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Experimental investigation of thermal performance enhancement of cavity receiver with bottom surface interior convex
Applied Thermal Engineering 168 (2020) 114847
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Experimental investigation of thermal performance enhancement of cavity receiver with bottom surface interior convex
T
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Yuan Yuanb, Lin Xiaojieb,a, Cheng Zimingb,a, Wang Fuqianga,b, , Shuai Yongb, Tan Hepingb a b
School of New Energy, Harbin Institute of Technology at Weihai, 2, West Wenhua Road, Weihai 264209, PR China School of Energy Science and Engineering, Harbin Institute of Technology, 92, West Dazhi Street, Harbin 150001, PR China
H I GH L IG H T S
cost biaxial sun-tracking concentrated solar thermal utilization system was designed. • Low with bottom bulging was designed and tested to increase thermal efficiency. • Receiver • Test show that thermal efficiency of receiver with bottom bulging was 4.1% higher.
A R T I C LE I N FO
A B S T R A C T
Keywords: Solar energy Cavity receiver Optical efficiency Thermal efficiency Radiative transfer Solar thermal utilization system
To solve the dead space problem of conventional cavity receiver and increase energy conversion efficiency, cavity receiver with bottom surface interior convex was designed and fabricated. A low cost biaxial sun-tracking concentrated solar thermal utilization system using Fresnel lens as concentrator was designed and fabricated to test the thermal performance of cavity receiver, which can give a guidance for lab test of thermal performance of cavity receiver. Optical performance and thermal efficiency of cavity receiver with bottom surface interior convex was analyzed and measured through optical analysis and experimental test. Optical analysis indicated that the optical efficiency of the cavity receiver with bottom surface interior convex was 6.02% higher than that of conventional cavity receiver. A 4-h outdoor test showed that the average thermal efficiency of the cavity receiver with bottom surface interior convex was 4.1% higher than that of conventional cavity receiver.
1. Introduction Solar energy plays a major role in reducing of CO2 emission [1] and alleviating energy crisis [2]. Of all the approaches for solar energy utilization, concentrated solar power (CSP) technology is one of the promising options because the energy density of solar irradiation can be greatly increased and heat loss can be reduced [3,4]. A receiver is one of the main components of a concentrated solar thermal system [5]. Cavity receiver is widely used in CSP systems because of its advantages of high efficiency of photo-thermal conversion, low reflective loss, and steady thermal performance [6,7]. Boyd et al. [8] initially introduced a cylindrical cavity receiver, where the cavity receiver was formed by a coiling receiver tube, and insulating material was lagged on the outer surface to reduce the heat losses. Heat transfer fluid (HTF) flowed through the inside of the receiver tube. Concentrated solar irradiation entered the cavity through the aperture of cavity. Because of the blackbody effect of the cavity, the
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majority of solar irradiation entering the cavity can be absorbed after times of bounces with the surface of cavity [9,10]. When the concentrated solar irradiation was absorbed by a cavity receiver, the HTF inside the receiver tube was heated [11,12]. Water [13], thermal oil [14], molten salt [15], and air [16,17] can be used as the HTF of cavity receiver, which enabled the cavity receiver to work in a wide temperature range. With the aim of improving the thermal performance of the conventional cavity receiver, several optimizing methods have been introduced. Cavity receiver for a solar tower was numerically analyzed by Tu et al. [18] to optimize the thermal performance of the receiver, and the optimal depth of the cavity receiver was determined. This optimization can enable the highest thermal efficiency and a relatively uniform heat flux distribution can be achieved. Aiming to improve the temperature uniformity of receiver, the influence of volume flow rate of HTF and aperture size were analyzed by Hamed et al. [19] by experiment, which indicated that the uniformity of HTF temperature
Corresponding author. E-mail address: [email protected] (W. Fuqiang).
https://doi.org/10.1016/j.applthermaleng.2019.114847 Received 29 July 2019; Received in revised form 20 December 2019; Accepted 23 December 2019 Available online 24 December 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
Applied Thermal Engineering 168 (2020) 114847
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Δη Δ¯η τ ρ
Nomenclature A cp D’ D0 D1 D2 Gd h hd H H1 k ṁ Q T V̇
area, m2 specific heat, J/(kg·°C,) minimum diameter of coiling, m aperture diameter, mm diameter of the outer contour of coiling receiver tube, m diameter of the outer contour of receiver, m direct solar irradiation, W/m2 height of bottom surface interior convex, m depth of focal plane, m depth of cavity receiver, m height of receiver, m correction factor mass flow rate, kg/s energy, J temperature, °C volume flow rate, m3/s
increment of thermal efficiency average increment of thermal efficiency transmittance density, kg/m3
Subscripts a abs Bb cav Conv Dim i lens m Max o therm
ambient absorbed by HTF bottom surface interior convex into the cavity conventional receiver dimensionless inlet fresnel lens reference parameter maximum outlet thermal
Greek symbols η
efficiency
coiled at the same plane at the bottom surface, which would generate high fabricating and residual forces near the center of bottom surface [26,27]. In addition, the bottom surface cannot be fully covered by metal tube and produced a dead space, which would decrease the optical and thermal efficiencies [28,29]. Yan et al. [29] proposed to install a reflecting cone on the bottom surface of the cavity receiver to solve the dead space problem. Experimental test of receiver with reflecting cone was conducted by Sumit et al. [30], but their experiment did not conduct comparisons between conventional receiver and receiver with reflecting cone. Wang and Shuai et al. [31–33] presented an angularspectral index of concentrated sunlight to instruct the design of a new type of high-optical and thermal-performance cavity receiver. The bottom surface interior convex (BSIC) cavity receiver was initially introduced by Wang and Shuai et al. [31–33], and optical analysis indicated that the BSIC cavity receiver can solve the dead space problem effectively with an optical efficiency improvement of as much as 5.55%. However, to the best of our knowledge, most investigations on the dead space problem of the conventional cavity receiver remain at the stage of numerical analysis and lack experimental research and comparison with conventional solar receiver. In this study, a cylindrical cavity receiver with bottom surface interior convex was fabricated with
increased with the decrease of aperture size. To decrease the natural convective heat loss, a cavity receiver with plate fins attached to the inner aperture surface was introduced by Ngo et al. [20]. The influence of cavity inclination and parameters of the fins on natural convective heat loss was numerically studied by Ngo et al. [20]. The results showed that the design of plate fins attached to the inner aperture surface could reduce the natural convective heat loss of the receiver up to 20%. Three types of receivers with different cavity shapes (cylindrical, spherical, and conical) were numerically studied by Daabo et al. [21,22], and the results indicated that conical cavity had the best uniformity of heat flux distribution and the highest optical efficiency. Furtherly, the experimental research of Jorge et al. [23] showed that the reverse-conical cavity shape offered higher efficiencies than cylindrical cavity shape. Through experiment, the influence of aspect ratio on thermal efficiency, exergy efficiency and overall heat loss were studied by Thirunavukkarasu et al. [24]. The results suggested that 0.8 was the optimal aspect ratio. A comparative experiment between cubical and cylindrical cavity receiver were conducted by Loni et al. [25], which presented that thermal efficiency of cubical receiver was higher than that of cylindrical receiver. For conventional cylindrical cavity receiver, the metal tube must be
a) Conventional cavity receiver
b) Cavity receiver with bottom bulging
Fig. 1. Schematics of a conventional cavity receiver and a cavity receiver with bottom surface interior convex. 2
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2.2. Two-axis sun-tracking concentrated solar thermal performance testing system
the aim of testing the overall thermal efficiency increase of the cavity receiver. The optimal structural parameters of the cylindrical cavity receiver with bottom surface interior convex were obtained through optical analysis. A low cost biaxial sun-tracking concentrated solar thermal utilization system using Fresnel lens as concentrator was designed and fabricated to test the thermal performance of cavity receiver through experiment, which can give a guidance for lab test of cavity receiver thermal performance.
