Aspect Ratio Effects in Unvented and Vented Dust Explosions

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Aspect Ratio Effects in Unvented and Vented Dust Explosions F. Tamanini*,† †

Research Division, FM Global, Norwood, Massachusetts 02062, United States ABSTRACT: The sizing of vents for explosion protection of equipment and buildings depends on many characteristics of the system, including details of the geometry of the protected enclosure. Its aspect ratio (H/D) has been recognized as an important parameter, with the general result that volumes of greater H/D require larger vent areas. Published data on dust explosions in elongated enclosures have been used to develop a new correlation for this effect. The data are for two dusts, cornstarch and wheat flour, and were obtained from tests in volumes of 1, 9.4, and 20 m3, for a range of aspect ratios. The experimental results, which have been analyzed using modeling techniques developed at FM Global, have yielded a correlation that is validated against more than 200 points and includes the effect of the location of the ignition source. Comparisons with the formulas recommended in VDI 3673 (2002) (also EN 14491, 2006) and NFPA 68 (2007) have shown these alternative methods to yield predictions that either overpredict (VDI and EN) or are in general agreement (NFPA) with those from the present correlation.

1. INTRODUCTION The sizing of vents for dust explosion protection is based on parameters that define various characteristics of the system. These parameters can generally be grouped in two categories. The first, which defines the reactivity of the explosive mixture, includes two quantities: explosibility factor, Kst [bar m/s]; and maximum unvented pressure, Pmax [bar]. The second category includes variables that describe the geometry and the operating conditions of the vented system, such as the following: protected volume, V [m3]; volume aspect ratio, H/D [-]; vent area, Av [m2]; vent panel surface density, σv [kg/m2]; vent duct length, Ld [m]; vent relief pressure, Pstat [bar]; mixture initial pressure, P0 [bar]; and fraction of protected volume occupied by explosive mixture, Xr [-]. The use of only ten parameters to fully characterize the complex physical processes involved in vented dust explosions is reflective of the relative simplicity of the calculation methods used to determine the required protection. While the simplicity extends to the definition of the geometry, the introduction of the H/D aspect ratio as a separate factor underscores the recognition of the effect of this parameter on the required vent area. Experimental data have shown that, in general, high aspect ratio volumes require more venting than semicubical ones. The extent of the increase, however, has remained uncertain due to the perception that current recommendations may not have a sufficiently strong foundation. The study detailed in this paper was undertaken to bridge this gap. The analysis, which is mostly based on the results generated by Radandt and Shi,1 will show that the process is influenced by two competing effects. In an unvented explosion, an increase in the aspect ratio, at a constant vessel volume, causes the effective reactivity of the mixture, expressed by the normalized peak rate of pressure rise, to decrease. The reason is that the average distance traveled by the flame increases. When venting is applied, however, the same measure of reactivity increases over its unvented value, as the vent parameter increases. This is probably due to additional turbulence generated by the venting process as the flame travels the (longer) distance toward the vent opening. r 2011 American Chemical Society

The interpretation of published data has yielded a means to account for the dependence of the vent area on the H/D of the vessel, through a correlation that is validated against more than 200 data points. In addition to its theoretical underpinnings and broad experimental support, the new correlation has the advantage of allowing for the effect of the location of the ignition source to be included. Comparisons with the formulas recommended in VDI 36732 and NFPA 683 will show that these alternative methods yield predictions that either overpredict (VDI) or are in general agreement (NFPA) with those from the present correlation.

2. H/D EFFECTS BY CURRENT VENT SIZING METHODS The German guideline VDI 36732 contains an empirical recommendation for vent sizing that accounts for the effect of volume aspect ratio as an incremental increase over the vent area that would be required for a semicubical vessel. Since the exact same method has been carried over into the European standard EN 14491,4 all references made in this paper to the VDI method should also be understood to apply to the EN method. The increase is a function of H/D and of the reduced pressure in the enclosure, Pred. For the aspect ratio, H/D, a maximum value of 20 is allowed, limited such that the maximum vent area shall not be greater than the cross-sectional area of the vessel or silo. Furthermore, the correction goes to zero at Pred = 1.5 bar and higher. A similar correction for the vent area of elongated vessels is available in the NFPA 683 standard. The correlation for semicubical volumes applies up to H/D e 2. For greater values and up to H/D = 6, the standard recommends an empirical formula which, similar to the VDI 3673 (and EN 14491) case, prescribes the vent area as an adjustment to the value for H/D = 1 that is a Special Issue: Russo Issue Received: July 20, 2011 Accepted: November 8, 2011 Revised: November 7, 2011 Published: November 08, 2011 7636

dx.doi.org/10.1021/ie2015747 | Ind. Eng. Chem. Res. 2012, 51, 7636–7642

Industrial & Engineering Chemistry Research function of H/D and Pred. An assessment of the magnitude of the H/D corrections introduced by the NFPA and VDI treatments will be presented later in this paper.

