bar. Johnston (1947), Dugger (1952), Halpern (1958), Babkin et al. (1964), Babkin and Kozachenko (1966), Barassin et al. (1967) (tube), Barassin et al. (1967) (burner), Flamelet Library, model 1: Eq. (10) by Andrews and Bradley (1972), model 2: Eq. (18) by Sharma et al. (1981). purpose) for the methane oxygen reaction which fits their experimental data, d[ch 4 ] dt ( ) 10 exp 13.2±0.20 RT [CH 4 ] 0.7 [O 2 ] 0.8 mole cm 3 s 1, (82) (R in cal mol 1 K 1 ). Since the overall reaction order is equal to the sum of the exponents of the reactant concentrations, this expression implies that the methane oxygen reaction has an overall reaction order of 1.5. On the assumption that the flame temperature is not affected by pressure and temperature, substitution of this value into Eq. (72) in combination with the estimates for c in Eq. (76) indicates that a must have a value close to 0.5 and that it must be in the range from 0.41 to Determination of the laminar burning velocity from closed vessel deflagrations This section describes how the thin-flame model and the three-zone model can be used to find the laminar burning velocity from the pressure time curve of a deflagration in a closed vessel. For this purpose, a number of gas explosions were carried out in the strengthened 20-l sphere described in Dahoe et al. (1995) and Dahoe (2000). All experiments were carried out with quiescent methane air mixtures at initial conditions of 1 bar and K, and the equivalence ratio was varied from 0.67 to A spark was used to ignite the mixtures at the center of the vessel to deflagration. The experimental pressure time curves are shown in Fig. 6. In all experiments, the pressure is seen to behave as follows. After ignition, the pressure in the explosion vessel increases progressively until the rate of pressure rise achieves a maximum (the maximum rate of pressure rise, (dp/dt) max ) and continues to increase towards a maximum (the maximum explosion pressure, P max ) with a decreasing rate of pressure rise. After completion of the explosion, the pressure is seen to decrease. To enable a comparison between our measurements and work by other researchers, the explosion severity parameters (P max and (dp/dt) max ) of our explosion curves are presented together with values reported by Cashdollar and Hertzberg (1985) in the lower part of Fig. 6. These authors used a 20-l explosion vessel which was not spherical, but consisted of a cylinder with a hemispherical bottom and top. Our explosion severity parameters are found to be in agreement with those of Cashdollar

86 470 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Fig. 6. Measured explosion pressure curves of fuel lean to stoichiometric methane air mixtures, the maximum explosion pressure, the maximum rate of pressure rise, and K G values ( our results, Cashdollar & Hertzberg, 1985). and Hertzberg for off-stoichiometric mixtures, but differences may be observed with near-stoichiometric mixtures. With stoichiometric mixtures, discrepancies of 6% and 13% are observed in P max and (dp/dt) max. Bartknecht (1981) measured the explosion behavior of stoichiometric methane air mixtures in a 20-l explosion sphere and found a P max of 8.4 bar and a K G value 5 of 55 bar 5 The K G value, also known as the gas explosions severity index, is a quantity which forms the design basis of a great deal of practical safety measures. It is defined as the product of the maximum rate of pressure rise and the cube-root of the volume of the explosion vessel, K G = (dp/dt) max V 1/3, and believed to be a mixture specific explosion severity index. The K G value was defined in this way because it was believed that maximum rates of pressure rise measured in differently sized vessels would become volume-invariant if they were multiplied by the cube-root of the volume. The practical significance of this quantity rests on the assumption that once it is known for a particular mixture from an experiment in a small laboratory test vessel, the maximum rate of pressure rise in a larger industrial vessel is predicted correctly by dividing it by the cube-root of the larger volume. ms 1. Our measurements show that for stoichiometric methane air mixtures, P max is 8.7 bar and K G is 80 bar ms 1. The occurrence of an inflection point in all our pressure time curves is attributed to the effect of buoyancy. Due to the density difference between the hot combustion products and the cold unburnt mixture, a flame ball accelerates in the upward direction while reactants are being consumed by the expanding flame surface. During this process, the pressure in the vessel increases with an increasing rate of pressure rise until the upper part of the flame reaches the wall. From this point onwards, there is still an amount of unburnt mixture is being consumed by the lower part of the flame. As this remainder of unburnt mixture is being consumed, the flame area decreases. Hence the decrease of the rate of pressure rise and the occurrence of an inflection point. If the thin-flame model and the three-zone model were to be fitted to the entire explosion curve, this process would bias the optimal

87 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) value of the burning velocity. To minimize the influence of buoyancy, our models were fitted to an initial part of the experimental pressure curves on the basis of the following considerations. Sapko, Furno, and Kuchta, 1976 studied the effect of buoyancy on methane air nitrogen flames in a 12-ft diameter spherical explosion vessel. They observed that the velocity of the geometric center of the rising flame ball increased with time according to v c 117t 0.44 cm s 1. (83) Using this correlation, one finds a shift of the geometric center (i.e. y = 81t 1.44 ) of about 0.1 cm in 10 ms, 1 cm in 50 ms, 3 cm in 100 ms, and 8 cm in 200 ms. These displacements obviously become significant in comparison with the radius of the 20-l sphere (17 cm) at later times. A rising flame ball also has a tendency to change its shape because the movement of the upper half of the flame is assisted by buoyancy, while that of the lower part is being counteracted. As a result, the upper part of the flame maintains its spherical curvature, while the lower hemispherical part tends to flatten out. When v c is larger than the flame speed, the lower hemispherical part of the flame may even change its shape from convexity towards the unburnt mixture into concavity. This continual change