Protective Walls Against Effects of Vapor Cloud ... - Wiley Online Library

Protective Walls Against Effects of Vapor Cloud Fast Deflagration: CFD Recommendations for Design Elena Vyazmina,a Simon Jallais ,a Alberto Beccantini,b and Sophie Tr elatc a Paris-Saclay Research Center, AIR LIQUIDE Research & Development, BP 126, 78354, Jouy-en-Josas, France; [email protected] and [email protected] (for correspondence) b CEA Saclay, DEN/DM2S/STMF/LATF, Gif-sur-Yvette, 91191, France c IRSN, B.P. 17, Fontenay-aux-Roses Cedex, 92262, France Published online 00 Month 2017 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/prs.11930

Protective walls are a well-known and efficient way to mitigate overpressure effects of explosions. For detonation there are multiple published investigations concerning interactions of blast waves and walls, whereas for deflagration no well-adapted and rigorous method has been reported in the literature. This article describes the validation of a new computational fluid dynamics (CFD) modeling approach for fast deflagrations. In a first step, the vapor cloud explosion involving a fast deflagration is substituted by an equivalent vessel burst problem. The purpose of this step is to avoid reactive flow computations. In a second step, CFD is used to model the pressure propagation from the equivalent (nonreactive) vessel burst problem. After verifying the equivalence of the fast deflagration and the vessel burst problem in the first step, the ability of two CFD codes FLACS and Europlexus is examined for situations with and without barriers. Parametric analysis by means of numerical simulations is performed to investigate the efficiency of finite barriers to mitigate blast waves. Another parametric study shows how the maximum overpressure value in the shade of the barrier depends on the magnitude of the incoming overpressure wave. On this basis, several recommendations are suggested C 2017 American Institute of for designing protective walls. V Chemical Engineers Process Saf Prog 000: 000–000, 2017

Keywords: Keywords: computational fluid dynamics; deflagration; blast; protective walls INTRODUCTION

Protective walls are an efficient way to protect people and infrastructures from overpressure effects due to accidental or malicious explosions. Two types of explosions characterized by two modes of flame propagation exist: deflagration and detonation. The main difference between the two regimes lies in the propagation speed of the flame, which is generally subsonic in the case of deflagration and largely supersonic (1500, 2000 m/s) in the case of detonation. The most important factors responsible for structural damage and injury to humans are overpressure and corresponding positive impulse (the integral of the overpressure over time corresponding to the duration of the positive phase). Assuming the same released energy, blast waves

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overpressures associated with detonations are much higher than for deflagration and the duration of the overpressure positive phase is shorter for detonation. For detonations, there are several engineering or computational fluid dynamics (CFD)-based design rules for barricades design in the literature, such as NOTA recommendations 2009 [1–3]. Feasibility and effectiveness of protective barriers against detonation waves were widely investigated in literature, see for instance [4–7]. These authors investigated the geometrical features of various barriers for detonation of solid high explosive. Eveillard [6] also suggested abacus for barricade-shape of the protection barriers. However, in case of a deflagration (the most probable industrial scenario), no adapted rigorous method has been published in the open literature. Hence this article is focused on the effect of the blast wave originated from deflagration. Due to the complexity of the phenomena associated with the interaction between a wall and the blast waves appearing from the fast deflagration, a CFD-based method is developed. The aim of this method is to reproduce the decay of the blast wave generated by a fast deflagration in a far field upstream and downstream of the barrier, without modeling the combustion process associated with the deflagration. As a first step, a 3D CFD code is validated against accurate 2D and 1D numerical solutions in a free field, then with a virtual infinite wall. As a second step, several design rules are discussed on the basis of a sensibility study using the validated CFD method. DEFLAGRATION “EQUIVALENT” PROBLEM

