Dust Dispersion Characteristics of Open Stockpiles and the Scale of Dust Suppression Shed

Abstract

The storage of bulk materials in open yards can easily lead to contamination in the form of suspended particles. The creation of enclosed spaces for open yards is an effective measure to stop the dispersion of dust to the outside. In this study, a reliable numerical model was developed to calculate the impact range of dust dispersion using the concentration–velocity distribution of pollutants based on the DPM-CFD simulation, and validated by field measurement data. Then, the hazard distance was defined as the basis for determining the boundary of the closed shed. Finally, we determined the dimensions of the boundaries by a comprehensive analysis of the structure and materials of the closed shed. Our results demonstrated that the most unfavorable wind speed determines the maximum concentration of dust at a height of 1.5 $\mathrm{m}$. As a result, hazard distance thresholds are obtained to be 63.5 $\mathrm{m}$ and then the shed boundary dimensions are calculated to be 127 $\mathrm{m}$. Our studies can provide some theoretical basis for the construction of closed sheds in field yards.

1. Introduction

With the increasing focus on the natural environment and human health, the control of fugitive dust emissions is receiving more and more attention [1]. Dust is released from a variety of sources, such as the unloading of bulk materials, mechanical transport of bulk materials, and the wind erosion of open storage piles. In the storage of bulk solids, dust emission often occurs because of air movement around or into and out of granular material.

There are few studies on the dust dispersion from open piles. Wind field analysis and the evaluation of dust emission rates are important aspects to study the dust dispersion from stockpiles. Prediction of dust emissions by numerical CFD simulations is conducted to obtain velocity distributions on individual pile surfaces [2]. Turbulence and complex topography have a significant effect on the dispersion of dust as well as the distribution of deposition [3]. Total fugitive dust emissions at high wind speeds (15 $\mathrm{m}/\mathrm{s}$, 25 $\mathrm{m}/\mathrm{s}$ respectively) were quantified [4]. Moreover, the factors influencing the dust release rate from storage piles have attracted attention in a few literature works. Schulz et al. proposed that the diffusivity of dust was positively correlated with the pressure drop. The shape of stockpile is also associated with dust emissions, e.g., conical stockpile [5] versus flat-topped stockpile [6]. Meanwhile, the sparseness of stockpile arrangement has a significant effect on the dust emissions [7]. In a close arrangement, the downwind direction of the sand pile creates a shadow that reduces dust release from the pile located downwind [4,7]. The shape of the sand pile also had a significant effect on dust dispersion, and he found that semi-circular piles produced less dust emissions than flat-topped and tapered piles for the same stockpile configuration [8]. Intermediate pile height configurations can also reduce dust emissions from stockpiles [9]. In terms of particle size, the impact of stockpiles on ambient PM10 concentrations on a large scale has also been predicted [1]. However, the effect of wind speed has not been studied thoroughly enough on dust dispersion from sand piles up to now.

In more detail, dust dispersion has been studied extensively, encompassing all aspects. First, in studying the mechanisms of diffusion and the factors that influence it, many scholars have investigated the effects of particle roughness [10], changes in airflow [11,12], spatial layout [13], and pore space in particle accumulation [14] on the dust diffusion. Second, some researchers have investigated dust suppression measures [15], such as the use of surfactants [16] and ventilation conditions [17] to suppress dust. Third, the research methods for dust dispersion are mainly experiments and numerical simulations to verify each other. Numerical calculation methods include discrete phase model (DPM) [5], discrete element method (DEM) [14,18,19], etc. The methods above have their own use scenarios, with the DPM method being more widely applicable.