To test the thermal performance of the cavity receiver with different bottom surface interior convex heights, a biaxial sun-tracking concentrated solar thermal performance testing system was designed and fabricated. The schematic of the biaxial sun-tracking concentrated solar thermal utilization system was shown in Fig. 3(a). A polymethylmethacrylate Fresnel lens was used to concentrate the incoming sunlight. The geometric dimensions of Fresnel lens were listed as follows: the diameter was 600 mm, the thickness was 3 mm, the ring distance was 0.7 mm, and the focal length was 300 mm. An optical focusing sensor was set up on the aluminum alloy frame, which was used to control the biaxial sun-tracking platform to guarantee the Fresnel lens always pointed to the sun (as shown in Fig. 3(b)). A direct solar radiometer (TBS-3) was used to record the real-time direct normal irradiance every minute. The temperatures of fluid inlet, fluid outlet and ambient were measured by thermal couples to record the absorbed concentrated solar energy by the cavity receiver. A flowmeter was used to measure and control the volume flow rate of the HTF (25 ml/min). The wind speed of the environment was also measured by an anemoclinograph recorder to guarantee that it was less than the second grade wind (< 4 m/s). During the thermal performance test, HTF was driven by the water pump which flowed through the flowmeter, receiver and finally returned back to the storage tank. Cavity receivers were fixed on the frames equipped with the biaxial sun-tracking system. Thermal performance tests of the conventional cavity receiver and cavity receiver with bottom surface interior convex were conducted simultaneously for comparison (as shown in Fig. 3(c)). To obtain the temperature on the interior surfaces of the cavity receiver, thermal couples were attached to the interior surface of cavity receivers. Positions selected to attach thermal couples were shown in Fig. 4 (red points). During the experimental test, temperature data and direct solar irradiance were recorded every minute, while the wind speed were recorded every 10 min. The physical dimensions of the experimental setup were shown in Table 1. The scale and accuracy of the test instruments used in this study were shown in Table 2.
2. Thermal performance test system 2.1. Design and fabrication of cavity receiver with bottom surface interior convex Fig. 1 presented the schematic of a conventional cavity receiver and cavity receiver with bottom surface interior convex. Theoretically, a cavity receiver with bottom surface interior convex can decrease the area of dead space effectively, and improve the optical efficiency and thermal efficiency. To design and fabricate a cavity receiver with bottom surface interior convex, the following parameters need to be determined: the aperture diameter (D0), depth (H), height of bottom surface interior convex (h), tube material, and diameter of metal tube. Before the determination of aperture diameter of the cavity receiver, a pre-test was conducted and showed that the facula diameter on the focal plane of Fresnel lens was 50 mm. Based on the comprehensive consideration of facula diameter, optical losses, and convective heat losses, the aperture diameters of the fabricated cavity receivers were set to be 80 mm. As described in Refs. [32,33], the threshold ratio of aperture diameter (D0) to height (H) of a cavity receiver was 9/10, at which ratio the convective heat transfer losses did not change with the variation of D0/H. Therefore, the height of the cavity receiver was set to be 120 mm, whereas the ratio of aperture diameter to height of a cavity receiver was 2/3. The metal tubes of a cavity receiver were well lagged with insulation materials to decrease conductive heat losses. To investigate the effects of bottom surface interior convex height on overall heat transfer performance, four cavity receives with different dimensionless heights (h/H), equaled to 0, 0.375, 0.625, and 0.875, were designed and fabricated. The thickness of metal tube was 1 mm, and the outer diameter of the metal tube was 8 mm. For easy fabrication, normal-sized PVC-U pipe with a height of 160 mm and thickness of was 4 mm was used as the shell of cavity receiver. Aluminum silicate wool was used as insulation material due to the advantages of low thermal conductivity, high temperature resistance, good thermal stability and non-corrosivity. According to the Hottel model [34], the thickness of the insulating layer was set to 28 mm with conductive heat losses less than 6.15%. The fabricated cavity receivers with different dimensionless bottom surface interior convex heights were presented in Fig. 2.
a) h/H = 0
3. Methodology 3.1. Optical analysis With the aim of studying the influence of the physical structure and focal plane position on the optical performance of the receiver, an optical simulation was conducted by Monte Carlo ray tracing method (MCRT) using Tracepro software. A total of 500,000 rays were used for sunlight concentration, transmission, and absorption analysis, and the local solar irradiance was set to be 1000 W/m2. For more detailed information about the ray tracing method, please refer to [35–40]. Based on the actual structural parameters of the receivers, 3D models of the cavity receivers were built and used for optical simulation. The 3D
b) h/H = 0.375
c) h/H = 0.625
d) h/H = 0.875
Fig. 2. Fabricated cavity receivers with different dimensionless bottom surface interior convex heights. 3
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c) Physical setup Fig. 3. Schematic of the biaxial sun-tracking concentrated solar thermal utilization system.
plane of cavity receivers. The optical properties of each component was presented in Table 3. To investigate the effects of the bottom surface interior convex height on optical performance, four cavity receivers with different
models built by Pro/E was opened by TracePro software. A circle shape ray source with diameter of 600 mm was used, while the incoming solar radiance was 1000 W/m2 (beam to the receiver) with uniformly distribution. The ray source was located 500 mm away from the aperture 4
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a) h/H = 0
b) h/H = 0.375
c) h/H = 0.625
d) h/H = 0.875 Fig. 4. Positions selected to attach thermal couples.
