Overpressure Effects from Propane Detonation: Comparison of Simulation Results with Experimental Data

Keywords: CFD, detonation, blast wave, protective walls, validation

Accidental gas explosion is a standard scenario considered in risk assessment for process industries. Blast walls or barriers are an efficient way to reduce the effects of pressure waves originated from an explosion. However, the proper design of a blast wall requires heavy investigation considering real accidental scenarios. CFD-based method can be used for a parametric investigation and for design optimization instead of experimental investigations. Nevertheless, the first CFD codes must be validated versus corresponding experimental data. The purpose of this paper is to present comparison of CFD simulations of propane/oxygen detonation and experimental measurements for small scale explosions.

INTRODUCTION

Accidental gas explosion is a standard hazard usually considered in risk assessment for process industries. Pressure waves originating from an explosion can result in unacceptable risk for infrastructures and people present on and outside the site. Blast walls are an efficient way to significantly decrease the effects of the overpressure, and hence to protect people and infrastructures. However, the proper design of a blast wall requires heavy investigation, considering real accidental scenarios. The prediction of blast effects behind the blast walls requires a detailed understanding of the phenomenon, taking into account the interaction of blast waves with the barrier and with the ground. This interaction strongly depends on the wall dimensions (height, width and thickness), the angle of the inclination of the front and the back side, the distance to the blast wall, etc.

Due to the complexity of the phenomenon associated with blast wave interactions with the wall, a computational fluid dynamics (CFD)-based method may be used for a parametric investigation or for design optimization.

In France, CFD is not commonly used for the modeling of on-shore explosions at industrial sites. In most cases engineering models [START_REF] Van Den | The Multi-Energy Method -a framework for vapour cloud explosion blast prediction[END_REF] are used for the definition of safety distances. These methods are developed for hemispherical or spherical symmetries, with explosions of constant flame speeds. They do not take into account different flow effects, obstacles, or the time history of the flame velocity. CFD can bring more accurate results, involving 3-D Navier-Stokes and combustion equations. However, first CFD the codes must be validated in terms of their correspondence with experimental data.

A French Workgroup led by INERIS including industrial companies, design offices, and national institutions was created to obtain a practical state-of-the-art on strengths and weaknesses of CFD tools. 10 explosion test cases were selected, each based on published experimental data.

Five partners (Air Liquide, INERIS, IRSN, Apsys, Fluidyn) joined together to perform comparison of CFD results and experimental data. The computations are compared to the experimental results for a laboratory-scale detonation of a hemispherical gaseous charge with (see Eveillard [START_REF] Eveillard | Propagation d'une onde de choc en présence d'une barrière de protection[END_REF]) and without (see Trélat [START_REF] Trélat | Impact de fortes explosions sur les bâtiments représentatifs d'une installation industrielle[END_REF]) the blast walls.

SMALL-SCALE EXPERIMENT

An explosion in a hemispherical soap bubble of 6cm radius is investigated. The bubble initially contained a propane oxygen mixture in stoichiometric proportions. This mixture was at rest initially.

Ignition was initiated by an exploded wire. The nominal electrical energy associated with the discharge according to Trélat [START_REF] Trélat | Impact de fortes explosions sur les bâtiments représentatifs d'une installation industrielle[END_REF] was 200 J. However, it is difficult to estimate exactly how much energy was transmitted to the flammable mixture.

A trapezoidal barrier made of a wood was used in the experiments of Eveillard [START_REF] Eveillard | Propagation d'une onde de choc en présence d'une barrière de protection[END_REF]. The barrier was 60 cm wide and 80 cm long, see Fig. 1. Pressure sensors (P1-9) were located on the centerline upstream and downstream of the barrier.

Fig. 1.

Experimental set-up of Eveillard [2]. The green dots are the pressure sensors positions; the red star is the explosive charge location.

According to Eveillard [START_REF] Eveillard | Propagation d'une onde de choc en présence d'une barrière de protection[END_REF], the experimental uncertainty was estimated to be +/-14% in pressure. The temporal uncertainty was 5-8%. Trélat [START_REF] Trélat | Impact de fortes explosions sur les bâtiments représentatifs d'une installation industrielle[END_REF] performed the same experiments as Eveillard [START_REF] Eveillard | Propagation d'une onde de choc en présence d'une barrière de protection[END_REF] but in a free field. The difference between the two experiments for the pressure at 10 cm (P1) was ~ 10%, which is in agreement with the values previously mentioned. Hence, 15% error on the experimental results is considered in the current investigation for the overpressure.

For comparison with simulations, only reliable sensors are considered: P1, P2, P4, P7 and P9.

Modeling approaches for the small scale experiments of a Rupture of a High Pressure, High Temperature Reservoir containing equivalent energies. All Participants used this modelling approach, and the 5 Bench Particpants used 5 different Codes.

MODELING APPROACHES FOR THE SMALL SCALE EXPERIMENT

Pressure waves from an explosive charge could be modelled by the ones originating from a rupture of a high pressure-high temperature reservoir containing the equivalent energy. All participants of the bench used this modeling approach.

For modeling, 5 bench participants used 5 different CFD codes.

Description of CFD codes and corresponding mesh

Air Liquide (AL) used a commercial CFD code FLACS V10.6 [START_REF]FLACS overview[END_REF]. FLACS solves the compressible Navier-Stokes equations on a Cartesian grid. Simulations are fully 3D, with the k-ϵ model used for turbulence representation. FLACS [START_REF]FLACS overview[END_REF] recommendations for a time step are applied in this investigation for the CFL number: CFLC = 0.1, CFLV = 0.1 and the option "keep low" is also applied. This option prevents the initial step from growing in a far-away distance to reduce diffusivity in the far field. AL models a computational domain of 1.2 m in downstream and crossstream directions [-0.6m; 0.6m] and 0.6 m in the vertical direction. APSYS used OpenFOAM (Open source Field Operation And Manipulation) [6], which is a C++ toolbox of customized numerical solvers and pre/post processing utilities for the solution of continuum mechanics problem, including CFD. It includes a varied range of solvers that are available for computation, either within structured / unstructured mesh, of simulation cases using the finite volume method. In the current simulations, "RhoCentralFoam" solver (solves the Euler equations with the central Kurganov and Tadmor scheme [START_REF] Kurganov | New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection-Diffusion Equations[END_REF] for the convection operator. A 3D domain (size 1.95 m x 0.6 m x 0.6 m) that contains around 1.8 billion elements is used. Mesh is refined along obstacles and in the near field of the explosion center, with cell size between 7.5 mm and 3.75 mm. Explosion was modelled by the pressure release of a compressed hot air hemisphere.

Hemisphere radius has been chosen to be close to the one used in experiment (6cm) and hemisphere Chapman-Jouguet Temperature was estimated to be T CJ = 3815 K. Knowing the energy contained in the hemisphere (around 4100 J), the Brode equation was used to determine initial hemisphere pressure.

FLUIDYN used a commercial code that they developed, fluidyn-VENTEX. VENTEX solves the compressible Navier-Stokes equations on structured or unstructured mesh. Several turbulence models are available; the k-ϵ model was used in the simulations presented here for turbulence representation. Among the possible numerical schemes, the Euler scheme was used for time resolution and the UDS scheme was used for convection resolution. The domain of simulation is a 2D-axisymetrical domain, with the vertical axis through the center of the explosive volume as symmetry axis. The domain size is 2 x 0.5m and the mesh was comprised of 363000 elements, with a cell size between 1 and 2 mm. A preliminary simulation was done for a similar experience, without the presence of the wall. The Chapman-Jouguet pressures and temperature were estimated to be T CJ = 3815 K and P CJ = 34.1 bar g. The explosion was modelled by the pressure release of a hemisphere containing compressed air, with a radius of 6 cm and with internal pressure and temperature those of Chapman-Jouguet. Hence, the energy inside the hemisphere is equal to 3900 J. The equation of state is that for a perfect gas. The choice had been made to take the volume of the equivalent hemisphere equal to the volume of the bubble to represent the case the same way Fluidyn should have done it with a more geometrically complex scenario.

INERIS used the OpenFoam 3.0.0 code [6] for this calculation. It has been decided to use the rhoCentralFoam solver i.e. to solve the Euler equations with the central Kurganov and Tadmor scheme [START_REF] Kurganov | New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection-Diffusion Equations[END_REF] for the convection operator. A 2D axisymmetric domain (centered on the explosive charge) of 2m by 1 was used, decomposed with a 4 million cell mesh (Δx = 0.7 mm). At such a scale both the wall and the charge can be explicitly resolved on the mesh with a satisfying accuracy. was chosen to rely on the Stanyukovich model [START_REF] Stanyukovich | Nonstationary motion of continuous media[END_REF] of an instantaneous detonation in the soap bubble. The detonation wave in propane travels at about 2360 m/s [START_REF] Shultz | Validation of Detailed Reaction Mechanisms for Detonation Simulation[END_REF], which implies a delay of 0.02 ms in the considered bubble. It corresponds to about one-tenth of the duration of the wave recorded on the first sensor, so we say it is still acceptable for our calculation. A theoretical approach based on a Riemann problem of a 1D detonation wave propagating in a tube, leads to relatively simple pressure temperature and velocity profiles in the bubble that can be found in almost any detonation course. Averaging those profiles over the distance on Cartesian coordinates, between the center of the detonated bubble and its shell leads to P = P CJ /2, T ≈ 0.9T CJ and u ≈ u CJ /4 (the CJ subscript standing for the Chapman Jouguet state). For our calculations, we chose to keep in the bubble P = P CJ /2 (P CJ = 35 bar according to [START_REF] Shultz | Validation of Detailed Reaction Mechanisms for Detonation Simulation[END_REF]. For the temperature, it is considered that thermal equilibrium does not have the time to be attained, and the maximum temperature T = T CJ is kept. Representing the speed is more difficult in terms of programming the initial conditions, because of the variable direction of the velocity vector, so we left it at 0. At last, due to the small size of the load, compared to the calculation volume, it was decided not to model the gases differently in the bubble, with respect to the atmosphere outside the bubble. Several approximations are made, but the calculations only rely on limited data for the firing configuration, (bubble size, position and dimensions of the merlon), These remain the same in the model, and the information published in the scientific literature (in the present case the measurements of pressure and detonation temperature CJ of the propane oxygen mixture, that are completely independent of the test modelled). Thus, this method is not based on any adjustment to the analyzed test, and aims to provide a generalizable and predictive result, rather than the best possible agreement with the experimental data.

