Experiment and simulation study on convective heat transfer of all-glass evacuated tube solar collector

Journal Pre-proof Experiment and Simulation Study on Convective Heat Transfer of All-glass Evacuated Tube Solar Collector

Qiong Li, Wenfeng Gao, Wenxian Lin, Tao Liu, Yougang Zhang, Xiang Ding, Xiaoqiao Huang, Wuming Liu PII:

S0960-1481(20)30108-7

DOI:

https://doi.org/10.1016/j.renene.2020.01.089

Reference:

RENE 12952

To appear in:

Renewable Energy

Received Date:

30 September 2019

Accepted Date:

19 January 2020

Please cite this article as: Qiong Li, Wenfeng Gao, Wenxian Lin, Tao Liu, Yougang Zhang, Xiang Ding, Xiaoqiao Huang, Wuming Liu, Experiment and Simulation Study on Convective Heat Transfer of All-glass Evacuated Tube Solar Collector, Renewable Energy (2020), https://doi.org/10.1016/j. renene.2020.01.089

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Experiment and Simulation Study on Convective Heat Transfer of Allglass Evacuated Tube Solar collector Qiong Lia, Wenfeng Gaoa*, Wenxian Lina,b*, Tao Liua, Yougang Zhanga, Xiang Dinga,Xiaoqiao Huangc, Wuming Liud aSolar

Energy Research Institute, Yunnan Normal University, Kunming, Yunnan, 650500, China

bSchool

of Engineering, James Cook University, Townsville, Qld. 4811, Australia

cYunnan

Key Lab of Opto-electronic Information Technology, Kunming, Yunnan, 650500 China

dInstitue

of Physics, Chinese Academy of Science, Beijing,100190, China

*Corresponding author: E-mail address: [email protected] (Wenfeng Gao), [email protected] (Wenxian Lin) Address: 768 Juxian Street, Chenggong District, Kunming, Yunan, China, 650500

Journal Pre-proof Experiment and Simulation Study on Convective Heat Transfer of All-glass Evacuated Tube Solar Collector Qiong Lia, Wenfeng Gaoa*, Wenxian Linb*, Tao Liua, Yougang Zhanga, Xiang Dinga, Xiaoqiao Huanga, Wuming Liuc aSolar

Energy Research Institute, Yunnan Normal University, Kunming, Yunnan 650500, China

bSchool cInstitue

of Engineering, James Cook University, Townsville, QLD. 4811, Australia of Physics, Chinese Academy of Science, Beijing, China

Abstract: Solar collector with horizontal double-row all-glass evacuated tubes has been extensively implemented in the solar water heating system engineering. The temperature distribution and stratification of horizontal double-row all-glass evacuated tubes collector with 24 evacuated tubes have been studied. Validation of instantaneous efficiency under different declination angle θm were studied by means of experiments. Moreover, numerical simulations are carried out for four different declination angle θm (0°/2°/4°/6°). The results showed that the declination angle θm has significant effect on energy conversion efficiency, flow patterns and stratification inside evacuated tubes. When θm > 0, with the declination angle increased, instantaneous efficiency increased, the less obvious the temperature stratification, and not a significant change in heat loss coefficient. Declination angle 6° allowed to achieve significant higher temperatures, nevertheless, along with inactive area at the bottom of evacuated tubes appears. If declination angle θm < 0, inversion phenomenon appears, with the increase of |θm|, more heat is trapped in the sealed end of the evacuated tube, which is not conducive to the flow heat transfer in evacuated tube solar collector. Keywords: solar collector, evacuated tube, heat transfer, declination angle, natural circulation

1. Introduction The all-glass evacuated tube solar collector (ETC) has been widely employed in the water heating and building heating systems due to its high thermal performance, convenient installation as well as flexible transportation. Compared with the flat panel system, the thermal performance of ETC system is greatly dependent on its own structure[1]. According to the structure, evacuated tube solar collector can be divided into vertical ETC, horizontal single-row ETC and horizontal double-row ETC[2]. Vertical ETC is regularly implemented in domestic water heating system. Evacuated tubes usually connected in series in east-west direction and in parallel in north-south direction. However, the solar hour angle is constantly changing due to the rotation of the earth, and there is mutual occlusion of light between vertical evacuated tubes, which affects the efficiency of heat collection. Moreover, it retains a large amount of unusable hot water in the tube, and the bottom of evacuated tube often has sludge impurities precipitation, forming a stagnant region, which also affects water sanitation[3]. For the horizontal ETCs, the evacuated tube is placed horizontally, each tube can absorb the same amount of radiation during the entire sunshine time, more solar radiation energy can be obtained. The tubes are often flushed by water, hence precipitation of sludge impurities rare appears, which will not affect the water sanitation. It can drain the water to prevent freezing when temperature is low in winter. Furthermore, the mounting bracket of horizontal ETC is reduced to make it close to the roof surface, and the wind resistance is greatly improved. The orientation angles of the a horizontal ETC influences on the thermal performance, the angles include: geographical latitude, solar incident angle, solar declination angle, azimuth and the inclination angle of the evacuated tube water collector. Therefore, in recent years, various researchers work on the evacuated tubes and their constituent hot water collectors[4].