For the combustion of a gaseous hemisphere we assume that, before the flame reaches the interface between the gaseous fresh mixture and the surrounding air, the problem can be reduced to 1D point-symmetric flow generated by a constant flame speed. If the medium is homogeneous, the flame width is negligible and the flame velocity is constant. Hence the solution will be self-similar, as pointed out in the works of Sedov [8] and Kuhl [9]. According to [10] and [11], this solution (called hereafter Sedov solution) reproduces the first stage (i.e., combustion stage) of a hemispheric Vapor Cloud Explosion (VCE). Once the combustion is over the second stage of a VCE can be assimilated to the temporal decay of Sedov solution and can be used for the validation of a nonreactive Euler solver of CFD codes used for VCE computations. Month 2017

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Figure 1. Time decay of the Sedov solution (left) and reservoir problem (right) in the case where the flame velocity equals 0.8 of the sound speed at times t 5 0.1072 s, t 5 0.1786 s, t 5 0.2501 s.

This article focuses on the effects of a fast deflagration in a far field (the propagation of the pressure waves). As shown in detail in [12], there is no need to model the combustion process since we are able to replace it by an equivalent vessel-burst problem. Summarizing, the pressure in the burst reservoir is taken equal to the maximum pressure P of the Sedov solution; the combustion temperature is the one of the burnt mixture. The radius of the reservoir is evaluated by imposing that the energy stored in the vessel is equal to the energy released by the combustion of the reactive mixture: 2 3 DP pR 5E; 3 rb g21

(1)

where E is the combustion energy of the mixture [J]; DP5P2Pambient —the overpressure inside the burst reservoir [Pa]; g—specific ratio for air; Rrb—the radius of the “equivalent” burst reservoir [m]. We have shown that in the case of a fast deflagration, the “vessel burst” temporal decay is equivalent to the decay of the Sedov solution (t), see Figure 1. (see [12] for details) In the current investigation, the following high-pressure and high-temperature reservoir is considered, see Table 1. This corresponds to a flame velocity of 270 m/s (0.8 of speed 2

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of sound), which is approximately equivalent to the strength index of 7 of the TNO multi-energy method (fast deflagration). Initial conditions for the equivalent reservoir burst problem are presented in Table 1, where Rrb is the radius of the reservoir.

FREE FIELD SOLUTION

The reference solution (for the vessel burst problem) is computed using a 1D point-symmetric finite volume approach (the spatial resolution is of 1 mm). This solution is then compared with solutions obtained from 2D simulations of Europlexus [13] and 3D simulations with FLACS [14]. Table 1. . Initial conditions for a vessel burst problem.

Overpressure (barg) Temperature (K) Density (kg/m3) Speed of sound (m/s)

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Vessel Burst (Rrb 2.657 m)

0.8561 3677 0.1759 1215

0 293 1.189 343.1


Figure 2. Solution of the reservoir burst problem at t 5 12 ms. Europlexus results using two meshes (green is Rrb/128 5 2 cm mesh, blue is Rrb/32 5 8 cm) versus the reference solution (red solid line). [Color figure can be viewed at wileyonlinelibrary. com]

Figure 3. The standard mesh and initial vessel representation using FLACS (dx 5 10 cm grid size). [Color figure can be viewed at wileyonlinelibrary.com]

Figure 4. Solution of the reservoir burst problem. Pressure as function of time at R 5 5.6 m: FLACS simulation results for various spatial resolutions versus reference solution. [Color figure can be viewed at wileyonlinelibrary.com]

The 2D simulation domain in Europlexus is chosen to be 8 m long and 6 m high. The solution sensitivity to the spatial resolution is investigated using two grids: one with a cell of Rrb/128 5 2 cm and the coarser one of Rrb/32 5 8 cm. The reference solution at t 5 12 ms is compared to the one obtained using Europlexus (for two different spatial resolutions), see Figure 2. A fine mesh is essential for a relatively accurate (with less than 10% error) representation of the overpressure. Moreover, as the distance from the reservoir increases, the relative error on the maximum overpressure also increases. The accuracy of the positive impulse (corresponding to the main pressure peak) is the same order of magnitude at 3.65 m and at 5.6 m. For 3D simulations, the 3D CFD commercial code FLACS developed by GexCon [14] is used. There are different versions of FLACS dedicated to the modeling of different phenomena. FLACS-Blast is a special version of FLACS for simulating blast waves propagation from detonation of condensed explosives. FLACS-Blast solves the Euler equations with a flux-corrected transport scheme [15]. This version was recently validated for three different charges of high explosive [16]. FLACS standard version is dedicated to the deflagration of gases and dusts. Since blast propagation from fast deflagration is considered here, the standard version of FLACS is considered in the study. In current simulations FLACS version 10.2 is used. FLACS v 10.2 solves the

