Reliability and applicability of empirical equations in predicting the reduced explosion pressure of vented gas explosions

Journal of Loss Prevention in the Process Industries 63 (2020) 104023

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Reliability and applicability of empirical equations in predicting the reduced explosion pressure of vented gas explosions Khairiah Mohd Mokhtar a, Rafiziana Md Kasmani b, Che Rosmani Che Hassan a, *, Mahar Diana Hamid a, Sina Davazdah Emami c, Mohamad Iskandr Mohamad Nor a a b c

Department of Chemical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia Department of Energy Engineering, School of Chemical and Energy Engineering, Universiti Teknologi Malaysia, 81310 Johor, Malaysia HSE management, NIOC, 8th Centre Building, Yaghma St., Tehran, Iran

A R T I C L E I N F O

A B S T R A C T

Keywords: Vented gas explosion Chambers Pred

Explosions caused by the rapid release of energy from the expansion of burnt gases, along with an associated pressure rise, in an enclosure can be mitigated by venting. Many empirical equations have been derived based on vented gas deflagration phenomena. In the present paper, four empirical equations for gas venting were reviewed, i.e., NFPA 68, the European Standard (EN 14994), Molkov et al. and Bradley and Mitcheson in order to assess their reliability and applicability for predicting the reduced explosion pressure (Pred) of propane-air, methane-air and hydrogen-air mixtures at three different chamber-scale volumes. The results showed that the NFPA 68 correlation is the most appropriate method for predicting Pred, while Bradley and Mitcheson gave values closer to those of experimental data for propane-air mixtures in medium and larger chambers, respectively. However, none of the predicted correlations was able to provide a reasonable prediction of Pred in a hydrogen-air explosion. In addition, these predicted correlations showed greater discrepancies in Pred values in the presence of vent area, ignition position and obstacles.

1. Introduction

1978a,b; Chao et al., 2011; Cooper et al., 1986; Harris, 1983; McCann et al., 1985; Solberg et al., 1980; Swift, 1984). Different fuels have been applied in different geometrical configurations with different ignition locations and obstacles present in order to understand the influence of these parameters. In addition, empirical correlations have been devel­ oped for predicting the reduced explosion pressure (Pred) and the vent area (Av) (Bradley and Mitcheson, 1978b; Chao et al., 2011; Chippett, 1984; Rasbash et al., 1976; Runes, 1972; Simmonds and Cubbage, 1960; Yao, 1974). Nevertheless, these correlations were derived from experi­ ments with validity ranges which were restricted to the specific condi­ tions used during the work done, which may have contributed to the discrepancy in the predicted and experimental values. Additionally, some of these correlations have been included in international standard guidelines, such as NFPA 68 and EN 14994, which were Swift’s and Bartknecht’s work, respectively. However, these correlations may have involved conflicting recommendations, depending on the specific sce­ narios under consideration and the assumptions made, particularly when turbulence was taken into account as one of the contributing

The occurrence of an explosion attributed to the rapid release of energy from the expansion of burnt gases with an associated pressure rise in an enclosure leads to structural damage, injuries and even fa­ talities. Such an explosion can be mitigated through the application of venting (Tomlin et al., 2015). Among all precautionary methods, the venting system has proven to be an efficient mitigation measure to reduce the pressure build-up in an enclosure system due to an interior explosion (Guo et al., 2016). Venting plays an important role in assisting the free release of expanding gas, which results in a decrease in pressure, as well as providing a semi-open space for flame propagation (Ma et al., 2014). Therefore, using an appropriately and reliably designed vent area is vital in venting out excessive overpressure developed during the explosion. Extensive experimental and theoretical studies have been conducted since the 1960s to understand the main phenomena and factors affecting the pressure profiles of vented deflagration (Bradley and Mitcheson,

* Corresponding author. E-mail addresses: [email protected] (K. Mohd Mokhtar), [email protected] (R. Md Kasmani), [email protected] (C.R. Che Hassan), mahar.diana@um. edu.my (M.D. Hamid), [email protected] (S. Davazdah Emami), [email protected] (M.I. Mohamad Nor). https://doi.org/10.1016/j.jlp.2019.104023 Received 3 October 2019; Received in revised form 11 November 2019; Accepted 23 November 2019 Available online 25 November 2019 0950-4230/© 2019 Published by Elsevier Ltd.

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Journal of Loss Prevention in the Process Industries 63 (2020) 104023

factors in explosion developments, alongside the size and shape of the enclosure, the mixture concentration, ignition location and energy, as well as the presence of obstacles in the chamber. To ensure that the correlation developed is universal, the validity and applicability of the correlation in the NFPA 68 standard have been reviewed by Razus and Krause (2001) and Sustek and Janovsky (2013), together with other available correlations. The latter used a scoring system to validate their applicability, while the former presented a relative average deviation for all 10 applied equations with different shapes of vessels, i.e., cubical, rectangular and cylindrical. Based on these two reviews (Razus and Krause, 2001; Sustek and Janovsky, 2013), it can be concluded that empirical correlations are strongly dependent on their range of applicability. For example, one can observe scattered data with quite significant deviations, but only when chamber sizes and shapes are considered, compared to experimental Pred values (Razus and Krause, 2001; Sustek and Janovsky, 2013). To date, there are only limited reviews on the validity and applicability of the predicted correlations based on the geometries, but not on chamber scale. It can be suggested that the flame front area and turbulence factor are dependent on chamber volume (Fakandu et al., 2015; Molkov, 1988; Molkov et al., 2000). For instance, Fakandu et al. (2015) observed the occurrence of the self-acceleration of spherical flames when the chamber’s volume increased, which directly affected the turbulence factor, with the tur­ bulence level increasing in line with the flame scale (Molkov et al., 2000). It is noteworthy that the effect of chamber volume is taken into account in all correlations, whether directly denoted as V or indirectly presented in different parameters. While EN 14494 directly applies the chamber’s volume in the form of V2/3 in the correlation, the surface area of the chamber (As), which is linearly related to V2/3 (Andrews and Phylaktou, 2010), is used in NFPA 68 and Bradley and Mitcheson’s correlation. Hence, this paper aims to analyse and generalize the venting experimental data available in the literature against the NFPA 68 cor­ relations, EN 14994, Molkov et al. (1997) and Bradley and Mitcheson (1978b) for hydrogen-air (at the lean concentration ratio), methane-air and propane-air mixtures (at their stoichiometric concentration ratio) in three different chamber sizes, i.e., small (0.1–9 m3), medium (10–29 m3) and large (30–65 m3), in order to evaluate the applicability and suit­ ability of the correlation and its major assumptions. The governing factors that influence vented gas explosion development were explored by studying the deviation in the predicted values, compared to the experimental values, under different initial conditions. The review starts with vented gas deflagration phenomena before exploring the available correlations for venting explosions. The next section will discuss the comparison between the predicted and experimental values and the effect on the overall suitability of each correlation in real case scenarios with recommendations that could give added value to the parameters, which are not being taken into account in venting correlations.