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Greek letters

NOMENCLATURE

τ - transmittance of cover glass tube (dimensionless); α - the absorptance of selective absorber coatings (dimensionless); η- instantaneous thermal efficiency of solar collector; θ - the tilt angle of evacuated tube (degree); θc - the declination angle of the tube to the manifold channel (degree); θm - the declination angle of the tube to the manifold plane (degree); ρg - reflectance of the ground (dimensionless); h - evacuated tube hemisphere emission ratio (dimensionless); k - the thermal conductivity, W/(m·K); h - the hemisphere emission ratio of evacuated tube (dimensionless).

AA - the collector surface area (m2); Ac - contour aperture area (m2); Cf - specific heat capacity of water (J/(kg·K); G - solar irradiance (W/m2); Ibn - the beam irradiation intensity in the normal direction (W/m2); Ieff - solar radiation intensity (W/m2); it - the incidence angle of beam irradiation on evacuated tube(degree); kc - conduction heat loss (W/K); L - the length of evacuated tube (m); m - tube working medium mass(kg); QA - total solar irradiation energy; QI - useful energy absorbed by the working medium; QL - the total heat loss of the evacuated tube to the environment; t - time (s); Tm - tube working medium average temperature (K); Ta -average ambient temperature (K); ULT - heat loss coefficient (W/(m2·K)).

Subscripts exp – experiment; sim– numerical simulation.

Abbreviations ETC - evacuated tube solar collector.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

There have been numerous studies investigating ETC to measure [5-7], analyze[5, 8, 9] or estimate[10] system performance. The existing literature on evacuated tube solar collector is extensive and focuses particularly on vertical ETC. Researchers attempted to evaluate the impact of environmental factors (solar radiation[3],ambient temperature[5], geographic location[11, 12], climate impact[4], etc.), structural influences (evacuated tube length[12-14], tube diameter[15], tube number[5], tube absorption area[15], tank size[6, 12], and collector tilt angle[16-19], etc.), flow characteristic parameter (mass flow rate [15]) on the thermal characteristics of ETC, and get the relationship of relevant parameters. These physical parameters that characterize thermal performance include annual efficiency[5], flow patterns, energy conversion efficiency, heat loss coefficient, and the stratification effect [18]. According to their research, widely accepted conclusion can be drawn that :1. For vertical ETC, the shorter tube length can reach the higher efficiency [6]. For U-pipe ETC, when tube length is less than 1.5m, the efficiency increases with tube length, otherwise, efficiency decreases [21]. 2. The collector tilt-angle has a significant effect on the daily collection radiation and solar thermal gain of the system, but has little effect on the heat dissipation from the solar tube to the water storage tank and the solar thermal conversion efficiency [7]. 3. several other factors such as the location of the system, geometric parameters also affect the heat collection effect of the system. On this basis, various scholars tried to modify the system structure of the evacuated tube collector to obtained the data reference of the optimized design. There are two ways to improve ETC: one is to optimize the overall structure of collecting system to improve the heat efficiency. For example, a bottom mirror reflector is arranged

20

beside the solar collecting plane[22], add bypass tube to evacuated tube[23], retrofitting shell-structure [24]，and

21 22 23 24 25

other structural optimization [25],et al. The other is to improve the structure of evacuated tube to reduce heat loss, or improve heat conversion efficiency. For instance, copper tube is introduced to the evacuated tube [25], coaxial heat pipe inserted into evacuated tubes [20], solar evacuated tubes with openings at both ends[26], solar evacuated tubes with heat shield [27],et al. These methods could improve the system performance of ETC to a certain extent, however its not be implemented extensively since the addition cost of the economic and human.

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26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