3. AVAILABLE EXPERIMENTAL DATA Published information on H/D effects in dust explosions is fairly plentiful, if not always easy to interpret. Probably the most complete research was carried out by Radandt and Shi,1 whose results form the basis for much of the analysis presented here. This study includes several tests with cornstarch and wheat flour in vessels of 1 m3 volume and four aspect ratios: H/D = 1, 2, 4, and 6. The same authors also carried out tests in two 9.4-m3 vessels with aspect ratios of H/D = 1.5 and 3. The importance of this work lies in the fact that the 1-m3 tests were performed both under vented and unvented conditions. This is an unusual feature, since enclosures used in vented experiments often cannot take the pressure developed by an unvented explosion. In their report, Radandt and Shi1 also mention additional testing in a 9-m3 silo carried out by Kossebau.5 Hauert et al.6 also reported useful information from vented tests in a 9.4-m3 silo. The experiments involved three different types of dust dispersion: forced injection through a ring nozzle as well as pneumatic vertical and horizontal feeding. Since the different injection methods introduce different levels of turbulence, these tests are more useful in highlighting the impact of that variable rather than that of the aspect ratio of the vessel. Tests by Bartknecht7,8 in 20-m3 vessels have also been considered. The design recommendation in VDI 3673 (and EN 14491) is largely based on these data. The experiments in this case were carried out in two vessels: one of semicubical shape (H/D = 1), the other a silo with an aspect ratio of H/D = 6.25. Tests in the latter vessel were performed for vertical and horizontal orientations and with bottom and middle ignition. It appears that the upper bound to the silo data was actually used as the basis for the correlation in the VDI (and, therefore, EN) standard. Finally, there is the important contribution to the problem represented by the work done by Eckhoff9 in a 500-m3 silo with H/D = 4 and in a 236-m3 silo with H/D = 6. These experiments underscored the importance of turbulence in determining the overpressure generated by the explosion, though the bulk of the tests was actually performed with the dust cloud in near quiescent conditions. 4. EVALUATION OF EXPERIMENTAL DATA 4.1. Interpretation of Vented Test Data. The main purpose of vented explosion tests is to determine the maximum reduced pressure, Pred, produced by venting the reactive system of interest through an opening of area, Av. A direct comparison of the Pred values, while instructive, falls short of extracting sufficiently general information from the test results. The maximum rate of pressure rise during the vented explosion is another parameter, which is often used to characterize the results. The data analysis presented by most authors of experimental work is typically limited to a discussion of the variations of these two variables over the range of test conditions. A different approach has been used at FM Global to evaluate the impact of parameter changes on the behavior of explosions. It involves use of a validated model to determine the effective reactivity, Kv, of the mixture during venting. Data comparisons and generalizations are then carried out by consideration of these

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calculated values of reactivity, rather than by reference to the raw data for Pred. The determination of Kv will be described by reference to the modeling approach introduced by Tamanini and Valiulis.10 The theoretical basis for the vent sizing method developed at FM Global is a model for the relationship between a normalized reduced pressure, Π, and a vent parameter, Γ. These two variables are defined as Π ¼

