Environmental Engineering Reference
In-Depth Information
The coefficient
k
f
-
a
is determined in a similar way. Although the air flow is driven
by buoyancy effect, the forced convection mechanism of the air flow is assumed. Thus
the calculations are based on the Reynolds number instead of the Grashof number.
In calculations the average flow velocity of air is assumed. The effective diameter
D
eff
for the air flow can be assumed as the average ratio of the respective flow cross-
section area
A
1
multiplied by four, to the respective average perimeter lengths;
D
eff
=
(4
/π
)
k
f
-
a
.
The following formulae are applied for energy exchange by radiation between:
·
A
1
/
(
D
f
+
D
2
). It was assumed that
k
a
−
d
=
floor and deck:
A
d
σ
(
T
f
,
eff
−
T
d
,
eff
)
E
f
-
d
=
(k)
deck and chimney:
E
d
-
ch
=
ϕ
d
-
ch
A
d
σ
(
T
d
,
eff
−
T
ch
)
(l)
deck and sky:
E
d
-
sky
=
ϕ
d
-
sky
A
d
σ
(
T
d
,
eff
−
T
sky
)
(m)
chimney and sky:
E
ch
-
sky
=
ϕ
ch
-
sky
A
ch
σ
(
T
ch
−
T
sky
)
(n)
chimney and ground beyond the floor:
E
ch
-
gr
=
ϕ
ch
-
gr
A
ch
σ
(
T
ch
−
T
gr
)
(o)
where the view factors fulfill the following relations:
ϕ
d
-
sky
+
ϕ
d
-
ch
=
1
(p)
ϕ
ch
-
sky
+
ϕ
ch
−
d
+
ϕ
ch
-
gr
=
1
(q)
The view factors
ϕ
ch
−
d
and
ϕ
d
-
ch
are determined based on equation (d), whereas
the configuration of chimney relative to sky determines view factor
ϕ
ch
-
sky
0
.
5.
Calculation of temperature
T
a
,2
is based on the equation for the isentropic expan-
sion in the turbine at assumed isentropic exponent
κ
for air and the internal efficiency
of the turbine
η
T
. Conversion of the energy of air into electric power occurs at an over-
all efficiency
η
o
which would include additionally mechanical and electric efficiencies
of the turbine-generator unit.
Additionally it was assumed that the air temperature distribution in the collector is
linear and thus
T
a
,
eff
=
=
0
.
95. The air temper-
ature drop in the chimney can be tentatively estimated as proportional to the chimney
surface and inversely proportional to the air mass rate;
T
a
,2
−
(
T
0
+
T
a
1
)/2. The diameter ratio
D
1
/D
2
=
H
3
/m
.
The presented mathematical model of SCPP is illustrated with exemplary computa-
tion results in which, for comparison to the 36-kW pilot SCPP plant in Manzares, near
T
a
,3
≈
0
.
154
·
D
2
·
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