On the Use of Concave Heliostats in a Beam‐ Down Central Receiver System

International Journal of Energy Science (IJES), Volume 6 Issue 1, 2016 www.ijesci.org doi: 10.14355/ijes.2016.0601.03

On the Use of Concave Heliostats in a Beam‐ Down Central Receiver System Erminia Leonardi*1 CRS4, Center for Advanced Studies, Research and Development in Sardinia, Loc. Piscina Manna, Edificio 1, 09010 Pula (Ca‐Italy) *1

ermy@crs4.it

Abstract The beam‐down design is standing out as a very promising technology in the field of solar central receiver systems. In this paper, we show that the use of concave heliostats strongly improves the overall performance of the system, allowing for a better concentration of the solar radiation at the receiver. To this aim, the spot at the horizontal plane containing the lower focus of the secondary reflector is analyzed under different conditions, such as secondary reflectors of different eccentricities and solar fields composed of concave or flat heliostats. The performance analysis of a realistic beam‐down system is also proposed to stress both the feasibility of the plant and the need of using concave heliostats. This study has been conducted with the use of the CRS4‐2 numerical code (an acronym for CRS4 research software for Central Receiver Solar System Simulation S), developed in our laboratory.

Keywords Characteristic Function; Beam‐Down; Central Receiver Systems; Concave Heliostats; Shading; Blocking, Cosine Effect

Introduction Since its first conceptualization (Rabl, 1976), the possibility of using a beam‐down system to concentrate at the ground the solar energy collected by the solar field of heliostats has asserted itself as a feasible alternative to the standard central tower systems (Winter, Sizmann and Vant‐Hull, 1991; Epstein and Segal, 1998; Kribus, Zaibel, Carrey, Segal and Karni, 1997, 1998; Segal and Epstein, 1997, 1998, 1999). The recent Tokyo Tech Project in Abu Dhabi, with the construction of a test plant (100 kW), represents a significant example of the increasing interest in this technology. This is a long term project, which will evolve, in a second phase, with the construction of a 20 MW demonstration plant with a cavity molten salt receiver heating the molten salt very efficiently, and, in a third phase, with the construction of commercial plants with a total heat collection capacity of 120 MW, comprising either four 30 MW plants or three 40 MW plants.

The main advantage of the beam‐down solar system is that instead of having the heat‐capturing system up on a big tower, a secondary reflector directs the light coming from the heliostats back down at the ground where it can be captured by a receiver system. In this way it is possible to reduce the parasitic energy losses due to the transport of the heat transfer fluid from the top of the tower to the storage system or the power block. On the other hand, the secondary reflector tends, in general, to magnify the image of the heliostats at the ground, and, therefore, a compound parabolic concentrator (CPC) must be placed above the receiver to further concentrate the solar radiation (Welford and Winston, 1989). The reflection of the solar radiation on both the secondary reflector and the inner surface of the CPC leads to a loss of optical efficiency of about 20% with respect to a conventional solar tower system.

Optical performances of flat and concave heliostats are compared in a series of simulations, where a systematic analysis is carried out to quantify the concentration ability in both cases when the solar field is coupled to a beam‐ down receiver system.

The remainder of the paper is organized as follow: the next section describes the mathematical algorithm implemented in the CRS4‐2 code (Leonardi and DʹAguanno, 2011; Leonardi, 2012) to consider concave heliostats; Sec. Results and Discussion presents the results of a series of simulations where the optical performances of

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concave and flat heliostats are compared for secondary reflectors of different eccentricities. The optical performance of a realistic test case completes the study. The Conclusion section presents some conclusive remarks.

Mathematical Model The possibility to consider concave heliostats has been implemented into the CRS4‐2 numerical code. The heliostats are chosen to be segments of spheres. In particular, if D(k) is the distance between the center of the k‐th heliostat and the upper focus, F1, of the hyperboloid, then, the concave heliostat is described as a segment of sphere of radius Rh(k)=2D(k), whose aperture radius, rh(k), and height, hh(k), are related through the expression (see also Fig. 1):

hh  k   Rh  k   Rh  k   rh  k  2

2

(1)

FIG. 1 CHARACTERISTIC PARAMETERS OF A CONCAVE HELIOSTAT.

The surface of the heliostat is divided into Nt tesserae and, from the center of each tesserae, a conic bundle of rays is directed towards the Sun and then reflected with respect to the normal to the spherical surface towards the hyperboloid. The reader is referred to our papers (Leonardi and D’Aguanno, 2011; Leonardi, 2012) for the details regarding the description of the conic bundle of rays and the procedure used to calculate shading and blocking effects.

