Simulations of vented dust explosions in a 5 m3 vessel

Powder Technology 321 (2017) 409–418

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Powder Technology journal homepage: www.elsevier.com/locate/powtec

Simulations of vented dust explosions in a 5 m3 vessel Alberto Tascón a,⁎, Pedro J. Aguado b a b

Departamento de Agricultura y Alimentación, Universidad de La Rioja, Av. Madre de Dios 51, 26006 Logroño, Spain Departamento de Ingeniería y Ciencias Agrarias, ESTI Agraria, Universidad de León, Av. Portugal 41, 24071 León, Spain

a r t i c l e

i n f o

Article history: Received 29 March 2017 Received in revised form 4 July 2017 Accepted 16 August 2017 Available online 19 August 2017 Keywords: Dust explosion Venting CFD Numerical modelling Sensitivity analysis

a b s t r a c t Vented dust explosions were simulated using the computational fluid dynamics code FLACS-DustEx. The results were compared with previously reported experimental tests performed with maize starch in a 5.2 m3 vessel with a length/diameter ratio equal to 1.05 using three different vent areas. In addition, a sensitivity study was conducted with respect to some of the parameters involved in the numerical simulations, including dust/air mixture reactivity, grid resolution and area size and activation pressure of the venting device. The simulation results were generally in good agreement with the experimental values, but the CFD code overpredicted explosion pressures for the scenario with the smallest vent area. The sensitivity analysis indicated that the results were dependent on both grid resolution and mixture reactivity. Further simulations confirmed the influence of the activation pressure of the venting device on the explosion overpressure when the vent area was large in comparison to the volume, i.e. with a low KV (=V2/3 / A). These simulations made it possible to study scenarios outside the range of validity of current venting standards. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Dust explosions pose a serious hazard in many industrial facilities. The simultaneous presence of a dust/air mixture with the appropriate concentration of both fuel and oxygen, a suitable ignition source and a certain degree of confinement can lead to a combustion process that propagates rapidly throughout the mixture and produces a significant increase in pressure [1]. Studies of major industrial accidents [2,3] indicate that dust explosions can occur in many different types of factories, involve equipment as diverse as silos, mills, dryers, conveyors and dust collecting systems, and can be triggered by a range of ignition sources, such as hot surfaces and flames, static electricity, electrical sparks, impact and friction sparks and self-heating processes. When it is not possible to achieve acceptable levels of safety through prevention and inherent safety alone, it is necessary to implement suitable mitigation measures [4]. Venting is the most widely used method for reducing the potential overpressures generated by an accidental explosion. However, although several vent size calculation methods exist [1,5,6], including widespread and internationally recognised standards [7–9], this remains a controversial issue [10]. The formulas given in European standard EN 14491 [8] and American standard NFPA 68 [9] are based on theoretical considerations and several series of experimental tests, and provide satisfactory safety levels for most industrial applications. However, these standards can result in significantly different vent areas in some cases [11], and the ⁎ Corresponding author. E-mail address: [email protected] (A. Tascón).

http://dx.doi.org/10.1016/j.powtec.2017.08.047 0032-5910/© 2017 Elsevier B.V. All rights reserved.

values obtained in several experiments and numerical simulations seem to be inconsistent with those calculated according to the standards [12–15]. In addition, some situations encountered in practice are not covered by the standards, such as complex industrial scenarios [16], silos with volumes N10,000 m3 [17] and venting devices with high activation pressures (N1 bar) [18]. Thus, there seems to be a clear need for further research in this area. A more advanced approach for predicting the consequences of industrial dust explosions is the use of computational fluid dynamics (CFD) codes [19], which can extend the study of explosion development and mitigation systems beyond the simplified, worst-case scenarios considered by guidelines and standards. Advanced CFD tools have been successfully applied to the study of various aspects related to dust explosions, including turbulent flow fields, dust lifting and dust concentrations [20–22], explosion experiments at laboratory scale [23–28] and protection systems design in largescale industrial scenarios [13,16,17,29,30]. In addition, explosion accidents can be investigated using CFD tools [31]. However, the application of CFD codes to large industrial scenarios usually requires a pragmatic approach that involves some simplifying assumptions, since detailed modelling of all aspects of dust explosions – transient turbulent multiphase reacting flows – is currently not within reach for industrial applications [32]. Therefore, repeated large-scale experiments are required for codes validation [19]. Despite the advances made during the last decades [33,34], dust explosions are not yet fully understood. One of the main difficulties is the complexity of flame propagation in dust clouds. Different processes can be involved during dust flame propagation [35], including heating, pyrolysis, mixing with oxidizer, ignition, burning and flame

