A new XX SMS concentrator

manufacture and operate in large sizes. Therefore the usual approach is to take ad-vantage of the low aspect ratio (lowf-number) values of focusing primary optics and use second stage concentration at the receiver, to increase the overall concentration value.

However, these second stage solutions introduce some limitations of their own.

Some will produce reflectors that touch the absorber which will result in thermal losses (thermal short circuits) and others, designed to accommodate a gap between the second stage reflectors and the absorber, will have the so called optical gap losses (“etendue” is lost) [7].

Another inconvenience results from transmission losses (Fresnel losses) from the glass envelope of the evacuated tubular receiver and still another from shading losses produced by the secondary on the primary mirror.

One particular limitation comes from the fact that primary and secondary con-centrators tend to have smaller rim angles (ϕ) resulting in a total system with a larger aspect ratio.

In this paper we propose a solution with second-stage concentration overcoming all of these different drawbacks. The solution is based on a method called Simulta-neous Multiple Surface (SMS) method, using reflective surfaces (hence the initials XX). The paper explains why, and presents the basic characteristics of the new op-tic, formed by a primary and a secondary concentrator. Next it evaluates its merits through two comparisons with conventional PT optics. The first is made with direct raytracing results and the second with a calculation of energy delivered by the new concept and the conventional one.

6.2 A new XX SMS concentrator

6.2.1 The XX SMS concentrator solution

Many possible solutions exist with second stage concentration. For instance in [11, 12] proposals were made for second stage optics with multiple second stage reflectors which in theory might be fitted inside a glass envelope. However these were not practical solutions for evacuated tubes and suffer from the fact that, particularly under vacuum, the energy absorbed (not reflected) might induce a self-destroying temperature increase effect, at least if conventional materials were used for their manufacture.

Besides, the idea is to seek a solution able to accommodate a large gap, like the one between the glass envelope and the receiver tube. Recently [13] proposals were made that could accommodate a large gap, without losses, and be compatible with the placement of the second stage mirrors outside a glass envelope, making use of the SMS method.

This method allows for the primary and the secondary concentrator to be si-multaneously designed to guarantee etendue matching, either having recourse to refractive (R) or to reflective surfaces (X). In the case of 2D optics it is necessary to use reflective surfaces (X), because refraction would affect the handling of the incoming radiation in the longitudinal direction in unwanted ways.

The new approach yielded the so called Snail and Helmet concentrators (mirror-based, i.e XX, where these letters stand for the fact that two reflective surfaces are used for primary and secondary) which managed to achieve: (i) a concentration very close to the maximum limit; (ii) a gap between the secondary and the receiver, prac-tically with no light losses (iii) be applied either to an asymmetrical optic (Snail) or to a symmetric optic (Helmet). Nevertheless, these solutions were designed for a large gap but for non-evacuated tubular receivers, i.e., a glass envelope was not included. When a glass envelope is considered, even though most of the light goes directly to the absorber, there are possible high multiple transmission losses; and not all light goes through the glass envelope in a perpendicular direction, i.e, concen-trated light hitting the glass envelope perpendicularly is an exception and not the rule, thus resulting in even higher losses than what might be expected at first sight.

In Fig. 6.1 a schematic explanation of this is presented, using a schematic secondary concentrator and an evacuated tubular receiver.

As can be seen from Fig. 6.1(a), some rays may have significant losses on their way to the receiver R. Fig. 6.1(a) shows a ray r entering the vacuum tube g at a point A, leaving it at another point B, bouncing off the secondary mirror m_S and crossing the vacuum tube again at a pointCbefore reachingR. A simpler light path would be as shown in Fig. 6.1(b) in which another ray r bounces off the secondary mirror m_S, crosses the vacuum tube at a point D and reaches R.

In the next section a solution is presented for a new XX-SMS secondary concen-trator that:

• Is optimized to approach the theoretical limit, that is, the CAP (CAP=Csinθ) is as close as possible to 1 (absorber in air or vacuum).

• Includes a gap without significant light losses.

• Minimizes the transmission losses through the glass envelope.

6.2.2 The XX SMS concentrator design method

The SMS method can be well described by direct application to the case at hand.

