Truncation effects in an evacuated compound parabolic and involute concentrator with experimental and analytical investigations

Accepted Manuscript Truncation effects in an evacuated compound parabolic and involute concentrator with experimental and analytical investigations Abid Ustaoglu, Junnosuke Okajima, Xin-Rong(Ron.) Zhang, Shigenao Maruyama PII: DOI: Reference:

S1359-4311(17)35378-4 https://doi.org/10.1016/j.applthermaleng.2018.04.062 ATE 12059

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

18 August 2017 27 February 2018 11 April 2018

Please cite this article as: A. Ustaoglu, J. Okajima, Xin-Rong(Ron.) Zhang, S. Maruyama, Truncation effects in an evacuated compound parabolic and involute concentrator with experimental and analytical investigations, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/j.applthermaleng.2018.04.062

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Truncation effects in an evacuated compound parabolic and involute concentrator with experimental and analytical investigations

Abid Ustaoglu1,*, Junnosuke Okajima2, Xin-Rong(Ron.) Zhang3, Shigenao Maruyama2

1

Mechanical engineering Department, Bartin University, Bartin, 74100, Turkey 2

3

Institute of Fluid Science, Tohoku University, Sendai, 980-8577, Japan

Department of Energy and Resources Engineering, College of Engineering, Peking University, Beijing 100871, China *Corresponding author Tel.: +90 378 501 10 00-1689, Fax: +90 378 501 10 21; E mail address: [email protected], [email protected]

Abstract

A two-stage line-axis solar concentrator composed of parabolic and involute reflectors with tubular absorber, have been designed and experimentally analyzed for thermal applications. The concentrator is covered by evacuated glass tube for low-heat loss configuration. Due to steep angle at the end of compound parabolic reflector, the concentrator tolerates to truncate a portion of the reflector with only slight reduction on the performance. Optimum truncation level is estimated by evaluating of ray acceptance, which is described as the ratio of aperture area of the concentrator to diameter of glass cover, concentration ratio, optical performance and thermal performance. The concentrator with truncation level of 50% shows preferable performance with only 1% reduction in thermal performance as well as significant reduction on material requirement. An experimental analysis was conducted for a 50% truncated concentrator to validate the ray tracing analysis and the thermal performance as a function of inlet temperature of water and the surface temperature of 1

absorber. The experimental results show good agreement with the ray-tracing program written for theoretical evaluation. Consequently, the truncation of the concentrator provides requirement of less amount of optical component through significant reductions in size of reflector and glass cover with a small reduction in concentrator rate to achieve the economic viability and attraction for buildings.

Key words: Thermal performance, Compound parabolic concentrator; involute reflector; ray tracing; uniformity, truncation, experimental analysis

1. Introduction

Effective utilization of primary energy sources by reducing energy losses or by energy conversion of waste heat in thermodynamic systems is an important issue for energy future (Alptekin et al., 2017; Ustaoglu et al., 2017a; Ustaoglu et al., 2017b). However, it doesn’t change the reality of that there is limited amount of primary energy source. In order to develop new energy alternatives as a way to solve the energy problem, solar energy draws considerably interest. On the other hand, solar energy requires high cost for the equipment to effectively use the energy such a moving energy source as the sun. However, as a result of the increase of the fossil and nuclear fuels prices, the feasibility of the solar energy as an energy alternative has been increased by effort of the cost reduction An enormous amount of radiation by the sun arrives at the earth surface in spite of attenuation by atmosphere (6% by reflection and 16% by absorption) and clouds (20% by reflection and 3% by absorption) (Smil, 1991). However, due to its low density, the incident radiation needs to be concentrated to make this energy more useful. Therefore, solar concentrating systems have been an option to utilize incident solar radiation more effectively by increasing radiative heat flux. This thermal energy can be used in thermal applications or to generate electricity in a solar power plant. 2

There are many studies about solar concentrator systems for various applications (Kandilli, 2013;2016; Kandilli and Külahlı, 2017) Non-imaging concentrators have received attention of optical physics, over last a few decades. These concentrators are also of interest for design of non-tracking solar concentrators, because they can utilize diffuse solar irradiation as well as direct irradiation, and can approach the maximum possible concentration (Suresh et al. 1990). This kind of concentrators have larger acceptance for diffuse solar irradiation compare to the concentrator which is using imaging optics and hold the potential for low cost of flat plate collectors (Winston, 1974). They are usually used for low temperature applications and have wide rage studies for different geometries. The most familiar one of these kinds of collectors is compound parabolic concentrator (CPC) which is an ideal concentrator because it actually reaches the ideal limit of concentration ratio. CPC was designed to collect light from Cerenkov counters by Hinterberger and Winston (1966a, 1966b). Winston (1974) described the CPC in 2D geometry. Rabl (1975) proposed some concentrators, including the use of CPC with conventional parabolic or Fresnel mirrors, to obtain higher concentration ratio. The optical and thermal properties of CPC were evaluated and these were compared with the truncated CPC (Rabl, 1976). Carvolho and Collares-pereira (1985) analyzed some degrees of truncation of CPC and its effect on monthly and yearly energy collection. Suresh et al. (1990) experimentally tested the CPC with different reflector surface and evaluated the performance characteristics of a properly truncated CPC that could be manipulated in two-stage thermal power generation system. There have been many studies carried out about CPC to improve the system with worldwide increasing interest (Acuña et al. 2016; Ma et al., 2017; Santos-González et al., 2017; Singh and Eames, 2011) In addition, involute concentrators have been an alternative for non-imaging solar collector systems to be used with tubular absorbers. A non-parabolic concentrator, which compounds of two involute reflectors, was proposed by Winston and Hinterberger (1975). Its required shape was calculated explicitly by Rabl (1975). Winston (1978) proposed an alternative design strategy to 3

preserve the ideal concentration on the enclosed absorber by slightly oversizing the reflector. Maruyama (1993) proposed an involute reflector to generate uniform and homogeneous emission from the absorber, and performed a ray-tracing calculation to evaluate its optical characteristics. Although concentrating collectors are suitable for solar energy utilization with higher radiative heat flux on the absorber, some difficulties and problems may arise from design and geometry. In the many concentrators, reflector surface is open to ambient and is affected by environmental factors such as dust and climate variation. Nostell et al. (1998) analyzed aging of several solarreflector materials and showed that their specular properties deteriorate after 5 years. Therefore, the optical performance decreases in the process of time. Therefore, the protection of the optical component can improve the effective life cycle of concentrator. On the other hand, non-uniform illumination on the receiving area can cause hot spots and have bad effects on the absorber in which working fluid is used for transporting of heat since undesirable temperature gradients can develop (Welford and Winston, 1978; Tabor, 1984). It is particularly important for photovoltaic systems using solar concentrator. The non-uniform distribution of incoming solar irradiation on the PV cell results in an uneven current distribution thereby decreasing electric output (Brogren et al., 2000). The truncation causes a significant reduction of hot spots on receiving area (Ustaoglu et al, 2016c). Other issues are the additional expense, power consumption, and maintenance requirement when a sun tracking system is used. A two-stage solar thermal concentrator designed with exploitation the advantages of involute and compound parabolic reflector was considered in terms of optical and thermal performance (Ustaoglu et al, 2016a). In order to increase the effective life cycle, the concentrator unit was covered with evacuated glass tube since glass is long-term stable and the transmittance at solar wavelengths. This also improved the thermal performance significantly because of minimizing convective heat loss from the absorber. In order to improve the ray acceptance, which can be described the ratio of the reflector aperture area to the diameter of glass cover; a dual form of concentrator was considered (Ustaoglu et al, 2016b). This configuration is preferable for multiple 4

