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Optical efficiency analysis of cylindrical cavity receiver with bottom surface convex
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Solar Energy 90 (2013) 195–204 www.elsevier.com/locate/solener
Optical efficiency analysis of cylindrical cavity receiver with bottom surface convex Fuqiang Wang a,⇑, Riyi Lin a, Bin Liu b, Heping Tan b, Yong Shuai b,⇑ a
College of Pipeline and Civil Engineering, China University of Petroleum (Huadong), 66, West Changjiang Street, Qingdao 266580, PR China b School of Energy Science and Engineering, Harbin Institute of Technology, 92, West Dazhi Street, Harbin 150001, PR China Received 8 September 2012; received in revised form 18 January 2013; accepted 21 January 2013
Communicated by: Associate Editor Michael Epstein
Abstract The bottom surface of conventional cavity receiver cannot be fully covered by coiled metal tube during fabrication, which would induce a dead space of solar energy absorption. The dead space of solar energy absorption can severely decrease the optical efficiency of cavity receiver. Two new types of cavity receiver with bottom surface convex are put forward with the objective to solve the problem of dead space of solar energy absorption and improve the optical efficiency of cavity receiver. The optical efficiency and heat flux distribution of the two new types of cavity receiver are analyzed by Monte Carlo ray tracing method. Besides, the optical efficiency comparisons between conventional cavity receiver and the two new types of cavity receiver are conducted at different characteristic parameter conditions. Ó 2013 Elsevier Ltd. All rights reserved. Keywords: Cavity receiver; Optical efficiency; Heat flux distribution; Irradiative heat transfer; Monte Carlo
1. Introduction Thermal utilization of solar energy is an effective way of sustainable energy development (Karoly and Krisztina, 2012). Sunlight with low energy density is concentrated on the surfaces of tube receiver or cavity receiver by concentrator system. Tube receiver or cavity receiver placed on the focal plane of concentrator system will absorb the highly concentrated sunlight and convert the concentrated sunlight to thermal energy or chemical potential by coupled heat transfer mode (Ananthanarayanan et al., 2012; Webb, 2009; Kumar and Reddy, 2009). The average efficiency of gas-fired power generation is about 50% and is expected to increase to 54% by 2015, the average efficiency of coal-fired power generation is about ⇑ Corresponding authors. Tel.: +86 532 8698 1767 (F. Wang).
E-mail addresses: [email protected] (F. Wang), Shuaiyong@ hit.edu.cn (Y. Shuai). 0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.01.017
38% and is expected to increase to 40% by 2015 (Wina and Ernst, 2009). Compared to fossil power plant, the average power generation efficiency of solar thermal power plant is very low, which is only about 12–20% (Gregory, 1998; Anto´ vila, 2011). High optical losses during the process nio and A of solar energy transmission and absorption are the primary cause of low solar thermal power generation efficiency. Therefore, the optical efficiency improvement of tube receiver or cavity receiver for the concentrator system is an effective way of power generation efficiency increasing (He, 2009; Segal and Epstein, 2000). Cavity receivers are more flexible due to their functionality and three-dimensional configuration compared to the quasi-two dimensional tube receiver. Cavity receivers are mainly used on the parabolic dish concentrator system and tower type concentrator system. Cavity receivers have been successfully used in the pioneers of solar power plants: the Solar One and CESA-1, as well as the SOLSR TRES power plant (Radosevich and Skinrood, 1989; Lata
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Nomenclature Ai E h H N ! N sun ns qr,i qs Rapr Ri
area of ith element, m2 error height of convex segment, mm height of receiver, mm amount of sunlight sunlight vector density of energy bundles flux of the ith element, W/m2 solar irradiance, W/m2 aperture radius, mm convex radius, mm
et al., 2008; Pitz-Pall et al., 1997; Epstein et al., 1991). As known, the higher allowable incident radiation flux produces higher efficiency, a smaller receiver area, and lower levelized energy cost. In the past 30 years, cavity receiver has significantly progressed in increasing the allowable incident heat flux to 1 MW/m2, and the operating temperature of cavity receiver reaches to 1000 K, even to 1350–1500 K (Segal and Epstein, 2003; Steinfeld, 2005). Generally, the shapes of cavity receiver have five types: cylindrical, conical, elliptic, spherical and hetero-conical (Li et al., 2010; Harris and Lenz, 1985; Shuai et al., 2008a,b). Among the five types of cavity receiver, cylindrical cavity receiver is one of the comprehensively adopted receivers during application due to the advantage of low manufacturing cost. The heat transfer surfaces of cylindrical cavity receiver are composed by coiled metal tube. Heat transfer fluid flows in the internal spaces of coiled metal tube, and the external surfaces of coiled metal tube would absorb the highly concentrated solar energy. Heat transfer surfaces of cylindrical cavity receiver will be covered by insulation layers to minimize heat losses (Qiang et al., 2012a,b). Metal tubes are coiled at the same plane at the bottom surface of conventional cylindrical cavity receiver during fabrication. As known, bending force is proportional to the bending strength of metal tube and inverse proportional to the bending cross-section radius (Orynyak and Radchenko, 2007). For metal tubes with low bending strength, it can be easily coiled at flat surface. However, copper tubes with high bending strength (about 700 Mpa) are adopted for cavity receivers due to high conductivity. Difficulty of copper tubes coiling is highly proportional to the coiling radius. The smaller coiling radius is, the higher fabricating force and residual force is, which is harmful to the reliability of cavity receiver. Therefore, the bottom surface of conventional cylindrical cavity receiver cannot be fully covered by coiled copper tubes during fabrication, which can induce a dead space of solar energy absorption. As shown in Fig. 1, dead spaces of solar energy
Greek symbols g efficiency e emissivity Subscripts abs absorb align alignment apr aperture bot bottom segment con conical segment opt optical p pointing
absorption can be found in the cylindrical cavity receivers fabricated by Harbin Institute of Technology (HIT) and Indian Institute of Technology (IIT) respectively, and the area of dead space occupies about 10% of bottom surface (Prakash et al., 2009, 2010). Besides, the other types of conventional cavity receiver also have the problem of dead space of solar energy absorption, for example, the conical cavity receiver illustrated in literature (Zhao et al., 2004). Therefore, two new types of cylindrical cavity receiver with bottom surface convex are put forward in this paper to achieve the following purposes: (1) Solving the dead space of solar energy absorption of conventional cavity receiver. (2) Improving the optical efficiency of conventional cavity receiver. Analysis of optical efficiency and heat flux distribution of the two new types of cylindrical cavity receiver are conducted by Monte Carlo ray tracing method. In order to compare the optical efficiency (gopt ) of cavity receiver between the two new types of cylindrical cavity receiver and conventional cylindrical cavity receiver reasonably, the following principles should be abided: (1) The two new types of cylindrical cavity receiver and conventional cylindrical cavity receiver are placed on the focal plane of the same concentrator system (aperture radius of concentrator is 2600 mm, focal length of concentrator is 3250 mm). (2) The height (H = 200 mm) and aperture radius (Rapr = 90 mm) of the two new types of cylindrical cavity receiver and conventional cylindrical cavity receiver are uniform, and the height of all the cases studied are kept unchanged. (3) Physical parameters of the copper tube for the two new types of cylindrical cavity receiver and conventional cylindrical cavity receiver are the same.
F. Wang et al. / Solar Energy 90 (2013) 195–204
197
0.5m 0.33m
Back wall Wind skirt
(a) Fabricated by HIT
(b) Fabricated by IIT
Fig. 1. Conventional cylindrical cavity receivers fabricated by HIT and IIT respectively.