in the shape of the flame undermines the assumption of a spherical flame surface in the thin-flame and the three-zone model. Sapko et al. (1976) observed that the radius of the flame ball grows in time as g flame 354t 1.13 cm. (84) From this information and Eq. (83) one finds the following values for the flame speed and the rising velocity as a function of time: 220 and 15 cm s 1 at 10 ms, 270 and 31 cm s 1 at 50 ms, 297 and 42 cm s 1 at 100 ms, and 325 and 58 cm s 1 at 200 ms. With the above estimations in mind, it was decided to fit the thin-flame model and the three-zone model to the part of the experimental curves where the pressure changed from 1.2 to 3.0 bar. The models were fitted to the experimental data by means of the Levenberg Marquardt method (Marquardt, 1963; Press, Teukolsky, Vetterling, & Flannery, 1992). More specifically, the routine mrqmin by Press et al. was extended to enable the fitting of a differential equation by its numerical solution to a set of discrete data points. The numerical solution of the differential equations that constitute the thinflame and the three-zone model was calculated by means of a fourth order Runge Kutta method, using the routine rkdumb by the same authors. For the thin-flame model, Eqs. (19) and (23) were used to describe the effect pressure and temperature on the laminar burning velocity and the optimal values of S ul and b 2 were sought. Redundancy in the degrees of freedom was avoided by keeping b 1 at a fixed value of For the three-zone model, Eqs. (76) and (77) were used to describe the dependence of the laminar burning velocity and the laminar flame thickness on pressure and temperature. The optimal values of S ul, c and a were sought by fitting the three-zone model to the experimental pressure time curves. The reference laminar flame thickness, d L, however, was kept at a fixed value of 1.0 mm. The upper-left part of Fig. 7 shows a comparison between the predicted pressure curves and the experimental data of a stoichiometric methane air explosion. The model curves are seen to be in good agreement with the experimental data and the corresponding results of the fit are shown in Table 2. With both integral balance models, the regression analysis yields a value of about cm s 1 for the initial laminar burning velocity, S ul, which is within the scatter of values reported by other researchers: 42 cm s 1 (Andrews & Bradley, 1972), 38 cm s 1 (Bradley, Gaskell, & Gu, 1996), 40 cm s 1 (Law, 1993: Chapter 2) and 37 cm s 1 (van Maaren, Thung, & de Goey, 1994). The optimal value of b 2 in Eq. (19) is about 0.36, which is close to the expected value of 0.28 and within the range from 0.40 to In case of Eq. (19), b 2 assumed a value of 0.46, which is close to the expected value of 0.41 and within the range from 0.60 to The values of c and a, namely, 0.27 and 0.52, are also close to the expected values of 0.25 and 0.5. These values are also within the error bands discussed in Section 5. All experimental pressure time curves were processed in this manner and the results are presented in Figs. 7 and 8. The corresponding numerical values with error estimates are shown in Tables 5 and 6. The lower-left part of Fig. 7 shows the laminar burning velocity as a function of the equivalence ratio. The shaded region represents the band of data shown in Fig. 3 and the markers correspond to the laminar burning velocity obtained by fitting the thin-flame model and the three-zone model. For the entire range of equivalence ratios investigated, our results are seen to be within the band of data reported by other researchers. Although scatter may be observed in our data, there appears to be no systematic difference between laminar burning velocities obtained on the basis of Eqs. (19),(23), or (76). It appears to arise from the scatter in the experimental pressure time curves (compare the scatter of the laminar burning velocity at a particular equivalence ratio with the difference between the corresponding experimental pressure time curves). The value of b 2 in Eqs. (19) and (23) appears to be decreasing as a function of the equivalence ratio and all values fall within the band of uncertainty (see the upper part of Fig. 8). When the following model is fitted to the data in the upper-left part of the figure, b 2 a 0 a 1 (f 1), (85)

88 472 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Fig. 7. Upper left: Correspondence between the model predictions and the experimental pressure curve for a stoichiometric methane air mixture. Upper right: Laminar flame thicknesses from the literature. Lower left: Comparison between our laminar burning velocities and literature data. Lower right: Comparison between our values and recent data. Andrews and Bradley (1972), Dixon-Lewis and Williams (1967), Janisch (from Andrews and Bradley, 1972), Dixon-Lewis and Wilson (1951), van Maaren et al. (1994), Bosschaart and de Goey (2003), Gu et al. (2000), Vagelopoulos and Egolfopoulos (1998). thin-flame model with Eq. (19), thin-flame model with Eq. (23), three-zone model with Eq. (76). Table 2 Optimal values of the various degrees of freedom in thin-flame and the three-zone model Parameter Value ± StdErr Thin-flame model Three-zone model Eq. (19) Eq. (23) Eqs. (76) and (77) S ul ( 10 4 ms 1 ) ± ± ± d L ( 10 3 m) 1.0 (fixed) b 1 ( 10 3 ) 1.89 (fixed) 1.89 (fixed) b 2 ( 10 3 ) ± ± 8.31 c ( 10 3 ) ± 4.16 a ( 10 3 ) ± 4.16 For a 95% confidence interval, multiply StdErr by

89 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Fig. 8. Optimal value of the exponents b 2, a and c in Eqs. (19), (23) and (76), as a function of the equivalence ratio. one finds that a 0 = ( ± 1.7) 10 3 and a 1 = ( 55.4 ± 8.4) These results are consistent with Eq. (21) as far as it concerns the value of a 0 and the decreasing trend with equivalence ratio. The value of a 1, however, appears to be about 20% of the slope of Eq. (21). An even greater discrepancy may be observed between the trend of the data in the upper-right part of Fig. 8 and Eq. (25): our data appear to decrease with increasing equivalence ratios while Eq. (25) suggests an increase. When Eq. (85) is fitted to these data one finds that a 0 = ( ± 4.2) 10 3 and a 1 = ( 10.7 ± 2.0) The laminar flame thickness at reference conditions, d L, was kept at a constant value of 1 mm in the application of the three-zone model to the experimental explosion curves. This value was chosen on the basis of observations reported by other researchers (see the upper-right part of Fig. 7) and the resulting laminar burning velocity is close to those obtained with the thin-flame model (see Table 2). The lower part of Fig. 8 indicates that the optimal values of c and a are close to the estimates made in the previous section. It should be emphasized that, in spite of the fact that the laminar burning velocities found in the present work appear to be within the band of data collected from the literature, far better methods are available to determine this quantity. This becomes evident when our results are compared with recent data on the laminar burning velocity of methane air mixtures which are currently believed to be the correct ones (see the lower-right part of Fig. 7). Obviously, our laminar burning velocities are systematically higher and this discrepancy is most severe when the stoichiometric limit is approached. At the stoichiometric concentration our method gives a laminar burning velocity of cm s 1. The methods used by other researchers indicate a value of 37 cm s 1. The cause of this discrepancy is due to the fact that the experimental information used by our method is too limited to compensate problems arising from buoyancy, flame front instability, and flame stretch. Additional measurements of flame position and flame shape would be necessary to improve the accuracy. The sensitivity of the degrees of freedom in Eqs. (76) and (77) was investigated by varying the flame thickness and the results are presented in Table 3. It is seen that a change in the laminar flame thickness by a factor of 8 is accompanied by a negligible change in the other degrees of freedom. This low sensitivity to variations in d L is caused by the fact that the volume occupied by the flame zone is small in comparison with that of the explosion vessel. As a result, variations in the thickness of the flame zone have little effect on the overall pressure. This low sensitivity is also reflected by the inaccuracy in the flame thickness when it is fitted as a degree of freedom. Table 4 shows the behavior of the inaccuracy in the flame thickness when the three-zone model is

90 474 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Table 3 Effect of flame thickness on the optimal values of the degrees of freedom in Eqs. (76) and (77) Fixed Value ± StdErr d L ( 10 3 m) S ul ( 10 4 ms 1 ) c ( 10 3 ) a ( 10 3 ) ± ± ± ± ± ± ± ± ± ± ± ± 4.15 For a 95% confidence interval, multiply StdErr by Table 4 Accuracy of the optimal value of the laminar flame thickness in the three-zone model Value ± StdErr Fixed d L ( 10 5 m) S ul ( 10 4 ms 1 ) c ( 10 3 ) a ( 10 3 ) ± ± ± ± For a 95% confidence interval, multiply StdErr by fitted to the experimental pressure time curve with the optimal values of S ul, c and a from Table 3 as constants. Ideally, one would expect laminar flame thicknesses which are close to the ones shown in Table 3, with a small degree of uncertainty. It is seen, however, that the optimal value in Table 4 which corresponds to a flame thickness of 0.5 mm deviates by about 30%. The uncertainty is a factor of 400 larger than the optimal flame thickness itself. Both the deviation of the optimal flame thickness as well as the uncertainty appears to decrease significantly as the flame thickness becomes larger. With a flame thickness of 4 mm, the deviation is less than 0.5% from the expected value and the uncertainty is about 3%. 7. Conclusions The potential of the idea of finding the laminar burning velocity of a combustible mixture by fitting the integral balance models of DZLS to the experimental pressure time curve of an explosion in a closed vessel was explored. The conclusions arising from this investigation are summarized as follows. Because the laminar burning velocity and the laminar flame thickness are known to depend pressure and temperature, correlations have been sought to incorporate this sensitivity into the integral balance models. The thin-flame model required a correlation for the burning velocity only. A number of correlations proposed by other researchers have been reviewed and two, namely, Eqs. (19) and (23), were found to be suitable for the aim of the present work. The three-zone model required an additional expression for the effect of pressure and temperature on the flame thickness. Hence, a new set of correlations has been derived from first principles. These correlations, namely, one for the laminar burning velocity, Eq. (76), and one for the laminar flame thickness, Eq. (77), are strongly coupled because they have two degrees of freedom, c and a, in common. This coupling arises from first principles and appears to be of crucial importance: it was observed that redundancy occurred in its absence (i.e. if the exponents c +(g 1)/g 1 +a and c a were replaced by totally independent degrees of freedom). To verify the methodology proposed in this work, a number of methane air explosions were carried out in a 20-l sphere. The equivalence ratio was varied between 0.67 and 1.36, and the pressure time curve was measured. Explosion severity parameters which are commonly used as a design basis for the protection and suppression of accidental explosions (P max and (dp/dt) max ) were determined from these curves and compared with results reported by other researchers. While good agreement exists between our findings and those of Cashdollar and Hertzberg with off-stoichiometric mixtures, an increasing discrepancy may be observed when the stoichiometric limit is approached from either side. With stoichiometric mixtures, a difference of 6% is observed in the value of P max and a difference of 13% in case of