DPM is advanced for modeling gas-solid two-phase flows of dilute bulk particles. The DPM method has been used in many studies on gas-solid two-phase flows [20,21,22]. DPM cannot simulate gas-solid two-phase flows with high volume fractions due to the fact that the DPM model ignores particle–particle forces. However, it has also been suggested that the loss of energy can be approximated to account for collisions between particles [19]. The subject of this study is a stockpile with a low volume fraction of gravel for dust dispersion. Therefore, the DPM method is applicable to this study. The gravel is reduced to a spherical particle model, which introduces a small degree of error. It is the gravel with a low water content that causes significant dust lifting. For this reason, we do not consider wet particles in simulations.

Research has been carried out in order to ensure that the fugitive dispersion of open storage piles does not affect the urban environment as well as human health. Building sheds for storage of material is an effective way to combat the dispersion of dust. We carried out on-site measurements of dust from the sand piles as well as numerical simulations to determine the size of the open stockpile shed.

2. Numerical Methods

2.1. Site Measurement

The open-storage sand site examined in this study is located in Hubei Province in central China. The average height of the piles is 3.2 $\mathrm{m}$, and the mean radius of the lower base is 9.2 $\mathrm{m}$. The dust was measured by the on line dust concentration sensor (OPM-6303M, Sifang Radio Inc., Wuhan, China). The wind speed was measured by the wind speed sensor (RS-FSJT, Jianda Renke Inc., Shandong, China).

2.2. Numerical Models

2.2.1. Physical Model

The geometric model created for the study has an overall rectangular shape with three storage piles distributed at the bottom. Geometric dimensions are 100 $\mathrm{m}$ in length, 150 $\mathrm{m}$ in width, and 15 $\mathrm{m}$ in height. The height of geometry was chosen to be 15 $\mathrm{m}$, taking into account the amount of calculations and the actual height of the dust raised. The stockpile was a circular platform with a height of 3.2 $\mathrm{m}$, an upper base radius of 6 m and a lower base radius of 9.2 $\mathrm{m}$. The pile was built with a 45 side slope angle. In addition, there are some positioning dimensions detailed in Figure 1. After the geometry was built, the steady-state flow field at different wind speeds was compared and analyzed. Figure 2 shows that the areas with large changes in velocity gradients are basically in the area below 10 m in height. Therefore, the airflow disturbance caused by the wind acting on the sand pile is less likely to affect the area above 10 m. The geometric height is hence reasonable.

In order to simplify the model, the effect of temperature on air flow and dust dispersion was negligible. Therefore, the calculation was carried out at room temperature and the model was calculated without substituting the energy equation. In addition, in the open yard, one boundary surface was selected as the velocity-inlet condition in the study.

2.2.2. Simulation Setup

The whole process of simulation was inseparable from computational fluid dynamics (CFD). CFD is a more convenient and economical option for solving complex problems in practice. CFD can provide a theoretical basis for the actual layout of the yard framework. The CFD method consists of the following steps: (1) pre-processing, (2) selection of the solver and setting of the computational model, and (3) post-processing. The pre-processing is mainly concerned with the construction of the geometric model and the delineation of mesh. Post-processing mainly covers the presentation of the simulation results and the summary analysis of the results.

For the meshing of the geometric model, ICEMCFD was used. Structured mesh was chosen for the stockpile model. Structured mesh is significantly more accurate than unstructured mesh for CFD with a simple geometry. The high mesh quality of the model provides a certain basis for the accuracy of the simulation. The grid near the sand pile is encrypted. In addition, appropriate dense treatment was also applied to the downwind side of the stockpile. In Figure 3, for the particular shape of the truncated cones, the structured mesh is created using O-gridding. The walls of the truncated cones and the ground in the vicinity of the truncated cones are grid encrypted, due to the fact that the velocity gradient changes the most in this region. The total number of meshes obtained for the model are 23 million.