Pred Av Pmax and Γ ¼ acd 2=3 Pmax K V

ð1Þ

where acd is a constant proportional to the speed of sound in air. It should be noted here that the details of the Π vs Γ relationship are not critical to the applicability of the following analysis. Alternative vent sizing curves with the appropriate asymptotic trends (Π µ Γ2 for large Γ and Π ≈ 1 for small Γ) could also be used (e.g., NFPA 68 correlation). The functional dependence between Π and Γ can be used to calculate the effective reactivity K, once all the other variables (i.e., Pred, Pmax, Pstat, Av, V, etc.) are known. In essence, a particular vented explosion is thought of as having “behaved” in accordance with the value of reactivity backed out from the model. It then follows that, in a series of vented tests with no additional effects present (i.e., semicubical vessel with no vent ducts, no panel inertia, etc.), where the only parameter varied is the vent area, Av, the calculated values of Kv should be all the same and equal to the known reactivity, K0, of the mixture. For best match, this latter quantity should be obtained from unvented tests in the same facility that has generated the vented results, rather than from standardized testing in other vessels. 4.2. Unvented Explosions in Elongated Vessels. The experimental work by Radandt and Shi1 in the four 1-m3 vessels used two ignition locations (middle and bottom) and three ignition delays (0.33, 0.38, and 0.6 s) with cornstarch and one (0.38 s) with wheat flour. In the case of cornstarch, these conditions resulted in effective reactivities in the semicubical vessel (H/D = 1) ranging from Kunv = 329 down to 118 bar m/s (the “unv” subscript flags the fact that K is obtained here from a direct measurement in unvented tests), depending on the delay and on the location of the ignition source. For the wheat flour, the variation was from about 100 down to 80 bar m/s for the single ignition delay used. The data show that the effective reactivity, Kunv, varies broadly and, for the same ignition delay, also decreases with increasing H/D. The observed variation of the normalized rate of pressure rise, Kunv, can be explained by considering the change of the characteristic dimension of the vessel as the aspect ratio increases. The maximum rate of pressure rise in the unvented explosion can be written by dividing the maximum pressure, Pmax, by a combustion time, tc. This time, in turn, can be expressed as the ratio between a characteristic dimension of the vessel, Lc, and an effective flame speed, uT. One can, therefore, write dp Pmax = uT ð2Þ dt max Lc For a cylindrical vessel, it is reasonable to postulate that Lc should lie somewhere between H and D. A possible choice, which will be validated below by comparison with experimental results, is the geometric average given by Lc ¼ H 3=4 D1=4 7637

ð3Þ

dx.doi.org/10.1021/ie2015747 |Ind. Eng. Chem. Res. 2012, 51, 7636–7642

Industrial & Engineering Chemistry Research

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Figure 1. Effective reactivity from unvented tests for cornstarch (td = 0.33 and 0.60 s) in 1-m3 vessels plotted vs the corrected aspect ratio. Data from Radandt and Shi.1

The characteristic dimension, Lc, can then be written as a function of volume, V, and aspect ratio, H/D, to yield sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5=4 3 4 V H 3=4 1=4 ¼ ð4Þ H D π D

Table 1. Result of Data Fitting of Unvented Explosions in 1-m3 Vesselsa dust type cornstarch

Combining eqs 24 with the general definition for the reactivity parameter, K, leads to the following final result K ¼ V 1=3

dp = uT Pmax dt max

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5=4 3 π H 4 D

wheat flour a

ð5Þ

If the dispersion of the dust and the ignition delay, hence the initial turbulence field, are adjusted in such a way that the effective flame propagation velocity, uT, remains unchanged, then eq 5 predicts that Kunv should be varying as the 5/12 (= 0.42) power of H/D. The use of a power fit to correlate the variation of the effective reactivity, Kunv, to the aspect ratio, H/D, is shown in Figure 1 with reference to data for cornstarch with 0.33 and 0.60 s ignition delay. Points for middle and bottom ignition are shown together in the same plot. The abscissa is a corrected aspect ratio defined as H H ð6Þ ¼ n D corr D where the factor, n, takes the value of 1 for tests with middle ignition and a different value (>1), which is obtained from a fit, for tests with bottom ignition. The introduction of the correction in eq 6 reflects the expectation that placement of the ignition at the bottom of the vessel increases the average distance that the flame has to travel and, therefore, is equivalent to increasing the H/D of the vessel. The data in the left plot of Figure 1 are best fitted by a single line when n = 2.25. The power exponent is 0.39. This value is close to 0.42, which was predicted by the analysis in the previous section. The plot on the right side shows a fit with n = 1.26 and an exponent of 0.208. Plots similar to those in Figure 1 for the other two conditions of the tests by Radandt and Shi1 would show that the quality of the fit is consistently good, even though the values of the constants vary from case to case. The fit constants, which are shown in Table 1, are defined by eq 6 and the following equation e H ð7Þ Kunv ¼ K0 D corr

td [s]

K0 [bar m/s]

e [-]

n [-]

0.33

329

0.388

2.25

0.38

284

0.459

1.97

0.60

118

0.208

1.26

0.38

95

0.477

1.40

K0 denotes the reactivity for middle ignition and H/D = 1.