91 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Table 5 Optimal values of the degrees of freedom in Eqs. (19) and (23). The parameter b 1 was kept at a fixed value of 1.89 No. f S ul = S T u ul T u0 b 1 1 +b 2 ln P P 0 S ul = S T u ul T u0 b1 P b 2 P 0 S ul ± StdErr 10 4 (m/s) b 2 ± StdErr 10 3 S ul ± StdErr 10 4 (m/s) b 2 ± StdErr ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 5.51 (dp/dt) max. When our results are compared with those of Bartknecht, a smaller discrepancy exists in P max, but a larger difference may be observed in the maximum rate of pressure rise. We found a K G value of 80 bar m s 1 while Bartknecht measured a value of 55 bar m s 1. The practical consequence of this observation is that explosion hazards are systematically being underestimated because a K G value of 55 bar m s 1 is widely believed to be the correct explosion severity index of stoichiometric methane air mixtures. The thin-flame model and the three-zone model were fitted to the pressure time curves of the methane air explosions and the laminar burning velocity was determined as a function of equivalence ratio. Our laminar burning velocities are found to be within the data band of those reported by other researchers (see Fig. 7). The scatter in our laminar burning velocities arising from the use of two different integral balance models, as well as the incorporation of a variety of correlations (i.e. Eqs. (19),(23) and (76)), appears to be insignificant in comparison with the scatter caused by the variation between pressure time curves measured at one particular equivalence ratio. The optimal value of b 2 in Eqs. (19) and (23), as well as that of c and a in Eqs. (76) and (77), are also seen to be in agreement with estimates made on the basis of literature data (see Fig. 8). It was discussed in the previous section that, although our laminar burning velocities appear to fall within the data band of values reported by other researchers, the method explored in the present work should not be the first choice if one desires to know the laminar burning velocity of a combustible mixture. In fact, it should only be used when there is no better alternative. This may be the case, for example, when an estimate is sought of the laminar burning velocity of a dust air mixture, a combustible spray, or a toxic gas mixture with unfavorable optical properties. There appeared to be a large uncertainty in the optimal value of the laminar flame thickness which was attributed to the fact that the laminar flame thickness of the

92 476 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Table 6 Optimal values of the degrees of freedom in Eqs. (76) and (77). The laminar flame thickness at reference conditions, d L, was kept at a fixed value of 1.0 mm No. f S ul = S P +(g 1)/g 1 +a and ul P 0 c d L = d P L P 0 c a S ul ± StdErr 10 4 (m/s) c ± StdErr 10 3 a ± StdErr ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 2.76 investigated mixtures is small in comparison with the radius of the 20-l sphere. It has also been observed that the uncertainty decreased to acceptable proportions when the flame thickness was increased to about 2% of the radius of the vessel (see Table 4). This implies that a 20-l explosion sphere is unsuitable if one desires to determine the laminar flame thickness of methane air mixtures with the methodology presented in this paper. An explosion vessel with a radius of no more than 50 times the laminar flame thickness would have to be used. References Agnew, J. T., & Graiff, L. B. (1961). The pressure dependence of laminar burning velocity by the spherical bomb method. Combustion and Flame, 5, Andrews, G. E., & Bradley, D. (1972). The burning velocity of methane air mixtures. Combustion and Flame, 19, Babkin, V. S., and Kozachenko, L. S. (1966). Study of normal burning velocity in methane air mixtures at high pressures. Fizika Goreniya i Vzryva, 2(3), (English translation: Combustion, Explosion and Shock Waves, 2, 46 52). Babkin, V. S., Kozachenko, L. S., & Kuznetsov, I. L. (1964). The effect of pressure on the normal burning velocity of a methane air mixture. Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fizika, 3, (English translation in 1966 by Scripta Technica, Inc., 275 Madison Avenue, New York 16, NY. Translated for the US Department of the Interior, Bureau of Mines, Washington, DC). Barassin, A., Lisbet, R., Combourieu, J., & Laffitte, P. (1967). Etude de l influence de la temperature initiale sur la vitesse normale de deflagration de melanges methane air en fonction de la concentration. Bulletin de la Societe Chimique de France, 104(7), Bartknecht, W. (1981). Explosions: Course prevention protection. Springer Verlag (Translation of Burg, H., and Almond, T. Explosionen, Ablauf und Schutzmabnahmen (2nd ed.)). Bosschaart, K. J., & de Goey, L. P. H. (2003). Detailed analysis of the heat flux method for measuring burning velocities. Combustion and Flame, 132, Bradley, D., Cresswell, T. M., & Puttock, J. S. (2001). Flame acceleration due to flame-induced instabilities in large-scale explosions. Combustion and Flame, 124,

93 A.E. Dahoe, L.P.H. de Goey / Journal of Loss Prevention in the Process Industries 16 (2003) Bradley, D., Gaskell, P. H., & Gu, X. J. (1996). Burning velocities, Markstein lengths, and flame quenching for spherical methane air flames: a computational study. Combustion and Flame, 104, Bradley, D., & Harper, C. M. (1994). The development of instabilities in laminar explosion flames. Combustion and Flame, 99, Bradley, D., Hicks, R. A., Lawes, M., Sheppard, C. G. W., & Woolley, R. (1998). The measurement of laminar burning velocities and Markstein numbers for iso-octane air and iso-octane n-heptane air mixtures at elevated temperatures and pressures in an explosion bomb. Combustion and Flame, 115, Bradley, D., and Hundy, G. F., Burning velocities of methane air mixtures using hot-wire anemometers in closed-vessel explosions. In Proceedings of the Thirteenth Symposium (International) on Combustion (pp ). The Combustion Institute, Bradley, D., Sheppard, C. G. 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95 International Journal of Hydrogen Energy 32 (2007) On the development of an International Curriculum on Hydrogen Safety Engineering and its implementation into educational programmes A.E. Dahoe, V.V. Molkov FireSERT, University of Ulster, Newtownabbey, BT37 0QB, Northern Ireland, UK Received 23 May 2006; received in revised form 6 July 2006; accepted 6 July 2006 Available online 7 September 2006 Abstract The present paper provides an overview of the development of an International Curriculum on Hydrogen Safety Engineering and its implementation into new educational programmes. The curriculum is being developed as part of the educational and training activities of the European Network of Excellence Safety of Hydrogen as an Energy Carrier (HySafe). It has a modular structure consisting of five basic, six fundamental and four applied modules. The reasons for this particular structure are explained. To accelerate the development of teaching materials and their implementation in training/educational programmes, an annual European Summer School on Hydrogen Safety will be held (the first Summer School was from August 2006, Belfast, UK), where leading experts deliver keynote