To date, although the horizontal double-row all-glass evacuated tube solar collector is selected as the collector array in several solar thermal and heating system engineering, there are few relatively historical studies on the internal flow and heat transfer of double-row all-glass ETC. Aiguo Song et al.[28, 29] compared shading effects and energy benefits of solar water heaters with horizontal and vertical evacuated tubes through experiments and numerical simulation. It was found that under the same structure parameters, intertube shading effect of vertical ETC is more serious than that of horizontal ETC. Ting Chai et al. [30] studied the optimization of the center distance of the tubes for solar evacuated tube water heater. Taking the performance and cost into comprehensive consideration, they concluded that the optimal distance between the adjacent tube centers was 1.2 times the diameter of the outer tube for the evacuated tube collector, with the diameter of 58mm. Thus far, few studies have reported on the flow heat transfer rule, optimal structure parameters and installation angle of the horizontal double-row ETC. Shah and Furbo [1] carried out a series of numerical simulations on the thermal performance inside a horizontal evacuated tube heater. They investigated the differential impact of three different tube lengths (0.59, 1.17 and 1.47 m) and five different inlet mass flow rates (0.05, 0.4, 1, 3 and 10 kg/min) on system efficiency, respectively. The results showed that the shorter horizontal evacuated tube, the higher efficiency of the system. Moreover, the mass flow rate was shown to have negligible effect on the efficiency of the evacuated tube. A simulation of transforming was conducted by Chunyun Zhao et al. [31] to find the variation of mass flow rate with inlet temperature and tube diameter in horizontal double-row ETC. At a certain solar absorption rate, the mass flow rate increases with the increase of inlet temperature and tube diameter. Zhang Tao et al. [32] established three-dimensional mathematical models of natural convection and forced convection of solar collectors, respectively. They analyzed flow and heat transfer data by applying field synergy and exergy theory. In their analysis of the optimum operating conditions for evacuated tube water collector, they identified the heat transfer effect of horizontal double-row ETC is better than that of vertical single ETC. Since the Reynolds number and the Nussel number and its entransy increment are both higher than that of vertical single collector. S. Ataee et al. [7] carried out a number of investigations into all-glass evacuated solar collector tubes with coaxial fluid conduit for T-type and H-type models which stand for evacuated tube vertical and horizontal respectively. They discussed the effects of collector tube parameters on the outlet temperature of the fluid, the energy and exergy efficiencies, to found that increasing the collector tube length lead to an increase in the outlet air temperature and exergy efficiency, but a reduction in the energy efficiency. In order to give full play to the optical efficiency of the evacuated tube solar collector, it is necessary to determine the collector orientation and correct the incident angle more carefully than flat collectors. Therefore, it is necessary to study the installation deflection of evacuated tube. Existing research summarized the impact of solar water collector and their performance on thermal efficiency of the system. However, there is not a study focused in the declination angle of horizontal double-row water-in-glass evacuated solar collectors. In light of this situation, the thermal performance and internal flow of horizontal double-row water-in-glass evacuated solar collectors with different declination angles are investigated. The three-dimensional simulation and analysis results were compared to experimental measured temperature inside the tubes of horizontal double-row ETC.

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2. Methodology

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2.1 Description of horizontal double-row ETC The cross-sectional structure of the horizontal double-row ETC studied in this paper is shown in Fig.1. The collector mainly composed of a manifold located in the middle, with 12 evacuated tubes inserted into it in parallel on each side. Many studies have analyzed the effect of ETC tilt angle on thermal performance, the tilt angle here usually represents the angle between the solar collection plane and the horizon. Due to the structural characteristics of the horizontal double-row ETC, there are two other declination angles besides the tilt angle, which may also affect the system performance. Both of two declination angles mentioned here are due to the flexible junction between the

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heat collecting plane and the manifold. The declination angle of evacuated tube to the manifold channel is denoted by declination angle θc, and the declination angle of evacuated tube to the manifold plane is denoted by declination angle θm, which is the focus of this paper. Consider that during the actual installation, the workers may cause the collector plane to tilt upward or downward compared to the standard plane due to operation errors. In this case, it is represented by θm>0 and θm<0 respectively. A schematic of the declination angle θm and θc of horizontal doublerow ETC under investigation is shown in Fig. 2

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Fig.1. CAD rendering of the horizontal double-row ETC.

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81 82 83 84 85 86 87

Fig.2. Two different kinds of declination angle. (a) declination angle θc, (b) declination angle θm. The manifold placed in the middle south-north direction is a rectangular parallelepiped shape, the flow channel is made of stainless steel, and the heat insulating material is made of polyurethane. Polyurethane has a thermal conductivity of less than 0.12 W/(m·K) at 350°C, which can provide good thermal insulation. The specifications and dimensions of the investigated collector in this paper are shown in table 1. Table.1. Specification parameter, physical properties and operating parameters for experimental and simulation Table 1a Specification parameter Collector tube length (mm) Outer/ Inner glass tube outer diameter (mm) Evacuated tube spacing (mm) Manifold sectional dimension (mm) Contour aperture area (m2) The depth of tubes inserted into manifold (mm) Insulation thickness (mm)

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1800 Φ 58/47 44 90×90 3.27 20 50

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Working fluid Table 1b Thermo – physical properties Glass tube transmittance (τ) Solar absorptance of selective coating (α) Water density (g/cm3) Cf of water (J/kg·K) Table 1c Operating range and reference values Surrounding air temperature (℃) Reynolds number (Re)

Water 0.91 0.92 0.998 4182 17-24 Re＜2500

88 89 90 91 92 93 94 95 96 97 98

2.2 Mathematical model In the operation of the horizontal double-row ETC, cold water enters from the lower inlet end of the manifold and flows through the evacuated tubes on both sides. Under the action of thermosiphon and pump, the hot water heated in the evacuated tube will return to manifold and flow out through the upper outlet end. The solar radiation passes through the glass tube of the evacuated tube, and most of it is absorbed by the selective absorption coating on the outer wall of the coaxial glass tube. It is converted into heat, which is transferred to the working medium in the tube through heat transfer, natural convection and heat radiation. （1）Total solar radiation For the horizontal double-row ETC, the evacuated tube is the main component to receive solar radiation, which consists of three parts [33], as shown in Fig.3, respectively.

