Design and experimental analysis of a cylindrical compound Fresnel solar concentrator

Available online at www.sciencedirect.com

ScienceDirect Solar Energy 107 (2014) 26–37 www.elsevier.com/locate/solener

Design and experimental analysis of a cylindrical compound Fresnel solar concentrator Hongfei Zheng a,b,⇑, Chaoqing Feng a,c, Yuehong Su b, Jing Dai a, Xinglong Ma a b

a School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China Institute of Sustainable Energy Technology, Department of Architecture and Built Environment, University of Nottingham, Nottingham NG7 2RD, UK c College of Energy and Power Engineering, Inner Mongolia University of Technology, Hohhot 010051, China

Received 21 October 2013; received in revised form 2 May 2014; accepted 5 May 2014 Available online 25 June 2014 Communicated by: Associate Editor Lorin Vant-Hull

Abstract This study presents the design of a cylinder shaped solar concentrator which is comprised of an arched Fresnel lens and a Fresnel mirror and a secondary reflector. An evacuated-tube or a concentrating photovoltaic cell can be used as the receiver being placed at the focus of the concentrator. This cylindrical compound Fresnel solar concentrator may have the advantages of good weather resistance, low driving force during tracking, good appearance and easy modularization. The dimensions of the Fresnel lens and the Fresnel reflector are calculated on the basis of optical principle. An optical simulation tool is used to obtain the optical efficiency of the concentrator for different incidence angles and therefore determine the allowable tracking error. It has been found that about 90% of the incident sunlight can still be gathered by the absorber when the tracking error is within 1.5°. Discussion is also made about the influence of the solar azimuth angle on the optical efficiency. A preliminary measurement of the optical efficiency of a prototype cylindrical concentrator is introduced. The experimental data generally agrees with the simulation result. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Solar concentrator; Compound Fresnel concentrator; Shaped-Fresnel lens; Cylindrical compound concentrator

1. Introduction Nowadays three main types of solar concentration power technologies are in various stages of development and commercialization, which are heliostat solar tower, parabolic dish and parabolic trough (Klaib et al., 1995; Siva Reddy et al., 2013). Among these three technologies, the widely recognized types of industrial scale solar power technologies are solar tower and parabolic trough. The parabolic trough technology is comparatively mature, the ⇑ Corresponding author at: School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China. Tel.: +86 13520480246. E-mail address: [email protected] (H. Zheng).

http://dx.doi.org/10.1016/j.solener.2014.05.010 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.

cost of power generation is lower; so it has gotten more attention from the public. Till 1990s, Luz Energy Corporation built nine parabolic trough solar power plants with total capacity 353.8 MW which were installed in the desert of California, United States (Pavlovic´ et al., 2012; Ferna´ndez-Garcı´a et al., 2010). The parabolic trough technology consists of a linear parabolic reflector that concentrates light onto a receiver positioned along the reflector’s focal line. Generally, the receiver is an evacuated-tube positioned directly above the middle of the parabolic mirror and filled with a working fluid. The reflector follows the sun during the daylight hours by tracking along a single axis. A working fluid is heated to 150–350 °C as it flows through the