lectures to an audience of researchers on topics covering the state-of-the-art in hydrogen safety science and engineering. The establishment of a postgraduate certificate course in hydrogen safety engineering at the University of Ulster (starting in January 2007) as a first step in the development of a worldwide system of hydrogen safety education and training is described International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Hydrogen safety; Education; Hydrogen economy 1. Introduction Hydrogen safety is known to be of vital importance to the onset and further development of the hydrogen economy. The development and introduction of hydrogen technologies, as well as the level of public acceptance of hydrogen applications, are presently being constrained by safety barriers. Hydrogen is perceived to be dangerous because it has some properties that make its behaviour during accidents different from that of most other combustible gases. It may cause material embrittlement and diffuses more easily through many conventional materials used for pipelines and vessels. Gaps that are normally small enough to seal other gases safely are found to leak hydrogen profusely. Unlike other combustible gases, it has a Joule Thompson inversion temperature (i.e. the temperature above which the Joule Thompson coefficient becomes negative and expansion leads to warming instead of cooling) which is well below that of many applications involving gaseous Corresponding author. Tel.: ; fax: address: ae.dahoe@ulster.ac.uk (A.E. Dahoe). hydrogen. This makes hydrogen more susceptible to ignition after sudden releases from high pressure containment. When hydrogen s greatest safety asset, buoyancy, is not properly taken into account in the design of infrastructures and technologies for production, storage, transportation and utilisation, it becomes more dangerous than conventional fuels such as gasoline, LPG and natural gas. Many countries building codes, for example, require garages to have ventilation openings near the ground to remove gasoline vapour, but high-level ventilation is not always addressed. As a result, even very slow releases of hydrogen in such buildings will inevitably lead to the formation of an explosive mixture, initially at the ceiling-level. The safety and combustion literature indicates that releases of hydrogen are more likely to cause explosions than releases of today s fossil fuels do. Moreover, combustion insights have revealed that burning behaviour becomes far less benign when the limiting reactant is also the more mobile constituent of a combustible mixture [1]. Owing to the extreme lightness of the molecule, this is particularly true with hydrogen. A mixture of hydrogen with air has a lower flammability limit which is higher than that of LPG (1.7% [2]) or gasoline (1.0% [2]), but the flammable /$ - see front matter 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi: /j.ijhydene

96 1114 A.E. Dahoe, V.V. Molkov / International Journal of Hydrogen Energy 32 (2007) range is very wide (4 75%) [2]. In the concentration range of 15 45%, the ignition energy of hydrogen is one-tenth of that of gasoline and the quenching gap, i.e. the smallest spacing through which a flame can propagate, is considerably smaller for hydrogen (0.61 mm [3]) than for today s fossil fuels (2.0 mm for methane, 1.8 mm for ethane and propane [3]). This implies that requirements for mitigation, such as flame arrestors and similar equipment, must be more stringent. For many decades, hydrogen has been used extensively in the process industries (e.g. refineries and ammonia synthesis) and experience has shown that it can be handled safely in industrial applications as long as appropriate standards, regulations and best practices are being followed. This is particularly true for the nuclear industry, where the high safety standards have resulted in the development of sophisticated hydrogen mitigation technologies [4]. Interestingly, these technologies rely on the same anomalous properties, such as the large diffusivity and extreme lightness that make hydrogen so different compared to conventional fuels. For example, these properties are used to preclude the formation of flammable mixtures after accidental hydrogen releases, and to prevent further development towards more dangerous concentrations, once the flammability limit is exceeded (hydrogen removal by buoyancy, application of catalytic re-combiners, or benign burns, dilution by mixing with an inert gas, e.g. steam). This experience, however, is very specific and cannot easily be transferred to the daily use of new hydrogen technologies by the general public. Firstly, because new technologies involve the use of hydrogen under circumstances that are not yet addressed by research, or taken into account by existing codes and recommended practices. For example, vehicle demonstration projects by manufacturers involve the use of hydrogen as a compressed gas at extremely high pressures (over 350 bar), or, in liquefied form at an extremely low temperature ( 253 C). There is no precedent for the safe handling of hydrogen by the general public at such conditions and current codes and standards for hydrogen were not written with vehicle fueling in mind. Secondly, in industries, hydrogen is handled by people who received specific training at a professional level, and, installations involving hydrogen are subject to professional safety management and inspection. The hydrogen economy, on the other hand, involves the use of hydrogen technologies by general consumers and a similar dedication to safety, e.g. training general consumers to a professional level, would become impractical. The safety of hydrogen technologies and applications must therefore be ensured before entering the consumer market. Presently, public acceptance and understanding of the safety of hydrogen is such that accidents with hydrogen not only cause resistance to its use, but also cause people to disregard social, economic, political and environmental improvements that may result from a hydrogen economy. Currently, hydrogen is being produced from fossil fuels, particularly from natural gas by steam reforming. But it can also be produced from a variety of other sources (e.g. nuclear, geothermal, solar, wind, hydroelectric plants, biomass, etc.), some of which can operate at large and small scale in areas that are currently suffering fuel poverty. The replacement of fossil fuels by