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This investigation focuses on the injection of an ammonia leak from the pipeline a cross to the free stream flow on a flat surface. The main size of model is obtained from Bouet et al. (2005). The computational domain selected for the present simulation is a surface 100 m-long and 30 m-high along the center of the leakage, and employs two dimensional in order to reduce computational expense. Fig. 2a illustrates the size of the main model of the domain and the barrier. The same geometry without the mesh barrier was also used to compare and evaluate the performance of this device.

Fig. 2. 
(a) Computational of domain and (b) grid generation of the main model.

A mesh barrier was used to control the dispersion of the ammonia leak. Various mesh sizes have been investigated to define the optimum size for mitigation of the dispersion. The height of the barrier was assumed to be 5 m.

In order to quantify the characteristic of each barrier configuration, it is necessary to define a proper nondimensional number known as the Mesh Coefficient (MC). The required relation is given as

Where Σ S is the sum of the areas of each block space, N is the number of the hole in the barrier and L is the total length of the block of the barrier. In the present study, eight types of mesh barrier, with various Mesh Coefficients (MC), have been investigated for different atmospheric conditions. Furthermore, the distance of the mesh barrier for main model is 3 m.

In 1961, Pasquill (1961) presented most commonly used method of categorizing the amount of atmospheric turbulence. He categorized the atmospheric turbulence into six stability classes named A, B, C, D, E and F with class A being the most unstable or most turbulent class, and class F the most stable or least turbulent class. In order to cover all aspects of the this method, three main atmospheric conditions (A, D, F) are chosen for this works.

In the present model, the main interactions occur close to the barrier and completely within the boundary layer. Since fine meshes were required to adequately resolve the flow features, the domain was broken down into separate computational units to work within the constraints of available computational resources, as shown in Fig. 2b.

Full structured grids were constructed for all cases. One of the main factors of the analyzing the grid is Y⁺. Y⁺ is a non-dimensional distance that is often used to describe how coarse or fine a mesh is for a particular flow pattern. It is important in turbulence modeling to determine the proper size of the cells near domain walls. The turbulence model wall laws have restrictions on the y⁺ value at the wall. In our study, cell refinement was achieved manually in the region immediately adjacent to each outlet of leak and, in the wall normal direction, the cells were arranged such that the distance from the wall to the first cell centroid provided a Y⁺ within the acceptable range (Y⁺<30) of turbulence model. The grid spacing was stretched ensure all regions of the boundary layer and injection flow structures close to the wall were adequately resolved. An example of the grid in the vicinity of an injector is shown in Fig. 2b together with a close-up view of the grid in the vicinity of the leakage and mesh barrier are displayed in the Fig. 2b.

One of the main factors for the numerical simulation is a proper grid arrangement. The structural grid is generated to improve the accuracy of results. Also, an extensive grid refinement study (mesh sizes from 860×260, 1100×340 and 1400×420 in the horizontal and vertical directions) was conducted to determine grid independence in mass distribution to resolve the boundary layers. The results of validation (Fig. 3) show that a fine grid (300000) has enough precision for the present investigation.

Fig. 3. 
Mass fraction of Ammonia on ground surface along the symmetry direction (validation).

The types of boundary conditions are defined as depicted in Fig. 2a. The conditions that apply to the inflow boundary are a velocity inlet, where profiles of wind speed, turbulent dissipation and TKE must be provided. The outlet is set to be a simple outflow condition. The top of the domain, assumed to be sufficiently far away from the mesh barrier as to not affect the flow in the area, is set to a symmetry condition.

The inlet condition of the domain needs careful attention as inlet flow conditions will greatly influence on the simulation results. The standard power law atmospheric boundary layer profile, turbulence kinetic energy (k) and dissipation (ε) at the inlet boundaries are given by equation (2).

Where P is an empirically determined coefficient which increases with increasing surface roughness and atmospheric stability (Huang, 1979). In this study, P is defined 0.15, 0.25 and 0.55 for the atmospheric condition of unstable (A), neutrals (D) and stable (F), respectively. In addition, U* is the velocity at reference height z*(U*=3 m/s), k_υ is von Karman’s constant (0.41) and Z_* is the surface roughness length in the vertical direction (Z), defined as 7 m, a typical average value for a non-urban area.