concentrator unit applications because of its comparatively less glazing material requirement. Moreover, the duel type design enables the applicability of U-type absorber tube and abolishes the requirement for the unilateral insolation cap on the vacuum glass tube. These are very important issues in practice. In order to reduce the material cost, the truncation of a conventional cylindrical CPC was evaluated (Ustaoglu et al, 2016c). The truncation level was decided in terms of thermal performance and uniformity of solar illumination on the receiving area. The optimum size of CPC in terms of the solar uniformity was achieved without any significant reduction on the performance The compound parabolic and involute concentrator design uses glass cover (Ustaoglu et al, 2016a; 2016b). Unwieldy size of the compound parabolic reflector in the concentrator increases occupying area of concentrator unit because of large size of glass tube in which there is idle areas out of aperture of reflector. Since the steep angle at the end of parabolic reflectors have very slight effect on the performance, truncation of the upper part of the reflector is essential. This can reduce the component cost significantly due to the substantial reduction on the size of reflector and glass tube diameter. On the other hand, deciding the optimum size is very important to minimize the performance reduction. The present work discussed about truncation of the compound parabolic and involute concentrator. The effect of the truncation was evaluated in terms of optical efficiency and thermal efficiency. The thermal performance of the concentrator was experimentally evaluated and compared with theoretical performance as function of absorber temperature and inlet temperature of working fluid. The main objective of this study is to determine the optimum size of the concentrator, to evaluate the truncation effect of the concentrator on the performance and to reduce the component cost by using small size of reflector and glass tube without any significant loss on performance to validate the theoretical model with experimental analysis results.

2. Analyzed model and method 2.1. Two-stage concentrator and truncation 5

The concentrator was designed by using compound parabolic and involute reflectors with tubular absorber. The design is mainly based on the exploitation of the uniform distribution of temperature on absorber and approaching to the highest possible concentration within the acceptance angle. Furthermore the concentrator is covered by an evacuated glass tube to eliminate the convective and conductive heat losses, to provide easy maintenance, and to protect the reflector from external condition. The cross section of the concentrator is shown in Fig. 1.

Fig. 1. Cross section of the concentrator (Ustaoglu et al, 2016a)

The compound parabolic reflector was used to eliminate the sun tracking system requirement and to achieve the highest concentration. Its acceptance angle was decided to utilize the sun between winter and summer solstices. On the other hand, acceptance angle of involute reflector was set to be 90, thereby concentrating all radiation, which crosses aperture of involute reflector, to the absorber. The involute reflector with tubular absorber was used to illuminate the all sides of the absorber. This can improve the temperature uniformity around absorber. Since the tubular absorber practically has no back-side, the back-side heat loss which occurs for a flat plate absorber is eliminated. The truncation was considered only at the end of compound parabolic reflector which has no significant effect on the concentration due to steep angle. The reduction in the concentrator rate can 6

be minimized by choosing of the optimum size of the reflector. To decide the optimum level of truncation, several evaluations were carried out including ray acceptance, optical and thermal efficiency. The basic geometry of the truncated concentrator is shown in Fig. 2, in which the dashed black-line figure represents the full concentrator and solid red-line figure represents the truncated concentrator. L indicates the aperture length of the concentrator, and s describes the aperture length of involute reflector or circumference of the absorber tube in 2D cross-section.

Fig. 2. Cross section geometry of the truncated concentrator

The coordinate system equation of the compound parabolic reflector can be determined by

y

x2 2s(1  sin  max )

(1)

The coordinate equation of the initial A (xs,ys) and end point C(xL,yL) of the parabolic reflector can be described by

xS  s cosmax ; yS  s(1  sin max ) / 2

(2)

and

 s 1  xL  (s  L) cos max ; yL  1  sin  max  1   2  sin  max  7

2

(3)

As the aperture length of the reflector varies from s to L value through the parabolic reflector, its x component differs with a value of Lcos as seen from Eq. (2) and Eq. (3). The L value of the equations can be changed as a variation parameter of the truncation level. The involute part constitutes 16% of the full reflector length. As the total length of the involute and parabolic reflectors was considered in the calculation, the truncation was carried out only for the parabolic reflector part of 84%. The ratio of the concentrator aperture area Ac to absorber area, or the aperture area of the involute reflector Aa, describes the concentration ratio C as given by Eq. (4):

C

Ac L 1   Aa s sin  max

(4)

where the value of 1/sinθmax is applicable only for the geometry of the full concentrator. In order to apprehend explicitly the reduction on the concentration ratio, the comparative concentration ratio was considered as expressed in following equation,

Ccom 

Ctrun C full

(5)

where Ctrun and Cfull represent the concentration ratio of truncated and full concentrator, respectively. Moreover, ray acceptance Ra, which was described as a ratio of the aperture area of the reflector to the glass cover diameter Dgl, were also evaluated for different truncation level since it may be important effective utilization of the occupying area of the concentrator. A full size of a non-imaging concentrator can concentrate all rays which cross the aperture area of the reflector within the acceptance angle to receiver either directly or after several reflections. A truncated reflector, however, may accept some incident rays which are out of the acceptance angle and reach aperture area of involute reflector. Figure 3 shows the cross section of the full and truncated concentrator. The extreme rays r1 and r2 come to aperture of involute reflector an incident angle which is higher than acceptance angle (θmax+). The solar rays between these extreme rays 8

can reach to the aperture of involute; then some rays hit the absorber directly and some of them reach after reflect from involute reflector. Therefore, the acceptance angle characteristic of a truncated concentrator can be considered to be 0 < |θ| < θt for the rays that reach the aperture of involute reflector. θt is the new acceptance angle. Beyond θt all rays are rejected.

Fig. 3. Truncation in terms of acceptance angle

2.2. Thermal Performance Evaluation

To evaluate the performance of the concentrator, a ray-tracing method was used for 2-D geometry. The ray tracing technique employed in the calculations was written in FORTRAN program to simulate the interaction of the light with the concentrator. A configurable number of rays are equally spaced across the aperture area of glass tube. To determine the direction of rays by passing through the glass tube, Snells law for refraction was adapted to program. As the incident rays pass through the glass cover, the direction of light changed depending on the refractive index of glass tube and transverse angle. The energy of the ray decreases depending on transmissivity and the direction of the ray changes again depending on the medium inside the glass tube. The 9

transmitted ray hits reflector and reflect with same angle of incident. An energy fraction of the ray is intermitted depending on reflectivity. The reflected ray strikes absorber and its energy is absorbed depending on absorptivity of absorber. The hit point of incident ray is memorized. Hence, the distribution of solar heat flux around the absorber can be determined. The model was validated in previous study (Ustaoglu et al., 2016a) by comparing the result of our calculation with those obtained from other studies for CPC, carried out by some authors such as Rabl (1976) and Su et al. (2012). The data were taken from references having same conditions are sufficiently close our results (Ustaoglu et al., 2016a). Thermal efficiency of the concentrator can be calculated as a function of absorber temperature or inlet temperature of working fluid.