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extinction. Gao et al. [35] analysed the effects of thermal characteristics and particle size distribution on the transition from kineticscontrolled to devolatilization-controlled flame propagation. The different effects of the smaller and larger dust particles on flame propagation behaviour have been reported in several studies [36–39]. Benedetto et al. [40] presented a model to quantify the effects of particle size on explosion development, in which pyrolysis, internal and external heat transfer and volatiles combustion were coupled. Phenomena such as dispersion, agglomeration and gravitational settling also play key roles in ignition and explosion development [41,42]. The explosion behaviour of nm-particles has also been investigated in recent years, including metal, plastic and carbon nano-size powders [43–46]. However, in spite of these numerous efforts, there are still many questions that need to be addressed in this research area [10,34]. As Skjold et al. [47] pointed out, it seems likely that our understanding of dust explosions will benefit from the interaction between computational fluid dynamics and experimental tests at various scales. In this study, the CFD code FLACS-DustEx [48] was used to simulate a series of dust explosions previously performed by Tascón et al. in a 5 m3 vented vessel [49]. Several of the explosion tests reported in [49] – namely those corresponding to large vent area sizes in comparison to the volume to be protected – either yielded results that were far removed from the values predicted by venting standards, or were beyond the scope of the standards. The main objective of the present research was to analyse these inconclusive experimental results and provide more insight into situations that fall beyond the scope of the standards. The results from the numerical simulations were compared with the experimental data and values calculated according to venting standards. In addition, a sensitivity study was performed with respect to some of the parameters involved in the numerical simulations.

2. Methodology 2.1. Previous experimental tests Tascón et al. [49] reported vented dust explosions carried out in a modular test silo. The present simulations corresponded to tests performed in one module of the silo, i.e. in a 5.2 m3 vessel. The 1-module vessel consisted of a horizontal circular silo measuring 1.9 m in diameter and 2.0 m in total length, with a blind Klopper-type bottom cover and a flat top cover with a rectangular aperture of the appropriate size to install the corresponding vent panel. The vessel was equipped with a dust dispersion system consisting of one 8-litre bottle, initially pressurised with air to 20 bar(g), a discharge pipe with a fast-acting valve and a nozzle placed inside the closure. The bottle was filled with the amount of dust required to produce the desired concentration in the vessel. The dispersed dust cloud was ignited by a 5 kJ chemical igniter with the composition specified in EN 14034-1 [50] and positioned near the centre of the vessel. The ignition delay, i.e. the time between activation of the dust injection system and activation of ignition, was 700 ms in all tests. The vent panels, which were rectangular in shape and made of stainless steel, measured 0.828, 0.524 and 0.347 m2. The activation pressure of the panel was also recorded and reported for each of the tests [49]. Table 1 gives the Table 1 Experimental tests in a 5.2 m3 vessel reported by Tascón et al. [49]. Test no.

Vent area (m2)

Pact (mbar)

Pred,exp (mbar)

7a 7b 8a 8b 9a 9b

0.83 0.83 0.52 0.52 0.35 0.35

200 130 196 208 134 156

234 210 251 286 246 282

main characteristics of the experimental tests reported by Tascón et al. and simulated in the present study. 2.2. Simulations The simulations were performed using the CFD code FLACS-DustEx from Gexcon [48], previously marketed as DESC [51]. This code solves the compressible Reynolds-averaged Navier-Stokes (RANS) conservation equations for mass, momentum, enthalpy and chemical species on a 3D Cartesian grid. The set of equations is closed by the ideal gas law and the standard k-ε model by Launder and Spalding [52]. To represent the particle-laden flow, the code assumes thermal and kinetic equilibrium between the dispersed and continuous phases. Thus, it cannot simulate phenomena such as agglomeration or gravitational settling of the dust particles, but nevertheless makes it possible to simulate large industrial scenarios with reasonable computational effort. The inclusion of the distributed porosity concept in the governing equations [53] enables the modelling of curved surfaces in a Cartesian grid and the representation of complex geometries; the code includes sub-grid models for the production of turbulence by sub-grid objects. A detailed description of the governing equations of the code was reported by the authors in a previous study [54]. The laminar burning velocity SL and the fraction of fuel that reacts λ [51], both estimated from pressure-time data histories measured in a 20-litre sphere [50], are used in the empirical combustion model to define the propagation of the reaction zone, i.e. the flame, and the rate of conversion from reactants to products. The turbulent burning velocity ST is modelled in FLACS-DustEx according to: 0:412