IRSN used a commercial software LS-DYNA that solves the compressible Euler equations. A very short time step of 0.2 µs is used. For the free field geometry IRSN uses for the size of the computational domain 1.5 m horizontal direction [0 m; 1.5 m] and 0.8 m in the vertical direction [0m, 0.8 m]. The grid is stretched from 1 up to 5 mm corresponding to ~120 000 cells. For the geometry with a protection barrier IRSN uses the same size of the computation domain and the same mesh, corresponding to ~450 000 cells. Finer cells are used close to the barrier to properly model the reflection of pressure waves in this area.

All the participants model the generation of the shock wave from the gaseous detonation by an equivalent burst. In AL and IRSN calculations, the radius R of this high-pressure and hightemperature equivalent hemispherical vessel is calculated as follows:

? u õg u ∆ö ÷U= •,
where ∆X is the overpressure inside the vessel, • is the energy released by the burst. Burst parameters used by bench participants are given in Table 1.

All bench participants use the same gas (air) at the same temperature. All modelers have chosen, except INERIS, a pressure about 35 barg (Chapman-Jouguet pressure) in the burst bubble. The choice of the radius value varies according to the modelers between 5.05 cm and 6 cm. Note, however, that the energy theoretically deposited varies by a factor of two between INERIS/IRSN modeling choices and AL/APSYS/Fluidyn ones. AL and APSYS chosen 3D approach, which could allow them to model lateral overturning waves, which is not possible to obtain by a 2D approach.

SIMULATION RESULTS FOR SMALL SCALE EXPERIMENT

For the detailed comparison of simulation results with experimental data, the following parameters can be used: maximum accidental overpressure; travel time of the pressure wave between sensors (more objective than the arrival time of the shock wave, since current approaches do not model the explosion combustion); pressure rise:

YX Y X Z[\ X M 6Z[\ 6M
.

The thickness of a shock wave in air is of the order of the mean free path, i.e. about 100 nm. With a pressure wave ranging from 5 bar to a few tens of mbar, impact velocities of 800 to 350 m/s are considered, i.e. a pressure rise time of 100 to 300 picoseconds. The reason for focusing on the pressure rise rate of the experimental, or simulated signal, is purely qualitative. As we are in the presence of a detonation in the soap bubble, a shock wave steep profile is expected outside. However, the time resolution of real sensors as well as simulated ones is being insufficient to capture the rate of rise in pressure. Consequently, we compare the dP/dt of the digital signals to know if we are approaching the shape of a shock or not. It is a qualitative estimate, to assess to which extent, the physical phenomenon is reproduced or not.

Free field geometry [3]

Free field geometry (Trélat [3]) was modeled only by 3 participants of the bench: AL, IRSN and Fluidyn. The corresponding source terms described in Table 1 are used.

Figure 2 shows the pressure signals at various distances from the center of the charge: 10 cm, 20 cm and 30 cm. Results of AL with FLACS and IRSN with LS-DYNA/CESE match well with experimental data for the maximum overpressure and for the corresponding impulse. AL pressure signal in slightly more diffusive compare to IRSN results due to two main differences. AL uses Navier-Stokes, whereas IRSN uses non-viscous equations (Euler equations), which are less diffusive. AL used mesh of 5 mm wide cells, whereas IRSN cells width is 1 mm. AL simulations with a finer mesh comparable to the one from IRSN should show less diffusion. However, in both simulations (from AL and from IRSN) the error on the maximum overpressure for each monitoring point is less than the experimental error (15%). Fluidyn overestimates the overpressure at 10 cm and 20 cm by 26% and 14% correspondingly and predicted a pressure at 30 cm lower than the experimental error.

Geometry with a protection barrier [2]

Figure 3 shows comparisons of predicted and measured of pressure signals at monitoring points P1 and P2 upstream to the barrier.

This comparison demonstrates that APSYS and Fluidyn overestimate the overpressure at both positions by 17.6, 26.6, 18.9, and 19.3 % respectively. AL slightly underestimates the overpressure at P1 by 15.2% and slightly underestimates at P2 by 17.7%. In the case of the monitor position P2 (located on the ground, 13.7 cm from the center of the explosive charge), the pressure signal has a two peak-shape. The first peak corresponds to the incident peak (from detonation), whereas the second one is the pressure reflection from the barrier. AL uses the coarsest grid compare to other bench participants, which does not allow for a correct separation of these peaks. The finest AL grid is of 0.25 cm, where the distance from monitor point to the barrier is only 0.3 cm. APSYS uses a coarse grid too, which also interferes a correct separation of two pressure peaks. For the correct resolution of this double-peak structure, the simulation grid should be at least twice smaller than the distance between the monitor point and the barrier.

INERIS computation underestimates the overpressure at P1 and P2 by ~25% and 20%, simulations show that the reflected pressure peak at P2 is higher than the accidental one.

IRSN results are in the best agreement with experimental data at both positions P1 and P2.

Figure 4 shows pressure signals at monitoring points P4 and P5 located on the barrier. INERIS computation underestimates the overpressure at P4 and P5 by ~19% and 14% (experimental error is 15%). APSYS overestimates the overpressure at P5 by 17%, all other results are within the experimental error.

Figure 5 demonstrates pressure signals at monitoring points P7 and P9 located behind the barrier. INERIS computation underestimates the overpressure at P7 and P9 by ~28% and 13% (experimental error is 15%). Results from all other bench participants are within the experimental error.

Part 3. Deflagration, DDT, Detonation Fig. 2. Simulation results for pressure wave propagation in a free field geometry, exp -data from Trélat [3]. Hence, the travel time of the pressure wave between sensors is also a very important parameter. In general all bench participants correctly estimate travel time, see Fig. 6.

CONCLUSION

Based on the current investigation several conclusions can be made:

• The methods based on 2D-axisymmetric approaches demonstrates a better conservation of the shock compared to the meshes 3D due to a finer mesh.

• The accuracy obtained by the 2D and 3D approaches for the overpressure magnitude, and wave arrival times are very similar. Nevertheless, the best results are obtained by a 2D mesh (IRSN simulations).

• Accurate modeling of the burst is essential for correct prediction of the far-field overpressure effects related to a charge explosion. INERIS suggested a universal model, which was previously tested for other configurations and gases. Additional bench participant will test this approche in the future.

• The underestimation of the overpressure peaks is related either to the source term or to the numerical diffusion. Hence, for the risk assessment it is better to use validated term source

• The results obtained for the peak of overpressure are quite satisfactory (max error and 26%) compared to the experimental measurement error (15%).

• The good agreement in terms of the travel time is found for AL, APSYS and IRSN calculations (the relative difference of simulation and lower than the measurement error).

• A fine mesh for pressure should be preferred to simulate the wave propagation: the effect of numerical diffusion due a coarse mesh can exceed the effect of physical diffusion. However, the numerical diffusion can also be due to the precision of the numerical scheme, corrective flux, artificial viscosity (for example, used in the k-epsilon model), Gibbs error etc.

• Euler equations (APSYS, INERIS and IRSN) give better conservation of the shock even for a coarse mesh. The Navier-Stokes approach requires a much finer mesh to keep the shock. In this case, it is also possible to assume the turbulent viscosity to be 0 with an ad hoc initiation of the characteristic sizes of the turbulence. Results will be less diffusive and this approach will help to conserve the shock.

• A qualitatively correct shape of the overpressure signal at the sensor close to the barrier (including the maximum overpressure, the impulse and the nature of the peak, incident or reflected) can be predicted if at least 1 cell is set between the sensor and the barrier. 3 cells is an ideal choice.

Fig. 3 .

 3 Fig. 3. Simulation results for pressure wave propagation in the presence of the barrier (exp -data from Eveillard [2]): pressure sensors located upstream of the barrier.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Simulation results for pressure wave propagation in the presence of the barrier (exp -data fromEveillard[START_REF] Eveillard | Propagation d'une onde de choc en présence d'une barrière de protection[END_REF]): pressure sensors located on the barrier.

Fig. 6 .

 6 Fig. 6. Scatter plot of comparison simulates with experimental data by Eveillard [2]: travel time.

Fig. 7 .

 7 Fig. 7. Scatter plot of comparison simulations with experimental data by Eveillard [2]: pressure rise.

Table 2

 2 gives description of physical and numerical approaches used by bench participants.