2.2.1. Thermal efficiency in terms of absorber temperature

After being transmitted through the glass cover and reflected from the specular surface, the insolation qs is absorbed by the receiver pipe based on the absorbing ability. The useful energy gain depends strongly on the energy losses from the absorber, due to both the convective heat loss to the ambient air and radiative heat loss to its surroundings. Regarding with the optical and thermal losses, the useful energy can be expressed as (Howell et al, 1982). 4 Qu (t )  qu (t ) Ac  opt qs (t ) Ac  hout Aa (Ta  Tamb )   Aa Ta4  Tamb 

(6)

In Eq. 6, the optical efficiency opt accounts for the effects of transmission, reflection and absorption losses due to the cover glass, reflectors and absorber. The following equation can describe the optical efficiency.

opt

 

i n i 1

rRn

Nr

 ab c

(7)

where Rn is number of reflection that was determined by Ray tracing analysis, Nr is the number of ray and n is the number of the captured ray by aperture of the concentrator. αab is the absorptivity of 10

absorber, τc is the transmissivity of glass cover and ρr is the reflectivity of reflector. The second and final terms of the Eq.6 represents the heat loss from the absorber through the conduction and convection, and radiation, respectively. Thus, the concentrator efficiency, which is the ratio of the useful to available energy, can be obtained as follows:

th 

4 4 Qu (t ) h A (T  T )  Aa Ta  Tamb   opt  out a a amb  qs (t ) Ac qs (t ) Ac qs (t ) Ac

(8)

The ratio of the concentrator aperture area to absorber area, or the aperture area of the involute reflector, describes the C as given by C

Ac 1  Aa sin  max

(9)

Rearranging Eq. 8 with considering concentration ratio:

th1  opt

4 4 hout Ta  Tamb   Ta  Tamb    qs C qsC

(10)

Corresponding with the second term, the convective and conductive heat losses must be considered. In comparison with a conventional CPC having a flat absorber, the design has a tubular absorber having no back side that can cause conduction heat loss. Therefore, the conduction loss may not be taken into account. As regards to the convective heat loss, the design is covered by glass cover, hence; the heat loss from the absorber may be considered by natural convection for nonvacuum case. When the transport medium between glass cover and absorber is evacuated, the heat loss through the convection can be eliminated as well. For a non-vacuum case, the hout can be calculated by following equations. hout 

kair Nu Dout

(11)

where kair is the conductivity of the air, Dout is the outer diameter of the absorber and Nu is Nusselt number, for which Churchill and Chu (1975) have recommended a single correlation for a wide 11

range Rayleigh number range RaD ≤ 1012 in the case of a long horizontal cylinder:   0.387 Ra1/D 6   Nu  0.6   8/ 27 1  (0.559 / Pr)9 /16     

(12)

In this equation Pr is Prandtl number. Rayleigh number RaD can be obtain by RaD 

3 g  (Ta  Tamb ) Dout

(13)



where g is acceleration of gravity,  is thermal expansion coefficient and equals to 1/Tave regarding to surface and ambient temperature. The  is kinematic viscosity and  is thermal diffusivity. The properties of the air around the absorber can be decided at the film temperature which can be defined as (Ta +Tamb)/2.

2.2.2. Thermal efficiency in terms of inlet temperature

From the different viewpoint, to simplify the test of the collectors, it may be desirable to put another evaluation in terms of fluid inlet temperature rather than in terms of the average surface temperature (Howell et al, 1982). The useful energy collected per unit time may be expressed as Qu  mc p (Tout  Tin )

(14)

It can be also expressed as follows (Bhowmik et al, 1985; Duffie and Beckman, 2013) U   Qu  Aa FR opt qs  L (Tin  Tamb )  C  

(15)

It is proper to define a quantity that relates the actual useful energy achievement to the useful energy when the whole absorber surface was at the fluid inlet temperature. That is known as the collector heat removal factor FR (Howell et al, 1982). The maximum possible useful energy gain occurs when the whole absorber is at the inlet temperature. The heat removal factor can be calculated by FR 

mc p

1  exp( AaU L F '/ mc p )  AaU L 

(16) 12

where m is the mass flow rate, F' is the efficiency factor that can be calculated by Uo/ UL. Uo is the overall heat transfer coefficient (Eq. 17)  1 D D ln( Dout / Din )  Uo    out  out  2k  U L ha Din 

1

(17)

where Din and Dout are the inner and outer diameter of the absorber. k is the thermal conductivity of the copper absorber. ha is the heat transfer coefficient to the working fluid and can be calculated by ha 

k flu Din

(18)

Nu

where kflu is the conductivity of the working fluid. Nusselt number can be calculated depending on the laminar and turbulent flow in the tube. For a laminar flow with an assumption of fully developed conditions, Nusselt number can be assumed to be 4.36. For the case of turbulent flow the Dittus-Boelter equation is an explicit function for calculating the Nusselt number and can be expressed as follows. 0.4 Nu  0.023Re0.8 D Pr

(19)

Reynolds number ReD can be calculated by following equation Re D 

4m  Din 

(20)

where  is viscosity. The properties of the working fluid can be evaluated at the average temperature of fluid regarding to inlet and outlet temperature. In Eq. 21, UL is the heat loss coefficient from the absorber trough the radiative and convective heat transfer and can be obtained by (Duffie and Beckman, 2013) U L  hout  hr

(21)

where hr is 4T3ave. Tave indicate the average temperature between the ambient and absorber temperature. Finally, the thermal efficiency can be considered as ratio of the useful energy to the input energy through the solar insolation may now be calculated by considering Eq. 14 and Eq. 15 (Bhowmik et al, 1985; Duffie and Beckman, 2013; Rifat and Mayere, 2013) as follow. 13

th 2  mc p (Tout  Tin ) / qs Ac 

th3  FR opt  

(22)

 UL Tin  Tamb  qs C 

(23)

These equations is solved to give the equation of the outlet temperature of the working fluid as follow (Bhowmik et al, 1985) Tout  Tamb 

Cqsopt UL

 (Tin  Tamb 

Cqsopt UL

)  exp( AaU L F / mc p )

(24)

Thermal efficiency was stated by three different equations. Equations (10) and (23) represent the thermal efficiency as function of the absorber temperature and inlet temperature of water, respectively, and can be considered for the theoretical evaluation of the thermal efficiency. On the other hand, the ratio of the energy change between the inlet and outlet of the concentrator or the attainable energy to the available incident energy represents the results of the experimental evaluation of the thermal efficiency as stated in Eq. (22).

2.3. Solar insolation

When the horizontal total global terrestrial insolation H and the total direct terrestrial insolation Ib are obtainable, the diffuse insolation Hd on the horizontal surface can be determined by following equation (Liu and Jordan, 1960)

H d  H  Hb  H  I sc sin  s

(25)

where Hb is direct solar irradiance on the horizontal surface. The insolation on the tilted surface can be obtained by qs  I b cos   H d cos 2

 2

 H r sin 2



(26)

2

where cos2 /2 indicates the radiative configuration factor from the tilted surface to sky and represents fraction of the diffuse insolation that reach the earth surface. sin2 /2 remain fraction of surface-to-sky-configuration factor. r is effective diffuse ground reflectance of the diffuse plus 14

beam insolation on the horizontal surface (Hunn and Calafell, 1977) Equation (26) is commonly written as follows (Howell et al, 1982): qs  Hb Rb  H d Rd  H r Rr

(27)

or basically qs  HR

(28)

where Rb 

cos  sin  s

Rd  cos 2 Rr  sin 2

(29)



(30)

2



(31)

2

 H R  1  d H 

Hd  Rd  r Rr  Rb  H 

(32)

