4
Navier-Stokes (RANS) form, considering mass and momen-
tum conservation. The analysis was performed using the
k-epsilon turbulence model with scalable wall function.
The coupling of momentum and continuity equations for
the pressure-velocity interactions was achieved using the
coupled scheme.
Because the intake and return portals were being posi-
tioned at same elevations and the minimal air resistance
posed by large-opening stone mines, it is inferred that the
airflow through the intake portals predominantly depends
on the size and capacity of intake booster fans and its oper-
ating condition. Consequently, a pressure inlet boundary
condition was assumed for the model’s inlets, while a pres-
sure outlet condition was defined for the model’s outlet.
The 1.83-meter booster fans (Figure 2d) within the model
were simulated using fan boundary conditions with con-
stant pressure gradients of 249 Pa. The fan casings, extend-
ing 1.37 m in length, were defined as smooth walls with
no-slip conditions. The left and right sections of the curtain
were identified as internal smooth walls with no-slip condi-
tions, while a gap between the wall sections (approximately
1.5 m) was modeled as an internal surface (Figure 2c). The
external walls of the model were defined as rough walls with
no-slip conditions, assuming a wall roughness of 0.04 m
(Gendrue et al., 2023). Furthermore, gravity was consid-
ered in the Z-direction, and the model was solved to achieve
a convergence level of 1 x 10-3 for velocity components (X,
Y, Z), mass flow, and turbulent energy. Typically, the mod-
els successfully converged within the range of 200–300
iterations. However, the solution process was continued up
to a total of 1,000 iterations to ensure that the monitored
velocities at the designated monitoring stations marked as
S1-S33 (see Figure 1) and the fan velocities had reached
their steady-state conditions.
For airflows within large-opening stone mines, where
wall-bounded effects are of lesser concern and separation
primarily arises from approaching stone pillars, the adop-
tion of a k-epsilon-based wall function approach is believed
to be suitable. In employing wall function models, it is
advisable to maintain a y-plus value greater than 30 to miti-
gate inaccuracies in modeling the buffer layer and laminar
sublayer. The CFD simulation of airflow within such mines
encompasses a broad spectrum of air velocity scales, with air
velocities at booster fans falling between 15–20 m/s while
other locations exhibit fractions of m/s. Consequently, the
model grid and near-wall refinement incorporate varying
levels of y-plus, potentially placing certain areas within
the viscous and buffer layers. Hence, the recommenda-
tion is to employ a scalable wall function in such scenarios.
In Ansys Fluent, this specialized wall function effectively
relocates the near-wall mesh to a y* value of 11.225 where
y* is another unit for dimensionless distance from the wall
similar to y-plus. This y* value of 11.225 marks the transi-
tion into the log-law region. It is important to acknowl-
edge that, for grids designed with a y* greater than 11.225,
the scalable wall function will yield results consistent with
those obtained using the standard wall function.
When using wall function models, a minimum of 10
cells is needed to accurately capture a boundary layer, but
values of 20 are more desirable. Therefore, the boundary
layer built at the external walls of the CFD model and cur-
tain wall was defined using the smooth-transition method
with 20 layers and a transition ratio of 0.242 (Figures 2c,
2e, and 2f). The height of the first element in the boundary
layer at the walls of booster fans casings was set at 0.005 m,
with 12 layers and a transition ratio of 0.272 (Figures 2e and
2f). The CFD model was meshed using polyhedral cells,
with a maximum cell length of 1.07 m and a growth rate of
1.2. Localized mesh sizes were specified at the booster fans
and the curtain of 0.05 m and 0.1 m, respectively, with a
growth rate of 1.2 (Figures 2c, 2e, and 2f).
MESH CONVERGENCE STUDY
It is essential to perform a mesh independence study to
determine the ideal mesh size to optimize computational
speed and model accuracy. In this study, three mesh sizes
were tested and screened to identify the optimized mesh
size. The mesh sizes are coarse, medium, and fine of about
7.6 M, 13.2 M, and 30.1 M cells, respectively. The mesh
refinement was defined in the surface meshing step of mesh
creation where the maximum size of surface mesh was
defined as 1.0 m, 0.8 m, and 0.5 m for coarse, medium,
and fine meshes, respectively.
Performing a mesh independence analysis is crucial
for identifying the optimal mesh size to enhance computa-
tional efficiency and model precision. This study involved
testing and evaluating three different mesh sizes: coarse,
medium, and fine, comprising approximately 7.6 M, 13.2
M, and 30.1 M cells, respectively. Mesh refinement was
applied during the surface meshing stage of ANSYS-Fluent
mesh generation, where the maximum surface mesh size
was set to 1.0 m, 0.8 m, and 0.5 m for coarse, medium, and
fine meshes, respectively.
Figures 3 and 4 illustrate the velocity profiles at stations
S6, S7, and S8 within Entry 93 (see Figure 1 for station
locations in the mine). These velocity profiles were obtained
at distances of 1.67 m (Figure 3) and 4.9 m (Figure 4)
above the floor for each station. It is notable that the veloc-
ity profiles derived from the medium and fine mesh con-
figurations demonstrate a high degree of consistency, while
Navier-Stokes (RANS) form, considering mass and momen-
tum conservation. The analysis was performed using the
k-epsilon turbulence model with scalable wall function.