The simulations were performed using an implicit in-house CFD code-FVsolver (Barzegar Gerdroodbary et al., 2016, 2015a-d, 2014, 2012, 2011, 2010; Amini et al., 2015). This code solves the Navier-Stokes equations using cell centered finite volume approach. A second order upwind scheme was used to discretize RANS equation and the species transport equation with a SIMPLE algorithm. Four types of equations are solved in each case: the continuity equation (3), RANS equations (4), and two turbulence closure equations (6)- (7) for realizable k-ε, for the turbulent kinetic energy (k), and for the dissipation rate of turbulent kinetic energy (ε). Tauseef et al. (2011) showed that the realizable k-ε model is seen to provide more realistic results for heavy gas dispersion in the presence of obstacles, compared to the standard k-ε model, both in time and space.

The continuity equation of incompressible fluid and the Reynolds-averaged Navier-Stokes (RANS) equations are written as follows:

where, u_j is the jth component of velocity, t is the time, x_j is the jth coordinate, ρ is the density, μ is the dynamic viscosity, and g is the gravitational body force which is in the vertical direction.

Equation (5) is the Reynolds stress equation, where, μt=ρCμk2ε is the turbulent viscosity. The governing equations of the realizable k-ε turbulence model are

Where , τij=2μtSij-23ρkδij and Sij=∂u¯i∂xj+∂u¯j∂xi. The model constants are C_μ=0.09, σ_k=1, σ_ε=1.3, C_ε1= 1.44 and C_ε2=1.92 (Tauseef et al., 2011; Sini et al., 1996). The pollutant dispersion patterns were analyzed, after solving the species transport equation, in conjunction with the turbulence model equations. The advection-diffusion (AD) module was applied to study the species transport process, by analyzing the mass fraction of pollutants in the mixture.

The code analyzes the mass diffusion process based on the species transport equation:

Where, J_j is the diffusion flux of the mixture (kg/m²s), ρ is the density of the mixture (kg/m³), D_i,m is the mass diffusion coefficient of the pollutant in the mixture (m²/s), Y_i is the mass fraction of the pollutant (kg/kg), and μ_t is the turbulent viscosity (kg·s/m). Similar to the other studies (Di Sabatino et al., 2008; Riddle et al., 2004), the turbulent Schmidt number was Sc_t specified as 0.7.

In order to increase convergence, the freestream without ammonia leak was solved as a first step. After the flow field in the vicinity of the barrier is formed, the pollution (NH₃) is issued through a single leak hole. When the jet is released from the leakage, it severely oscillates. After a few iterations, the oscillations are limited and the pollution flow approximately forms a steady flowfield, though some small fluctuations remain. This issue will be completely discussed in the following sections.

In numerical simulations, the validation of the data is essential for the evaluation of the results. In this paper, the numerical results of NH₃ free dispersion along the downstream surface of the leak are compared with other experimental results to validate the precision of the present study.

To validate the numerical accuracy and obtain a better understanding of fundamental wind-buoyancy-driven flow, the three-dimensional computational domain used in this study is kept identical with the experimental model proposed by Bouet et al. (2005), which consists of 3 cases with the different atmospheric conditions and leak rates. The height H of the barrier is 3 m. In addition, the distance of the barrier to leak position is 1 m and 3 m for the second and third tests. The height of the computational domain is kept at 4H. Three experimental tests of Bouet et al. (2005) are chosen with/without solid barrier arrangement to compare the dispersion of the ammonia in downstream of leakage (Table 1). Fig. 3 compares the numerical result of the present study and the experimental data of Bouet et al. (2005). The experimental data are obtained from a ground-level linesource of ammonia leak. Since the real distribution of gas in the experimental study is in three directions (streamwise, spanwise and vertical directions), the three dimensional domain with 2700000 grids is chosen for the validation. The results in Fig. 3 show good agreement between the simulations and other correlation in models with/without a solid barrier. Furthermore, the comparison verifies that the two dimensional results of the numerical simulation present a small discrepancy from experimental data.