A pyranometer was used to measure the total global solar irradiation. In order to determine the diffuse radiation, the pyranometer is used with a shadow band. This band was adjusted along the direction parallel to the earth’s axis to make shadow to direct sunlight and remained still during the measurement until the measured value of the solar irradiation was fixed. Thus, the value of H and Hd were attained to determine the incident solar insolation on a tilted surface. When the concentrator is orientated with its long-axis along east-west direction, only the projection of direct irradiance component on north-south vertical surface can be considered, because east-west component is parallel to absorber pipe and is not contribute energy flow on the absorber surface but shadow effect due to the vacuum tube cap. Assuming that the absorber pipe of the line-axis concentrator has infinite length allows end effects to be ignored; a two-dimensional ray tracing approach can be adopted to calculate the performance for any oblique angles. In order to decide the performance, the projection of the incident angle on north-south vertical plane must be calculated since it is essential for the evaluation of the performance of a line-axis concentrator. The incident angle for a concentrator facing equator and for which its surface azimuth angle is 0, can be calculated by following equation (Howell et al., 1982): 15

cos 3D  cos  s cos  s sin   sin  cos 

(32)

 sin(   )sin   cos(   )cos  cos 

where s is the solar azimuth angle. s is the solar altitude angle.  is the tilt angle of the concentrator which was decided to be 38.25 by similar way of the determination of the maximum acceptance angle for Sendai.  is the latitude of the location and  is the declination angle. By solving geometric equations of the earth orbit around the sun, the projection of the incident angle can be calculated as shown in the following equation (Ustaoglu et al, 2016b).

cos  2D 

cos 3D

(33)

cos  s tan 2  s  cos 2  s

The incident angles of θ3D and θ2D are considered for two different cases. First, to calculate incident energy, the oblique incident angles θ3D must be considered since it will be the main factor of the incident solar insolation on the earth surface. In order to determine the performance of the concentrator, the projection angle θ2D of the incident ray must be considered, because this angle indicates the actual incident angle for the acceptability of the line-axis concentrator.

3. Results and discussions 3.1. Theoretical optical and thermal performance evaluation 3.1.1. Evaluation of ray acceptance for different truncation levels

The ray acceptance, which can be described as ratio of the aperture area of the reflector to diameter of the glass tube, may be an important parameter to utilize the occupying area of the concentrator effectively. The parabolic reflector part of the concentrator has unwieldy size due to steep angle at the end of the reflector. This unwieldy size makes some gap in the side of the reflector which is disabled for solar energy utilization. Therefore, the parabolic reflector part may be truncated to increase ray acceptance by reduction of these disabled area with only slight reduction on the concentration ratio. The length of reflector was changed as a calculation parameter. 16

The concentrator is discretized into 3500 elements. The concentrator was assumed to be ideal and free from fabrication errors. In order to illuminate clearly the reduction of the concentration ratio, comparative-concentrator ratio was defined as ratio of concentrator rate of the truncated and full concentrator as shown in the following equation.

Ccom 

Ctrun Cfull

(34)

Figure 4 illustrates the ratio of the ray acceptance and comparative-concentrator ratio in terms of the reflector length. The solar radiation was assumed coming with normal incident angle. The ray acceptance of the full concentrator was about 52% with a concentration ratio of 2.51. The ray acceptance increases up to a truncation level of 74.6% as the length of parabolic reflector decreases. The best ray acceptance of 98.6% was obtained for a comparative concentration ratio Ccom of 57.6 % (Ctrun = 1.45). After that level of truncation, the ray acceptance starts to decrease as the Ccom decreases. Although this higher ray acceptance is preferable to decrease ray loss from the side of the concentrator, the concentration ratio reduces significantly. This results in reductions in the heat flux and the performance. It is apparent that any truncation of the reflector will improve the ray acceptance compare to full concentrator. Therefore, optical and thermal efficiency evaluations are

Ratio

required.

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

Ray acceptance (Ac/Dgl) Concentration ratio (Ctrun/Cfull)

0.2

0.4

0.6

0.8

1.0

Unit length of reflector Fig. 4. Ray acceptance and concentration ratio as a function of reflector length

17

3.1.2. Evaluation of efficiency for different truncation levels The performances of non-imaging concentrator are strongly related with the reflectivity of the reflectors due to multiple internal reflections. The optical performance may decrease, as the number of reflection increases. Thus, truncation of reflector may result in an enhancement on optical performance due to the reduction on the number of reflection. Although the ray acceptance is important to utilize the area of collector unit effectively, reduction of concentration ratio can cause drop of heat flux and thermal performance. To decide the optimum truncation level with slightly reduction on the concentration ratio, thermal and optical performance must be evaluated. Theoretical evaluation was carried out using 2-D ray tracing analysis. The thermal efficiency was evaluated as a function of absorber temperature (Eq. 10). In order to facilitate the evaluation some assumptions were done. Absorptivity, transmissivity and reflectivity are independent of incidence angles. All reflections on the reflector surfaces are specular. Incident solar irradiance is divided into 1000 rays. Only direct solar irradiation is accounted. The calculation parameters were assumed as mentioned in Table 1. Table 1 Specification of the calculation parameter Calculation parameter

Symbol

Value

Solar beam intensity

Iin (W/m2)

1000

Ambient temperature

Tamb (K)

293

Absorber temperature

Ta (K)

373

Transmissivity of the glass tube

τc

0.95

Reflectivity of the reflector

ρr

0.9

Absorptivity of absorber

αab

0.9

Emissivity of absorber (gray surface)

εg

0.9

18

Optical Efficiency Thermal Efficiency Concentration Ratio Ray Acceptance Ratio

0.2

0.4 0.6 0.8 Unit length of reflector

Efficiency

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.0

Ratio

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Fig. 5. Thermal efficiency, optical efficiency, concentration ratio and ray acceptance ratio of reflector as a function of reflector length.

Figure 5 shows the performance of the concentrator as a function of reflector length for normal incident angle. The system performance can be defined with optical and thermal efficiency. The optical efficiency shows the ratio of absorbed radiation after being transmitted through glass cover and reflected from specular surface to solar insolation pass through the aperture area of the reflector. The thermal performance shows the ratio of useful energy after taking into account the heat losses to incident solar insolation on the aperture of reflector. The comparative concentration ratio and ray acceptance ratio were added to Fig.5 in order to show the relevance between the performances and these ratios. The absorber was considered having gray surface since the selective surface reduces the effect of radiative heat loss, thereby reducing the reduction effect of concentration ratio. The optical performance of the reflector inclines predictably as reflector length decreases until the reflector length of about 40%. After that truncation level, the performance remains almost stable because there is no apparent increment in the optical performance. On the other hand, thermal performance is a function of the concentration ratio for a gray surface absorber. As the optical performance increase, thermal performance decreases because of reduction on the concentrator rate. 19

The thermal efficiency remains almost constant up to a certain length due to the steep angle at the end part of the concentrator. The concentrator without truncation operates with an efficiency of 48.4%. Due to the slight rise in the optical performance for the truncation of 20%, the thermal efficiency slightly increases to 48.8%. In this stage, the reduction of concentration ratio does not affect the performance that much. Then, the value of efficiency remains nearly constant up to the reflector length of about 63%. For the reflector length of 50%, the thermal performance decreases only about 1 % and then the reduction increase gradually. This significant reduction on the reflector length reduces the required diameter of glass tube. Hence, the cost of optical component can be reduced considerably with only slightly reduction on the performance. After the truncation level of 50%, reduction on the performance becomes significant. Therefore, the performance of the concentrators having truncation levels of 20%, 37%, 50% and full concentrator can be evaluated in

Optical efficiency opt

terms of incident angle and absorber temperature.