H. Zheng et al. / Solar Energy 107 (2014) 26–37

receiver and is then used as a heat source for a power generation system (Thomas and Guven, 1993). However, the parabolic trough technology still has some demerits in its design, manufacture and operation. These are (Price et al., 2002): (1) In order to receive a large quantity of sunlight, the aperture of a parabolic trough is wide up to 6–8 m, that makes its wind resistance very big. So the support frame and post of a parabolic trough should be strong enough to stand both the weight of mirror reflectors and the wind force. Otherwise, the mirror reflectors may be distorted by wind to cause the concentration efficiency to be reduced. On the other hand, the heavy frame would increase the power consumption of the tracking motor. (2) The concentrator facing upwards is prone to accumulate dust, which decreases the optical efficiency. In winter, it is also prone to accumulate the snow. To remove dust or snow, the trough may be periodically turned downwards, but this operation consumes power. (3) Its receiver is installed on top of the concentrator. Although, the receiver is covered by a glass evacuated-tube, this cannot reduce the radiation heat transfer, the total heat loss is still very big in winter when the receiver operates on high temperature. In order to overcome the drawbacks of parabolic trough, many innovative concentrator designs have been proposed on the basis of Fresnel lens or reflector (Xie et al., 2011), and many demonstration systems have been established in the world (Abbas et al., 2013; Zhu et al., 2013). For example, Zhu (2013) gave the summary to the History, current state, and future of linear Fresnel concentrating solar collectors. Xie et al. (2012, 2013) carried out many theoretical and experimental researches about the line-focus Fresnel lens solar collector using different cavity receivers. Morin et al. (2012) discussed the comparison of linear Fresnel and parabolic trough collector power plants and indicated the linear Fresnel systems have more advantage in some special regions. The mirrors of a Fresnel reflector can be installed near the ground, so this kind of system is characteristic of small wind resistance and easy cleaning (Gharbi et al., 2011). Because the reflector is comprised of plane mirrors, its price is relatively low. However, this kind of system cannot obtain a small linear focus. It needs a secondary concentrator which will shade some of sunlight. A flat plate Fresnel lens can obtain a high concentration ratio so that it could obtain high temperature heat. However, it needs to track the sun accurately. Also, when the sunlight comes with an azimuth angle to a linear Fresnel lens, the focus line will have an excursion which will reduce the optical efficiency. Actually, many shaped Fresnel concentrators have been researched. For example, O’Neill and Waller (1980) introduced a transmittance optimized linear Fresnel lens solar concentrator. Araki et al. (2010) also introduced a dome-shaped Fresnel lens which was used in a 30 kW concentrator photovoltaic system. Leutz et al. (1999) introduced a new design of shaped non-imaging Fresnel lens to be used with evacuated-tube

27

solar collector. Leutz et al. (2000) in another paper discussed some theoretical analysis methods about the wedge-shaped Fresnel lens. The receiving half angle of the wedge for a flat plate absorber was given out. Also, Atsushi Akisawa et al. (2012) researched a dome-shaped non-imaging Fresnel lens with ultrahigh concentration ratio and its dispersive problems. A challenge of the shaped Fresnel lens is that its wedge elements will become more and more thick when they are farther from the centre, and this would cause more optical absorption loss. Therefore, it limits the application of shaped Fresnel lens when only single refraction lens is used. This paper presents a cylindrical compound Fresnel solar concentrator which consists of an arched Fresnel lens, a Fresnel mirror and a secondary reflector. It may overcome some drawbacks of parabolic trough concentrators. It is in a cylindrical form, so it is easy to be operated with a low wind or snow resistance performance. Also, it has the characteristics of the greenhouse effect to the receiver and easy to clean its outside. 2. Working principle The structure of the proposed cylindrical compound Fresnel solar concentrator is shown in Fig. 1. The concentrator incorporates a Fresnel lens and a Fresnel reflector to form a cylindrical structure with a secondary reflector and an absorber enclosed inside. Use of the secondary reflector may be helpful to reduce the requirement of tracking precision and thus increase the concentration efficiency. The working principle of this cylindrical concentrator can be described as follow: Ignoring sunshape and beam errors, a beam of sunlight rays come in parallel with the symmetry line of the cylindrical concentrator. When the rays reach the outer surface of Fresnel lens (1), they will be refracted onto the evacuated-absorber (4), where sunlight is absorbed and transformed into heat. When the rays strike on the surface of Fresnel reflector (2), they would be reflected onto the absorber. When there exist a tracking error or sunshape effects, the incoming sunlight will tilt slightly from the symmetry line of the concentrator, so some of the refracted or reflected rays will deviate from the evacuated-tube absorber, however they may be redirected by the secondary reflector (3) onto the absorber. Therefore, the secondary reflect can allow more tolerance in tracking precision. In comparison with a parabolic trough, the advantages of the cylindrical concentrator is as follows: (1) all the components are assembled in a cylinder, which may have a better capacity to resist climate such as resisting dust, wind and rain; (2) because of the function of secondary reflector, the requirement of tracking precision is comparatively low; (3) the center of gravity of the cylinder can be designed in superposition with the center of cylinder, and this therefore help to reduce the driving power during tracking.