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Fig.3. Cross section of solar radiation received by horizontal double-row ETC. Total solar radiation reaching the aperture surface is the sum of the beam radiation directly exposed to the front of the evacuated tube Ibn, the isotropic diffused radiation intensity IDθ, and the reflective radiation from the ground IRθ. 𝐼𝑇 = 𝐼𝑏,𝐸𝑇𝐶 + 𝐼𝐷𝜃 + 𝐼𝑅𝜃

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𝜃

𝜃

= 𝐼𝑏𝑛cos 𝑖𝑡 + 𝐼𝐷𝐻cos2 2 + 𝐼𝐻(1 ― cos2 2) 𝜌𝑔

（1）

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Where, Ibn is the beam irradiation intensity in the normal direction (W/m2); it is the incidence angle of beam irradiation on evacuated tube (degree); θ is the tilt angle of evacuated tube (degree); ρg is reflectance (dimensionless) of the ground. The heat collection efficiency and natural convection of ETC was studied based on the standard of ISO 9806[34]. According to the environment control requirements of the standard, formula (1) was simplified as follows.

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• The incidence angle of beam solar radiation at the collector aperture should be no more than ±2% at the normal

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incidence. According to this constraint, the horizontal double-row ETC was placed on the two-axes tracking system to track solar altitude angle and azimuth angle. Here, the incident angle it is essentially zero, the influence on shade of incident solar radiation between adjacent evacuated tubes can be neglected.

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• According to the standard, with the aim to study the outdoor operating performance of ETC, diffused and

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reflected radiance is assumed to come isotropically of hemispherical. The test environment should to be strictly controlled to make sure that no obvious solar radiation reflected to the collector on the surrounding, and diffuse solar irradiance influence will be neglected if it is less than 20%.

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（2）Energy balance equation

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Assuming that the total solar irradiation energy received by the horizontal double-row collector is QA, the useful energy absorbed by the working medium is QI, and the total heat loss of the evacuated tube to the environment is QL. The main heat loss of evacuated interlayer is thermal radiation loss, while the main heat loss of the opening end and the sealed end of the evacuated tube are conduction and thermal radiation loss. In this process, it is assumed that the manifold of horizontal double-row collector is adiabatic, and heat absorbed by glass tube and inner glass tube is ignored. According to the law of conservation of energy,

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QI = QA ― QL

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（2）

Equation (2) can also be expressed as: dTm

Cfm dt = AC(τα)G - AAULT(Tm - Ta)

（3）

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Where, cf for specific heat pipe working medium (J/(kg·K)), m (kg) for tube working medium mass, t is time (s), Ac is the aperture area (m2), τ for cover glass tube transmittance (dimensionless) and α for the solar absorptance of selective coatings (dimensionless), G for solar irradiance (W/m2), AA for the collector surface area (m2), ULT for heat loss coefficient (W/(m2·K)), Tm for tube working medium average temperature (K), and Ta is the average ambient temperature (K). (3) Efficiency equation

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The instantaneous thermal efficiency η of the solar collector is the ratio of the actual useful power QI obtained

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by the collector to the solar radiation power G received on the collector surface under steady-state conditions, it can be represented as follows:

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QI

η = QA =

(τα)G - AAULT(Tm - Ta) AcG

=

Ieff - ULTπ(Tm - Ta) Ieff

Where, Ieff for the solar radiation intensity on a single tube. (4) Heat loss analysis The heat insulation material of the manifold of the horizontal double-row collector is polyurethane, which can play a good role in heat preservation, and its area occupies a small share of the whole collector area. Therefore, in numerical simulation, its heat loss is ignored, and it is assumed to be adiabatic. Therefore, the main heat loss of the horizontal double-row ETC in this paper is the heat loss of the evacuated tube which is the main heat exchange component. It mainly consists of the following elements: heat loss caused by supporting parts at the open end and sealed end of evacuated tube; the radiant heat loss of evacuated tube inserted into manifold, as well as the getter covered part at the sealed end; conduction heat loss of working medium in tube; the radiant heat loss of the selective absorption coating on the outer wall of the inner glass tube. When the evacuated tube hemisphere emission ratio h (dimensionless) is extremely small, the radiant heat loss can be obtained by the following equation: Qr = σεhAA(T4m - T4a)

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（4）

Where,  is Stefan-Boltzmann constant, 5.67 ×10-8 W/(m2·K4).

