Note: Descriptions are shown in the official language in which they were submitted.
3292
TILTED PANEL LINEAR ECHELON
SOLAR COLLECTOR
This inventlon relates to a solar concentrator
for receiving and collectin~ incident solar radiation to
a line focus~
Linear Fresnel or echelon reflectors are being
increasingly used for solar energy concentration because
of the accuracy with which these optical surfaces may be
mass produced. However, conventional prior art solar
concentrators which incorporate such reflectors suffer
from a number of defects. In the interests of
intercepting as much incident solar radiation as
possible, designers have adapted large apertures for
solar collector systems. When the echelon reflector
aperture becomes large relative to the focal distance of
the reflector, the echelon surface loses efficiency due
to a partial blockage of radiation directed toward the
line focus by the riser steps of the echelon surface.
Conse~uently, some portion of incident radiation which is
intercepted by the echelon surface is not dlrected to the
line focus. This causes a reduction in optical
efficiency which is undesirable.
The present invention overcomes the
deficiencies of the prior art by means of a novel
reflector design which eliminates riser step blockage and
results in a large aperture solar concentrator structure
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which may be used ~ith conventional tracking apparatus to track the sun.
According to a broad aspect of the present inventionJ there isprovided a solar collector for concentrating and directing incident solar
radiation to a receiver located along a line focus comprising a smooth sur-
$ace defining a planar base surface and a configured first surface comprising
an array of reflective planar elements separated by risers, wherein said
base surface is inclined at an angle ~ with respect to the normal of said
incident radiation~ and each of said reflective elements is inclined with
respect to said base surface at an angle ~' to reflect incident radiation to
said line focus and where the quantity ~' is less than or equal to zeroJ but
greater than or equal to - ~J such that all riser step blockage of radiation
is eliminated.
More specificallyJ the echelon reflector structure according to a
preferred embodiment of the present invention is formed in a thin polymeric
sheet. The sheet has a smooth surface and a surface configured as an echelon
reflector surface. The smooth surface of the sheet defines a planar base
surface or base plane. The sheet is bonded to a flat base support structure
which may be of conventional design. The surface configured as an echelon
reflector structure comprises a plurality of reflective planar elementsJ each
of which ara inclined at its predetermined angle ~' with respect to the planar
base surface of the structure. The echelon reflector elements are separated
by riser steps which extend substantially vertically from the planar base
surface.
In operation the reflective planar elements receive incident
radiation and direct this to a line focus. By inclining the echelon reflector
structure at a minimum tilt angle ~ with respect to a line normal ~the normal)
to the incident radiationJ all riser step blockage is eliminated.
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Two orthogonal X-Y coordinate sys-tems are used to describe the
geometric relationships het~een the echelon angles ~' and the minimum tilt
angle ~ ~hich results in the elimination of riser step blockage. The X-Y
coordinate system has the X axis extending normal to the incident solar
radiation and the Y axis extending
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vertically parallel to the incident radiation. The X'-Y'
coordinate system has the X' axis e~tending along the
planar base surface and the Y' axis extending normally
thereto. The base plane is rotated such that the slope
of the reflective planar element is negative in the X'-Y'
coordinate system and positive with respect to the X-Y
coordinate system. This slope change causes the riser
steps to move out of the path of both incident and
reflected radiation, thus eliminating all riser step
blockage. The reflective planar element has a negative
slope with respect to the X'-Y' coordinate system and is,
therefore, defined as a negative angle with respect to
this coordinate system. This geornetric constraint which
determines the minimum tilt angle ~ required to achieve
the elimination of riser step blockage requires that the
quantity a' be greater than or equal to zero and less
than or equal to ~ ,
A pair of these linear echelon reflector
structures may then be arranged in a V shape. Each
2~ linear echelon re~lector structure may be symmetrically
arranged about the bisector of the vertex of the V shape.