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

100% 80% 63% 50%

50%

100%

0

5

10 15 20 25 30 35 40 45 Incident angle  ( ) o

Fig. 6. Optical efficiency of the concentrator for concentrators having sizes of 100%, 80%, 63% and 50%. Figure 6 shows the optical performance in terms of incident angle for different truncation level. In Fig. 6, 100% indicates a full concentrator without truncation and 80%, 63% and 50% represent 20

that 20%, 37% and 50% of the reflector are truncated, respectively. The best optical performances of about 76% are observed at the incident angle of about 12.7° for all concentrators. The average optical performance increases slightly while the truncation level increases. The average optical efficiencies of the concentrators between the normal incident and original acceptance angle (23.44°) are 72.8%, 73.6%, 74.2% and 74.6% for the concentrator size of 100%, 80%, 63% and 50%, respectively. Due to smaller size in the truncated concentrator, number of reflection decreases thereby improving the average optical performance. The performance curve remains more stable for the truncation level of 50% due to less number of reflections and the acceptance angle increases up to 44°. The truncation increases the acceptance angle of the concentrator. The largest increment in the acceptance angle occurs for the case of 50% truncated concentrator and increases to 45 and followed by 37% and 20% truncated concentrators with acceptance angles of about 36 and 29, respectively. This kind of characteristic is very important to increase annual energy collection in a stationary concentrator. Figure 7 shows the thermal performances of the concentrators having gray surface and selective surface absorber as a function incident angle with the absorber temperature being kept constant at 373 K. Selective coating is very important treatment in the thermal performance of a solar collector system. Selective surface can absorb the incident solar radiation from the visible range (0.39-0.78 mm) to the near infrared (0.78-2.5 mm) as it will emit only a small fraction of far infrared (5-10 mm) which can be described the thermal radiation. They increase the efficiency of the systems including photo-thermal conversion and solar collectors, particularly at high temperatures by reducing the radiative heat loss. Due to higher radiative heat loss in the case of gray surface absorber, the thermal performance is lower than that of the concentrator with selective coating absorber. The full concentrator has a maximum efficiency of 51.8% for the incident angle of about 12.7°. Its average efficiency is about 47.8%. The concentrator with the truncation of 20% shows quite similar performance characteristic with the full concentrator. However, the performance of the full concentrator slightly decreases after the incident angle of 17°. The concentrator with the 21

truncation of 50% remains stable for almost all incident angle between the normal incident and acceptance angle with only a slight notch down in the performance around the incident angle of 12.7°. The acceptance angle enhancement owing to the truncation characteristic is not observed for the concentrator having a gray surface absorber, since the low radiation intensity out of the original acceptance angle is not enough to compensate the high radiative heat losses from the gray surface absorber.

Thermal efficiency th

a

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Thermal efficiency th

b

100% 80% 63% 50%

100%

50%

0

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

10

20

30 Incident angle  (o)

40

100% 80% 63% 50%

50%

100%

0

10

20

30

40

Incident angle  ( ) o

Fig. 7. Thermal efficiency of the truncated concentrators as a function of incident angle for gray surface ( = 0.9) (a) and selective surface ( = 0.07) (b) absorbers for concentrators having sizes of 100%, 80%, 63% and 50% (Tab = 373 K, Iin = 1000 W/m2) 22

Figure 7.b illustrates the thermal performance of the concentrator having selective surface absorber as function of incident angle. The selective coating reduces radiative heat loss effect on the performance. Therefore, the thermal efficiency is mostly influenced by the optical performance. Thus, the thermal efficiency of truncated concentrator is higher than that of the full one in the selective coating case because of the higher optical efficiency, as full concentrator has mostly better efficiency for the gray surface absorber. The thermal efficiency of the truncated concentrator is more stable than full concentrator. When the incident angle reaches the acceptance angle, thermal efficiency decreases rapidly, and then the efficiency of the full concentrator become zero, as the efficiency of the truncated concentrator (50%) degressively continue till the incident angle of about 42.5°, which is the useful acceptance angle range for the thermal performance. The maximum performance of 74.9% is observed for the full concentrator for the incident angle of about 12.9°, and that of the truncated concentrator (50%) is 73.97%. However, the average efficiency of the truncated concentrator (50%) is about 72.4% while that of full concentrator is 70.9% between the normal incident and original acceptance angle (23.44°). These results show that the truncated concentrator having selective surface absorber shows significant advantages compare to that with gray surface absorber.

3.2. Experimental evaluation 3.2.1. Experimental setup The experiment was conducted on the rooftop of the 2nd building of the Institute of Fluid Science (IFS) in the Katahira campus of the Tohoku University located in Sendai, Japan with an elevation of 59 m (38.26° N, 140.86° E). The experimental model consists of flow meter, water pump, a storage tank that includes an online heater and cooler system, pyranometer and solar collector system.

23

Fig. 8 Cross section geometry of the reflector block (a) and Teflon fixer (b)

The reflector compounds of the aluminum reflector blocks and Teflon fixers for the absorber. The cross section geometry of reflector block and Teflon fixer is shown in Fig. 8. Reflector was manufactured by using machining of aluminum cylindrical blocks to eliminate production errors occur in a bended reflector plate. The width of each block is 100 mm. In order to constitute a concentrator of 1000 mm length, 10 blocks were used and these were connected to each other from the hole on the block by using a threaded stick passing through the each reflector. The outer diameter of the cylinder block of reflector is 170 mm. Teflon pattern shown in Fig. 8b were used to fix the absorber on the focal point of the reflector. In order to eliminate the shadow effect, the thickness of the fixer teflons was adjusted to be 1 mm. Aluminum surface was polished to achieve a reasonable reflectance. In order to attain the spectral values of the reflector, a spectrophotometer was used. The reflectivity of the reflector was obtained by considering the average reflectivity in visible region for the wavelength rage of 390-780 nm. A copper pipe was considered as the absorber. The thermal conductivity of the absorber, k stated in Eq. 17 was 395.7 W/m·K and was assumed to be constant through the pipe. The inner and outer diameters of the absorber were 16 mm and 20 mm, respectively. As a first approximation, the copper absorber was painted by black body paint to improve the absorptivity of the absorber. The spectral properties of black painted absorber as a function of wavelength were measured using 24

Shimadzu UV-2450 spectrophotometer for UV-VIS region measurement and Shimadzu IRPrestige-21 spectrophotometer for NIR-MIR region measurement to find out the solar absorptivity and thermal emissivity of the absorber surface, respectively. Different treatments may be applied to the absorber surface to improve the performance of the concentrator. Selective coating takes advantage of the differing wavelengths of incident radiation and the emissive radiation from the absorber. Selective coating is a preferable treatment for high temperature applications such as solar concentrating collectors. The thermal efficiency is increased by a high absorptance in the solar radiation of the electromagnetic spectrum and a high reflectance that indicates low emittance in the infrared region of the electromagnetic spectrum. The glass tube was selected as Pyrex tube which is made of low-thermal-expansion borosilicate glass which is known for having very low coefficients of thermal expansion that makes them resistant to thermal shocks. A glass tube length of 1100 mm was provided to cover the concentrator. The inner diameter of the glass is 173 mm as the outer diameter is 180 mm. A glass tube having a length of 1100 mm was provided to cover the concentrator. The end caps made of Polycarbonate were used to cover ends of the glass tube. The end caps include a vacuum hole, a working fluid circulation hole and supporter holes for thermocouple, pressure gauge and so on. The sealing of circulation and supporter holes was provided with lids and silicon. The end caps include groove to place o-rings for vacuum sealing. The vacuum was provided by using a vacuum pump. The inside pressure of collector was measured by a pressure gauge that was connected to glass tube via supporter hole on the cap. The experimental set-up is a closed loop circuit with the required components and measurement tools as sketched in Fig. 9. A circulation pump is used to circulate the working fluid between the collector and the storage tank. The mass flow rate can be adjusted in pump by using a valve manually for flow rate range of 100-1100ml/min. The pump includes a storage tank in which temperature of the water can be adjusted with an internal online heater and cooler. The water heats up or cools down to make the water in a constant temperature for initial condition in the storage 25

tank that includes online heater-cooler system. The temperature range of the online heater-cooler is between 10 and 80 C. Thus, the inlet temperature of working fluid can be kept in a constant temperature for the experiment. In order to measure mass flow rate of the working fluid, a Coriolis flowmeter was used. The rated flow range is between 0 and 2000mL/min. The fluid temperature range is within 0-100 C no boiling and freezing. The accuracy of the flow meter is ±1%. Thus, the mass flow rate can be measured with an acceptable accuracy. The pyranometer is intended to be used in horizontal position. The direction and straightness of the experimenting place was adjusted by using a compass and a bubble level. This will provide to determine the global solar insolation in horizontal surface. In order to determine the diffuse solar insolation, the pyranometer is used with a shadow band. This band is adjusted along with a direction parallel to the earth axis to make shadow to direct sunlight.

