Environmental Engineering Reference
In-Depth Information
For a sphere, the plane stress is the same as cylindrical longitudinal stress.
The equations above for plane stress in a tank show that the radius of the
tank and the thickness of the tank material are the effective parameters for
safe design. Another important parameter is tank temperature.
Thermal Strain
Since the materials used in thermal energy storage undergo very high tem-
peratures, one must fully understand the effect of temperature on the mate-
rials used. The thermal expansion of a material must be known in order to
calculate how much tension the tank will undergo when it expands due to
elevated storage temperatures. Thermal strain is calculated as
∆
x
= α
∆
TL
(7.4)
The combination of mechanical stress and thermal strain must be considered
when designing a storage tank to ensure the resulting stress is well below
the ultimate strength of the material [3].
Heat Loss from Storage Vessels and Insulation
Heat loss to the environment is a function of a storage vessel's surface area-
to-volume ratio [10]. Insulation is an effective way to reduce heat loss to
the environment. The appropriate design of insulation in a storage vessel
depends on a balance of the ambient heat loss and cost of insulation. Since
heat loss to the environment depends on the surface area-to-volume ratio, it
will be considered separately for cylindrical and spherical vessels.
Heat Loss from Cylindrical Vessels
The heat loss through insulation of a cylindrical tank [5] can be calculated:
(
)
k L T T
R R
2
π
−
s
a
Q
=
(7.5)
ln(
/ )
+
( /
k h R
)
2
1
t
2
Equation 7.5 allows calculation of heat loss for a tank based on the condi-
tions in Table 7.6 which gives the variable meanings, units and representa-
tive values of each variable.
To quantify whether a cylindrical tank should be insulated, Table 7.7 and
Figure 7.7 show the insulation costs and insulation thickness as a function of
heat loss, assuming a 42% efficient Rankine cycle and an electricity cost of
$0.10/kWh. These data show the economic effectiveness of insulating a stor-
age tank. Applying just 10 cm of insulation dramatically reduces ambient heat
loss and returns the investment in 3 years.