The coupling of momentum and continuity equations for
the pressure-velocity interactions was achieved using the
coupled scheme.
Because the intake and return portals were being posi-
tioned at same elevations and the minimal air resistance
posed by large-opening stone mines, it is inferred that the
airflow through the intake portals predominantly depends
on the size and capacity of intake booster fans and its oper-
ating condition. Consequently, a pressure inlet boundary
condition was assumed for the model’s inlets, while a pres-
sure outlet condition was defined for the model’s outlet.
The 1.83-meter booster fans (Figure 2d) within the model
were simulated using fan boundary conditions with con-
stant pressure gradients of 249 Pa. The fan casings, extend-
ing 1.37 m in length, were defined as smooth walls with
no-slip conditions. The left and right sections of the curtain
were identified as internal smooth walls with no-slip condi-
tions, while a gap between the wall sections (approximately
1.5 m) was modeled as an internal surface (Figure 2c). The
external walls of the model were defined as rough walls with
no-slip conditions, assuming a wall roughness of 0.04 m
(Gendrue et al., 2023). Furthermore, gravity was consid-
ered in the Z-direction, and the model was solved to achieve
a convergence level of 1 x 10-3 for velocity components (X,
Y, Z), mass flow, and turbulent energy. Typically, the mod-
els successfully converged within the range of 200–300
iterations. However, the solution process was continued up
to a total of 1,000 iterations to ensure that the monitored
velocities at the designated monitoring stations marked as
S1-S33 (see Figure 1) and the fan velocities had reached
their steady-state conditions.
For airflows within large-opening stone mines, where
wall-bounded effects are of lesser concern and separation
primarily arises from approaching stone pillars, the adop-
tion of a k-epsilon-based wall function approach is believed
to be suitable. In employing wall function models, it is
advisable to maintain a y-plus value greater than 30 to miti-
gate inaccuracies in modeling the buffer layer and laminar
sublayer. The CFD simulation of airflow within such mines
encompasses a broad spectrum of air velocity scales, with air
velocities at booster fans falling between 15–20 m/s while
other locations exhibit fractions of m/s. Consequently, the
model grid and near-wall refinement incorporate varying
levels of y-plus, potentially placing certain areas within
the viscous and buffer layers. Hence, the recommenda-
tion is to employ a scalable wall function in such scenarios.
In Ansys Fluent, this specialized wall function effectively
relocates the near-wall mesh to a y* value of 11.225 where
y* is another unit for dimensionless distance from the wall
similar to y-plus. This y* value of 11.225 marks the transi-
tion into the log-law region. It is important to acknowl-
edge that, for grids designed with a y* greater than 11.225,
the scalable wall function will yield results consistent with
those obtained using the standard wall function.
When using wall function models, a minimum of 10
cells is needed to accurately capture a boundary layer, but
values of 20 are more desirable. Therefore, the boundary
layer built at the external walls of the CFD model and cur-
tain wall was defined using the smooth-transition method
with 20 layers and a transition ratio of 0.242 (Figures 2c,
2e, and 2f). The height of the first element in the boundary
layer at the walls of booster fans casings was set at 0.005 m,
with 12 layers and a transition ratio of 0.272 (Figures 2e and
2f). The CFD model was meshed using polyhedral cells,
with a maximum cell length of 1.07 m and a growth rate of
1.2. Localized mesh sizes were specified at the booster fans
and the curtain of 0.05 m and 0.1 m, respectively, with a
growth rate of 1.2 (Figures 2c, 2e, and 2f).
MESH CONVERGENCE STUDY
It is essential to perform a mesh independence study to
determine the ideal mesh size to optimize computational
speed and model accuracy. In this study, three mesh sizes
were tested and screened to identify the optimized mesh
size. The mesh sizes are coarse, medium, and fine of about
7.6 M, 13.2 M, and 30.1 M cells, respectively. The mesh
refinement was defined in the surface meshing step of mesh
creation where the maximum size of surface mesh was
defined as 1.0 m, 0.8 m, and 0.5 m for coarse, medium,
and fine meshes, respectively.
Performing a mesh independence analysis is crucial
for identifying the optimal mesh size to enhance computa-
tional efficiency and model precision. This study involved
testing and evaluating three different mesh sizes: coarse,
medium, and fine, comprising approximately 7.6 M, 13.2
M, and 30.1 M cells, respectively. Mesh refinement was
applied during the surface meshing stage of ANSYS-Fluent
mesh generation, where the maximum surface mesh size
was set to 1.0 m, 0.8 m, and 0.5 m for coarse, medium, and
fine meshes, respectively.
Figures 3 and 4 illustrate the velocity profiles at stations
S6, S7, and S8 within Entry 93 (see Figure 1 for station
locations in the mine). These velocity profiles were obtained
at distances of 1.67 m (Figure 3) and 4.9 m (Figure 4)
above the floor for each station. It is notable that the veloc-
ity profiles derived from the medium and fine mesh con-
figurations demonstrate a high degree of consistency, while