Based on the values shown in the table, there is no universal set of fit parameters that can describe the data for all conditions. The exponent of the power decay is around 0.4/0.45 for three cases out of four. However, the cornstarch data with the long ignition delay display a significantly weaker decay. The multiplier factor (n) seems to take values around 2 in the high reactivity cases, whereas it is equal to about 1.31.4 when the reactivity, K0, drops to about 100 bar m/s. A value for n of about 2 is consistent with the idea of a doubling of the flame travel distance when ignition is at one end of the vessel as opposed to the middle. On the basis of these data alone, it is hard to determine whether the decreasing trend of n with reactivity is real. The lack of a similar trend in the values of the exponent, e, would seem to indicate that it is not. Despite these questions, assumptions will be introduced later to generalize these results for use in the correlation of the vented test data. 4.3. Vented Explosions in Elongated Vessels. The data from Radandt and Shi1 will be presented next in terms of an effective reactivity, either measured directly (Kunv) in the case of unvented tests or calculated (Kv) for vented tests (cf. Section 4.1). An example of such data is shown in Figure 2, which refers to cornstarch for an ignition delay of 0.33 s and displays results for middle and bottom ignition on the left and right side of the figure, respectively. A small offset has been applied to the abscissa values (unvented to the left, vented to the right) in order to prevent overlap of the error bars. For unvented tests, the bars represent the scatter of repeat tests. For vented experiments, they correspond to the range of values calculated for Kv for different amounts of venting (Av). Inspection of similar data plots for the other two cornstarch conditions and for the wheat flour tests would confirm the good repeatability of the reactivity values obtained from the unvented tests (Kunv). In addition to data variability, the error bars for the reactivity (Kv) obtained from the vented tests generally reflect a combination of two factors: variation of this quantity as a function of the vent area when H/D > 1 and errors introduced 7638



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Figure 2. Variation of effective reactivity with aspect ratio in vented and unvented tests with cornstarch (td = 0.33 s) in 1-m3 vessels. Data from Radandt and Shi.1

Figure 3. Reactivity increase in vented explosions with cornstarch in 1-m3 vessels plotted as a function of the normalized vent parameter. Data from Radandt and Shi.1

• Unvented explosion in semicubical vessel (H/D = 1) Mixture reactivity, K0; best if directly measured and matched to the Kst of the dust. • Unvented explosion in elongated vessel (H/D > 1) Mixture reactivity, Kunv; either measured directly or inferred from the correlation given by eq 7. For middle ignition, it must be Kunv = K0 when H/D = 1. • Vented explosion in vessel of any aspect ratio Mixture reactivity, Kv; inferred from the results of vented explosion tests by using a validated vent sizing method. If the method is properly calibrated, it should be Kv = K0 when H/D = 1 (middle ignition). The analysis of data from vented tests, described in the previous sections, provides a set of Kv values for the range of conditions covered by the experiments. The same explosion (i.e., same dust at the same level of turbulence, in a vessel of the same volume and vent area), in a semicubical vessel (H/ D = 1), ideally would be proceeding at the rate defined by K0. The successful correlation should provide the functional relationship between Kv, Kunv and the other parameters that define the vented system. It will be assumed that the only additional parameters needing to be considered are as follows:

by the method used to infer Kv. The latter is particularly noticeable in the data for H/D = 1, a condition for which, ideally, there should be no variation observed. Much of the noted discrepancy, however, is caused by a single point in the set, usually corresponding to very high values of Pred. Another interesting feature of the data is that the vented reactivities (Kv) are consistently higher than those measured in the unvented (Kunv) tests with bottom ignition. In the case of middle ignition, however, this is true only when the mixture reactivity is generally low. On the other hand, significant overlap between Kv and Kunv values was observed for middle ignition in the two high-reactivity data sets for cornstarch (one of which is shown in Figure 2).

5. DATA ANALYSIS APPROACH 5.1. General Considerations. The approach taken here in the search for a correlation, which would improve on the ones currently available, follows up on the idea of using the effective reactivity, Kv, to characterize the behavior of the explosion. Three different situations are considered, each with a particular value of K to quantify the intensity of the reaction: 7639



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Figure 4. Best fit values of effective reactivity of cornstarch and wheat flour from vented explosion tests in vessels of 9.4-m3 volume. Middle and bottom ignition data from Radandt and Shi1 and Kossebau.5