difference across the vent opening, which triggers the occurrence of Helmholtz oscillation, causes the pressure inside the enclosure to oscillate around the equilibrium pressure (Bauwens et al., 2008, 2010; Tomlin et al., 2015). At this stage, burning rates are enhanced by the turbulence generated in the shear layer between the outflowing burnt gas and the unburnt gas within the enclosure (Cooper et al., 1986). Next, Taylor instabilities are induced, in which the less dense burnt gas is accelerated into a denser unburnt gas-air mixture, resulting in an in­ crease in the mass combustion rate (McCann et al., 1985; Tomlin et al., 2015). Based on these phenomena, a different number of pressure peaks is identified based on vent size, ignition location and the presence of ob­ stacles. Cooper et al. (1986) characterized four major pressure peaks which correspond to a particular physical process occurring inside or outside the vessel. The first pressure peak is associated with volume ejection; this is attributed to venting, which exceeds the volume pro­ duction caused by combustion. A sharp increase in the internal pressure, marked as a second pressure peak (P2), results from the ignition of an unburnt fuel-air mixture, which has previously been expelled from the vessel. A decrease in the production rate of the burnt gas volume is caused by a reduction in flame area, giving rise to the third pressure peak (P3). Meanwhile, the fourth pressure peak (P4) is generated when pressure waves resulting from the combustion process are combined with the acoustic modes of the vessel, hence producing sustained pres­ sure oscillations. In contrast with this finding, later research has re­ ported a different number of pressure peaks associated with vented deflagration processes. Besides the pressure peak attributed to the vent cover failure pressure (which is denoted as Pv), two dominant pressure peaks are identified, which are linked to an external explosion that triggers Helmholtz oscillations and, subsequently, Rayleigh-Taylor instability (i.e., denoted as P1) and the internal combustion where flame acoustic coupling occurs (i.e., denoted as P2). However, these pressure peaks may change with the presence of obstacles in the enclosure and with changes in ignition location. For instance, the pressure peak, which is controlled by resonant coupling between the flame and the acoustic modes generated by the geometry and the physical response of the enclosure (P2), may be eliminated or reduced when obstacles are placed in the path of the propagating flame (Alexiou et al., 1997; Bradley et al., 2000). 3. Empirical equations in predicting Pred Based on the vented deflagration phenomena presented in the pre­ vious section, empirical equations were derived with the application of different variables in many studies in order to estimate the vent size requirements, with the aim of mitigating the adverse impact of an accidental gas explosion. These variables, including Pred, attempt to accommodate the coupling effects of the turbulence and the dynamic gas of venting. In the current review, four correlations are chosen and compared with experimental data from the literature, i.e., NFPA 68, EN 14994, and correlations published by Molkov et al. (1997) and Bradley and Mitcheson (1978b). EN 14994, which underlines the empirical correlation based on Barknecht’s experimental data (Bartknecht, 1993) uses mixture reactivity KG in the venting guideline. As shown in Eq. (1), the equation also includes the vent area Av as a function of the vessel volume V2/3 and the static vent burst pressure Pstat. � � Av ¼ ð0:1265 log KG 0:0567ÞPred0:5817 � � þ 0:1754Pred0:5722 ðPstat 0:1barÞ V 2=3 (1)

2. Vented gas deflagration phenomena At the initial stage of a vent explosion, the vent cover of an enclosure begins to rupture when the internal pressure of the enclosure produced from burnt gas exceeds the burst pressure of the cover. In this case, the vent burst pressure is denoted as Pv (Cooper et al., 1986). The unburnt fuel-air mixture is discharged from the enclosure through the vent, which is then reignited by the emerging flame front of the vent, subse­ quently causing an external explosion (Alexiou et al., 1997; Tomlin et al., 2015). In this condition, the volume ejection due to venting initially exceeds the volume of gases produced by combustion and, as the flame continues to expand, the net rate of production volume by combustion exceeds the volumetric flow rate through the vent. An in­ crease in flame area is caused by flame expansion and surface distortion as well as the formation of cellular structures, known as self-acceleration and flame instability (Bradley et al., 2000; Clarke, 2002; Molkov et al., 1999). On the other hand, the onset of burnt gas venting out from the enclosure coincides with the start of Helmholtz oscillation. The pressure

Meanwhile, the other international standard venting guideline, namely, NFPA 68 (2018), uses the gas reactivity term, given by the C coefficient, which comprises detailed parameters, such as the burning velocity Su, the vent flow discharge coefficient Cd and the turbulent enhancement factor, λ. The details of the equations are given in Eqs. (2)– (4). NFPA 68 adopts Swift’s work (Swift, 1984), in which the turbulence 2

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Journal of Loss Prevention in the Process Industries 63 (2020) 104023

enhancement factor, denoted as λ in Swift’s correlation, is typically counted as 5, except for extremely high initial turbulence in which the values can be up to 10 (Swift, 1984). However, in NFPA 68 (2018), λ is calculated with more detailed parameters including Reynold’s flame front number Ref and venting number Rev, as shown in Eqs. (5)–(10).

Su ρu λ 2Gu Cd

�� �1=γb Pmax þ 1 Po þ 1

� 1 ðPo þ 1Þ1=2

(4)

λ0 ¼ ϕ1 ϕ2

(5)

where, 9 8 1; if Ref < 4000 > > < = ϕ1 ¼ � Ref �θ > : ; ; if Ref � 4000 > 4000 Ref ¼

ρu Su ðDhe =2Þ μu (

�

ϕ2 ¼ max 1; β1

Rev ¼

Rev 106

u

ρu uv ðDv =2Þ μu

nm ¼ nl þ ðPe

Pecl Þ

(6)

(7) � �0:5 ) � βS2

(8) (9)

∂fns nl þ fns ¼ 2∂Pe 2

(10)

On the other hand, Bradley and Mitcheson (1978b) introduced the dimensionless parameter A= SO in their equation as shown in Eq. (11). However, differences between theoretical and experimental data exist, due to uncertainty about the effects of turbulence and pressure wave generation. Hence, Molkov et al. (1999) introduced the Bradley number (Br) and the so-called deflagration outflow-interaction number χ/μ in a ‘universal correlation’ (as shown in Eq. (13)), which accommodates the turbulent combustion coupled with the gas dynamics of venting. The application of the two dimensionless numbers (Br and χ/μ), which principally determines the deflagration dynamics, results in a satisfac­ tory best fit between the theoretical pressure-time profiles and the experimental values under a wider range of conditions; hence, it is called a ‘universal correlation’ (Molkov et al., 1997, 1999, 2000). Additionally, the two dimensionless numbers (Br and χ/μ) (refer to Eqns. (14) and (15)) play a similarly significant role in representing the turbulence factor as the flame and the vent outflow Reynolds numbers (Ref and Rev) which are executed in NFPA 68. However, Lautkaski (2012) argued that Eq. (13) may not give conservative predictions in all cases since the ‘universal correlation’ was obtained as the best fit for the experimental data (Lautkaski, 2012). � � 1:25 Pred ¼ 4:82P0:375 A (11) =s stat O

C d Av Suo ; SO ¼ ðEo As co

co

� 1 1=γ b 1 1=γ u

VT ðdP = dtÞ ¼ As PSO ðE

where, A¼

� SO E

1Þ

(13)

qffiffiffiffiffiffiffiffiffi E=γ u Br ffiffiffiffiffiffiffi Brt ¼ p 3 36π χ=μ

(14)

1Þ

(16)

On the other hand, the application of Bradley and Mitcheson’s cor­ relation for all chamber categories in the methane-air mixtures reveals an underestimation of the Pred values, compared to those of experi­ mental data (refer to Table 2). The closer predicted Pred to the experi­ mental values can be observed in Molkov et al. and NFPA 68 correlations for small and larger scale chambers, respectively. This is not only due to the direct influence of the fundamental burning velocity on this corre­ lation, but also due to the effect of the expansion ratio (refer to Eq. (11)).

