WO1980002604A1

WO1980002604A1 - Solar radiation reflector

Info

Publication number: WO1980002604A1
Application number: PCT/AU1980/000015
Authority: WO
Inventors: C Letham; D Langridge; P Mccormick; J Foi
Original assignee: Solar Energy Res Inst Western; C Letham; D Langridge; P Mccormick; J Foi
Priority date: 1979-05-21
Filing date: 1980-05-19
Publication date: 1980-11-27
Also published as: EP0028623A4; JPS56500546A; EP0028623A1

Abstract

Solar radiation reflector and method of forming the same, where the solar radiation reflector comprises a length of resilient sheet material having a reflective face, said sheet being elastically deformed substantially into the shape of an elastica such that said reflective face is concave by application of opposed inwardly directed forces to the sides thereof, a transparent cover located between the sides, the sides of said cover being adapted to engage and retain the sides of the sheet to counteract the resilient tendency of the sheet to return to its undeformed configuration. The method of forming the solar radiation reflector comprises providing a reflective surface on one face of a substantially rectangular resilient sheet of material applying opposed inwardly directed forces to the sides of the sheet to elastically deform the sheet to a substantially cylindrical elastical shape such that the reflective surface is concave, retaining the sides of the sheet in the deformed condition by the application therebetween of a transparent cover having at its sides means to engage and retain the sides of said sheet to counteract the resilient tendency of the sheet to return to its undeformed configuration.

Description

SOLARRADIATIONREFLECTOR

THIS INVENTION relates to solar radiation collectors and in particular reflector means for use with such collectors.

A large potential for energy conservation using solar energy is the production of medium temperature (80 C-150 C) thermal energy for commercial, industrial and mineral process heating. For there to be any significant realisation of this potential, the availability of low cost cylindrical concentrating collectors is required.

An object of this invention is to provide for a reliable low cost cylindrical reflecting concentrator that would be capable of operating at acceptable efficiencies in the medium temperature range.

A major cost factor with concentrating collectors is the focussing component and it is a further object of the invention to provide a cylindrical reflecting concentrator which uses low-cost, robust materials, and does not require any special tools or processes to form the reflector profile.

The invention is based on the observation that the shape of a piece of sheet material when buckled elastically by the application of equal and opposite compressive forces along opposite sides of the sheet is, for certain deflections, an approximation to a parabola. The name given to the shape formed in this manner is an "elastica" and collectors with reflectors formed in this manner have been called by the inventors cylindrical elastical concentrating collectors.

In one form the invention resides in a solar radiation reflector comprising a length of resilient sheet material having a reflective face, said sheet being elastically deformed substantially into the shape of an elastica such that said reflective face is concave by application of opposed inwardly directed forces to the sides thereof, a transparent cover located between the sides, the sides of said cover being adapted to retain the sides of the sheet to counteract the resilient tendancy of the sheet to return t its undeformed configuration.

In another form the invention resides in a method of formin a solar radiation reflector comprising providing reflective surface on one face of a substantiall rectangular resilient sheet of material, applying oppose inwardly directed forces to the sides of the sheet t elastically deform the sheet to a substantially cylindrica elastical shape such that the reflective face is concave retaining the sides of the sheet in the deformed conditio by the application therebetween of a transparent cove having at its sides means to retain and engage the sides o said sheet to counteract the resilient tendancy of the shee to return to its undeformed configuration.

The invention will be more fully understood in the light o the following description of one specific embodiment. Th description is made with reference to the accompanyin drawings of which:-

Fig. 1 is a perspective view of the reflector accordin to the embodiment; and;

Fig. 2 is a sectional elevation along A-A of Figure 1

:The embodiment is directed to a cylindrical elastica concentrating reflector to be mounted in association with fluid conduit which is to be located at the focus of th reflector. The reflector is formed from a substantiall planar sheet 11 of light gauge galvanised sheet steel havin an aluminized plastic film applied to one face thereof. Th sheet 11 is substantially rectangular in plan and i provided at each side with a flange 17 which is disposed a an acute angle to the sheet 11.