Fig. 9. Schematic view of the experimental model

26

The temperatures were measured by using T-type thermocouple. For the inlet and outlet temperature, thermocouples were immersed into the pipe. In order for accurate temperature measurement, the pipe around TCs was insulated by insulation material and water temperature was mixed at the inlet and outlet stages by additional apparatus. TCs were attached in three different spots on the absorber surface and the average value of these measurements was considered the surface temperature of absorber. It is important to mention the reason of three point measurement of TCs. The first point is that the temperature around the absorber was assumed to be uniform. The heat flux and temperature distribution around the absorber were evaluated for different absorber materials including copper, aluminum and stainless steel and different incident angles in a previous study (Ustaoglu et al. 2016a). The numerical analysis was carried out and the absorber was split into 360 elements. The results showed the temperature distribution around the absorber is quite uniform in particular for a copper pipe. The temperature difference between the maximum and minimum element temperature was only 0.13 C for normal incident angle of solar radiation and 0.44 C for the incident angle of 22 which is around the maximum acceptance angle. The other study (Ustaoglu et al. 2016c) verified that the truncation of the concentrator increases the uniformity of the heat flux thereby increasing the temperature uniformity. Therefore, it is assumed that the temperature around the absorber is uniform so we may not need to put the TCs around the absorber. The second point is that, there may need to split a number of average surface temperatures, to measure more points and to make a number of heat loss analysis for a more appropriate assumption of a long absorber tube. However, the absorber pipe in the experimental model has only one-meter length. Therefore, three TCs may be enough to make an average surface temperature. A pyranometer was used to obtain the global and diffuse solar irradiation.

27

Fig. 10. A photo of experimental model for single concentrator

Figure 10 shows a photo of the experimental model. The concentrator is orientated with its line axis along with east-west direction. Its aperture is tilted southward. The tilt angle was adjusted to be 38.25 for Sendai location. The vacuum was provided by using a vacuum pump. The inside pressure of collector was measured by a pressure gauge that was connected to glass tube via supporter hole on the cap.

3.2.2. Experimental performance evaluation The experiments were conducted on May 29 and June 01 for non-vacuum and vacuum cases, respectively. The convective heat loss from the surface of absorber to the ambient was also taken into account for the non- vacuum case on May 29 while that effect was mostly eliminated for the vacuum case and only the radiative heat losses from the absorber surface to sky and the convection to the working fluid were considered on June 01. The vacuum and non-vacuum evaluations were carried out for a comparison of theoretical and experimental models.

The site has a rainy season

that usually begins from June to early July. The experiments were conducted within this rainy season by selecting one of the sunniest days during this period; however, the selected day was partly sunny. This experimental evaluation was conducted to validate the results of theoretical model. The 28

glass tube was selected as Pyrex tube which is made of low-thermal-expansion borosilicate glass which is known for having very low coefficients of thermal expansion that makes them resistant to thermal shocks. The spectral properties of the absorber, the average value in visible region is considered to decide the absorptivity of absorber and reflectivity of reflector and, the average value in the mid and long wave infrared region is considered to decide the thermal emissivity of the black body painted absorber. For this purpose, two spectrophotometers were used. The first spectrophotometer is Shimadzu UV-2450 which can measure the ultraviolet (UV) and visible (VIS) ranges from (280nm- 850nm). The other one, Shimadzu IR-Prestige-21 spectrophotometer which is based on Fourier Transform Spectrophotometry (FTIR), is used to measure near infrared (NIR), mid and long wave infrared regions. The spectral properties of the optical components are seen in Table 1. Table 2 Spectral properties of the optical components Optical component

Value

Wavelength

Transmissivity of glass

0.92

(390-780nm)

Reflectivity of reflector

0.774

(390-780nm)

Solar absorptivity of absorber

0.958

(390-780nm)

Thermal emissivity of absorber

0.934

(5000-10000nm)

The flow rate was set to be 100 ml/min in order to obtain a clear temperature difference between inlet and outlet water temperature since the length of reflector is only 1m. Thus the mass flow rate equals to 1.667x10-3 kg/s. Reynolds Numbers were calculated to be about 155.9 ±2 and 174.85 ±0.9 on May 29 and June 1, respectively. Therefore, the flow was considered as laminar. In order to make a constant inlet temperature, a storage tank that includes an online heater and cooler system was used. However, the inlet temperature was even a little changed. Therefore, it is important to show the temperature difference between inlet and outlet to find out energy gain. Figure 11 shows the temperature measurement of the water inlet, water outlet, ambient and average surface temperature of the absorber. The surface temperature was considered as an average value of 29

the tree different measurement spots along the absorber. The average inlet temperature of was 296.6K±0.4 and 301.3K±0.26 on May 29 and June 1, respectively. The average ambient temperatures were 294.5K±1.6 and 306.25K±2 on the measured points of the experiment on May 29 and June 1, respectively. The experiments were conducted mostly during the noon time due to the weather conditions. During the noon time, the weather was clear sky as it was windy and cloudy in the afternoon as shown in Fig. 12. The average wind speed was about 10km/h for both days before the noon. The average humidity was 48% and 94% before noon on May 29 and June 1, respectively.

a

320

Temperature (K)

315 310 305 300 295 290 285 280

Ambiend temperature Absorber surface Temperature Water inlet temperature Water outlet temperature

275 10:30 11:00 11:30 12:00 12:30 13:00 13:30 14:00 Time (hour)

b

320 315

Temperature (K)

310 305 300 295 Ambiend temperature Absorber surface Temperature Water inlet temperature Water outlet temperature

290 285 280 275 10:30

11:00

11:30 12:00 Time (hour)

12:30

13:00

Fig. 11 Temperature measurement data on May 29 (a) and June 1 (b) 30

Fig.12 Photos of the sky during experiments on May 29 (a) and June 1 (b)

The inside pressure of the system was measured by a pressure gauge that was connected to glass tube via supporter hole on the cap. The vacuum was provided by using a vacuum pump and the pressure was reduced into 0.1 bars on June 1. Due to this vacuum degree, the convective loss was mostly eliminated. The theoretical evaluations on the June 1 were made both for absolute vacuum case model and for a model taking into account one tenth of convective heat loss from the absorber surface to the ambient due to a pressure of 0.1 bars in the glass tube. The convective heat loss effect on the performance is low due to comparatively low temperature of absorber surface. Along with that vacuum degree, the convective heat loss effect was mostly disappeared and there was almost no difference between these two models. It is important to compare the differences between the inlet and outlet temperature of the systems 31

for the experimental and theoretical model; because it give us the difference in the energy obtained by the system. Figure 13 shows the difference between the inlet and outlet temperature of experimental measurement and analytical result on May 29 (a) and Jun 1(b) for non-vacuum and vacuum cases, respectively. In order to define the outlet temperature of the water, Eq. 24 was used.