The theoretical focal spot radius of concentrator system is 24.1 mm, which is much smaller than the aperture radius of cavity receiver to guarantee that the sunlight on the focal plane of concentrator system can project into the cavity of receiver entirely. 2. Numerical methods Monte Carlo ray tracing method is a very powerful method to solve the heat flux distribution problems of solar concentrator and receiver system. Many investigators have adopted this method previously to investigate the heat flux distribution problems (Li et al., 2011; Maarten et al., 2005; Nedea et al., 2009; Jeter, 1986; Cheng et al., 2010). Based on the Monte Carlo ray tracing method, a code has been developed by the authors for solving solar energy gathering and transmission problems (Wang et al., 2012a, 2010; Shuai et al., 2012). The methodology of Monte Carlo ray tracing is the stochastic trajectories of a large number of rays as the rays intersecting with surfaces. Each ray carries the same amount of energy and has a specific direction determined by several probability density functions. The fate of each ray is determined by the emissive, reflective, and absorptive behavior on the surface described by a set of statistical relationships. The reflection direction of each energy ray follows the Fresnel optics rule. Owing to no truncation errors, the solutions of Monte Carlo ray tracing method are generally used as reference datum of numerical methods for discrete differential–integral equation (Huang et al., 2005; Wang and Modest, 2007). For sunlight, the value of solar radiation heat flux qs in the air adopted in this paper is 1000 W/m2 (Hasuike et al., 2006). The number density of energy bundles ns is defined as the number of energy bundle samplings emitting in every square ! millimeter where the sunlight vector N sun is perpendicular to the emission surface. Therefore, the energy carried by each ray is qs =ns . According to the energy conservation principle, the concentrated heat flux qr,i on the surface of receiver can be expressed as the following equation:
apr qs X Mj Ai ns j¼1 i
N
qr;i ¼
ð1Þ
where qr,i is the radiation flux of the ith surface element of receiver, Ai is the corresponding area, and N apr is the total ray number arrived at the aperture plane. If the jth ray arrives at the ith surface element, M ji = 1, otherwise M ji = 0. In short, the mechanism of solving solar energy gathering and transmission problems by Monte Carlo ray tracing method is: the Sun is regarded as massive and independent rays, each ray carries the same energy to guarantee the uniformity of sunlight distribution, the transmission process of each ray is composed by a series of independent sub-process (emission, reflection, transmission and absorption), and each independent sub-process follows a specific probability model (Shuai et al., 2008a, 2012; Wang et al., 2012a, 2010). As the Monte Carlo ray tracing method is a stochastic technique, the calculation accuracy of the Monte Carlo ray tracing method depends on the number of dispatched energy bundles and randomness performance of the pseudorandom number generator (Li et al., 2011; Maarten et al., 2005; Nedea et al., 2009; Jeter, 1986; Cheng et al., 2010). The larger density of energy bundles is, the higher calculation precision is, but the lower calculation efficiency is. A number of ray-sampling studies are also performed for the physical model to ensure that the essential physics is independent of the ray-sampling number. For the numerical study in this paper, the number density of energy bundles is set to 107 W/m2, and the calculation conditions are: the non-parallelism angle of sunlight is 160 , the sun shape is taken to be a distribution with a circumsolar-ratio of 0.05 and a limb darkening parameter of 0.8 (Shuai et al., 2008a,b). The dimensionless heat flux distribution calculated by Monte Carlo ray tracing method codes is validated against the experimental results performed by Johnston (Johnston, 1998). The comparison results are shown in Fig. 2. As seen from this figure, the results calculated by Monte Carlo ray
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bending cross-section radius and coiling space is increased compared to be coiled at a flat surface, and the bending force can be decreased (Orynyak and Radchenko, 2007). Therefore, the copper tubes are coiled to be a conical shape can be easier compared to be coiled at a flat surface and the convex radius can reach to the theoretical minimum magnitude.
Dimensionless heat flux
1.2
0.9
0.6 Calculated in this paper Measured by Johnston
0.3
3.2. Optical analysis of the CCCR
0.0 -6
-4
-2
0
2
4
The defining equation of optical efficiency of cavity receiver is:
6
Angular distance (mrad)
gopt ¼ N abs =N apr
Fig. 2. Comparisons of dimensionless heat flux distribution with experimental data.
tracing method codes developed by the authors are in good agreement with the experimental results in the reference. 3. Cylindrical with conical combined receiver (CCCR) 3.1. Introduction of the CCCR The CCCR is put forward in this paper with the purpose to improve the optical efficiency of conventional cylindrical cavity receiver. The schematic diagram of CCCR is shown in Fig. 3. As shown in this figure, the shape of lateral segment is cylindrical to guarantee the aperture radius of CCCR. The conical shape is adopted for the bottom segment of CCCR with the aim to solve the problem of dead space of solar energy absorption. As is seen in Fig. 3, copper tubes of CCCR will not be coiled at a flat surface with the convex radius (Ri) decreasing and the shape of bottom segment will be formed into an inverted ‘V’ shape. For the CCCR, the convex radius decreases with height increasing. When the copper tubes coiled to be a conical shape, the z
ð2Þ
where the symbol Napr designates the amount of sunlight reached the aperture plane of cavity receiver, the symbol Nabs denotes the amount of sunlight absorbed by cavity receiver. Fig. 4 presents the variation of optical efficiency of the CCCR with the increasing of dimensionless height (h/H), where the pointing error is 3 mrad and the alignment error is 0 mm. Generally, the absorptivity of copper tubes is between 0.023 (polished) and 0.78 (with oxide layer) He, 2009. Besides, the copper tubes can be coated with black to increase the absorptivity. Therefore, 0.60 is chosen for the absorptivity of copper tubes in this manuscript as a compromise. From the area comparison between the dashed line and solid line of bottom segment of the CCCR (shown in Fig. 3), it can be seen that the absorption area decreases with the dimensionless height increasing. Due to absorption area decreasing, the optical efficiency of the CCCR decreases sharply with the dimensionless height increasing when the dimensionless height is between 0.125 and 0.5. When the dimensionless height is between 0.5 and 0.85, the decreasing rate of optical efficiency grows slower with the dimensionless height increasing. This phenomenon is caused by combined effects of absorption area decreasing and absorption characteristic improving: the absorption area decreases with the dimensionless height increasing, but the heat flux distribution of lateral wall
Fluid inlet 0.70 Conventional with 10% dead space Conventional with no dead space CCCR
h
ηopt
0.68
Ri
0.66
H
0.64 0.62
x
x
0.60
Fluid outlet
0.2
0.4
0.6
0.8
h/H Concentrated sunlight Fig. 3. Schematic diagram of the CCCR.
Fig. 4. Variation of optical efficiency of the CCCR with the increasing of dimensionless height (e = 0.60, Ep = 3 mrad, Ealign = 0 mm).
F. Wang et al. / Solar Energy 90 (2013) 195–204
199
Table 1 Variation of Ncon/Napr of CCCR with the change of dimensionless height. h/H Ncon/Napr
0.125 0.245
0.25 0.309
0.375 0.415
4.1. Introduction of the BSIC receiver Though the CCCR can solve the problem of dead space of solar energy absorption, the capability of optical efficiency improving is very limited. Therefore, BSIC receiver is put forward to realize the above two purposes (Wang et al., 2012b). The schematic diagram of BSIC receiver is shown in Fig. 5. As shown in this figure, copper tubes in the bottom segment of conventional cylindrical cavity
0.75 0.621
0.875 0.621
0.95 0.622
z Fluid inlet
Ri h
4. Cylindrical receiver with bottom surface interior convex (BSIC receiver)
0.625 0.585
H
tends to be zero when the height of lateral wall is lower than a specific magnitude, the effects of absorption area on heat flux distribution decreases with the height of lateral wall increasing. When the dimensionless height is 0.125, the optical efficiency of CCCR (68.25%) is a little higher than that of conventional cylindrical cavity receiver with no dead space (67.91%) and conventional cylindrical cavity receiver with 10% dead space (65.79%). The optical efficiency of CCCR decreases to 66.2% when the dimensionless height increases to 0.375, which is only 0.4% higher than that of conventional cylindrical cavity receiver with 10% dead space (65.8%). The effects of absorption area on heat flux distribution will be higher than that of path deflection when the dimensionless height is higher than 0.375, and the optical efficiency of CCCR would be even lower than that of conventional cylindrical cavity receiver with 10% dead space. Table 1 illustrates the variation of proportion of sunlight received by conical segment (Ncon/Napr) of CCCR with the change of dimensionless height. As seen in this table, the proportion of sunlight received by conical segment increases quickly with the increasing of dimensionless height when the dimensionless height is between 0.125 and 0.75. When the dimensionless height is between 0.75 and 0.95, the proportion of sunlight received by conical segment has very little change with the increasing of dimensionless height. Combining the above analysis, it can be seen that the CCCR cannot improve optical efficiency through the entire dimensionless height variation range, and there is a dimensionless height limiting for optical efficiency improving. Compared to the conventional cylindrical cavity receiver with no dead space, the capability of optical efficiency improving is very limited, and the maximum improved optical efficiency is only 0.34%. Compared to the conventional cylindrical cavity receiver with 10% dead space, the maximum improved optical efficiency of CCCR is only 2.46%.