To form the reflector an inward force is applied to eac side of the sheet 11 to cause it to bend to a substantiall elastical configuration. Having achieved the desire elastical configuration the side edges are retained in tha position by means of a transparent cover 13 formed of a acrylic or like material having formed at each side a down turned flange 19 which is intended to receive the flanged edges of the formerly planar sheet 11. The flanges 19 formed at the sides of the acrylic sheet are of a_ corresponding angle to the flanges 17 formed on the steel sheet 11 which is the edge angle of the elastica formed by the deformed sheet such that the flanged edges of the steel sheet 11 are snugly engaged by the flanged edges of the acrylic sheet 13 when the sheet 11 is retained into its elastical configuration. The space defined between the sheet 11 and the transparent sheet 13 is closed at each end by an end plate of corresponding configuration to the cross- sectional configuration of the space. The end plate 15 is provided with a flange 21 along its upper edge to support the end of the transparent acrylic sheet while the curved lower edge of the end plate 15 is formed with a flange 23 to enable it to be fixed to the normally planar sheet 11. The end plates 15 are provided with an aperture 25 located at the focus of the cylindrical elastical reflector which is produced by the deformed sheet 11. The apertures 25 are intended to accomodate an absorber such as a fluid conduit which passes above the reflector along its focus. If desired any other form of suitable absorber such as a set of photo¬ voltaic devices may be installed at the focus of the reflector.

As a result of the embodiment a concentrating reflector is produced which is simple in manufacture requiring very little fixing by means of screws, rivets, welding, soldering or the like and yet is very rigid since the normally planar sheet 11 is retained in the elastical configuration by the transparent sheet 13 and thus is itself in a state of tension as well as inducing a state of tension in the transparent acrylic sheet 13. The presence of the end plates 15 serves in enclosing the space defined between the steel sheet 11 and the transparent sheet 13 and also in providing further reinforcement of the reflector.

To further illustrate the invention a theoretical analysis of the elastica and its application to cylindric concentrating reflection is given below.

Figure 3 illustrates the contour of an elastica elastical buckled by a force P. From a mathematical analysis of t theoretical equations relating to elastica it can be sho that for isotropic materials the elastical contour is function of the edge angle c^— (ref. S.P. Ti eshenko & J. Gere, "Theory of Elastic Stability", McGraw - Hill, New Yo (1961)) and it may be shown that the length AL, and leng YA, of the reflector may be expressed in terms of t aperture XA and the edge angle o as

AL = XA K(P) 2K(P) (

2E(P) - K(P) k

YA = XA sin (CX/2) 2P ( 2E(P) - K(P) k

where .k = —2(ⁱ2E(P) ' - K(—P)—)

and where P = sin (c^/2) and K(P) and E(P) are comple elliptic integrals of the first and second kind respec ively. The coordinates of any point given by

,. _ 2E ( ,P) - 1 K( ,P) ( ^{x ~} k k

2P (1-cosø) ( ^" k

wh .ere si.n

and E ( ,P) and K(0.P) are incomplete elliptic integrals the first and second kind respectively.

OMP Equations (1) to (4) have been utilised to produce reflector contours for edge angles of 40 , 45 , 50 and 55 which are in excellent agreement with experimentally measured contours providing the elastic limit is not exceeded.

Figures 4, 5, 6 and 7 illustrate ray traces for edge angles of 40 , 45 , 50 and 55 respectively. With an edge angle of 40 an excellent focal point is obtained for rays incident on the central 70% of the aperture. Rays incident on the sides of the apertures are not well focussed mainly because the curvature decreases to zero at the edge of the reflector. With increasing edge angle the central focus becomes increasingly dispersed while the side rays are reflected closer to the focus. In addition for edge angles exceeding 41 the focus lies below the reflector edge.

