Environmental Engineering Reference
In-Depth Information
Energy analysis
is based on the energy conservation equations. The energies
E
are
used in six equations written successively for: floor surface, air in collector, collector
(including floor, air and deck), turbine, chimney and chimney surface:
=
+
E
S
-
f
E
f
-
a
E
f
-
d
(2.4.75)
E
f
-
a
+
E
d
-
a
=
E
a
1
+
E
w
1
+
E
p
1
(2.4.76)
E
S
-
f
=
E
a
1
+
E
w
1
+
E
p
1
+
E
d
-
sky
+
E
d
−
0
+
E
d
-
ch
(2.4.77)
E
a
1
+
E
w
1
+
E
p
1
=
E
a
2
+
E
w
2
+
E
p
2
+
E
P
(2.4.78)
E
a
2
+
E
w
2
+
E
p
2
+
E
d
-
ch
=
E
a
3
+
E
w
3
+
E
p
3
+
E
ch
−
0
+
E
ch
-
sky
+
E
ch
-
gr
(2.4.79)
E
a
−
ch
+
E
d
-
ch
=
E
ch
−
0
+
E
d
-
sky
+
E
ch
-
gr
(2.4.80)
Energies
E
have the following subscripts:
S
-
f
- solar radiation arriving at the floor,
f
-
a
- convection heat from floor to air,
f
-
d
- energy exchanged by radiation between floor and deck,
d
-
a
- convection heat from deck to air,
d-sky
- energy exchanged by radiation between deck and sky,
d
-0 - convection heat from deck to atmosphere,
d-ch
- energy exchanged by radiation between deck and chimney,
ch-0
- convection heat from chimney surface to atmosphere,
ch-sky
- energy exchanged by radiation between chimney surface and sky,
ch-gr
- energy exchanged by radiation between chimney surface and ground,
a-ch
- heat transferred from chimney air to the chimney surface,
a
1,
a
2,
a
3 - enthalpy of air at points 1, 2 and 3,
w
1,
w
2,
w
3 - kinetic energy due to the air flow velocity w
1
,w
2
and w
3
,
p
1,
p
2,
p
3 - potential energy of air at points 1, 2 and 3,
P
- turbine power.
Kinetic energies are calculated as
E
w
=
w
2
/2, where
m
is the air mass flow
m
·
D
1
·
rate;
m
=
0
.
25
·
π
·
w
1
·
ρ
a
1
. Enthalpy of air is
E
a
=
m
·
c
p
·
(
T
a
−
T
0
) where
c
p
is
the specific heat of air at constant pressure.
The potential energy of the considered air, at its constant density
ρ
, depends on the
altitudinal variation of atmospheric air density and gravity acceleration. The solution
of the differential formula (2.2.16) on potential energy
E
p
, J/kg, equal to potential
exergy
B
p
, is determined by Petela (2010):
m
a
2
6
a
4
a
3
)
2
1
a
4
ρ
a
1
2
(
ρ
a
3
)
3
E
p
=
−
(
ρ
−
+
−
(a)
=
9
.
7807 m/s
2
,a
2
=−
×
10
−
6
1/s
2
,a
3
=
where the constant values are a
1
3
.
086
10
−
5
kg/m
4
.
Total solar energy received by the floor is:
1
.
217 kg/m
3
, and a
4
=−
9
.
973
×
E
S
-
f
=
τ
d
ε
f
SA
d
(b)
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