0.5 0.497
O Fluid outlet Concentrated sunlight Fig. 5. Schematic diagram of the BSIC receiver.
receiver are coiled to be an internal convex surface and the shape of bottom segment will be formed into a normal ‘V’ shape. Similar to the conical bottom segment of the CCCR, the normal ‘V’ shape for bottom segment of BSIC receiver can be easily coiled and the convex radius can reach to the theoretical minimum magnitude. As the bottom segment of BSIC receiver is coiled convex toward the interior direction, the absorption area would be increased compared to conventional cylindrical cavity receiver with no dead space as well as the CCCR. Besides, the shape of BSIC receiver keeps being cylindrical and the height of receiver does not need to be changed when the BSIC receiver is adopted to replace conventional cylindrical cavity receiver. 4.2. Effects of interior convex dimensionless height Fig. 6 presents the variation of optical efficiency of BSIC receiver with the change of interior convex dimensionless height (h/H), where the absorptivity of copper tube is 0.60, the pointing error is 3 mrad and the alignment error is 0 mm. When the dimensionless height is 0, the BSIC receiver evolves into conventional cylindrical cavity receiver with no dead space. As shown in this figure, the optical efficiency of BSIC receiver increases with the dimensionless height increasing when the dimensionless height is between 0 and 0.875. The optical efficiency of BSIC receiver attains its peak magnitude when the dimensionless height increased to 0.875, which is 73.46%. The optical efficiency of BSIC receiver for a dimensionless height of 0.875 is 5.55% higher than that of conventional cylindrical cavity receiver with no dead space (67.91%). The optical efficiency
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F. Wang et al. / Solar Energy 90 (2013) 195–204 0.74
ηopt
0.72
0.70
Conventional with 10% dead space Conventional with no dead space BSIC
0.68
0.66 0.0
0.2
0.4
0.6
0.8
1.0
h/H Fig. 6. Variation of optical efficiency of BSIC receiver with the change of dimensionless height (e = 0.60, Ep = 3 mrad, Ealign = 0 mm).
of BSIC receiver for a dimensionless height of 0.875 is 7.67% higher than that of conventional cylindrical cavity receiver with 10% dead space (65.79%). As seen from Fig. 5, the absorption area of BSIC receiver increases with the dimensionless height increasing which can induce the optical efficiency increasing. Fig. 6 illustrates that the increasing rate of optical efficiency decreases with the dimensionless height increasing. It should be noted that the absorption characteristics of cavity receiver are influenced when the bottom surface changed from flat to interior convex. When the dimensionless height is higher than 0.875, the effects of absorption characteristics change on optical efficiency variation is dominant, the optical efficiency of BSIC receiver begins to decrease with the dimensionless height increasing. When the interior convex dimensionless height increased to 1.0, the optical efficiency of BSIC receiver is 70.22%, which is 2.31% higher than that of conventional cylindrical cavity receiver with no dead space of solar energy absorption. The definition of bottom absorption percentage (Nbot/ Napr) is the ratio of amount of sunlight absorbed by the bottom segment to the amount of sunlight reached to the aperture plane of receiver. Fig. 7 shows the variation of
bottom absorption percentage of BSIC receiver with the change of dimensionless height. As shown in this figure, the bottom absorption percentage increases with dimensionless height increasing due to absorption area increase. The bottom absorption percentage of BSIC receiver for a dimensionless height of 1.0 is 14% higher than that of conventional cylindrical cavity receiver with no dead space. When the bottom segment changes from flat surface to convex surface, the Monte Carlo ray tracing analysis shows that the heat flux distribution change. Fig. 8 illustrates the heat flux distribution on the bottom segment of BSIC receiver along radius direction at different dimensionless height conditions. When the bottom segment is flat surface (conventional cylindrical cavity receiver with no dead space), the heat flux distribution along radius direction of bottom segment has very small fluctuation. With the dimensionless height increasing, the heat flux distribution along radius direction of bottom segment becomes to be highly nonuniform. When the dimensionless height is less than 0.875, the heat flux distribution at different dimensionless height conditions present as monotonically decreasing distribution, and the positions of peak magnitude locate at the same position – the center of bottom segment, which increases with the dimensionless height increasing. When the dimensionless height reaches to 0.875 or higher, the heat flux distribution along radius direction becomes to be unimodal distribution, and the positions of peak magnitude move away from the center of bottom segment with dimensionless height increasing. Fig. 9 shows the heat flux distribution on the lateral wall segment of BSIC receiver along the height direction at different dimensionless height conditions. As shown in this figure, the heat flux distribution on the lateral wall segment presents as a unimodal distribution. According to the geometrical optics theory, the sunlight is highly concentrated on the center of focal plane (Shuai et al.,2008a,b). When concentrated sunlight projects into the cavity of receiver, the concentrated sunlight begins to scatter. Due to rectilinear propagation of sunlight, very little sunlight reaches the near aperture region 3
0.44
Nbot /Napr
2
0.40
q ( W/mm )
Conventional with 10% dead space Conventional with no dead space BSIC
0.36 0.32
h/H= 0 h/H= 0.125 h/H= 0.375 h/H= 0.625 h/H= 0.875 h/H= 1.0
2
1
0.28 0
0.24
0
0.0
0.2
0.4
0.6
0.8
1.0
h/H Fig. 7. Variation of bottom absorption percentage of BSIC receiver with the change of dimensionless height (e = 0.60, Ep = 3 mrad, Ealign = 0 mm).
15
30
45
60
75
90
R (mm) Fig. 8. Heat flux distribution on the bottom segment of BSIC receiver along the radius direction at different dimensionless height conditions (e = 0.60, Ep = 3 mrad, Ealign = 0 mm).
F. Wang et al. / Solar Energy 90 (2013) 195–204 0.20
2
q (W/mm )
0.15
0.10
h/H= 0 h/H= 0.125 h/H= 0.375 h/H= 0.625 h/H= 0.875 h/H= 1.0
0.05
0.00 0
40
80
120
160
200
z (mm)
Fig. 9. Heat flux distribution on the lateral wall segment of BSIC receiver along the height direction at different dimensionless height conditions (e = 0.60, Ep = 3 mrad, Ealign = 0 mm).
of lateral wall (z < 50 mm) and the heat flux is close to zero in this region. Most of the sunlight gathers on the middle region of lateral wall, where the peak magnitude of heat flux distribution on the lateral wall is found. Due to the bottom surface is interior convex, the BSIC receiver can not only change the absorption and reflection characteristic of cavity receiver, but also can increase the absorption area. Therefore, the BSIC receiver can achieve the goal of optical efficiency improving. Besides, the BSIC cavity receiver minimizes the heat flux distribution of the lateral segment. 4.3. Effects of wall absorptivity
of copper tube is 0.60, the pointing error is 3 mrad and the alignment error is 0 mm. As shown in this figure, the optical efficiency of BSIC receiver is higher than that of conventional cylindrical cavity receiver with no dead space in the whole wall absorptivity variation scope (except a = 1.0). When the wall absorptivity is 1.0, sunlight reached the cavity of receiver would be absorbed thoroughly regardless of BSIC receiver or conventional cylindrical cavity receiver with no dead space. Therefore, the optical efficiency of BSIC receiver (gopt = 1.0) is equal to that of conventional cylindrical cavity receiver with no dead space. The variation of improved optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of wall absorptivity is shown in Fig. 11. Compared to conventional cylindrical cavity receiver with no dead space, the magnitude of improved optical efficiency reaches the maximum when the wall absorptivity is 0.4, which is 6.44%. Compared to conventional cylindrical cavity receiver with 10% dead space, the magnitude of improved optical efficiency reaches the maximum when the wall absorptivity is 0.5, which is 7.80%. 4.4. Effects of pointing error As known, pointing error represents the accuracy of rays pointing to the predetermined target. Fig. 12 presents the variation of optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of pointing error, where the absorptivity of copper tube is 0.60 and the alignment error is 0 mm. As shown in this figure, the optical efficiency of BSIC receiver for a dimensionless height of 0.875 is higher than that of conventional cylindrical cavity receiver with no dead space in the whole pointing error variation range. When the pointing error increased from 0 mrad to 14 mrad, the optical efficiencies of BSIC receiver for a dimensionless height of 0.875, conventional cylindrical cavity receiver with no dead space and conventional cylindrical cavity receiver with 10% dead space have very small fluctuation. The maximum optical efficiency
1.0
0.08
0.8
0.06
0.6
η imp
ηopt
As known from the above analysis, the BSIC receiver has the highest optical efficiency when the dimensionless height is 0.875. Therefore, the dimensionless height of BSIC receiver adopted in the succeeding analysis is 0.875. The variation of optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of wall absorptivity is illustrated in Fig. 10, where the absorptivity
0.4 BSIC with h/H=0.875 Conventional with no dead space Conventional with 10% dead space
0.2
201
0.04
0.02
Conventional with no dead space Conventional with 10% dead space
0.00
0.2
0.4
0.6
0.8
1.0
α Fig. 10. Variation of optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of absorptivity (Ep = 3 mrad, Ealign = 0 mm).