Results and Discussion In a beam‐down system, the solar energy reflected by the field of heliostats is not converted into heat at the top of the tower, but it is further reflected by a secondary reflector (hyperboloidal or ellipsoidal), which directs it vertically downwards towards the receiver system. In the following, a two sheets hyperboloid secondary reflector is considered with the upper sheet describing the real surface of the hyperboloid. Therefore, in such a system, a solar ray reflected from the heliostat towards the focus F1, intersects the surface of the hyperboloid and it is reflected towards the focus F2.

It is obvious that in a beam‐down system, the concavity of the heliostat affects the shape and size of its image at the horizontal plane, pF2, containing the lower focus, F2, of the secondary reflector. This aspect can be crucial because it, in turn, can affect the size of the compound parabolic concentrator (CPC), that in general is located above the receiver, and therefore, its ability to further concentrate the radiation coming from the solar field.

In the following, the effect of the concavity of the heliostats on the performances of the beam‐down system is discussed in a systematic way. To this aim, two different types of hyperboloids (secondary reflectors) are considered, indicated hereafter as type A and type B hyperboloids, respectively. In particular, the type A hyperboloid has a significant concavity (e=3) while the type B hyperboloid is flat (e=) and located at a height corresponding to the minimum height of the type A hyperboloid. The two hyperboloids have the lower focus, F2, at the same height, and, therefore, their upper focus, F1, at different heights. For sake of completeness, the equation of the hyperboloid is hereafter indicated: z

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 F1  F2 2 4e2



x 2  y 2 F1  F2 (2)  2 e2  1

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The size of the solar field affects the size of the hyperboloid. In the present case, we assume that the farthest heliostats of the solar field are located 150 m far from the center of the system of coordinates. The characteristics of the two types of hyperboloids are summarized in Table 1, while a pictorial representation of them is given in Fig. 2.

TABLE 1 CHARACTERISTIC PARAMETERS CORRESPONDING TO TYPE A AND TYPE B HYPERBOLOYD, RESPECTIVELY

e

F1 (m)

F2 (m)

rhyp (m)

zmin (m)

zmax (m)

type A

3

75.00

5.00

50.00

51.67

61.18

type B



98.34

5.00

87.00

51.67

51.67

FIG. 2 SHAPE AND SIZE OF THE TYPE A(e=3) AND TYPE B(e=) HYPERBOLOID. THE RAYS REFLECTED BY THE CENTER OF A HELIOSTAT LOCATED, IN METERS, AT P=(0,150,5) ARE ALSO INDICATED

Both flat and concave circular heliostats of the same radius have been considered and their spots at the pF2 plane have been compared. The heliostats have a radius rh=5 m and their center is 5 m above a flat ground. Both the heliostats and the hyperboloids have reflectivity equal to 0.95. The solar rays intercepting the surface of the heliostat are modeled as a conic bundle of Nrays rays, lying on concentric cones, with semi‐angle varying from min=0 (central ray) to max. The chosen number of rays per solar beam is Nrays=37. The sunshape, the curvature and waiveness errors of the reflecting heliostatʹs surface are taken into account. These non‐systematic errors are supposed to have a Gaussian distribution with a collective effect characterized by the same distribution with a standard deviation, , which is a measure of the beam quality:



F    2 2



1

 2  exp   2  , 0    max (3)  2 

We have chosen, max =8x10‐3 rad and =8x10‐3 rad, corresponding to a low quality solar beam (Romero‐Alvarez and Zarza, 2007). In this way, the effect of the heliostat concavity and hyperboloid eccentricity on the size of the spot at the pF2 plane is analyzed under the worst conditions.

The surface of the heliostats has been subdivided into Nt=400 tesserae. As already demonstrated (Leonardi and D’Aguanno, 2011), the results of the simulations do not significantly change for further increases of Nt when circular heliostats of 5 m of radius are considered.

A Single Heliostat We start our analysis considering a single heliostat, whose center is located at the position P (in meters) [0, 150, 5] in a system of coordinates where East is the positive x direction and North is the positive y direction.

Hereafter, we indicate the zenith and azimuth angles as z and , respectively. In particular, z is the angle that the sun ray forms with the normal to the ground and is the angle that the projection of the sun ray on the xy‐plane forms with the South direction.