u0 rms ‘ 0:196 ST ¼ 15:1S0:784 L I

ð1Þ

where SL is the laminar burning velocity, u′rms is the root-mean-square of the turbulent velocity fluctuations and ‘I is the turbulence lengthscale. Skjold [51,55] presented the modelling approach adopted in the code, including its limitations and capabilities, and the basis of the combustion and flow models. Whereas the laminar burning velocity SL is a well-defined and readily available parameter for many gas-air mixtures, this is not the case for dust clouds, and its determination presents inherent difficulties. The approach adopted in FLACS-DustEx is to estimate values for SL from data on pressure-time histories measured in the 20-litre vessel, focussing on values in the inflection point of the pressure-time curve in order to avoid uncertainties caused by energetic ignition sources and wall effects. The procedure consists of calculating the turbulent burning velocity, decay of u′rms and decay of ‘I through the correlations described by Dahoe and coworkers [56–58], using the data obtained in the 20-litre vessel. Then, these three parameters are used to estimate SL values from an inverse version of Eq. (1) for a set of dust concentration values; the results can then be modified by the non-dimensional multiplication factor CL, which was introduced to account for uncertainties in the assumptions behind the calculations of SL, u′rms and ‘I. The combustion model also requires an estimate of the mass fraction of fuel converted to products (λ) for various dust concentrations, since combustion reactions in dust-air mixtures seldom go to completion; this is determined as the fraction of the initial fuel that must react with air to produce the explosion pressure recorded in the 20-litre vessel, which is corrected to take account of the influence of strong igniters and the cooling effects of vessel walls. Lastly, the data generated for several concentrations, SL and λ, are uploaded in the program prior to simulations in the form of an input fuel file. During the CFD simulations, turbulent burning velocities are given by Eq. (1), with SL taken from the fuel file, u′rms provided by the k-ε model, and ‘I estimated from the algebraic expression ‘I = min (0.025∙RF, 0.08∙LS), where RF is the flame radius and LS is the minimum spatial dimension of solid boundaries surrounding the flame [51].

A. Tascón, P.J. Aguado / Powder Technology 321 (2017) 409–418 Table 2 Characteristics of the dust selected for the simulations. Properties

Maize starch

Pmax (bar) KSt (bar·m/s) Enthalpy of formation (MJ/kg) Heat capacity (J/(kg·K)) Particle density (kg/m3) Particle diameter (μm)

8.2 174 −4.58 400 1180 15

Maize starch was used in all simulations. Table 2 gives its main characteristics. Tascón et al. [49] reported a summary of the results obtained in the 20-litre vessel tests. The theoretical mean dust concentration was set to 775 g/m3 and the moisture content was 11.5%, in accordance with the values reported in [49]. Cubic grid cells of size 0.10 m were used in the present study. The test vessel described above was used as the model to perform the simulations. However, it was necessary to adapt the geometry of the vessel to fit the orthogonal grid, so the smooth curved bottom cover was transformed into a prolongation of the cylindrical silo wall. Thus, the final vessel used for the simulations consisted of a cylinder measuring 1.9 m in diameter and 1.8 m in length (V = 5.1 m3) placed 0.20 m above the ground. The 5 kJ ignition point was located near the longitudinal axis of the vessel at 0.75 m from the vessel bottom. Steel vent panels were simulated as pop-out panels of 5 kg/m2 that divided into 0.10 × 0.10 m2 subpanels when activated, imitating the behaviour of bursting devices. The activation pressure of the vent panel was selected for each simulation in accordance with the value reported for the corresponding experimental test (see Table 1). The dispersion system was modelled as a transient fuel jet consisting of a 3D leak with five opened sides, i.e. five sides of the cell affected by the leak opened up and acted as mass sources when the leak started. Fig. 1 illustrates the geometry implemented. The flow domain was initially defined with the standard atmospheric pressure (100,000 Pa = 1 bar) and a temperature of 20 °C. Although the previous experimental tests were carried out in summer, the ambient temperature for each test was not recorded [49]. An open boundary condition was set for the outer boundaries of the computational domain, except for the lower horizontal boundary, where a solid plane surface was used to model the ground. In the open boundaries the CFD code calculates fluid flow properties using Euler equations [48]. 2.3. Sensitivity analysis In addition to regular simulations that replicated the experiments reported by Tascón et al. [49], this study also explored the effects of the venting device activation pressure, grid resolution and mixture reactivity. Tables 3 and 4 present a summary of the simulated scenarios included in the present study. In Table 3, the test no. indicates the experimental test on which the simulation was based. As described above, three different vent area sizes A were used in the experimental tests. In FLACS-DustEx, the geometry of the vent panels was fitted to the 0.10 m grid: 0.50 × 0.70 (= 0.35) m2, 0.60 × 0.90 (= 0.54) m2 and 0.70 × 1.20 (= 0.84) m2. The vent panel activation pressure Pact was set in each test according to the experimental values in [49]. However, in some further simulations for A = 0.84 m2, the activation pressure was varied from 0.30 bar to 0.10 bar, 0.05 bar and 0.00 bar (opening without vent cover) in order to analyse the effects of the activation pressure in the case of large vent areas; Tascón et al. [49] had noted that tests 7a and 7b seemed to indicate that the vent area implemented was excessive and that the activation pressure determined the explosion overpressure recorded. The combustion model in FLACS-DustEx assumes that empirical correlations derived from experiments with gas/air mixtures [59] can be used to estimate the turbulent burning velocity ST of dust clouds (Eq. (1)). This approach only applies to fine dusts with a high volatile

