Environmental Engineering Reference
In-Depth Information
r
r
h
FIGURE 7.4
Cylindrical and spherical tank geometries.
TABLE 7.5
Comparison of Surface Area and Volume of Cylindrical Tank
Geometries Based on Radius
Surface
Area/Volume
TESGeometry
SurfaceArea
Volume
Sphere
4
π
r
2
3
r
π
r
4
3
3
Cylinder of variable
height
rh
r
π
r h
2
2
π
r r
(
h
)
+
2(
+
h
)
Optimized cylinder
(where
h
=2
r
)
3
2
r
π
r
π
r
6
2
2
3
Figure 7.5 illustrates the relations in Table 7.5: the surface areas and vol-
umes of cylindrical and spherical tanks depend on the radius of each ves-
sel and as the radius increases, the areas and volumes of both geometries
increase. At large radii, the cylindrical geometry results in a much greater
surface area and volume.
These simple geometric comparisons lead one to opt for a cylindrical geom-
etry for a TES tank. Additionally, the materials used in a storage tank are
much more difficult to customize for a spherical tank and a spherical tank
is far more difficult to construct. Ensuring mechanical support for a spheri-
cal tank is also more difficult. For these reasons, spherical tanks are often
more practical for underground use. The requirement for more customized
materials will inevitably increase the cost of an entire system and the time
needed to complete it. Figure 7.6 shows the longitudinal cross-section view
of a representative cylindrical storage tank with heat exchangers.
Tank
Materials
The materials used for a tank are critical to its performance. The tank materi-
als will exert almost as much influence on the efficiency of heat storage as the