28

H. Zheng et al. / Solar Energy 107 (2014) 26–37

1

2

4

3

Fig. 1. Structure of a cylindrical compound Fresnel concentrator. 1. Fresnel lens; 2. Fresnel reflector; 3. Secondary reflector; 4. Evacuated-tube absorber; 5. Spindle; 6. Support frame; and 7. Tracking sensor.

3. Design of the cylindrical compound Fresnel solar concentrator 3.1. Design of the cylindrical Fresnel lens Fig. 2 illustrates the optical principle of the cylindrical Fresnel lens comprising of a number of wedge-shaped element with their thicknesses in the range of dl. The minimum thickness d should be chosen to ensure the structure strength of the cylindrical Fresnel lens, while the maximum thickness l should be chosen to be as thin as possible so as to increase the transmission efficiency of lens. For any wedge in air, when a ray parallel to the y axis strikes at one point on the outer circular surface of the wedge with an incidence angle i and the refraction angle j, the incidence angle and refraction are a and b on the lower side of the wedge. Based on the Snell’s law, we may have:

n¼

sin i sin j

and

n¼

sin b sin a

where n is the refractive index of wedge material. It can be seen from Fig. 2 that the lower side of the wedge has a very important influence on the direction of the refracted light. If its lower side is horizontal, the wedge may not be able to refract the incident ray to the target. Therefore, the angle of the lower side of the wedge should be adjusted, for example, tilted at an angle c so that the wedge could just refract the ray to the target. Generally, there is: n¼

sin b0 sin ðb  cÞ ¼ sin a0 sin ða  cÞ 0

ð1Þ

where a0 and b is the incidence and refraction angles on the tilted lower side, respectively.

Fig. 2. Optical principle of shaped Fresnel lens and some angle relationships.

H. Zheng et al. / Solar Energy 107 (2014) 26–37

xi r

If neglecting the thickness of a wedge, one can get such geometrical relationship:

sin hi ¼

x2 þ y 2 ¼ r 2

tan hi0 ¼

where, x and y is the coordinates of the incident point. At the same time, one can obtain: x pffiffiffiffiffiffiffiffiffiffiffiffiffiffi tgb  ð3Þ r þ r 2  x2 The gradient of the circular surface of lens at the point (x, y) is: dy x ¼ dx y So, the incidence angle i may be given by:  y dx x i ¼ arctg ¼ arctg  ¼ arctg dy x y

ð4Þ

ð5Þ

From the above equations, the required tilt angle c can be determined for every wedge. Afterwards, the width of ith wedge can be calculated as follows, Si ¼

S oi cos ci

ð6Þ

where Si is the width of the horizontal lower side of the ith wedge, ci is the tilt angle, Soi is the width of the tilted lower side. For the given radius r, maximum thickness l and minimum thickness d, one can determine the coordinate (x1, y1) of the right-hand edge on the outer surface of the first wedge, i.e. qffiffiffiffiffiffiffiffiffiffiffiffiffiffi y1  r  l þ d and x1 ¼ r2  y 21 : According to the geometrical relationship in Fig. 2, the coordinates (x2, y2) of the second wedge can be given with reference to (x1, y1),   l cos h1;o d y2 ¼ y1  ð7Þ cos ðh1  h1;o Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 ¼ r2  y 22 ð8Þ

ð13Þ

xi r þ yi

Once the coordinate of each wedge is determined, the refraction angle bi can be given: xi tan bi ¼ ð15Þ r þ yi Then, other angles including i, j, b and a could be calculated using Eqs. (1)–(6). Finally, c can be obtain from Eq. (1). To simplify the calculation, the middle point of each wedge could be chosen as long as the incidence ray could be refracted to the centre of the target. If more accurate design is required, the thickness of each wedge should be considered in calculation. 3.2. Design of the Fresnel mirror For a cylindrical concentrator, it may be not good to cover its semicircle arch only with a shaped Fresnel lens because the thickness of a wedge in the lens becomes bigger when it is farther from the y axis and this would cause more optical absorption loss, and more blocking by the vertical edges of each facet. Instead, a Fresnel mirror could be placed in the section beyond the Fresnel lens to form a compound Fresnel solar concentrator, as shown in Fig. 3. They are all contained in a cylindrical structure and there is no optical interaction between these two sections of this compound concentrator. Supposing that the ith mirror is fixed at (xi, yi) and its installation angle is di (to the vertical direction), for a given secondary concentrator entrance width b, the length of the ith mirror could be given by:

