WO2015123788A1

WO2015123788A1 - Solar concentrator

Info

Publication number: WO2015123788A1
Application number: PCT/CH2015/000027
Authority: WO
Inventors: Thomas Cooper
Original assignee: Airlight Energy Ip Sa
Priority date: 2014-02-20
Filing date: 2015-02-20
Publication date: 2015-08-27

Abstract

Disclosed is a non-parabolic concentrator which is designed to achieve the maximum possible concentration C_g for concave collectors with a rim angle Φ and an acceptance angle Θi. A method for producing a concentrator of this type uses a differential function u to determine the concentrator cross-section z(x) in such a way that the maximum geometric concentration C_g can be achieved. In a preferred embodiment, the concentrator according to the invention has circular arc segments.

Description

solar concentrator

The present invention relates to a concentrator according to the preamble of claim 1 and a method for producing such a concentrator according to claim 8.

Solar collectors with concave concentrators are mainly used in solar power plants. These are known to the person skilled in the art, they produce heat which is continuously converted into a recycling unit downstream of the solar field, for example by a turbine arrangement into electricity. On the other hand, the heat can also be used in an industrial process of any kind requiring the supply of heat.

Finally, the solar radiation concentrated by the solar collector can also be used photovoltaically. Then the absorber unit can be equipped with photovoltaic cells.

Today, three basic forms of solar thermal power plants are in use: dish systems, solar tower power plant systems and parabolic trough systems, which generally use single - mirror arrays.

Dish systems are equipped with paraboloid-shaped mirrors that focus the sunlight onto a focal point where a heat receiver is located. The mirrors are rotatably mounted biaxially in order to be able to follow the current position of the sun and have a diameter of a few meters up to 10 m and more, which then achieves powers of up to 50 kW per module. For example, a Sterling engine installed on the heat receiver converts the thermal energy directly into mechanical work, which in turn generates electricity. On the other hand, a photovoltaic module can also be provided at the location of the heat receiver.

Solar tower power plant systems have a central, raised (on the "tower") mounted absorber for hundreds to thousands of individual mirrors with mirrored to him sunlight, so that the radiation energy of the sun over the many mirrors or concentrators in the absorber concentrated and thus temperatures up to 1300 ° C can be achieved, which for the efficiency of the downstream thermal machines (usually a steam or fluid turbine power plant for power generation) is low. California Solar has a capacity of several MW. Parabolic trough power plants have a large number of collectors which have long concentrators with a comparatively small transverse dimension, and thus do not have a focal point but a focal line or a focal line area. These line concentrators today have a length of 20 m to 250 m. In the focal line runs an absorber tube for the concentrated heat, which transports to the power plant. At the location of the absorber tube and a photovoltaic device can be provided. As a transport medium for heat is for example thermal oil or superheated steam in question, or even air. Increasingly, the temperatures achievable in the absorber tube are increased, from 400 ° C now generally to around 500 ° C, with 600 ° C or even more, for example 650 ° C sought and kept realistic in the near future. Higher temperatures than those are important, as this can increase the efficiency in the downstream technical process. Likewise, higher concentrations of light are important for photovoltaic exploitation.

It is conceivable to provide a photovoltaic arrangement at the location of a concentrated heat absorber tube so that either heat, light or both heat and light are removed in the absorber area, depending on the technology used.

Parabolic trough power plants are becoming increasingly popular, with heat produced to varying degrees, for example the Martin Next Generation Solar Energy Center in Florida, which delivered 89Ό00 MWh of solar energy in 2012.

The pa rabeiförmige cross section of the solar panels is basically suitable to deliver high concentrations (which, as also mentioned, are also desirable or necessary in photovoltaic applications) and thus also the desired, above-mentioned higher temperatures in the absorber area.

However, high concentrations are difficult to achieve for two reasons: On the one hand, the radius of the solar disk of 0.27 ° (opening angle seen from Earth) is highly limiting: in fact, the sun's rays do not fall parallel to it, but spread over an angle of 0.54 ° on a concentrator. Calculated for an ideal concentrator, this results in a maximum theoretical concentration of 212 for a concentric to a line concentrator and 45032 for a concentrator without symmetrical restrictions. Then it is always the case that the physical realization of a theoretical concept hardly ever reaches even the theoretically possible performance - certainly not when expensive expensive custom-made products have to be avoided, but rather the effort in a reasonable, ie industrially competitive (ie, for example, free from subsidies). This is especially true for the production of an exact parabolic concentrator with, for example, the above dimensions (width 10 m, length 250 m).

For this reason, despite the ever-intensive technical development, channel concentrators with a geometric concentration of more than 60 (with an acceptance angle of 0.27 °) are still technically demanding and correspondingly expensive to produce.