Fluent was used for the computational simulation. The solver performs step-by-step iterative solutions using pressure coupling. For the gas phase, the $k-\omega$ SST dual equation model was used, which was more applicable to the bypass phenomenon. For the particle phase, the DPM method was used as described in the previous section. The simulation was decomposed into two parts, one for the steady calculation of the gas phase and the other for the unsteady calculation of the solid phase. A stable flow field can be obtained because the velocity of the boundary conditions was stable. The unsteady state calculation of the particles was closer to reality, and it can reduce the errors in the simulation. In this study, the mass flow rate of the particles was assumed to be constant. The particles on the sand pile were not immediately spread by the wind, due to the friction between the gravels. Therefore, the sands and gravels were only released when the wind speed reached a certain level.

To simulate the particle transport, many static particles initially were assumed to be distributed uniformly on the surface of the stockpile. Then, the total number of particles was determined by the time of particle transport and the number of grids on the surface of the stockpile. An overview of the simulation parameter and particle/fluid phase properties for the coupled DPM-CFD simulations was given in

Table 1. Simulation of general setups.

Bulk Particle Properties (DPM)
Material	${\mathrm{SiO}}_2$
Density ${\rho }_{\mathrm{p}}$	$2300\mathrm{kg}/{\mathrm{m}}^3$
Particle diameter $d_{\mathrm{p}}$	$8.5{\mathrm{m}}^{-5}$
Inject source	Surface-injection
Gas Phase Properties (CFD)
Material	Air
Density ${\rho }_{\mathrm{a}}$	$1.25\mathrm{kg}/{\mathrm{m}}^3$
Turbulence models	Shear-stress transport (SST) $k-\omega$ model

. Boundary conditions settings were shown in Figure 1.

In order to simulate the flow field accurately, instead of using a single wind speed at the velocity inlet, a variable wind speed associated with height was used. In Figure 4, variation of wind speed was exponentially distributed with height. The distribution of inlet velocity can be calculated from the following equation:

$$u_y=u_0·{\left(\frac{y}{y_0}\right)}^{\alpha }$$

(1)

where $u_y$ is the velocity at a vertical height of y. $u_0$ is the velocity at a vertical height of $y_0$, and $\alpha$ is the surface roughness coefficient, chosen as 0.15 in this study.

2.3. Governing Equations of Airflow and Particles

2.3.1. Governing Equations of Airflow

In this study, we assumed that the gas phase was incompressible with constant properties. For incompressible and steady state flow, the governing equations are as follows:

Conservation of mass equation

$$▽·\overrightarrow{v}=0$$

(2)

Momentum conservation equation

$$\frac{\partial \overrightarrow{\overline{v}}}{\partial t}+\overrightarrow{\overline{v}}·▽\overrightarrow{\overline{v}}=-\frac{1}{\rho }▽\overline{p}+▽·(\overline{\tau }+{\tau }^t)+\overrightarrow{\overline{f}}$$

(3)

where the mean velocity and pressure fields are $\overrightarrow{\overline{v}}$ and $\overline{p}$, respectively, employing a data-driven closure term for the Reynolds tensor ${\tau }^t$. The time, density, molecular stress tensor and mean momentum source term are denoted by t, $\rho$, $\tau$ and $\overrightarrow{\overline{f}}$, respectively.

Analytical calculations of the flow in the computational domain showed that the flow reached a turbulent state. Turbulence closure was achieved through application of the two-equation $k-\omega$ SST model. This is more accurate and reliable for a wider class of flow. This coincides with the computational domain of our study.

The $k-\omega$ SST turbulence model requires solving the turbulence kinetic energy (k) and specific dissipation rate ($\omega$) equations:

$$\frac{\partial }{\partial t}\left(\rho k\right)+\frac{\partial }{\partial x_i}\left(\rho k{u}_i\right)=\frac{\partial }{\partial x_j}\left({\mathsf{\Gamma }}_k\frac{\partial \mathrm{k}}{\partial x_j}\right)+\widetilde{G_k}-Y_k$$

(4)

$$\frac{\partial }{\partial t}\left(\rho \omega \right)+\frac{\partial }{\partial x_j}\left(\rho \omega u_j\right)=\frac{\partial }{\partial x_j}\left({\mathsf{\Gamma }}_{\omega }\frac{\partial \omega }{\partial x_j}\right)+G_{\omega }-Y_{\omega }+D_{\omega }$$