where h1 and h1,o is the angle between y axis and the lines connecting from point (x, y) to the origin point and the receiver, respectively. If the effect of thickness can be neglected, the angles can be given by: x1 sin h1 ¼ ð9Þ r x1 tan h1;o ¼ ð10Þ r þ y1 Similarly, there may be a general relationship between two adjacent points:   l cos hi0 d y iþ1 ¼ y 1  ð11Þ cos ðhi  hi0 Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð12Þ xiþ1 ¼ r2  y 2iþ1

ð14Þ

(

Fig. 3. Schematic view of the Fresnel mirror.

(

ð2Þ

29

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H. Zheng et al. / Solar Energy 107 (2014) 26–37

Di ¼

b cos 2di sin di

ð16Þ

The distance between two mirrors is: d i ¼ xiþ1  xi ¼ Diþ1 sin diþ1

ð17Þ

If the mirror width and the distance between the mirrors are given, the angle di could be determined from Eqs. (16) and (17), and the coordinate of the mirror could be also given, that is: xi ¼ xi1 þ Di sin di

ð18Þ

1 y i  y i1  Di cos di1 2

ð19Þ

The angle di can be also given by: xi tan 2di ¼ r þ yi

ð20Þ

Fig. 4 illustrates the designed compound Fresnel solar concentrator with 3 mirrors on each side of the Fresnel lens. The diameter of the cylindrical concentrator is 2000 mm and the chord length of Fresnel lens is 1300 mm. Adding the Fresnel mirror increases the aperture of the concentrator to 2000 mm to form a semi circle, therefore the aperture area is increased by 54%. When the width of the receiver is 60 mm, the concentration ratio of the compound Fresnel solar concentrator is about 33.3. 4. Simulation study According to the above reference discussions, the CAD model of a designed cylindrical concentrator was made and

imported to LightTools for optical simulation analysis. LightTools is a set of optical modeling tools that allow you to set up, view, modify, and analyze optical systems graphically, in a manner similar to sophisticated CAD programs. Unlike typical CAD programs, however, LightTools has the extended numerical precision and a specialized ray tracing tool that is very helpful for optical design analysis. The theory of ray tracing is based on Monte Carlo theorem, which can trace the chosen number of rays from any interface of a light source. Choice of the starting point and the direction of rays are based on a statistical function which describe the trait of the light source. Then the number of rays collected on a specified receiver is used to do statistical analysis and the results of the analysis can be shown graphically. The ray path through the cylindrical concentrator is illustrated in Fig. 4. In the simulation, the material of Fresnel lens was set as PMMA and the optical properties of PMMA are already in the library of LightTools (refractive index of PMMA n = 1.49). Other assumptions are given as follows, (1) The cylindrical Fresnel lens is of external diameter 2 m and foci (distance from top of lens to the center of receiver) 1.92 m. The reflectivity of both outer surface and inner surface of Fresnel lens are zero. Also, the absorptivity of Fresnel lens is zero. (2) Fresnel reflector and secondary reflector are set to be ideal mirrors, which mean that their reflectivity values are 100% with no surface error. (3) The configuration of secondary reflector is an involute with entrance width of 120 mm, and the receiver is an absolute optical absorber with diameter of 60 mm. (4) The sun’s real shape is ignored and all lights are considered as parallel rays. (5) If there is no specific indication, the number of rays for the Monte Carlo ray tracing is set to be 200. (6) The solar spectrum distribution is omitted. The PMMA only has the average refractivity.

4.1. Analysis of tracking precision requirement

Fig. 4. Optical simulation of the designed compound Fresnel solar concentrator.