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FIG. 3 SPOT PRODUCED BY A CIRCULAR CONCAVE HELIOSTAT (P=[0,150,5], rh=5 M), AT THE pF2 PLANE WHEN THE SUN, THE AIMING POINT F1 AND P ARE ALIGNED, AND ONLY THE CENTRAL RAY OF THE SOLAR BEAM IS CONSIDERED. THE RED FULL LINE AND THE BLUE DASHED LINE CORRESPOND TO THE TYPE A AND TYPE B HYPERBOLOID, RESPECTIVELY

The concavity of the heliostat is chosen according to Eq. 1. It is worth noticing that the shape and size of the heliostatʹs spot at the pF2 plane change with the Sun position. When the Sun, the aiming point, F1, and the center of the heliostat, P, are aligned, the spot of the concave heliostat at the pF2 plane is the smallest possible. Note that if only the central ray of the solar beam is considered, the spot of the heliostat at the pF2 plane is confined within a surface of few millimeters of radius, as shown in Fig. 3, where both the spots corresponding to the hyperboloid of type A and type B are plotted. Therefore, in case of alignment between Sun, F1 and P, the size of the spot is dominated by the amplitude of the conic bundle composing the solar beam, as it is shown Fig. 4a (type A hyperboloid; z =64.98o, =0o) and Fig. 4b (type B hyperboloid; z =58.11o,  =0o), where a comparison with the spot produced by the corresponding flat heliostat is also given.

(a) z =64.98o, =0o (b) z =58.11o,  =0o

FIG. 4 COMPARISON OF THE SPOTS PRODUCED AT THE pF2 PLANE BY A FLAT HELIOSTAT (RED FULL LINE) AND A CONCAVE HELIOSTAT (BLUE DASHED LINE), WHEN P,F1 AND THE SUN ARE ALIGNED, FOR THE CASE OF THE TYPE A (ON THE LEFT) AND TYPE B (ON THE RIGHT) HYPERBOLOID. THE CENTER OF THE HELIOSTAT IS AT P=[0,150,5]

As the Sun moves away from alignment with F1 and P, the spot of the concave heliostat at pF2 becomes larger, as it is shown, for example, in Figs. 5a and 5b and in Figs. 6a and 6b, for the cases with z =45o, =45o and z=85o, =85o, respectively.

However, we note that, even when there is a strong deviation from the alignment, the spot at the pF2 plane of the concave heliostat is definitely smaller than that of the flat one. For example, for z=85o, =85o, the concave heliostat produces a spot at pF2 almost 80% smaller than that of a flat heliostat. It is also worth noticing that the spots produced by the type B hyperboloid are, in all cases, smaller than those produced by the type A hyperboloid.

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(a) z =45o, =45o (b) z =45o,  =45o

FIG. 5 COMPARISON OF THE SPOTS PRODUCED AT THE pF2 PLANE BY A FLAT HELIOSTAT (RED FULL LINE) AND A CONCAVE HELIOSTAT (BLUE DASHED LINE), WHEN z =45o and  FOR THE CASE OF THE TYPE A (ON THE LEFT) AND TYPE B (ON THE RIGHT) HYPERBOLOID. THE CENTER OF THE HELIOSTAT IS AT P=[0,150,5]

(a) z =85o, =85o (b) z =85o,  =85o

FIG. 6 COMPARISON OF THE SPOTS PRODUCED AT THE pF2 PLANE BY A FLAT HELIOSTAT (RED FULL LINE) AND A CONCAVE HELIOSTAT (BLUE DASHED LINE), WHEN z =85o and  FOR THE CASE OF THE TYPE A (ON THE LEFT) AND TYPE B (ON THE RIGHT) HYPERBOLOID. THE CENTER OF THE HELIOSTAT IS AT P=[0,150,5]

The areas of all spots plotted in Figs. 4, 5 and 6 have been calculated and the results are reported in Table 2. This analysis is completed from the results indicated in Table 3, where the heliostat’s optical performance is considered as a function of its distances from the beam‐down system. In particular, the area of the spot produced at the pF2 plane is calculated for the case of a flat and a concave heliostat at four different positions, for the case of the type A hyperboloid and two different solar coordinates (one representing a perfect alignment Sun, F1 and P, when the heliostat is located at d=150 m, and one representing a strong dis‐alignment). It is worth noticing that, for z64.98 the concave heliostat produces a very small spot at d=50 m, although there is significant dis‐ alignment Sun‐F1‐P. In the case of the flat heliostat, the trend of the spot to decrease with increasing distance, d, is in competition with the broadening effect due to the conical shape of the solar radiation.

TABLE 2 COMPARISON OF THE AREA OF THE SPOTS AT THE PF2 PLANE, PRODUCED BY A FLAT AND A CONCAVE HELIOSTAND LOCATED (IN METERS) AT P=[0,150,5], FOR THE CASE OF THE TYPE A AND TYPE B HYPERBOLOIDS

type A hyperboloid (degrees)

Aflat (m2)

Aconcave (m2)

Aconcave/Aflat (%)

64.98,0.00

333.5

15.0

4.5

45.00,045.00

315.7

22.3

7.0

85.00,85.00

267.33

55.04

20.59

type B hyprboloid (degrees)

Aflat (m2)

Aconcave (m2)

Aconcave/Aflat (%)