Figure 8 is a graph for reflectors having an edge angle of 40 , 45 and 50 where the normal incidence intercept factor (ie. ratio of the total radiation incident on the aperture to the total radiation incident on the absorber) is plotted as a function of the concentration ratio (ie. ratio of aperture area to the absorber surface area) assuming perfect specular reflection and a parallel incident beam. For low concentration ratios as used in medium temperature collectors, it is apparent that the dispersion of the focus is not important and that high intercept factors are obtained using elastical shaped reflectors. In addition, it can be shown that for such concentration ratios, the accuracy of absorber positioning and edge angle is not critical. With increasing concentration ratio the intercept factor decreases and the intercept factor is greatest at large concentration ratios with an edge angle of 40 because of the sharper focus as illustrated in Figure 4.

In Figure 9, the maximum concentration ratio is shown as a function of the edge angle for a circular absorber assuming an angular acceptance half angle of X = 8.7 m rad (.5 degree). The maximum concentration ratio is seen to be highest at

It is evident from Figures 4 to 7, that an improvement the maximum concentration ratio may be obtained truncating the sides of the reflector in a manner which do not influence the elastica shape of the untruncated porti of the reflector. Since the curvature at any position the profile only depends on the local bending moment, ed truncation may be accomplished by plastically bending up t reflector as indicated by the solid curve in Figure 1

As shown in Figure 10, a truncated reflector may be treat by joining together the relevant sections of two elasti profiles of differing length each buckled by the same for F. The shorter of the two curves is buckled to the requir edge angle, o , while the length of the other curve chosen to give o = 90 and the desired truncation. T total width of the truncated reflector is equal to the s of the length of the central portion of the profile, and t lengths of the sides of the profile 2; X = X, + ZX₂ and t reflector is plastically bent up by the angle Λ at distance X₂ from both edges. In general, o<L may be a angle between c? _ and 90 , however, the following results a

In Figure 11 the effect of edge truncation on the maxim concentration ratio ( £ = 8.7 m rad) is shown for ed angles of 40, 45 and 50 degrees. It is seen that while ed truncation improves the maximum concentration ratio of a of the edge angles considered, the optimum truncation is function of c . For c = 40 edge truncation results in substantial increase in the concentration ratio because the sharp focus obtained for rays incident on the centr portion of the reflector. The maximum concentration rat of 27.4 for oL = 40° and 35% aperture truncation comparable to the maximum concentration ratio of 36.5 for parabolic trough concentrator with a circular absorber (3) and the same value of ζ. .

Further improvement to the maximum concentration ratio edge truncated elastica profiles may be obtained by trj

O tion of the centre. From the ray trace in Figure 12a, it may be seen that the dispersion of the focus is such that the position of maximum concentration of rays from one side of the reflector is not at the centre-line. The maximum- concentration ratio may therefore be increased by displacing the centre-line of the reflector to the effective focal point. This is accomplished by shortening the total width of the reflector by 2 ₁ , as shown in Figure 12a, and plastically bending the reflector along its centre-line by an amount equal to twice the slope, , of the reflector at

In Figure 12b a ray trace for the reflector of Figure 12a with optimum centre truncation is shown. The improvement in the focus resulting from centre truncation is clearly evident. In Figure 13, the effect of centre truncation on the maximum concentration ratio of side truncated reflectors is shown.

In addition to increasing the maximum concentration ratio, centre truncation may be used to define the flux distribution on the receiver for applications, such as photovoltaic concentrators, where uniformity of illumination is important. In Figure 14 the flux distribution of reflected rays incident on a flat receiver is shown for a reflector of c^-= 43 and 30% edge trunction, with (curve b) and without (curve a) centre trunction, assuming an r s beam spread of 5 m rad. It is seen, as discussed previously, that without centre truncation the position of maximum flux density does not coincide with the centre-line of the reflector. Centre trunction effectively translates the intensity peaks together, resulting in a relatively uniform flux distribution on the receiver.

The elastic buckling of a sheet material provides a simple method of forming the reflector for a linear focus concent¬ rating collector. A dispersed focus is obtained with the concentration ratio depending on the edge angle of the reflector, and edge and centre truction. With untrunc.

OMPI reflectors concentration ratios on the order of 6 may obtained. Optimum edge and centre truncation results concentration ratios approaching that of parabolic trou concentrators. In addition, the use of centre truncati allows a degree of freedom in defining the flux distributi at the receiver.