Since the position of the sun in the sky changes all the time, a high concentration solar concentrator usually needs to keep track of the sun. The cylindrical concentrator should be also driven to track the sun, although there may be a lag between the tracking position and the actual position of the sun. This lag leads to tracking error. The requirement for tracking precision means the maximum deviation angle that is allowed in tracking and it is a main factor that influences the performance of a solar concentrator. Generally speaking, the higher tracking precision requirement is, the more complicated and energy consuming a tracking system is. The tracking precision requirement may be determined in simulation by varying the angle of rays to the symmetry

31

1.0

1.0

0.9

0.9

0.8

0.8

0.7

0.7

0.6 0.5

Q/Qmax

of the concentrator. The optical path diagrams of simulated rays for various incidence angles are presented in Fig. 5. It can be seen that when tracking is precise, almost 100% incident rays are received by the absorber; when tracking error increases, some of the refracted or reflected rays tend to be deviated from the absorber. In addition, the focus of the reflected rays is separate from that of the refracted rays. When the incident rays come slightly from the right-hand side, the focus of the refracted rays moves towards left while the focus of the reflected rays moves opposite. Fig. 6 shows the relationship between the collection efficiency and the tracking error angle. When the tracking error angle is within 1.5°, the cylindrical concentrator has a relatively high collection efficiency of more than 95%; when the tracking error angle is bigger than 2°, the collection efficiency decreases sharply, realistic sunshape or beam errors would decrease these values significantly. From this analysis, we can conclude that the tracking precision requirement should be about 1.5°. This value is relatively large. Generally speaking, the tracking precision requirement of the parabolic trough solar collector is within 10 mrad (Cheng et al., 2014). Although, Li et al. (2013)

Collection efficiency

H. Zheng et al. / Solar Energy 107 (2014) 26–37

0.6 simulation collection efficiency experimental Q/Qmax

0.5

0.4 0.4 0.3 0.0

0.5

1.0

1.5

2.0

2.5

Tracking error angle/° Fig. 6. Relationship between collection efficiency and tracking error.

introduced a Fresnel lens with 1.4° allowable tracking error, the bright spot width of the lens is only 30 mm. Therefore, large allowable tracking error is a merit of the system which is propitious to utilization of a simple tracking system. As our previous analysis has ignored sunshape and surface errors, these results are optimistic by perhaps 0.5°.

4.2. Effect of longitudinal incidence angle For a linear Fresnel lens, the focal line of the refracted rays will change with the longitudinal incidence angle even when the transverse tracking error is 0. A simulation was also conducted to evaluate this effect by changing the longitudinal incidence angle and the results are shown in Fig. 7 in which the number of rays for the Monte Carlo ray tracing is 1000. It is can be seen that when the longitudinal inci-

Fig. 5. Light distribution in the cylindrical concentrator for various different tracking errors.

Fig. 7. Simulated light distribution in the cylindrical concentrator for various longitudinal incidence angles.

32

H. Zheng et al. / Solar Energy 107 (2014) 26–37

dence angle increases, the refracted rays are more scattered around the absorber and unorderly. However, when the longitudinal incidence angle is within 20°, most of the incidence rays can still reach absorber due to the effect of secondary reflector. If surface error, sun shape and other factors have been taken into account, the number of rays collected by receiver will be decreased, just as the experimental curve shown in Fig. 7. The relationship between collection efficiency and longitudinal incidence angle can be concluded and shown in Fig. 8. Considering this effect, a cylindrical Fresnel solar concentrator is suggested for installation in low latitude regions when system is required to install horizontally and to be placed with its longitudinal direction to be north-south. 4.3. Intensity distribution on the focal plane

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

simulation collection efficiency experimental Q/Qmax

0.2 0.0

0

10

20

30

40

The use of the secondary reflector is to re-direct some scattered or deviated rays to the absorber to accommodate effects due to sunshape, the tracking error or lens manufacturing error. For the simulated cylindrical concentrator, a trough formed from an involute was used as the secondary reflector with the entrance width of 240 mm. The secondary reflector consists of two parts of which one is an involute based on a circle with 30 mm and another is a parabolic. The equation of the involute is:  x ¼30  ðsin h  h cos hÞ ð21Þ y ¼  30  ðcos h þ h sin hÞ where the radius of the circle is r = 30 mm; h denotes the involute angle and the normal line at any point of the involute is tangent with the circle. The original equation of the parabolic is: x2 ¼ 4f  y ¼ 159:6y