Figure 5. Reservoir burst problem with a wall, monitoring positions. [Color figure can be viewed at wileyonlinelibrary.com] Process Safety Progress (Vol.00, No.00)


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Table 2. . Mesh description used by Europlexus. Point

Coarsest

Medium

Finest

x 5 9.75 m, z 5 3 m x 5 10.75 m, z 5 3 m x 5 12.75 m, z 5 3 m Number of grid points

0.11678 0.0676 0.03784 35 816

0.12246 0.07323 0.0413 139 264

0.12762 0.0779 0.04307 557 638

Table 3. Various wall lengths considered. Wall Length L (m) 7.8 15.6 31.2 infinite

Ratio L/h 3.12 6.24 12.48 infinite

compressible Navier-Stokes equations on a 3D Cartesian grid using a finite volume method. FLACS solves the ReynoldsAveraged Navier-Stokes (RANS) k-E model equations for turbulence, see Refs. [14,17]. The SIMPLE pressure correction algorithm is used as in Ref. [18]. The simulation domain in FLACS is 20 m in both horizontal directions (x and y) and 10 m in the vertical z direction. The influence of the computational domain size is checked by using a larger domain (30 m 3 30 m 315 m), and the solution is found to be independent on the domain size. The gravity is activated and is parallel to the vertical z axis. A very short-time step is used (CFLC 5 0.1, CFLV 5 0.1, also the option “keep low” is activated to prevent time step from growing). The solution is computed with five different spatial resolutions, with a mesh size equal to 20 cm, 10 cm, 8 cm, 7 cm, and 5 cm. The meshes are regular with constant cell size (see Figure 3). The overpressure computed with spatial resolutions of 5 cm, 7 cm, and 8 cm shows an error of the same order of magnitude (see Figure 4) compared to the reference solution. The positive impulse of the main pressure peak is closer to the reference solution for the finest resolution (5 cm). However, the error, even in this case, is greater than

Figure 6. Overpressure at different positions: comparison of Europlexus simulations (black solid line) to FLACS simulations obtained with different spatial resolutions (dx 5 5 cm in cyan and dx 5 10 cm in magenta dashed lines). [Color figure can be viewed at wileyonlinelibrary.com]

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Figure 7. Maximum overpressure versus distance: comparison of FLACS solutions of vessel burst problem with an infinite wall (dashed blue line) and in a free field or no-wall solution (red solid line).

10%. As the distance from the reservoir increases, the error on the positive impulse remains the same. Both softwares FLACS and Europlexus give fair results (see Figures 2 and 4). Concerning FLACS the main (first) pressure peak and the corresponding positive impulse are slightly overestimated. The best match with the reference solution is obtained for the finest grid (around 10%), however, the grid with spatial resolution of 10 cm also gives acceptable results. SOLUTION WITH A WALL

The approach of vessel burst is applicable if the barrier is far enough from the combustion region (the fireball does not interact with the barrier). The aim of this section is to investigate numerically the efficiency of