It should be appreciated that the scope of the prese invention need not be limited to the particular scope of t embodiment described above.

OMP

Claims

The Claims defining the invention are as follows :-

1. A solar radiation reflector comprising a length of resilient sheet material having a reflective face, said sheet being elastically deformed substantially into the shape of an elastica such that said reflective face is concave by application of opposed inwardly directed forces to the sides thereof, a transparent cover located between the sides, the sides of said cover being adapted to engage and retain the sides of the sheet to counteract the resilient tendancy of the sheet to return to its undeformed configuration.

2. A solar radiation reflector as claimed at claim 1 wherein the sides of the cover are formed with flanges which are in opposed relation to each other and wherein said flanges engage and retain the sides of said sheet.

3. A solar radiation reflector as claimed at Claim 2 wherein said flanges form an angle to the main body of the cover which substantially corresponds to the edge angle of the elastica.

4. A solar radiation reflector as claimed at anyone of Claims 1, 2 or 3 wherein end plates enclose the space between the ends of the sheet and the cover.

5. A solar radiation reflector as claimed at anyone of the preceeding claims wherein an absorber is located along the line focus of the reflector.

6. A solar radiation reflector as claimed at Claim 5 wherein the absorber comprises a fluid conduit.

7. A solar radiation reflector as claimed at Claim 5 wherein the absorber comprises at least one photovoltaic device.

A solar radiation reflector wherein the edges of the

OMPI sheet are plastically bent along a line spaced from bu parallel with the sides such that the reflector has th combines shape of the elastica formed by the edges and th elastica formed by the central portion of the sheet betwee the edges.

9. A solar radiation reflector as claimed at Claim wherein the edge of the elastica formed by the edges i greater than the edge angle formed by the central portion

10. A solar radiation reflector as claimed at anyone of th preceeding claims wherein the sheet is plastically ben along a central axis parallel with the sides.

11. A solar radiation reflector as claimed at Claim 1 wherein the degree of plastic bending along the central axi is such that the slope of the portion of the reflecto adjacent to and to each side of the central axis is twic the slope of a corresponding undeformed elastica at th point which is located below a focus of the undeforme elastica.

12. A solar radiation reflector substantially as herei described with reference to the accompanying drawings

13. A method of forming a solar radiation reflecto comprising providing a reflective surface on one face of substantially rectangular resilient sheet of materia applying opposed inwardly directed forces to the sides o the sheet to elastically deform the sheet to a substantiall cylindrical elastical shape such that the reflective surfac is concave, retaining the sides of the sheet in the deforme condition by the application therebetween of a transparen cover having at its sides means to engage and retain th sides of said sheet to counteract the resilient tendancy o the sheet to return to its undeformed configuration.

14. A method of forming a solar radiation reflector a claimed at Claim 3 wherein the transparent cover is forme O ~ from a sheet of transparent material said method comprising the step of forming opposed flanges at the side of the cover, wherein said flanges comprise the means to retain and engage the side edges.

15. A method of forming a solar radiation reflector as claimed at claim 14 wherein the flanges are formed at an angle to the cover substantially corresponding to the edge angle of the elastica.

16. A method of forming a solar radiation reflector as claimed at anyone of Claims 13 to 15 wherein prior to elastic deformation of the sheet the edges thereof are bent plastically along a line parallel with the sides of the sheet.

17. A method of forming a solar radiation reflector as claimed at Claim 16 wherein the edge angle of the elastica formed by the edges is greater than the edge angle formed by the central portion of the sheet between the edges.

18. A method of forming a solar radation reflector as claimed at any one of the preceeding claims wherein prior to elastic deformation of the sheet the sheet is bent plastically along a central axis parallel to the sides.

19. A method of forming a solar radiation absorber as claimed at Claim 18 wherein degree of plastic bending at the central axis is such that the slope of the portion of the reflector adjacent to and to each side of the central axis is twice the slope of an undeformed elastica at the point which is located directly below a focus of the undeformed elastica.

20. A method of forming a solar radiation reflector sub-

_ OMPI stantially as herein described with reference to t accompanying drawings .

OMPI