hydrogen from alternative sources will not only benefit people in fuel poverty areas by reducing their dependency on the diminishing resource of imported fossil fuels it might also enable fossil fuel importing economies to become leading exporters of hydrogen [5]. The consequential demand for ever increasing quantities of hydrogen, and the possibility of producing hydrogen in fuel poverty areas will lead to social improvement by employment opportunities [5]. The replacement of fossil fuels by hydrogen also contributes to averting disastrous effects from pollutant emissions and global warming. It is well-known that combustion products from fossil fuels cause health problems and acid rain due to emissions of particulates, carbon monoxide, sulfur and nitrogen oxides, and other local air pollutants. Continued fossil fuel consumption will not only increase the number of pollution related deaths in cities like Delhi, Beijing and Mexico City [5], but also the magnitude of problems involving reduced agricultural productivity and the loss of biodiversity [5]. There is also an increasing scientific community which has come to the belief that the use of fossil fuels is causing the world s climate to change because of carbon dioxide emissions [5]. Hydrogen is a clean fuel with no carbon dioxide emissions and can be produced by carbon-free or carbon-neutral processes. When utilised in combustion processes, it produces water only, and reduced amounts of nitrogen oxides. Educational and training programmes in hydrogen safety are considered to be a key instrument in lifting barriers imposed by the safety of hydrogen. Owing to the impracticality of training general consumers to a professional level in hydrogen safety, such training programmes should primarily target professionals engaged in the conception or creation of new knowledge, products, processes, methods, systems, regulations and project management in the hydrogen economy. Between this community of scientific and engineering professionals, including entrepreneurs developing hydrogen technologies, and general consumers of hydrogen applications, there is another group of vital importance to the successful introduction of hydrogen into our social infrastructure that needs to be targeted as well. These are the educators, local regulators, insurers, fire brigades and rescue personnel, investors, and public service officials. Their involvement is indispensable to the acceptance and use of the new technology by the general public, and hence a consolidated consumer market as the principal driving force behind the hydrogen economy. Without their involvement there will be no transition from our present fossil-fuel economy into a sustainable one based on hydrogen. With this in mind, the European Network of Excellence Safety of Hydrogen as an Energy Carrier (NoE HySafe) has begun to establish the e-academy of hydrogen safety. The e-academy of hydrogen safety is part of the dissemination cluster of the NoE HySafe, whose objectives are [6,7]: (i) to achieve common understanding and common approaches for addressing hydrogen safety issues; (ii) to integrate experience and knowledge within industrial organisations familiar with hydrogen processing technology and research organisations with facilities for experimental research and exploitation of results from numerical prediction tools; (iii) to integrate and harmonise the fragmented research base; (iv) to provide

97 A.E. Dahoe, V.V. Molkov / International Journal of Hydrogen Energy 32 (2007) contributions based on safety and risk studies to EU-legal requirements, standards, codes of practice and guidelines; (v) to support education and training in hydrogen safety to achieve an improved technical culture for the safe handling of hydrogen as an energy carrier. To establish the e-academy of hydrogen safety, the following activities are employed: (i) development of international curriculum on hydrogen safety engineering; (ii) coherent implementation of teaching/learning on hydrogen safety into existing courses and modules; (iii) development of new courses and modules, including optional modules for existing safety courses; (iv) joint training exploiting different modes of education: short courses, summer schools, block-releases, continuous professional development courses, etc.; (v) creation of a pool of specialists from both academic and non-academic institutions able to deliver teaching on hydrogen safety engineering at the highest level by introduction of latest research results into the educational process; (vi) promotion of academic mobility programmes, e.g. by integration of regional academic programmes into a common European course on hydrogen safety engineering with the possibility to distribute course modules in different countries; (vii) joint supervision of research (PhD) students; (viii) creation of a database of organisations working in hydrogen industry to form a market of potential trainees and to disseminate the results from mutual activities of the network; (ix) and the introduction of joint distance teaching/learning courses in hydrogen safety on the international market. Due to the absence of a curriculum on the subject, a substantial effort is being devoted to the development of an International Curriculum on Hydrogen Safety Engineering as a first step in the establishment of the e-academy of hydrogen safety. The development of the International Curriculum on Hydrogen Safety Engineering is led by the University of Ulster and carried out in cooperation with international partners from four other universities (Universidad Politecnica de Madrid, Spain; University of Pisa, Italy; Warsaw University of Technology, Poland; University of Calgary, Canada), three research institutions (Forschungszentrum Karlsruhe and Forschungszentrum Juelich, Germany; Building Research Establishment, United Kingdom), one enterprise (GexCon, Norway) and one foundation (Det Norske Veritas, Norway). This development is also aided by experts from within the NoE HySafe and external experts from all over the world (see Table 1), representing educational institutions, research organisations, industrial corporations and governmental bodies. This paper exposes the current structure of the International Curriculum on Hydrogen Safety Engineering, the motivation behind it, and further steps in the development of a system of hydrogen safety education and training are described. 