(12)

π red ¼ Brt 2:4

(15)

Details of the comparison between predicted and experimental values of Pred for the stoichiometric concentration of propane-air mix­ tures, methane-air mixtures and hydrogen-air mixtures, which is only considered for centrally ignited locations, are presented in Tables 1–3 for three categories of chamber volumes: small (0.1–9 m3) (Bartknecht, 1993; Chow et al., 2000; DeGood and Chatrathi, 1991; Kumar et al., 1989; Zalosh, 1979), medium (10–29 m3) (Donat, 1977; Thorne et al., 1983) and large (30–65 m3) (Bauwens et al., 2010; Donat, 1977; Solberg et al., 1981; Zalosh, 1979). The relative error (RE) presents the deviation in predicted Pred values compared to experimental values. The ‘universal correlation’ is expected to be agreeable in all three categories (Molkov et al., 1999); nevertheless, the results show that the ‘universal correla­ tion’ only gives the closest values for experimental Pred in the small chambers. Among all the calculated Pred values, the NFPA 68 correlation gives the nearest Pred values when comparison is made with experimental data in all the case of all three chamber scales, as shown in Tables 1–3. The smaller RE of the Pred values from NFPA 68 correlation as compared to the other three correlations can be observed in small chamber for propane-air mixture, and medium and large scale chambers for methane-air mixtures. This result is attributed to the parameters accounted for in the correlation (refer to Eq. (2)) by considering the turbulent enhancement factor λ and the Reynolds number, Re of the gas flow before and during venting. The Reynolds number (Eqs. (7)–(9)) used in the correlation express the development of the flame front sur­ face due to its cellular structure, which could in turn represent the physical and dynamic changes in overall burning rate and flame speed (Bradley et al., 2000; Chippett, 1984). Additionally, Eq. (10) illustrates the parameters involved in the self-acceleration phenomenon through the development of a cellular flame, represented by the wave number nm , in which the amplitude of the flame instability growth rate is at its greatest (i.e., dominant during cellular flame formation). Further, one can observe that the vent and hydraulic diameters of the chamber significantly affect predicted Pred, alongside the constant mass density value, the dynamic velocity and the sound speed of the unburnt gas-air mixture in the NFPA 68 correlation (2018). However, Bradley and Mitcheson’s correlation gives the closest Pred values for experi­ mental Pred, but only for medium and large chambers. From both cor­ relations, i.e., NFPA 68 (2018) and Bradley and Mitcheson, it can be soundly claimed that the surface area has a significant influence on the predicted Pred values for each system’s volume. To further justify the statement, Eq. (16) shows that the surface area (As) is directly propor­ tional to the rate of pressure rise (dP/dt). Therefore, it can be understood that the Bradley and Mitcheson correlation is more applicable to larger chambers. Since there are no data available for chambers larger than 63.7 m3, it is highly recommended that more experimental in­ vestigations are conducted on a larger scale in future in order to deter­ mine whether or not this correlation can be applied using variable sizes.

(3)

C ¼ 0:0223λSu bar1=2 ; when ​ the ​ Pmax ​ value ​ is ​ less ​ than ​ 9 ​ bar

Av V 2=3

4. Comparison between the predicted values of Pred and experimental data

(2)

Pred ¼ ðCAs Þ2 AV 2 C¼

Br ¼

3

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Journal of Loss Prevention in the Process Industries 63 (2020) 104023

Table 1 Comparison of the experimental and predicted Pred values of the propane-air mixture. Classification of chambers (scale)

Volume (m3)

Experimental Pred values (bar)

Calculated Pred values (bar) EN 14994

Relative error

NFPA 68

Relative error

Bradley and Mitcheson

Relative error

Molkov et al.

Relative error

Small

0.056 0.056 0.17 0.17 0.18 0.18 0.77 0.77 0.77 1 2 2.42 2.42 2.6 2.6

0.170 0.075 0.021 0.030 0.740 0.570 0.185 0.035 0.010 0.280 0.290 0.087 0.035 0.199 0.282

0.0056 0.0186 0.7725 8.3733 1.3525 2.7155 1.0533 0.3789 0.1389 0.3213 0.9061 1.6985 1.6985 0.4931 0.5249

0.9671 0.7520 35.7857 278.110 0.8277 3.7640 4.6935 9.8257 12.8900 0.1475 2.1245 18.5230 47.5286 1.4779 0.8613

0.1347 0.4591 0.0262 0.0375 0.7289 1.5282 0.4765 0.0130 0.0375 0.3870 0.4579 0.0857 0.0778 0.2540 1.0147

0.2076 5.1213 0.2476 0.2500 0.0150 1.6811 1.5757 0.6286 2.7500 0.3821 0.5790 0.0149 1.2229 0.2764 2.5982

0.0084 0.0200 0.4528 2.5615 0.6917 1.1483 0.8724 0.3391 0.1487 0.0385 0.7655 0.6246 0.6246 0.5163 0.5548

0.9506 0.7333 20.5619 84.3833 0.0653 1.0146 3.7157 8.6886 13.8700 0.8625 1.6397 6.1793 16.8457 1.5945 0.9674

0.0002 0.0007 0.0600 1.2900 0.1333 0.3093 0.1432 0.0434 0.0134 0.0378 0.1588 0.3720 0.3720 0.0834 0.0895

0.9988 0.9907 1.8571 42.000 0.8199 0.4574 0.2259 0.2400 0.3400 0.8650 0.4524 3.2759 9.6286 0.5809 0.6826

10 10 10 10 22 22 22 30 30 30 35 35 35 35 35 35 60 60 60 63.7 63.7 63.7 63.7 63.7 63.7 63.7

0.320 0.240 0.300 0.500 0.025 0.200 0.250 0.200 0.300 0.500 1.050 0.180 0.710 0.190 0.720 0.100 0.300 0.500 1.000 0.196 0.204 0.134 0.005 0.025 0.056 0.186

4.1174 2.9048 0.2232 0.3423 0.0609 0.2553 0.6615 14.502 0.4562 0.7517 3.0402 1.0003 3.0402 1.0003 3.0402 1.0003 0.4479 0.7335 3.5442 1.2657 1.2657 1.2657 0.3881 0.3881 0.3881 0.3881

11.867 11.103 0.2560 0.3154 1.4360 0.2765 1.6460 71.512 0.5207 0.5034 1.8954 4.5572 3.2820 4.2647 3.2225 9.0030 0.4930 0.4670 2.5442 5.4577 5.2044 8.4455 76.620 14.524 5.9304 1.0866

0.1638 0.1082 0.1683 0.3361 0.0215 0.1298 0.3795 0.3188 0.5055 0.8986 2.7003 0.6583 2.5907 0.6620 2.5945 0.6185 0.1759 0.4523 2.7611 0.3740 0.3756 0.3593 0.0690 0.0818 0.0891 0.0621

0.4881 0.5492 0.4390 0.3278 0.1400 0.3510 0.5180 0.5940 0.6850 0.7972 1.5717 2.6572 2.6489 2.4842 2.6035 5.1850 0.4137 0.0954 1.7611 0.9082 0.8412 1.6813 12.800 2.2720 0.5911 0.6661