58.11,0.00

209.8

11.12

5.30

45.00,45.00

201.1

14.6

7.3

85.00,85.00

168.8

36.8

21.8

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TABLE 3 COMPARISON OF THE AREA OF THE SPOTS AT THE PF2 PLANE, PRODUCED BY A FLAT AND A CONCAVE HELIOSTAND LOCATED (IN METERS) AT A DISTANCE D FROM THE ORIGIN OF THE SYSTEM OF COORDINATES. IN PARENTESES ARE INDICATED THE VALUES OBTAINED WHEN THE SOLAR RADIATION IS DESCRIBED BY A SINGLE RAY

z =64.98o, =0o d (m)

Aflat (m2)

Aconcave (m2)

50

310.7 (238.0)

7.3 (0.25

75

312.7 (228.8)

7.4 (0.0)

100

316.8 (219.4)

8.7 (0.0)

125

323.8 (211.5)

11.6 (0.0)

150

333.5 (205.4)

15.0 (0.0)

z =85o, =85o d(m)

Aflat (m2)

Aconcave (m2)

50

251.9 (184.2)

33.6 (11.7)

75

249.8 (173.3)

37.9 (12.3)

100

253.0 (164.4)

43.0 (12.5)

125

259.9 (158.1)

48.9 (12.6)

150

268.4 (153.0)

55.5 (12.7)

The flux density, defined as the power per unit area at the pF2 plane, has also been computed. A comparison of this quantity when a flat and a concave heliostat are considered, is given in Figs. 7 and 8, for the case of the type A and type B hyperboloid, respectively, for z=85o and =85o and a direct normal irradiation (DNI) of 1 kW/m2.

(A) FLAT HELIOSTAT (B) CONCAVE HELIOSTAT

FIG. 7 COMPARISON OF THE FLUX DENSITY (IN KW/M2) OF THE SPOT AT THE PF2 PLANE, PRODUCED BY A FLAT (TOP) AND A CONCAVE (BOTTOM) HELIOSTAT, LOCATED, IN METERS, AT P=[0,150,5], FOR THE CASE OF THE TYPE A HYPERBOLOID. z =85O AND =85O. DNI=1KW/M2. THE TOTAL POWER IS 52.94 KW. NOTE THAT THE FLUX DENSITY SCALE IS TEN TIMES SMALLER FOR (A) THAN FOR (B)

(A) FLAT HELIOSTAT (B) CONCAVE HELIOSTAT

FIG.8 COMPARISON OF THE FLUX DENSITY (IN kW/m2) OF THE SPOT AT THE pF2 PLANE, PRODUCED BY A FLAT (TOP) AND A CONCAVE (BOTTOM) HELIOSTAT LOCATED, IN METERS, AT P=[0,150,5], FOR THE CASE OF THE TYPE B HYPERBOLOID. z=85o AND =85o. DNI=1 kW/m2. THE TOTAL POWER IS 53.04 kW. NOTE THAT THE FLUX DENSITY SCALE IS TEN TIMES SMALLER FOR (A) THAN FOR (B)

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It is worth noticing that the scale of the flux densities of Figs. 7a and 8a is ten times smaller than that of Figs. 7b and 8b, respectively. The fraction of the total power collected at the pF2 plane within circular surfaces centered in F2 and of increasing radius is given in Fig. 9, for z =85o and =85o. Note that in the case of a concave heliostat, a surface of radius equal to 5 m centered in F2 collects 100% of the total power reaching the pF2 plane, while with a flat heliostat, this value is only 44.8% (type A) and 57.5% (type B).

FIG. 9 FRACTION OF THE TOTAL POWER AT THE PF2 PLANE AS FUNCTION OF THE RADIUS OF THE SURFACE CENTERED IN F2, FOR THE CASE OF A FLAT AND A CONCAVE HELIOSTAT, LOCATED, IN METERS, AT P=[0,150,5]. z=85o, =85o. DNI=1 kW/m2

From this single mirror analysis, it is apparent that the concave heliostat gives a spot at the pF2 plane much smaller than the flat one, even when very unfavorable conditions are considered, such as a low quality solar beam, a hyperboloid with a high concavity (which tends to magnify the solar spot), and unfavorable Sun positions in the sky (that is, strong dis‐alignment between P, F1, and the Sun).

A Solar Field Composed of 786 Heliostats We consider now a solar field with 786 circular heliostats assembled around the beam‐down system with a triangular configuration. The heliostats are located on a flat land with their centers at 5 m from the ground. A maximum and minimum radius, Rmax=150 m and Rmin=30 m, characterize the distance of the farthest and closest heliostats from the center of the system of coordinates, so that the solar field assumes the shape of a circular crown, as shown in Fig. 10. The radius of the heliostats is rh=5 m. The land coverage is =0.91 (the maximum allowable for the chosen configuration of the solar field).