2. The International Curriculum on Hydrogen Safety Engineering 2.1. Motivation Sufficient and well-developed human resources in hydrogen safety and related key areas are of vital importance to Table 1 List of contributors to the draft for development of the International Curriculum on Hydrogen Safety Engineering Adams, P. Volvo Technology SE Amyotte, P.R. Dalhousie University CA Baraldi, D. The European Commission s Joint NL Research Center Bauwens, L. University of Calgary CA Bell, J.B. Lawrence Berkeley National Laboratories US Bjerketvedt, D. Telemark University NO Bradley, D. University of Leeds UK Braken, A.M. van den Akzo-Nobel Safety Services NL Cant, R.S. University of Cambridge UK Carcassi, M. University of Pisa IT Crespo, A. Universidad Polytecnica de Madrid ES Dahoe, A.E. University of Ulster UK Donze, M. Delft University of Technology NL Dorofeev, S.B. FM Global US Engebo, A. Det Norske Veritas NO Fairweather, M. University of Leeds UK Faudou, J.-Y. Air Liquide FR Gallego, E. Universidad Polytecnica de Madrid ES Garcia, J. Universidad Polytecnica de Madrid ES Hansen, O. GexCon NO Jordan, T. Institut fur Kern- und Energietechnik, DE Forschungszentrum Karlsruhe Hawksworth, S. Health and Safety Laboratory Kirillov, I. Kurchatov Institute RU Kuhl, A.L. Lawrence Livermore National US Laboratories Kumar, S. Building Research Establishment UK Law, C.K. Princeton University US Lee, J.H.S. McGill University CA Makarov, D.V. University of Ulster UK Makhviladze, G. University of Central Lancashire UK Marangon, A. University of Pisa IT Martinfuertes, F. Universidad Polytecnica de Madrid ES Migoya, E. Universidad Polytecnica de Madrid ES Molkov, V.V. University of Ulster UK Nilsen, S. Norsk Hydro NO Palliere, H. Commissariat a l Energie Atomique FR Pasman, H.J. Delft University of Technology NL Reinecke, E. Forschungszentrum Juelich DE Roekaerts, D.J.E.M. Delft University of Technology NL Schitter, C. BMW DE Schneider, H. Fraunhofer Institut Chemische DE Technologie Shebeko, Yu. N. All-Russian Scientific Research RU Institute for Fire Protection Simmie, J.M. National University of Ireland IE Tchouvelev, A.V. Tchouvelev and Associates CA Teodorczyck, A. Warsaw University of Technology PL Tsuruda, T. NRIFD JP Westbrook, C.K. Lawrence Livermore National US Laboratories Williams F.A. University of California, San Diego US the emerging hydrogen economy. With our present fossil-fuelbased economy increasingly being replaced by a hydrogen economy, a shortfall in such knowledge capacity will hamper Europe s innovative strength and productivity growth. A lack of professionals with expert knowledge in hydrogen safety and related key areas will not only impose a serious setback on

98 1116 A.E. Dahoe, V.V. Molkov / International Journal of Hydrogen Energy 32 (2007) innovative developments required to propel this transition, but also thwart ongoing efforts to achieve public acceptance of the new technology. Recently, the European Commission identified a shortage of experts in the key disciplines (natural sciences, engineering, technology [8 10]) relevant to hydrogen safety. The workforce in R&D is presently relatively low, as researchers account for only 5.1 in every thousand of the workforce in Europe, against 7.4 in the US and 8.9 in Japan [10,11]. An even larger discrepancy is observed if one considers only the number of corporate researchers employed in industry: 2.5 in every thousand in Europe, against 7.0 in the US and 6.3 in Japan [9]. Moreover, the number of young people attracted to careers in science and research appears to be decreasing. In the EU, 23% of the people aged between 20 and 29 years are in higher education, compared to 39% in the USA [10]. Knowing that research is a powerful driving force for economic growth, and a continuous supply of a skilled workforce is of paramount importance to the emerging hydrogen economy, this situation calls for drastic improvement. To explore possibilities for improvement it would be helpful to consider what might have caused this situation in the first place. Firstly, there are the quality and attractiveness of Europe for investments in research and development in relation to that of other competing knowledge economies. The quality of research, and the number of young people embarking on higher education in natural sciences, engineering, and technology, depend primarily on investments made in R&D-activities. Presently, this amounts to 1.96% of GDP in Europe, against 2.59% in the United States of America, 3.12% in Japan and 2.91% in Korea. The gap between the United States of America and Europe, in particular, is more than 120 billion euro a year [8], with 80% of it due to the difference in business expenditure in R&D. At this point it is important to notice that the quality of the European research base will not improve, unless larger investments are made in R&D. It has been diagnosed [12] that multinational companies accounting for the greater share of business R&D expenditure, increasingly tend to invest on the basis of a global analysis of possible locations. This results in a growing concentration of transnational R&D expenditure in the United States of America. Moreover, there appears to be a decline in the global attractiveness of Europe as a location for investment R&D as compared to the United States of America. This alarming development could be reversed by improving the quality of the European research base, such that corporate investments in R&D are increased to 3% of GDP in Europe [12]. Secondly, there is the problem of a retiring science and technology workforce that needs to be succeeded by a younger generation of experts. The identified lack of experts in natural sciences, engineering, and technology creates an unstable situation for investment in R&D. This is particularly true if one considers that innovative developments take place over a timespan of several years. No investor will commission research projects to a retiring workforce without a prospect of succession by a capable younger generation. Thirdly, there is the problem of changes in the skill-set sought by employers and investors. The purpose of science and engineering education is to provide the graduate with sufficient skills to meet the requirements of the professional career, and a broad enough basis to acquire additional skills as needed. Because of the transitional nature of the hydrogen economy, and the consequential development and implementation of new technologies, the skill-set