Temperature difference T

a

20 18

Experimental Theoretical

16 14 12 10 8 6 4 2 0

10:40 11:20 12:00 12:40 13:20 14:00

Time (hour)

Temperature difference T

b

20 18 16 14 12 10 8 6 4 2 0 10:30

Experimental Theoretical

11:00

11:30

12:00

12:30

Time (hour) Fig. 13. Temperature difference between the inlet and outlet temperature of experimental measurement and analytical results on May 29 (a) and Jun 1(b)

In recognition of a quantitative evaluation, the average temperature difference between the experimental and theoretical model is about 0.43C and the relative error between these two models is about 4.8% before the noon on July 1. On the other hand, the average temperature difference 32

between the experimental and theoretical models is only 0.156 C and a deviation of 1.8% between two models is occurred before the noon on May 29. However, in the afternoon, some clouds appeared as wind stiffened and the solar insolation and outlet temperature measurement became unstable. These may affect the experimental results. Therefore, the average temperature difference increases to 0.65 C for all experimental evaluation. The temperature differences between the theoretical and experimental results have good accordance.

Efficiency

900 800 700 600 500 Experimental Thermal Efficiency th2

400

Theoretical Thermal Efficiency th3 Theoretical Thermal Efficiency th1

300

Optical Efficiency Global solar irradiation

200

2

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Global solar irradiation (W/m )

a

10:40 11:20 12:00 12:40 13:20 14:00

Time (hour)

Efficiency

10:30

1000 900 800 700 600 500 Experimental Thermal Efficiencyth2

400

Theoretical Thermal Efficiency th3

300

Theoretical Thermal Efficiency th1

200

Optical Efficiency Global solar irradiation

100

11:00

11:30

12:00

2

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Global solar irradiation (W/m )

b

0

12:30

13:00

Time (hour) Fig. 14. Experimental and theoretical thermal efficiency, optical efficiency and global solar irradiation of experimental model on May 29 (a) and June 1 (b)

33

Figure 14 illustrates the optical efficiency and thermal efficiency for theoretical and experimental results and global solar irradiation as a function of day time. Eqs. 10 and 24 indicate theoretical evaluations of the thermal performance while the experimental results were obtained by using Eq. 24. The theoretical evaluation results are almost identical for both days and the average value of the relative error between two theoretical models is about only 0.5% on May 29 and 2% on June 1. Moreover, the theoretical and experimental results show good agreement. The average value of relative errors between theoretical and experimental model is about 2.1% in the case of thermal efficiency on May 29 and 5.7% on June 1 before the noon. However, after 12:45 the wind slightly affected the measurement of ambient temperature since the thermocouple was in open-air. Moreover, some clouds appear so that the measurement of global radiation is affected particularly on May 29 although the all theoretical and experimental results have perfectly good agreement before the noon.

3.2.3. Uncertainty analysis An uncertainty analysis was carried out to provide accuracy of the experimental results. The uncertainty analysis was done by considering the method stated by Kline and McClintock (1953). The uncertainty of the experimental variables can be calculated by 1/ 2

2  R 2  R 2  R   wR   w1    w2   ...   wn    x  x1   x2   n  

(35)

where R is the measured dependent variable, xi (i=1,2,..,n) is an independent variable and wi is the uncertainty of the independent variable, wR is uncertainty of R variable. Errors in measurements of solar radiation, temperature and mass flow rate were 1.5%, 0.75% and 1.0%, respectively. Thus, the maximum relative uncertainty was estimated to be about 1.25% for the experimental analysis. Figure 15 shows the thermal efficiency of experimental model. The errors bars in figure represent the uncertainty obtained in the experimental measurement.

34

Thermal Efficieny

0.60 0.55 0.50 0.45 0.40 0.35

Experimental resutls on May 29 Experimental resutls on June 1

0.30 10:40 11:20 12:00 12:40 13:20 14:00 Time (hour) Fig. 15. Thermal efficiency of experimental model with error analysis

4. Conclusion

In this study, the truncation effect on the compound parabolic and involute concentrator was analytically evaluated. The truncated concentrators were compared with the full concentrator to evaluate the advancement of the performance. The optimum truncation level was decided and the performance of the solar concentrator was evaluated for its optical and thermal efficiency. The truncated concentrator was experimentally and analytically evaluated. The results of the theoretical and experimental models were compared to validate the analysis. The following points summarize the results. (1) The concentrator was evaluated by analyzing of ray acceptance, concentration ratio, optical efficiency and thermal performance for different truncation level to determine the optimum size of reflector. As the reflector size is truncated, concentration ratio decreases. However, it ensures a significant increase in ray acceptance, which indicates the useful area for solar energy utilization on whole surface area of the collector, with more cost-effective design by reducing the size of optical component such as reflector and glass tube. Moreover, the optical and thermal efficiency were evaluated for normal incident angle for all truncation level. Due to the steep angle at the end of 35

parabolic reflectors, the thermal efficiency remains stable up to a truncation level of 37%. For truncation level of 50%, the thermal efficiency decreased only 1%. On the other hand, the optical efficiency increased as the reflector length decreased because of lower number of reflection. (2) A detail evaluation of optical and thermal efficiency of the evacuated compound parabolic and involute concentrator was carried out for the full size and the selected truncated concentrators having a truncation of 20%, 37% and 50% in the case of gray and selective surface absorber. The optical performance improved substantially for the 50% truncated concentrator. Besides, the acceptance angle also improved up to about 42.5° because some rays can reach to the aperture area of involute reflector out of maximum acceptance angle without any reflection from the parabolic reflector. Since the involute reflector has an acceptance angle of 90 , all radiation, which cross the aperture area of involute reflector, could concentrate on the absorber area. The thermal performance of the truncated one for normal incident angle is about 1% lower than the full size of concentrator. However, as the incident angle gets close to the acceptance angle, the truncated one showed an apparent advancement. In the case of gray surface absorber, the full concentrator showed a better performance. On the other hand, the truncated concentrators showed preferable performance for selective surface absorber case compare to that of the full one. Because the selective coating reduces the effect of radiative heat loss, thereby increasing the effect of optical performance in thermal efficiency. (3) The results of the experimental and theoretical results of the thermal efficiency and outlet temperature show good agreement. The average uncertainty is about ±0.00624 and ±0.00685 out of 1 on May 29 and June, respectively. The error of the experimental evaluations was about % 1.25. Thus, the results indicate the reliability of the ray-tracing program. Consequently, the truncated concentrator showed a preferable performance compare to full concentrator without any significant reduction in the performance. The truncated concentrator shows a cost-effective design characteristic due to its less size for the reflector and glass tube. Therefore, the truncation becomes a promising advancement of the compound parabolic and 36

involute design to achieve the economic viability and attraction for adoption on buildings.