Table 1 . Description of the equivalent source used by bench participants

 1

		AL	APSYS	Fluidyn	INERIS	IRSN
	Eq. source	Hemisphere, R=5.05cm	Hemisphere, R=6cm	Hemisphere, R=6cm	Hemisphere, R=6cm	Hemisphere, R=5.05cm
	T	3843 K	3815 K	3815 K	3830 K	3843 K
	P	35.1 barg	36.3 barg	34.1 barg	17.5 barg	35.1 barg
	Gas	air	air	air	air	air
	γ	1.213	1.4	1.4	1.4	1.4
	ρ	3.26kg/m 3	3.3 kg/m 3	3.18 kg/m 3	1.65 kg/m 3	3.18 kg/m 3
	E	4.4kJ	4.1 kJ	3.9 kJ	1.9 kJ	2.4 kJ

Table 2 . Modeling approaches used by bench participants

 2

		AL	APSYS	Fluidyn	INERIS	IRSN
	Transport equations	Navier-Stokes	Euler	Navier-Stokes	Euler	Euler
	Domain topology	3D	3D	2D-axi	2D-axi	2D-axi
	Grid size in zone of inter.	2.5 mm	3.75 -7.5 mm	1 -2 mm	0.7 mm	1 -5 mm
	Numerical schemes	Time: Euler Conv.: weighted centered 2nd order/Upwind	Time: Euler Conv.: Tadmor /Kurganov	Time: Euler Conv.: UDS	Time: Euler Kurganov Conv.: Tadmor/	Time: Euler Conv.: CE-SE

Table 3 . Simulation results for the maximum overpressures

 3

			P1	P2	P4	P5	P7	P9
	Exp. P (barg)	5.21	3.28	0.2	0.074	0.055	0.044
		Sim P(barg)	4.42	3.86	0.2	0.065	0.056	0.045
	AL	Error, %	-15.2	17.7	within	within	within	within
					exp. error	exp. error	exp. error	exp. error
		Sim P(barg)	6.13	4.15	0.19	0.087	0.056	0.042
	APSYS	Error, %	17.6	26.7	within	17.2	within	within
					exp. error		exp. error	exp. error
		Sim P(barg)	3.9	2.6	0.16	0.063	0.045	0.038
	INERIS	Error, %	-25.2	-20	-19.2	within	-18	within
						exp. error		exp. error
		Sim P(barg)	4.9	3.3	0.19	Not	0.058	0.044
	IRSN	Error, %	within exp.	within exp.	within	calculated	within	within
			error	error	exp. error		exp. error	exp. error
	Fluidyn Sim P(barg)	6.2	3.9	0.2	0.077	0.058	Not
		Error, %	18.9	19.3	within	within	within	calculated
					exp. error	exp. error	exp. error

Table 3

 3 shows the comparison of simulations results with experimental measurements in terms of maximum overpressure at each pressure sensor. According to this table, results of IRSN are in the best agreement with experimental data: the error between simulations and measurements is within the experimental error for all pressure detectors. Fluydin & APSYS overestimate the overpressure at the closest pressure sensors P1 & P2 (upstream of the barrier). AL underestimates the overpressure at P1 and overestimates at P2, whereas pressure at other pressure sensors is within the experimental error. INERIS underestimates the overpressure at sensors P1, P2, P4 and P7 by 20-25%. This underestimation is due to the difference in the burst energy: energy used by INERIS is ~20% less than the energy used by IRSN. All bench participants demonstrate a better match with the experimental data behind the barrier.

  Figure7illustrates the comparison of simulation results with experimental data for pressure rise behind the barrier. Underestimation of the preesure rise can be attributed to numerical (mesh) and physical (Navier-Stokes equations) diffusion. The best results for the pressure rise are obtained by INERIS who uses Euler equation and the finest grid compare to other bench participants. IRSN results are slightly more diffusive due to a coarser grid. APSYS uses the coarsest grid, which increases the numerical diffusion and leads to the lowest pressure rise compare to other bench participants. Actually, this numerical diffusion is more important than the physical diffusion specified by the approach of Navier-Stokes equations used by AL and Fluidyn. Behind the barrier AL and Fluidyn use similar meshes (2.5 mm for AL and 2 mm for Fluidyn), that is why the pressure rise is almost the same.


Function Testing of Passive Explosion Isolation Flap Valves

Keywords: Dust explosions, explosion mitigation, phenomenological modelling

Passive isolation flap valves are relatively simple devices that are widely used in the process industries. However, as an explosion mitigation technique, they function only within well-defined conditions and the physics at stake make their definition challenging. INERIS method and findings are presented in the current paper. They concern passive flap valves tested on 1 and 10 m 3 vessels with pipes of diameters of 150, 300 and 800 mm. The relatively simple configuration of a flap valve connected to a vented vesselstraight duct arrangement is considered. The initially opened flap valve is triggered by the explosion in the vessel and must close within a delay, short enough to prevent the flame passing. Before valve closure, the flow is accelerated by the explosion and large velocities can be reached in the duct (typically on the order of 200 m/s with a vented vessel, but as much as 800 m/s is possible). Upon valve closing the kinematic energy of the flow is converted into heat and pressure in front (on the explosion side) of the valve while a depressurisation is observed behind it (on the isolated side). Typically, a factor of 4 between the pressure in the vessel and the pressure measured at the valve can be observed. Phenomenological modelling is used in extension to a parametric experimental study to investigate the limits of the valve, its possible installation distances and a practical method for dimensioning is proposed.

INTRODUCTION

As a notified body, INERIS performs functioning tests of various explosion protection devices from many manufacturers, as a means of assessing their efficiency, and limits whilst eventually delivering an ATEX certificate. This is required for their distribution on the European market. Certification of such devices may be done following specific standards, such as EN14797 [1] for vent panels. However, in some occurrences the standard requirements for the testing are very unpractical or lack fundamental information and need the use of equipment, barely accessible to any notified body. For instance, the EN16447 [2] standard for isolation flap valves requires the largest size of the valve to be tested on a vessel duct arrangement with a volume corresponding to the minimum accepted for the intended use of this valve. Several reasons motivate these choices: in smaller volumes, the pressure rises more significantly, while larger devices are less resistant to the explosion and usually slower (as the flap is bigger it has more inertia, but it can be compensated by a spring). In practice several questions appear, some concern the physical mechanisms investigated, and other the limits of the testing capabilities. According to the standard, it is necessary to use a fan on the installation, to produce the "pushed" or "pulled flow" situation needed for the tests. However not only can such a system be tremendously costly (as the valve diameter can be of the order of 1 m), but it is also very unpractical. From a purely scientific point of view, controlling an explosive dust atmosphere (concentration, turbulence) then becomes extremely complicated. When it comes to modelling, significant difficulties are encountered [START_REF] Sippel | New Findings for the Application of Systems for Explosion Isolation with Explosion Venting[END_REF], as the problem formulation is complicated: the effects observed are dependent, not only on the experimental set-up (vessel volume, vent dimension, ignition location), but also on the chosen location for the valve on the pipe. Therefore, there is a need to find other solutions. INERIS methods and findings are presented in the current paper: they concern 3 types of passive flap valves tested on 1 and 10 m 3 vessels, with pipe diameters of 150, 300 and 800 mm.

GENERAL FUNCTIONING OF THE SYSTEMS CONSIDERED

This paper considers 3 types of devices produced by different manufacturers: one type in DN150, another in DN300, and the third in DN300 and DN800. These were tested to assess their performance. Despite the devices being of different designs (use of counterweight or springs, variable angular amplitude), all relied on the same general principle of an inclined flap in a cylindrical tunnel that is kept open by the flow during normal operation, and closed by flow reversal in the event of an explosion (see Fig. When such a system is to be installed in an industrial application, certain conditions must be fulfilled. As in any explosion mitigation system, these flap valves only function within a welldefined range. The passive valve is triggered by the explosion and must close within a delay short enough to prevent the flame passing. Before and during the valve closing, the flow is accelerated by the explosion and large velocities can be reached in the duct, typically of the order of 200 m/s, with a vented vessel, but as much as 800 m/s is possible [START_REF] Roux | Méthodes de protection contre les explosions: évents[END_REF] and [START_REF] Grégoire | Dust explosion development in a vessel-duct arrangement[END_REF] for experimental measurements). For this reason, and because the valve closing cannot be instantaneous, (in comparison to the explosion characteristic times), it is quite intuitive to understand that the shorter the flap closing delay is, the closer it can be placed from the explosion origin. This limiting distance is referred to as a minimum installation distance or L min in the EN16447 standard. Also, explosion in long ducts are often associated with flame acceleration and pressure build-up, which implies that after a certain distance the explosion effects can become too large and exceed the valve resistance. This leads directly to the possible existence of a maximum installation distance of the valve, named L max . As both distances are linked to very different aspects, it makes it possible to have a wrongly conceived valve with L max < L min . In this case either the flame passes before the flap closes, or the device is destroyed potentially leading to flame propagation downstream of it. Because there is necessarily a limit to the pressure from which the flap valve integrity cannot be guaranteed, the certificate of such devices also mentions a maximum admissible pressure. However, as the pressure at the valve in the event of an explosion is hardly accessible to the end-users, this pressure limit is traduced in terms of the maximum P red allowed in the vessel. Constraints also exist on the rate of pressure rise (K St ), the nature of the dust (organic, metallic, etc.), and the vessel to be connected to the ducts (volume, presence of vents, or suppressors). When testing such devices the scope of certification of all those constraints on the intended uses, as well as the dimensioning model, must be verified.

EXPERIMENTAL SETUP

The experimental campaign followed at INERIS slightly differs from what is stated in the normative document EN16447. This document is organized around 3 modules which aim, respectively, at assessing the explosion pressure resistance of the valve, and examining the flame isolation capabilities of the closed valve. The third module consists in verifying the functioning of the initially opened valve within its installation distances L min and L max on a vessel-pipe arrangement in which a dust air flow must be produced. In practice the tests of the first two modules can be performed on the relatively simple setup consisting of a vessel being connected to a short piece of duct, then the flap valve, which does not require additional dust injection devices in the duct. According to the third module, it is necessary to use a fan on the installation, to produce a "pushed" or "pulled flow" situation (if the fan is placed after the valve, or before the vessel). However not only can such system be tremendously costly (as the valve diameter can be on the order of 1 m), but it is also very unpractical as controlling an explosive dust atmosphere (concentration, turbulence) becomes extremely complicated. An alternative is proposed at INERIS: an explosive dust atmosphere is generated in the whole volume (vessel and ducts). After dust ignition in the vessel, the flame expands then propagates in the duct. However; the flap valve is maintained open by an external device until the flow velocity, due to the explosion, exceeds a certain limit (typically of the order of 10 to 30 m/s) representative of the valve's intended use. Once this velocity threshold is reached, the flap is released and starts closing freely. To attain better control of the events observed, at small scale (up to a DN300 for the pipes), transparent ducts are used. A picture of this setup, for the 1 m 3 vessel is presented in Fig. 2. The events are recorded by a high-speed camera at 2000 frames per second and with a window resolution wide enough to see the whole pipe. An indicator is systematically added on the valves tested to measure the flap opening angle as a function of time. Pressure is measured in the dust injection bottle (P b ), in the vessel (P v ), just before (P f1 ) and after (P f2 ) the flap valve (following the explosion direction). In this study organic dusts of wheat flour, cornstarch and maltodextrine were tested, with K St varying from 100 to 200 bar.m/s. This test setup was used for the DN150 and DN300 valves. A DN800 valve was tested on a 10 m 3 vessel. In such a case the transparent pipes cannot be used, and steel pipes equipped with photodiodes, are used to track flame positions. The overall setup remains the same. When necessary (above 4 m of pipeline) an additional injection of dust is added in the pipes, so that the whole experimental device is filled with an explosive atmosphere. The dust injection devices are placed at regular intervals on the transparent tubes. They allow having a combustible atmosphere along the entire length of the pipe. Calibration tests are systematically performed to ensure the combustible atmosphere is present when the flame enters the pipes and allows its propagation over the whole length of the pipe. The vessel is vented on the side opposite to the pipes. However, this new setup imposes two main restrictions: first it is necessary to ensure the closing delay of the device is predictable as in the absence of the fan, the differential pressure applied on the flap at the beginning of its trajectory could be higher than in a pushed flow situation. Consequently, the testing is first performed in the absence of any explosion, in view of assessing the flap closing delay when it is submitted only to the gravity force. Second, a fan driven flow may lead to re-openings of the valve once the explosion has been vented. To ensure we remain far from this situation, it is necessary to measure the flame position during the experiments, which is done thanks to the use of transparent pipes when possible (<DN300) or with several photodiodes for large scale tests.