sought by employers is expected to change more rapidly than ever before. This phenomenon has already manifested itself in the information technology sector, and is anticipated to occur in the hydrogen economy as well. Science and engineering education related to the hydrogen economy must therefore be broad and robust enough, such, that when today s expert-skills have become obsolete, graduates possess the ability to acquire tomorrow s expert-skills. The International Curriculum on Hydrogen Safety Engineering, aims at tackling these three causes of detriment to Europe s research base and innovation strength by extracting the state-of-the-art in hydrogen safety and related key areas, and by the rapid dissemination of this knowledge at all levels in higher and further education and training. According to the Strategic Research Agenda [13], which acts as a guide for defining a comprehensive research programme that will mobilise stakeholders and ensure that European competences are at the forefront of science and technology worldwide, education will continue to play a pivotal role in spreading hydrogen applications to the broader public until In the short term outlook from 2005 to 2015, training and education efforts are needed to build the necessary human resources to lead research and to allow a steady stream of trained scientists and technicians to develop the area. The Workgroup on Cross Cutting Issues [14], dealing primarily with the non-technical barriers to the successful implementation of the deployment strategy for hydrogen and fuel cells in Europe, indicates that educational and training efforts are needed during this period to avoid any dissonances that might hinder the building of consumer and non-technical executive confidence. The Workgroup on Cross Cutting Issues [14] has estimated that during the framework 7 period ( ), the educated staff needed may amount to 500 new graduates from postgraduate studies on an annual basis in all of Europe. The hydrogen economy requires professionals with a postgraduate degree dedicated to hydrogen safety, which is a subset of the aforementioned 500 new graduates. A preliminary study (see Section 2.3) indicates that this subset amounts to 119 graduates on an annual basis. Because graduates in hydrogen safety will be involved in all aspects of the hydrogen economy to ensure safety, it is important that the following issues are taken into account by the curriculum: what kind of organisations will employ graduates in hydrogen safety (process industry, energy industry, civil works, aerospace industry, automotive industry, transport and distribution, fire and rescue brigades, insurance, teaching institutions, research institutions, legislative bodies, etc.), at what level will graduates in hydrogen safety operate within the organisation (consulting, manufacture, design, teaching, research, operation, construction, legislation, etc.), and, which mode of education is the most appropriate to match the skill-set sought at the various levels of engagement within these organisations (undergraduate education, postgraduate

99 A.E. Dahoe, V.V. Molkov / International Journal of Hydrogen Energy 32 (2007) degree, continuing professional development, short courses, etc.). Moreover, the undergraduate programme should be wellrounded in the engineering science core (see Fig. 1) and supplemented by topics and additional courses with an emphasis on hydrogen safety. Duplication of educational efforts may be avoided by defining hydrogen safety engineering in relation to other branches of engineering, and cross-fertilisation with existing engineering programmes may be achieved by the introduction of topics relevant to hydrogen safety into the engineering science core. The postgraduate programme consists of specialised courses covering the nodes of the HySafe activity matrix shown in Fig. 2. Because the topics connected to the nodes in Fig. 2 are subject to continuous development as the hydrogen economy evolves, the curriculum needs to be comprehensive enough to absorb these changes as new knowledge becomes available. Fig. 1. Hydrogen safety in relation to other branches of engineering science Structure of the curriculum To comply with the aforementioned requirements, the Draft for Development of the International Curriculum on Hydrogen Safety Engineering is designed to consist of basic modules, fundamental modules, and applied modules. This approach was inspired by Magnusson et al. [15], who adopted a similar approach for the development of a model curriculum for fire safety engineering. The current modular structure is summarised in Table 2, and the current detailed topical content of the Draft for Development of the International Curriculum on Hydrogen Safety Engineering is available at the e-academy page of the NoE HySafe ( = 68). The five basic modules, i.e. thermodynamics; chemical kinetics; fluid dynamics; heat and mass transfer; solid mechanics, are intended for undergraduate instruction (although these modules contain topics belonging to the postgraduate level). They are similar to any other undergraduate course in the respective subject areas, but comprehensive enough to provide a broad basis for dealing with hydrogen safety issues involving hydrogen embrittlement, unscheduled releases of liquefied and gaseous hydrogen, accidental ignition and combustion of hydrogen, etc. The purpose of these modules is twofold. Firstly, to enable the coupling of knowledge relevant to hydrogen safety into existing engineering curricula, and secondly, to support the knowledge framework contained in the fundamental and applied modules. The six fundamental modules, i.e. introduction to hydrogen as an energy carrier; fundamentals of hydrogen safety; release, mixing and distribution; hydrogen ignition; hydrogen fires; explosions: deflagrations and detonations, form the backbone of hydrogen safety. While these modules, except for the first one, are intended for instruction at the postgraduate level, their topical content may also be used to develop teaching materials for undergraduate instruction to supplement existing engineering curricula with courses dedicated to hydrogen safety. The topical content of these modules is connected to the nodes in the HySafe activity matrix. These topics are initially based on the existing literature, and updated continuously as new knowledge becomes available, particularly from the NoE HySafe. Fig. 2. The HySafe activity matrix.