A real concentrator with high concentration (in the following statements, the geometric concentration C _g is always meant), but at the same time can be produced at relatively low cost, is proposed in WO 2010/037243. There, it is disclosed to approximate the parabolic cross-section of a target concentrator by spherical or arcuate, adjacent segments of a reflective membrane, which allows to achieve the desired, higher concentrations by a comparatively favorable construction. However, the approximation of the parabolic shape by spherical segments leads inter alia to spherical aberration, ie to a deterioration compared to the concentration which can be achieved per se by a parabola.

Accordingly, it is the object of the present invention to provide a concentrator for a solar collector, which at realistic costs in industrial use (for example, production in large quantities or with large dimensions), but also in small or very small applications, still further improved concentration allowed.

This object is achieved by a concentrator having the characterizing features of claim 1 and by a method for producing such a concentrator. The fact that the concentrator is not parabolic, opens the way to a more easily realizable shaping. The fact that the geometric concentration of the concentrator corresponds to that of its reference parabola results in a concentrator which can achieve the thermodynamic limit for a given one-mirror system. By using the differential inequalities of the firing range, a method for producing such a concentrator results, with which, inter alia, for the production optimized forms of the concentrator can be realized. The invention is explained below with reference to the figures.

It shows:

FIG. 1 a schematically shows a conventional trough collector with a pressure-loaded concentrator membrane,

FIG. 1b shows a cross section through the concentrator arrangement for a single-reflector solar collector according to the prior art, with parabolic cross-section FIG. 2a shows a cross-section through a concentration arrangement with a flat absorber,

2b shows a cross section through a concentration arrangement with a round absorber,

FIG. 3 a shows a diagram for the embodiment of the concentrator according to the invention with a rim angle Φ = 60 ° and an acceptance angle 9 _in = 5 ° for a flat absorber concentration arrangement. FIG. 3 b shows a diagram of the slope of the concentrator of FIG.

FIG. 3c shows a diagram of the differential function u of the focal region of the concentrator of FIG. 3a, FIG. 4 a shows a diagram for the embodiment of the concentrator according to the invention with a rim angle Φ = 90 ° and an acceptance angle θ, _η = 5 ° for a concentrator arrangement with a round absorber,

FIG. 4b shows a diagram of the slope of the concentrator of FIG. 4a,

FIG. 4c shows a diagram of the differential function u of the focal zone of the concentrator of FIG. 4a,

FIG. 5 shows a diagram for the embodiment of the concentrator having a plurality of arcuate segments according to the invention with a rim angle Φ = 60 ° and an acceptance angle O _in = 0.5 ° for a flat absorber concentration arrangement,

Figure la shows a solar collector 1 (which is designed here as a trough collector) according to the prior art, as it has been disclosed by WO 2008/037108. The solar collector 1 has a pressure cell 2, which has the shape of a cushion and is formed by an upper, flexible membrane 3 and a hidden in the figure, lower flexible membrane 4. Via a fluid channel 5, the pressure cell 2 is maintained under operating pressure, wherein further a fluid channel 6 is provided, the function of which is described in more detail with reference to Figure lb and the expert from WO 2008/037108 known.

The membrane 3 is permeable to sun rays 7, which fall inside the pressure cell 2 onto a concentrator membrane (for example a concentrator membrane 15 according to FIG. 1b or a simple, unsupported membrane) and are reflected by these as jets 7 ' to an absorber tube 9, in which a heat-transporting medium circulates and dissipates the heat concentrated by the collector. As mentioned above, it is also possible, for example, to form the absorber tube as a holder for photovoltaic cells. The absorber tube 9 is held by supports 10 in the focal line region of the concentrator membrane 8.

The pressure cell 2 is clamped in a frame 11, which in turn is mounted according to the position of the sun pivotally mounted on a frame. Frame and frame as such are known to the person skilled in the art and will be removed in the following figures for the purpose of relief. let or only schematically indicated. The FIGURE shows a one-mirror system with a concentration arrangement which has a concentrator, namely the concentrator membrane 15 and a round absorber, here an absorber tube 9.

1 b shows a cross-section through a further one-reflection concentration arrangement for a trough solar collector according to the prior art of the type shown in FIG. 1 a, wherein, however, the concentrator according to the invention of WO 2010/037243 is formed:

A concentrator membrane 15 is clamped under pressure in a pressure cell 16 during operation, wherein the operating pressure for the concentrator membrane 15 and for this associated clamping membrane 15 ', 15 "by a series of preferably designed as fans fluid pumps 16 to 19 is generated. Membrane 15 concentrates solar radiation 7, 7 'on an absorber tube 20, which is functionally designed as a flat absorber because of its slot-shaped thermal opening 24. Due to its special clamping and segmental support by clamping diaphragm 15', 15 ", the concentrator Membrane 15 arcuately curved, juxtaposed segments 21 to 23, which emulate a parabola, each of the segments rays concentrated in a focal line area, but coincide the focal line areas due to the simulated parabolic shape at the location of the absorber tube 20. The concentrator membrane 15 extends continuously through the segments 21 to 23 and is, as mentioned, in segments on a clamping membrane, in the segment 23 on the two clamping membrane 15 ', 15 ", in the segment 22 on a clamping membrane 15', in the segment 21, it is guided freely without it resting on a tensioning membrane The person skilled in the art knows the structure of this arrangement from WO 2010/037243.