TESTS RESULTS

Three sizes of valves (DN150,300 and 800), of different industrials, were tested on the 1 and 10 m 3 vessels. Test configurations and measurements are summarized in Tables 1 and2. Pressure and time values are rounded up to the closest multiple of 5. The experimental measurement error given by the pressure sensors producer is ± 2 mbar, at a sampling frequency of 5 kHz. In Table 2, the columns t act and t d correspond respectively to the time from which the flap valve starts to move and the duration up to its full closing. Note that the flow reversal at the valve position is always reached a few dozen ms after ignition of the dust-air mixture in the vessel. In test 3, with a type A valve, the vent on the vessel opened during dust injection, leading to a depression in the duct shortly after the flap started to move. The pressure rose again a few ms later, with the growth of the fireball in the vessel. The closing delay time of the valve was increased because of a lack of upstream pressure compared with other tests with the same equipment. The type B valve of DN300 was not able to isolate the explosion, for the pipe length investigated, due to a too large closing delay. In test 13 the transparent duct burst a few hundred ms after reaching the complete closure of the valve and successful isolation. In test 14 the transparent ducts burst about at the same time the flap closed. For this reason, it is impossible to tell whether the isolation would have been successful or not. Furthermore, the P f1 sensor was ejected after reaching an overpressure of 1500 mbar, which made the calculation of P fM uncertain.

DISCUSSION

In the successful isolation tests (with no flame passing), the comparison of the maximum pressure levels recorded before and after the valve, respectively named P f1,max and P f2,max give a rough indication of the isolation capabilities of the valve. The maximum pressure in front of the valve is always higher (roughly by a factor 2 to 2.5) than that measured in the vessel. A phenomenological analysis is needed to shed light on these results. A representative test is chosen as an example to illustrate some of the specific phenomena involved in explosion isolation by a flap valve. The case of test 17, a DN300 flap valve located at 8 m from the 1 m 3 vessel is considered. Wheat flour at a concentration of 1000 g/m 3 is ignited in the vessel near the entrance of the pipeline. A set of images captured with the high-speed camera during this test are presented in Fig. 5.

Fig. 3.

Images of a representative isolation test (17) with a DN300 pipe and a wheat flour explosion (vessel on the right side of the frames).

The flame progresses in the tube for 150 ms then stops only 1 m from the flap valve. From t = 150 ms, it is observed that the tube downstream of the valve is emptied and gradually becomes transparent, at which time the valve is closed. This observation is correlated with the pressure signals shown later (Fig. 4) where the maximum overpressure is applied on the flap around t = 140 ms. Due to confidentially reasons, the part with the valve indicator is not visible in Fig. 4, but it shows that the flap reopens from t = 250 ms (as there is no flap locking device in the sample tested). At t = 500 ms, it is still open. Initially the flap bounces under the effect of the shock when it closes, then it is sucked towards the vessel because of the pressure difference in the pipe (the pressure is larger around the valve than in the vessel, despite the explosion, see Fig. 4). Then the visible area occupied by the flame in the tube is decreased significantly, probably because all the combustible dust in the first half of the pipe is burned. Finally, at this point the explosion is over: the pressure effects have become negligible. Later (t = 1000 ms), the valve closed by gravitational effect and the flame is eventually extinguished (after 1.5 s).

The pressure signals measured in the vessel (P v ), and in the pipe before and after the valve, respectively P f1 and P f2 , as well as the difference P f = P f1 -P f2 , are represented in Fig. 5 (left). P v and P f are then plot together with flame position in the pipe in Fig. 5 (right). In Fig. 4, the three pressure signals have a similar evolution (but shifted in time) in the first moments of the explosion. During this period, the difference between the green curve corresponding to the rear of the valve and the red curve corresponding to the pressure in front of the valve is due to head losses at the valve and to the influence the end of the pipeline. The dust explosion in the vessel pushes the flow into the pipeline. Towards t = 100 ms the vent on the vessel opens and the pressure rise is stopped. Combustion is not complete yet, as there is competition between two phenomena, the discharge of the explosion gases through the vent and the explosion that continues in the vessel and produces flue gas. The valve starts closing at t = 53 ms and is completely shut at t = 138 ms, when a maximum pressure is observed on the front face of the flap and the minimum on its rear face. A few milliseconds before its complete closure, there is a break between the front pressure curves (in red) and after the valve (in green). At the sensor in front of the valve the pressure increases rapidly while behind the inner flap of the valve it becomes negative. On one side of the valve the air flow is stopped, and the pressure wave is reflected. On the other side of the flap, the flow velocity in the pipe (which depends on the pressure in the vessel but remains strictly positive) suddenly goes to zero: it creates a suction on the back of the flap, theoretically equal to the opposite of the dynamic pressure. When the flame passes before the valve has been able to close, the pressure signals are very different from those shown in Fig. 4. There is no blockage of the flow and the sensors before and after the valve have a similar evolution (with a delay in time and a lower amplitude for the sensor downstream of the valve).

The force applied on the flap of the valve is the difference between the pressure applied on its front face, measured by the sensor P f1 and the pressure measured on its rear face, at the P f2 sensor, the signal thus constructed being P f = P f1 -P f2 . The maximum pressure actually applied to the flap is therefore 1200 mbar, instead of the 850 mbar suggested by the P f1 curve. A direct implication for the design of such device is that the actual pressure resistance of the flap valve must be a few times (3-4x) larger than the P red measured in the vessel. It is important to understand that the pressure pilling at the valve is due to the accumulation of two distinct phenomena. The first is the acoustic part of the pressure wave that is also measured when the pipe is left open, which signal shows a shape similar to the overpressure signal in the vessel, delayed and slightly damped. When the valve is closed, it is reflected. For this reason, one can expect a factor up to 2 between the vessel pressure and P f1 . The second part is due to the sudden deceleration and stopping of the dust-gas column in front of the valve, whose inertia is converted into pressure, thus leading to another increase of P f1 . In this specific example, the configuration is some sort of a worst-case scenario in which both the acoustic part of the pressure wave and the dynamic stopping of the gas column are superposed. In any case, this factor of two to three between the pressure in the front of the flap and the driving pressure in the vessel indicates roughly the conservation of the energy in the pipe, which means that there is barely any pressure build up due to the combustion in the pipe. This might not remain true for more reactive dusts. When the vessel is not supporting sufficiently the flame propagation in the pipe (i.e. the explosion in the vessel is (almost) finished when the flap closes), which can happen at other scales (in particular at large scale or when the volume of the duct is to large in comparison to the vessel volume), or when the ignition location is changed (ignition close to the vent) both contributions may be decoupled in time. Such a situation may lead to dangerous misinterpretation of the flap valve capabilities. Thus, a major difficulty in the testing procedure is to identify and test configurations in which the explosion is still ongoing in the vessel when the flame reaches the end of the pipe. Under those conditions, the flame in the pipes is not moving in a medium at rest but is continuously pushed by the explosion in the vessel. However, the opposite situation must also be tested, to ensure the closing of the flap is achieved even when the flame propagation is slow, and the pressure effects are weak.

Also, during a certain period, this pressure difference P f becomes negative, which can lead to the reopening of the flap, in the absence of a locking system. The flap can therefore reopen by two mechanisms: the rebound once arrived in its abutment and a suction effect when P f is negative. In the absence of a locking system it is thus necessary to ensure the flame remains far enough from the valve to prevent any risk of transmission. In these specific conditions, flame transmission relies on the blockage of the flow and is not a problem of Maximum Experimental Safe Gap (MESG) anymore. Indeed, in these specific conditions, a pressure higher than that in the vessel can be generated in front of the valve, leading to a reversal of the flow in the pipe. If this reversed flow velocity is equal to, or larger than, the flame velocity, the flame cannot travel towards the valve anymore. However, this observation may not remain true for all dust types and should be verified, in particular for the most reactive ones such as metal dusts in which case the physical mechanisms responsible for flame propagation can be different.

In Fig. 5, the flame position and velocity extracted from the cinematographic records are compared with the pressure signals. The flame trajectory is compared first with the pressure signals in the vessel and the pressure difference between each side of the flap. The flame propagating in the pipeline is driven by the explosion in the vessel. In this example, it reaches 7 m before stopping, going back and stopping at about 6 m from the vessel. In the section between the vessel and the flap valve, the pressure difference between the upstream (the vessel, P v sensor) and the front of the valve (P f1 sensor) is expected to fully determine the velocity of the flow. It is thus compared with the measured flame velocity of the right side of Fig. 5. One can notice that the flame velocity initially follows the same evolution as the pressure in the vessel: it increases gradually and then stagnates at the opening of the vent, around 100 m/s. When the pressure difference P v -P f1 becomes negative, the flame moves back towards the vessel. From t = 160 ms this difference is again positive and the flame velocity re-increases then converges to 0 when the pressures are balanced, at t = 180 ms. This confirms that the trajectory of the flame is dominated by the flow in the pipeline. These fundamental mechanisms must be considered in the realization of the dimensioning model of the final system.

