Finite Element Analysis
of a Suspended
Aluminum Water Channel
MANE 6960 – ADVANCED TOPICS IN FINITE ELEMENT
ANALYSIS
THOMAS PROVENCHER
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Introduction:
This model analyzes the stress and displacement of a suspended water channel carrying hot water
in a cool environment. A deep U channel made of aluminum carries hot water at 80 C° while the
outer surface of the channel is kept at -20 C°. The section of channel being analyzed is
suspended over a short gap and is part of a much longer channel that is fully supported. The
weight of the water was also simulated while establishing the model’s load conditions.
Formulation and Solution:
The model created for this analysis will simulate the stress and displacement of a suspended
aluminum water channel. A deep U section, shown in Figure 1, was developed within the
COMSOL modeling environment and was assigned the material properties of aluminum using
the built-in material properties. The channel is 2 meters long, has an outer radius of .25 meters,
an inner radius of .15 meters, and an overall height of .75 meters. The inner and outer surfaces
of the channel were given temperature boundary conditions of 80 and -20 C°, respectively, as
shown in Figure 2. Both ends of the simulated section were fully clamped, as shown in Figure 3,
to simulate the fully supported condition of the rest of the channel. The mass of the water was
applied to the lower section of the inner surface of the channel as shown in Figure 4.
Figure 1: Water channel model and dimensions
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Figure 2: Interior and exterior temperature boundary conditions
Figure 3: Clamped ends with a zero displacement condition
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Figure 4: Weight of the water added as a load case in the negative "y" direction
four different meshes were chosen for this analysis; all were derived from COMSOL’s physics
based mesh creator and were constructed of Lagrange quadratic elements. Coarser, Normal,
Finer, and Extra Fine meshes were chosen, the extra fine mesh can be seen in Figure 5.
Figure 5: Extra Fine mesh density of the flow model
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The variational formulation is shown below:
(𝑢′ , 𝜐′) = (𝑓, 𝜐)
The COMSOL model was run four times, once for each mesh density to verify the mesh was
sufficiently dense. Figures 6, 7, and 8 show the stress, vertical displacement, and horizontal
displacement maps, respectively, of the model. Table 1 shows the maximum values provided by
the three maps for all four mesh densities.
Figure 6: Von Mises Stress map of the water channel model
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Figure 7: Vertical Displacement of the water channel model
Figure 8: Horizontal displacement of the water channel model
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Table 1: Stress and displacement maximum values
Maximum velocity potential and fluid pressure values
Maximum
Percent
Maximum
Percent
Maximum
Mesh
VonMises Change to
Vertical
Change to
Vertical
Density
Stress
Lesser
Displacement
Lesser
Displacement
(Pa)
Density
(m)
Density
(m)
Coarser
2.07E+08
5.106
8.67E-04
0.423
4.94E-03
Normal
2.18E+08
9.487
8.71E-04
0.161
4.95E-03
Finer
2.41E+08
5.930
8.69E-04
0.845
4.93E-03
Extra Fine 2.56E+08
N/A
8.77E-04
N/A
4.92E-03
Percent
Change to
Lesser
Density
0.202
0.542
0.065
N/A
The data provided in Table 1 shows that quadratic Lagrange elements are able to provide
accurate results independent of the mesh density. The results provided by all four mesh densities
varied only a small amount among each other and with no discernable trend as the mesh density
increased. This shows that the coarsest mesh density was sufficient and that thermal problems
are not as sensitive to mesh density as some others.
Conclusions:
This model was able to approximate the stress and displacement imparted on a U shaped water
channel subjected to a 100 C° temperature variance across is thickness as well as a weight load.
The ends of the channel were given zero displacement boundary condition to simulate the
remainder of the fully supported channel not modeled. The analysis results show that the sides
of the channel bow out due to the growth of the metal from the temperature variance across the
material. The results also indicate that the mesh densities chosen were all approximately equally
accurate indicating that the least dense mesh was sufficiently dense.
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