protection barriers to mitigate the propagation of pressure wave from deflagration. For this purpose, the pressure decay in a free field is compared to the pressure spreading in the environment with a protective barrier (a wall). The wall is located 9.2 m downstream of the center of the vessel. This position corresponds to an incoming overpressure of 150 mbarg. The height of the wall is set to 2.5 m, its thickness to 0.5 m. In the reference case, the wall is considered to have an infinite length (the same size as the computational domain width). Monitoring points are located upstream, downstream, and on the wall to study its mitigation effects, see Figures 5. Monitoring points located at 1.5 m height are of special interest since they correspond to the average height of the lungs of an adult. In order to evaluate the protection barrier efficiency (its mitigation factor) and its dependence on the barrier length, 3D simulations must be validated. For this purpose, 3D solution obtained with FLACS for reference case is compared to a finer resolved 2D solution from the Eulerian Europlexus code. Numerical Settings In the case of FLACS the grid is the same as in the case of free field. The independence of the numerical solution on the size of the computational domain is verified by comparison of simulation results in three different domains of 90 m, 34 m, and 26 m. However, the largest simulation domain is used (in order to reduce the effect of boundary conditions) for the parametric studies considering different lengths of the wall. The sensitivity of simulation results to spatial resolution is verified for two different grids with cell sizes of 5 cm and 10 cm: simulation results match closely. Hence the solution is independent on grid resolution. The 2D axisymmetric Euler equations are solved using a finite volume approach. In the case of 2D solution the wall is circular (not infinite), however close to the wall curvature effects are negligible. The height of the computational domain is 10 m. The mesh is not uniform: close to the barrier the mesh size is 10 times smaller than far from it. The sensitivity of the simulation results with respect to the mesh size are verified using three different meshes,

Figure 8. Overpressure at different positions: comparison of FLACS solutions of vessel burst problem with a wall (dashed blue line) and in a free field (red solid line): upstream of the wall. [Color figure can be viewed at wileyonlinelibrary. com]



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Figure 9. Comparison of pressure signal behind the wall: free field solution is shown by red solid line, solution with a wall is shown by blue dashed line. [Color figure can be viewed at wileyonlinelibrary.com]

see Table 2. Simulations show that at the points investigated behind the barrier (x >9.7 m), the difference between the maximum overpressure is more pronounced (10% between coarse and finest grids, 5% between medium and finest grids) in the points with z 5 3 m and is not sensibly important close to the soil. The results from the fine mesh are used in the current work. Initial conditions for 2D Europlexus simulations are imposed by projecting on the 2D axial-symmetric mesh the 1D pointsymmetric results of the reservoir burst problem just before the interaction with the barrier occurs. In all computations, the predictor-corrector of Van Leer–Hancock (second order in time and quasisecond order in space) is used (space reconstruction is performed on conservative variables and Barth-Jespersen limiter is employed). CFL is equal to 0.5, and the HLLC method is applied to compute the numerical fluxes at the interfaces. Simulation Results: Cross-Comparison Between Europlexus and FLACS Figure 6 shows a comparison of simulations results obtained by Europlexus and FLACS for vessel burst problem with a wall. The first two frames correspond to monitoring 6

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points located upstream of the wall, whereas other frames correspond to monitoring points located behind the wall. FLACS results are in close agreement with Europlexus simulations. The overpressure computed by FLACS with a spatial resolution of dx 5 5 cm is slightly closer to the results of Europlexus in terms of maximum overpressure, time of arrival, and corresponding impulse. The solution obtained with FLACS with a spatial resolution of 10 cm shows in general a slightly higher pressure than the one computed with a spatial resolution of dx 5 5 cm. The pressure signal is stiffer for resolution of dx 5 5 cm, hence pressure curves for dx 5 10 cm are slightly larger. Thus, the impulse computed at the grid with cell size of 10 cm is higher. However, FLACS simulation results obtained with dx 5 10 cm are acceptable for further analysis. In terms of the time corresponding to the detection of the maximum pressure, the error between simulations performed by Europlexus and FLACS (both with dx 5 5 cm and dx 5 10 cm) is negligible. This comparison shows that FLACS results are in very close agreement with Europlexus for the maximum overpressure, for the corresponding impulse and for the time of overpressure arrival. DOI 10.1002/prs


Figure 10. Mitigation factor for the overpressure versus downstream distance. [Color figure can be viewed at wileyonlinelibrary.com]