References 1. Alptekin, M, Calisir, T., Baskaya, S., 2017, Design and experimental investigation of a thermoelectric self-powered heating system, Energy Conversion and Management 146, 244– 252 2. Acuña, A., Velázquez, N., Sauceda, D., Rosales, P., Suastegui, A., Ortiz, A., Influence of a compound parabolic concentrator in the performance of a solar diffusion absorption cooling system. Applied Thermal Engineering 102, 1374–1383. 3. Brogren, M., Nostell, P., Karlsoon, B. 2000, Optical efficiency of a pv-thermal hybrid CPC module for high latitudes. Solar Energy, 69, 173-185. 4. Baum, H.P., Gordon, J.M., 1984. Geometric characteristics of ideal nonimaging (CPC) solar collectors with cylindrical absorber, Technical Note, Solar Energy, 33-5, 455-458. 5. Carvalho, M.J., Collares-Pereira, M., 1985. Truncation of CPC solar collectors and its effect on energy collection. Sol. Energy. 35-5, 393-399. 6. Glassner, A.S., 1991. An introduction to Ray Tracing. Academic Press, San Diego, pp.131141. 7. Guiqiang, Li., Gang, P., Yuehong, S., Jie, J., Riffat, S.B, 2013. Experiment and simulation study on the flux distribution of lens-walled compound parabolic concentrator compared with mirror compound parabolic concentrator. Energy, 58, 398-403. 8. Hatwaambo, S., Hakansson, H., Nilsson, J., Karlsson, B., 2008. Angular characterization of low concentrating PV–CPC using low-cost reflectors. Sol. Energy Mater. Sol. Cells 92, 1347–1351. 9. Hinterberger, H., Winston, R., 1966a. Efficient light coupler for threshold Cerenkov counters. Rev. Sci. Instrum. 37, 1094–1095. 10. Hinterberger, H., Winston, R., 1966b. Gas Cerenkov counter with optimized light-collecting 37

efficiency. Proc. Int. Conf. Instrumentation High Energy Phys. 205–206. 11. Hiraki H., Hiraki A., Maeda M., Takahashi Y.. Unique features of cylindrical type solarmodule contrasted with plane or conventional type ones. Journal of Physics Conference Series 379 (2012) 012002. 12. Howell, J.R., Bannerot, R.B., Vliet, G.C., 1982. Solar-Thermal Energy Systems Analysis and Design, McGraw-hill, 22. 13. Kalogirou, S. 2007. Recent patent in solar energy collectors and applications. Recent Patents on Engineering 1, 23-33 14. Kandilli, C., 2013, Performance analysis of a novel concentrating photovoltaic combined system, Energy Conversion and Management, 67, 186-196. 15. Kandilli, C., 2016, Exergoeconomic analysis of a novel concentrated solar energy for lighting-power generation combined system based on spectral beam splitting, International Journal of Exergy, 21, 239-260. 16. Kandilli , C., Külahlı, G., 2017, Performance analysis of a concentrated solar energy for lighting-power generation combined system based on spectral beam splitting, Renewable Energy, 101, 713-727. 17. Ma, X., Zheng, H., Chen, Z., 2017. An investigation on a compound cylindrical solar concentrator (CCSC). Applied Thermal Engineering 120, 719–727 18. Maruyama, S. 1991. Uniform isotropic emission from an aperture of a reflector. Proceedings Fourth ASME/JSME Joint Thermal Engineering Conference, Nevada 19. Maruyama, S., 1993. Uniform Isotropic Emission from an Involute Reflector. J. Heat Trans.T ASME 115 (2), 492-495 20. Mills, D.R., Bassett, I.M., Derrick, G.H., 1986. Relative cost-effectiveness of Cpc reflector designs suitable for evacuated absorber tube solar collectors, Sol. Energy. 199-206. 21. Nostell, P., Roos, A. and Karlsson, B., 1998. Ageing of solar booster reflector materials. Sol. Energ. Mat. Sol. C. 54, 235-246. 38

22. Patankar, S.V., 1980. Numerical Heat Transfer and Fluid Flow, Taylor and Francis. pp. 4179. 23. Rabl, A., 1975. Comparison of solar concentrators. Sol. Energy. 18, 93-111. 24. Rabl, A., 1976. Optical and thermal properties of compound parabolic concentrators. Sol. Energy 18, 497-511. 25. Rably, A., 1976. Solar concentrators with maximal concentration for cylindrical absorbers. Appl. Optics. 15(7), 1871-1873. 26. Santos-González, I., García-Valladares, O., Ortega, N., Gómez, V.H., 2017. Numerical modeling and experimental analysis of the thermal performance of a Compound Parabolic Concentrator. Applied Thermal Engineering 114, 1152–1160. 27. Singh, H., Eames, P.C., 2011, A review of natural convective heat transfer correlations in rectangular cross-section cavities and their potential applications to compound parabolic concentrating (CPC) solar collector cavities. Applied Thermal Engineering, 31, 2186-2196 28. Smil, V.,1991. General energetics: energy in the biosphere and civilization. 1 st ed. New York: John Wiley&Sons 29. Soum-Glaude, A., Bousquet, I., Bichotte, M., Quoizola, S., Thomas, L., Flamant, G., 2014. Optical characterization and modeling of coatings intended as high temperature solar selective absorbers. Energy Procedia, 49, 530-537. 30. Suresh, D., O’Gallagher, J., Winston, R., 1990. Thermal and optical performance test results for compound parabolic concentrator (CPCs), Sol. Energy, 44-5, 257-270. 31. Su, Y., Pei, G., Riffat, S.B., Huang, H., 2012. A novel lens-walled compound parabolic concentrator for photovoltaic applications, J. Sol. Energ. Eng. 134, 021010.1–021010.7. 32. Tabor, H., 1984. Comment –The CPC concept, theory and practice. Sol. Energy 33, 629– 630. 33. Ustaoglu A., Okajima J., Zhang X.R., Maruyama S., 2016a, Performance Evaluation of a Proposed Solar Concentrator in Terms of Optical and Thermal Characteristics, 39

Environmental Progress & Sustainable Energy. 35-2, 553-564 34. Ustaoglu A., Okajima J., Zhang X.R., Maruyama S., 2016b, Evaluation of the Efficiency of Dual Compound Parabolic and Involute Concentrator. Energy for Sustainable Development, 32, 1-13. 35. Ustaoglu A., Alptekin, M., Okajima, J., Maruyama, S., (2016c) Evaluation of Uniformity of Solar Illumination on the Receiver of Compound Parabolic Concentrator (CPC). Solar Energy. 132, 150–164. 36. Ustaoglu, A., Alptekin, M., Akay, M.E., 2017a, Thermal and exergetic approach to wet type rotary kiln process and evaluation of waste heat powered ORC (Organic Rankine Cycle), Applied Thermal Engineering, 112, 281-295. 37. Ustaoglu, A., Alptekin, M., Akay, M.E., Selbaş, R., 2017b, Enhanced exergy analysis of a waste heat powered ejector refrigeration system for different working fluids, International Journal of Exergy, 24, 2/3/4. 38. Winston, R., 1974. Principles of solar concentrators of a novel design. Sol. Energy. 16, 8995. 39. Winston, R., Hinterberger, H., 1975. Principles of cylindrical concentrators for solar energy. Sol. Energy. 17, 255-258. 40. Winston, R., 1978. Ideal flux concentrator with reflector gaps (Letter to the Editor). Appl. Optics 17, 1668–1669. 41. Winston, R., Minano, J.C., Benitez, P. 2005. Nonimaging Optics. Elseiver Academic Press. Burlington, London, San Diego 42. Welford, W.T., Winston, R., 1978. The optics of Nonimaging concentrators, Light and Solar Energy. Academic Press. London, New York 43. Duffie, J.A., Beckman, W.A., 2013 Solar Engineering of Thermal Processes, Wiley, Hoboken,New Jersey. 44. Kline SJ, McClintock FA. Describing uncertainties in single-sample experiments. Mech Eng 40

1953;75(1):3–8.

Highlights 

An ideal non-imaging concentrator was designed and experimentally tested.



Optimum design geometry is decided for different truncation level of concentrator.



The truncated concentrator is operated without significant reduction on performance



The experimental investigation shows good agreement with theoretical model.



The truncated concentrator has advantages for economic viability and building app.

41