FIG. 10 SOLAR FIELD CONFIGURATION

An extensive series of simulations has been performed to describe the effect of the heliostatʹs concavity on the energy distribution at the pF2 plane. To this aim, the use of flat and concave heliostats has been compared for both the type A and type B hyperboloids. We remark that each heliostat has its own concavity, according to Eq. 1.

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We assume that the solar field is located in Cagliari (South Sardinia, Italy) at latitude: 39o:15’ North, and longitude: 8o:57’ East. The DNI satellite data used in the simulations, expressed in Wh/m2, are provided by DLR (German Aerospace Center) and correspond to the direct solar irradiation during the year 2005, at 20 m of height above the ground, with a yearly value of 1694.35 kWh/m2.

The overall energy collected at the pF2 plane has been computed for January and July, and its value is indicated in Table 4 for each considered case. The simulations take into account the shadow of the hyperboloid on the solar field.

TABLE 4 MONTHLY ENERGY COLLECTED AT THE PF2 PLANE, FOR THE CASE OF FLAT AND CONCAVE HELIOSTATS, WITH TYPE A AND TYPE B HYPERBOLOID

type A hyperboloid

type B hyperboloid

Eflat (GWh)

Econc (GWh)

Eflat (GWh)

Econc (GWh)

January

1.8747

1.8722

1.6324

1.6301

July

6.5922

6.6388

5.4863

5.5195

From Table 4 one can note that, when, for each type of hyperboloid, we compare the monthly energy collected at the pF2 plane by the flat and the concave heliostats, we find small differences in the two cases. They are due to different shading and blocking contributions when flat or concave heliostats are considered.

The results of the simulations indicate that the density of energy at the pF2 plane changes dramatically depending on the use of a solar field of flat or concave heliostats, as it is evident from the comparisons shown in Figs. 11, 12, 13 and 14, corresponding to monthly energies computed for January and July.

(A) FLAT HELIOSTATS (B) CONCAVE HELIOSTATS

FIG.11 MONTHLY DENSITY OF ENERGY (IN MWh/m2) AT THE pF2 PLANE FOR JANUARY 2005 IN CAGLIARI AND TYPE A HYPERBOLOID. NOTE THAT THE FLUX DENSITY SCALE IS SEVEN TIMES SMALLER FOR (A) THAN FOR (B)

(A) FLAT HELIOSTATS (B) CONCAVE HELIOSTATS FIG.12 MONTHLY DENSITY OF ENERGY (IN MWh/m2) AT THE pF2 PLANE FOR JANUARY 2005 IN CAGLIARI AND TYPE B HYPERBOLOID. NOTE THAT THE FLUX DENSITY SCALE IS MUCH SMALLER FOR (A) THAN FOR (B)

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(A) FLAT HELIOSTATS (B) CONCAVE HELIOSTATS

FIG.13 MONTHLY DENSITY OF ENERGY (IN MWh/m2) AT THE pF2 PLANE FOR JULY 2005 IN CAGLIARI AND TYPE A HYPERBOLOID. NOTE THAT THE FLUX DENSITY SCALE IS MUCH SMALLER FOR (A) THAN FOR (B)

(A) FLATS HELIOSTATS (B) CONCAVE HELIOSTATS

FIG.14 MONTHLY DENSITY OF ENERGY (IN MWh/m2) AT THE pF2 PLANE FOR JULY 2005 IN CAGLIARI AND TYPE B HYPERBOLOID. NOTE THAT THE FLUX DENSITY SCALE IS MUCH SMALLER FOR (A) THAN FOR (B)

Note that the concave heliostats, besides giving a higher concentration of the solar radiation, also produce an almost symmetric shape of the spot, unlike the flat heliostats. This aspect is emphasized in Fig. 15, where a top view of Figs. 11a and 11 b is given. Such an asymmetry of the density of energy can affect the performances of the receiver apparatus.

(A) FLAT HELIOSTATS (B) CONCAVE HELIOSTATS FIG.15 MONTHLY DENSITY OF ENERGY (IN MWh/m2) AT THE pF2 PLANE FOR JULY 2005 IN CAGLIARI WITH TYPE A HYPERBOLOID

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The yearly energy collected at the pF2 plane has also been calculated. To this aim, the intersection of each ray of the solar beam reflected by every neither shaded nor blocked tesserae of each heliostat should be calculated for each sunny hour of the year (the DNI data used in the simulations are hourly cumulated values). Such calculation requires a very high computational effort and therefore, a different strategy has been followed to obtain the same information without renouncing to the accuracy of the calculations.