ð22Þ

where the foci of the parabolic is f = 39.9 mm. The involute is connected by the parabolic smoothly. An optical simulation of the secondary reflector was also carried out and the results are shown in Fig. 10. It can be seen that this secondary reflector has a suitable acceptance angle. Until incidental angle reaches 35°, the receiving rate of the lights is still more than 90%. 5. Experiment and analysis A cylindrical Fresnel lens was fabricated using CNC (computer numerical control) cutting of a thermal-forming PMMA sheet. The cylindrical Fresnel lens has a diameter 2 m, length of 0.5 m and chord of 1.3 m. It was fixed on a rigid arc to maintain its shape, as shown in Fig. 11. The lens and its support can be rotated along the cylindrical axis to track the sun. A flat sheet was placed on the focal patch which is about 2.0 m below the top of the lens. The sheet has a graduated scale in order to indicate the width of the focal patch. 5.1. Effect of tracking error on the position of focal patch

Q/Qmax

Collection efficiency

When the cylindrical solar concentrator is used for concentrating photovoltaic, it would be necessary to know the intensity distribution on the focal plane. The arch-shaped Fresnel lens is comprised of a number of wedged elements and it may not have a clear focus line but rather a focus patch. This issue could perhaps be alleviated with use of a secondary reflector, which also helps to reduce the tracking precision requirement. From the optical simulation results, the intensity distribution on the focal plane can also be studied. For the condition without a secondary reflector and with the longitudinal offset to be 0°, the energy distribution on the focus plane is shown in Fig. 9 for 0°, 0.5°, 1°, 1.5°, 2° and 2.5° tracking error. In this simulation, sunshape and beam errors are ignored and the number of tracing rays is 5000. In this figure, x-axis represents the width direction of the bright spot and z-axis represents the symmetry axis direction of the cylindrical Fresnel concentrator. It can be seen that the focal patch gradually becomes wider and more scattering when the tracking error angle increases. When the tracking error angle is 1°, the width of the patch is about 60 mm.

4.4. The design of the secondary reflector

0.2 0.0 50

Tilt incidence angle/° Fig. 8. Variation of the collection efficiency with longitudinal incidence angle.

An experiment was carried out at the solar noon of 10 April 2013 in Beijing (latitude: 39°540 ). The cylindrical Fresnel lens and its support structure were rotated (in 1D) to give a 0° incidence angle for the sunlight at that time. A clear bright focal patch was seen at the centre of the receiver sheet which was placed on the design focal patch. This indicates this Fresnel lens was successful designed and fabricated for solar concentration. The Fresnel lens was then kept stationary for a period when the change of the focal patch was recorded every minute using a camera. The position of the focal patch was indicated using a scale paper. Fig. 12 shows some photos of the focal patch and the change of its position with the tracking error,

H. Zheng et al. / Solar Energy 107 (2014) 26–37

33

X, mm

(a) 0°

(b) 0.5°

(c) 1°

(d) 1.5°

(e) 2°

(f) 2.5°

Z, mm

Fig. 9. Simulated energy intensity distribution on the focal plane with the error angles.

Fig. 11. Photo of the experimental cylindrical Fresnel lens.

i.e. deviation angle from the sunlight ray. It can be seen that for the tracking error of 1.5° the focal patch is offset about 4 cm, but, as discussed before, this angle could be considered as the allowable tracking error angle when a second reflector is used. 5.2. Effect of longitudinal incidence angle on the focal patch

Fig. 10. The structure and the acceptance angle of the secondary reflector.

When the incident light is not perpendicular to the axis of the cylindrical Fresnel lens, the focal patch would have an axial shift. In another experiment, the cylindrical Fresnel lens was tilted axially to the sunlight and to observe

34

H. Zheng et al. / Solar Energy 107 (2014) 26–37

Fig. 12. Experimental effect of tracking error on the focal patch at the focal plane.

how the focal patch will move and change. The results are shown in Fig. 13. From Fig. 13, it can be found that the focal patch includes two parts, i.e. main bright spot and appendant bright spot. Main bright spot is formed by those lights which are refracted only two times in the wedge (on upside

10

and downside). Appendant bright spot is formed by those lights which are refracted more than two times in the wedge (on upside and downside). When the axial tilt angle or longitudinal incidence angle was increased, two parts of the focal patch became wider and had obscure images, which means a reduced intensity of light. For 10° longitudinal

10

cm

cm

5

5

0

0

-5

-5

-10

-10

10 5 0 -5 -10

cm

Width of the focal patch/cm

27 24

main bright spot appendant bright spot

21 18 15 12 9 6 3 0

5

10

15

20

25

Axis deviation angle of incident light/° Fig. 13. Experimental effect of the longitudinal incidence angle at the focal plane.