0.2
0.4
0.6
0.8
1.0
α Fig. 11. Variation of improved optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of absorptivity (Ep = 3 mrad, Ealign = 0 mm).
202
F. Wang et al. / Solar Energy 90 (2013) 195–204 0.75
ηopt
0.72
BSIC with h/H=0.875 Conventional with no dead space Conventional with 10% dead space
0.69
0.66
0.63 0
2
4
6
8
10
12
14
Ep (mrad) Fig. 12. Variation of optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of pointing error (e = 0.60, Ealign = 0 mm).
4.5. Effects of alignment error The alignment error represents the distance between the focal plane of parabolic concentrator and aperture plane of
0.40
6.0
0.36
4.5 BSIC with h/H=0.875 Conventional with no dead space Conventional with 10% dead space
0.32
q (W/mm2)
Nbot /Nfoc
fluctuations of BSIC receiver for a dimensionless height of 0.875, conventional cylindrical cavity receiver with no dead space and conventional cylindrical cavity receiver with 10% dead space are 0.4%, 0.9% and 1.2% respectively. As illustrated previously, the aperture radius of cavity receiver is much higher than the focus spot radius of concentrator, and the special structure of BSIC receiver for a dimensionless height of 0.875 can effectively absorb the sunlight projected into the cavity. The above two characteristics of BSIC receiver for a dimensionless height of 0.875 induce the phenomenon of lowest optical efficiency fluctuation with the change of pointing error. When pointing error is considered, though the optical efficiency of cavity receiver has small fluctuation with the change of pointing error, the reflection and absorption characteristics as well as the heat flux distribution would be affected which influences the bottom absorption percentage. Fig. 13 illustrates the variation of bottom absorption percentage with the change of pointing error, where the dimensionless height of BSIC receiver is 0.875. As seen from this figure, the bottom absorption percentage increases quickly with the increasing of pointing error. When the pointing
error of BSIC receiver for a dimensionless height of 0.875 is 7 mrad, the magnitude of bottom absorption percentage reaches the peak magnitude, which is 6.72% higher than that of BSIC receiver for a dimensionless height of 0.875 without any pointing error, and then the bottom absorption percentage decreases slowly with the increasing of pointing error. However, the bottom absorption percentage increases slowly with the increasing of pointing error for conventional cylindrical cavity receiver with no dead space and conventional cylindrical cavity receiver with 10% dead space through the entire pointing error variation range. When pointing error is considered, the path of sunlight would be changed which would influence the bottom absorption percentage. The different shapes of bottom segment between BSIC receiver and conventional cylindrical cavity receiver induces the different changes of the bottom absorption percentage with the variation of pointing error. The heat flux distribution on the bottom segment of BSIC receiver for a dimensionless height of 0.875 at different pointing error conditions is shown in Fig. 14. The heat flux distribution on the bottom segment presents as monotonically decreasing distribution of exponential type when the pointing error is 0 mrad. With the increasing of pointing error, the heat flux distribution on the bottom segment changes from monotonically decreasing distribution to unimodal distribution, and the higher pointing error is, the lower peak magnitude of heat flux distribution is. This phenomenon can be explained as follows: when the pointing error is 0 mrad, the parabolic concentrator concentrates the sunlight perfectly and the center of bottom segment has the peak heat flux. With the increasing of pointing error, the accuracy of concentrated sunlight pointing the determined target decreases, the location of peak heat flux moves away from the center of focal plane and the concentration ratio of concentrator system decreases.
0.28
0 mrad 4 mrad 8 mrad 12 mrad
2 mrad 6 mrad 10 mrad 14 mrad
3.0
1.5
0.24 0
2
4
6
8
10
12
14
Ep (mrad) Fig. 13. Variation of bottom absorption percentage of BSIC receiver for a dimensionless height of 0.875 with the change of pointing error (e = 0.60, Ealign = 0 mm).
0.0 0
30
60
90
R (mm) Fig. 14. Heat flux distribution on the bottom segment of BSIC receiver for a dimensionless height of 0.875 at different pointing error conditions (e = 0.60, Ealign = 0 mm).
F. Wang et al. / Solar Energy 90 (2013) 195–204 0.80 BSIC with h/H=0.875 Conventional with no dead space Conventional with 10% dead space
ηopt
0.76
0.72
0.68
0.64 0
3
6
9
12
15
Ealign (mm)
0.40 BSIC with h/H=0.875 Conventional with no dead space Conventional with 10% dead space
Nbot /Napr
0.32
0.28
0.24 0
3
6
9
The variation of bottom absorption percentage of BSIC receiver for a dimensionless height of 0.875 with the change of alignment error is illustrated in Fig. 16. The bottom absorption percentage variation tendencies of both the conventional cylindrical cavity receiver and BSIC receiver for a dimensionless height of 0.875 are similar to the variation tendencies of optical efficiency. The bottom absorption percentage of conventional cylindrical cavity receiver presents as linear decrease with the increasing of alignment error, and the bottom absorption percentage of BSIC receiver for a dimensionless height of 0.875 exhibits as overall undulatory decrease. 5. Conclusion
Fig. 15. Variation of optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of alignment error (e = 0.60, Ep = 3 mrad).
0.36
203
12
15
Ealign (mm) Fig. 16. Variation of bottom absorption percentage of BSIC receiver for a dimensionless height of 0.875 with the change of alignment error (e = 0.60, Ep = 3 mrad).
cavity receiver along the z axis direction. When the alignment error is zero, the focal plane of concentrator system coincides with the aperture plane of cavity receiver. When the alignment error is larger than zero, the aperture plane of cavity receiver is away from the focal plane of concentrator system along positive z axis direction. Fig. 15 illustrates the variation of optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of alignment error, where the pointing error is 3 mrad, and the wall absorptivity is 0.60. As seen from Fig. 15, the optical efficiency of BSIC receiver is higher than that of conventional cylindrical cavity receiver with no dead space and conventional cylindrical cavity receiver with 10% dead space among the whole alignment error variation range. The optical efficiency variation of conventional cylindrical cavity receiver presents as linear decrease with the increasing of alignment error. However, due to the special configuration of bottom segment interior convex, the optical efficiency variation of BSIC receiver exhibits as overall undulatory decreasing.
The CCCR and BSIC receivers are put forward in this paper with the objective to improve the optical efficiency of conventional cylindrical cavity receiver. The optical efficiency and heat flux distribution of the CCCR and BSIC receivers are analyzed by Monte Carlo ray tracing method. The following conclusions have been drawn: (1) The CCCR cannot improve optical efficiency through the entire dimensionless height variation range, and there is a dimensionless height limiting for optical efficiency improving. (2) Among the whole interior convex dimensionless height variation range, the optical efficiency of BSIC receiver is higher than that of conventional cylindrical cavity receiver with no dead space, and the BSIC receiver for dimensionless height of 0.875 has the highest optical efficiency. (3) Among the whole wall absorptivity variation range, pointing error variation range and alignment variation range, the optical efficiency of BSIC receiver for a dimensionless height of 0.875 is higher than that of conventional cylindrical cavity receiver. (4) The BSIC receiver can effectively reach the objective of optical efficiency improving.