It should be added that a pressure-loaded membrane does not form exactly spherical or arcuate, but only almost, wherein the assumed shape for rotationally symmetric membrane by the Henky - function is described. Although the Henky function shows a slightly greater deflection in the edge zones and somewhat weaker center deflection, the term "circular arc" is always used in the present description because the deviation of a circular arc from, for example, the Henky function, in particular Is negligible with respect to the geometric concentration of an on - mirror concentrator. Figure 2a shows schematically the geometric relationships in a concentration arrangement 25 with a flat absorber 26, wherein to relieve the figure, only the right side 27 of a concave concentrator 28 and a part of the left side 29 of the concentrator and from the concentrator 28 illuminated from below, flat Absorber surface 30 is shown. An axis of symmetry 31 divides the right, illustrated half 27 of the concentrator and the left, not shown half 28 and lies on the optical axis of the concentrator 28. The absorber 26 shadows a portion 32 of the right 27 and left side 29 of the concentrator 28, the is indicated approximately by the dashed lines.

In operation, the concentrator assembly 25 is oriented such that central beams 32 from the center of the sun 33 (or parallel beams) parallel to the axis of symmetry 31, i. paraxial, incident on the concentrator 28. Edge rays 34,34 'of the sun fall with respect to the central rays 32 at the acceptance angle Θ, a. The acceptance angle Θ is determined by the person skilled in the art for the design of the concentrator in a specific case, it may for example be 0.27 °, which corresponds to the radius of the solar disk, or be chosen larger, if radiation from the corona of the sun also with should be detected, or if errors in alignment or other geometrical deviations are to be considered.

A coordinate system with the horizontal axis x and the vertical axis z has its origin on the absorber surface 30. The concentrator has a general, concave cross section, which is described by the function z of the concentrator cross section. The outermost point P _{0 of} the concentrator has the coordinates (x ₀ , -z ₀ ), a central ray 32 incident there is reflected into the point Q on the absorber surface 30, which due to the general function z does not lie on the axis of symmetry 31 either can. The edge beams 34, 34 'incident in the point Q.sub.i are reflected in the points A and B on the absorber surface 30, respectively. The rim angle Φ denotes the angle between the central ray 32 reflected from P ₀ to the point O. The rim angle Φ is used to determine the aperture width a, for a given function z.

With regard to the geometric concentration C _{g of} the concentrator, the figure also shows that this is determined by Θ, and Φ: Θ, the cone of the reflected rays, starting from the outermost point P ₀ , Φ, again determines the slope of the function z im Point P ₀ , which determines the direction of the cone. If P _{0 is} varied, the width of the absorber surface 30 also changes. Since the geometric concentration C _{g is} defined as the ratio of the aperture width a to the width of the absorber a ₀ , in the variation of P ₀ (always given a Φ), the concentration C _g remains constant. The geometric concentration C _g remains the same if the system is enlarged or reduced by uniform stretching (geometric similarity)

The rim angle Φ and the acceptance angle Θ are thus the two parameters which characterize a concentration arrangement 25 with regard to the geometric concentration C _g . C _g is described here by the half-concentrator with the corresponding absorber surface a ₀ = 1 and the aperture width aj of 1 to x ₀ , the shaded area of the concentrator extending from x = 0 to x = 1.

The choice of a ₀ = 1 is made because of the simplicity of the equations discussed below. There is no loss of general validity, as the resulting construction is stretchable to any size.

FIG. 2b shows a cross-section through a concentration arrangement 40 which corresponds to the concentration arrangement of FIG. 2a, with the exception of the here round absorber 41, which has the radius r ₀ . In addition to FIG. 2a, in a general point of the function z of the concentrator cross-section, the slope m = z 'of the function z is plotted, wherein the perpendicular 42 encloses the running angle φ with a central ray 32 on a tangent to the curve z (x) , FIGS. 2 a and 2 b show cross sections through channel concentrators (2D concentrators), with a rotation about the axis of symmetry 31 resulting in dish concentrators (3D concentrators), which are likewise in accordance with the invention.