(5)

where $\widetilde{G_k}$ represents the generation of turbulence kinetic energy due to mean velocity gradients. $G_{\omega }$ represents the generation of $\omega$. ${\mathsf{\Gamma }}_k$ and ${\mathsf{\Gamma }}_{\omega }$ represent the effective diffusivity of k and $\omega$. $Y_k$ and $Y_{\omega }$ represent the dissipation of k and $\omega$ due to turbulence. $D_{\omega }$ represents the cross-diffusion term.

Symmetry boundary conditions were used for the lateral sides and the upper limits of the computational domain. The lower boundary surface as well as the pile were considered as rough walls. In accordance with the measurement, the roughness lengths on both the stockpile surface and the wall were fixed to be 0.03 $\mathrm{mm}$ [23]. Pressure–outlet condition was used for the right side. In addition, velocity–inlet condition was applied on the left side of the computational domain. Profiles of velocity u, turbulent kinetic energy k, and specific dissipation rate $\omega$ were used to define the entry of calculation domain.

The initial turbulence conditions at the boundary change accordingly for different inlet velocities. The inlet initial values of the turbulent kinetic energy k and the turbulent dissipation rate $\omega$ are each given by the equation:

$$k=\frac{3}{2}{\left(\overline{u}I\right)}^2$$

(6)

where $\overline{u}$ is the average flow velocity at the inlet, $\overline{u}Y={\int }_0^Y{u}_{y}ydy$, $Y=15$. I is the turbulence intensity, $I=0.16{\left(Re\right)}^{-\frac{1}{8}}$:

$$\omega =\frac{k^{\frac{1}{2}}}{C_{\mu }l}$$

(7)

where l is the turbulence length scale, $l=\frac{0.07L}{C_{\mu }^{3/4}}$. $C_{\mu }=0.09$.

2.3.2. Particle Transport Equations

Dust from sand storage piles in the presence of wind is not a dense particle flow (fluid with a large volume fraction of solid particles). Therefore, the DPM was chosen to simulate the transport of particles in the study. By performing a force balance analysis on the particles, a DPM can be constructed. The equation [17] can be obtained as shown below:

$$\frac{\mathrm{d}{u}_{\mathrm{p}}}{\mathrm{d}t}=\overrightarrow{F_D}\left(\overrightarrow{u_{\mathrm{g}}}-\overrightarrow{u_{\mathrm{p}}}\right)+\frac{\overrightarrow{g}\left({\rho }_{\mathrm{g}}-{\rho }_{\mathrm{p}}\right)}{{\rho }_{\mathrm{p}}+\overrightarrow{F_D}}$$

(8)

where $\overrightarrow{F_D}\left(\overrightarrow{u_{\mathrm{g}}}-\overrightarrow{u_{\mathrm{p}}}\right)$ is the drag force per unit mass, $\overrightarrow{F_D}=\frac{18\mu }{{\rho }_{\mathrm{p}}{d}_{\mathrm{p}}^2\frac{C_D{R}_e}{24}}$. $\overrightarrow{u_{\mathrm{g}}}$ is the continuous phase velocity; $\overrightarrow{u_{\mathrm{p}}}$ is the particle velocity; $\mu$ is the molecular viscosity coefficient of the fluid; ${\rho }_{\mathrm{g}}$ and ${\rho }_{\mathrm{p}}$ are the densities of the fluid and the particles, respectively; $d_{\mathrm{p}}$ is the particle diameter [24,25]; $Re$ is the relative Reynolds number, determined by:

$$Re=\frac{{\rho }_{\mathrm{g}}{d}_{\mathrm{p}}\left|\overrightarrow{u_{\mathrm{g}}}-\overrightarrow{u_{\mathrm{p}}}\right|}{\mu }$$

(9)

The resistant coefficient, $C_D={\alpha }_1+\frac{{\alpha }_2}{Re}+\frac{{\alpha }_3}{R{e}^2}$ [26], where ${\alpha }_1$, ${\alpha }_2$, and ${\alpha }_3$ are constants and are obtained based on the experimental results of smooth spherical particles.