0.2431 0.1886 0.2754 0.3758 0.0590 0.2168 0.4711 0.6177 0.3549 0.5086 1.9679 0.8769 1.9679 0.8769 1.9679 0.8769 0.3519 0.5034 1.5824 0.0681 0.0681 0.0681 0.0288 0.0288 0.0288 0.0288

0.2403 0.2142 0.0820 0.2484 1.3600 0.0840 0.8844 2.0885 0.1830 0.0172 0.8742 3.8717 1.7717 3.6153 1.7332 7.7690 0.1730 0.0068 0.5824 0.6526 0.6662 0.4918 4.7600 0.1520 0.4857 0.8452

1.6056 1.0496 0.0469 0.0776 0.0143 0.0753 0.2311 10.651 0.1591 0.2862 1.6324 0.4271 1.6324 0.4271 1.6324 0.4271 0.1942 0.5079 3.4185 0.7108 0.7108 0.7108 0.1739 0.1739 0.1739 0.1739

4.0175 3.3733 0.8437 0.8448 0.4280 0.6235 0.0756 52.258 0.4697 0.4276 0.5547 1.3728 1.2992 1.2479 1.2672 3.2710 0.3527 0.0158 2.4185 2.6265 2.4843 4.3045 33.780 5.9560 2.1054 0.0651

Medium

Large

Large

Reference

By giving more attention to Eqs. (12) and (17), it can be stipulated that burning velocity and Pred have an interrelated effect on each other, which can be observed in higher recorded Pred values for hydrogen and propane fuels than for methane. This statement indicates that kinetic parameters are strongly determined by the dynamics of the vented ex­ plosion mechanism, and hence the overall pressure development. Basi­ cally, burning velocity is the velocity of the flame front movement relative to the unburnt mixture immediately ahead of it (Harris, 1983). Referring to Eq. (16), the velocity is induced by the gas expansion, E occurring behind the flame front. Therefore, the burning velocity is affected by both the burnt and unburnt gas density and the flame

Bartknecht (1993) Bartknecht (1993) Chao et al. (2011) DeGood and Chatrathi (1991) Donat (1977)

Thorne et al. (1983) Donat (1977) Solberg et al. (1980)

Donat (1977) Bauwens et al. (2010)

Mitcheson’s correlation. For a better understanding, the correlation between these parameters is listed below: 1Þ

(18)

SL αðλÞð1=2Þ

(19)

SL αρðn=2

�

Yo2;0 υo2 hc;R ¼ cp ðT∞

T0 Þ

(20)

In the case of lean hydrogen-air concentration, the predicted corre­ lations show the majority of overestimated Pred values for both small and larger chambers. An increase in preferential diffusion regions causes turbulent flame propagation to decrease progressively (Aung et al., 2002), corresponding to the lower flame-stretch interaction (Im and Chen, 2002; Kwon and Faeth, 2001). Hence, it is suggested that, when the preferential diffusion effect is apparent, it tends to result in the retardation of flame distortion through excessive flame stretching, which will cause the flame to be partially quenched (Bradley et al., 2008). Simultaneously, a turbulent flame also develops due to the various mechanisms of flame instability involved during flame propa­ gation, i.e., thermal diffusion and Darrieus-Landau and hydrodynamic instability, which are themselves the result of interactions between the flame front and the acoustic waves (Bradley and Harper, 1994; Bradley et al., 2008; Ciccarelli and Dorofeev, 2008; Gamezo et al., 2008; Lib­ erman et al., 2010). This phenomenon is especially significant in a

dr

propagation density ( dtf ) (Annamalai and Puri, 2006).

drf ρu ¼ SL;u dt ρb

Chow et al. (2000) Zalosh (1979)

(17)

Eqs. (18)–(20) indicate that initial pressure, thermal conductivity, specific heat capacity and mixture stoichiometry are directly influenced by the burning velocity values (Annamalai and Puri, 2006). For instance, higher thermal conductivity and initial pressure causing a higher burning velocity occur due to rapid heat feedback (Kasmani et al., 2013). Moreover, a lower specific heat capacity causes a higher average reaction temperature and rate (Annamalai and Puri, 2006). Hence, it is expected that the higher burning velocity of hydrogen and propane subsequently affects the calculated Pred values arising from Bradley and 4

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Journal of Loss Prevention in the Process Industries 63 (2020) 104023

Table 2 Comparison of the experimental and predicted Pred values of the methane-air mixture. Classification of chambers (scale)

Volume (m3)

Experimental Pred values (bar)

Calculated Pred values (bar) EN 14994

Relative error

NFPA 68

Relative error

Bradley and Mitcheson

Relative error

Molkov et al.

Relative error

Small

0.011

0.054 0.058 0.090 0.030 0.050 0.070 0.200 0.430 1.400 0.280 0.490 0.020 0.070 0.016 0.040 0.070 0.900 0.500 1.300

0.1721 0.1721 0.1721 0.3761 0.3761 0.3761 0.6317 0.7024 1.3309 1.1101 0.1757 0.1864 0.1864 0.0445 0.1864 0.4829 1.2286 0.6655 0.6273

2.1870 1.9672 0.9122 4.7367 6.5220 4.3729 0.8805 0.4691 0.4983 3.7532 1.2655 7.7850 1.6629 10.650 0.1125 1.6629 0.4634 1.4572 0.4881

0.0257 0.0259 0.0273 0.0291 0.0031 0.0032 0.1173 0.1814 1.6489 0.8098 0.1157 0.0801 0.0933 0.0163 0.0871 0.2640 1.0248 0.4882 0.5727

0.5241 0.5534 0.6967 0.0300 0.9380 0.9543 0.4135 0.5781 0.1778 1.8921 0.7639 3.0050 0.3329 0.0187 1.1775 2.7714 0.1387 0.0236 0.5595

0.0058 0.0058 0.0058 0.0194 0.0175 0.0175 0.3073 0.3860 1.5240 0.6020 0.1576 0.1874 0.1874 0.0387 0.1548 0.3445 0.9578 0.6355 0.3976

0.8926 0.9000 0.9356 0.3533 0.6500 0.7500 0.5365 0.1023 0.0886 1.1500 0.6784 8.3700 1.6771 1.4188 2.8700 3.9214 0.0642 0.2710 0.6942

0.0789 0.0789 0.0789 0.0449 0.0450 0.0450 0.3982 0.5766 0.5542 1.1101 0.1757 0.1864 0.1864 0.0445 0.1864 0.4829 0.7152 0.3416 0.3435

0.4611 0.3603 0.1233 0.4967 0.1000 0.3571 0.9910 0.3409 0.6041 2.9646 0.6414 8.3200 1.6629 1.7813 3.6600 5.8986 0.2053 0.3168 0.7358

0.113 0.146 0.054 0.047

0.9239 0.9239 0.2833 0.2833

4.5513 5.3281 16.109 5.0277

0.0303 0.0313 0.0761 0.0748

0.7319 0.7856 0.4093 0.5915

0.0411 0.0411 0.0174 0.0174

0.6363 0.7185 0.6778 0.6298

0.6708 0.6708 0.1645 0.1645

4.9363 3.5945 2.0463 2.5000

0.22 1 Medium

11.2 22

Large

30 34 63.7

Reference

Wen et al. (2015) Park et al. (2007) Bartknecht (1993) Zalosh (1979) Thorne et al. (1983)

Bartknecht (1993) Zalosh (1979) Chao et al. (2011)

Table 3 Comparison of the experimental and predicted Pred values of the hydrogen-air mixture. Classification of chambers (scale)

Volume (m3)

Experimental Pred values (bar)

Calculated Pred values (bar) EN 14994

Relative error

NFPA 68

Relative error

Bradley and Mitcheson

Relative error

Molkov et al.