For the arrangements with a flat or with a round absorber can be stated:

Starting from the general equation for the thermodynamic limit of an ideal concentrator (conservation of etendue) ideaUD = «A = sin 0 _o / sin0 _i , (1) where 8j denotes the acceptance angle and θ ₀ the maximum angle of the radiation at the exit of the ideal concentrator. (It should be noted that in the case of a dishconcentrator, ie a 3D concentrator instead of a trough (ie 2D) concentrator, the relation A, / A ₀ = sin ² 0 _o / sin ² Oj applies, where A, and A _{0 are} the projected incidence and exit areas ·)

For a flat absorber applies

-a ₀ (cos (20) + cos (2ej)) / sin (29i)), which represents the maximum possible concentration of an arrangement 25 according to FIG. 2a (where a ₀ = 1 and a, corresponds to the x-coordinate of P ₀ ) gives:

^C g, _m ax, 2D, concave, flat = «i /« o = ^{sin Φ C0S Φ} / ( ^{Sm 'C0S} ) ^" (2)

For a round absorber applies

r _o cos <D / sin0i), which gives the maximum possible concentration of an array 40 (FIG. 2b):

^C g, max, 2D, concave, circular = * i / O ₀ ) = Slll Φ / Ο SU1 θ _{ ). (3)

The equations (2) and (3) thus show the respective limit for the geometric concentration C _g , taking into account the parameters Φ and 8j for concave concentrators. The maximum concentration according to equations (2), (3) is always smaller than that of (1).

With the relationship Α ·, / Α ₀ = sin ² 9 _o / sin ² 0i for dish concentrators (3D concentrators) mentioned _above , the equations for the dish concentrators (3D concentrators) can be compared to (2) and (3) ) are set up. In the present case, however, only embodiments with 2D concentrators are described, although, as mentioned above, 3D concentrators can also be designed according to the invention.

It should be noted here that the geometric concentration differs according to the configuration of the absorber: equation (2) describes this for a flat absorber, equation (3) for a round absorber. In addition, of course, many different forms of absorber are conceivable, which determines the expert in the specific case. Then the equations equivalent to (2) and (3) have to be set up, which the person skilled in the art will be able to do analogously to the above equation. showed way for the flat and the round concentrator can do. This also applies to the differential function u of the combustion region described below and its application for the determination of a function z of the concentrator cross section according to the invention. As a result, a concave concentrator for a trough collector with a flat (or round) absorber surface is described herein as preferred embodiments, wherein, as mentioned, the invention also includes 3D concentrators and, for both, all imaginable embodiments of the absorber (ie not only flat or round ).

The function z of the concentrator cross section can now be determined according to the invention such that a corresponding concentrator can be produced in a simplified manner but nevertheless reaches the limit of equations (2) or (3) - or their equivalent equations for other embodiments of the absorber - which means in that a concentrator which can be produced in a simplified manner (or for other reasons with a different cross-section) can be optimally concentrated, ie not further improved with regard to the geometric concentration C _g .

Above, the geometric concentration C _{g has been determined} by means of the point P ₀ , ie without making sure that the concentrator over its entire reflecting surface, here in the interval [1, Xo], actually all in the range between ± Q, incident rays within 2a ₀ (Figures 2a and 2b) concentrated on the absorber. But this is an implicit condition of etendue according to equation (1).

The profile of the concentrator can be indicated by its slope or the angle φ = arctg (z ') in a running point P on z (x), s. Figure 2b, where then the equation of the reflected beam is: ΐ (φ, ί θ) = ν (φ) + ν (φ) ΐ. (4) where Ρ (χ (φ), ζ (φ)) is the point at which the steel strikes the concentrator, and ν (φ) = (- sin (2 <p-9), cos (2 <p -6)) is the unit vector of the reflected beam, and t is the parameter for the distance traveled by the reflected beam.

For a flat absorber (2a) applies the reflected beam at point X _fla t (u, 0) on this on. In this case, u denotes the value for the x coordinate of the point of impact of the reflected beam on the absorber. Solving equation (4) with X _flat results in u: u ((p; 9) = χ (φ) + ίΒϊΐ (2φ-θ) ζ (φ) as a parametric form, and by substituting arctg (z ') for φ, z'(z'sin6 ^l + 2cos6 ^l ) -sin6 ^l

^M nat \ ^x > v) - ^{x ~ z ~} rr ^~ , ^ -. _^ - · as non-parametric form (5b) z (z cos # -2sin #) - cos # of a function u of the focal area.

For a round absorber (FIG. 2b), correspondingly by solving equation (4) with X _circ (ucoso), usinu)), taking into account that the smallest absorber radius u results when the reflected beam impinges tangentially on the round absorber (then is ω = 2φ-θ):

^M _«rc (<P>^' θ) = ^χ (<Ρ) cos (2 <p-θ) + ^ζ (φ) sin (2 ^ - θ) parametric form (6a)

u ci ■ rc (χ; θ) = | [.τ - ζ '{χζ' - 2 /)] cos θ

non-parametric form (6b)

- [ζ - ζ '(ζζ' + 2x)] sin θ] / (I + ζ ' ² ).

(The angle ω is limited to [0, π], so that u assumes values in the range -1 <u <1, as is the case with the flat absorber, see the description below).