In this configuration each reflector structure will focus
incident solar radiation to a line focus located along
the bisector of the vertex of the V shape. The panels
may be supported in the V-shaped structure by a rigid
support frame. Although the design examples given here
relate to the simple V-shaped configuration, it should be
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appreciated that other configurations are possible. For
example, a multiplicity o~ contiguous panels may be used
where each panel is oriented at a different tilt angle
~ , where ~ is tlle minimum tilt angle for no riser step
blockage. It should be appreciated that the panels rnay
be tilted at an angle greater than ~ if some loss in the
effective aperature can be tolerated. This allows larger
effective apertures with no riser step blockage. This
segmented configuration permits the individual segments
to be held flat, and permits them to be individually
tuned for focusing control.
The planar base structure is required to permit
reflector elements to accurately focus at the line
receiver. Accurate focus control requires that each
echelon angle a' be oriented correctly with regard to the
focus. An error of a ~ in the echelon angle gives a ray
deviatlon of d (Figure 3). The magnitude of d = D~
(Figure 3), where Q~ = 2 Qa'. The echelon angle errors
Q' may arise from inaccuracies in master cutting,
deviations ~rom panel flatness and errors in the panel
orientation. To a good approximation the displacement of
the ray in a direction normal to the ray near the focal
point is d = DQ~ , where D is the distance from the
reflecting echelon to the focal point. This causes a
focus spreading or defocusing near the line receiver.
The magnitude of this defocusing depends upon the
distance from the line focus to the echelon reflector.
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Inclinin~ the panel with respect to the lncident
radiation not only elirninates riser step blockage, but
also advantageously reduces the average distance
variation of each step from the focus. Consequently,
inclining the panel with respect to the incident
radiation permits one to achieve better focus control.
The individual reflective planar elements are
separated by riser steps which, as illustrated, are
substantially perpendicular to the base plane. The
reflective planar surface is inclined at angle a with
respect to the X-Y coordinate system to direct incident
radiation toward the line focus. Inclination of the base
plane with respect to the direction of the X-Y coordinate
system permits riser steps to be out of the path of both
the incident and reflected radiation such that no
incident or reflected radlation will strike the riser
steps.
The planar refleotor surfaces may be configured
as either a first surface reflector or a second surface
reflector. ~lowever, an additlonal correction must be
made to compensate for refraction at the transparent
planar surface of the second surface embodiment.
In the case of the first surface reflector
embodiment, te geometrical constraint which eliminates
riser step blockage through slope reversal of the planar
reflective surfaces requires that ~ > ~ > 0, or -
< a'< 0 where a' = a- ~.
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In the case of the second surface reflector
embodiment the geornetrical constralnt which eliminates
riser step blockage through slope reversal requires that
~ > a > 0 or - ~ < ~ < 0, where ~' = a -~ . The
fact that a is always greater than zero results from the
refraction at the transparent surface of this embodiment.
The use of the second surface reflectors
permits the reflective surface to be protected from
environmental weathering since the only exposed surface
is the planar plastic surface of the reflector structure.
Appropriate weather protecting surfaces may be applied to
the polymeric planar surface to prevent weathering and
degradation of this optical surface.
Figure 1 shows a schematic elevational view of
a non-tilted conventional linear echelon reflector for
directing light to a focus;
Figure 2 shows a schematic elevational view of
applicants' invention defining the coordinate system used
ln describing the geo~etry of applicants' invention;
Flgure 3 is a schematic elevational view of
applicants' invention describing the control of focusing
error of applicants' invention;
Figure 4 is a schematic elevational view of
applicants' invention embodying a first surface linear
echelon reflector;
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Figure 5 is a schernatic elevational view of
applicants' invention embodying a second surface linear
echelon reflector;
Figure 6 is a schematic elevational view of one
embodiment of applicants' invention showing the support
structure for the echelon reflector optics;
Figure 7 is a schematic elevational view of a
specific example of applicants' invention defining
geometrical parameters used in discussing the collector
efficiency; and
Figure 8 is a graphical representation of
effective aperture and panel length as a function of half
acceptance angle.