Wall Effect on the Overpressure To investigate how the presence of a wall affects the overpressure propagation upstream and downstream of the wall, the overpressure maxima in time are compared for geometries with and without wall. This comparison is demonstrated on Figure 7. Here, the pressure decay is shown versus the distance from the center of the hightemperature and high-pressure reservoir (z 5 1.5 m above ground level). The solutions for the free field and for the geometry with a wall (at 9.2 m) overlap until 8.5 m. Very close to the barrier a significant rise of the overpressure is detected. This pressure rise is the pressure reflection from the wall. Here, the reflected overpressure is almost 1.9 times higher than the corresponding free field overpressure, see Figure 8. The first overpressure peak (frame 1, Figure 8) corresponds to the overpressure front propagation from the reservoir burst (this peak is identical to the free field solution), whereas the 2nd peak on the blue curve (solution with a wall) is the reflected pressure. The closer the monitoring point is located to the wall, the smaller the time gap between these two peaks is and the higher the second peak is. At the monitoring point located 5 cm upstream from the wall, these two peaks add up, leading to the appearance of a single overpressure maximum, which is almost twice as high as the corresponding free field overpressure. Figure 9 shows the pressure wave propagation downstream of the wall (propagation behind the wall), demonstrating a region of reduced pressure behind the wall (compared to the free field). This is the so-called “wall shade” effect. The overpressure is significantly reduced compared to the one obtained for the free field. Figure 9 also demonstrates that behind the barrier (in the reference case) the overpressure does not exceed 32 mbarg at z 5 1.5 m height from the ground level, which is significantly lower than the overpressure in a free field. The wall not only reduces the pressure wave maximum in its shade, but also leads to the dispersion of the pressure front


Figure 11. Comparison of maximum overpressure (in the shade, at z 5 1.5 m from the ground) for walls with various lengths: no wall (red solid line), wall with L/h 5 3.12 (green dashed line), wall with L/h 5 6.24, wall with L/h 5 12.48, infinite wall (black dashed line). [Color figure can be viewed at wileyonlinelibrary.com]

(reducing the wave front stiffness and increasing its thickness). The mitigation factor for the overpressure (Pmax free field/ Pmax wall) demonstrates the efficiency of the protective barrier. Figure 10 shows the pressure mitigation factor versus the downstream distance normalized by the barrier height. This factor shows how many times the free field overpressure is reduced due to the presence of the wall. At long distances the mitigation factor decreases to 1, meaning that at long distances the pressure in the wall shade approaches the pressure in the free field. Unfortunately, in order to catch this phenomenon one should use a much longer simulation domain. However, this becomes very expensive in terms of CPU time. Effect of the Wall Length on the Wall Mitigation An important parameter strongly affecting mitigation of a barrier is its length. The barrier length can significantly reduce its mitigation properties. For the comparison with the infinite barrier, three finite length walls are considered see Table 3. The mitigation effect of these walls on the overpressure in the wall shade is shown in Figure 11. In Figure 11, the blue curve overlaps the magenta curve. This means that for walls with aspect ratio larger than 6 (L/h > 6), the mitigation factors are approximately the same and they approach the mitigation factor of the infinite wall (black curve). For shorter walls, see here for instance L/h3, the mitigation effect is strongly reduced. The overpressure for short walls is much higher than for the infinite wall, due to the pressure wave lateral overturning, see Figure 12. Figure 12 demonstrates snapshots of overpressure (in the horizontal plane at 1.5 m from the ground) for infinite wall (on the left) and for the wall with aspect ratio L/h3 (on the right). Pressure waves are the same at t 5 0.015 s (before interaction with the wall) for both walls. Reflection of the pressure wave from the wall is observed (t 5 0.02 s). At t 5 0.03 s and t 5 0.04 s wave


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Figure 12. Comparison of pressure snapshots infinite wall (on the left) and for wall with L/h3: horizontal plane at z 5 1.5 m from the ground. [Color figure can be viewed at wileyonlinelibrary.com]

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Figure 12. (Continued).