2.4. Dust Exposure Assessment

The average daily dose (ADD) is the exposure dose of harmful substances to the human body calculated by the exposure parameter method, the absorbed dose of harmful substances to the human body in an environment where the harmful substances reach a certain concentration. In a part of the health risk assessment, the most critical aspect is the accurate calculation of the ADD [27]

$$ADD=\frac{C_A·IR·EF·ET·ED}{BW·AT}$$

(10)

where $C_A$ is the concentration of silica dust ($\mathrm{mg}/{\mathrm{m}}^3$), $IR$ is the inhalation rate (${\mathrm{m}}^3/\mathrm{h}$), $EF$ represents the continuous exposure frequency of site personnel ($\mathrm{d}/\mathrm{a}$), $ET$ represents the workers’ average daily exposure time ($\mathrm{h}/\mathrm{d}$), $ED$ represents the workers’ continuous exposure duration ($\mathrm{a}$), $BW$ represents the workers’ average weight ($\mathrm{kg}$), and $AT$ represents the workers’ average exposure time ($\mathrm{d}$).

The dust particles in this study were mainly silicon dust [28]. The current health risk assessment system is considered to be a threshold compound contaminant [29]. According to relevant studies [30], the risk index was determined by

$$R=\frac{ADD}{RfD}\times {10}^{-6}$$

(11)

where R represents the risk index for health damage by dust, and $RfD$ represents the reference dose of dust ($\mathrm{mg}/(\mathrm{kg}·\mathrm{d})$). The $RfD$ of dust is assigned a value of 0.4 $\mathrm{mg}/(\mathrm{kg}·\mathrm{d})$ [31].

3. Results and Discussion

3.1. Validation

In order to evaluate the numerical model, the results of numerical simulation are compared with the data measured in the field. Some of the necessary data were measured at the stockpile site at different wind speeds, 4 $\mathrm{m}/\mathrm{s}$ and 16 $\mathrm{m}/\mathrm{s}$, respectively. Particle concentration at 20 $\mathrm{m}$ and 50 $\mathrm{m}$ downwind from the center of pile, maximum particle concentration, and maximum height of particulate dispersion at 50 $\mathrm{m}$ were measured. The particle concentration was measured at the height of the human breathing zone, which was equal to 1.5 $\mathrm{m}$. The error of compared results with the simulated model is shown in Figure 5. The simulated particle concentrations are smaller than the experimental ones, but the concentration trend is similar. For the maximum height of dust dispersion, the error between simulation and test results was less than 5%. As can be seen, the numerical results indicate a good agreement with the experimental data.