3.2. Comparison test
Table 1 Physical dimensions and operational parameters of experimental setup. Physical dimension or operational parameters
Value
Diameter of Fresnel lens Thickness of Fresnel lens Ring distance of Fresnel lens Focal length of Fresnel lens Concentrate ratio of Fresnel lens Distance between the central of Fresnel and the aperture plane of receiver Volume flow rate of water
600 mm 3 mm 0.7 mm 300 mm 144 270 mm
Three groups of comparison test were conducted to investigate the thermal performance enhancement by using a cavity receiver with bottom surface interior convex. Cavity receivers with different dimensionless heights, h/H = 0.375, 0.625, and 0.875 were investigated. Thermal efficiency of cavity receiver was defined as the ratio of energy absorbed by HTF to the solar energy entering the cavity. The reference temperature Tm was defined as the average temperature of the fluid inlet temperature and fluid outlet temperature:
25 ml/min
Tm = Table 2 Scale and accuracy of the test instruments used in this study.
(1)
Energy absorbed by HTF (Qabs ) was expressed as:
Test instrument
Scale
Accuracy
Anemometer Wind direction meter Solar direct radiometer
0–60 m/s 0–359° 400–1100 nm 0–2000 W/m2 0–250 ml/min −100 to 1370 °C
± 0.1 m/s ± 1° ± 1 W/m2
Flowmeter Thermocouple and temperature recorder
Ti + To 2
Qabs = c p ṁ (To − Ti ) = c p ρV̇ (To − Ti )
In Eq. (2), the symbol V̇ was the volume flow rate of water. The specific heat at constant pressure and density of water at a specific temperature could be obtained through linear interpolation from Ref. [41]:
± 6% ± 0.5 °C
⎧ ρ10 + ⎪ ρm = ρ20 + ⎨ ⎪ ρ30 + ⎩
Table 3 Optical properties of concentrated solar thermal utilization system [40]. Optical parameters
Value
Absorptivity of cavity receiver tube Absorptivity of cavity receiver insulation Transmittance of Fresnel lens Absorptivity of cavity receiver shading board
0.65 0.25 0.8 0.3
(2)
ρ20 − ρ10 10 ρ30 − ρ20 10 ρ40 − ρ30 10
where ρ10 = 999.7 ρ30 = 992.2 kg/m3 .
⎧Cp10 + ⎪ Cpm = Cp + ⎨ 20 ⎪ 4.178, ⎩
dimensionless heights, h/H = 0, 0.375, 0.625, and 0.875 were investigated to identify the optimal dimensionless surface interior convex height. Five focal plane positions of the Fresnel lens, hd/H = 0, 0.25, 0.5, 0.75, and 1.0 were investigated. The distance between Fresnel lens and aperture plane of receiver was 300 mm, 270 mm, 240 mm, 210 mm and 180 mm correspondingly.
× (Tm − 10),
10 ° C⩽ Tm ⩽ 20 °C
× (Tm − 20),
20 ° C⩽ Tm ⩽ 30 °C
× (Tm − 30),
30 ° C⩽ Tm ⩽ 40 °C
kg/m3 ,
Cp20 − Cp10 10 Cp30 − Cp20 10
ρ20 = 998.2
kg/m3 ,
ρ30 = 995.7
(3)
kg/m3 ,
× (Tm − 10),
10 ° C⩽ Tm ⩽ 20 °C
× (Tm − 20),
20 ° C⩽ Tm ⩽ 30 °C 30 ° C⩽ Tm ⩽ 40 °C
kJ/(kg·° C) ,
kJ/(kg·° C) ,
where Cp20 = 4.183 Cp10 = 4.191 4.178 kJ/(kg·° C) , and Cp40 = 4.178 kJ/(kg·° C) . Solar energy entering the cavity Qcav was defined as:
Q cav = G d A lens τlens k 1 k 2
and
(4)
Cp30 =
(5)
The value of k1 was obtained by optical simulation with the value of 0.88281 and denoted that 88.281% of the sunlight concentrated by Fresnel lens entered the cavity. The experimental correction factor (k2) 5
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was introduced to compensate for the observed center point deviation of the focal plane during the test with the value of 0.9. The thermal efficiency of the cavity receiver η therm was defined as:
η therm =
Qabs Qcav
(6)
The increment of the thermal efficiency Δη was defined as the difference in thermal efficiency between the cavity receiver with bottom surface interior convex and the conventional cavity receiver.
Δη = ηBb − ηConv
(7)
According to the calculation process of thermal efficiency, the uncertainty of thermal efficiency was defined as: 2
δη =
2
2
2 ⎛ δη ⎞ (δη)2 + ⎛ δη ⎞ (δTo )2 + ⎛ δη ⎞ (δTi )2 + ⎛ δη ⎞ (δGd )2 ̇ ⎝ δV ⎠ ⎝ δTo ⎠ ⎝ δTi ⎠ ⎝ δGd ⎠ ⎜
⎟
⎜
⎟
⎜
⎟
(8) Fig. 6. Effects of h/H on the optical efficiency of cavity receiver.
4. Results and discussion receiver tube on the sidewall of the cavity receiver could be shined by a large amount of sunlight entering the cavity directly and part reflected light when hd/H = 0 and 0.25, which resulted in non-uniform heat flux distribution on the side wall. When the focal plane of the Fresnel lens was moved inside the cavity receiver, the value of heat flux distribution on the side wall decreased sharply. When the focal plane of the Fresnel lens moved inside the cavity receiver at hd/H = 0.50, the heat flux on the side wall of the cavity receiver was very small. Only the metal tube on the sidewall near the bottom surface of the cavity receiver could be shined directly, where the other part of the sidewalls could only heated by a very small amount of reflected sunlight. When the focal plane of
4.1. Optical analysis Fig. 5 presented the effects of focal plane position on heat flux distribution on the sidewall of cavity receiver. Five focal plane positions of the Fresnel lens, hd/H = 0, 0.25, 0.5, 0.75, and 1.0 were investigated. As shown in Fig. 5(a), the heat flux distribution on the sidewall of the conventional cavity receiver without a with bottom surface interior convex changed dramatically with height and a peak value of heat flux was observed, when the focal plane of the Fresnel lens located on the front of the cavity receiver was hd/H = 0 and 0.25. The
Fig. 5. Heat flux distribution on the sidewalls of receivers with different values of hd/H. 6
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Fig. 7. Measurements of direct solar irradiance, wind speed and temperature.
irradiation and could only be heated by reflected sunlight, which resulted in a near zero heat flux distribution on the sidewall. As shown in Fig. 5(b) and (c), the heat flux distribution on the sidewalls of the cavity receivers with bottom surface interior convex was similar to that of the conventional cavity receiver when the dimensionless heights were 0.375 and 0.625. When the dimensionless height was increased to 0.875, as seen in Fig. 5(d), more concentrated sunlight was able to reach the side wall of the cavity receiver with bottom surface interior convex. Fig. 6 presented the effects of dimensionless surface interior convex
Table 4 Uncertainty value of thermal efficiency in each experiment.