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content, where flame propagation is principally driven by gas phase reactions [60]. Previous studies have indicated that this model simulates explosions for fuels such as maize starch or coal dust with reasonable accuracy [26]. However, the reactivity of the modelled dust is a major source of uncertainty in this type of study [32]. As described above, the laminar burning velocity derived from 20-litre sphere tests can be corrected by a dimensionless multiplication factor CL. According to previous studies, the recommended value for CL is 1.25 for 0.10 m grid cells [15,61]. In the present simulations, the estimated laminar burning velocity was modified by varying CL from 1.0 to 2.0 to investigate the effects of mixture reactivity (see Table 3). Previous reports have indicated that the results are also sensitive to the grid resolution defined in FLACS-DustEx [62]. Thus, cubic cells of 0.05 m in size were used in several simulations to investigate the effects of grid resolution (see Table 4). These simulations were carried out considering no venting, i.e. for a closed vessel. In addition, the factor CL was varied to study the combined effect of grid resolution and mixture reactivity. In these simulations, a simplified approach was adopted for the initial conditions: instead of simulating dust injection from a pressurised bottle, a homogenous dust cloud was considered which completely filled the vessel prior to ignition, with average values for initial air velocity (0.3 m/s), relative turbulence intensity (140%) and dust concentration (700 g/m3). This approach has previously been applied to dust explosion simulations in silos [13,17,54]. In addition, one vented explosion was also simulated for the finer grid resolution (0.05 m), as indicated in Table 3 (simulation 101015). 2.4. Comparisons with venting standards Some of the simulation results were compared with the values predicted by venting standards. For EN 14491 [8], the general equations for isolated enclosures were applied. With respect to NFPA 68 [9], the method used was the correlation for minimum necessary vent areas without any correction for slenderness, which is necessary when L/D N 2, or for high-velocity equipment, which is necessary when the air velocity exceeds 20 m/s. The formulas applied in this study have previously been reported in detail by Tascón et al. [49]. 3. Results and discussion A summary of the results obtained using FLACS-DustEx for vented explosions is presented in Table 3, which gives the maximum explosion overpressure recorded from all the data obtained inside the vessel for each of the simulations (Pred,sim), together with the experimental explosion overpressure (Pred,exp) reported in [49]. The vent panel activation pressure Pact considered in each simulation, which was equal to the value recorded in the corresponding experimental test, is also included in the table. The results of the unvented explosion simulations are shown in Table 4. Pressure is given in bars throughout this paper (1 bar = 100 kPa), since the formulas for vent area sizing [8,9] define the different pressures in bars, and KSt and Pmax should also be presented in bar·m/s and bar, respectively, according to standards [50,63]. Gauge pressure is used in all tables and figures. Fig. 1 shows a cross section of the calculation domain, illustrating three steps of the flame propagation represented by the mass fraction of combustion products. As can be seen in Fig. 1, the flame propagated out of the computational domain. Although it is a good practice that the flame does not cross the boundaries, it is not expected that this situation would significantly affect the results, since the external explosion did not determined the maximum pressure peak in the scenarios simulated in the present study. However, it is important to remark that if the aim of the simulations were to study the external effects of the explosion (pressure and flame) or simulate scenarios where the pressure peak produced by the external explosion was relevant, it would be essential to increment the dimensions of the computational domain.

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Fig. 1. Vented dust explosion simulated with FLACS-DustEx. Flame represented by mass fraction of combustion products (kg/kg). Three time steps are plotted. A = 0.54 m2.

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pressure, which is inconsistent. These particular tests are discussed in Section 3.4.

Table 3 Simulated scenarios for vented explosions. Simulation no.

Test no.

