4
defined, steady and transient-state CFD simulations were
developed.
SIMULATIONS SET UP
Once the computational mesh was established, the fol-
lowing steps were followed to set up and run the CFD sim-
ulations. The simulations were run at Penn State’s Institute
of Computations and Data Science’s (ICDS) supercomput-
ing clusters.
Steady-state simulations: We used the RNG κ-ε tur-
bulence model to solve the Navier-Stokes’ equations using
the medium mesh with about 2.48 million elements. The
inlet was assigned to a normal velocity, and the outlet was
assigned a 0 Pa static pressure. This pressure mimics its
connection to the atmosphere. Inlet velocity magnitude
was changed throughout the simulations. This assisted in
identifying the zones where velocity is low, and particles
may be trapped. Residuals were monitored with over 500
iterations. Reports were obtained for velocities at each of
the five probe points added during the mesh independence
studies.
Transient-state simulations and particle tracking:
Different particle sizes were tested for the transient- state
simulations to determine the ability of the PAPR to cap-
ture them. Simulations were developed to demonstrate the
PAPR operations for 60.0 s as shown in Table 5. After 60.0
s, the percentage of the particles captured was calculated.
The inlet velocity at the flow domain was set to 0.01 m/s to
mimic a miner working in a closed volume such as a main-
tenance bay where the airflow is not strong and directional.
This also enhances the velocity contours around the PAPR,
enabling the visualizations of streamlines of particle motion
around the PAPR.
It is important to note that the time steps were changed
for all sets of transient-state simulations with varying inlet
airflow speeds to ensure that the average Courant-
Freidrichs-Lewy condition was met. We chose the time-
step sizes accurately to keep the average Courant number
under 1.00 this is shown in Table 6 and Figure 4.
We monitored the values of normalized wall distance
(y+) throughout the simulations, which enabled us to
determine the flow field resolution near the impermeable
surfaces. Very low y+ values (Figure 5) show that the flow
was resolved well.
RESULTS FROM THE CFD MODELS
We present the results from steady and transient-state sim-
ulations in the following sections.
STEADY-STATE SIMULATIONS
The residuals attained low values at the end of 500 itera-
tions during the simulations. The simulations did not show
any signs of divergence. We observed random fluctuations
Table 6. Courant number for all simulation cases
Inlet Velocity
(m/s)
Time-Step
(s)
Total time
steps
CFL
number
1.0 0.008 2,500 1.0000
1.5 0.005 4,000 0.9375
2.0 0.004 5,000 1.0000
2.5 0.003 6,667 0.9375
3.0 0.002 10,000 0.7500
Table 4. Mesh quality metrics
Parameters Minimum Maximum Average SD
Element
quality
0.012 0.999 0.840 0.107
Aspect ratio 1.014 98.621 1.830 0.565
Orthogonal
quality
0.006 1.000 0.775 0.135
Skewness 1.3e‑10 0.994 0.223 0.137
Table 5. Simulation procedure
Time (s) Activity
1–15 Let air velocity stabilize
15–20 Inject particles at the five probe points
20–60 Let the PAPR capture the particles
Figure 4. Courant number
defined, steady and transient-state CFD simulations were
developed.
SIMULATIONS SET UP
Once the computational mesh was established, the fol-
lowing steps were followed to set up and run the CFD sim-
ulations. The simulations were run at Penn State’s Institute
of Computations and Data Science’s (ICDS) supercomput-
ing clusters.
Steady-state simulations: We used the RNG κ-ε tur-
bulence model to solve the Navier-Stokes’ equations using
the medium mesh with about 2.48 million elements. The
inlet was assigned to a normal velocity, and the outlet was
assigned a 0 Pa static pressure. This pressure mimics its
connection to the atmosphere. Inlet velocity magnitude
was changed throughout the simulations. This assisted in
identifying the zones where velocity is low, and particles
may be trapped. Residuals were monitored with over 500
iterations. Reports were obtained for velocities at each of
the five probe points added during the mesh independence
studies.
Transient-state simulations and particle tracking:
Different particle sizes were tested for the transient- state
simulations to determine the ability of the PAPR to cap-
ture them. Simulations were developed to demonstrate the
PAPR operations for 60.0 s as shown in Table 5. After 60.0
s, the percentage of the particles captured was calculated.
The inlet velocity at the flow domain was set to 0.01 m/s to
mimic a miner working in a closed volume such as a main-
tenance bay where the airflow is not strong and directional.
This also enhances the velocity contours around the PAPR,
enabling the visualizations of streamlines of particle motion
around the PAPR.
It is important to note that the time steps were changed
for all sets of transient-state simulations with varying inlet
airflow speeds to ensure that the average Courant-
Freidrichs-Lewy condition was met. We chose the time-
step sizes accurately to keep the average Courant number
under 1.00 this is shown in Table 6 and Figure 4.
We monitored the values of normalized wall distance
(y+) throughout the simulations, which enabled us to
determine the flow field resolution near the impermeable
surfaces. Very low y+ values (Figure 5) show that the flow
was resolved well.
RESULTS FROM THE CFD MODELS
We present the results from steady and transient-state sim-
ulations in the following sections.
STEADY-STATE SIMULATIONS
The residuals attained low values at the end of 500 itera-
tions during the simulations. The simulations did not show
any signs of divergence. We observed random fluctuations
Table 6. Courant number for all simulation cases
Inlet Velocity
(m/s)
Time-Step
(s)
Total time
steps
CFL
number
1.0 0.008 2,500 1.0000
1.5 0.005 4,000 0.9375
2.0 0.004 5,000 1.0000
2.5 0.003 6,667 0.9375
3.0 0.002 10,000 0.7500
Table 4. Mesh quality metrics
Parameters Minimum Maximum Average SD
Element
quality
0.012 0.999 0.840 0.107
Aspect ratio 1.014 98.621 1.830 0.565
Orthogonal
quality
0.006 1.000 0.775 0.135
Skewness 1.3e‑10 0.994 0.223 0.137
Table 5. Simulation procedure
Time (s) Activity
1–15 Let air velocity stabilize
15–20 Inject particles at the five probe points
20–60 Let the PAPR capture the particles
Figure 4. Courant number