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（5）

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In conclusion, the heat loss coefficient ULT of the evacuated tube is the sum of the above four parts, namely:

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ULT =

kc + kg AA

(

kb

)

+ σεh + AA (T2m + T2a)(Tm + Ta)

（6）

In this paper, the structure model of evacuated tube is simplified as the inner glass tube coated with selective absorption coating on the outer wall surface of the coaxial tube, and the sealed end is replaced by two hemispheres. Therefore, the heat loss coefficient of evacuated tube studied in this paper is: kc

ULT = AA +σεh(T2m + T2a)(Tm + Ta)

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（7）

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3. Experiment

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3.1. Experimental setup and instrumentation

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In this study, instantaneous efficiency of horizontal double row all-glass evacuated tube solar collector were studied by experiments. According to ISO 9806 standard, the comprehensive performance testing platform of solar energy is built in Yunnan Normal University, in Kunming (25°N, 102°E), China. Fig. 4 shows the schematic of experiment. The system mainly consists of 24 horizontal double-row evacuated tubes, manifold, central control unit (including control unit, data acquisition unit, automatic sun tracking unit, and a computer), temperature control unit, water storage tank, platinum resistance, pumps, flow meters, valves, and pipes.

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Fig.4. Schematic diagram of experiment system.

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(a) Front view.

(b)Back view

Fig.5. Photograph of the measuring device.

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Fig.6. Layout diagram of temperature sensors.

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During the experiments, the integrated test system which named “TYD-BL solar collector thermal performance test platform” was used to carry out the measurement. Fig.5 shows the photograph measuring equipment. With this system, the hardware can be operated by computer control unit, and the corresponding test data can be obtained, including: inlet and outlet temperature, surrounding air temperature, mass flow, total radiation, wind speed, etc. The solar energy two-axes tracking system can track solar altitude angle and azimuth angle of the sun respectively, and can drive the solar collector to move smoothly with the trajectory of sun during the test. The main measurement instruments and parameters are shown in Table 2. The calibrated pyranometer and anemometer are placed on the same plane adjacent to the collector to measure parameters such as instantaneous irradiance and instantaneous wind speed on the collector surface. The ambient temperature near the collector and the temperature inside the evacuated tubes of collector were measured by Pt-100 which were also calibrated. In order to understand the temperature distribution in the tube, the temperature sensor is arranged in the tube. However, considering that too many temperature sensors in a single tube will affect the flow disturbance and temperature in the tube, there are no more than three temperature sensors in a single tube in the experiment. Moreover, the temperature sensors selected for the test shall be small and the data line shall be thin. Eight groups of Pt-100 sensors are arranged in the collector to measure the temperature distribution at different positions in the evacuated tubes, as shown in the Fig.6. For evacuated tube length L = 1800 mm, the distance from the open end of solar tube is respectively: location 1 (1600mm), location 2 (L/2), location 3 (20mm), location 4 (20mm), location 5 (L/4), location 6 (L/2), location 7 (3L/4), location 8 (L-50 mm). At location 1, 2 and 3, three temperature sensors arranged from top to bottom along the vertical central line of the evacuated tube. Table 2. Measurement instruments and parameters

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Measuring

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Measuring instruments

Equipment

Measuring

model

range

Parameters temperature

platinum resistance

Pt-100

length, distance

steel tape

Accuracy

0-100℃

±0.1℃

5m

0-5m

±1mm ±50W/m2 ±0.5%

solar irradiance

pyranometer

TBQ-2

0-1400W/m2

mass flow

liquid flowmeter

LW-B11

0.2-1.2 m3/h

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3.2. Measurement procedure

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At the beginning of the experiment, the solar collector was covered with tarpaulins and began to inject water into it. When the water temperature reached ambient temperature, the timing is started and the parameters such as ambient temperature, starting water temperature and irradiance are collected by using the data acquisition instrument of TRM2. The difference of the optical properties of the evacuated tube was negligible tested by spectrophotometer. During the experiment, the collector was always facing the sun.