Grid (m)

CL

Vent area (m2)

Pact (mbar)

Pred,exp (mbar)

Pred,sim (mbar)

102005 102006 101006 101007 103005 103006 102001 102002 101001 101002 101003 103001 103002 102003 102004 101004 101005 103003 103004 101015 103011 103012 103013 103014

9a 9b 8a 8b 7a 7b 9a 9b 8a–8b 8a 8b 7a 7b 9a 9b 8a 8b 7a 7b 8b – – – –

0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.05 0.10 0.10 0.10 0.10

1.00 1.00 1.00 1.00 1.00 1.00 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.50 1.50 1.50 1.50 1.50 1.50 1.00 1.25 1.25 1.25 1.25

0.35 0.35 0.54 0.54 0.84 0.84 0.35 0.35 0.54 0.54 0.54 0.84 0.84 0.35 0.35 0.54 0.54 0.84 0.84 0.54 0.84 0.84 0.84 0.84

134 156 196 208 200 130 134 156 202 196 208 200 130 134 156 196 208 200 130 208 100 300 50 0

246 282 251 286 234 210 246 282 – 251 286 234 210 246 282 251 286 234 210 286 – – – –

205 213 221 235 225 147 407 418 239 233 244 233 154 738 757 259 265 245 162 253 121 349 77 71

Fig. 2 shows the pressure-time history inside the vessel corresponding to the explosion illustrated in Fig. 1. The first pressure peak P1 (t = 0.891 ms) was produced by the vent panel activation. The second pressure peak P2 occurred when the flame reached the vent (t = 902 ms) and the burned gas, which has a much lower density, began to be expelled from the vessel [54]. Pressure then increased very slightly, and a series of small pressures peaks were observed, which might be related to the external flame propagation and explosion and subsequent flame oscillations, as explained in [54]. In addition, Fig. 2 illustrates the pressure values simulated at 2 points outside the vessel, placed along its longitudinal axis at 1.55 m and 2.55 m from the vent opening, and the instant when the flame reached the boundary of the computational domain (t = 950 ms).

3.1. Effects of vent area on Pred Fig. 3 shows a comparison between the explosion overpressures recorded in the set of experiments in Table 1 and the corresponding simulations performed for CL = 1.25. As can be seen, the predictions obtained with FLACS-DustEx were in reasonably good agreement with experimental data, although the CFD simulations appeared to overpredict explosion overpressures in the case of A = 0.35 m2. Values according to standards EN 14491 and NFPA 68 are also included in Fig. 3; these were calculated using the average activation pressure of the vent panels for the set of tests (171 mbar). However, the tests for A = 0.84 m2 were beyond the scope of the venting standards, since this area is so large that the formulas predict lower overpressures than the vent panel activation Table 4 Simulated scenarios for confined explosions. Simulation no.

Grid (m)

CL

Pmax,sim (bar)

[dP/dt]max,sim (bar/s)

KSt,sim (bar·m/s)

100080 100090 100081 100084 100085 100087

0.10 0.10 0.05 0.05 0.05 0.05

1.00 1.25 1.00 1.25 1.50 2.00

8.92 8.92 8.91 8.92 8.92 8.91

67 85 87 115 143 201

115 146 150 198 246 346

3.2. Effects of dust cloud reactivity on Pred All the experimental tests were simulated using three different values of CL. As can be seen in Table 3, the higher the value of CL, the greater the maximum overpressure reached in the simulated explosion. The value assigned to CL modifies the laminar burning velocity of the dust cloud, which in turn influences the turbulent burning velocity ST (see Eq. (1)). An increase in ST produces a higher rate of production of hot gases and thus a greater Pred pressure for a fixed vent area. It is important to note that two competing phenomena define the venting process: combustion and the subsequent production of hot gases, which increases the pressure in a confined volume, and flow discharge through the vent. However, Fig. 4 shows that the effect of CL on Pred was more obvious for A = 0.35 m2, whereas it was quite insignificant for A = 0.54 m2 and A = 0.84 m2. As described in Section 3.4, the vented explosion for the two largest vent areas seems to be controlled by Pact, and this could partly explain the different behaviour. Moreover, a significant part of the combustion process could occur outside the vessel in the case of large vent areas with a low Pact. Table 4 summarized the simulation results for confined explosions with a 5 cm grid resolution for values of CL from 1.00 to 2.00 (simulations 100081, 100084, 100085 and 100087). As can be seen, the maximum explosion overpressure (Pmax,sim) reached approximately the same value in all cases; the overpressure in unvented explosions depends on the energy content of the dust cloud and this is not influenced by CL. On the other hand, the maximum pressure rise per unit time ([dP/dt]max) was clearly influenced by burning velocity and the CL factor, i.e. it depends on the velocity of energy release. The standardised reactivity of the mixture in the simulations (KSt,sim) was calculated from [dP/dt]max,sim values following the cubic law [63] in order to compare the simulation results with the experimental KSt value (174 bar·m/s) obtained in the 20-litre vessel [49]. However, the comparison of these reactivity values is a simplification, since the KSt value should have been obtained from confined tests in the 5.2 m3 vessel, not from the 20-litre vessel [15]. Figs. 5, 6 and 7 show the simulated and experimental pressure vs. time histories of tests 7b, 8b and 9b, for the three CL values considered. For comparison purposes, the curves were moved along the axes to set the initial relative pressure to zero, eliminating any pressure variation prior to ignition, and to set the explosion ignition to the same instant in all cases. The effect of CL on the pressure curves is clear. As can be seen, there was a notable correspondence between the experimental tests and the CFD simulations with a vent area of 0.84 m2 or 0.54 m2. However, the shape of the simulated and experimental pressure curves differ appreciably for tests with A = 0.35 m2. This suggests that the initial level of turbulence in the simulations might have been too high or that the empirical correlation of the combustion model might tend to overpredict the burning velocities in the explosion scenario considered [26]. Unfortunately, the experimental tests by Tascón et al. [49] did not include measurements of initial turbulence or dust concentration. In addition, various phenomena that are not modelled by the numerical code can reduce the explosion overpressure, such as dust settling and agglomeration or partial flame quenching [62]. Previous studies have also obtained overpredictions for other explosion scenarios [15,61,62]. 3.3. Effects of grid resolution on Pred Table 4 shows that the maximum overpressures obtained in the confined explosion simulations did not depend on grid resolution (simulations 100080 and 100081). In contrast, the pressure rise [dP/dt]max was strongly influenced by grid resolution. Fig. 8 considers