Relative error

Small

0.0038

0.031 0.110 0.130 0.789 0.050 0.250 0.278 0.615 0.135 0.500 0.640

0.1343 0.7779 1.8457 5.8691 0.1343 0.7779 1.8457 5.8691 1.2903 0.7606 2.1404

3.3323 6.0718 13.197 6.4387 1.6860 2.1116 5.6392 8.5433 8.5578 0.5212 2.3444

0.0182 0.1407 0.3823 1.4950 0.0183 0.1425 0.3869 1.4891 0.2728 0.1616 1.4949

0.4129 0.2791 1.9408 0.8948 0.6340 0.4300 0.3917 1.4213 1.0207 0.6768 1.3358

0.0631 0.2263 0.4241 0.9836 0.0631 0.2263 0.4241 0.9836 0.4001 0.3584 5.8011

1.0355 1.0573 2.2623 0.2466 0.2620 0.0948 0.5255 0.5993 1.9637 0.2832 8.0642

0.0422 0.2705 0.7083 2.7256 0.0422 0.2705 0.7083 2.7256 1.9051 1.0381 5.7241

0.3613 1.4591 4.4485 2.4545 0.1560 0.0820 1.5478 3.4319 13.112 1.0762 7.9439

0.234 0.314 0.171 0.111 0.149 0.428

2.4749 2.4749 2.4749 0.7589 0.7589 0.7589

9.5765 6.8818 13.473 5.8369 4.0933 0.7731

1.2135 1.2191 1.2076 0.3064 0.3079 0.3130

4.1859 2.8825 6.0620 1.7604 1.0664 0.2687

1.2817 1.2817 1.2817 0.5426 0.5426 0.5426

4.4774 3.0818 6.4953 3.8883 2.6416 0.2678

13.753 13.753 13.753 3.6568 3.6568 3.6568

57.774 42.800 79.428 31.944 23.542 7.5439

1 6.37 Large

63.7

Reference

hydrogen-air explosion compared to a hydrocarbon explosion, due to its flame reactivity and diffusivity (Aspden et al., 2011; Emami et al., 2016; Hu et al., 2014). However, as there are no data available for medium-scale chambers and very lean hydrogen concentration, better insights are needed into the validity and applicability of the predicated correlations for hydrogen-air vented explosions. To further understand this situation, the relationship between con­ tinuum mechanics and thermal energy are explored in terms of gov­ erning equations associated with balance equations for mass, momentum, energy and chemical species. The momentum balance is directly proportional to thermal energy and temperature increase, and inversely proportional to density. Therefore, all these equations are closely proportional to each other. For instance, the planar jet’s corre­ lations for turbulent combustion, via an empirical diffusivity relation, highlight the significant influence of the mass, momentum and species of initial mixtures on released energy (Annamalai and Puri, 2006). Mass,

Rocourt et al. (2014)

Bartknecht (1993) Kumar et al. (1989) Chao et al. (2011)

momentum and species conservations are respectively identified as shown in Eqns. (21)–(24) as follows: � ∂ ∂ ðρv Þ þ ρv ¼ 0 ∂x x ∂y y �

(21) �

ρvx

∂vx ∂vy ∂ ∂v ρεT;M x þ ρvy ¼ ∂x ∂y ∂y ∂y

ρvx

∂Yk ∂Yk ∂ ρεT;s ∂Yk þ ρvy ¼ þ ω_ k’’’ ∂x ∂y ∂y ScT ∂y

�

(22) �

(23)

Therefore, the released energy can be calculated as: � � ∂bT ∂bT ∂ ρ2 εref * ∂bT ω_ F bc vx’ ’ þ vy’ ’ ¼ ’ þ ε T;M ∂x ∂y ∂y ScT p2ω ∂y’ ρ Note that ε*T;S ¼ εT;s , and ScT ¼ ref ε

5

εT;m εT;s

(24)

¼ momentum turbulent diffusivity

K. Mohd Mokhtar et al.

Journal of Loss Prevention in the Process Industries 63 (2020) 104023

over turbulent species. Moreover, Newton’s law and Fick’s law state that dynamic viscosity and diffusion flux are proportional to the symmetric and concentration gradient, respectively. Therefore, since thermo-diffusion is also pro­ portional to the temperature gradient, the most general form of multi­ component diffusion in the transporting process is identified in Eq. (25) (Peters, 2010): ji ¼

k Wi X ρDij Wj gradXj W j¼1

DTi gradT; i ¼ 1; 2; …:; k: T

underestimated Pred values were observed when Kv values were lower than 1 in all correlations except for NFPA 68. This may have been due to the influence of a larger vent area (indicated by a lower Kv), which induced large disturbances in the flame front, leading to a high turbu­ lence factor, consequently affecting the Pred (Molkov, 1988; Molkov et al., 1997). However, no turbulence factor value is taken into account in EN 14994. Meanwhile, Bradley and Mitcheson’s correlation suggests a constant value for the turbulence factor (i.e., 4.82), whereas Molkov et al.’s correlation includes some constant values, known as Brt. These constant values are seemingly insufficient for expressing the turbulence factor, giving a lower predicted Pred if Kv > 10 and Kv < 1 than the experimental values. It can be stated that, by including the turbulence factor in the correlation with the correct parameters, the NFPA 68 cor­ relation offers better agreement with the experimental Pred. The Rey­ nolds number is taken into account in the NFPA 68 correlation in order to express the turbulence factor associated with the cellular flame, which would directly affect the mass burning rate, flame speed and overall overpressure in a vented explosion, while acknowledging the formation of flame instabilities. On the other hand, a different trend is observed in the predicted Pred values of the methane-air mixture as illustrated in Figs. 3 and 4. A scattered trend was observed with regard to Pred values, compared with Kv, in the methane-air mixture explosions for all correlations except for Bradley and Mitcheson’s correlation, which gave values closer to those of experimental Pred for Kv of between 2 and 10. Significant parameters involving vent area, surface area, expansion ratio and burning velocity, as embedded in Bradley and Mitcheson’s correlation, provide satisfac­ tory agreement between predicted Pred and experimental values. Although the Molkov et al. correlation also takes into consideration these parameters, many constant values used in the correlation might contribute to the huge divergence in predicted Pred values. This also might explain the overestimation of Pred values for hydrogen-air mixture on Kv values from 3 to 6 in Molkov et al. correlation (see Fig. 6), besides the fact that hydrogen has a higher burning velocity than propane and methane. The higher burning velocity of hydrogen directly affects both the physics and the dynamic mechanism of a vented explosion, as explained in detail in Section 4. This also justifies the higher estimation of Pred in EN 14994 correlation as compared to the experimental values, as shown in Fig. 5, since burning velocity is not taken into consideration in that correlation. More data on hydrogen-air mixtures are needed for from future studies in order to provide a better insight into the validity and applicability of predicted correlations in hydrogen vented explosions. Previous studies (Bauwens et al., 2010; Du et al., 2006; Fakandu et al., 2013; Jiang et al., 2005; Tomlin et al., 2015) have also identified the influence of vent areas on the occurrence of external explosions, due to the reversal propagating wave propagating back into the explosion chamber, attenuating the Taylor instabilities and, hence, increasing the overall pressure during a vented explosion. A small vent area causes the flammable unburnt gas-air mixture, ahead of the flame front, to be vented at far higher velocities compared to larger vent areas. Conse­ quently, greater turbulence within the external flammable gas cloud is