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3.3 Uncertainty analysis

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For the solar collector placed on the two-axes tracking system, according to the analysis of the measurement method and calculation formula, the uncertainty of the instantaneous efficiency measurement of the solar collector comes from the following components: (1) uncertainty U(m) caused by flowmeter when measuring mass flow; (2) uncertainty U(L) caused by steel tape when measuring the aperture area of collector contour; (3) uncertainty U(T) caused by Pt-100 temperature sensors thermometer and data collector when measuring inlet temperature and outlet temperature of collector; (4) uncertainty U(G) caused by the pyranometer when measures the solar radiation intensity of the collector's aperture surface. Each uncertainty component is not related, and the relative uncertainty of each component is synthesized by calculating the square root of the relative uncertainty of each component as follows:

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∆𝜂 =

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[(

2 ∂𝜂 ∂𝑚𝛥𝑚

𝑈(𝜂) =

) +(

𝑈(𝑚) 2 𝑚

2 ∂𝜂 ∂𝐿𝛥𝐿

) +(

𝑈(𝐿) 2 𝐿

2 ∂𝜂 ∂𝑇𝛥𝑇

) +(

𝑈(𝑇) 2 𝑇

2 ∂𝜂 ∂𝐺𝛥𝐺

)]

𝑈(𝐺) 2 𝐺

[( ) + ( ) + ( ) + ( ) ]

1 2

1 2

（8）

（9）

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Under the range of the measurement instruments and based on the accuracy, as is shown in Table 2, the maximum uncertainty is 3.1% of the collector thermal efficiency.

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4. Numerical Simulation

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In this work, a three-dimensional numerical model is developed using ANSYS simulation software. Under the physical model of the horizontal double-row ETC mentioned above, the following simplification and hypothesis treatment of the model: (1) According to the conclusion of Alfaro et al. [21], the Boussinesq approximation can simulate the buoyancy effects of all-glass evacuated tube solar collector more accurately, so the Boussinesq approximation is selected. (2) In the Solver setting, the DO mode is selected, the transient calculation is used for the fluid, and the gravity action is taken into account. The energy equation and laminar flow model are selected by the calculation model. (3)The solar load model was taken into account, so that both beam radiation and diffuse radiation can follow the changes of the sun.

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(4) The geometrical dimension structure of the evacuated tube water collector is consistent with the actual model, and the boundary condition setting is obtained by experiments and certain hypotheses. The transmittance of the cover glass tube and the absorptance of the solar selective absorber coating are obtained by experimental measurement.

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5. Results and discussion

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5.1 validation

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The environmental conditions in the experiment were controlled and tested and the relevant environmental parameters were used for numerical simulation. Specifically, the globe solar irradiance, diffused irradiance and ambient temperature for September 15th, 2019, was measured and is shown in Fig. 7.

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Fig.7. Climate parameters for the experiment. For horizontal double-row ETC, the temperature rise at the three location of 0.02m, 0.9m, 1.6m from the open end within the central line of the evacuated tube is monitored. These three positions respectively represent the location of the open end, L/2 tube length and close to the bottom of the tube. Fig.8 shows the temperature change at the four locations monitored by experiment (the ‘exp’ curves) and numerical simulation (the ‘sim’ curves). At the beginning of the experiment, the first operating temperature should be close to the ambient temperature (± 3K). In the experiment, after sufficiently quasi-steady-state period, there comes the steady-state conditions. Temperatures at the three locations were recorded every minute from the beginning of the experiment to steady state. The simulation follows the same process.

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Fig.8.Variations of water temperature in the three location of evacuated tubes. It can be seen from Fig.8 that the temperature rise trend of the experimental and numerical simulation at the three location are in good agreement. The temperature curves have different temperature rise rates, among which the

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temperature rise is the fastest at the monitoring point 1.6m, and the slowest is at the 0.02m. The temperature curve at 0.02m of the monitoring point reached the steady-state fastest, but the stagnation temperature was the lowest. After a period of heating process, the collector had reached the steady-state. From the figure, we can perceive that the differences between simulated and experimental are mainly in the following two aspects: • The required time to enter steady-state is different (simulation takes about 15 minutes, experimental takes about 25 minutes). The first reason is that the actual experimental operation is affected by the initial temperature in the evacuated tube of the collector, the flow rate at the inlet of the collector, ambient temperature, wind speed, changes in irradiation intensity, Pt-100 temperature sensor arranged in the evacuated tube, etc., which is inevitable. Secondly, according to ISO 9806 standard, sufficient good pass-steady-state conditions (at least 15 minutes) are required to ensure the accuracy of the test before entering steady-state. • The temperature difference in steady-state condition. Temperature difference of simulated and experimental are: 0.82K (for location 0.02m), 0.356K (for location 0.9m), 0.811K (for location 1.6 m), respectively.

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5.2 Effects of declination angle on heat transfer inside solar tubes

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In order to ensure the comparability and reliability of the test results, a multi-day sunny experiment was carried out with different input conditions by varying the declination angle θm of the tube to the manifold plane. The test data with similar surrounding air temperature, solar irradiation, and wind speed were selected for comparison and analysis. For the horizontal double-row ETC listed in table 1, adjust the system mass flow rate to 0.02kg/s per square metre of collector gross area.

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Fig.9. Instantaneous efficiency of horizontal double-row ETC at declination angle θm=0° and 2°.