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Fig. 2. Pressure-time curves obtained by numerical simulation with FLACS-DustEx (simulation no. 101001).

the effects of grid size and mixture reactivity simultaneously. As can be seen, the 0.05 cm grid cells enhanced the rate of energy release. The reasons for this behaviour have been indicated by Skjold et al. [32]: firstly, a finer grid resolution results in a thinner flame with a larger flame area, considering that the flame model in FLACS-DustEx yields a flame that is three grid cells thick; and secondly, on a finer grid it takes less time for the initial flame ball, which is governed by a sub-grid model with a low rate of combustion, to reach a size where the 3-cell thick flame model starts to govern the combustion, which then propagates through a higher turbulent flow field in the case of flows with rapidly decaying turbulence. The results shown in Fig. 8 also indicate that [dP/dt]max is directly proportional to the factor CL. It can be deduced from Fig. 8 and Table 4 that for the explosion scenarios considered in the present study, similar simulation results might be achieved using either a condition set of 0.10 m cells and CL = 1.25 or a condition set of 0.05 m cells and CL = 1.00. Skjold [60] noted that modifying mixture reactivity by varying CL can compensate for the effect of grid resolution. The results in Fig. 8

suggest that for coarse grid resolutions, normally used for large scenarios, the factor CL should be higher than for fine grid resolutions; this statement agrees with other previous studies [15,26,62]. Simulations 101007 and 101015 (see Table 3) serve to compare the results obtained in vented explosions for two different grid resolutions with the same mixture reactivity (CL = 1.00). The variation in Pred was approximately 8%, with the smaller grid leading to a higher Pred and a smaller difference with the experimental value. Moreover, the finer grid resolution (0.05 m) would yield a better fit of the real vessel geometry to the grid – there are some small differences between the volume and vent areas of the experimental vessel and those used in the simulations with a 0.10 m grid resolution – but it is not clear that this modest increase in accuracy justifies the associated increase in computational cost, especially for larger explosion scenarios [15]. As described above, the use of the correction factor CL can compensate for the differences due to grid resolution or, in other words, CL should be selected considering the grid size chosen for the simulations and the corresponding code guidelines. 3.4. Effects of activation pressure on Pred

Fig. 3. Simulated explosion overpressures compared with experimental data [49] and standards EN 14491 [8] and NFPA 68 [9]. Results obtained for CL = 1.25.