overturning (for the short wall) from the lateral sides develops. At t 5 0.05 s these lateral waves merge into the one, leading to the appearance of a new overpressure maximum. And this maximum is significantly higher than the corresponding pressure for the infinite wall (at t 5 0.07 s). Effect of the Magnitude of the Incoming Overpressure The effect of the amplitude of the incoming pressure on the mitigation of a barrier is an important parameter for the design of a protective wall. To understand this effect, the wall location is varied in order to obtain different levels of the incoming overpressure. Three levels of the overpressure are considered: 410 mbarg (corresponding to a wall at 4 m), 300 mbarg (wall at 6 m), and 150 mbarg (wall at 9.7 m). The mitigation effect of these walls on the overpressure is shown in Figure 13. Here, the maximum overpressure in time for three wall positions is compared to the overpressure in a free field. Process Safety Progress (Vol.00, No.00)

The reflected pressure is observed for the three wall positions. Table 4 demonstrates the coefficient of reflection for the three cases (here the overpressure is taken at the position just before the front side of the wall). The comparison shows that the coefficient of the reflection increases with the incoming overpressure. The overpressure behind the wall for the three cases does not exceed 60 mbars, see Table 5. However, in the wall shade the maximum overpressure is not located just behind the wall but rather at a distance equivalent to 0.7 h (where h is the wall height), see Figure 14. This effect is more visible for higher incoming overpressure levels. Figure 15 shows the maximum overpressure in the wall shade versus incoming free field overpressure. CONCLUSION

The comparison of results from FLACS v10.2 3D simulations to 2D Europlexus simulations shows good agreement for the free field solution and the solution with a wall. This demonstrates FLACS capacities to be used for simulations of


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Figure 13. Comparison of FLACS solutions without wall (red solid line), with a wall at 4 m (410 mbarg)—back dashed line, at 6 m (300 mbarg)— green dashed line, and at 9.7 m (150 mbarg)—blue dashed line. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 14. Overpressure maxima in a wall shade measured at z 5 1.5 m from the ground versus distance from the wall for incoming overpressures (for wall of 2.5 m height): black curve corresponds to 410 mbarg, green—to 300 mbarg and blue—to 150 mbarg. [Color figure can be viewed at wileyonlinelibrary.com]

Table 4. Free field and reflected overpressure for various incoming overpressure levels (wall positions). Wall Position (m)

Free Field Overpressure (mbarg)

Reflected Overpressure (mbarg)

Coefficient of the Reflection

410 300 150

1 017 634 321

2.4 2.1 2.1

4 6 9.7

Table 5. The mitigation factor (Pmax free field/Pmax wall) of these walls (the overpressure is taken at the position just behind the back side of the wall). Wall Position (m)

Free Field Overpressure (mbarg)

Overpressure Behind the Wall (mbarg)

Mitigation Factor Just Behind the Wall

410 300 150

55 46 32

7.4 5.97 5

4 6 9.7

pressure wave propagation in a far field for both geometries: free field and with a wall. Parametrical simulations performed by FLACS showed that for short walls with aspect ratio L/h < 6 the mitigation factor for the overpressure (Pmax free field/Pmax wall) is significantly reduced compared to the infinite wall, due to the appearance of the lateral overturning waves. Hence, it is recommended to build walls with aspect ratio L/h > 6 to avoid overturning. Another parametric study showed that the maximum overpressure value in the shade of the barrier depends on the magnitude of the incoming overpressure wave (see Figure 15). For instance, in order to obtain an overpressure less

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Figure 15. Maximum overpressure in wall shade 1.5 m high from the ground versus incoming overpressure (for wall of 2.5 m height). [Color figure can be viewed at wileyonlinelibrary.com]

than 50 mbarg behind the wall at 1.5 m from the ground (for the infinite wall), the incoming pressure (at the wall) must be less than 300 mbarg. However, the wall must be designed for much higher overpressures, due to the pressure reflection from the wall (see Table 4). Hence for instance, the wall must be designed for 650 mbarg instead of 300 mbarg. The next step will be to investigate the effectiveness of protection barriers against detonation and to compare with deflagration to detonation.

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