DIMENSIONING

Phenomenological modelling can be used in an extension to the parametric experimental study to investigate the limits of the valve. We first look at the distance L min , which corresponds to the minimum distance for which the system will be able to isolate the flame, preventing its transmission downstream of the pipe. To isolate a flame, the valve must be closed before its arrival. For the investigated valve without a locking system, successful isolation occurs if the flame stops at about 3 diameters of pipe before the valve. Note that it might not remain true for other devices, this limit should be verified experimentally. To trigger the closure of the flap, it is necessary that the overpressure in the vessel reaches a minimum value, sufficient to reverse the flow in the duct (typically on the order of 10 mbar). This condition is fulfilled after a noted time t exp . The information of this reversal reaches the valve after a time t sound, corresponding to the delay for the acoustic wave to travel the distance in the pipe between the vessel and the valve. Note that the time t act described in Table 2 corresponds to the sum t exp + t sound . Then, the flap makes its complete run from the open state to the closed state, which takes time t flap . The total time of closure of the system t tot is obtained by summation of t exp , t sound and t flap . This delay t tot will be compared with t f , that required for the flame to reach the position of the valve x flap minus a certain safety length close to 3 diameters of pipe (in the current case). Alternatively, the second installation limit is the distance L max , from which the valve becomes unable to withstand the pressure forces generated by the explosion in the pipe and eventually let through the flame. L max is directly related to the resistance of the valve. To determine L min and L max , it is necessary to describe: the behaviour of the valve subjected to a pressure wave, the explosion in the vessel, the propagation of the flame in the pipeline. Note that the solution of the problem, the distance between the valve and the vessel, will be needed to compute t sound and t f . The problem is implicit and must be solved iteratively.

The pressure rise due to the dust explosion is directly linked to the quantity of gases produced by the combustion minus the gases lost by the various openings on the filter (ducts, opened vents). Thus, the pressure rise curve as function of time can be estimated with a model such as that of Lewis and Von Elbe (1987):

= ö ö Þ • / U/ ¢ ~ , (1)
where P, V and γ are the vessel pressure, its volume and the specific heat ratio of the gaseous species. Q produced and Q lost are respectively the volumetric fluxes produced by the combustion and lost through the vent. Such a model clearly indicates that the effect of the explosion is directly linked to the reacting products, which will determine the rate of the gaseous production and the environment through the action of the vessel volume and vents in the denominator and the Q lost parameter. Q lost can be estimated with the generalized Bernoulli's laws. Consequently,. the time t exp will be shorter if the vessel or vent volume is smaller. A shorter t exp implies a shorter delay for the flame to reach the valve thus a larger L min . For this reason, limits in terms of minimum vessel volume, vent area, and maximum P max and K St (that play a role in Q produced ) are specified in the flap valve certificates.

To estimate the flame propagation delay, t f , one can rely on the experimental observation that the flame flow is driven by the vessel overpressure. Phenomenological models based on Bernoulli's law can be found in [START_REF] Grégoire | On the usefulness of phenomenological approach to model explosions in complex industrial systems[END_REF].

Finally, the closing delay of a valve t flap is also of critical importance. In the absence of an explosion, independent of the flap valve diameter, the trajectory of the inner flap can be well predicted with a simple model of a damped pendulum. The valve considered in the current example is based on the use of a counterweight to allow shorter closing delays. A similar model can be used for valves equipped with a spring. When there is an exploding dust-air flow pushing on the valve, the closing delay is reduced. It can be quite satisfyingly calculated adding a pressure force contribution to the earlier equation. The pressure signal can itself be approximated by a Gaussian, leading to the equation:

S ˜• sin Z • | X •,Z[\ • NOP U ~ ?• • cos • ¤•£ a•Z , ( 2
)
where m is the mass (kg), r is the radius between the axis and the flap barycentre (m), k is the damping factor, and θ is the flap angle with the horizontal and the standard deviation of the normal law σ to be adjusted to fit with the explosion duration (σ roughly equal to 1/4 to 1/3 of the explosion duration). An experimental measurement without an explosion can be used to determine k for each valve.

With this model the determination of L min is possible for a given configuration (fuel reactivity, ignition location, vessel, and vent and valve dimensions) but the determination of L max is more challenging as it requires the pressure in the duct to be computed as a function of flame propagation. An alternative to costly modelling or experiments can be the use of the formulas listed in the EN standards for vent duct applications. NFPA68 also provides a chart describing pressure increase in a duct with a closed end, in which a dust-air flame of K St 100, 200, or 300 propagates. This approach does not consider the presence of a vent and is expected to be conservative. From these data, it is also possible to estimate the duct length that should be investigated experimentally for a given flap valve diameter of a given pressure resistance.

CONCLUSIONS

Three different models of passive flap valve, of three diameters (DN150, 300 and 800) were tested with wheat flour and cornstarch dust explosions, in the scope of ATEX certification, on a 1 m 3 vessel (valves of DN150, DN300) and a 10 m 3 vessel. Recommendations for the testing of such devices are described in the normative document EN16447, which was chosen as an initial baseline to conduct the experiments. Practical and scientific limits of the standard are exposed, such as the impossibility to conducting large scale testing with the use of fans at a reasonable cost, or in controlled conditions. Some recommendations for the testing are also given. It appears to be fundamental to go farther than the configurations presented in the EN16447 and identify practically which configurations should be investigated. In particular, ignition location is of critical importance. Depending on the vent and pipe locations on the vessel the worst case scenario may correspond to an ignition close to the pipe or at the farthest point from it. Specific attention is also given to the explosion duration in the vessel: our test setup was arranged, where possible, to keep the explosion pressure in the vessel close to its maximum value when the flap valve is closed. This implies that for a given duct diameter, the explosion volume must be sufficiently large and the vent area sufficiently small to maintain the P red . Finally, a phenomenological analysis of the test results reveals, for such devices, the critical importance of their pressure resistance (which should be of the order of 4 times the P red in the vessel and also determines the maximum installation distance L max ) as well as their closing delay (that can be estimated with equation (2), which determines their minimal installation distance (L min ). Both phenomena being decoupled, is is possible to have L min > L max . This corresponds to a non-functioning device. It is interesting to point out that the determination of the possible installation distances for a given valve depend on the time t f for the flame to reach the valve position. Thus, the problem is implicit and must be solved iteratively.

Fig. 1 .

 1 Fig. 1. Functioning of a passive flap valve.

Fig. 2 .

 2 Fig. 2. Image of the test setup for a DN300 flap valve located at 8 m from the explosion vessel. The flap valve is hidden due to confidentiality reasons. P v , P f1 and P f2 indicate the positions of the pressure sensors.

  Reactivity parameters K St and P max were characterised in closed vessel tests in the 1 m 3 vessel (ISO 6184-1) for 1000 g/m 3 of maltodextrin (200 bar•m/s and 7.4 bar), 1000 g/m 3 of cornstarch (150 bar•m/s and 7.1 bar), 1000 g/m 3 of wheat flour (95 bar•m/s and 7.25 bar) and in the 10 m 3 vessel with 700 g/m 3 of wheat flour (105 bar•m/s and 7.3 bar).

Fig. 4 .

 4 Fig. 4. Pressure measurements at each sensor location (left side)) and comparison with flame position (right side) for the representative test with a DN300 flap valve and wheat flour.

Fig. 5 .

 5 Fig. 5. Flame position (left side) and velocity (right side) compared with selected pressure records.

Table 1 . Summary of the tests performed with the 3 types of flap valve

 1

	Test #	Type of flap valve	Diameter (mm)	Installation distance (m)	Dust type	Vessel volume (m 3 )	Vent area (m 2 )	Ignition location
	1		150	4	maltodextrin	1	0.096	Back of vessel
	2		150	4	wheat flour	1	0.096	Back of vessel
	3 4	A	150 150	3 3	wheat flour maltodextrin	1 1	0.096 0.096	Back of vessel Back of vessel
	5		150	2	wheat flour	1	0.096	Back of vessel
	6		150	2	maltodextrin	1	0.096	Back of vessel
	7		300	6	wheat flour	1	0.159	central
	8		300	6	cornstarch	1	0.159	central
	9	B	300	8	wheat flour	1	0.159	central
	10		300	8	cornstarch	1	0.159	central
	11		300	8	cornstarch	1	0.159	central
	12		300	8	wheat flour	1	0.159	central
	13		300	8	wheat flour	1	0.159	central
	14		300	8	wheat flour	1	0.159	central
	15 16	C	300 300	8 8	wheat flour wheat flour	1 1	0.159 0.159	Pipe entrance Pipe entrance
	17		800	18	wheat flour	10	1	Pipe entrance
	18		800	18	wheat flour	10	1	Back of vessel

Table 2 . Pressure measurements (mbar) and times (ms) corresponding to the configurations listed in Table 1

 2

	Test #	P v,max	P f1,max	P f2,max	P fM = max(P f1 -P f2 ) P fM /P v,max	t act	t d	Success of isolation
	1	315	665	280	750	2.4	25	65	yes
	2	195	410	75	500	2.6	35	45	yes
	3	155	340	115	400	2.6	40	100	yes
	4	685	1185	143	1200	1.8	20	50	yes
	5	150	340	105	450	3.0	30	60	yes
	6	435	870	190	1000	2.3	20	50	yes
	7	265	130	85	105	0.4	35	245	no
	8	270	165	105	80	0.3	30	240	no
	9	420	250	150	125	0.3	55	230	no
	10	255	130	85	80	0.3	35	340	no
	11	335	200	120	205	0.6	35	n.d.	no
	12	390	485	205	695	1.8	55	85	yes
	13	420	870	215	1110	2.6	55	110	yes
	14	740	> 1500	160	> 2000	>2.7	55	60	n.d.
	15	325	825	300	1040	3.2	55	85	yes
	16	335	865	295	1220	3.6	55	85	yes
	17	100	120	65	165	1.7	165 180	yes
	18	95	175	95	225	2.4	285 170	yes
	19	170	300	115	365	2.1	155 145	yes


On the Usefulness of Phenomenological Approach to Model Explosions in Complex Industrial Systems