It follows:

The differential function u of the focal region describes the location at which a beam incident on the general point P at an angle Θ in the concentrator z is reflected onto the absorber. In this case, "concentrator z" means a concentrator whose cross section is formed according to the general function z (x). If all the values of u for x = 1 to x ₀ of z (x) in the interval -1 <u <1 are followed, then all beams of our concentrator z according to FIGS. 2a and 2b are reflected onto the absorber shown there and additionally the smallest possible Absorber, so maximum geometric concentration C _g is present. The latter results from equations (2) and (3), which have been set up with u _max = ± 1 (FIGS. 2 a and 2 b).

Thus, for maximum geometric concentration C _g , the following system of differential inequalities applies in general:

It should also be noted that the differential function u naturally looks different for each embodiment of the absorber; for a flat absorber, the equations (5a, 5b) apply to μ and the equations (6a, 6b) for a round absorber, for further embodiments of the concentrator established equations for u.

If a function z for the concentrator profile satisfies the differential inequalities (7), it follows that each beam reflected by the corresponding (to P ₀ reaching) concentrator hits the absorber such that the point of impact is within the maximum geometric concentration range C _g .

This results in a method for producing a concave concentrator in which from predetermined values for the acceptance angle Θ, and the rim angle Φ a function z of the concentrator cross-section is determined such that z satisfies the differential inequalities (7) for a function u of the combustion region, and that the concentrator of the function z is formed corresponding to a desired value for a.

The differential inequalities (7) are abstract and do not show what a function z fulfilling this function looks like. Presumably, the parabola is a solution. For the corresponding assumption (the function z is a parabola), it follows from the geometry of FIG. 2a that its focal length f = ₀ cot <I>) and the focal point of which is the coordinates F (0, z ₀ + x ₀ cot <D) having. This determines the parabola and can be recorded: FIG. 3 a shows a diagram with cross-sections of flat concentrators, in which the parabola assumed above is plotted as a function z _Pb for Φ = 60 ° and Θρ5 °, at the same time the extreme right solution z _R and the extreme left solution z _L are plotted Differential inequalities (7), namely those functions z _R and z _L , which are a solution if the differential inequalities u as differential equations

1 and u (x; -θ,) = -1. A concentrator profile according to a general function z can correspondingly only reflect all the rays within the acceptance angle onto the absorber if z lies within the region B spanned by z _R and z _L , ie does not break it. If z lies in the region B, ie within z _R , z _L , the reflection of all rays within the acceptance angle to the absorber is possible, but not mandatory. For the time being, the result is that the parabola can be a solution of the differential inequalities (7) and thus enable maximum geometric concentration C _g , as long as it captures all the rays within the acceptance angle for the absorber. FIG. 3 b shows a diagram with the slopes z 'of the functions z _Pb , z _R and z _L , of FIG. 3 a, ie in turn for a concave concentrator with the parameters Φ = 60 ° and θ, = 5 °. Registered are the functions z ' _Pb , z' _R and z ' _L,.

The Applicant has found (see the description below) that each function z whose derivative z 'lies in the region B' spanned by z ' _R and z' _{L represents} a solution of the differential inequalities (7), e.g.

It turns out that a concentrator function z for maximum geometric concentration C _g can be found by computationally determining a function z 'in the interval graphically or from z' _R and z ' _L and then numerically or, if possible, analytically integrated. (It should be noted that a function z whose derivative z 'leaves the interval P may still be a solution to the differential inequalities.)

Furthermore, a method results from the above, wherein for determining the function z the two extreme solutions of the differential inequalities for the function u for the predetermined values of the acceptance angle Θ and of the rim angle Φ (u with z '(x ₀ ) = tan (l / 2 <t>)) and from this the two extreme solutions for z 'are determined, and in the interval formed by them a specific solution for the function z' selected and by integration as a function z for the formation of the concentrator is used. Of course, it is also possible to check whether a function (assumed on whatever basis) z describes a concentrator cross-section for maximum geometric concentration. Then a possible function z is assumed and equation (7) is used to determine if all rays are reflected on the absorber. If Equation (7) is satisfied, the concentrator reflects all the rays onto the concentrator, thus reaching the maximum concentration.

Since the derivative z ' _{Pb of} the parabola lies in region B', the presumed parabola is also a solution of equations (7) and allows maximum geometric concentration C _g . In addition, there are thus infinitely many non-parabolic concentrator cross sections z (x) with maximum geometric concentration C _g , which can be determined according to the previous section. This further shows that the parabola can serve as a reference for whether a non-parabolic function z describes a concentrator cross-section with maximum geometric concentration C _g . The parabola allows maximum geometric concentration - if a general concentrator concentrates equally well in comparison, it is a concentrator according to the invention. Of course, the comparison must be an equivalent to the general concentrator, ie the parabola referred to here as the "reference parabola", which can simply be determined from the geometry of the general concentrator. First, its rim angle Φ can be measured and an acceptance angle Θ, known for this (or simply assumed), can be determined. Thus, the reference parabola is determined, preferably this can be assumed with the same aperture width a.