First, it is expected that the size of the mesh barrier play a significant role in the performance of this device. Therefore, various mesh barriers are examined to evaluate the efficiency of each formation on dispersion. Table 2 shows various arbitrary configurations of the mesh barrier with different Mesh Coefficients.

Fig. 4 compares the influence of different mesh barriers on the dispersion of the ammonia leak (mass flow=0.2 Kg/s) within a stable atmospheric condition (F). The color region in figures depicts the danger zone where the mass fraction of ammonia is more than 500 ppm. The results illustrate that danger zones extensively varied in the downstream as different mesh barriers are presented. In the case of no barrier, the general features of the ammonia dispersion are typical leakage, such as that presented by previously published works (Bouet et al., 2005). The distribution of the NH₃ clearly shows that the danger zone expands as the ammonia moves to downstream. Since several studies (Schulte et al., 2014; Sklavounos et al., 2014; Steffens et al., 2013, 2012; Dandrieux et al., 2001; Khan et al., 1999a, b) have extensively described about the flow structure of the leak without a barrier, the discussion in this area is referred to these works. However, the presence of low coefficient mesh barrier (case 1 and case 2) leads to the reflection of the free stream immediately downstream of the mesh barrier and the stream patterns form similar distribution as they interact with a solid barrier. Then, the danger zone is not only limited but also increased, and the height of the dispersion becomes larger. As the mesh coefficient of the barrier increases, the adverse pressure gradient caused by the solid barrier vanishes and the ammonia disperses at limiting height downstream. In other words, a high amount of the ammonia leak diffuses through the holes of the mesh barrier, and the danger zone is thereby significantly declined.

Fig. 4. 
Influence of various mesh barriers on flow structure and mass concentration of Ammonia leak (Atmospheric condition=F, m°=0.2 Kg/s). All dimension is in meter.

The height of the danger zone is a crucial factor for the safety and design of the industrial plant where the risk of the leakage is presented. Therefore, extensive efforts were performed to know the risk region. Fig. 5 illustrates the variation of the height of the danger zone along the streamwise direction for various causes in the stable atmospheric condition (F) with low leak rate (mass flow=0.2 Kg/s). The results clearly show that the danger zone is diminished as a mesh barrier with high Mesh Coefficient are presented in downstream of the leak. In addition, the height of the danger zone significantly reduces when the mesh coefficient is increased. Also, the performance of the mesh on the dispersion is approximately the same in cases with high mesh coefficient (MC=12 and 16). Thus, incase 5, MC=12 is chosen as an optimum choice for comparisons of this device in different conditions.

Fig. 5. 
Comparison of the height of danger zone along the streamwise direction.

Since the efficiency of this method is significantly high in low leak rate, the careful study of this device will improve our insight and reduce the risk of danger in industrial plants. As the flow pattern due to interaction with a mesh barrier highly influences the dispersion of leaking gas, precise inspection of the flow offers valuable information about the dispersion; and therefore the performance of this device is fully revealed.

Fig. 6 compares three main flow parameters (mass fraction, streamwise velocity and turbulence intensity) to investigate the effects of mesh barrier (case 5) on the dispersion of the ammonia. Fig. 6a illustrates the mass concentration profile of the ammonia leak with/without mesh barrier in two distances (x/H=4 and x/H=8) from the leakage. The plot depicts that the high volume of the ammonia is directed to ground surface in downstream under the influence of the mesh barrier. Furthermore, the presence of mesh barrier significantly reduces the variation of ammonia mass concentration along the downstream in comparison of no barrier. Therefore, it can be easily detected and collected in the downstream.

Fig. 6. 
Comparison of (a) Mass fraction (b) streamwise velocity (c) turbulence intensity with/without mesh barrier with MC=12 (case 5) on two surfaces (x/H=4 and x/H=8) downstream of the leakage (m°=0.2 Kg/s, Atmospheric condition=F).

The momentum of free stream is highly affected by the presence of the barrier. Fig. 6b clearly shows that the streamwise velocity is reduced (height of the mesh barrier is 5 m) when the mesh barrier is presented in downstream. In fact, uniform flow forms as a free stream passes the mesh barrier and new boundary layer is created.