As firstly described in our previous works (Leonardi and D’Aguanno, 2011, Leonardi, 2012), the solar power collected at the receiver, which in the present case can be considered the surface of radius rrc at the pF2 plane, can be expressed as the product of the DNI with an effective area, Aeffrec, called “characteristic functionʹʹ of the solar plant (where the apex $rec$ refers to the receiver), which depends on the sun position (z and ). Given a certain distribution of heliostats in the solar field, the total solar power collected at the receiver at a given time t (that is, for a given value of (z (t) and (t)) is rec Ptot  t   DNI  t   Aeff  z  t  ,   t   , (4)

where DNI and Aeffrec are expressed in W/m2 and m2, respectively, and rec Aeff  z  t  ,   t     Akeff  z  t  ,   t  , (5) Nh

k 1

where Akeff((z(t) and (t)) is the effective area of the heliostat k once the cosine, shading and blocking effects have been considered (see Leonardi and D’Aguanno, 2011 and Leonardi, 2012 for the details regarding its calculation).

The strategy here adopted is to compute Aeffrec (z,) on a regular grid in z (0oz90o) and , with spacing of 5o, with the CRS4‐2 code.

Once Aeffrec is known on the regular grid, the values of Aeffrec(z, ) for the solar coordinates corresponding to the Sun positions along the year in Cagliari can be obtained in a very effective way by bilinear interpolation on such a grid, thus avoiding a hour by hour full calculation.

An extensive series of calculations has been performed to calculate the solar energy reaching receivers of different radius, rrc, for both the type A and type B hyperboloid, with both flat and concave heliostats.

The results of such calculations are reported in Table 5, where, for each value of rrc, the concentration ratio, Cr, and the yearly energy, E, corresponding to concave and flat heliostats, with the type A and type B hyperboloid, is given.

Cr is here defined as the ratio between the total mirror surface of the solar field and the area of a surface of radius rrc, at the pF2 plane.

TABLE 5 CONCENTRATION RATIO, Cr, AND YEARLY ENERGY, E, COLLECTED AT THE PF2 PLANE, FOR THE CASE OF FLAT AND CONCAVE HELIOSTATS, FOR TYPE A AND TYPE B HYPERBOLOID. BESIDE THE ENERGY, THE FRACTION OF THE TOTAL ENERGY, IN PERCENTAGE, IS ALSO INDICATED WITHIN PARENTHESIS

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type A hyperboloid

rrec (m)

Cr

concave E (GWh)

12.0

136.46

41.46 (100)

type B hyperboloid

flat E (GWh)

concave E (GWh)

flat E (GWh)

41.46 (100)

34.83 (100)

34.69 (100)

10.0

196.50

41.46 (100)

41.18 (99.3)

34.83 (100)

34.69 (100)

8.0

307.03

41.46 (100)

39.71 (95.8)

34.83 (100)

34.67 (99.9)

7.0

401.02

41.45 (100)

37.14 (89.6)

34.83 (100)

34.61 (99.8)

5.5

649.59

41.34 (99.7)

30.69 (74.0)

34.81 (99.9)

34.08 (98.2)

5.0

786.00

41.25 (99.5)

28.03 (67.6)

34.79 (99.9)

33.33 (96.1)

4.5

970.37

41.06 (99)

25.23 (60.8)

34.75 (99.8)

31.84 (91.8)

4.0

1228.12

40.72 (98.2)

22.32 (53.8)

34.68 (99.6)

29.49 (85.0)

3.5

1604.08

40.09 (96.7)

19.36 (46.7)

34.53 (99.1)

26.98 (77.8)

3.0

2183.33

38.40 (92.6)

16.37 (39.5)

34.22 (96.3)

22.55 (65.0)

2.5

3144.00

37.09 (89.5)

13.40 (32.3)

33.56 (96.3)

18.61 (53.6)

2.0

4912.50

33.65 (81.2)

10.45 (25.2)

32.04 (92.0)

14.60 (42.1)

1.5

8733.33

27.58 (66.5)

7.82 (18.9)

28.64 (82.2)

10.64 (30.7)

International Journal of Energy Science (IJES), Volume 6 Issue 1, 2016 www.ijesci.org

From the analysis of the data indicated in Table 4, some interesting issues can be drawn out.

First of all, the concentration ability of the concave heliostats, observed previously for the case of the monthly simulations, is found even for a yearly time period. One can note, for example, that, for the case of the type A hyperboloid, 99.5% of the yearly energy reaching the pF2 plane is collected within a surface of radius rrc=5 m when concave heliostats are considered. This value must be compared with 67.6%, which corresponds to flat heliostats.

In the case of the type B hyperboloid, the effects due to the use of flat and concave heliostats become pronounced at lower values of rrc. In fact, 99.6% of the yearly energy reaching the pF2 plane is collected within a surface of radius rrc=4.0 m in the case of concave heliostats. This value must be compared with that equal to 85.0%, corresponding to flat heliostats.

