Environmental Engineering Reference
In-Depth Information
Figure 5.2 Earth-level peak sun s power
spectrum, unitsW/(m 2 eV). This is the AM1.5
spectrum characteristic, appears at noon on a
clear day for moderate climates, and 48 from
normal incidence. The area under this curve
represents 1 kW/m 2 . The shaded areas in range
1.7 - 3.1 eV represent red, green, and blue parts
of the visible spectrum. About half the energy is
in wavelengths longer than visible, energies less
than 1.7 eV. A small portion of this light intensity
comes indirectly by Rayleigh scattering [54].
300 K for ambient, the value
of is 0.95. This analysis can be extended to better simulate a solar thermal power
plant. In such a case, a focused light systemputs sunlight on an intermediate collector
heat reservoir, which rises to an intermediate temperature T c . The collector reservoir
then is the hot reservoir for the heat engine. In this case, radiation back from the
intermediate collector to the sun is an important part of the analysis. In Figure 5.1,
one can imagine the intermediate reservoir being the black surface at the bottom of
the field, which we now say will come to temperature T c and radiate a power density
s SB T c back to the sun through the optical system, which is a Fresnel lens in
Figure 5.1. In this circumstance, which was investigated by Landsberg, the efficiency
is expressed as
If we evaluate this at T s ¼
6000 K for the sun and T a ¼
T c =
T s Þð
g L ¼ð
1
1
T a =
T c Þ
d
:
ð
5
:
3a
Þ
The maximum value of this ef
ciency, g L
¼
0.854, setting the correction d to its
minimum, zero, with T s
¼
6000 K and T a
¼
300 K, occurs at collector temperature
T c ¼
2544 K. The terms in this expression clearly relate to radiation equilibrium
between the sun and the collector, and to Carnot ef ciency of the heat engine working
between the collector at T c and the ambient exhaust temperature T a . The correction d
is related to entropy generation,
T a (d S /d t )/ P s , where P is the power from the
sunlight. Entropy d S
d Q / T is accepted from the sun by black body absorption,
some is returned to the sun by the black body emission from the collector, and a
contribution d S c /d t
¼
¼
P c / T c is created by black body radiation fromthe collector to the
Carnot engine.
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