3.2. Studied Cases

To provide a theoretical basis for the selection of the construction dimensions of enclosed frames for yards, the simulation is carried out by varying the magnitude of the inlet wind speed, while keeping other factors constant. Some researchers [32] carried out simulations at low and medium wind speeds, so only partial conclusions have been drawn. Some others [4] analyzed the total dust emissions at high wind speeds (15 $\mathrm{m}/\mathrm{s}$, 25 $\mathrm{m}/\mathrm{s}$, respectively), without analyzing the spatial distribution of dust. Figure 6 compares the distribution of particle concentrations in the lateral direction at different wind speeds and at two heights. It is clear that the maximum value of the concentration is around the coordinate z = 75 m. This is just downstream of the center of the pile, so that we only need to analyze the distribution of the longitudinal distribution of dust to obtain the boundary values of the dust concentration. Figure 7 demonstrates the variation of dust concentration with distance on the leeward slope of the sand pile for different wind speeds (25 $\mathrm{m}/\mathrm{s}$, 16 $\mathrm{m}/\mathrm{s}$, 12 $\mathrm{m}/\mathrm{s}$ and 4 $\mathrm{m}/\mathrm{s}$, respectively). The wind speed mentioned refers to the wind speed at a height of 1.5 m, based on the height at which the wind speed was measured in the field. It can be seen that, at a height of 1.5 $\mathrm{m}$, the particle concentration at different wind speeds shows a trend of rapid increase followed by a rapid decrease and then a slow decrease. The concentration increases because the sand particles are concentrated on the leeward slope of the pile by the wind. The decrease in concentration is due to the decrease in particle mass per unit volume as the spread of sand particles increases. Although the overall trend is similar for different wind speeds, the same location does not show a single trend in the change of particle concentration at different wind speeds. It can be found that particle concentrations are lower in the overall range for wind speeds of 4 $\mathrm{m}/\mathrm{s}$ and 25 $\mathrm{m}/\mathrm{s}$. However, they are highest at wind speeds of 12 $\mathrm{m}/\mathrm{s}$. Therefore, we added the distribution of particle concentrations with distance from the stockpile at wind speeds of 15 $\mathrm{m}/\mathrm{s}$ and 9 $\mathrm{m}/\mathrm{s}$ in Figure 8. A similar pattern to the previous one was found, so that an inflection point should exist at around wind speed 12 $\mathrm{m}/\mathrm{s}$. At this wind speed, the concentration of dust reaches its maximum.

The purpose of this study is to provide a theoretical basis for the size of the enclosed shed for the construction of the stockyard. We consider that there are two limiting conditions. Firstly, the dust reaches a certain concentration, which is harmful to human health. Secondly, the dust diffuses into the atmosphere, which is not environmentally friendly. With the addition of containment measures to the yard, most of the dust that pollutes the atmosphere is confined to the yard. Therefore, the impact of dust pollution on the environment is not strongly correlated with the size of the enclosed shed. It is the first constraint that has a major influence on the sizing of the shed. Studies on the evaluation of health risks associated with dust exposure showed that the impact of dust pollution on human health can be determined by the risk index R which can be calculated using Equation (11). We calculated the threshold value of $C_A$ by assigning a value to the parameter. Below the threshold value, the effect of silica dust on human health can be ignored. In accordance with the relevant research, we assigned separate values to the parameters: $IR=1$, $EF=323$, $ET=7$, $ED=0.5$, $BW=60$, and $AT=182.5$. $C_A$ can be calculated as 4 $\mathrm{mg}/{\mathrm{m}}^3$ using Equation (10). Therefore, when dust concentrations reach 4 $\mathrm{mg}/{\mathrm{m}}^3$, the dust exposure assessment index R exceeds the USEPA recommendation of ${10}^{-6}$, and the effects on the human respiratory tract cannot be ignored. It has been suggested that, when dust concentrations reach 4 $\mathrm{mg}$, the effect on human respiratory tract cannot be ignored. Therefore, we have studied the nearest distance from the center of the stockpile at which the dust concentration reaches 4 $\mathrm{mg}/{\mathrm{m}}^3$ at different wind speeds, which we regard as the hazard distance, as shown in Figure 9. We simulated the dust dispersion under 13 kinds of wind speed conditions. We first obtained the distribution of dust concentration with distances as in Figure 7 and Figure 8. Then, the hazard distances at different wind speeds for a concentration of 4 $\mathrm{mg}/{\mathrm{m}}^3$ are found in the graph. In Figure 9, the relationship between wind speed and hazard distance can be derived. At a wind speed of 12 $\mathrm{m}/\mathrm{s}$, the hazard distance achieved its maximum value, which is equal to approximately 63.5 $\mathrm{m}$.

