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Description  |
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BACKGROUND OF THE INVENTION
The present invention relates generally to electromagnetic energy
collection and more particularly to devices useful in the collection and
utilization of energy emanating from a source of finite dimension and
finite distance from the collection device, wherein the collection device
is a nonimaging cylindrical type collector. For example, a secondary solar
energy collector is a device which is positioned to receive energy
reflected by a primary collector. The primary collector, which is of fixed
dimension and fixed distance from the secondary collector can be
considered as a source of electromagnetic energy. Prior art secondary
collectors have not provided side wall shapes capable of reflecting all
incident energy from the primary source onto the body of a smoothly shaped
energy absorber, but rather require extended fins and protrusions to
capture all of the desired energy. Further, the prior art schemes do not
provide a satisfactory solution for secondary collector design where it is
desirable to position the secondary collector asymmetrically disposed with
respect to the light source.
The inventor, in a prior U.S. application for Radiant Energy Collector,
Ser. No. 492,074, filed July 25, 1974, and in a publication, Solar Energy,
Vol. 16, No. 2, pages 89-95, (1974) has shown designs for nonimaging
collectors. In these disclosures, however, the inventor has been dealing
with an energy source, such as the sun, which is considered to be at an
infinite distance from the collector so that all light rays incident from
the infinite energy source on the collector are considered to be parallel
and, further, that the collector itself is assumed to be aligned
symmetrically with respect to the envelope containing the incoming rays.
It is therefore an object of this invention to provide a device for
efficiently collecting and concentrating radiant energy.
Another object of this invention is to provide a non-imaging energy
collection device for collecting energy from a source of finite dimension
and finite distance from the collection device.
Another object of this invention is to provide a non-imaging energy
collection device positioned asymmetrically with respect to an energy
source of finite dimension and finite distance from the collector.
SUMMARY OF THE INVENTION
An electromagnetic energy collection device is provided for collecting
energy from a source of finite dimension and finite distance from the
collector. It includes a convex energy absorber bounded by a first
reference axis and having a second reference axis therethrough and being
positioned between two side walls on either side of the second axis which
reflect substantially all energy directly onto the energy absorber. Each
side wall begins at a tangent point along the first axis where a line from
the conjugate edge of the energy source is tangent with the absorber and
is so shaped that all energy directed from the conjugate edge of the
energy source intersecting the axis of the absorber at any angle, and
striking any point on the wall, is directed along a line tangent to the
energy receiver. Each wall extends no more than to a line from the second
edge of the energy source, conjugate to the other side wall, to a point of
tangency with the energy absorber along the first axis.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows the cross section of the invention with an energy absorber
symmetrically disposed with respect to the energy source,
FIG. 2 shows the cross section of the invention with the energy absorber
asymmetrically disposed with respect to the energy source, and
FIG. 3 shows the trough-shaped structure of this invention as utilized as a
secondary collector.
DETAILED DESCRIPTION OF THE INVENTION
Referring to FIG. 1, there is shown the transverse cross section of the
cylindrical electromagnetic energy concentration and collection device of
one embodiment of this invention. As the disclosed device is a cylindrical
collector, the physical structure of the collector is formed by extending
the cross section shown in FIG. 1 along an axis perpendicular to the plane
of the cross section to form a trough-like structure, as will be described
with reference to FIG. 3. The function of the collector device is to
concentrate light from source 10 which impinges on entrance aperture 11
onto the surface of an energy absorber 12. The energy absorber 12 may be,
for example, a pipe containing fluid, a photovoltaic cell, or any other
type of energy receiver responsive to radiant energy. Source 10 is of
finite dimension defined by edge points 14 and 16 and is of finite
distance from the absorber 12. In the embodiment shown in FIG. 1, the
absorber 12 is symmetrically disposed with respect to source 10.
For a given cross section of an energy absorber 12, the present disclosure
deals with developing the contour of side walls for reflecting energy
incident on the side walls onto that portion 19 of the cross section of
the absorber 12 which lies between axis 20 and light source 10. The
portion 19 is limited to being convex so that any line tangent to the
perimeter of portion 19 does not cross the perimeter of portion 19 of
absorber 12. Note, that a convex portion 19 also includes within its
definition a flat plane absorber along axis 20. Axis 20 is a line
connecting tangent points 22 and 24. Tangent points 22 and 24 are
determined by tangent lines 28 and 30, respectively. Each tangent line
extends from an edge point 14 or 16 of source 10, intersecting axis 32 of
the porton 19. Axis 32 is a reference axis perpendicular to axis 20 and
passes through portion 19. Each tangent line extending from an edge point
14 or 16 intersects the conjugate tangent point 22 or 24 along the
perimeter of absorber 12 and is tangent to the absorber 12 along axis 20
at the tangent point. Another way of describing tangent lines 28 and 30 is
that the angles .alpha..sub.1 or .alpha..sub.2 each line makes when
intersecting axis 32 is the minimal angle for a line from an edge point
tangent to the perimeter of portion 19 without crossing the boundary of
portion 19.