Referring to Figure 1 which shows a non-tilted
prior art linear echelon reflector for directing light
rays 1 and 2 to a line focus 3. Incident light ray 1
strikes the reflective surface 4 of an echelon reflector
6 whlch is inclined with respect to the base line 7 of
the echelon reflector elements at an angle 5. This angle
is appropriately selected to direct the incident light
ray to the focus 3. An incident ray 2 striking an
adjacent echelon reflector surface 9 is reflected by the
reflective surface 8 in the correct direction to reach
line focus 3; however, the reflected ray is intercepted
by the riser step 11 which separates echelon reflector
surfaces ~ and 8. It-should be clear by inspection of
Figure 1 that this riser step blockage becomes
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progressively more severe in the case of echelon
reflector surfaces located greater distances from the
focus. Incident radiation which is blocked by the riser
steps does not re~ch the focus, and conse~uently, reduces
the optical efficiency of the solar collector system.
Inclining such a linear echelon reflector system with
respect to the focus does not lmprove the optical
performance since incident rays will first strike the
riser surfaces and be redirected toward the sky.
In applicants' invention shown in Figure 2 each
echelon angle a~ formed as the lncluded angle between
base plane 20 and the planar re~lector sur~ace 21. This
angle ' faces the tilt angle ~ which is formed
between the base plane 20 and the x-axis, which is normal
to the direction of the incident solar radiation. In
discussing the orientation of the planar reflector
surfaces, it is useful to define two coordinate systems.
In the coordinate system X-Y, the planar re~lector
sur~ace has a positive slope. When the slope of the
planar re~lector sur~ace 21 is considered in the X'-Y'
coordinate system, the slope of the reflector surface is ~-
reversed with respect to the X-Y coordinate system. This
permits every incident light ray striking the reflective
surface of planar reflector element 21 to-be directed to
a line focus 23 without riser step blockage. For a glven
collecting aperture A, the minimum tilt angle ~ is that
tilt angle which results in positive slope for all planar
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reflector surfaces in the X-Y coordinate system while
directing incident light from each planar reflector
surface to the line focus posltioned at 23.
As shown in Figure 2, ~ncident radiation rays
24, 25 and 26 are always reflected toward the line focus
and the riser portion separating each planar reflector
surface never intercepts incident or reflected solar
radiation.
A further advantage of the inclined linear
echelon reflector structure described with reference to
Figure 3 results in improved focus control of the solar
concentrators. The angle ~' corresponding to each of
the planar reflector eleMents 31, 32, 33, 34 is ~'31,
a 32~ a 33, ~'34, a'3s. These angles are designed to
lS direct incident solar radiation to a line focus 39 when
the panel is tilted at the minimum tilt angle ~ .
Deviations in this echelon angle Aa' for any ~' may be
caused by inaccuracies in master cuttinæ~ deviations from
panel flatness and errors in panel orientation. These
deviations will cause a ray to be misdirected ~
sli~htly ~rorll the focus. The amount of this defocusing d
is given to a good appro~imation by d = D~ , where D is
the distance from the reflecting surface 33 to the focal
point 39. The inclined configuration of applicants'
invention minimizes the average variation in distances D
from each of the planar reflector surfaces to the focus
39, over the aperture of the echelon reflector structure.
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Consequently, the defocusing variation is less severe
across the aperture of applicants' tilted echelon
reflector structure. This permits closer control over
line focus spread which is advantageous when a line
receiver locaked at line focus 39 has an efficiency which
depends strongly upon the energy flux which it receives.
Figure 4 and Figure 5 show first and second
surface embodiments of applicants' invention. Referring
to Figure 4, the planar reflective surfaces such as 40
are formed in a polymeric material 41. This sheeting may
be bonded by means of an adhesive 42 to a flat panel 43.