Keywords: Dust explosions, explosion mitigation, phenomenological modelling

Explosion protection is the object of various national and international documents, which are focused on the functions, the intended uses or the dimensioning rules for specific systems. However, despite a few application examples are described in the usual guidelines, they are limited to the description of a protection that can be added on a single piece of equipment while it is not the case in industrial processes. Furthermore, in an ATEX explosion there is a strong coupling between the explosion and its environment. Because of this the guidelines recommendations cannot be transposed on an industrial site without due consideration. In this paper, a way to consider the real explosion conditions is given allowing a choice and dimensioning of a set of safety systems. An example is shown based on the example of a model of a real installation. The functional properties of the safety system are extracted from the certification tests whereas the explosion characteristics are extracted both from the standard combustion properties of the dust and from the latest knowledge about flame propagation. A specific focus is made on two fundamental aspects: on the one hand, the critical importance to understand how the flame propagates in a given complex system. On the other hand, the behaviour of the protection systems that can be used with caution as they quite systematically influence the explosion driven flow

INTRODUCTION

ATEX directives introduce everywhere in Europe the obligation to take dispositions to protect the workers in industry from the explosion risk. In many situations, and especially when dust explosions are identified, prevention measures are insufficient, and protection should be ensured. Explosion protection is the object of various national and international documents that are focused on the functions, the intended uses or the dimensioning rules for specific systems: NFPA68:2012 [START_REF]Standard on Explosion Protection by Deflagration Venting[END_REF], EN14797:2007 (testing) [START_REF]Explosion venting devices[END_REF] and EN14991:2014 (dimensioning) [START_REF]Dust explosion venting protective systems[END_REF] for dust explosion venting techniques. Despite a few application examples are described in the usual guidelines, they are limited to the description of a protection that can be added on a single piece of equipment in which an explosion may occur, in quite an ideal configuration with fully known turbulence conditions, combustible reactivity, repartition or concentration. Such observation is general to most of the safety barrier used in the industry. However, in real installations, the device to be protected is rarely isolated but often connected to various ducts and vessels in which the explosion may propagate. This is a critical point as in an ATEX explosion there is a strong coupling between the explosion and its environment. A direct consequence of this is that the guidelines recommendations cannot be transposed on an industrial site without due consideration. In such occurrence modelling of the explosion phenomenon at stake can be helpful firstly to understand the possible course of events, then to dimension a protection strategy accordingly. When a complex system at an industrial scale is considered, the most evolved tools such as CFD models can be used but their use can be associated with prohibitive costs. They most often require, in addition to engineering skills, large computing power as well as significant post-processing works to ensure the consistency of the results. In this paper a phenomenological approach is suggested in view of grasping the physics at stake. An example is show based on a real installation. The example of coal grinding installation is considered and is schematized in Fig. 1. It consists of a mill, a cyclone and a dust collecting filter, connected by pipes. The supply and product circuits are excluded from the present study. After passing through the mill, the grinded coal-gas mixture is sucked into the cyclone, where the coarsest particles are isolated, then resent towards the mill. Alternatively, the thinner particles travel towards the filter after which they are collected. The major objective is to protect the installation from the explosion effects as well as to limit the explosion effects in the medium range. However, the very first step is to identify the explosion risk. Filters are prime causes of powder explosion but the same can be said on the mills. In fact, not only there is a large multiplicity and complexity of industrial installations, but also, once the choice is made on a setup, the process itself can vary. For example, some coal installations may also operate occasionally with petcoke. Different phases of the process (starting, usual operation, maintenance) imply different risks. At last the explosion may be triggered at various stages of the installation then propagate to the totality of it. This illustrates the needs behind the use of comprehensive phenomenological tools such as the one described here.

PHENOMENOLOGICAL MODELLING OF THE EXPLOSION IN A PROCESS

To model such explosion phenomena and keep a satisfying understanding on the course of the events, INERIS developed the EFFEX code [START_REF] Proust | The usefulness of phenomenological tools to simulate the consequences of dust explosions: the experience of EFFEX[END_REF], phenomenological software consisting of interlinked models each dedicated to a single aspect such as flame propagation in a volume, turbulence characteristics prediction, combustion rates, mechanical resistance, pressure effects… Most of the physics is derived from fundamental research. Each model is qualified separately, and the overall consistency can be compared to realistic full-scale experimentation or actual accidents.

The typical situation is that of a flammable cloud of suspended particles in a confined or semiconfined space. A reactive fuel-air mixture is formed. The size, composition and internal level of agitation ("turbulence") depend on the type of leakage and the geometric characteristics of the containment. If an adequate source of ignition is present inside the flammable area of the cloud, it will ignite, and a flame will propagate step by step from the ignition point. Figure 2 illustrates the development of the flame in the containment.

The flame develops spherically around the source of ignition. On its way, it almost instantaneously transforms cold reactants into hot combustion products (typically from 1000 to 2000 ° C). Hot gases being less dense than cold ones, it results in a high-volume expansion of the gases. This process is directly responsible for increasing the pressure in the enclosure.

The pressure rise due to the dust explosion is directly linked to the quantity of gases produced by the combustion minus the gases lost by the various openings on the filter (ducts, opened vents). Thus, the pressure rise curve as function of time can be estimated with a model such as that of Lewis and Von Elbe [START_REF] Lewis | Combustion, flames and explosions of gases: 3rd edition[END_REF]:

$ Ó gÓ g€ Ô ¦ Õ}µ•Ö×Ø• #¦ ÙµÚ• ª (1)
where P, V and γ are the enclosure pressure, its volume and the specific heat ratio of the gaseous species. Q produced and Q lost are respectively the volumetric fluxes produced by the combustion and lost through the vent. Such model clearly indicates that the effect of the explosion will be directly linked to the reacting products, which will determine the rate of the gases production and the environment through the action of the vents in the Q lost parameter. Q lost can be estimated through some various models derived from the generalized Bernoulli's laws. In practice whether the flow is subsonic or supersonic it is possible to estimate the Q lost term through equation ( 2) or (3) respectively for the subsonic and supersonic cases:

Û Ü € g M m Ó • Ó © s $ Ý - Þ 1•Ý Ý#$ • Ó © -© • .1 m Ó • Ó © s ßà© ß 3 , (2)
Û Ü € g M Þ Ô Ó © -© m 1 ÝŽ$ s ßá© ßà© . (3)
However, the problem of the estimation of the produced gases flux Q produced is more challenging as it depends both on the products that are reacting but also on their environment which will influence the flame surface or impose concentration or turbulence gradients. The excess volume produced per unit of time, is proportional: on the surface of the flame, the burn rate of reactant consumed per unit of flame surface (this parameter has the dimension of a speed and is often called "burning rate"), and the volume expansion ratio (which is linked to the temperature of the products: the hotter the more volume is produced). Gas production through combustion can be approximated as follows in our model: the fresh combustible mixture is instantaneously transformed in hot burnt products through the passage of the flame whose thickness is zero. Thus, it is a function of the area of the reacting surface Af, its velocity St and an expansion ratio α:

Û ¬+Q^N 0^ M • Goe … 1! (4)
Firstly, the expansion ratio α is a thermodynamic data which depends only on the heat released by the combustion and can be expressed through the first principle of thermodynamics:

… -â}ØÚã -äÖ}å• & °äÖ}å• °â}ØÚã ∆z aeµoä -˜°â}ØÚã 1 , (5)
where ∆f -ƒ is the reaction enthalpy, and ƒ¢ £€ are the temperatures of the reactants and the burnt products, and ƒ¢ £€ are the densities of the reactants and the burnt gases, and Ó is the specific heat of the burnt products. The expansion ratio α is a fundamental parameter which depends strongly on the combustible mixture composition and is poorly influenced by the propagation. For most common mixtures found in the process industries it is comprised between 6 and 8 [START_REF] Eckhoff | Dust explosions in the process industries[END_REF]. Alternatively, the shape of the confined structure suffering the explosion can have an influence on the flame surface Af and so is the case for the local flow velocities, or when obstacles are present. Even in a medium initially at rest, the flame grows spherically until the spherical front reaches the closest wall. When contacting the wall, the flame front is stopped then reversed. During this phase the flame front surface can become cellular or be curved toward the combustion products most likely because of local perturbations such as Landeau-Darrieus instabilities [START_REF] Darrieus | Propagation d'un front de flamme. Essais de théorie anormales de déflagration par développement spontané de la turbulence[END_REF]. In all case the maximal flame area is linked to the dimensions of the volume and its cross section. Extensive comparisons of EFFEX calculations with experiments indicate that a decent agreement can be achieved when the flame surface is roughly equivalent to the largest inscribed sphere in the enclosure [START_REF] Proust | Prévoir les effets des explosions de poussières sur l'environnement, EFFEX, un outil de simulation[END_REF].

Finally, the flame velocity in a mixture attached referential is also expected to be a property intrinsic of the mixture. The fundamental combustion velocity S lad obeys to the laws of thermokinetics (thermodynamic equilibrium, Arrhenius law) and can be described as the volume of reactants consumed by a square meter of the flame surface. However, this definition corresponds to a configuration in which the reactive mixture is at rest in which case the effect of an explosion would be limited to the maximum. For a more realistic approach, it is necessary to consider a turbulent flame velocity St that can be determined for industrial applications based on the empirical definition of K st :

ç ¥€ m gÓ g€ s Kb $ 6 - (6)
Replacing this in equation ( 1) (and assuming no openings on the vessel), we obtain:

$ Ó opq ç ¥€ Ô ¥€•è opq • "#$! ª • é - X M & ê Ú• ÝÓ opq "#$! (7)
Even in the isolated enclosure the effects of the dust explosion are strongly dependent not only on the nature of the reactants but also on the specificities of their environment such as the geometry or local turbulence effect. The model described in the previous paragraphs is only applicable if the flame propagation velocity is sufficiently low (typically < 30 m/s) for the internal pressure to remain "uniform". This condition is very generally satisfied when the ratio between the largest and the smallest dimension of the apparatus is less than 5 [START_REF] Proust | The usefulness of phenomenological tools to simulate the consequences of dust explosions: the experience of EFFEX[END_REF], which is not the case for pipes for example. In practice, there would be an explosion at one end, for example in a mill and the atmospheric pressure at the other end. For ST1 class dusts (which is the case here), the contribution of the duct combustion to the overpressure in the installation studied is low and the flow is largely dominated by the pressure differences between the upstream and downstream sides of the pipes [START_REF] Proust | Dust explosion in pipes: a review[END_REF]. A direct consequence of this is that the flame velocity in such situation quickly reaches hundreds of meters per second. Empirical data show that the flame velocity in a duct downstream an enclosure is well correlated with the square-root of the overpressure P red (stands for "reduced explosion pressure" a term often used to design the maximal overpressure in a vented vessel) in the enclosure (analogy to a Bernoulli model): Fig. 3. Correlation between vessel overpressure and maximal flame velocity in a connected in a duct [START_REF] Grégoire | Dust explosion development in a vessel-duct arrangement[END_REF].