30

H. Zheng et al. / Solar Energy 107 (2014) 26–37

incidence angle, the main bright spot is about 4 cm wide, while the appendant bright spot has a width of about 12 cm. 5.3. The concentrating efficiency of the experimental Fresnel lens To investigate the actual performance of the cylindrical Fresnel lens, an evacuated-tube solar absorber with effective length 0.5 m was installed at the main bright spot of lens and coupled with a secondary reflector with reflectance 0.92, as shown in Fig. 14. The dimensions of the cylindrical Fresnel lens and the secondary reflector is same as that of the simulation model. The water flow through the absorber is heated by the concentrated sunlight, and the inlet and outlet temperatures of water flow can be measured to calculate the absorbed solar heat. The total solar irradiation was measured by TQ-1 solar meter and the direct solar radiation measured by TQ-3 direct solar meter. The meters are with 5% relative error. The inlet and outlet temperatures of water were recorded by TYD-WD multiple channel digital temperature-recording meter through K-type thermal couples. The thermal couples are with ±0.1 °C absolute errors. Afterwards, the optical efficiency of the cylindrical Fresnel lens can be calculated from the incident irradiation and the absorbed heat. 5.3.1. Collecting efficiency under different tracking error angles The experiments were carried out on 10/09/2013 in Beijing. That day was a sunny day. When the altitude of the sun approached the maximum i.e. within 11:0811:20, let the cylindrical Fresnel lens track the sun exactly. The water flowed from the receiver was heated. The inlet and outlet temperatures of water and flow rate were measured. At the same time, the total and direct solar radiation was recorded. In the experiment, the cylindrical Fresnel lens was fixed. When the sun moves across the sky with speed of 0.25°/min, the sun lights go into the concentrator with different angles. The deviation angle was considered to be the tracking error. Due to the experimental period being short, the altitude of the sun is considered to be unchanged. Fig. 15 shows the inlet and outlet temperatures of water and direct solar radiation value along with Beijing time. The water flow rate was 26.92 g/s. The figure indicates that the water temperature at the beginning had a little drop Receiver plate

which was caused by the heterogeneous water temperature in the tank. Based on the test data, the transient collecting efficiency of the system can be calculated and also shown in Fig. 15. It can be found from Fig. 15 that the efficiency substantially keeps steady in the first 4 min. That is to say that the collecting efficiency is essentially constant when the tracking error angle is less than 1°. The collecting efficiency decreases quickly when the tracking error angle is bigger than 1°. When the tracking error angle is 1.5° (sun moved 6 min), the efficiency will decrease to 75%. At 12:08, the total and direct solar radiation is 1034 and 740 W/m2, respectively. The maximum collecting efficiency reached about 83.1% which is near to the optical efficiency. It is noteworthy that the diffused solar radiation received by the secondary reflector was omitted in efficiency calculation. Based on the meter’s relative error and the absolute error of the thermal couple, the absolute error of the calculated efficiency is 0.03 which also shows in Fig. 15. 5.3.2. Collecting efficiency under different longitudinal incidence angles In practical engineering, this kind of concentrator only tracks the sun with one axis. Therefore, in most cases, the sun light goes into the device with longitudinal incidence angles. The collecting performance of the device with longitudinal incidence angles was tested on 15/9/2013. It is difficult to give out a continuous curve on the different longitudinal incidence angles because it needs time to adjust the device to different longitudinal angles. The experimental results are given in Table 1. The collecting efficiency is calculated on the basis of the direct solar radiation. From Table 1, it can be found that the collecting efficiency on the basis of the direct solar radiation will decrease with the longitudinal incidence angle. However, when the longitudinal angle is less than 10°, the decrease is not clear. When the longitudinal angle is 20°, the efficiency will decrease to 85% that of 0°. Meanwhile, the diffused solar radiation received by the secondary reflector was omitted in efficiency calculation. 5.3.3. The comparison between the experiment and simulation Let Q represent the collected heat of the device with incidence deviation angle or longitudinal angle and Qmax represent that without deviation angle or longitudinal angle. Then, Q/Qmax can approximately describe the proportion

Vaccum tube

Receiver plate

T2 Water out Cool water 500mm (a) Vaccum tube receiver

35

T1

Secondary reflector (b) The receiver section

Fig. 14. The evacuated-tube solar absorber coupled with the secondary reflector.