Side walls 36 and 38 which are of a material capable of reflecting radiant
energy have shapes generated by choosing contours such that singly
reflected rays originating from the conjugate edge points 14 or 16 are
tangent to the perimeter of portion 19. Thus ray 50 from edge point 14 is
directed by wall 38 along line 51 to be tangent to portion 19 and likewise
ray 52 is directed by wall 36 along line 53 to be tangent to portion 19.
The contour is terminated by the intersection of the wall with the tangent
line at points 54 and 56 for walls 36 and 38, respectively. Note that in
FIG. 1, the perimeter of portion 19 is extended away from source 10 along
tangent lines 28 and 30 from points 40 and 42. The tangent lines 28 and 30
will remain unchanged no matter how far the extension is made from the
initial points of tangency 40 and 42, although the contour of walls 36 and
38 will vary depending upon the actual length of the perimeter of portion
19.
Note that the solution herein disclosed differs from that shown in prior
disclosures of the inventor previously referred to, in that in those
cases, since the source was considered to be of infinite distance from the
collector, the side wall contour was determined by the condition that all
energy crossing the axis 32 at the maximum acceptance angle and striking
any point on the contour of the side wall was directed along a line
tangent to the absorber. In this case, only light directed from the edge
of the light source which may cross axis 32 at any angle and which is
incident on a side wall is directed along a line tangent to absorber 12.
The method herein disclosed for developing the side wall contours is not
limited to absorbers which have only a portion 19. For cross sections on
the opposite side of axis 20 from portion 19, the principle of the
involute second portion of a side wall described in U.S. application Ser.
No. 492,074 is applicable. FIG. 1 illustrates an absorber aligned
symmetrically with respect to the light source. With the special case of a
flat receiver, the contour of each side wall is an ellipse with the foci
at the conjugate point of tangency and at the conjugate edge point of the
light source. Thus, if in FIG. 1 the perimeter of portion 19 was a flat
plane along axis 20, point 22 and point 16 would be the foci of a ellipse
which would be the contour of wall 36.
Referring to FIG. 2, there is shown an absorber 60 which is asymmetrically
disposed with respect to light source 10. By asymmetric is meant that a
central line 62 passing through source 10 does not pass centrally through
portion 19. The same limitations as to the contour of portion 64 as
described for portion 19 apply. Thus, portion 64 is convex with respect to
axis 20. Tangent line 66 extends from edge point 14 to conjugate tangent
point 68, intersecting axis 32 at an angle .alpha..sub.1, line 66 being
the line with the smallest angle .alpha..sub.1 tangent to portion 64
without crossing the boundary of portion 64. Tangent line 70 extends from
edge point 16 to conjugate tangent point 72, intersecting axis 32 at an
angle .alpha..sub.2, line 70 being the line with the smallest angle
.alpha..sub.2 tangent to portion 64 without crossing the boundary of
portion 64. Note that since portion 64 need not have symmetry, axis 32 is
merely a reference axis perpendicular to axis 20 passing through portion
64. The contour of each side wall 74 and 76 is determined so that singly
reflected rays from edge points 14 and 16 intersecting axis 32 at any
angle are directed by the wall upon which they are incident in a line
tangent to the perimeter of portion 64. Thus, ray 78 from point 14 is
directed by wall 76 along line 79 tangent to portion 64 and ray 80 from
point 16 is directed by wall 74 along line 81 tangent to portion 64. Each
wall 74 and 76 terminates at the point of intersection with tangent line
66 or 70, points 82 and 83, respectively.
The solutions presented for collecting energy from sources of finite
dimension and finite distance for the collectors are developed by applying
the principle that all energy trajectories originating outside the source
are excluded from reaching the energy absorber. We seek to collect all
radiation from the source which impinges on the entrance aperture of the
collector and concentrate it onto the absorber. Moreover, we wish to
minimize the length S of the perimeter of the portion of the absorber. We
treat, in the initial example shown in FIG. 1, a system that is symmetric
about the axis 32 (z). It is first necessary to establish the maximum
possible concentration, i.e., the minimum value of S. This is conveniently
done by using a hamiltonian description of the ray trajectories
propagating in the z direction. Introducing the direction cosine of the
ray k.sub.x conjugate to x, the conserved phase space is given by
.intg. dxdk.sub.x is conserved. 1
z = constant
Evaluating the phase space at the entrance aperture we obtain the simple
result
1/2 .intg. dxdk.sub.x = (q - p) 2
where q is the distance from an edge point to its conjugate wall
termination point, e.g. from point 14 to point 56, and p is the distance
from an edge point to its nonconjugate wall termination point, e.g. from
point 14 to point 54. Thus (q - p) is the difference in distance between
an edge of the source and the edges of the entrance aperture.