Acknowledgements This work was supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51121004) and the key program of the National Natural Science Foundation of China (Grant No. 50930007). References Ananthanarayanan, V., Andrej, L., Bekir, Y., Salem, A., Evelyn, N., 2012. Analytical model for the design of volumetric solar flow receivers. International Journal of Heat and Mass Transfer 55, 556–564. ´ vila, M., 2011. Volumetric receivers in solar thermal power Antonio, L., A plants with central receiver system technology: a review. Solar Energy 85, 891–910.
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Solar Energy 90 (2013) 195–204 www.elsevier.com/locate/solener
Optical efficiency analysis of cylindrical cavity receiver with bottom surface convex Fuqiang Wang a,⇑, Riyi Lin a, Bin Liu b, Heping Tan b, Yong Shuai b,⇑ a
College of Pipeline and Civil Engineering, China University of Petroleum (Huadong), 66, West Changjiang Street, Qingdao 266580, PR China b School of Energy Science and Engineering, Harbin Institute of Technology, 92, West Dazhi Street, Harbin 150001, PR China Received 8 September 2012; received in revised form 18 January 2013; accepted 21 January 2013
Communicated by: Associate Editor Michael Epstein
Abstract The bottom surface of conventional cavity receiver cannot be fully covered by coiled metal tube during fabrication, which would induce a dead space of solar energy absorption. The dead space of solar energy absorption can severely decrease the optical efficiency of cavity receiver. Two new types of cavity receiver with bottom surface convex are put forward with the objective to solve the problem of dead space of solar energy absorption and improve the optical efficiency of cavity receiver. The optical efficiency and heat flux distribution of the two new types of cavity receiver are analyzed by Monte Carlo ray tracing method. Besides, the optical efficiency comparisons between conventional cavity receiver and the two new types of cavity receiver are conducted at different characteristic parameter conditions. Ó 2013 Elsevier Ltd. All rights reserved. Keywords: Cavity receiver; Optical efficiency; Heat flux distribution; Irradiative heat transfer; Monte Carlo
1. Introduction Thermal utilization of solar energy is an effective way of sustainable energy development (Karoly and Krisztina, 2012). Sunlight with low energy density is concentrated on the surfaces of tube receiver or cavity receiver by concentrator system. Tube receiver or cavity receiver placed on the focal plane of concentrator system will absorb the highly concentrated sunlight and convert the concentrated sunlight to thermal energy or chemical potential by coupled heat transfer mode (Ananthanarayanan et al., 2012; Webb, 2009; Kumar and Reddy, 2009). The average efficiency of gas-fired power generation is about 50% and is expected to increase to 54% by 2015, the average efficiency of coal-fired power generation is about ⇑ Corresponding authors. Tel.: +86 532 8698 1767 (F. Wang).
E-mail addresses: [email protected] (F. Wang), Shuaiyong@ hit.edu.cn (Y. Shuai). 0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.01.017
38% and is expected to increase to 40% by 2015 (Wina and Ernst, 2009). Compared to fossil power plant, the average power generation efficiency of solar thermal power plant is very low, which is only about 12–20% (Gregory, 1998; Anto´ vila, 2011). High optical losses during the process nio and A of solar energy transmission and absorption are the primary cause of low solar thermal power generation efficiency. Therefore, the optical efficiency improvement of tube receiver or cavity receiver for the concentrator system is an effective way of power generation efficiency increasing (He, 2009; Segal and Epstein, 2000). Cavity receivers are more flexible due to their functionality and three-dimensional configuration compared to the quasi-two dimensional tube receiver. Cavity receivers are mainly used on the parabolic dish concentrator system and tower type concentrator system. Cavity receivers have been successfully used in the pioneers of solar power plants: the Solar One and CESA-1, as well as the SOLSR TRES power plant (Radosevich and Skinrood, 1989; Lata
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Nomenclature Ai E h H N ! N sun ns qr,i qs Rapr Ri
area of ith element, m2 error height of convex segment, mm height of receiver, mm amount of sunlight sunlight vector density of energy bundles flux of the ith element, W/m2 solar irradiance, W/m2 aperture radius, mm convex radius, mm
et al., 2008; Pitz-Pall et al., 1997; Epstein et al., 1991). As known, the higher allowable incident radiation flux produces higher efficiency, a smaller receiver area, and lower levelized energy cost. In the past 30 years, cavity receiver has significantly progressed in increasing the allowable incident heat flux to 1 MW/m2, and the operating temperature of cavity receiver reaches to 1000 K, even to 1350–1500 K (Segal and Epstein, 2003; Steinfeld, 2005). Generally, the shapes of cavity receiver have five types: cylindrical, conical, elliptic, spherical and hetero-conical (Li et al., 2010; Harris and Lenz, 1985; Shuai et al., 2008a,b). Among the five types of cavity receiver, cylindrical cavity receiver is one of the comprehensively adopted receivers during application due to the advantage of low manufacturing cost. The heat transfer surfaces of cylindrical cavity receiver are composed by coiled metal tube. Heat transfer fluid flows in the internal spaces of coiled metal tube, and the external surfaces of coiled metal tube would absorb the highly concentrated solar energy. Heat transfer surfaces of cylindrical cavity receiver will be covered by insulation layers to minimize heat losses (Qiang et al., 2012a,b). Metal tubes are coiled at the same plane at the bottom surface of conventional cylindrical cavity receiver during fabrication. As known, bending force is proportional to the bending strength of metal tube and inverse proportional to the bending cross-section radius (Orynyak and Radchenko, 2007). For metal tubes with low bending strength, it can be easily coiled at flat surface. However, copper tubes with high bending strength (about 700 Mpa) are adopted for cavity receivers due to high conductivity. Difficulty of copper tubes coiling is highly proportional to the coiling radius. The smaller coiling radius is, the higher fabricating force and residual force is, which is harmful to the reliability of cavity receiver. Therefore, the bottom surface of conventional cylindrical cavity receiver cannot be fully covered by coiled copper tubes during fabrication, which can induce a dead space of solar energy absorption. As shown in Fig. 1, dead spaces of solar energy
Greek symbols g efficiency e emissivity Subscripts abs absorb align alignment apr aperture bot bottom segment con conical segment opt optical p pointing
absorption can be found in the cylindrical cavity receivers fabricated by Harbin Institute of Technology (HIT) and Indian Institute of Technology (IIT) respectively, and the area of dead space occupies about 10% of bottom surface (Prakash et al., 2009, 2010). Besides, the other types of conventional cavity receiver also have the problem of dead space of solar energy absorption, for example, the conical cavity receiver illustrated in literature (Zhao et al., 2004). Therefore, two new types of cylindrical cavity receiver with bottom surface convex are put forward in this paper to achieve the following purposes: (1) Solving the dead space of solar energy absorption of conventional cavity receiver. (2) Improving the optical efficiency of conventional cavity receiver. Analysis of optical efficiency and heat flux distribution of the two new types of cylindrical cavity receiver are conducted by Monte Carlo ray tracing method. In order to compare the optical efficiency (gopt ) of cavity receiver between the two new types of cylindrical cavity receiver and conventional cylindrical cavity receiver reasonably, the following principles should be abided: (1) The two new types of cylindrical cavity receiver and conventional cylindrical cavity receiver are placed on the focal plane of the same concentrator system (aperture radius of concentrator is 2600 mm, focal length of concentrator is 3250 mm). (2) The height (H = 200 mm) and aperture radius (Rapr = 90 mm) of the two new types of cylindrical cavity receiver and conventional cylindrical cavity receiver are uniform, and the height of all the cases studied are kept unchanged. (3) Physical parameters of the copper tube for the two new types of cylindrical cavity receiver and conventional cylindrical cavity receiver are the same.
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197
0.5m 0.33m
Back wall Wind skirt
(a) Fabricated by HIT
(b) Fabricated by IIT
Fig. 1. Conventional cylindrical cavity receivers fabricated by HIT and IIT respectively.
