Environmental Engineering Reference
In-Depth Information
on this definition. Thus, the concentration ratio of a typical parabolic through
collector of an aperture width of 5.8 m and an absorber tube diameter of 70 mm
amounts to approximately 26. With regard to parabolic through collectors,
sometimes the ratio of aperture width to absorber tube diameter is referred to as
concentration ratio; this quantity differs from the concentration ratio defined by
Equation (5.1) by factor π.
A
ap
C
=
C
=
(5.1)
geom
A
abs
-
On the other hand, the concentration ratio
C
can be defined as the ratio of the
radiation flux density
G
ap
at the aperture level and the corresponding value
G
abs
of the absorber (
C
flux
, Equation (5.2)). However, this definition is only men-
tioned here to complete the picture.
G
ap
C
=
C
=
(5.2)
flux
G
abs
On the basis of the second fundamental theorem of thermodynamics the maximum
possible concentration ratios for two-dimensional (parabolic trough-type) and
three-dimensional (e.g. paraboloids of revolution) concentrators can be deduced
/5-1/. For this purpose the "acceptance angle" 2θ
a
is required. This angle covers
the entire angular field of solar beams to be focussed by the collector, without
having to move the collector or part of it.
For single-axis concentrators (e.g. parabolic trough), for instance, the maxi-
mum concentration ratio
C
ideal,
2
D
for a given acceptance semi-angle θ
a
is calcu-
lated according to Equation (5.3).
1
C
=
(5.3)
ideal
,
2
D
sin
θ
a
For two-axis concentrators (e.g. paraboloids of revolution) the maximum con-
centration ratio
C
ideal,3D
is calculated according to Equation (5.4).
1
C
=
(5.4)
(
)
2
ideal
,
3
D
sin
θ
a
Since on the earth's surface the acceptance angle 2θ
a
for the sun amounts to
0.53° or 9.3 mrad, maximum ideal concentration factors of 213 are determined for
two-dimensional geometries (line focussing parabolic through) and of 45,300 for
three-dimensional (point focussing) geometries.
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