Environmental Engineering Reference
In-Depth Information
Heat Loss from Spherical Vessels
T. Brumleve developed relations to describe sensible heat loss from spheri-
cal thermal energy storage volumes. The heat loss from a spherical tank,
Q
L
,
with constant temperature,
T
avg
, is shown in Equation (7.6) [5]. The heat stored
in the tank,
Q
S
, is given by Equation (7.7) [4].
4
k R t
L
π
2
Q
=
(
T
−
T
)
(7.6)
L
avg
C
T
+
2
T
T
=
H
C
(7.7)
avg
Typical values of each parameter for a 20 m diameter spherical energy stor-
age tank filled with water are shown in Table 7.8. These values can be used
with Equations (7.6) and (7.7) to find the heat loss from a tank and the amount
of heat stored in the tank over time. Figure 7.8 shows heat loss from a spheri-
cal tank as a function of time and the tank's thermal capacity. Solar Two
(discussed later in this chapter) is a 10 MW
e
power tower that stores molten
salt in hot and cold tanks. The hot tank is 11.6 m in diameter and 8.4 m tall.
It was designed to store 105 MWh
t
of thermal energy and supply 3 hours of
full scale electricity production. Solar Two's heat loss to the environment was
measured from the hot and cold tanks, steam generator, and receiver sumps.
A total of 185 kW of heat loss from these components is equivalent to 2% of
the collected thermal energy on a winter day. Table 7.9 is a demonstration of
where calculated and measured heat losses arise within a thermal energy
storage system.
TABLE 7.8
Thermal Storage Parameters for Spherical Tank
Sample
Value
Parameter
Unit
Description
Q
L
J
Heat loss to environment
Q
S
J
Heat stored in tank
K
0.035
W/m×K
Thermal conductivity of insulation
R
10
M
Radius of tank
T
S
Storage time
L
0.5
M
Thickness of insulation
T
ave
368
K
(T
H
+T
L
)/2 for diurnal storage
T
amb
293
K
Temperature of ambient medium
T
H
393
K
Temperature of hot fluid
T
C
343
K
Temperature of cool fluid
C
p
4217
J/kg×K
Specific heat of water
ρ
958
kg/m
3
Density of water