The theoretical focal spot radius of concentrator system is 24.1 mm, which is much smaller than the aperture radius of cavity receiver to guarantee that the sunlight on the focal plane of concentrator system can project into the cavity of receiver entirely. 2. Numerical methods Monte Carlo ray tracing method is a very powerful method to solve the heat flux distribution problems of solar concentrator and receiver system. Many investigators have adopted this method previously to investigate the heat flux distribution problems (Li et al., 2011; Maarten et al., 2005; Nedea et al., 2009; Jeter, 1986; Cheng et al., 2010). Based on the Monte Carlo ray tracing method, a code has been developed by the authors for solving solar energy gathering and transmission problems (Wang et al., 2012a, 2010; Shuai et al., 2012). The methodology of Monte Carlo ray tracing is the stochastic trajectories of a large number of rays as the rays intersecting with surfaces. Each ray carries the same amount of energy and has a specific direction determined by several probability density functions. The fate of each ray is determined by the emissive, reflective, and absorptive behavior on the surface described by a set of statistical relationships. The reflection direction of each energy ray follows the Fresnel optics rule. Owing to no truncation errors, the solutions of Monte Carlo ray tracing method are generally used as reference datum of numerical methods for discrete differential–integral equation (Huang et al., 2005; Wang and Modest, 2007). For sunlight, the value of solar radiation heat flux qs in the air adopted in this paper is 1000 W/m2 (Hasuike et al., 2006). The number density of energy bundles ns is defined as the number of energy bundle samplings emitting in every square ! millimeter where the sunlight vector N sun is perpendicular to the emission surface. Therefore, the energy carried by each ray is qs =ns . According to the energy conservation principle, the concentrated heat flux qr,i on the surface of receiver can be expressed as the following equation:
apr qs X Mj Ai ns j¼1 i
N
qr;i ¼
ð1Þ
where qr,i is the radiation flux of the ith surface element of receiver, Ai is the corresponding area, and N apr is the total ray number arrived at the aperture plane. If the jth ray arrives at the ith surface element, M ji = 1, otherwise M ji = 0. In short, the mechanism of solving solar energy gathering and transmission problems by Monte Carlo ray tracing method is: the Sun is regarded as massive and independent rays, each ray carries the same energy to guarantee the uniformity of sunlight distribution, the transmission process of each ray is composed by a series of independent sub-process (emission, reflection, transmission and absorption), and each independent sub-process follows a specific probability model (Shuai et al., 2008a, 2012; Wang et al., 2012a, 2010). As the Monte Carlo ray tracing method is a stochastic technique, the calculation accuracy of the Monte Carlo ray tracing method depends on the number of dispatched energy bundles and randomness performance of the pseudorandom number generator (Li et al., 2011; Maarten et al., 2005; Nedea et al., 2009; Jeter, 1986; Cheng et al., 2010). The larger density of energy bundles is, the higher calculation precision is, but the lower calculation efficiency is. A number of ray-sampling studies are also performed for the physical model to ensure that the essential physics is independent of the ray-sampling number. For the numerical study in this paper, the number density of energy bundles is set to 107 W/m2, and the calculation conditions are: the non-parallelism angle of sunlight is 160 , the sun shape is taken to be a distribution with a circumsolar-ratio of 0.05 and a limb darkening parameter of 0.8 (Shuai et al., 2008a,b). The dimensionless heat flux distribution calculated by Monte Carlo ray tracing method codes is validated against the experimental results performed by Johnston (Johnston, 1998). The comparison results are shown in Fig. 2. As seen from this figure, the results calculated by Monte Carlo ray
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bending cross-section radius and coiling space is increased compared to be coiled at a flat surface, and the bending force can be decreased (Orynyak and Radchenko, 2007). Therefore, the copper tubes are coiled to be a conical shape can be easier compared to be coiled at a flat surface and the convex radius can reach to the theoretical minimum magnitude.
Dimensionless heat flux
1.2
0.9
0.6 Calculated in this paper Measured by Johnston
0.3
3.2. Optical analysis of the CCCR
0.0 -6
-4
-2
0
2
4
The defining equation of optical efficiency of cavity receiver is:
6
Angular distance (mrad)
gopt ¼ N abs =N apr
Fig. 2. Comparisons of dimensionless heat flux distribution with experimental data.
tracing method codes developed by the authors are in good agreement with the experimental results in the reference. 3. Cylindrical with conical combined receiver (CCCR) 3.1. Introduction of the CCCR The CCCR is put forward in this paper with the purpose to improve the optical efficiency of conventional cylindrical cavity receiver. The schematic diagram of CCCR is shown in Fig. 3. As shown in this figure, the shape of lateral segment is cylindrical to guarantee the aperture radius of CCCR. The conical shape is adopted for the bottom segment of CCCR with the aim to solve the problem of dead space of solar energy absorption. As is seen in Fig. 3, copper tubes of CCCR will not be coiled at a flat surface with the convex radius (Ri) decreasing and the shape of bottom segment will be formed into an inverted ‘V’ shape. For the CCCR, the convex radius decreases with height increasing. When the copper tubes coiled to be a conical shape, the z
ð2Þ
where the symbol Napr designates the amount of sunlight reached the aperture plane of cavity receiver, the symbol Nabs denotes the amount of sunlight absorbed by cavity receiver. Fig. 4 presents the variation of optical efficiency of the CCCR with the increasing of dimensionless height (h/H), where the pointing error is 3 mrad and the alignment error is 0 mm. Generally, the absorptivity of copper tubes is between 0.023 (polished) and 0.78 (with oxide layer) He, 2009. Besides, the copper tubes can be coated with black to increase the absorptivity. Therefore, 0.60 is chosen for the absorptivity of copper tubes in this manuscript as a compromise. From the area comparison between the dashed line and solid line of bottom segment of the CCCR (shown in Fig. 3), it can be seen that the absorption area decreases with the dimensionless height increasing. Due to absorption area decreasing, the optical efficiency of the CCCR decreases sharply with the dimensionless height increasing when the dimensionless height is between 0.125 and 0.5. When the dimensionless height is between 0.5 and 0.85, the decreasing rate of optical efficiency grows slower with the dimensionless height increasing. This phenomenon is caused by combined effects of absorption area decreasing and absorption characteristic improving: the absorption area decreases with the dimensionless height increasing, but the heat flux distribution of lateral wall
Fluid inlet 0.70 Conventional with 10% dead space Conventional with no dead space CCCR
h
ηopt
0.68
Ri
0.66
H
0.64 0.62
x
x
0.60
Fluid outlet
0.2
0.4
0.6
0.8
h/H Concentrated sunlight Fig. 3. Schematic diagram of the CCCR.
Fig. 4. Variation of optical efficiency of the CCCR with the increasing of dimensionless height (e = 0.60, Ep = 3 mrad, Ealign = 0 mm).
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Table 1 Variation of Ncon/Napr of CCCR with the change of dimensionless height. h/H Ncon/Napr
0.125 0.245
0.25 0.309
0.375 0.415
4.1. Introduction of the BSIC receiver Though the CCCR can solve the problem of dead space of solar energy absorption, the capability of optical efficiency improving is very limited. Therefore, BSIC receiver is put forward to realize the above two purposes (Wang et al., 2012b). The schematic diagram of BSIC receiver is shown in Fig. 5. As shown in this figure, copper tubes in the bottom segment of conventional cylindrical cavity
0.75 0.621
0.875 0.621
0.95 0.622
z Fluid inlet
Ri h
4. Cylindrical receiver with bottom surface interior convex (BSIC receiver)
0.625 0.585
H
tends to be zero when the height of lateral wall is lower than a specific magnitude, the effects of absorption area on heat flux distribution decreases with the height of lateral wall increasing. When the dimensionless height is 0.125, the optical efficiency of CCCR (68.25%) is a little higher than that of conventional cylindrical cavity receiver with no dead space (67.91%) and conventional cylindrical cavity receiver with 10% dead space (65.79%). The optical efficiency of CCCR decreases to 66.2% when the dimensionless height increases to 0.375, which is only 0.4% higher than that of conventional cylindrical cavity receiver with 10% dead space (65.8%). The effects of absorption area on heat flux distribution will be higher than that of path deflection when the dimensionless height is higher than 0.375, and the optical efficiency of CCCR would be even lower than that of conventional cylindrical cavity receiver with 10% dead space. Table 1 illustrates the variation of proportion of sunlight received by conical segment (Ncon/Napr) of CCCR with the change of dimensionless height. As seen in this table, the proportion of sunlight received by conical segment increases quickly with the increasing of dimensionless height when the dimensionless height is between 0.125 and 0.75. When the dimensionless height is between 0.75 and 0.95, the proportion of sunlight received by conical segment has very little change with the increasing of dimensionless height. Combining the above analysis, it can be seen that the CCCR cannot improve optical efficiency through the entire dimensionless height variation range, and there is a dimensionless height limiting for optical efficiency improving. Compared to the conventional cylindrical cavity receiver with no dead space, the capability of optical efficiency improving is very limited, and the maximum improved optical efficiency is only 0.34%. Compared to the conventional cylindrical cavity receiver with 10% dead space, the maximum improved optical efficiency of CCCR is only 2.46%.