Tascón et al. [49] indicated that there might be a vent area size, with respect to a given volume to be protected, after which it is no longer possible to reduce the explosion overpressure, even when the vent area is increased further. For this vent area size, Pred might be determined by the vent activation pressure. This situation is illustrated in Fig. 3. As can be seen, the increment in vent area from 0.35 m2 to 0.52 m2 and 0.83 m2 did not produce any significant effect on overpressures recorded in the tests. This specific aspect was further investigated through simulations using FLACS-DustEx with different activation pressures for the case of A = 0.84 m2 (simulations 103001, 103002, 103011, 103012, 103013 and 103014). The simulation results are shown in Fig. 9 and indicate a quasi-linear relationship between Pact and Pred when Pact N 50 mbar. The results reported by Cooper et al. [64] and Fakandu et al. [65] for vented gas explosions also showed a linear trend between Pact and Pred. The simulation results in Fig. 9 indicate a good agreement between CFD modelling and the experimental data and venting standards. The Pred value at Pact = 0 mbar (free venting) was no lower than at Pact = 50 mbar; this somewhat unexpected result was identified and explained in detail by Fakandu et al. [65], who pointed out that the initial flame propagation inside a vessel with a covered vent opening

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Fig. 5. Comparison between numerical simulations using FLACS-DustEx (A = 0.84 m2) and experimental test 7b. Simulation 103006 corresponds to CL = 1.00, 103002 to CL = 1.25 and 103004 to CL = 1.50.

activation pressure determined in static conditions [66] for commercial venting devices. Pstat is the value used by venting standards [8,9] to calculate vent area sizes. The dynamic activation pressure is greater than the static value because materials are stronger under short dynamic pressure pulse loading than under slow static pressure loading [7,9]. However, to calculate the EN and NFPA curves in Fig. 9, it was assumed that Pstat = Pact, since this assumption would not modify the general trends deduced from the figure. Unfortunately, very few large-scale test programmes have simultaneously reported the static and dynamic activation pressures of the vents. DeGood and Chatrathi [67] reported an extensive set of propane explosions with a mean difference for

Fig. 4. Experimental and simulated explosion overpressures vs. activation pressure of the vent panel. Results obtained for three values of the correction factor CL (1.00, 1.25 and 1.50). Experimental data from [49].

(with Pact = 0.035 mbar) is slower than with free venting and can result in a slightly lower Pred for covered vents. Standards EN 14491 and NFPA 68 are also included in Fig. 9: the Pred value that would be achieved was calculated by means of the general calculation formulas, considering A = 0.84 m2 and the corresponding activation pressure value recorded in the experimental test. However, only values between Pstat = 0 bar (free venting) and Pstat = 40 mbar could be calculated and included in Fig. 9, since for Pstat values higher than 40 mbar, the EN 14491 and NFPA 68 standards yielded Pred values lower than Pstat, which is inconsistent. Thus, the “Pred = Pstat” line was included in Fig. 9 for situations with Pstat N 40 mbar (by definition, the Pred value should be ≥ Pstat). It is also important to note that in Fig. 9 the EN 14491 standard has been applied beyond its range of application; this venting correlation is only valid for Pstat ≥ 0.1 bar. The activation pressure of the venting device – here, Pact – is associated with the vent panel bursting during an explosion event and corresponds to the dynamic activation pressure, while Pstat is the static

Fig. 6. Comparison between numerical simulations using FLACS-DustEx (A = 0.54 m2) and experimental test 8b. Simulation 101007 corresponds to CL = 1.00, 101003 to CL = 1.25 and 101005 to CL = 1.50, with 0.10 m grid resolution. Simulation 101015 (dotted line) corresponds to CL = 1.00 and 0.05 m grid resolution.

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Fig. 9. Correlation of the explosion overpressure with the activation pressure of the vent panel. A = 0.84 m2. Comparison of simulations with experimental data [49], EN 14491 [8] and NFPA 68 [9]. Fig. 7. Comparison between numerical simulations using FLACS-DustEx (A = 0.35 m2) and experimental test 9a. Simulation 102006 corresponds to CL = 1.00, 102002 to CL = 1.25 and 102004 to CL = 1.50.

(Pact − Pstat) of 23 mbar, which corresponds to Pact/Pstat = 1.23 for panels with Pstat = 100 mbar. It can be deduced from Fig. 9 that Pact determined the maximum explosion overpressure in the case of the 5 m3 vessel with A = 0.84 m2. Fakandu et al. [65] indicated that the parameter KV (=V2/3 / A), which is the porosity of the vessel walls or the cross sectional area of a cube of equivalent volume divided by the vent area, influences the role that Pact plays in Pred. According to the gas explosion tests carried out in a 10-litre vessel by Fakandu et al. [65], Pred seems to be controlled by Pstat for a KV of 7.2 or lower. In the explosion scenarios simulated here, the parameter KV was equal to 3.62, 5.77 and 8.58 for a vent area of 0.83 m2, 0.52 m2 and 0.35 m2, respectively. Thus, the tests with KV = 3.62 and KV = 5.77 would correspond to explosions with overpressures determined by the activation pressure of the venting device, while the