Then it is further to determine the known or an assumed absorber for the general concentrator, since the formation of the absorber affects the geometric concentration C _g . Thus, the geometric concentration C _{g of} the reference parabola can be determined - if the geometric concentration C _{g of} the general concentrator z is equal to or essentially the same (for example manufacturing tolerances), the general concentrator z is a concentrator according to the invention. It is immaterial which absorber or which acceptance angle Q _{t is} possibly accepted - the only essential is that they are then also used for the reference parabola. This comparison can be much simpler than the analysis of whether a generally shaped concave concentrator satisfies the differential inequalities (7). In addition, the reference parabola can be easily determined from the structure of a general concentrator z, and thus (possibly assuming an equal absorber and acceptance angle θ,) of its geometric concentration C _g .

It can be seen that a concave concentrator according to the invention is characterized in that it is not parabolic, but designed such that in operation its geometric concentration C _g essentially corresponds to that of its reference parabola with absorber of the same design, which with the concave concentrator is parallel to the axis incident central rays of the sun has the acceptance angle Θ, and the rim angle Φ in common.

A further check as to whether a function (assumed on whatever basis) z describes a concentrator cross-section z for maximum geometric concentration is shown in FIG. 3c, which shows a diagram on whose horizontal axis the span x of the concentrator with the concentrator cross-section z (FIG. x) and on whose horizontal axis the values for the differential function u of the combustion region are plotted.

As mentioned above, for a given function z, the extreme solutions z _R and z _L can be solved by solving u for u (x; 9,) = 1 and u (x; -θ,) = -1 in the interval up to x ₀ ( that is, to point P ₀ at the outer edge of the concentrator). These extreme solutions z _R and z _L must not exceed the values of -1 <u <1 for our assumed function z to be checked, otherwise the differential inequalities (7) would not be satisfied, ie the assumed function z would describe a concentrator that does not allow maximum geometric concentration. Conversely, a concentrator with a cross-section of a general function z allows maximum geometric concentration when the extreme solutions z _R and z _{L are} in the ranges B _g , that is, do not exceed the values of -1 <u <1. The result is an (analytical or numerical) method in which a possible function z (on whatever basis) is assumed and checked whether an extreme solution of the differential function u formed in z leaves the validity range B _g , in which case z is rejected, otherwise but is used to form the concentrator.

The diagrams of FIGS. 4a to 4c show for the sake of completeness analogous to FIGS. 3a to 3c the regions B, B 'and B _u for the parameter values Φ = 60 ° and θ _ί = 5 ° of a concave concentrator _comprising a round absorber 90 according to FIG Figure 2b illuminated. Again, there is a parabola z _Pb that has its focal point in the origin. which is a solution of the differential inequalities (7) and extreme solutions z _R and z _L , which are based on equations (6a) and (6b). For the focal length of the parabola z _Pb , f =

As is the case with the flat absorber, the extreme solutions z _R and z _{L can be given} by the equation u (x,

are determined, where, as mentioned, u is now determined by the equations (6). The resulting concentrator functions z (x) reflect + Θ, and - _{ί ί} marginal rays such that they always run tangentially to the top and bottom of the round absorber.

It should also be noted that for a flat absorber, the extreme solutions z _R and z _{L describe} a tilted parabola whose focal point lies at points A and B (FIGS. 2 a and 2 b). The left extreme solution z _L is found by solving u (x, -θ,) + 1 = 0 by transforming the second inequality of (7) into an equation. The resulting curve is a parabola with the focal point in B whose axis is parallel to the - Θ, rays. The same applies to the extreme right solution z _R , where a parabola with the focal point in A results, the axis of which is parallel to the + Θ rays.

For a favorable production of a concentrator according to the invention, it is possible to form it at least partially from circular-arc-shaped segments (or essentially circular-arc-shaped segments with regard to the Henky function, see above).

FIG. 5 shows a two-part diagram (parts (a) and (b)) for the formation of a concentrator 100 according to the invention and having a plurality of arcuate segments a rim angle Φ = 60 ° and an acceptance angle 6 _in = 0.5 ° for a concentration arrangement with a flat, schematically illustrated absorber 101. The concentrator 100 is shown in cross section (part (a)), which is represented by a function z (x) is described. The concentrator 100 is formed by arcuate segments 101, 102 and 103 bounded by the outermost point P ₀ and the points Ni, N ₂ and the innermost point N ₃ . Two adjacent segments have a common point Νχ or N ₂ . Generally speaking there are j segments, where j = 1 to N, where 1 denotes the outermost segment, here the segment 101 starting at P ₀ . A point on the jth segment can be found by

QO) = C, + r, (sin φ, - cos φ), (13) where rj denotes the radius of curvature and Cj (Cx, j, Cz, j) the center of the jth segment and φ serves as a parameter, a maximum value at the outer endpoint <p _ouW and a minimum value at the inner endpoint φ, _α; accepts. The endpoints of each segment are the points N _j , for which in turn:

is.