Equivalently, this is the difference in distance between an edge of
entrance aperture and the edges of the source.
To achieve maximal concentration it is necessary to exclude stray light
trajectories originating outside the source from reaching the receiver. In
FIG. 1, we therefore require the profile curve of the portion 19 to be
tangent to the extreme directions, i.e. lines 28 and 30, at points 22 and
24, respectively. Since portion 19 is convex with respect to axis 20, a
tangent to portion 19 is prevented from crossing the portion boundary. The
solution to obtaining maximal concentration is to so choose the profile
curve of side wall 36 that singly reflected rays originating from edge
point 16 are tangent to portion 19 and to so choose the profile curve of
side wall 38 that singly reflected rays originating from edge point 14 are
tangent to portion 19. This means portion 19 becomes the envelope of such
rays. In other words, the perimeter of portion 19 is a caustic surface. If
we denote the ray distance from edge point 14 to conjugate wall 38, e.g.
line 50, by 1 and from wall 38 to the conjugate point of tangency on the
caustic, e.g. line 51, by r and the arc length along the caustic by s,
our solution imposes a specific relation between these quantities as
follows
d(1 + r) = ds 3
Integrating Eq. 3 over the profile curve of wall 38, we obtain
##EQU1##
demonstrating that our solution indeed minimizes the absorber perimeter S
consistent with phase space conservation.
The solution shown for FIG. 1 can be readily adapted to a variety of less
restrictive assumptions about the relationship of source to absorber. In
FIG. 2 we have permitted the receiver to be asymmetrically disposed
relative to the source. For this case, the phase space at the entrance
aperture becomes
1/2 .intg. dxdk.sub.x = 1/2[(q - p) + (n - m)] 5
where q is the distance from one edge point 14 to its conjugate wall
termination point 83, p is the distance from edge point 14 to its
nonconjugate wall termination point 82, n is the distance from the other
edge point 16 to its conjugate wall termination point 82 and m is the
distance from edge point 16 to its nonconjugate wall termination point 83.
Eq. 5 is a natural generalization of Eq. 2. To solve the asymmetric
problem, we choose the profile curve of wall 76 so that singly reflected
rays from point 14 form the caustic curve portion 64, as before. Similarly
we choose the profile curve of wall 74 so that singly reflected rays from
point 16 form the same caustic curve portion 64. Let us denote by l and r
the optical path length from point 14 to wall 76, e.g. line 78, and of the
reflected ray from wall 76 to the caustic curve portion 64, e.g. line 79,
and let us denote by l' and r' the optical path length from point 16 to
wall 74, e.g. line 80, and of the reflected ray from wall 74 to the
caustic curve portion 64, e.g. line 81. Then, integrating along wall 76
(with point 16 as origin), we obtain
##EQU2##
Integrating along wall 74 (with point 14 as origin), we obtain
##EQU3##
Therefore, adding Eqs. 6 and 7 we find
S = 1/2[(q - p) + (n - m)] 8
which is the maximal concentration condition required by Eq. 5. Thus the
collector herein disclosed achieves maximal concentration of light from a
source of finite dimension and finite distance from the collector.
An example of the practical application of the principles herein disclosed
is shown in FIG. 3. Here the collector disclosed is used as a secondary
collector. Energy from the sun 90 is initially collected by primary
collector 92, which might be an array of mirrors. The energy incident on
collector 92 is directed to the secondary collector 94. Collector 94 has a
transverse cross section developed with respect to the edge points of
primary source 92 and which is generated along an axis perpendicular to
the cross section to form the trough-like or cylindrical collector. Flat
reflective end walls 96 and 97 fully enclose the collector. Where, as in
FIG. 3, the device is to collect solar radiation, the side walls have a
reflecting material thereon which would reflect substantially all of the
solar energy from primary collector 92, as, for example, aluminum or
silver. Of course, the principles herein disclosed are applicable to any
source of finite dimension and finite distance from the collector. Note
further, that in practical application the collector side walls may be
truncated so that they do not extend all the way to the tangent lines.
However, the contour still will follow the definition herein disclosed.
While the invention has been described in detail as a collector and
concentrator of energy and within an energy receiver, it is not limited to
this form. Any electromagnetic energy transducer, receiver or transmitter
can be used. Thus, if it is desired to transmit energy onto a finite area
of finite distance from the transducer, an energy radiator could be
substituted for the energy receiver.
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