The hyperboloid of type A allows the collection of more energy than that of type B, unless very small values of rrc (< 2 m) are considered. For example, for rrc=5 m, the system composed of concave heliostats and the type A hyperboloid collects a yearly energy equal to 41.25 GWh, while the system composed of concave heliostats and the type B hyperboloid collects a yearly energy of 34.79 GWh. This is an effect of the smaller shadow of the type A hyperboloid on the solar field with respect to that of the type B hyperboloid. On the other hand, the type B flat hyperboloid does not produce a magnification of the solar field image at the pF2 plane, unlike the type A hyperboloid. In fact, a ``flatʹʹ hyperboloid reflects the solar beam without modifying its cone aperture, and this makes a difference with the ``concaveʹʹ hyperboloid (the reader can refer to Leonardi E., 2012 for an extensive analysis of this aspect.) Therefore, the type B hyperboloid is a better concentrator. For example, with concave heliostats, the type A hyperboloid collects 81.16% of the total energy within a surface with rrc=2 m, while, within the same surface, the type B hyperboloid collects as much as 98.24% of the total energy.

The results of Table 5 have also been plotted in Fig. 16 in terms of the fraction of the total yearly energy reaching the pF2 plane and collected within surfaces of increasing radius, rrc.

(A) HYPERBOLOID OF TYPE A (B) HYPERBOLOID OF TYPE B

FIG.16 FRACTION OF THE YEARLY ENERGY REACHING THE pF2 PLANE AND COLLECTED WITHIN A SURFACE OF INCREASING RADIUS rrc. DNI DATA USED IN THE CALCULATIONS CORRESPOND TO CAGLIARI (SOUTH SARDINIA) DURING THE YEAR 2005

It is worth noticing that the presence of a compound parabolic concentrator (CPC) with the entrance aperture at the pF2 plane could further increases the concentration factor of the system, but this analysis is out of the scope of the present paper.

The results of the calculations presented up to now have been obtained considering for each heliostat its own concavity (Eq. 1). Visibly, this approach is not feasible to design an actual solar field, in particular, when it is composed of a large number of heliostats. Therefore, a reduced number of selected concavities should be defined.

We have selected 6 and 5 different concavities for the case of the type A and type B hyperboloids, respectively. In particular, we have assumed that all the heliostats whose center is located at a distance R from the center of the system of coordinates so that RinRRout have the same concavity, and, therefore, the same value of Rh (see Eq. 1).

Such concavity is the average value computed considering the concavities of all the heliostats located between Rin and Rout. Table 6 reports the values of Rin, Rout, and Rh, for the case of the type A and type B hyperboloids.

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TABLE 6 VALUES OF RIN, ROUT AND RH FOR TYPE A AND TYPE B HYPERBOLOID

type A hyperboloid

type B hyperboloid

no

Rin (m)

Rout (m)

Rh (m)

Rin (m)

Rout (m)

Rh (m)

1

30.00

50.00

160.05

30.00

50.00

202.20

2

50.00

70.00

186.28

50.00

80.00

230.32

3

70.00

90.00

214.34

80.00

110.00

268.66

4

90.00

110.00

245.08

110.00

130.00

304.37

5

110.00

130.00

278.17

130.00

150.00

335.82

6

130.00

150.00

312.26

‐

‐

‐

By using these selected concavities, we have computed the yearly energy collected at the pF2 plane within a surface of radius rrc=5 m and, then, we have compared the results with those obtained using for each heliostat its own concavity. For the case of the type A hyperboloid, a value of yearly energy equal to 41.16 GWh obtained when only 6 selected concavity are considered, must be compared with the value of 41.25 GWh obtained when each heliostat has its own concavity. In the case of the type B hyperboloid, the difference is even vanishing (E=34.79 GWh in both cases!).

These selected concavities still give very satisfactory results even when rrc=3 m, with yearly energy of 38.87 GWh (type A) and 34.19 GWh (type B) to be compared with a value of 38.40 GWh (type A) and 34.22 GWh (type B), obtained when each heliostat has its own concavity. Of course, these few selected concavities can be obtained as the results of an optimization procedure, and, therefore, it is expected that the differences could be further reduced.

Anyway, the expected improvement is of marginal utility and this analysis is out of the scope of the present paper.

Performance Analysis of a Realistic Test Case Since the discussion presented above was aimed to compare, in a systematic way, the performance of flat and concave heliostats in a beam‐down system, no attention was payed to the feasibility of the system, as well evidenced from the unrealistic size of the secondary reflector.

In the present section, a more realistic system is presented to complete such analysis.

A test case, composed of 26 circular heliostats with rh=5 m, is considered. The heliostats are placed around the beam‐down system according to a biomimetic field layout (Noone, 2012).

For sake of completeness, the mathematical expression corresponding to such a pattern is here recalled:

k  2 2 k rk  ak b ,

, with k=1,Nh (6)

where In the present case, reasonable values for the parameters a and b, are 2.10 and 0.85, respectively.