Figure 5. Best fit values of effective reactivity of cornstarch and wheat flour from vented explosion tests in vessels of 20-m3 volume. Middle and bottom ignition data from bartknecht.7

the reactivity of the mixture at H/D = 1, K0; the aspect ratio, H/D; the location of the ignition source, through n in eq 6; and the dimensionless vent ratio, Γ. In other words, the sought correlation will be of the form H ð8Þ Kv ¼ Φ1 Kunv , Γ, n, D where, Kunv

H ¼ Φ2 K0 , n, D

An example of one such plot is shown in Figure 3, again for the case of the cornstarch data at the shortest ignition delay (td = 0.33 s) carried out in the 1-m3 vessels. As can be seen, there is a general, and roughly linear, increase in the Kv/Kunv ratio with Γunv. This trend is confirmed by the remaining data from the 1-m3 vessel tests reported by Radandt and Shi.1 In keeping with the behavior suggested by these plots, the data have been correlated by using the following empirical expression Kv ¼ Kunv ð1 þ b ½1 expð c Γunv Þ ½ðH=DÞcorr 1d Þ

ð9Þ

The following sections illustrate the application of this general approach to the various data sets. The 1-m3 data by Radandt and Shi1 will provide guidance in the development of the form of the correlation. The data at larger scale will be used to introduce an appropriate level of conservatism in the correlation. 5.2. Selection of Correlation Formula. The data from the vented tests at varying H/D values have been analyzed by plotting the ratio Kv/Kunv as a function of the normalized vent parameter, Γunv, calculated using the unvented value of the reactivity, Kunv.

ð10Þ where Kunv is given by eq 7 with n = 2.0, e = 0.333, (H/D)corr is given by eq 6 and the constants assume the values b ¼ 3:0;

c ¼ 0:1;

d ¼ 0:50

ð11Þ

An example of the performance of the correlation when applied to the larger scale data from 9.4 and 20-m3 vessels is presented in Figures 4 and 5. In developing the fit, errors were biased by giving a higher weight to those that placed points on the nonconservative side of the line of perfect agreement. This is the 7640



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Figure 6. Values predicted by the present correlation vs experimental vent areas for published test results in vessels of 1, 9.4, and 20-m3 volume.

Figure 7. Increase in vent area to account for H/D effects as predicted by the present correlation for different reduced pressures for middle (left) and bottom (right) ignition.

reason why, in these two figures, the points are found to be preferentially located above the line of perfect agreement.

6. VENT AREA PREDICTIONS 6.1. Comparisons with Experimental Data. The correlation in eq 10, with the constants given by eq 11 and Kunv obtained as explained in the previous section, was used to calculate values for the vent area, Av, for all the available experiments taking the measured values of Pred as input. The result is shown in Figure 6, which presents the predictions by the correlations in the present proposal versus the actual vent areas used in the tests. The data for middle ignition are shown on the left side of the figure and those for bottom ignition on the right side. It should be noted that, in this representation, conservative predictions are denoted by points above the line of perfect agreement. In addition to this reference line, the plots also have two lines corresponding to predicted vent areas that are twice (dotted) and half (dashed) the experimental value. The predicted values can be seen to be within a factor of 2 of the measurements. Similar plots developed using the NFPA and VDI (EN) correlations would show somewhat worse agreement, particularly in the case of the latter correlation.

Unlike the VDI and NFPA correlations, the predictions by the present proposal make a distinction between the cases of middle and bottom ignition. This is introduced through the definition of (H/D)corr (cf. eq 6), which has the effect of doubling the aspect ratio used in the correlation formula when the ignition is at the bottom. Overall, the bulk of the bottom ignition data are conservatively predicted. There is a problem with the large-scale tests with middle ignition. See, for example, the points for cornstarch (represented by the “X” symbol). If all middle ignition data were to be treated as though they had been obtained for bottom ignition, the present correlation would generate conservative predictions for the large majority of the points. The elimination of the distinction based on the location of the ignition source, and use of the correlation for bottom ignition, would essentially remove the lack of conservatism of the correlation that is otherwise present when dealing with some of the results from large-scale tests with middle ignition. The penalty associated with this step is in the form of added conservatism. 6.2. Vent Area Changes as a Function of H/D. The final comparison is for the increase in vent area, ΔAv, relative to that of a semicubical vessel, Av, predicted by the various methods as a function of the aspect ratio, H/D. In the case of the correlation introduced in this paper, it is not possible to obtain ΔAv/Av from 7641



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Table 2. Increase in Vent Area Due to H/D Effects Predicted by Different Methods. Pred = 0.1 bar area increase ratio, ΔAv/Av