0.5 0.497
O Fluid outlet Concentrated sunlight Fig. 5. Schematic diagram of the BSIC receiver.
receiver are coiled to be an internal convex surface and the shape of bottom segment will be formed into a normal ‘V’ shape. Similar to the conical bottom segment of the CCCR, the normal ‘V’ shape for bottom segment of BSIC receiver can be easily coiled and the convex radius can reach to the theoretical minimum magnitude. As the bottom segment of BSIC receiver is coiled convex toward the interior direction, the absorption area would be increased compared to conventional cylindrical cavity receiver with no dead space as well as the CCCR. Besides, the shape of BSIC receiver keeps being cylindrical and the height of receiver does not need to be changed when the BSIC receiver is adopted to replace conventional cylindrical cavity receiver. 4.2. Effects of interior convex dimensionless height Fig. 6 presents the variation of optical efficiency of BSIC receiver with the change of interior convex dimensionless height (h/H), where the absorptivity of copper tube is 0.60, the pointing error is 3 mrad and the alignment error is 0 mm. When the dimensionless height is 0, the BSIC receiver evolves into conventional cylindrical cavity receiver with no dead space. As shown in this figure, the optical efficiency of BSIC receiver increases with the dimensionless height increasing when the dimensionless height is between 0 and 0.875. The optical efficiency of BSIC receiver attains its peak magnitude when the dimensionless height increased to 0.875, which is 73.46%. The optical efficiency of BSIC receiver for a dimensionless height of 0.875 is 5.55% higher than that of conventional cylindrical cavity receiver with no dead space (67.91%). The optical efficiency
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ηopt
0.72
0.70
Conventional with 10% dead space Conventional with no dead space BSIC
0.68
0.66 0.0
0.2
0.4
0.6
0.8
1.0
h/H Fig. 6. Variation of optical efficiency of BSIC receiver with the change of dimensionless height (e = 0.60, Ep = 3 mrad, Ealign = 0 mm).
of BSIC receiver for a dimensionless height of 0.875 is 7.67% higher than that of conventional cylindrical cavity receiver with 10% dead space (65.79%). As seen from Fig. 5, the absorption area of BSIC receiver increases with the dimensionless height increasing which can induce the optical efficiency increasing. Fig. 6 illustrates that the increasing rate of optical efficiency decreases with the dimensionless height increasing. It should be noted that the absorption characteristics of cavity receiver are influenced when the bottom surface changed from flat to interior convex. When the dimensionless height is higher than 0.875, the effects of absorption characteristics change on optical efficiency variation is dominant, the optical efficiency of BSIC receiver begins to decrease with the dimensionless height increasing. When the interior convex dimensionless height increased to 1.0, the optical efficiency of BSIC receiver is 70.22%, which is 2.31% higher than that of conventional cylindrical cavity receiver with no dead space of solar energy absorption. The definition of bottom absorption percentage (Nbot/ Napr) is the ratio of amount of sunlight absorbed by the bottom segment to the amount of sunlight reached to the aperture plane of receiver. Fig. 7 shows the variation of
bottom absorption percentage of BSIC receiver with the change of dimensionless height. As shown in this figure, the bottom absorption percentage increases with dimensionless height increasing due to absorption area increase. The bottom absorption percentage of BSIC receiver for a dimensionless height of 1.0 is 14% higher than that of conventional cylindrical cavity receiver with no dead space. When the bottom segment changes from flat surface to convex surface, the Monte Carlo ray tracing analysis shows that the heat flux distribution change. Fig. 8 illustrates the heat flux distribution on the bottom segment of BSIC receiver along radius direction at different dimensionless height conditions. When the bottom segment is flat surface (conventional cylindrical cavity receiver with no dead space), the heat flux distribution along radius direction of bottom segment has very small fluctuation. With the dimensionless height increasing, the heat flux distribution along radius direction of bottom segment becomes to be highly nonuniform. When the dimensionless height is less than 0.875, the heat flux distribution at different dimensionless height conditions present as monotonically decreasing distribution, and the positions of peak magnitude locate at the same position – the center of bottom segment, which increases with the dimensionless height increasing. When the dimensionless height reaches to 0.875 or higher, the heat flux distribution along radius direction becomes to be unimodal distribution, and the positions of peak magnitude move away from the center of bottom segment with dimensionless height increasing. Fig. 9 shows the heat flux distribution on the lateral wall segment of BSIC receiver along the height direction at different dimensionless height conditions. As shown in this figure, the heat flux distribution on the lateral wall segment presents as a unimodal distribution. According to the geometrical optics theory, the sunlight is highly concentrated on the center of focal plane (Shuai et al.,2008a,b). When concentrated sunlight projects into the cavity of receiver, the concentrated sunlight begins to scatter. Due to rectilinear propagation of sunlight, very little sunlight reaches the near aperture region 3
0.44
Nbot /Napr
2
0.40
q ( W/mm )
Conventional with 10% dead space Conventional with no dead space BSIC
0.36 0.32
h/H= 0 h/H= 0.125 h/H= 0.375 h/H= 0.625 h/H= 0.875 h/H= 1.0
2
1
0.28 0
0.24
0
0.0
0.2
0.4
0.6
0.8
1.0
h/H Fig. 7. Variation of bottom absorption percentage of BSIC receiver with the change of dimensionless height (e = 0.60, Ep = 3 mrad, Ealign = 0 mm).
15
30
45
60
75
90
R (mm) Fig. 8. Heat flux distribution on the bottom segment of BSIC receiver along the radius direction at different dimensionless height conditions (e = 0.60, Ep = 3 mrad, Ealign = 0 mm).
F. Wang et al. / Solar Energy 90 (2013) 195–204 0.20
2
q (W/mm )
0.15
0.10
h/H= 0 h/H= 0.125 h/H= 0.375 h/H= 0.625 h/H= 0.875 h/H= 1.0
0.05
0.00 0
40
80
120
160
200
z (mm)
Fig. 9. Heat flux distribution on the lateral wall segment of BSIC receiver along the height direction at different dimensionless height conditions (e = 0.60, Ep = 3 mrad, Ealign = 0 mm).
of lateral wall (z < 50 mm) and the heat flux is close to zero in this region. Most of the sunlight gathers on the middle region of lateral wall, where the peak magnitude of heat flux distribution on the lateral wall is found. Due to the bottom surface is interior convex, the BSIC receiver can not only change the absorption and reflection characteristic of cavity receiver, but also can increase the absorption area. Therefore, the BSIC receiver can achieve the goal of optical efficiency improving. Besides, the BSIC cavity receiver minimizes the heat flux distribution of the lateral segment. 4.3. Effects of wall absorptivity
of copper tube is 0.60, the pointing error is 3 mrad and the alignment error is 0 mm. As shown in this figure, the optical efficiency of BSIC receiver is higher than that of conventional cylindrical cavity receiver with no dead space in the whole wall absorptivity variation scope (except a = 1.0). When the wall absorptivity is 1.0, sunlight reached the cavity of receiver would be absorbed thoroughly regardless of BSIC receiver or conventional cylindrical cavity receiver with no dead space. Therefore, the optical efficiency of BSIC receiver (gopt = 1.0) is equal to that of conventional cylindrical cavity receiver with no dead space. The variation of improved optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of wall absorptivity is shown in Fig. 11. Compared to conventional cylindrical cavity receiver with no dead space, the magnitude of improved optical efficiency reaches the maximum when the wall absorptivity is 0.4, which is 6.44%. Compared to conventional cylindrical cavity receiver with 10% dead space, the magnitude of improved optical efficiency reaches the maximum when the wall absorptivity is 0.5, which is 7.80%. 4.4. Effects of pointing error As known, pointing error represents the accuracy of rays pointing to the predetermined target. Fig. 12 presents the variation of optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of pointing error, where the absorptivity of copper tube is 0.60 and the alignment error is 0 mm. As shown in this figure, the optical efficiency of BSIC receiver for a dimensionless height of 0.875 is higher than that of conventional cylindrical cavity receiver with no dead space in the whole pointing error variation range. When the pointing error increased from 0 mrad to 14 mrad, the optical efficiencies of BSIC receiver for a dimensionless height of 0.875, conventional cylindrical cavity receiver with no dead space and conventional cylindrical cavity receiver with 10% dead space have very small fluctuation. The maximum optical efficiency
1.0
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η imp
ηopt
As known from the above analysis, the BSIC receiver has the highest optical efficiency when the dimensionless height is 0.875. Therefore, the dimensionless height of BSIC receiver adopted in the succeeding analysis is 0.875. The variation of optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of wall absorptivity is illustrated in Fig. 10, where the absorptivity
0.4 BSIC with h/H=0.875 Conventional with no dead space Conventional with 10% dead space
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0.00
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α Fig. 10. Variation of optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of absorptivity (Ep = 3 mrad, Ealign = 0 mm).