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Through experimental measurement and calculation, the instantaneous efficiency of horizontal double-row ETC

274

is shown in Fig.9, which is 74.1% at declination angle θm =2° , 72.4% at θm =0° , and 2.3% higher than θm =0°

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horizontal double-row ETC. And the total heat loss coefficient of ETC is 1.775 at θm =2°, 1.79 at θm =0°, which

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decreases by 0.008%.Therefore, with the increase of declination angle, the instantaneous efficiency of the collector is increased and its heat loss coefficient nearly the same. In order to understand the reason and influence of the declination angle on the instantaneous efficiency of the collector, it is necessary to make a further study on the flow condition in evacuated tubes.

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5.3 Effects of declination angle (θm >0) on temperature distribution inside solar tubes

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In the experiments, four steady-state temperature points were selected, which were 293K, 305K, 321K, and 335K respectively. Temperature data from the second steady-state condition for 307K, were analysed. Fig.10 shows the temperature distribution inside the collector when the temperature of the constant temperature water tank of the test system is set at 307K with the inlet temperature fluctuates in the range of ±1 K. The position 0.02, 0.9, 1.6m indicates the distance from the opining end of evacuated tubes. Pt-100 temperature sensors arranged in the evacuated tube, as

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is shown in Fig.6. It can be found from Fig.10 that when θm =0°, obvious stratification appeared, and the temperature

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tends to be equal at the same height. However, the temperature difference between the top layer and the bottom layer is greater than 5K, and the maximum radial temperature difference in the tube occurs at the position of 0.9m while the minimum radial temperature difference occurs at the position of 1.6m. The results are in good agreement with

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numerical simulation result of LI [35]. When θm =2°, The lowest temperature occurs at position 1.6m, that is, there

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is an inactive water area at the bottom of the evacuated tube of the collector. With the increase of inlet temperature of the operation condition, the temperature difference becomes more obvious, while the difference between other positions in the evacuated tube is not large.

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Fig.10. The internal temperature distribution with different declination angles θm =0° and θm =2°.

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The simulation results of radial section temperature at 0.02 m, 0.9m and 1.6m from the open end of evacuated tube after running for four different declination angles θm, as shown in Fig.11. For the declination angle θm=0°, the temperature stratification is obvious, especially at the sealed end of the evacuated tube. at the farther away from the open end of the evacuated tube, the more obvious the thermal stratification is. Along with the declination angle chang from 0° to 6°, the temperature stratification of the water in the tube becomes less obvious and the flow is more sufficient. For the same angle, the farther away from the open end of the evacuated tube, the more obvious the thermal stratification is. Along with the declination angle transform from 0° to 6°, the temperature stratification of the water in the tube becomes less obvious and the flow is more sufficient.

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Fig.11. Temperature contours at three location (0.02m\0.9m\1.6m) from open end of evacuated tube with different declination angles (θm >0). Fig.12 is the velocity contours diagram of the open end of the evacuated tube after 60 minutes of solar irradiation with different installation angles of horizontal double-row ETC. The water in the evacuated tube absorbs heat and natural convection causes, which presents the reverse laminar flow in the upper and lower layers. This phenomenon is consistent with the visualization experiments result presented by Wang [36]. The axial velocity curve of the central cross section of the horizontal ETC described by LI [35], which is consistent with the results in this paper (orange curve ①). A part of hot water near the shear layer does not flow into the manifold, but is brought back to the evacuated tube by cold water from the bottom of the tube and re-added to the cycle. Thus, the secondary flow is formed, as shown by the red line ② in Fig.12. The phenomenon is in good agreement with the simulation result of Li [35]. As can be found in Fig.10, the declination angles θm increases as the phenomenon of secondary flow intensified. This effect, which turn out that a small amount of heat can be transferred directly into the internal main water, can improve the heat transfer.

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Moreover, when the declination angles θm is 0°, the cold water can flow into and out of the evacuated tube

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steadily. When the θm is increased, the flow velocity in the tube increases (as is show in Fig.12(b)), which can promote the circulation heat transfer. However, when the angle continues to increase, the secondary flow results in the strong vortex opposite to the flow direction in the tube, and the natural convection in the tube is restrained.

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Fig 12. The velocity vector contours of open end of evacuated tube with different declination angles (θm >0) It is possible to observe from Fig.13 that the temperature distribution of open end of evacuated tube changes with different declination angles (θm >0). The cold water area increases with the increase of declination angles θm. When the cold water flow into the tube from the lower part of the open end of tube in a stable laminar flow pattern, it is heated directly from the circumferential wall of the tube, the heated water rises and resulting the hot water flowing toward the manifold. The temperature difference of the upper layer and lower layer increased when θm change from 0° to 4°, but decreased from 4° to 6°. It also indicates that convective heat transfer is weaker when θm= 6°, which is consistent with the conclusion in Fig 12.