(25)

j6¼1

It is noticeable that most combustion processes in thermo-diffusion can be safely neglected. Consequently, in a special case, the diffusion flux can be determined and measured approximately by using the Lewis number with an effective diffusion coefficient Di, as shown in Eq. (26). Le ¼

λ

ρcp Di

(26)

For assessing relationships between momentum diffusivity and thermal diffusivity, the Prandtl number (Pr) is identified as in Eqns. (27). Pr ¼

μcp λ

(27)

Based on the aforementioned parameters which affect interactions between the flame front and the acoustic waves, flame reactivity is more apparent in hydrogen-air explosions (Aspden et al., 2011; Emami et al., 2016). It is highly recommended that more attention is given to these parameters when implementing predicted correlations for higher reac­ tivity fuels, such as hydrogen and acetylene. The important role played by detailed parameters in theoretical correlations has been observed, and it is found that the NFPA 68 correlation gives Pred values for the hydrocarbon/air mixture (i.e., propane and methane) closer to those of experimental data. 5. Factors governing vent explosions Providing an adequate venting area is crucial in order to ensure the sufficient release of pressure during an explosion. Maximum pressure which develops during a vented explosion is governed by the balance between the rate of the production of combustion products and the rate of outflow throughout the venting process (Bao et al., 2016; Tomlin et al., 2015). These are influenced by factors such as vent area (Chao et al., 2011; Donat, 1977; Solberg et al., 1980; Thorne et al., 1983; Zalosh, 1979), ignition position (Chao et al., 2011; Solberg et al., 1980; Wen et al., 2015) and the presence of obstacles (Bauwens et al., 2010; Chao et al., 2011; Park et al., 2007; Wen et al., 2015). Hence, in the present section, the Pred results from different vent areas, the presence of obstacles and the different ignition positions (i.e., end, centre and front of the chamber) are reviewed in order to highlight the influence of these factors. 5.1. Influence of vent area Ensuring the effective release of gases during an explosion and subsequently, reducing explosion pressure is critically rely on the size of the vent area (Chao et al., 2011; Ma et al., 2014). The influence of the vent area is expressed in terms of the vent coefficient (Kv) where V2/3 is divided by the vent area (Av) (Bartknecht, 1993; Harris, 1983). By expressing the predicted Pred from Bartknecht’s method in terms of the Kv values, it can be observed in Fig. 1 that the predicted Pred of EN 14994 is proportionate to the Kv values. Overall, it is demonstrated that the NFPA 68 and the Bradley and Mitcheson correlations are in good agreement with regard to the experimental propane-air mixtures data, particularly for Kv values ranging between 1 and 11, as illustrated in Figs. 1 and 2. Nevertheless,

Fig. 1. Influence of Kv on Pred value of propane-air based on NFPA 68 and EN 14994 correlations. 6

K. Mohd Mokhtar et al.

Journal of Loss Prevention in the Process Industries 63 (2020) 104023

Fig. 2. Influence of Kv on Pred value of propane-air based on Bradley and Mitcheson and Molkov et al. correlations.

Fig. 6. Influence of Kv value on Pred of hydrogen-air based on Bradley and Mitcheson and Molkov et al. correlation.

ignition position changed from the centre to the end wall of the cham­ ber, but was reduced when the mixture ignited nearer to the vent. Following ignition, the flame area increased with time, resulting in an increase of burnt gas and causing the flame front to rapidly accelerate along the axis towards the vent. The hemispherical shape of the flame resulted from the end ignition (Bychkov et al., 2007; Chow et al., 2000) while the centre point ignition produced a spherical flame (Chao et al., 2011), as shown in Fig. 7. When ignited at the centre, the flame prop­ agated in both directions, causing a decrease in the flame area and a reduction in the mass burning rate of gases, in turn affecting the flame speed and Pred value. Meanwhile, the end ignition resulted in a larger flame surface area, as the flame was completely stretched in the direc­ tion of the vent, prompting speedy flame acceleration (Kasmani et al., 2013; Ugarte et al., 2016). As for front ignition (i.e. ignition near to the vent area), the flame propagates in the direction opposite to venting, resulting to the flame deceleration due to the quick venting of burned gas mixtures, and subsequently lowering the flame speed and the Pred value (Guo et al., 2015). The relationship between mass burning rate, flame speed and burning velocity is shown in Eq. (28) (Glassman et al., 2014) and Eq. (29) (Annamalai and Puri, 2006).

Fig. 3. Influence of Kv on Pred value of methane-air based on NFPA 68 and EN 14994 correlation.

(28)

m_ ¼ ρSL Af Sf ¼ ðρu = ρb ÞSL

�

�

Vb ρb Af ðdpb = dtÞ

(29)

On the other hand, it is a fact that the heat liberation rate would have been different from the heat loss rate when ignition occurred in the system (Annamalai and Puri, 2006). Therefore, the sensibility of the energy of the mixture is equal to the heat generated by the chemical reaction, less than the heat loss by convection and radiation (as in Eq. (30)). � mcv dT dt ¼ Q_ gen Q_ loss (30)

Fig. 4. Influence of Kv value on Pred of methane-air based on Bradley and Mitcheson and Molkov et al. correlation.

Therefore, by assuming a first-order reaction with fuel and oxygen and a global one-step reaction in the early stages of ignition, Eq. (31) becomes: � � � � E mcv dT dt ¼ A’ exp (31) bH SðT T∞ Þ εSσ T 4 T 4∞ RT Hence, factors such as the dissipation of kinetic energy, strain rate, universal gas constant, kinetic energy and ambient temperature have a direct influence on energy release in the early ignition stage of fuel gases (Annamalai and Puri, 2006). Nevertheless, these factors are not considered by the predicted correlations; consequently, the calculated Pred for all ignition positions are the same for each predicted correlation, except in the NFPA 68 correlation as tabulated in Table 4. The predicted Pred values from the NFPA 68 correlation decreases as the mixtures of gases is ignited nearer to the vent area. The lowest Pred value is recorded at front ignition, nearest point to the vent area. For instance, predicted Pred values for propane-air mixtures in a 63.7 m3 chamber are 0.0690 bar, 0.0818 bar and 0.0891 bar for the front, centre and end ignition, respectively. These differences are attributed to the influence of the Reynolds number in the NFPA 68 correlation, as

Fig. 5. Influence of Kv on Pred value of hydrogen-air based on NFPA 68 and EN 14994 correlation.

formed, causing faster burning velocities, flame speeds and higher external overpressures. Further discussion on the mechanism of this phenomenon is presented elsewhere (Bauwens et al., 2011; Emami et al., 2016; Liu et al., 2015). 5.2. Effect of ignition position The point at which ignition takes place is a vital factor during the initial stages of combustion (Phylaktou and Andrews, 1991), especially in vented chambers. As shown in Table 4, Pred increased when the 7

K. Mohd Mokhtar et al.

Journal of Loss Prevention in the Process Industries 63 (2020) 104023

Table 4 Influence of ignition position on experimental Pred values. Gas mixture

Propane/air

Volume of chamber (m3)

Ignition position

Experimental Pred value (bar)

Predicted Pred value (bar) EN 14994

NFPA 68

Bradley and Mitcheson

Molkov et al.