0.2
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α Fig. 11. Variation of improved optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of absorptivity (Ep = 3 mrad, Ealign = 0 mm).
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ηopt
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Ep (mrad) Fig. 12. Variation of optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of pointing error (e = 0.60, Ealign = 0 mm).
4.5. Effects of alignment error The alignment error represents the distance between the focal plane of parabolic concentrator and aperture plane of
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4.5 BSIC with h/H=0.875 Conventional with no dead space Conventional with 10% dead space
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fluctuations of BSIC receiver for a dimensionless height of 0.875, conventional cylindrical cavity receiver with no dead space and conventional cylindrical cavity receiver with 10% dead space are 0.4%, 0.9% and 1.2% respectively. As illustrated previously, the aperture radius of cavity receiver is much higher than the focus spot radius of concentrator, and the special structure of BSIC receiver for a dimensionless height of 0.875 can effectively absorb the sunlight projected into the cavity. The above two characteristics of BSIC receiver for a dimensionless height of 0.875 induce the phenomenon of lowest optical efficiency fluctuation with the change of pointing error. When pointing error is considered, though the optical efficiency of cavity receiver has small fluctuation with the change of pointing error, the reflection and absorption characteristics as well as the heat flux distribution would be affected which influences the bottom absorption percentage. Fig. 13 illustrates the variation of bottom absorption percentage with the change of pointing error, where the dimensionless height of BSIC receiver is 0.875. As seen from this figure, the bottom absorption percentage increases quickly with the increasing of pointing error. When the pointing
error of BSIC receiver for a dimensionless height of 0.875 is 7 mrad, the magnitude of bottom absorption percentage reaches the peak magnitude, which is 6.72% higher than that of BSIC receiver for a dimensionless height of 0.875 without any pointing error, and then the bottom absorption percentage decreases slowly with the increasing of pointing error. However, the bottom absorption percentage increases slowly with the increasing of pointing error for conventional cylindrical cavity receiver with no dead space and conventional cylindrical cavity receiver with 10% dead space through the entire pointing error variation range. When pointing error is considered, the path of sunlight would be changed which would influence the bottom absorption percentage. The different shapes of bottom segment between BSIC receiver and conventional cylindrical cavity receiver induces the different changes of the bottom absorption percentage with the variation of pointing error. The heat flux distribution on the bottom segment of BSIC receiver for a dimensionless height of 0.875 at different pointing error conditions is shown in Fig. 14. The heat flux distribution on the bottom segment presents as monotonically decreasing distribution of exponential type when the pointing error is 0 mrad. With the increasing of pointing error, the heat flux distribution on the bottom segment changes from monotonically decreasing distribution to unimodal distribution, and the higher pointing error is, the lower peak magnitude of heat flux distribution is. This phenomenon can be explained as follows: when the pointing error is 0 mrad, the parabolic concentrator concentrates the sunlight perfectly and the center of bottom segment has the peak heat flux. With the increasing of pointing error, the accuracy of concentrated sunlight pointing the determined target decreases, the location of peak heat flux moves away from the center of focal plane and the concentration ratio of concentrator system decreases.
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0 mrad 4 mrad 8 mrad 12 mrad
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Ep (mrad) Fig. 13. Variation of bottom absorption percentage of BSIC receiver for a dimensionless height of 0.875 with the change of pointing error (e = 0.60, Ealign = 0 mm).
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R (mm) Fig. 14. Heat flux distribution on the bottom segment of BSIC receiver for a dimensionless height of 0.875 at different pointing error conditions (e = 0.60, Ealign = 0 mm).
F. Wang et al. / Solar Energy 90 (2013) 195–204 0.80 BSIC with h/H=0.875 Conventional with no dead space Conventional with 10% dead space
ηopt
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The variation of bottom absorption percentage of BSIC receiver for a dimensionless height of 0.875 with the change of alignment error is illustrated in Fig. 16. The bottom absorption percentage variation tendencies of both the conventional cylindrical cavity receiver and BSIC receiver for a dimensionless height of 0.875 are similar to the variation tendencies of optical efficiency. The bottom absorption percentage of conventional cylindrical cavity receiver presents as linear decrease with the increasing of alignment error, and the bottom absorption percentage of BSIC receiver for a dimensionless height of 0.875 exhibits as overall undulatory decrease. 5. Conclusion
Fig. 15. Variation of optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of alignment error (e = 0.60, Ep = 3 mrad).
0.36
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Ealign (mm) Fig. 16. Variation of bottom absorption percentage of BSIC receiver for a dimensionless height of 0.875 with the change of alignment error (e = 0.60, Ep = 3 mrad).
cavity receiver along the z axis direction. When the alignment error is zero, the focal plane of concentrator system coincides with the aperture plane of cavity receiver. When the alignment error is larger than zero, the aperture plane of cavity receiver is away from the focal plane of concentrator system along positive z axis direction. Fig. 15 illustrates the variation of optical efficiency of BSIC receiver for a dimensionless height of 0.875 with the change of alignment error, where the pointing error is 3 mrad, and the wall absorptivity is 0.60. As seen from Fig. 15, the optical efficiency of BSIC receiver is higher than that of conventional cylindrical cavity receiver with no dead space and conventional cylindrical cavity receiver with 10% dead space among the whole alignment error variation range. The optical efficiency variation of conventional cylindrical cavity receiver presents as linear decrease with the increasing of alignment error. However, due to the special configuration of bottom segment interior convex, the optical efficiency variation of BSIC receiver exhibits as overall undulatory decreasing.
The CCCR and BSIC receivers are put forward in this paper with the objective to improve the optical efficiency of conventional cylindrical cavity receiver. The optical efficiency and heat flux distribution of the CCCR and BSIC receivers are analyzed by Monte Carlo ray tracing method. The following conclusions have been drawn: (1) The CCCR cannot improve optical efficiency through the entire dimensionless height variation range, and there is a dimensionless height limiting for optical efficiency improving. (2) Among the whole interior convex dimensionless height variation range, the optical efficiency of BSIC receiver is higher than that of conventional cylindrical cavity receiver with no dead space, and the BSIC receiver for dimensionless height of 0.875 has the highest optical efficiency. (3) Among the whole wall absorptivity variation range, pointing error variation range and alignment variation range, the optical efficiency of BSIC receiver for a dimensionless height of 0.875 is higher than that of conventional cylindrical cavity receiver. (4) The BSIC receiver can effectively reach the objective of optical efficiency improving.
Acknowledgements This work was supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51121004) and the key program of the National Natural Science Foundation of China (Grant No. 50930007). References Ananthanarayanan, V., Andrej, L., Bekir, Y., Salem, A., Evelyn, N., 2012. Analytical model for the design of volumetric solar flow receivers. International Journal of Heat and Mass Transfer 55, 556–564. ´ vila, M., 2011. Volumetric receivers in solar thermal power Antonio, L., A plants with central receiver system technology: a review. Solar Energy 85, 891–910.
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