Since equation (13) represents the curve z (x) of an arcuate segment of the concentrator to be determined, (13) can be used in equation (5), with the following for the jth segment:

* sc (ψ \ Θ) = C _X + r. sin φ + tan (<p-20) (C _zj - η cos φ)

+ tan (<- 2Θ) [Ν _Ζ ._, - r _} (cos φ - cos φ _] _)].

This means that a separate function z of the concentrator cross-section (equation (13)) has been formed for the j-th segment, which of course can also be done for the other segments of the concentrator, so that according to the invention there is a method in which preferred the function z is formed from a plurality of functions z _N for a respective subarea B _{N of} the area B (diagram (b) of FIG. 5). Particularly preferred here is at least one function z _N a circle equation, s. Equation (13).

Now it is desirable to provide as few segments as possible, and of course the differential inequalities (7) must be satisfied for maximum geometric concentration C _{g to be} present. As mentioned above, this calculation starts at point P ₀ , ie at x = x ₀ , and works to the left at x = 1. The outer point of the first segment is N ₀ = P ₀ , the slope is there. The radius of curvature of the first segment 101 is chosen such that the function u of the focal region has a maximum for the + Θ, edge ray 104 according to Equation (14) u = 1, as can be seen in the figure in part (b) of the diagram. Since ri is now determined, it is the first segment 101 as well, as soon as the value φΐη, ι · is selected for its parameter cp. For the minimum number of segments, the segment 101 should extend as far as possible, but must not violate the differential inequality (7). This is ensured by choosing <p _in i SO such that u _f | _Ati As (<Pin, i, - 9 = -1 is not violated, ie the - θ | marginal ray 105 does not exceed the value for u = -1, so that the first segment 101 is defined.

Since the adjacent segments 101, 102 and 103 are to have a common point and the same slope in this, it follows that

Thus, the procedure described above for the second segment 102 can be repeated, since the location and slope of the first point _{x are} known and from there the radius of curvature r ₂ can again be chosen such that the maximum value for u _f | _atiS egment (<Pout i, + θ,) = 1 (edge ray 104 in the 2nd segment) is, as shown in part (b) of the figure, where in the 2nd segment the u value for the + θ _ί edge ray 104 assumes the amount 1, but does not exceed. Then the inner value <ρ _{/ Πι2 of} the parameter cp of the 2nd segment is determined via Ufi _{at | Segment} ((p _{/ n 2} , - θ,) = - 1, resulting in the point N ₂ Segments is determined until a segment crosses the x coordinate x = 1, ie the concentrator is completely determined, and the index j at this location gives the number of segments, where N = 3.

The segments 101 to 103 extend from x = 1 to x ₀ , the construction satisfies the differential inequalities (7), with the result that the concentrator consisting of the arcuate segments 101 to 103 allows the maximum geometric concentration C _g . As a result, by the method according to the invention, the subrange B _N for the function z _{N is} bounded by the location where the derivative function u based on the function z _N leaves the range B bounded by u = + 1 and u = -1, as in the diagram (b) can be seen from Figure 5. Since u = +1 and u = -1 are the two extreme values for u, it is generally the case that the subrange B _N for the function z _{N is} bounded by the location where the functions On the basis of z _N , the differential function u leaves the region B formed by the two extreme solutions of the function u (where u is placed here for the predetermined values of ± Θ, and Φ). In this case, the expansion of the subarea B _{N is} maximized by optimizing at least one parameter of the function z _N accordingly. In the case of the arcuate segments, this is done by optimizing the radius of curvature of the circle equation, in the case of another desired contour, the skilled person can identify and adapt the analog parameter.

In summary, it is preferable that a first function z _{x is} assumed starting at the outermost point P ₀ and the first area B _{1 is} bounded by the location where the function z _x leaves the limits of the differential function u and in the subsequent interval h for the function z ₂ the slope of Zi is taken over at the location of the common point of the functions Zi and z ₂ , and so on, until the entire interval I has passed. In the illustrated embodiment, the minimum number of arcuate segments is realized. Of course, a larger number of segments can be provided, depending on the needs in the specific case. Likewise, another contour of the segments can be provided by substituting the parameters for the other contour in equation (5) instead of the elements for one circle (radius of curvature and center of the circle) and then determining the concentrator function z analogously to the method described above becomes. This also makes it possible to provide one (or more) planar segments, or possibly even a convex one, always so far, and arranged and designed so that the differential inequalities (7) remain satisfied.