2.42

End Centre Front Centre End Front Centre End End Centre End Centre Front Centre End

0.087 0.035 0.710 1.050 0.720 0.005 0.025 0.056 0.054 0.047 0.113 0.146 0.171 0.234 0.314

1.699 1.699 3.040 3.040 3.040 0.388 0.388 0.388 0.283 0.283 0.924 0.924 2.475 2.475 2.475

0.086 0.078 2.591 2.700 2.595 0.069 0.082 0.089 0.076 0.075 0.030 0.031 1.208 1.214 1.219

0.625 0.625 1.968 1.968 1.968 0.029 0.029 0.029 0.017 0.017 0.041 0.041 1.282 1.282 1.282

0.372 0.372 1.632 1.632 1.632 0.174 0.174 0.174 0.165 0.165 0.671 0.671 13.753 13.753 13.753

35 63.7 Methane/air

63.7

Hydrogenair

63.7

Reference

Chao et al. (2011) Solberg et al. (1980) Chao et al. (2011) Chao et al. (2011)

Chao et al. (2011)

correlation, involving a wider range of chamber scales and fuel equiv­ alence ratios – especially for hydrogen – is carried out in the future. 5.3. Effect of the presence of obstacles Another important factor in vent explosions is the presence of ob­ stacles. As shown in Table 5, the presence of an obstacle in the chamber causes the Pred value to increase along with the blockage ratio. This was because the flame-obstacle interaction triggers a highly turbulent com­ bustion, which can lead to a higher burning rate generated ahead of the propagating flame, leading to higher overpressure (Ibrahim et al., 2001; Ibrahim and Masri, 2001b; Wen et al., 2012, 2015). The findings for a small square cross-section combustion chamber also showed that square obstacles lead to the highest overpressure and a circular obstacle results in the lowest overpressure among all applied obstacles (Ibrahim and Masri, 2001a). Moreover, an investigation into a cylindrical chamber showed that the presence of obstacles with both ends open can increase the flame speed by about 24 times more than without obstacles (Bau­ wens et al., 2008). Referring to Table 5, the calculated Pred values in the NFPA 68 cor­ relation are closer to those of experimental data. This result might be attributed to the inclusion of the turbulence factor λ in that correlation. Before reaching the obstacle, the flame travels at the laminar flame speed, since the flow field ahead of the flame remains undisturbed (Cong and Bi, 2008). When the flame hits the obstacle, it starts to interact with a modified flow field where the turbulence levels and length scales are likely to be different due to the influence of the size and geometry of the obstacle (Ibrahim and Masri, 2001a). The gas velocity in the gap around the obstacle is likely to increase along with the turbulence levels,

Fig. 7. Flame shape attributed to a) end ignition and b) centre ignition (Chow et al., 2000).

reported by Chippett (1984), as well as discussed in an earlier section (refer to Eqs. (9)–(5)), highlighting the relationship between the Rey­ nolds number and the gas flow through the vent. Nevertheless, due to limited experimental data, these results are applicable only to large-scale chambers for methane-air and hydrogen-air mixtures. Hence, it is highly recommended that a further investigation into the NFPA 68 Table 5 Influence of obstacles on experimental and predicted Pred values. Volume of chamber (m3)

Gas mixture

0.011

Methane/air

0.22 63.7 63.7

Propane/air

63.7

Hydrogen/ air

Blockage ratio (%)

Experimental Pred value (bar)

Predicted Pred value (bar) EN 14994

NFPA 68

Bradley and Mitcheson

Molkov et al.

N/A 5 10 N/A 5 10 N/A 7 N/A 7 N/A 7

0.054 0.058 0.090 0.030 0.050 0.070 0.054 0.214 0.056 0.186 0.149 0.428

0.172 0.172 0.172 0.376 0.376 0.376 0.283 0.283 0.388 0.388 0.759 0.759

0.026 0.026 0.027 0.029 0.003 0.003 0.076 0.090 0.089 0.062 0.308 0.313

0.006 0.006 0.006 0.019 0.018 0.018 0.017 0.017 0.029 0.029 0.543 0.543

0.079 0.079 0.079 0.045 0.045 0.045 0.165 0.165 0.174 0.174 3.657 3.657

8

Reference

Wen et al. (2015) Park et al. (2007) Bauwens et al. (2010)

K. Mohd Mokhtar et al.

Journal of Loss Prevention in the Process Industries 63 (2020) 104023

resulting in an increase in the flame speed and reaction rates, in turn causing a higher overpressure (Ibrahim and Masri, 2001a; Lowesmith et al., 2011). It should be noted that, as the flame front impinges on the obstruc­ tion, the flame becomes wrinkled due to the blockage from the obstacles and the expansion of the burnt gas volume. The propagating flame front then travels laterally along the vent with an increase in flame surface area, pushing the unburnt mixture ahead of it (Ibrahim et al., 2001; Park et al., 2007, 2008a). This wrinkling flame affects the flame area, which results in massive changes to the mass burning rate, as illustrated in Eq. (28). The work of Chao et al. (2011) estimated the area of the spherical flame propagating through obstacles from the ratio of the flame area with obstacles to the flame area without obstacles, as shown in Eq. (32), where BR represents blockage ratio, and N is the average number of layers of obstacles in the flame path. � �2 � Af A ¼ 1 þ 4 3⋅σ1 α ðBRÞ1=2 N α (32)