The pattern of variation of concentration with wind speed is revealed in Figure 7 and Figure 8, which is that the dust concentration at the same distance on the leeward side will show an increase and then a decrease with increasing wind speed. Therefore, we suspect that there are factors except wind speed that influence the particle concentration at lower altitudes. After analysis, the increase of wind speed will cause the dust to spread more into higher places. In Figure 10, the trends in percentage of particle mass over a range of heights from 0 to 3 $\mathrm{m}$ were compared for different distances and wind speeds. The percentage weight decreases significantly with the increase of wind speed at different distances (X = 50 $\mathrm{m}$, X = 75 $\mathrm{m}$ and X = 100 $\mathrm{m}$). This result is also clearly demonstrated in Figure 11. The more distant the location from the sand pile, the greater the decrease in occupancy with increasing velocity. In the range of 40 $\mathrm{m}$ to 50 $\mathrm{m}$, the specific gravity drops quickly, indicating a significant dispersion of dust into higher space. At X = 50 $\mathrm{m}$ to 100 $\mathrm{m}$, the specific gravity changes smoothly, and the curve can be approximated by the data points at 75 $\mathrm{m}$ and 100 $\mathrm{m}$.

We have determined the hazard distances for the stockpiles under the most unfavorable conditions, based on the analysis of the simulated data. However, it does not mean that the frame structure of the yard is square. When working on site, only the front and rear sides of the shed are open on all four sides, leaving the remaining two sides closed. Non-open sides are built with ventilated windows only. The wind blowing in through the small window can hardly act as a dust fugitive for the stockpile, so the distance between the two enclosed walls is not determined by the hazard distance. The structural design of the shed netting plays a very important role in the overall aspect ratio of the yard frame. Considering the structural stability and seismic resistance of the net frame, a two-way orthogonal diagonal release net frame was chosen. Moreover, considering the economical and two-way orthogonal structure of the mesh frame, a length to width ratio of 1.5 can be satisfied to all aspects.

According to the analysis of hazard distances in the previous section of the article, a maximum hazard distance of 63.5 $\mathrm{m}$ was obtained. At a distance of 0–63.5 $\mathrm{m}$ from the center of the sand pile, under the most unfavorable wind conditions, it is dangerous to the human respiratory tract. We have defined this area as dust contaminated areas. At this point, the shed in the yard plays an important role. It stops the stockpiles from spreading to higher ground, and it also serves to stop non-staff from entering the dust contaminated areas of the yard. Herein, we chose the form of closure of the yard. The C-shaped structure has the advantage of high storage capacity per unit area (the surrounding retaining wall increases the maximum stack height of the stockpile). At the same time, the membrane material used for capping is very suitable for C-shaped structures. The membrane material has properties such as corrosion resistance, poor thermal conductivity, and translucency. Hence, the membrane material is used for the closure of the yard with a simple construction process and low running costs during yard operations. The wind direction under simulated conditions is unidirectional and does not reflect the actual complexity of the situation. As the wind direction is variable, the shed should be symmetrical. The one-way hazard distance is 63.5 $\mathrm{m}$, and the total length of the yard should be twice the one-way distance. Therefore, as shown in Figure 12, we propose a length dimension of 127 $\mathrm{m}$ for the yard shed.

4. Conclusions

The distribution pattern of particle concentrations was obtained, making a theoretical guide for the construction of the frame dust suppression in the stockyard, based on DPM-CFD simulation of the two-phase flow of gravel emissions. For the first, we model dust emission patterns consistent with those of field yards and verified the reliability. This was achieved by testing different turbulence models and referring to relevant studies by other scholars. For the second, the distribution of dust concentration downwind of the sand pile with distance was obtained for wind speeds in the wider interval. The overall variation of dust concentration with distance increases first to the extreme point and then decreases. In that, an inflection point for the variation of dust concentration with wind speed is observed and the hazard distance is defined. The hazard distances provide the most important data for the problem we are trying to solve, i.e., the determination of the frame boundary dimensions of the stockyard.