Pred = 0.7 bar

Pred = 1.5 bar

H/D = 3

H/D = 6

H/D = 3

H/D = 6

VDI 3673

2.42

3.94

0.68

1.11

0

0

NFPA 68

0.59

1.68

0.38

1.07

0.07

0.20

FM (middle)

0.92

1.94

0.06

0.17

0.09

0.12

FM (bottom)

1.94

3.08

0.17

0.64

0.12

0.04

an explicit formula. Instead, one has to calculate the area increase through an iterative procedure. Since the approach introduced here makes a distinction between middle and bottom ignition, predictions by the method are shown in two plots in Figure 7. Comparison with the VDI (EN) and NFPA methods for the normalized vent area increase, ΔAv/Av, is made in Table 2 based on selected values for Pred (0.1, 0.7, and 1.5 bar) and aspect ratio (H/D = 3 and 6). On average, the VDI (EN) method is the most conservative. NFPA 68 predicts an increase in required vent area even for the highest Pred considered in the table. On the other hand, VDI (EN) and the current proposal predict either no increase or a slight decrease at this high level of reduced explosion pressure. The current proposal for middle ignition yields lower values than the other two methods for Pred > ∼0.2 bar. However, this should not be interpreted as unwarranted lack of conservatism, as the present correlation is supported by a larger body of data than either of the two alternative approaches.

7. CONCLUSIONS An extensive set of literature data has been used to study the effect of the aspect ratio of a vessel on its venting requirements. The wide range of experiments carried out by Radandt and coworkers1,5 has revealed an interesting feature of the phenomenon. In an unvented vessel, an increase in its aspect ratio, while all other parameters are being held constant, reduces the effective reactivity of the mixture expressed by the normalized peak rate of pressure rise. In the presence of venting, the same reactivity increases over its unvented value, as the vent parameter increases. The availability of data over a broad range of conditions, and the use of theoretical tools in the analysis, has allowed for the identification of the role played by different parameters in defining the effect. As a result, the present proposal is believed to have a better foundation than any of those that have preceded it. In addition, it has the advantage to account for the location of the ignition source, by properly predicting the increase in explosion severity which generally results when the ignition source is moved away from the vent. The proposed correlation reproduces the experimental data to within a factor of 2, a performance which is better than that of existing alternatives and which would be difficult to improve given the poor reproducibility of dust explosion data and the degree of success that can be expected of empirical correlations.

H/D = 3

H/D = 6

cole Nationale Superieure de Mechanique et d’Aerotechnique E (ENSMA) in Poitiers, France. His efforts in assembling the data available in the literature and in carrying out a preliminary analysis are greatly appreciated.

’ REFERENCES (1) Radandt, S.; Shi, J. Y. Dust Explosion in Different Vessels Ranged by Height to Diameter Ratios. Berufsgenossenschaft Nahrungsmittel und Gastst€atten, Mannhein, Germany, May 1995. (2) VDI Standard No. 3673, Part 1. Pressure Venting of Dust Explosions. Verein Deutscher Ingenieure, D€usseldorf, November 2002. (3) NFPA Standard No. 68. Standard on Explosion Protection by Deflagration Venting. Technical Committee on Explosion Protection System, 2007 Edition. (4) EN 14491 European Standard. Dust Explosion Venting Protective Systems. European Committee for Standardization (CEN), 2006. (5) Kossebau, F. 9 m3-Behalter. BGN, 02.02.1993. (6) Hauert, F.; Vogl, A.; Radandt, S. Dust Cloud Characterization and its Influence on the Pressure-Time-History in Silos. Process Saf. Prog. 1996, 15 (3), 178–184. (7) Bartknecht, W. Dust Explosion Course, Prevention, Protection; Springer-Verlag: Berlin, Heidelberg, 1989. (8) Bartknecht, W. Explosions-schutz Grundlagen und Anwendung; Springer-Verlag: Berlin Heidelberg, 1993. (9) Eckhoff, R. K. Dust Explosion in the Process Industries, 2nd ed.; Butterworth-Heinemann: Oxford, England, 1997. (10) Tamanini, F.; Valiulis, J. Improved Guidelines for the Sizing of Vents in Dust Explosions. J. Loss Prev. Process Ind. 1996, 9 (1), 105–118 Special Issue on Dust Explosions.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The work presented in this report was initiated as part of a summer internship by Rapha€el Grangeon, a student from the 7642


Aspect Ratio Effects in Unvented and Vented Dust Explosions

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