References Alexiou, A., Andrews, G.E., Phylaktou, H., 1997. A comparison between end-vented and side-vented gas explosions in large L/D vessels. Process Saf. Environ. Prot. 75, 9–13. Andrews, G.E., Phylaktou, H.N., 2010. Explosion Safety. Annamalai, K., Puri, I.K., 2006. Combustion Science and Engineering. Taylor & Francis. Aspden, A., Day, M., Bell, J., 2011. Lewis number effects in distributed flames. Proc. Combust. Inst. 33, 1473–1480. Aung, K., Hassan, M., Kwon, S., Tseng, L.-K., Kwon, O.-C., Faeth, G., 2002. Flame/stretch interactions in laminar and turbulent premixed flames. Combust. Sci. Technol. 174, 61–99. Bao, Q., Fang, Q., Zhang, Y., Chen, L., Yang, S., Li, Z., 2016. Effects of gas concentration and venting pressure on overpressure transients during vented explosion of methane–air mixtures. Fuel 175, 40–48. Bartknecht, W., 1993. Explosions-Schultz. Springer-Verlag, Berlin. Bauwens, C.R., Chaffee, J., Dorofeev, S., 2008. Experimental and numerical study of methane-air deflagrations in a vented enclosure. Fire Saf. Sci. 9, 1043–1054. Bauwens, C.R., Chaffee, J., Dorofeev, S., 2010. Effect of ignition location, vent size, and obstacles on vented explosion overpressures in propane-air mixtures. Combust. Sci. Technol. 182, 1915–1932. Bauwens, C.R., Chaffee, J., Dorofeev, S., 2011. Vented explosion overpressures from combustion of hydrogen and hydrocarbon mixtures. Int. J. Hydrogen Energy 36, 2329–2336. Bradley, D., Harper, C.M., 1994. In: 25th Symposium (International) on Combustion PapersThe Development of Instabilities in Laminar Explosion Flames, vol. 99. Combustion and Flame, pp. 562–572. Bradley, D., Lawes, M., Liu, K., 2008. Turbulent flame speeds in ducts and the deflagration/detonation transition. Combust. Flame 154, 96–108. Bradley, D., Mitcheson, A., 1978. The venting of gaseous explosions in spherical vessels. I—Theory. Combust. Flame 32, 221–236. Bradley, D., Mitcheson, A., 1978. The venting of gaseous explosions in spherical vessels. II—theory and experiment. Combust. Flame 32, 237–255. Bradley, D., Sheppart, C., Woolley, R., Greenhalgh, D., Lockett, R., 2000. The development and structure of flame instabilities and cellularity at low Markstein numbers in explosions. Combust. Flame 122, 195–209. Bychkov, V., Akkerman, V.y., Fru, G., Petchenko, A., Eriksson, L.-E., 2007. Flame acceleration in the early stages of burning in tubes. Combust. Flame 150, 263–276. Chao, J., Bauwens, C.R., Dorofeev, S.B., 2011. An analysis of peak overpressures in vented gaseous explosions. Proc. Combust. Inst. 33, 2367–2374. Chippett, S., 1984. Modeling of vented deflagrations. Combust. Flame 55, 127–140. Chow, S., Cleaver, R., Fairweather, M., Walker, D., 2000. An experimental study of vented explosions in a 3: 1 aspect ratio cylindrical vessel. Process Saf. Environ. Prot. 78, 425–433. Ciccarelli, G., Dorofeev, S., 2008. Flame acceleration and transition to detonation in ducts. Prog. Energy Combust. Sci. 34, 499–550. Clarke, A., 2002. Calculation and consideration of the Lewis number for explosion studies. Process Saf. Environ. Prot. 80, 135–140. Cong, L.-X., Bi, M.-S., 2008. Effects of obstructions on impulse of flammable gas cloud deflagrations. J. Loss Prev. Process. Ind. 21, 118–123. Cooper, M., Fairweather, M., Tite, J., 1986. On the mechanisms of pressure generation in vented explosions. Combust. Flame 65, 1–14. DeGood, R., Chatrathi, K., 1991. Comparative analysis of test work studying factors influencing pressures developed in vented deflagrations. J. Loss Prev. Process. Ind. 4, 297–304. Donat, C., 1977. Pressure relief as used in explosion protection. Loss Prev. 11, 87–92. Du, Z., Jin, X., Cui, D., Ye, J., 2006. The investigation of correlated factors of external explosion during the venting process. J. Loss Prev. Process. Ind. 19, 326–333. Emami, S.D., Sulaiman, S.Z., Kasmani, R.M., Hamid, M.D., Hassan, C.R.C., 2016. Effect of pipe configurations on flame propagation of hydrocarbons–air and hydrogen–air mixtures in a constant volume. J. Loss Prev. Process. Ind. 39, 141–151. Fakandu, B., Yan, Z., Phylaktou, H., Andrews, G., 2013. The effect of vent area distribution in gas explosion venting and turbulent length scale influence on the external explosion overpressure. In: Paper Presented at the Seventh International Seminar on Fire & Explosion Hazards (ISFEH7), Providence, Rhode Island. Fakandu, B.M., Andrews, G.E., Phylaktou, H.N., 2015. Vent burst pressure effects on vented gas explosion reduced pressure. J. Loss Prev. Process. Ind. 36, 429–438. Gamezo, V.N., Ogawa, T., Oran, E.S., 2008. Flame acceleration and DDT in channels with obstacles: effect of obstacle spacing. Combust. Flame 155, 302–315. Glassman, I., Yetter, R.A., Glumac, N.G., 2014. Combustion. Elsevier Science. Guo, J., Sun, X., Rui, S., Cao, Y., Hu, K., Wang, C., 2015. Effect of ignition position on vented hydrogen–air explosions. Int. J. Hydrogen Energy 40, 15780–15788. Guo, J., Wang, C., Li, Q., Chen, D., 2016. Effect of the vent burst pressure on explosion venting of rich methane-air mixtures in a cylindrical vessel. J. Loss Prev. Process. Ind. 40, 82–88. Hall, R., Masri, A.R., Yaroshchyk, P., Ibrahim, S.S., 2009. Effects of position and frequency of obstacles on turbulent premixed propagating flames. Combust. Flame 156, 439–446. Harris, R.J., 1983. The Investigation and Control of Gas Explosions in Buildings and Heating Plant. E. & FN Spon in association with the British Gas Corp. Hu, G., Zhang, S., Li, Q.F., Pan, X.B., Liao, S.Y., Wang, H.Q., Yang, C., Wei, S., 2014. Experimental investigation on the effects of hydrogen addition on thermal characteristics of methane/air premixed flames. Fuel 115, 232–240. Ibrahim, S., Masri, A., 2001. The effects of obstructions on overpressure resulting from premixed flame deflagration. J. Loss Prev. Process. Ind. 14, 213–221.

=

f0

Nevertheless, the effects of many parameters on blockage ratio, including the shape of obstacles, separation distance, fuel concentration, and ignition energy (Hall et al., 2009; Ibrahim and Masri, 2001a; Masri et al., 2000; Na’inna et al., 2013; Oh et al., 2001; Park et al., 2008b,c) have not been considered on these predicted correlations. For instance, previous studies on the influence of obstacles on flame acceleration of fuel gases in tube vessels showed that the number of obstacles and the distance between each of the obstacles has significant effects on Pred, the rate of pressure rise and flame speed (Na’inna et al., 2013). Since there is no further data available for these concepts, it is highly recommended that more experimental and numerical investigations on chambers be considered for future studies. 6. Conclusion The present paper aims to review the applicability and its range of validity for venting correlations in NFPA 68, EN 14994, Bradley and Mitcheson (1978a,b) and Molkov et al. (1997), and also to determine the governing factors that greatly influence the development of vented ex­ plosions by considering different initial conditions. From the discussion and exploration of the available correlations reported in the literature, it can be stated that: 1) The correlation offered in NFPA 68 for predicting Pred was shown to be the most conservative, particularly in the case of small chambers for propane-air mixtures and medium chambers for methane-air mixtures. The Bradley and Mitcheson correlation is much more suitable for predicting Pred for larger-scale chambers. 2) However, there is no reliable theoretical prediction available for hydrogen-air vented explosions. Further experimental and theoret­ ical works are required, and it is recommended that the dynamic mechanism should be embedded in the correlation, such as diffusion flux, diffusion coefficient, momentum diffusivity and thermal diffusivity. 3) Based on the analytical observations, ignition position and the presence of obstacles in vented chambers, which are not accounted for in all predictive correlations except in NFPA 68, lead to either the underprediction or overprediction of Pred. Acknowledgement This work was supported by theMinistry of Education Malaysia [FRGS Grant No.:FP013-2014B], University of Malaya [PPP Grant No.: PG270-2015B], and Universiti Teknologi Malaysia [Tier 1 Grant No.:Q. J130000.2546.14H41, Q.J130000.2546.17H82].

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