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Fig.13. Temperature contours of open end of solar tube with different declination angles (θm >0)

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5.4 Effects of inversion angle (θm <0) on temperature distribution inside solar tubes

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In the actual installation of horizontal double-row ETC, due to the unequal processing and installation surface of the bracket, the installation angle θm of the evacuated tube is often slightly inverted. That is, when the evacuated tube is inserted into the manifold, it inclines upward and the sealed end of the evacuated tube warps upward. In the case of this operation, when θm<0, it is considered that the inversion angle θm of the evacuated tube is produced. Fig.14 shows the temperature contours at the sealed end of evacuated tube in the first steady-state condition(293K) for the collector with different inversion angles. It is observed that under the influence of inversion angle, cold water from the manifold cannot flow naturally to the sealed end of solar tube, and heat exchange with the hot water flowing back to the manifold is becoming less sufficient. Since the hot water is trapped in the sealed end of solar tube, the average temperature at the sealed end increases gradually with increases in inversion angle |θm|. Furthermore, the greatest temperature difference at the open end of solar tube is 12K under θm = -6° condition. It indicates that less heated water was transferred from the solar tube to manifold by convection with the increase of the inversion angle.

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Fig.14. Temperature contours of open end of solar tube with different declination angles (θm<0)

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Fig.15. Temperature contours of open end of manifold with different declination angles (θm<0) Fig.15 is temperature contours at the open end of the evacuated tube in the first steady-state condition(293K) with different declination angle θm. As can be seen from Fig.15, with the increase of inversion angle θm, more cold water return back directly to manifold and never reached the sealed end. At the open end of the solar tube, the cold water area becomes larger, while the highest temperature of hot water at the top layer of solar tube decreases, and the temperature difference between cold and hot water decreases. It showed that with the increase of declination angle |θm|, more heat is retained at the end of evacuated tube closure, which is not conducive to flow exchange. Together with results shown in Fig.14, it can be concluded that with the increase of declination angle |θm|, the hot water is mainly trapped at the sealed end of the tube, while the heat transfer is insufficient and the efficiency becomes decreased. Furthermore, the increase of water temperature in the sealed end of evacuated tube will increase the heat

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loss with the environment, thus reducing the thermal efficiency of the collector. Therefore, it is necessary to avoid the inverted installation of inversion angle θm as far as possible in the project.

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6.CONCLUSIONS

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The distribution and variation trend of the temperature field and velocity field of the horizontal double-row allglass evacuated tube solar collector are studied, while declination angle changed. Since the declination angle hardly change in the actual project, 0°, 2°, 4° and 6° are selected for experiment, analysis and simulation in this paper. Both numerical and experimental investigations of double-row ETC have been carried out. The following conclusions are drawn: • The instantaneous efficiency of horizontal double-row ETC increases with the increase of declination angle θm , while heat loss coefficient is not significant change. • The declination angle θm significantly influences the temperature distribution and velocity field inside solar tubes of horizontal double-row ETC. With the increase in θm, the velocity of cold water from the manifold and hot water returning to the manifold increased, and the natural convection became more intense. But noticeable inactive region near the sealed end of solar tube was observed when declination angle increased to 6°. • If inversion angle θm < 0 appears, along with the increasing of the |θm|, more hot water is trapped at the sealed end of solar tube, while the flow heat transfer is insufficient and the efficiency becomes decreased. Therefore, the inverted angle θm should be avoided as far as possible in engineering. The results of this work can be helpful in the design of horizontal double-row ETC due to the declination angle of collectors that could be adjusted, so the thermal performance could be improved without increasing the economic cost.

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ACKNOWLEDGEMENTS

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This research was funded by the National Natural Science Foundation of China (51866016, 11662021). Experiments were conducted at the National Quality Supervision and Testing Centre for Solar Heating Systems (Kunming), and simulation were supported by Computational Fluid Mechanics and Heat Transfer Laboratory (CFMHTL) in Yunnan Normal University.

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Disposed Tube，and Daily Collected Energy by the Shadow Between Tubes," Journal of Capital Normal University

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Journal Pre-proof Author Contribution Statements:

Q. L. and W. G conceived of the presented idea. W. L. and T. L. developed the theory and performed the computations; Y. Z. analysed and interpreted the results; Q. L. and X.D. took the lead in writing the manuscript; both X. H and W. L. contributed to the final version of the manuscript. Q. L. and W. G. supervised the project. Q. L., W. L. and T. L. contributed to the design and implementation of the research, to the analysis of the results and to the writing of the manuscript.

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Declaration of interests ☒ 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. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Journal Pre-proof Highlights • The declination angle θm (the angle of the evacuated tube to the manifold plane) have been found. • The efficiency of solar collector is affected by the declination angle θm. • Flow characteristics inside horizontal double-row all-glass evacuated tubes collectors have been studied. • The declination angle θm will contribute to improving the efficiency of solar collectors.