The points N] can also be shifted, for example when the last, innermost segment extends inwards over the coordinate x =. Then it is conceivable to "drive back" with the innermost segment towards the outside, maximally until its inner point i _{nj is} at location x = 1, and accordingly also to retract the subsequent outer segments or to shorten one of these segments. Since the differential inequalities (7) are still satisfied, this flexibility has no influence on the concentration C _g . Preferably, the arcuate segments (or at least one) are formed by a reflective, flexible pressure-loaded membrane in operation, analogous to the configuration of Figure lb. More preferably, then the reflective membrane extends over several segments of the concentrator, s. also Figure lb. The required radius of curvature may be adjusted by one skilled in the art as follows:

The curvature of a pressurized membrane is described by the relationship T ₀ = PoRo known to those skilled in the art. T ₀ is the line voltage (N / m, ie the force acting per m membrane length at the edge of the membrane as a result of its clamping into it), whereby the thickness of the membrane does not matter). p ₀ is the pressure on the membrane, the (arcuate) curvature causing (difference) pressure and R ₀ the resulting radius of curvature of the membrane. At a given pressure p ₀ , therefore, the length of the radius of curvature R _{0 can be} adjusted via the variation of the line tension T ₀ , ie the force with which the membrane is prestressed or unclamped.

The concentrator according to the invention therefore preferably has the following structural elements which the person skilled in the art can suitably combine:

¹¹¹ The concentrator has at least one essentially arcuate segment,

* The concentrator consists of essentially arcuate segments,

* The concentrator has at least one substantially planar segment,

^■ The concentrator has a reflective, flexible, pressure-loaded during operation membrane preferably extends over a plurality of segments of the concentrator,

^■ The reflective membrane of the concentrator is placed in segments on other membranes, such that the segments have a different curvature.

Claims

claims

1. Concave concentrator (28, 100), characterized in that it is not parabolic, but designed such that in operation its geometric concentration C _g substantially those of its reference parabola with the same trained absorber

(26, 40, 90), which has the acceptance angle θ _in and the rim angle Φ in common with the concave concentrator (100) for axially parallel incident central rays (32) of the sun (33).

2. concave concentrator according to claim 1, wherein it has at least one substantially circular arc-shaped segment (101,102,103).

3. concave concentrator (100) according to claim 1, wherein it consists of substantially circular arc-shaped segments (101,102,103).

A concave concentrator according to claim 1, wherein it has at least one substantially planar segment.

5. concave concentrator according to claim 1, wherein this is designed as a dish concentrator.

6. concave concentrator (100), wherein this has a reflective, flexible, pressure-loaded in operation membrane, which preferably extends over several segments te (101,102,103) of the concentrator.

7. concave concentrator (100) according to claim 6, wherein the reflective membrane rests in segments on other membranes, such that the segments (101,102,103) have a different curvature.

8. A method for producing a concave concentrator (28, 100) according to claim 1, characterized in that from predetermined values for the acceptance angle Θ, and the rim angle Φ a function z of the concentrator cross section is determined such that z the differential inequalities for a function u of the firing area, and that the concentrator (28, 100) of the function z is formed corresponding to a desired value of ai.

9. The method of claim 8, wherein for determining the function z, the two extreme solutions of the differential inequalities for the function u for the predetermined values of the acceptance angle θι and the rim angles Φ and therefrom the two extreme solutions for z 'are determined, and in the a specific solution for the function z 'is selected through this formed region B' and used by integration as a function z for the formation of the concentrator.

10. The method according to claim 8, wherein a possible function z is assumed and it is checked whether an extreme solution of the differential function u formed from z leaves the validity range B _G , in which case z is rejected, but otherwise used to form the concentrator.

A method according to claim 8, wherein a possible function z is assumed to form its derivative z 'and to write it to the region B' determined from the extreme solutions of z 'given in turn by the extreme solutions to the differential function u are, where the possible function z is discarded when its derivative z 'leaves this area.

12. The method of claim 8, wherein the function z is formed of a plurality of functions z _N for a respective portion B _{N of} the area B.

13. The method of claim 12, wherein the subrange B _N for the function z _{N is} bounded by the location where the function u based on the function z _N comprises the range B formed from the two extreme solutions of the function u for the predetermined ones Values of ± 9, and Φ leaves.

14. The method of claim 12, wherein the extent of the portion B _{N is} maximized by optimizing at least one parameter of the function z _N accordingly.

15. The method of claim 12, wherein at least one function z _{N is} a circle equation.

16. The method of claim 14 and 15, wherein for maximizing the portion B _{N of} the radius of curvature of the circle equation is optimized.

17. Method according to claim 12, wherein a first function Zi is assumed starting at the outermost point P ₀ and its first region B i is bounded by the location where the

Function r _x leaves the range of the two extreme solutions of the differential function u, and in the subsequent interval l ₂ for the function z ₂ the slope of z _x at the location of the common point of the functions z _x and z _{2 is} adopted, and so on until the entire interval I has passed.