3
MESH INDEPENDENCE
To perform CFD simulations, the flow volume must be
discretized into fine grids, called mesh. It is one of the
most important stages of simulation. A good quality mesh
will provide accurate and reliable results. It also plays an
important role in simulation convergence. Some important
parameters are defined in Table 1 these thresholds were
obtained from the operations manual of the ANSYS Fluent
software [15]. The meshes developed for this research con-
form to the prescribed parameters.
a. Aspect ratio: It is the ratio between the height
and width of the element. It ranges between 1 and
infinite.
b. Element quality: This corresponds to the ratio
between the volume and the square root of the cube
of the sum of the edge lengths. It ranges between 0
and 1.
c. Orthogonal quality: It compares the vector between
two nodes and the normal vector for each surface
integration point associated with the edge. It ranges
between 0 and 1.
d. Skewness: It is the principal quality metric. It indi-
cates how close an element is to an ideal equilateral
or equiangular element. It ranges from 0 to 1.
After obtaining good quality meshes, it is important to
establish mesh independence. This is critical to ensure that
the simulation results are independent of the discretization
scheme and the number of grid elements. For this, we com-
pared three different meshes. These were categorized into
coarse, medium, and fine classes depending on the average
size of the grid elements. All meshes met the quality require-
ments. To compare the meshes, an average element size
parameter was used. This was calculated by obtaining the
cube root of the average grid volumes. The growth ratio of
average element size across the three meshes was kept con-
stant at about 1.3. The parameters for each mesh are shown
in Table 2. The fluid volume was 1.26913 m3.
Five probe points were placed around the helmet to
compare the air velocity. A steady-state simulation with an
inlet air velocity of 2.0 m/s was used for mesh indepen-
dence studies. The results are shown in Table 3. As can be
seen, there are no significant differences in velocities at
those probe points. The biggest differences are found in
places where recirculation is expected.
With this information, the medium mesh will be
selected, as it offers enough accuracy and is not too expen-
sive computationally. The mesh quality metrics are shown
in Table 4. Even if a few elements are not within the opti-
mum range, quality is not bad enough to make the simu-
lation fail or give inaccurate results. Once the mesh was
Table 2. Element size calculations and mesh comparison
Parameters Coarse Medium Fine
Element count (million) 1.101 2.481 5.325
Avg. volume [mm3] 1,152 512 238
Avg. size [mm] 10.48 8.00 6.20
Cell count growth ratio 1.31 1.29
Table 3. Probe points velocities (m/s)
Locations Coarse Medium Fine
v1 (Side 1) 2.35 2.36 2.35
v2 (Side 2) 2.35 2.35 2.37
v3 (Top) 2.43 2.44 2.47
v4 (Front) 1.51 1.34 1.4
v5 (Back) 1.65 1.8 1.96
Figure 2. Real helmet (left), 3D points cloud (center),
faceted body (right)
Figure 3. The final geometry
Table 1. Mesh quality parameters
Parameters Threshold
Max aspect ratio 1,000
Min element quality 5e‑4
Min orthogonal quality 5e‑3
Max Skewness 0.999
MESH INDEPENDENCE
To perform CFD simulations, the flow volume must be
discretized into fine grids, called mesh. It is one of the
most important stages of simulation. A good quality mesh
will provide accurate and reliable results. It also plays an
important role in simulation convergence. Some important
parameters are defined in Table 1 these thresholds were
obtained from the operations manual of the ANSYS Fluent
software [15]. The meshes developed for this research con-
form to the prescribed parameters.
a. Aspect ratio: It is the ratio between the height
and width of the element. It ranges between 1 and
infinite.
b. Element quality: This corresponds to the ratio
between the volume and the square root of the cube
of the sum of the edge lengths. It ranges between 0
and 1.
c. Orthogonal quality: It compares the vector between
two nodes and the normal vector for each surface
integration point associated with the edge. It ranges
between 0 and 1.
d. Skewness: It is the principal quality metric. It indi-
cates how close an element is to an ideal equilateral
or equiangular element. It ranges from 0 to 1.
After obtaining good quality meshes, it is important to
establish mesh independence. This is critical to ensure that
the simulation results are independent of the discretization
scheme and the number of grid elements. For this, we com-
pared three different meshes. These were categorized into
coarse, medium, and fine classes depending on the average
size of the grid elements. All meshes met the quality require-
ments. To compare the meshes, an average element size
parameter was used. This was calculated by obtaining the
cube root of the average grid volumes. The growth ratio of
average element size across the three meshes was kept con-
stant at about 1.3. The parameters for each mesh are shown
in Table 2. The fluid volume was 1.26913 m3.
Five probe points were placed around the helmet to
compare the air velocity. A steady-state simulation with an
inlet air velocity of 2.0 m/s was used for mesh indepen-
dence studies. The results are shown in Table 3. As can be
seen, there are no significant differences in velocities at
those probe points. The biggest differences are found in
places where recirculation is expected.
With this information, the medium mesh will be
selected, as it offers enough accuracy and is not too expen-
sive computationally. The mesh quality metrics are shown
in Table 4. Even if a few elements are not within the opti-
mum range, quality is not bad enough to make the simu-
lation fail or give inaccurate results. Once the mesh was
Table 2. Element size calculations and mesh comparison
Parameters Coarse Medium Fine
Element count (million) 1.101 2.481 5.325
Avg. volume [mm3] 1,152 512 238
Avg. size [mm] 10.48 8.00 6.20
Cell count growth ratio 1.31 1.29
Table 3. Probe points velocities (m/s)
Locations Coarse Medium Fine
v1 (Side 1) 2.35 2.36 2.35
v2 (Side 2) 2.35 2.35 2.37
v3 (Top) 2.43 2.44 2.47
v4 (Front) 1.51 1.34 1.4
v5 (Back) 1.65 1.8 1.96
Figure 2. Real helmet (left), 3D points cloud (center),
faceted body (right)
Figure 3. The final geometry
Table 1. Mesh quality parameters
Parameters Threshold
Max aspect ratio 1,000
Min element quality 5e‑4
Min orthogonal quality 5e‑3
Max Skewness 0.999