Turbulence intensity is a main parameter that clearly shows the status (laminar or turbulence) of the free stream pattern. The variation of turbulence intensity is plotted for two distances from the leak in Fig. 6c. The turbulence intensity is defined as the ratio of the root-mean-square of the velocity fluctuations, u′, to the mean flow velocity, u_ave. A turbulence intensity of 1% or less is generally considered low and turbulence intensities greater than 10% are considered high. The comparison of the turbulence intensity downstream of the mesh barrier and no barrier clearly shows that the turbulent flow is significantly reduced and flow behaves as laminar in low level. This variation confirms that this device performs as a flow reducer to control the dispersion of gases downstream.

The mass flow rate and direction of ammonia leak is expected to have a great influence on the performance of the mesh barrier especially on the height of the danger zone. In this section, those changes in structure of dispersion are investigated for four mass flow rates (0.1, 0.2, 0.4 and 0.8 Kg/s) and three leak directions (co-flow, cross flow and counter-flow). To illustrate the effects of mass flow rate, Fig. 7 comparesmass concentration contours along the leak centerline with streamline patterns for a stable atmospheric condition (F). As expected, the danger zone is expanded as the leak rate is increased. Furthermore, the influence of the mesh barrier is more visible in the limitation of ammonia dispersion in the low flow rate (equal or less than 0.4 Kg/s). As expected, the size of danger zone does not change when the leak rate is high. In fact, this method cannot limit the height of the danger zone, and the mesh barrier with high mesh coefficient (12) performs in the same way as free dispersion (no barrier). However, the profile of the ammonia mass fraction is similar in the vertical direction for all leak rates.

Fig. 7. 
Comparison of Ammonia dispersion with/without mesh barrier with MC=12 (case 5) for various leak rates (Atmospheric condition=F). All dimension is in meter.

Fig. 8 illustrates the dispersion of NH₃ leak with three directions (co-flow, cross flow and counter-flow) in the presence of a mesh barrier (case 5) for a small leak rate (m^o=0.2 Kg) under stable atmospheric condition (F). The result shows a significant structure to the danger zone downstream of the leak. In cases of no barrier, the leak distribution is approximately the same domain although the slope of boundary of danger zone is different. On the other hand, the expansion of danger zone is significantly reduced within specific level when the mesh barrier is presented downstream of the leak. In all cases with a mesh barrier, the height of the danger zone is fixed at the same level that a leak gas passes the barrier.

Fig. 8. 
Influence of leak direction on dispersion with/without mesh barrier with MC=12 (case 5) (Atmospheric condition=F, m°=0.2 Kg/s). All dimension is in meter.

Fig. 9 depicts the influence of the mesh barrier (case 5) on the distribution of ammonia (m^o=0.2 Kg/s) in three atmospheric conditions (unstable, neutral and stable). In order to present a different atmospheric conditions, inlet velocity profiles are varied corresponds to atmospheric stability conditions. As expected, the danger zone highly expands under the stable atmospheric condition (F) in free dispersion. As a mesh barrier is presented in the downstream of the leak, the height of the toxic region is reduced. The maximum concentration of ammonia is at the vicinity of the leak in the free dispersion. As the mesh barrier is presented in the domain, the maximum ammonia concentration is occurred in the ground surface along the domain. In fact, the mesh barrier performs in the same way in various conditions and the height of the danger zone is limited.

Fig. 9. 
Comparison of atmospheric condition on size of danger zone with/without mesh barrier with MC=12 (case 5) (m°=0.2 Kg/s). All dimension is in meter.

Fig. 10 exhibits the mass dispersion of ammonia leak in the presence of the mesh barrier with three different distances (1.5, 3 and 4.5 m) from the leak position. As the barrier moves downstream, the penetration of ammonia increases in the vertical direction and the height of the danger zone is extended in the streamwise direction. The mesh barrier fixes the height of dispersion as the gas emitted from holes. The performance of the device increases significantly as it moves to the leak position.

Fig. 10. 
The influence of the mesh barrier distance on dispersion of Ammonia (Atmospheric condition=F, m°=0.2 Kg/s). All dimension is in meter.