Case 1 Case 2 Case 3
h/H = 0
h/H = 0.375
h/H = 0.625
h/H = 0.875
± 1.1% ± 1.1% ± 0.9%
± 1.2% – –
– ± 1.2% –
– – ± 1.2%
the Fresnel lens moved inside the cavity receiver at hd/H ≥ 0.75, the receiver tube on the sidewall could barely receive direct sunlight 7
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Fig. 8. Dimensionless thermal efficiency of the cavity receiver.
when the focal plane position of Fresnel lens was placed at hd/H = 0.5. For the cavity receiver with bottom surface interior convex, the top surface of the bottom surface interior convex was close to the aperture of cavity receiver, which enabled the bottom surface interior convex surface absorb more sunlight. Take the value of hd/H = 0.5 as an example, the optical efficiency of the cavity receiver with bottom surface interior convex was 6.02% higher than that of the conventional cavity receiver. In addition, the average optical efficiency of the cavity receiver with bottom surface interior convex having a dimensionless height of 0.625 could be 12.03% higher than that of the conventional cavity receiver. 4.2. Measurements of direct solar irradiance, wind speed and temperature Measurements of direct solar irradiance, wind speed and temperature of cavity receivers with/without bottom surface interior convex were shown in Fig. 7. For each comparison test, the HTF need to flow in the cavity receiver for at least 120 min to reach a stable state. As seen in Fig. 7, at the same test time point, the fluid outlet temperature of the cavity receiver with bottom surface interior convex was higher than that of the conventional cavity receiver.
Fig. 9. Average thermal efficiency enhancement by the cavity receiver with bottom surface interior convex.
height (h/H) on the optical efficiency of cavity receiver. The optical efficiency of cavity receiver was defined as the ratio of absorbed sunlight by cavity receiver to the amount of sunlight entering the cavity receiver. As shown in Fig. 6, the optical efficiency of cavity receiver varied with dimensionless surface interior convex height and the focal plane position of Fresnel lens. Cavity receiver with a dimensionless height of 0.625 had the highest optical efficiency with a value of 95.1%
4.3. Thermal performance analysis of cavity receiver As observed from Fig. 7, the outlet temperature of HTF was relative steady with the time ranged from 30 min to 150 min during the experimental test. Therefore, measured data from 30 min to 150 min were used for thermal performance analysis of cavity receiver used in 8
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Acknowledgements
following analysis. The uncertainty values of thermal efficiency according to Eq.8 during each experimental test were listed in Table 4. As presented in Table 4, the uncertainty value (also the absolute error) of thermal efficiency was lower than 1.2%, it was believed that the uncertainty value of thermal efficiency of cavity receiver was acceptable. Fig. 8 presented the dimensionless thermal efficiency ηtherm (η dim = η ) of both the cavity receiver with bottom surface
This work was supported by the China National Key Research and Development Plan Project (No. 2018YFA0702300), the Natural Science Foundation of China (Grant No. 51676061), Taishan Scholars of Shandong Proviance (tsqn201812105), and the Fundamental Research Funds for the Central Universities (HIT.NSRIF.201706). Appendix A. Supplementary material
therm, Conv, Max
interior convex and the conventional cavity receiver, while ηtherm, Conv, Max represented the maximum thermal efficiency of conventional cavity receiver. As seen in this figure, the dimensionless thermal efficiency of both the cavity receiver with bottom surface interior convex and the conventional cavity receiver fluctuated with time. In general, the dimensionless thermal efficiency of the cavity receiver with bottom surface interior convex was higher than that of the conventional cavity receiver. The maximum increase in dimensionless thermal efficiency of the cavity receiver with bottom surface interior convex can reach 26.4% when the dimensionless height was 0.375. During the 240 min experimental test, measured data from 30 min to 150 min was used to calculate the average thermal efficiency of cavity receivers. Fig. 9 presented the average thermal efficiency enhancement by the cavity receiver with bottom surface interior convex. As shown in Fig. 9, the thermal efficiency enhancement of the cavity receiver with bottom surface interior convex was generally positive. Besides, the average increase thermal efficiency by cavity receiver with bottom surface interior convex increased with the increase of dimensionless surface interior convex height. Although the maximum increase in thermal efficiency was obtained by the cavity receoiver with bottom surface interior convex having a dimensionless height of 0.375, the average increase in thermal efficiency was obtained by that with dimensionless height of 0.875, which was 4.1% higher than that of conventional cavity receiver. Based on the above analyses, it can be seen that cavity receiver with bottom surface interior convex can increase the optical efficiency and thermal efficiency effectively.
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5. Conclusion A low cost biaxial sun-tracking concentrated solar thermal utilization system using Fresnel lens as concentrator was designed and fabricated to test the thermal performance of cavity receive, which can give a guidance for lab test of cavity receiver thermal performance. To solve the dead space problem of a conventional cavity receiver and increase thermal efficiency, a cavity receiver with bottom surface interior convex was designed and fabricated. The optical performance and thermal efficiency of the cavity receiver with bottom surface interior convex was analyzed and tested. The following results were obtained: (1) The optical efficiency of the cavity receiver with bottom surface interior convex was 6.02% higher than that of the conventional cavity receiver. (2) The average optical efficiency of the cavity receiver with bottom surface interior convex was 12.03% higher than that of the conventional cavity receiver. (3) The average thermal efficiency increase can reach 4.1% when cavity receiver with bottom surface interior convex with dimensionless height of 0.875was used. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 9
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195–204. [33] F.Q. Wang, Y. Shuai, H.P. Tan, L. Gong, Proposal of a shape layout of trapezoid cavity receiver to improve optical efficiency, Heat Transf. Res. 46 (5) (2015) 429–446. [34] H.C. Hottel, A simple model for estimating the transmittance of direct solar radiation through clear atmospheres, Sol. Energy 18 (2) (1976) 129–134. [35] F.Q. Wang, J.Y. Tan, Z.Q. Wang, Heat transfer analysis of porous media receiver with different transport and thermophysical models using mixture as feeding gas, Energy Convers. Manage. 83 (2014) 159–166. [36] F.Q. Wang, H. Wang, D.Y. Gong, Z.M. Cheng, Radiative transfer analysis of semitransparent medium with particles having non-uniform size distribution by differential-integration method, Int. J. Heat Mass Transf. 130 (2019) 342–355. [37] F.Q. Wang, Q.Z. Lai, H.Z. Han, J.Y. Tan, Parabolic trough receiver with corrugated tube for improving heat transfer and thermal deformation characteristics, Appl. Energy 164 (2016) 411–424. [38] X. Chen, F.Q. Wang, Y.F. Han, R.T. Yu, Z.M. Cheng, Thermochemical storage analysis of the dry reforming of methane in foam solar reactor, Energy Convers. Manage. 158 (2018) 489–498. [39] Z.D. Cheng, Y.L. He, Cui FQ Numerical investigations on coupled heat transfer and synthetical performance of a pressurized volumetric receiver with MCRT–FVM method, Appl. Therm. Eng. 50 (2013) 1044–1054. [40] Y. Qiu, M.J. Li, Y.L. He, W.Q. Tao, Thermal performance analysis of a parabolic trough solar collector using supercritical CO2 as heat transfer fluid under nonuniform solar flux, Appl. Therm. Eng. 155 (2017) 1255–1265. [41] S.M. Yang, W.Q. Tao, Heat Transfer, fourth ed., Higher Education Press, Beijing, China, 2006, pp. 369–370.