overpressures in the tests with KV = 8.58, which is near to the critical value of KV = 9 proposed by Fakandu et al., would be determined by the flow through the vent and the effect of Pstat would be lower. The CFD simulations of maize starch explosions and the experimental data reported in [49] seem to agree with the results for methane explosions by Fakandu et al. From the results shown in Fig. 9 and the above discussion, it follows that for situations with low KV, the explosion overpressure could be calculated from the static activation pressure of the vent panels. Eq. (2) gives the line of best fit to the simulation results shown in Fig. 9 for the 5 m3 vessel with A = 0.84 m2 (KV = 3.62) and Pact ≥ 50 mbar. To calculate the explosion overpressure Pred, it is proposed that Pstat should be increased by means of two correction terms: the first, Cd (dynamic activation correction factor), would take account of the increment between the static and the dynamic activation pressure of the vent panel and would be equal to the Pact/Pstat ratio, while the second, Cb (burst pressure peak correction factor), would take account of the difference between Pred and the dynamic activation pressure Pact, and would be equal to the Pred/Pact ratio. P red ¼ C b  P act ¼ C b  ðC d  P stat Þ

Fig. 8. Correlation of the maximum rate of explosion pressure rise with the correction factor CL. Comparison of results obtained for two different grid resolutions in confined explosions.

ð2Þ

For the simulations included in Fig. 9 with Pact ≥ 50 mbar, the mean Cb (=Pred/Pact) was 1.18. According to the set of experimental results presented by DeGood and Chatrathi [67], the value of Cd (=Pact/Pstat) would be approximately 1.23 if using panels with Pstat = 100 mbar. Following Eq. (2), the total correction parameter (=Cd · Cb) by which to multiply Pstat to give Pred is 1.45, showing close agreement with the value (1.37) obtained by Fakandu et al. [65], and with the constant of 1.5 given by one of the Rasbash equations for gas explosion venting [68]. It is important to note the multi-peak nature of vented explosions. Several pressure transients can be generated during a vented explosion, each of which is influenced by different physical phenomena. This fact has been studied for gas explosions by a number of researchers [64,69, 70]; in addition, several pressure peaks have been obtained for vented dust explosions using CFD simulations [54]. In all the explosions shown in Fig. 9, except for the simulations for Pact = 0 mbar and for Pact = 50 mbar, the Pred value reported as the maximum overpressure corresponded to the first peak of the curve, i.e. the peak produced by the vent panel opening, which has sometimes been referred to by other researchers as Pburst or P1 [65]. For this reason, Eq. (2) would predict the first pressure peak.

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The correlation proposed in Eq. (2) is simply intended to draw attention to some cases that are not contemplated by venting standards. It is clear that more work is required to investigate the influence of Pact and KV on Pred, including other scenarios involving different mixture reactivities, different volumes and KV values, and different length-todiameter ratios of the vessel. Experimental determination of both static and dynamic activation pressures in explosion test programmes seems indispensable. 4. Conclusions The numerical simulations carried out in the present study made it possible to further elucidate the results obtained in previous experimental tests and to conduct a more in-depth analysis of some scenarios that are not contemplated by standards or are beyond their limits of applicability. The results obtained with FLACS-DustEx were generally in good agreement with the experimental tests, but in some cases the simulations overpredicted the explosion pressure. Several conclusions can be drawn from the simulation results: • The simulation results were quite sensitive to grid resolution and mixture reactivity, but the analysis carried out indicates that it is possible to achieve results in excellent agreement with experiments. The recommended value for the reactivity correction factor CL is approximately 1.25 for 0.1 m grid cells, although this value tended to overestimate Pred for the smallest vent area (A = 0.35 m2). • The parameter Kv (=V2/3 / A) plays an important role in the explosion development. When Kv was low, the results indicated a clear dependence of the maximum explosion overpressure Pred on the activation pressure of the vent panel P act, which controlled the explosion development. • When the explosion overpressure is determined by Pact, reducing Pred by increasing the vent area is no longer possible. • The present results suggest the importance of determining both the static and dynamic activation pressures of the venting devices in future explosion test programmes. • Standard EN 14491 [8] does not consider situations with P stat b 0.1 bar. This limit represents a restraint for those design scenarios with a low Kv, where Pred needs to be further reduced by lowering the activation pressure of the venting device. In particular, these cases represent an important area of vent protection in some industrial applications, such as silos and other low-strength equipment. • CFD simulations enable analysis of selected aspects of explosion venting that cannot be studied through the ordinary use of venting standards. However, considerable inherent uncertainties exist in both large-scale tests and simulated values. There is still a clear need for further research in this area, including repeated large-scale experiments with detailed measurements of variables other than pressure, such as flame arrival times during explosion and dust concentration and turbulence levels in the particle-laden flow prior to ignition.

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