A suitable reflective coating 44 is applied to the
exposed surface of the planar reflector structures. The
completed reflector structure is inclined at a tilt angle
~ with respect to the normal of the direction of the
incident solar radiation.
Referring to Figure 5, a second surface
embodiment of the present invention is shown. In this
embodlment, the planar reflector surfaces such as 50 are
formed on the underside of a transparent polymeric sheet
51. A suitable reflective coating 52 ls applied to
create a reflective surface. The reflective panel
structure 53 thus formed is bonded by a suitable means 54
to a flat support panel 55. The prlncipal advantage of
the second surface reflector as shown in Figure 5 is that
a smooth planar surface 56 is exposed to the environment
and the reflective coating 52 can be protected from the
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environment. The smooth surface may be coated with a
suitable abrasion resistant coat or antireflective
coating.
One suitable support structure for applicants'
reflector concentrators is shown in Figure 6, wherein a
rigid support structure 60 is provided to align the
reflector panels 61 and 62 with respect to the line
receiver 63. Although the refIector elements shown in
the drawing are of the first surface type, it should be
appreciated that the rigid support structure may be used
for the second surface reflector embodiment as well.
Figure 7 refers to a specific design example,
for a first surface reflector panel. The solar energy
absorber or receiver is placed at the line focus of the
solar collector which is located a distance FD away from
the vertex of the panels. The receiver may be of any
conventional type including photovoltaic cells or heat
absorbing pipe. The half acceptance angle y at the
receiver or absorber is chosen by the designer, depending
upon the type of solar absorber the designer wishes to
focus incident solar radiation upon. Once the half
acceptance angle is determined, the minimum tilt angle ~
of the panel which results in no riser step blockage may
be determined by ~ = r/2. The required panel length PL
may then be calculated by PL = cOsne (~ ) x FD. The
effective aperture of the total solar collector then
becomes EA = PL x cos ~ . For the specific case
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described FD = 48 inches, PL = 48 inches~ ~ = 30,
~ = 600 and EA = 41.57 inches. The following table
gives representative values of X', ~' and a, where a
is the angle of planar re~lector elements in the X-Y
coordinate system and X' is the position of each planar
reflective element along the panel.
X' a c~ '
0.05 0.02 -29.97
4,05 2.18 -27.81
9.05 5.10 -24.89
14.05 8.26 -21.73
19.05 11.60 -18.39
24.05 15.03 -14.96
29.05 18. 46 -11.53
33.05 21.14 - 8.85
38.05 24.33 - 5.66
43.05 27.31 - 2.68
47.95 29.97 _ o .02
A ~lat panel de~ign ( ~ = 0) o~ the same
equivalent aperture and focal distance has a calculated
loss due to echelon riser step blockage of 9. 2 percent
(RMS value over all reflecting steps~. The til~ed panel
is therefore about nine percent more efficient than the
25 flat panel.
Figure 8 is a graph showing the effect of the
half acceptance angle upon the panel length and effective
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aperture of the solar collector with a focal distance ~D
of 48 inches. Although it can be seen from the graph
that half acceptance angles between 0 and 180 are
theoretically possible with zero step blockage, the
effective aperture of the solar collector drops o~f to
zero near these values. The specific case given in the
table of values and in ~igure 7 is marked on the graph.
It can be seen from the graph that the larger the half
acceptance angle, the greater the requisite panel length
to achieve a given effective aperture. ~owever, a hal~
acceptance angle of 90 is practically obtainable. This
is impossible to achieve with a non-tilted panel.
As mentioned previously, to obtain larger
effective apertures or acceptance angles, several
contiguous panels may be individually tilted, using the
design principles of the present invention. This
arrangement eliminates riser step blockage, pznel
flatness control is improved, and the panels may be
individually aligned.
In some very wide aperture applications,
a small amount of riser step blockage may be tolerable.
In these instances the panels may be extended into the
region o~ riser step blockage. It should be understood,
however~ that the magnitude of riser step blockage will
be low in this extended region.
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