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Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental investigation of thermal performance enhancement of cavity receiver with bottom surface interior convex
T
⁎
Yuan Yuanb, Lin Xiaojieb,a, Cheng Zimingb,a, Wang Fuqianga,b, , Shuai Yongb, Tan Hepingb a b
School of New Energy, Harbin Institute of Technology at Weihai, 2, West Wenhua Road, Weihai 264209, PR China School of Energy Science and Engineering, Harbin Institute of Technology, 92, West Dazhi Street, Harbin 150001, PR China
H I GH L IG H T S
cost biaxial sun-tracking concentrated solar thermal utilization system was designed. • Low with bottom bulging was designed and tested to increase thermal efficiency. • Receiver • Test show that thermal efficiency of receiver with bottom bulging was 4.1% higher.
A R T I C LE I N FO
A B S T R A C T
Keywords: Solar energy Cavity receiver Optical efficiency Thermal efficiency Radiative transfer Solar thermal utilization system
To solve the dead space problem of conventional cavity receiver and increase energy conversion efficiency, cavity receiver with bottom surface interior convex was designed and fabricated. A low cost biaxial sun-tracking concentrated solar thermal utilization system using Fresnel lens as concentrator was designed and fabricated to test the thermal performance of cavity receiver, which can give a guidance for lab test of thermal performance of cavity receiver. Optical performance and thermal efficiency of cavity receiver with bottom surface interior convex was analyzed and measured through optical analysis and experimental test. Optical analysis indicated that the optical efficiency of the cavity receiver with bottom surface interior convex was 6.02% higher than that of conventional cavity receiver. A 4-h outdoor test showed that the average thermal efficiency of the cavity receiver with bottom surface interior convex was 4.1% higher than that of conventional cavity receiver.
1. Introduction Solar energy plays a major role in reducing of CO2 emission [1] and alleviating energy crisis [2]. Of all the approaches for solar energy utilization, concentrated solar power (CSP) technology is one of the promising options because the energy density of solar irradiation can be greatly increased and heat loss can be reduced [3,4]. A receiver is one of the main components of a concentrated solar thermal system [5]. Cavity receiver is widely used in CSP systems because of its advantages of high efficiency of photo-thermal conversion, low reflective loss, and steady thermal performance [6,7]. Boyd et al. [8] initially introduced a cylindrical cavity receiver, where the cavity receiver was formed by a coiling receiver tube, and insulating material was lagged on the outer surface to reduce the heat losses. Heat transfer fluid (HTF) flowed through the inside of the receiver tube. Concentrated solar irradiation entered the cavity through the aperture of cavity. Because of the blackbody effect of the cavity, the
⁎
majority of solar irradiation entering the cavity can be absorbed after times of bounces with the surface of cavity [9,10]. When the concentrated solar irradiation was absorbed by a cavity receiver, the HTF inside the receiver tube was heated [11,12]. Water [13], thermal oil [14], molten salt [15], and air [16,17] can be used as the HTF of cavity receiver, which enabled the cavity receiver to work in a wide temperature range. With the aim of improving the thermal performance of the conventional cavity receiver, several optimizing methods have been introduced. Cavity receiver for a solar tower was numerically analyzed by Tu et al. [18] to optimize the thermal performance of the receiver, and the optimal depth of the cavity receiver was determined. This optimization can enable the highest thermal efficiency and a relatively uniform heat flux distribution can be achieved. Aiming to improve the temperature uniformity of receiver, the influence of volume flow rate of HTF and aperture size were analyzed by Hamed et al. [19] by experiment, which indicated that the uniformity of HTF temperature
Corresponding author. E-mail address: [email protected] (W. Fuqiang).