In this last situation, the velocity flow is driven by the pressure difference between both ends of the pipe, and so is the flame. It is also noted that in such case, until the flame has reached the other end of the pipe, the pressure in the upstream equipment (the mill) continues to increase as if the duct was closed [START_REF] Grégoire | Dust explosion development in a vessel-duct arrangement[END_REF]. The pressure rise is then less related to thermal expansion than to the inherent dynamics of the flame (speed and acceleration). There is therefore a piston effect and the main problem of the propagation of the explosion in a pipeline is to determine the speed of the flame, because ducts usually show large overpressure resistance and it is this same fast flame that is transmitted in equipment downstream. Moreover, the presence of singularities on the pipe such as bends is likely to modify the flame surface and accelerate it. In EFFEX, a relatively simple model of the compressible Bernoulli equation type has been implemented to estimate this velocity. The basic assumption is that the flame propagates at a speed St* which depends, as for non-elongated enclosures, on the turbulence and reactivity of the dust (thus on the usual turbulent flame velocity St) but also on "Ve", the forced flow by the pressure difference between the upstream and downstream of the pipeline. Singularities such as elbows are therefore ignored. The cases of subsonic and shocked flows are differentiated. Noting P 1 and P 2 the pressures at each sides of the duct, and with P 2 > P 1 . If the condition

Ó • Ó © X m ÝŽ$ 1 s ß
ßà© is fullfield then the flow is chocked, and the Mach number M is 1. In the other case, M can be computed as follows:

J Þ 1 Ý#$ m Ó • Ó © s ßà© ß . ( 8
)
From the temperature T and the molar mass M, we obtain the flow velocity by computing the speed of sound which depends on the temperature T. In the chocked and subsonic case, we obtain respectively these 2 equations for the flow velocity:

0 ë 4.6$, { 1•Ý ÝŽ$ and 0 J ë 4.6$, { 1•Ý ÝŽ$ °ßà© • •{ • Ž$ . ( 9
)
Although they remain approximate, the results provided by this model give satisfactory orders of magnitude, they have been successfully confronted with experiments carried out at INERIS as well as with published data. Again, the major objective here is to be able to estimate the characteristic times of the explosion propagation rather than the pressure built up in the pipes. When an explosion occurs in a structure made of interconnected enclosures the explosion can be transmitted from one vessel to its neighbours and the flame propagation can become of an extreme complexity [START_REF] Phylaktou | Explosion development in pipeline systems and linked vessels UKELG 25th meeting[END_REF]. In such case. A schematic of a possible course of events is presented in Fig. 4: the dust ignition in the primary enclosure induces a first explosion (4a) and generates a significant turbulence and flow velocity in the connected pipe (4b). Then large quantities of the combustible mixture will be pushed in the downstream enclosure and pressurize it. After its significant acceleration in the duct, the flame will enter the pressurized and highly turbulent combustible mixture in the secondary volume.

A secondary explosion, of much greater violence can then happen (4c). It can also reverse the flow completely and push the reactive front back in the primary vessel where the combustion is not terminated (4d).

Fig. 4. Schematic representation of explosion development in interconnected enclosures [11].

Because in a wide range of situation the decoupling of 2 enclosures in only partial or impossible, it is of a great importance to account for this phenomenon. In other words, it is necessary to estimate the turbulence in the model structure and adapt the turbulent flame velocity St in the downstream equipment accordingly. Phenomenological semi-empirical models are available to estimate the pressure effects due to the flame arrival in the turbulent mixture of the secondary volume. In most situations, the turbulent flow will be induced by jets which characteristics are relatively well known (see [START_REF] Ruffin | Etude des jets turbulents à densité variable à l'aide de modèles de transport au second ordre[END_REF] for further details on jet theory). A prediction tool was elaborated from this knowledge database. Analytic models can be to estimate the local turbulence velocity u' and the characteristic sizes of the turbulent structures Lt were proposed by Hinze [START_REF] Hinze | Turbulence[END_REF]. The two flow turbulence parameters u' and Lt can then be used to estimate the turbulent flame velocity with a Gülder empirical model [START_REF] Gülder | Turbulent premixed flame propagation models for different combustion regimes[END_REF]. Further details on the application of this model have been published more recently by Proust [START_REF] Proust | The usefulness of phenomenological tools to simulate the consequences of dust explosions: the experience of EFFEX[END_REF]. The main interest here is the order of magnitude to the flame velocities enhancement due to the turbulence effect that can be on the order of 5 to 20 times that observed in the same mixture at rest. Empirical estimations can be made on the turbulence parameters Lt and u'.

Tamanini [START_REF] Tamanini | The role of turbulence in dust explosions[END_REF] proposed an integral version of the well-established k-epsilon model for turbulence.

For the present illustration, we retain the steady state version of k-epsilon equation where the production rate (P k ) is equal to the dissipation rate (ε). Proust [START_REF] Proust | Differentiated routes for the simulation of the consequences of explosions[END_REF] assumed that Lt might be chosen constant and proportional to a linear dimension of the volume since this parameter can be seen as a measure of the mean velocity gradients so that:

I ™ © é ' 6 1 N 1 5 ž $ 1 ‰£F O Ó ì { I í é î ž é • ï . ( 8
)
where q m is the injected mass flowrate with the velocity U inj in the volume V of mass M. C µ and C L are constants of the order of 0.05 and 0.09 [START_REF] Tamanini | The role of turbulence in dust explosions[END_REF]. Proust compared the model results with experimental results and published data and showed a satisfying compatibility in both cases [START_REF] Proust | Differentiated routes for the simulation of the consequences of explosions[END_REF].

THE EXPLOSION SCENARIO

Because of the specific phenomenology of flame development in the complex structure made of interconnected enclosures it is necessary to define first an explosion scenario which is the baseline for the comprehensive analysis of the explosion effects in the structure. In face of the multiplicity of the possible explosion scenario at stake in the current example, we will consider the example of an ignition in the mill during normal operation, that is then transmitted to the cyclone and to the filter.

In the present case, the explosible dust is coal powder which is known to have a K St value close to 150 bar.m/s and a P max on the order of 8 bar (data from the Staubex database). Depending on the technology, mills and cyclones can resist to explosion pressures up to 3 bar. The filter is however of a lesser resistance, 500 mbar in this example. For this reason, let's assume it is sold to the industrial already equipped with 5 m 2 of vent panels. In this case we consider a volume of and 60, 20 and 300 m 3 respectively for the mill, cyclone and filter. They are connected by DN800 ducts of length 15 m.

The explosion is initiated in the mill and is transmitted to the first duct. The flame propagates to the cyclone, pushed by the overpressure in the mill at a speed of 200 m/s. Under these conditions, when the flame arrives in the cyclone, the mixture is highly turbulent as not only the flame has a very high velocity but also it is pushing large amounts of the reactive dust (as much as 70 to 90 % of the reactants in the duct [START_REF] Proust | Dust explosion in pipes: a review[END_REF], [START_REF] Phylaktou | Explosion development in pipeline systems and linked vessels UKELG 25th meeting[END_REF]) inside the cyclone. The combustion occurs at a quasi-constant volume inside the cyclone will occur (despite the exhaust ducts). An overpressure of the order of the dust P max , 8 bars seems possible but again a complete failure of the cyclone happen before reaching this value (we assume a resistance of the cyclone of 3 bar in this case study). Such scenario was simulated with the EFFEX code and the results support this summary of events: The flame should continue to the filter at speeds more than 400 m/s at the beginning of its propagation but is eventually slowed down to less than 100 m/s before reaching the filter, because of the sudden bursting of the cyclone. Note that while the vents in the filter strongly limited the overpressure, in the mill the reversal of the flow lead to a significant increase of turbulence and an intensification of the combustion. It appears that in the current example, the filter and the mill withstood the internal explosion, but the consequences of such scenario are not acceptable because of the bursting of the cyclone. It implies the projection of fragments up to several tens of meters and the emission of a pressure wave corresponding to a bursting energy of 20 MJ, that is roughly equivalent to the detonation of 5 kg of TNT, the effects of which are known to be dangerous for humans from 20 to 40 m in open field.

IMPLEMENTING THE EXPLOSION PROTECTION STRATEGY

The potential effects of an explosion within such installation are not acceptable and make it absolutely essential to equip it with explosion protection devices. As the most fundamental principle is the safety of people. As a result, the cyclone protection is a requirement here. Different techniques may be used such as deflagration venting which consists in discharging the explosion through an orifice. The vent area must be calculated so that the maximum pressure reached in the protected vessel, P red remains significantly lower than the mechanical pressure resistance of the enclosure. A mistake would be to consider the cyclone separately: knowing the dust reactivity parameters (K St = 150 bar.m/s, P max = 8 bar) in this "independent" volume, one would estimate vent areas on the order of 0,5 m 2 to limit the P red to 1 bar in the cyclone (calculations based on EN14991:2014 [START_REF]Dust explosion venting protective systems[END_REF]). However, proceeding such way completely occults the flow and flame acceleration effects in the pipes (supported by the upstream exploding enclosure) and the significantly enhanced combustion effects downstream the pipes, thus rendering the protective equipment completely inefficient. A simulation of this scenario in EFFEX shows that despite the vent, the cyclone burst because of the large flame velocity transmitted from the pipe. Thus, a much larger vent area is needed, 3 m 2 are computed with EFFEX. However, protecting the cyclone alone is not sufficient: Fig. 6. Overpressure calculated in the mill, cyclon and duct; with 3 m 3 vents protection on the cyclone. Now that the mill-cyclone system is protected, there is still a large overpressure responsible for significant flame acceleration in the second duct section, between the cyclon and the filter. The flame reaches the filter at a velocity close to 300 m/s, and the vent area installed on the filter becomes clearly insufficient.