A compound parabolic concentrator (CPC) is located at ground level, with its centre corresponding to the origin of the system of coordinates. Moreover, in order to simplify the analysis, the receiver is simply the exit plane of the CPC. The characteristic parameters of the beam‐down system are indicated in Table 7, while Fig. 17 shows a top view of the plant. Moreover, we assume a reflectivity of the inner CPC surface of 0.94. It is worth noticing that a concentration ratio equal to 104 is given for the present system set‐up. The plant is assumed to be located in Cagliari.

The design point of the system has been chosen corresponding to 21th March at noon (z =43.4o, =0o) with DNI=940 W/m2.

The potential power of the system (corresponding to the energy collected by the solar field when cosine, shading and blocking effects are neglected) is  rh2NhDNI=1919.5 kW, while the power collected by the field of concave and flat heliostats is 1537.6 and 302.7 kW, respectively. Therefore, the field of concave heliostats gives a field efficiency of 80.1%, to be compared with that of only 15.8% of the flat heliostats.

The yearly performance of the plant has also been calculated for both the case of flat and concave heliostats. It is

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worth noticing that for both the case of the design point and the yearly performance, simulations have been carried out taking account of all relevant effects, comprising the atmospheric attenuation of the solar radiation (Noone, 2012) and the shadow of the secondary reflector on the solar field. The yearly potential energy of the plant is equal to 3.42 GWh. The yearly energy collected by the flat and concave heliostats is 0.66 GWh and 2.27 GWh, respectively.

Therefore, the field efficiency is 66.37 % in the case of concave heliostats and only 19.30 % in the case of flat heliostats. A more accurate study should imply an optimization of the field parameters (in particular, the parameters a and b of the biomimetic field and the CPC size), but such analysis is out of the scope of the present work.

TABLE 7 CHARACTERISTIC PARAMETERS OF THE BEAM‐DOWN SYSTEM

Hyperboloid e

3.0

F1 (m)

150.0

F2 (m)

5.0

rhyp (m)

16.6

zmin (m)

101.7

zmax (m)

102.4 CPC

ra (m)

4.3

rexit (m)

2.5

hcpc (m)

5.3

Fig.17 SCHEMATIC OF THE BEAM‐DOWN SYSTEM (TOP VIEW)

Conclusions The effect of using concave heliostats in beam‐down systems has been analyzed in a systematic way. To this aim, two types of secondary reflectors have been considered, a flat hyperboloid with eccentricity e= and a concave one with eccentricity e=3. The shape and size of the spot produced by circular heliostats at the horizontal plane containing the lower focus of the hyperboloid, pF2, has been determined for both flat and concave mirrors. The comparison of the results has been presented for the case of a single heliostat and for the more interesting case of a solar field composed of a large number of heliostats (Nh=786). In this last case, the solar field has been supposed hypothetically located at Cagliari (South Sardinia‐Italy), and using satellite DNI data of that site, monthly (January

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and July) and yearly energy distributions at the pF2 plane have been computed.

The results of the analysis demonstrate that the performance of the beam‐down system is strongly improved by the use of concave heliostats, even when a hyperboloid of small eccentricity is considered. In this case, for example, the yearly energy reflected by the solar field of concave heliostats is almost entirely concentrated at the pF2 plane, within a surface of 5 m of radius. The same amount of energy is contained within a surface of 10 m of radius when flat heliostats are considered. A surface of radius equal to 1.5 m collects 66.5% of the total solar radiation reaching the pF2 plane in the case of concave heliostats and only 18.9% of it in the case of flat heliostats. The improvement due to the use of concave heliostats is even more evident when a flat hyperboloid is considered. In fact, in this case, the concave heliostats concentrate 82.2% of the total energy within a surface of 1.5 of radius, to be compared with 30.7% for the flat ones.

It is worth noticing that, when the solar field is composed of concave heliostats, our results allow also to conclude that to concentrate the solar radiation a CPC is no longer an essential equipment of the beam‐down system, and the energy losses caused by reflections on the CPC inner surface can be avoided.

The design of an actual solar field where each heliostat has its own concavity is not reasonable, in particular in the case of solar fields of large dimensions. Therefore, the use of a reduced number of selected concavities for the entire solar field has also been considered. The results of the simulations, even though such concavities have not been optimized, have shown that also in this case the concentration of the solar radiation is almost equal to that obtained when each heliostats is characterized by its own concavity.

Finally, the optical performances of a realistic beam‐down system have been considered and the results obtained for both the design point and yearly efficiency clearly evidence the need of using concave heliostats. The analysis should be completed by a comparison of optical performance with a conventional tower system, but such study is out of the scope of the present work and it will be the subject of a future work.

ACKNOWLEDGMENT

The work has been carried out with the financial support of the UE project STAGE‐STE. REFERENCES

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