https://doi.org/10.1016/j.applthermaleng.2019.114847 Received 29 July 2019; Received in revised form 20 December 2019; Accepted 23 December 2019 Available online 24 December 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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Δη Δ¯η τ ρ
Nomenclature A cp D’ D0 D1 D2 Gd h hd H H1 k ṁ Q T V̇
area, m2 specific heat, J/(kg·°C,) minimum diameter of coiling, m aperture diameter, mm diameter of the outer contour of coiling receiver tube, m diameter of the outer contour of receiver, m direct solar irradiation, W/m2 height of bottom surface interior convex, m depth of focal plane, m depth of cavity receiver, m height of receiver, m correction factor mass flow rate, kg/s energy, J temperature, °C volume flow rate, m3/s
increment of thermal efficiency average increment of thermal efficiency transmittance density, kg/m3
Subscripts a abs Bb cav Conv Dim i lens m Max o therm
ambient absorbed by HTF bottom surface interior convex into the cavity conventional receiver dimensionless inlet fresnel lens reference parameter maximum outlet thermal
Greek symbols η
efficiency
coiled at the same plane at the bottom surface, which would generate high fabricating and residual forces near the center of bottom surface [26,27]. In addition, the bottom surface cannot be fully covered by metal tube and produced a dead space, which would decrease the optical and thermal efficiencies [28,29]. Yan et al. [29] proposed to install a reflecting cone on the bottom surface of the cavity receiver to solve the dead space problem. Experimental test of receiver with reflecting cone was conducted by Sumit et al. [30], but their experiment did not conduct comparisons between conventional receiver and receiver with reflecting cone. Wang and Shuai et al. [31–33] presented an angularspectral index of concentrated sunlight to instruct the design of a new type of high-optical and thermal-performance cavity receiver. The bottom surface interior convex (BSIC) cavity receiver was initially introduced by Wang and Shuai et al. [31–33], and optical analysis indicated that the BSIC cavity receiver can solve the dead space problem effectively with an optical efficiency improvement of as much as 5.55%. However, to the best of our knowledge, most investigations on the dead space problem of the conventional cavity receiver remain at the stage of numerical analysis and lack experimental research and comparison with conventional solar receiver. In this study, a cylindrical cavity receiver with bottom surface interior convex was fabricated with
increased with the decrease of aperture size. To decrease the natural convective heat loss, a cavity receiver with plate fins attached to the inner aperture surface was introduced by Ngo et al. [20]. The influence of cavity inclination and parameters of the fins on natural convective heat loss was numerically studied by Ngo et al. [20]. The results showed that the design of plate fins attached to the inner aperture surface could reduce the natural convective heat loss of the receiver up to 20%. Three types of receivers with different cavity shapes (cylindrical, spherical, and conical) were numerically studied by Daabo et al. [21,22], and the results indicated that conical cavity had the best uniformity of heat flux distribution and the highest optical efficiency. Furtherly, the experimental research of Jorge et al. [23] showed that the reverse-conical cavity shape offered higher efficiencies than cylindrical cavity shape. Through experiment, the influence of aspect ratio on thermal efficiency, exergy efficiency and overall heat loss were studied by Thirunavukkarasu et al. [24]. The results suggested that 0.8 was the optimal aspect ratio. A comparative experiment between cubical and cylindrical cavity receiver were conducted by Loni et al. [25], which presented that thermal efficiency of cubical receiver was higher than that of cylindrical receiver. For conventional cylindrical cavity receiver, the metal tube must be
a) Conventional cavity receiver
b) Cavity receiver with bottom bulging
Fig. 1. Schematics of a conventional cavity receiver and a cavity receiver with bottom surface interior convex. 2
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2.2. Two-axis sun-tracking concentrated solar thermal performance testing system
the aim of testing the overall thermal efficiency increase of the cavity receiver. The optimal structural parameters of the cylindrical cavity receiver with bottom surface interior convex were obtained through optical analysis. A low cost biaxial sun-tracking concentrated solar thermal utilization system using Fresnel lens as concentrator was designed and fabricated to test the thermal performance of cavity receiver through experiment, which can give a guidance for lab test of cavity receiver thermal performance.
To test the thermal performance of the cavity receiver with different bottom surface interior convex heights, a biaxial sun-tracking concentrated solar thermal performance testing system was designed and fabricated. The schematic of the biaxial sun-tracking concentrated solar thermal utilization system was shown in Fig. 3(a). A polymethylmethacrylate Fresnel lens was used to concentrate the incoming sunlight. The geometric dimensions of Fresnel lens were listed as follows: the diameter was 600 mm, the thickness was 3 mm, the ring distance was 0.7 mm, and the focal length was 300 mm. An optical focusing sensor was set up on the aluminum alloy frame, which was used to control the biaxial sun-tracking platform to guarantee the Fresnel lens always pointed to the sun (as shown in Fig. 3(b)). A direct solar radiometer (TBS-3) was used to record the real-time direct normal irradiance every minute. The temperatures of fluid inlet, fluid outlet and ambient were measured by thermal couples to record the absorbed concentrated solar energy by the cavity receiver. A flowmeter was used to measure and control the volume flow rate of the HTF (25 ml/min). The wind speed of the environment was also measured by an anemoclinograph recorder to guarantee that it was less than the second grade wind (< 4 m/s). During the thermal performance test, HTF was driven by the water pump which flowed through the flowmeter, receiver and finally returned back to the storage tank. Cavity receivers were fixed on the frames equipped with the biaxial sun-tracking system. Thermal performance tests of the conventional cavity receiver and cavity receiver with bottom surface interior convex were conducted simultaneously for comparison (as shown in Fig. 3(c)). To obtain the temperature on the interior surfaces of the cavity receiver, thermal couples were attached to the interior surface of cavity receivers. Positions selected to attach thermal couples were shown in Fig. 4 (red points). During the experimental test, temperature data and direct solar irradiance were recorded every minute, while the wind speed were recorded every 10 min. The physical dimensions of the experimental setup were shown in Table 1. The scale and accuracy of the test instruments used in this study were shown in Table 2.
2. Thermal performance test system 2.1. Design and fabrication of cavity receiver with bottom surface interior convex Fig. 1 presented the schematic of a conventional cavity receiver and cavity receiver with bottom surface interior convex. Theoretically, a cavity receiver with bottom surface interior convex can decrease the area of dead space effectively, and improve the optical efficiency and thermal efficiency. To design and fabricate a cavity receiver with bottom surface interior convex, the following parameters need to be determined: the aperture diameter (D0), depth (H), height of bottom surface interior convex (h), tube material, and diameter of metal tube. Before the determination of aperture diameter of the cavity receiver, a pre-test was conducted and showed that the facula diameter on the focal plane of Fresnel lens was 50 mm. Based on the comprehensive consideration of facula diameter, optical losses, and convective heat losses, the aperture diameters of the fabricated cavity receivers were set to be 80 mm. As described in Refs. [32,33], the threshold ratio of aperture diameter (D0) to height (H) of a cavity receiver was 9/10, at which ratio the convective heat transfer losses did not change with the variation of D0/H. Therefore, the height of the cavity receiver was set to be 120 mm, whereas the ratio of aperture diameter to height of a cavity receiver was 2/3. The metal tubes of a cavity receiver were well lagged with insulation materials to decrease conductive heat losses. To investigate the effects of bottom surface interior convex height on overall heat transfer performance, four cavity receives with different dimensionless heights (h/H), equaled to 0, 0.375, 0.625, and 0.875, were designed and fabricated. The thickness of metal tube was 1 mm, and the outer diameter of the metal tube was 8 mm. For easy fabrication, normal-sized PVC-U pipe with a height of 160 mm and thickness of was 4 mm was used as the shell of cavity receiver. Aluminum silicate wool was used as insulation material due to the advantages of low thermal conductivity, high temperature resistance, good thermal stability and non-corrosivity. According to the Hottel model [34], the thickness of the insulating layer was set to 28 mm with conductive heat losses less than 6.15%. The fabricated cavity receivers with different dimensionless bottom surface interior convex heights were presented in Fig. 2.
a) h/H = 0
3. Methodology 3.1. Optical analysis With the aim of studying the influence of the physical structure and focal plane position on the optical performance of the receiver, an optical simulation was conducted by Monte Carlo ray tracing method (MCRT) using Tracepro software. A total of 500,000 rays were used for sunlight concentration, transmission, and absorption analysis, and the local solar irradiance was set to be 1000 W/m2. For more detailed information about the ray tracing method, please refer to [35–40]. Based on the actual structural parameters of the receivers, 3D models of the cavity receivers were built and used for optical simulation. The 3D
b) h/H = 0.375
c) h/H = 0.625
d) h/H = 0.875
Fig. 2. Fabricated cavity receivers with different dimensionless bottom surface interior convex heights. 3
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c) Physical setup Fig. 3. Schematic of the biaxial sun-tracking concentrated solar thermal utilization system.
plane of cavity receivers. The optical properties of each component was presented in Table 3. To investigate the effects of the bottom surface interior convex height on optical performance, four cavity receivers with different
models built by Pro/E was opened by TracePro software. A circle shape ray source with diameter of 600 mm was used, while the incoming solar radiance was 1000 W/m2 (beam to the receiver) with uniformly distribution. The ray source was located 500 mm away from the aperture 4
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a) h/H = 0
b) h/H = 0.375
c) h/H = 0.625
d) h/H = 0.875 Fig. 4. Positions selected to attach thermal couples.