36

H. Zheng et al. / Solar Energy 107 (2014) 26–37 800

33 90

700 80

Temperature /ºC

30 70

29 28

60

27 26

50

input water temperature output water temperature

25

40

24

600 500 400 300 200

Direct solar radiation / W/m2

direct solar radiation efficiency

31

Collection efficiency / %

32

100 30

23

0 12:08

12:10

12:12

12:14

12:16

12:18

Local time / hh:mm Fig. 15. The variation of the experimental parameters with local time for a collector fixed at 12:08.

Table 1 The experimental results on the longitudinal incidence angles. Longitudinal angle (°)

DT (°C)

IT (W/ m2)

Id (W/ m2)

Collection efficiency (%)

0 2 5 8.5 10 12 15 20 25 30

3.14 3.12 3.12 3.10 3.01 2.95 2.88 2.73 2.48 2.04

937 940 925 930 933 950 955 960 965 970

703 705 701 706 709 713 715 719 723 733

79.3 78.5 78.4 77.7 75.4 73.4 71.6 67.4 61.4 49.5

of the light number arrived the receiver. That is to say, this ratio may be considered as the relative optical efficiency of the cylindrical Fresnel lens approximately. When sun light goes into the cylindrical Fresnel lens with tracking error angle, the variation of Q/Qmax with different tracking error angles is shown in Fig. 6. It can be seen from Fig. 6 that the change of the ratio with the tracking error angle is same as the simulation trend. However, the experimental quantity is lower than that of the simulating results, especially in large error angle range. When sun light goes into the cylindrical Fresnel lens with different longitudinal angles, the variation of Q/Qmax with longitudinal angle is shown in Fig. 8. Similarly, one can see the same trend between them. Also, the experimental quantity is lower than that of the simulating results, especially in the large longitudinal angle range. These therefore verified the simulation and also the design calculation. It is noticeable that the measuring time is different to Q and Qmax, so as to the solar radiation in Q and Qmax is different. Also, it only is a primary approximate using Q/Qmax to describe the optical efficiency. The experimental results indicate that the experimental quantity is lower than that of the simulating result. The reason for the deviations is some loss to be included in

the practical system, for example, the heat loss from the receiver and optical loss in several optical surfaces. The optical losses might be main reason for that, which includes: (1) Optical absorption by the lens. Some wedges of the Fresnel lens are relatively thick, up to 12 mm (average thickness is about 6 mm); (2) Optical escape due to the surface reflection of the glass tube and the deviated rays from the receiver; (3) Heat loss of the absorber; (4) Other effects due to sun shape, areole, or surface errors.

6. Conclusions In this study, a cylindrical compound Fresnel solar concentrator has been devised and investigated. All the optical elements of the concentrator are mounted in an entire cylinder, so this cylindrical concentrator has a better weather resistance compared with a parabolic trough. In addition, use of a secondary reflector has reduced the requirement of tracking precision and hence helps to increase the optical efficiency in practice. An optical simulation analysis has been done to evaluate the optical efficiency of the cylindrical concentrator for different incidence angles and the results indicate the allowable tracking error could be less than 1.5° for the geometrical concentration ratio of 33.3. Use of a secondary reflector also contributes to reduce the requirement of tracking precision. A prototype cylindrical compound Fresnel concentrator has been constructed and tested to investigate its characteristics of solar concentration. The variation of the focus width and position with the incidental angle has been given and the optical efficiency of up to 84% has been also measured.

Acknowledgements This work is supported by the National Natural Science Foundation of China (No. U1261119). The authors would

H. Zheng et al. / Solar Energy 107 (2014) 26–37

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