A critical aspect in this example scenario is the coupling between the three enclosures, that need to be accounted for when choosing and dimensioning an explosion mitigation technique. Several options exist, a few are presented in the subsequent paragraphs:

• vents protection of the cyclone and the filter,

• vents protection in addition to decoupling system on the ducts,

• isolation of the duct and vent protection of the enclosures,

• explosion suppression,

• mixed systems protection.

Vents protection of the cyclone and filter

In the normative document EN14491:2014 [START_REF]Dust explosion venting protective systems[END_REF], a dimensioning method is proposed to limit the violence of the explosion in an assembly "enclosure 1 -duct -enclosure 2". The vent areas to install are often much wider as those predicted by the usual method in the same document. In such situation, the purpose of the vents is not only to unload the explosion but also to reduce the flame acceleration in the duct. The EN14491:2014 [START_REF]Dust explosion venting protective systems[END_REF] document indicates an order of magnitudes for these vent areas, which imply typically a coefficient (Av/V 0,753 ) of 0,4. It can be highlighted that inconsistencies exist between such recommendations and the calculations that can be made with the formulas concerning the vents connected to ducts. Nonetheless the use of such technique is theoretically feasible in the present case with some additional calculations. Knowing the available vent area on the cyclone and the acceptable reduced explosion pressure P red , one can estimate a maximal flame velocity acceptable in the duct. Then the vent area to install on the filter will selected in view of unloading the explosion but also limiting the flame velocity in the duct to the maximal acceptable value. In practice, this is barely achievable on the scale considered: according to Fig. 3, one would need to limit the overpressure in each enclosure to 0.5 bar, so that the flame speed remains low enough to allow a vent protection. This implies the use of much larger vent areas. Consequently, this is not a practical solution for the current example.

It is also important to point out that these vents only solution relies on the hypothesis of an ignition in the mill. When the explosion starts in the filter it is be necessary to perform new, yet similar, calculations. Also note that the environment around the enclosures (a road, workers, a wall, etc.) may impose to have vent ducts, deflectors or flame arrestors at the exhaust of the vents. All these systems impede the explosion discharge and induce a lower vent efficiency, thus the necessity again to install larger vent areas.

Vents protection in addition to decoupling system on the ducts

The previous mitigation solution imposes to have large vent areas on each device, which may not be feasible for practical reasons such as the bulk around the structure. The smallest possible vent areas Av, for each equipment, can be estimated separately form the EN14491:2014 [START_REF]Dust explosion venting protective systems[END_REF] formulas. For instance, for the cyclone we computed earlier 0.5 m 2 , and for the furnisher of the filter sold it with 5 m 2 of vent area. In the case of isolated enclosures, this is expected a conservative approach as the P max and K St terms are measured in more penalizing conditions (dust concentration, turbulence) than they are supposed to exist in the industrial process. However, for this model to be valid for connected enclosures, the violence of the explosion must correspond to the limitations defined in the standard, which implies that the turbulence level must remain in the range of the test that were performed to establish this formula. A direct consequence of this is that these lower venting areas may be used provided the duct effect can be neglected, which can be done when the explosion is either decoupled or isolated. Firstly, we will consider the option of the explosion decoupling.

Explosion decoupling devices are designed to limit the flame velocity in a duct. It can be realized by adding vents on the duct that are designed to open before the flame arrival and slow down the flow in the event of an explosion. Such systems may also be constructed in view of forcing the flame to change directions, to prevent excessive accelerations. Those decoupling systems can be dimensioned so that the turbulence induced in the downstream enclosure remain at an acceptable level, however they will not stop the flame but only slow it down. Experiments performed at INERIS confirmed that an explosion generating a 2 bar overpressure in an enclosure can induce a flame velocity on the order of 400 m/s in the connected duct without any protection while having vents on the duct close to the exploding vessel can limit significantly the pressure effects and reduce the flame velocity by a factor 2 to 4 [START_REF] Roux | Méthode de protection contre les explosions: évents -explosions de poussières[END_REF]. In the present case this would not be sufficient but reducing the flame velocity level between the two enclosures can make it possible to use smaller vent areas than those presented in the earlier paragraph, in fact one can use the vent area calculated earlier with EN14491:2014 [START_REF]Dust explosion venting protective systems[END_REF] for the isolated cyclone. A calculation was performed with two explosion decouplers located at the middle of each duct, and with the 0.5 m 2 vent on the cyclone (in addition to the already installed 5 m 2 vents on the filter). The measured overpressure are presented in Fig. 7. Fig. 7. Overpressure calculated in the mill, cyclone and duct; with 0.5 m 3 vents protection on the cyclone and an explosion decoupler on each duct.

In this case the installation is protected. Thanks to the decouplers, the flame velocity is sufficiently limited in the ducts, also leading to a lesser turbulence level in the cyclone and the filter, thus allowing the vents to fulfil their role efficiently.

Isolation of the duct and vent protection of each volume

If an isolation system is present on the duct, the flame will not propagate from one enclosure to the other one and then standard venting protection rules for isolated enclosures may be applied. These isolating devices can be of several types and based on very different technologies, for example: active (electronic detection of the explosion) or passive (purely inertial) flap valves, gate valves, pinch valves or chemical flame extinguishers. However, as any explosion mitigation device, they have their own limits that need to be accounted for. Firstly, some of those, such as the flap valves can only function in one direction, to stop a flame traveling in a direction opposed to the usual flow observed during the functioning of the process. Secondly some of these systems rely on the mechanical closing of the duct, which imply there are not efficient before a certain amount of time.

From past experience on systems tested at INERIS, sometimes in the scope of ATEX certification, this delay is typically ranging around a few ms for active devices (with actual explosion detection and non-passive closing system such as in the case of gate valves or pinch valves) to a several dozens of ms when the device is fully passive and actuated by the explosion generated flow. Depending on the flame velocity (which can hardly be lower than 150 m/s in the present configuration) and the duct length (15 m here) it is necessary to ensure that the chosen system is really able to stop the flame. Also, quite regularly singularities, such as bends or a restriction generating a Venturi effect, are present on the ducts of industrial processes; they may alter the flow significantly. This needs to be considered when installing the isolation devices. Finally, there is also an upper limit in time (chemical isolation) or installation distance (mechanical isolation) after which the extinguishing cloud has settled down or the duct pressure has become too high and the isolating system will fail mechanically.

Explosion suppression in the mill and the cyclone

Alternatively, it is possible to use explosion suppressors on the mill and the cyclone. Those are based on the active and early detection of explosions coupled with a chemical agent that is injected at a sufficient rate so that the explosion can be quenched before it becomes too damaging for the structure. Typical delays for flame quenching are on the order of a few dozens of ms. As it is intended to extinguish the flame in each of the capacities, there should not be significant acceleration effect through the pipe between the cyclone and the filter, so that it is not necessary to install an isolation device. However, this is only true in the specific case of this installation and because a ST1 dust is chosen. Under these conditions, the risk of dust explosion in the filter persists.

It is therefore a fundamental requirement to have vents on the filter. Methods for modelling the suppression devices have been implemented in EFFEX but they will not be described at this stage. Further details on this specific aspect may be found in [START_REF] Chatrathi | Dust deflagration extinction[END_REF].

Mixed systems protection

The solutions presented in the previous paragraphs can be combined, but again without losing the perspective that the enclosures are connected by a duct. For example, if the filter is outside of the building and the cyclone is located inside, the former can be protected by a vent while the later cannot (it is assumed that people are working in the same building). It would be possible in such case to protect the cyclone with explosion suppressor. Again, it cannot be done without a due consideration of flame velocity / acceleration in the duct. Explosion suppressors are certified within limits in terms of dust reactivity (among other limits such as the throw of the extinguishing cloud or the activation delay) that are applicable to the case of isolated enclosures. This is not the case if the flame has been significantly accelerated in a duct before reaching an enclosure in which the turbulence has been significantly increased compared to the standard process conditions. Consequently, for the suppression technique to remain effective in this situation a decoupling device or an isolation valve might be needed between the mill and the cyclone. The limitations referred to in the preceding paragraphs for the different explosion mitigation devices apply.

CONCLUSION

A strategy to implement an explosion mitigation solution has been presented around the example of a simplified industrial coal grinding process made of a mill, a cyclone, and a filter. A phenomenological analysis of explosion development and propagation in dual enclosure-duct systems was presented. The scenario of an explosion starting from the mill was selected as a reference to highlight the critical mechanisms involved when explosions propagate between interconnected enclosures. In the fourth part a way to account for the real explosion conditions is given, allowing a choice and dimensioning of a set of safety systems. Vent area calculations were presented together with the order of magnitudes of the characteristic functioning parameters of the other safety systems that may be implemented. Beyond that an important focus is given on the actual strategy of protection to implement, which aims at protecting firstly the people working close by then the structure and must always rely on a physical understanding of the dust flame propagation (in enclosures and in ducts) as well as its interaction with its environment (turbulence generation, pressure effects). A specific focus can thus be made on two fundamental aspects: on the

Fig. 1 .

 1 Fig. 1. Schematized coal grinding installation.

Fig. 2 .

 2 Fig. 2. Flame front evolution as a function of time.

Fig. 5 .

 5 Fig. 5. Overpressure calculated in the mill, cyclone and duct; explosion ignition in the mill.

one hand, it is of critical importance to understand how the flame propagates in a given complex system. On the other hand, the behaviour of the protection systems that might be used must also be carefully studied as it cannot be dissociated form the previous analysis, those systems will indeed systematically have an effect on the explosion driven flow.