3.2. Comparison test
Table 1 Physical dimensions and operational parameters of experimental setup. Physical dimension or operational parameters
Value
Diameter of Fresnel lens Thickness of Fresnel lens Ring distance of Fresnel lens Focal length of Fresnel lens Concentrate ratio of Fresnel lens Distance between the central of Fresnel and the aperture plane of receiver Volume flow rate of water
600 mm 3 mm 0.7 mm 300 mm 144 270 mm
Three groups of comparison test were conducted to investigate the thermal performance enhancement by using a cavity receiver with bottom surface interior convex. Cavity receivers with different dimensionless heights, h/H = 0.375, 0.625, and 0.875 were investigated. Thermal efficiency of cavity receiver was defined as the ratio of energy absorbed by HTF to the solar energy entering the cavity. The reference temperature Tm was defined as the average temperature of the fluid inlet temperature and fluid outlet temperature:
25 ml/min
Tm = Table 2 Scale and accuracy of the test instruments used in this study.
(1)
Energy absorbed by HTF (Qabs ) was expressed as:
Test instrument
Scale
Accuracy
Anemometer Wind direction meter Solar direct radiometer
0–60 m/s 0–359° 400–1100 nm 0–2000 W/m2 0–250 ml/min −100 to 1370 °C
± 0.1 m/s ± 1° ± 1 W/m2
Flowmeter Thermocouple and temperature recorder
Ti + To 2
Qabs = c p ṁ (To − Ti ) = c p ρV̇ (To − Ti )
In Eq. (2), the symbol V̇ was the volume flow rate of water. The specific heat at constant pressure and density of water at a specific temperature could be obtained through linear interpolation from Ref. [41]:
± 6% ± 0.5 °C
⎧ ρ10 + ⎪ ρm = ρ20 + ⎨ ⎪ ρ30 + ⎩
Table 3 Optical properties of concentrated solar thermal utilization system [40]. Optical parameters
Value
Absorptivity of cavity receiver tube Absorptivity of cavity receiver insulation Transmittance of Fresnel lens Absorptivity of cavity receiver shading board
0.65 0.25 0.8 0.3
(2)
ρ20 − ρ10 10 ρ30 − ρ20 10 ρ40 − ρ30 10
where ρ10 = 999.7 ρ30 = 992.2 kg/m3 .
⎧Cp10 + ⎪ Cpm = Cp + ⎨ 20 ⎪ 4.178, ⎩
dimensionless heights, h/H = 0, 0.375, 0.625, and 0.875 were investigated to identify the optimal dimensionless surface interior convex height. Five focal plane positions of the Fresnel lens, hd/H = 0, 0.25, 0.5, 0.75, and 1.0 were investigated. The distance between Fresnel lens and aperture plane of receiver was 300 mm, 270 mm, 240 mm, 210 mm and 180 mm correspondingly.
× (Tm − 10),
10 ° C⩽ Tm ⩽ 20 °C
× (Tm − 20),
20 ° C⩽ Tm ⩽ 30 °C
× (Tm − 30),
30 ° C⩽ Tm ⩽ 40 °C
kg/m3 ,
Cp20 − Cp10 10 Cp30 − Cp20 10
ρ20 = 998.2
kg/m3 ,
ρ30 = 995.7
(3)
kg/m3 ,
× (Tm − 10),
10 ° C⩽ Tm ⩽ 20 °C
× (Tm − 20),
20 ° C⩽ Tm ⩽ 30 °C 30 ° C⩽ Tm ⩽ 40 °C
kJ/(kg·° C) ,
kJ/(kg·° C) ,
where Cp20 = 4.183 Cp10 = 4.191 4.178 kJ/(kg·° C) , and Cp40 = 4.178 kJ/(kg·° C) . Solar energy entering the cavity Qcav was defined as:
Q cav = G d A lens τlens k 1 k 2
and
(4)
Cp30 =
(5)
The value of k1 was obtained by optical simulation with the value of 0.88281 and denoted that 88.281% of the sunlight concentrated by Fresnel lens entered the cavity. The experimental correction factor (k2) 5
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was introduced to compensate for the observed center point deviation of the focal plane during the test with the value of 0.9. The thermal efficiency of the cavity receiver η therm was defined as:
η therm =
Qabs Qcav
(6)
The increment of the thermal efficiency Δη was defined as the difference in thermal efficiency between the cavity receiver with bottom surface interior convex and the conventional cavity receiver.
Δη = ηBb − ηConv
(7)
According to the calculation process of thermal efficiency, the uncertainty of thermal efficiency was defined as: 2
δη =
2
2
2 ⎛ δη ⎞ (δη)2 + ⎛ δη ⎞ (δTo )2 + ⎛ δη ⎞ (δTi )2 + ⎛ δη ⎞ (δGd )2 ̇ ⎝ δV ⎠ ⎝ δTo ⎠ ⎝ δTi ⎠ ⎝ δGd ⎠ ⎜
⎟
⎜
⎟
⎜
⎟
(8) Fig. 6. Effects of h/H on the optical efficiency of cavity receiver.