It takes advantage of the degrees of freedom provided by the shape of both primary and secondary mirrors, using one or the other in alternation from set of points to the next, conserving the etendue [7] in the process.

6.2 A new XX SMS concentrator 71

Fig. 6.1: Fresnel losses in a glass enclosed receiver combined with a second-stage concen-trator optic. (a) A rayr enters the vacuum tubegat pointA(two Fresnel losses), exits at point B(two Fresnel losses), bounces off the secondary mirrormS (reflection loss), enters the vacuum tube at point C (two Fresnel losses) and finally reaches the receiver R. (b) Another ray hits the mirror, crosses the glass tube at pointD and reaches the receiverR.

The circular receiver is chosen and the initial points P₀ for the primary mirror and S₀ for the secondary mirror are as shown in Fig. 6.2(a). The way to choose these initial points, just like in other SMS optics [13], is done by coupling the ´etendue captured by the primary and the ´etendue captured by the receiver [7]. As shown in Fig. 6.2(b), the point S₀ is chosen along the flow-line f_S0 (perpendicular to the receiver) and the point S₁ and the flow-line f_S1 are symmetric with respect to the symmetry axis of the concentrator.

The angleαbetween these two flow-lines can be defined as an angular gap, which, in the ideal case, should be zero in order to maximize the ´etendue captured by the receiver (the receiver “sees” the light in an angle of 2π). Nevertheless, this cannot be done since the secondary mirror will surround completely the receiver and, therefore, the light reflected by the primary cannot reach it. Thus, the maximum ´etendue that the receiver (immersed in air or vacuum, n = 1) can capture,ER, is given by:

E_R= 2L_R(α) (6.3)

Where L_R(α) is the length of the arc between f_S0 and f_S1 as a function of α, given by:

Fig. 6.2: The XX SMS design method; and (b) The initial points S0 and P0 are chosen through an ´etendue conservation balance between the primary mirror and the receiver.

LR(α) = (2π−α)r (6.4)

Withr being the radius of the receiver.

The point P0 can be chosen in a very similar way. In this case the flow-line f_P0 comes from a source at an infinite distance, that is, the flow-line is a vertical line bisecting the edge-rays r₂ and r₃. Again, P₁,f_P1, r⁰₂ and r⁰₃ are symmetric with respect to the symmetry axis of the concentrator. Now, the ´etendue captured by the primary, E_P, is given by:

EP = 2[P0,P1] sinθ (6.5)

Where [P₀,P₁] is the distance between P₀ and P₁. Naturally, these points must be chosen in a way that ER=EP.

6.2 A new XX SMS concentrator 73 The incoming rays reflected at edgeP₀ of the primary are reflected by portions₁ of the secondary in directions tangent to the “bottom” of the circular receiver (rays r₂ and r₃).

Reflecting a set of rays coming from the top of the circular receiver (r1 is an example of one of these rays) on s₁ a new portion p₂ of the primary is calculated;

next, reflecting a set of rays parallel tor₂ (coming from the sun) onp₁ a new portion s₂ of the secondary is calculated.

Repeating the process [7], a primary mirror approximately parabolic is obtained step by step, as shown in Fig. 6.3. The process stops at point Ajust below the right-most point of the secondary in order to ensure that the secondary concentrator does not produce any shading over the primary. The other half of the optic is symmetric with respect to the origin (center of the receiver).

It should be noticed that no edge rays are directly reflected by the primary towards the receiver. According to the edge ray principle, incoming edge rays are instead first reflected by the primary mirror and then by the secondary mirror which redirects them towards the edges of the receiver (see Fig. 6.3) [2]. This method is the key to ensure that all rays cross the glass tube close to the perpendicular direction, minimizing Fresnel losses. In practice this is not always possible, especially when a highly compact and optimized optic is desired, since some of the light reflected on the primary mirror hits the receiver rather than the ideal primary-secondary-receiver optical path. Nevertheless, this effect can be controlled and managed, that is, the great majority of the light follows the optical path mentioned before.

When compared to the Helmet, this design increases reflection losses but reduces Fresnel losses at the vacuum tube glass envelope.

Fig. 6.3: The complete XX SMS optic.