4. Results and discussion receiver tube on the sidewall of the cavity receiver could be shined by a large amount of sunlight entering the cavity directly and part reflected light when hd/H = 0 and 0.25, which resulted in non-uniform heat flux distribution on the side wall. When the focal plane of the Fresnel lens was moved inside the cavity receiver, the value of heat flux distribution on the side wall decreased sharply. When the focal plane of the Fresnel lens moved inside the cavity receiver at hd/H = 0.50, the heat flux on the side wall of the cavity receiver was very small. Only the metal tube on the sidewall near the bottom surface of the cavity receiver could be shined directly, where the other part of the sidewalls could only heated by a very small amount of reflected sunlight. When the focal plane of
4.1. Optical analysis Fig. 5 presented the effects of focal plane position on heat flux distribution on the sidewall of cavity receiver. Five focal plane positions of the Fresnel lens, hd/H = 0, 0.25, 0.5, 0.75, and 1.0 were investigated. As shown in Fig. 5(a), the heat flux distribution on the sidewall of the conventional cavity receiver without a with bottom surface interior convex changed dramatically with height and a peak value of heat flux was observed, when the focal plane of the Fresnel lens located on the front of the cavity receiver was hd/H = 0 and 0.25. The
Fig. 5. Heat flux distribution on the sidewalls of receivers with different values of hd/H. 6
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Fig. 7. Measurements of direct solar irradiance, wind speed and temperature.
irradiation and could only be heated by reflected sunlight, which resulted in a near zero heat flux distribution on the sidewall. As shown in Fig. 5(b) and (c), the heat flux distribution on the sidewalls of the cavity receivers with bottom surface interior convex was similar to that of the conventional cavity receiver when the dimensionless heights were 0.375 and 0.625. When the dimensionless height was increased to 0.875, as seen in Fig. 5(d), more concentrated sunlight was able to reach the side wall of the cavity receiver with bottom surface interior convex. Fig. 6 presented the effects of dimensionless surface interior convex
Table 4 Uncertainty value of thermal efficiency in each experiment.
Case 1 Case 2 Case 3
h/H = 0
h/H = 0.375
h/H = 0.625
h/H = 0.875
± 1.1% ± 1.1% ± 0.9%
± 1.2% – –
– ± 1.2% –
– – ± 1.2%
the Fresnel lens moved inside the cavity receiver at hd/H ≥ 0.75, the receiver tube on the sidewall could barely receive direct sunlight 7
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Fig. 8. Dimensionless thermal efficiency of the cavity receiver.
when the focal plane position of Fresnel lens was placed at hd/H = 0.5. For the cavity receiver with bottom surface interior convex, the top surface of the bottom surface interior convex was close to the aperture of cavity receiver, which enabled the bottom surface interior convex surface absorb more sunlight. Take the value of hd/H = 0.5 as an example, the optical efficiency of the cavity receiver with bottom surface interior convex was 6.02% higher than that of the conventional cavity receiver. In addition, the average optical efficiency of the cavity receiver with bottom surface interior convex having a dimensionless height of 0.625 could be 12.03% higher than that of the conventional cavity receiver. 4.2. Measurements of direct solar irradiance, wind speed and temperature Measurements of direct solar irradiance, wind speed and temperature of cavity receivers with/without bottom surface interior convex were shown in Fig. 7. For each comparison test, the HTF need to flow in the cavity receiver for at least 120 min to reach a stable state. As seen in Fig. 7, at the same test time point, the fluid outlet temperature of the cavity receiver with bottom surface interior convex was higher than that of the conventional cavity receiver.
Fig. 9. Average thermal efficiency enhancement by the cavity receiver with bottom surface interior convex.
height (h/H) on the optical efficiency of cavity receiver. The optical efficiency of cavity receiver was defined as the ratio of absorbed sunlight by cavity receiver to the amount of sunlight entering the cavity receiver. As shown in Fig. 6, the optical efficiency of cavity receiver varied with dimensionless surface interior convex height and the focal plane position of Fresnel lens. Cavity receiver with a dimensionless height of 0.625 had the highest optical efficiency with a value of 95.1%
4.3. Thermal performance analysis of cavity receiver As observed from Fig. 7, the outlet temperature of HTF was relative steady with the time ranged from 30 min to 150 min during the experimental test. Therefore, measured data from 30 min to 150 min were used for thermal performance analysis of cavity receiver used in 8
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Acknowledgements
following analysis. The uncertainty values of thermal efficiency according to Eq.8 during each experimental test were listed in Table 4. As presented in Table 4, the uncertainty value (also the absolute error) of thermal efficiency was lower than 1.2%, it was believed that the uncertainty value of thermal efficiency of cavity receiver was acceptable. Fig. 8 presented the dimensionless thermal efficiency ηtherm (η dim = η ) of both the cavity receiver with bottom surface
This work was supported by the China National Key Research and Development Plan Project (No. 2018YFA0702300), the Natural Science Foundation of China (Grant No. 51676061), Taishan Scholars of Shandong Proviance (tsqn201812105), and the Fundamental Research Funds for the Central Universities (HIT.NSRIF.201706). Appendix A. Supplementary material
therm, Conv, Max
interior convex and the conventional cavity receiver, while ηtherm, Conv, Max represented the maximum thermal efficiency of conventional cavity receiver. As seen in this figure, the dimensionless thermal efficiency of both the cavity receiver with bottom surface interior convex and the conventional cavity receiver fluctuated with time. In general, the dimensionless thermal efficiency of the cavity receiver with bottom surface interior convex was higher than that of the conventional cavity receiver. The maximum increase in dimensionless thermal efficiency of the cavity receiver with bottom surface interior convex can reach 26.4% when the dimensionless height was 0.375. During the 240 min experimental test, measured data from 30 min to 150 min was used to calculate the average thermal efficiency of cavity receivers. Fig. 9 presented the average thermal efficiency enhancement by the cavity receiver with bottom surface interior convex. As shown in Fig. 9, the thermal efficiency enhancement of the cavity receiver with bottom surface interior convex was generally positive. Besides, the average increase thermal efficiency by cavity receiver with bottom surface interior convex increased with the increase of dimensionless surface interior convex height. Although the maximum increase in thermal efficiency was obtained by the cavity receoiver with bottom surface interior convex having a dimensionless height of 0.375, the average increase in thermal efficiency was obtained by that with dimensionless height of 0.875, which was 4.1% higher than that of conventional cavity receiver. Based on the above analyses, it can be seen that cavity receiver with bottom surface interior convex can increase the optical efficiency and thermal efficiency effectively.
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5. Conclusion A low cost biaxial sun-tracking concentrated solar thermal utilization system using Fresnel lens as concentrator was designed and fabricated to test the thermal performance of cavity receive, which can give a guidance for lab test of cavity receiver thermal performance. To solve the dead space problem of a conventional cavity receiver and increase thermal efficiency, a cavity receiver with bottom surface interior convex was designed and fabricated. The optical performance and thermal efficiency of the cavity receiver with bottom surface interior convex was analyzed and tested. The following results were obtained: (1) The optical efficiency of the cavity receiver with bottom surface interior convex was 6.02% higher than that of the conventional cavity receiver. (2) The average optical efficiency of the cavity receiver with bottom surface interior convex was 12.03% higher than that of the conventional cavity receiver. (3) The average thermal efficiency increase can reach 4.1% when cavity receiver with bottom surface interior convex with dimensionless height of 0.875was used. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 9
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