Heat transfer mathematical model for a novel parabolic trough solar collecting system with V-shaped cavity absorber

Sustainable Cities and Society 52 (2020) 101837

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Heat transfer mathematical model for a novel parabolic trough solar collecting system with V-shaped cavity absorber Yu Biea,b, Ming Lib, Fei Chena, Grzegorz Królczykc, Zhixiong Lid,

T

⁎

a

Faculty of Chemical Engineering, Kunming University of Science and Technology, Kunming 650500, PR China Solar Energy Research Institute, Yunnan Normal University, Kunming 650500, PR China c Department of Manufacturing Engineering and Automation Products, Opole University of Technology, Opole 45758, Poland d Department of Marine Engineering, Ocean University of China, Qingdao, 266100, China & School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, NSW 2522, Australia b

A R T I C LE I N FO

A B S T R A C T

Keywords: Parabolic trough solar collector Heat transfer model Environmental factors Heat transfer characteristics

Solar heat utilization in medium temperature range (80–250℃) has attracted more and more attentions in the field of building and industry energy conservation. A heat transfer model for a novel parabolic trough solar collecting system with V-shaped cavity absorber is established based on the thermal resistance network method. Experimental validation was performed in different weather conditions to investigate the calculation accuracy of the proposed model. The analysis results demonstrate that the model calculation error mainly lies in the influence of wind speed deviation and the difference between the theoretical and actual temperature rise rate with the sudden changes of solar direct normal irradiation (DNI). By carrying out bias correction, the model calculated results were perfectly consistent with the experimental results. Based on the proposed model, the effects of different environmental factors on the outlet temperature and collecting efficiency were compared, and the comparison results can be used to correct the proposed model in different weather and environmental conditions, which make the proposed heat transfer model more reliable to the practical operation situation. As a result, the proposed model may provide a theoretical basis for the operation optimization of the solar collecting system.

1. Introduction Compared with traditional fossil energy, solar thermal utilization system presents a higher overall exergy efficiency for building energy conservation (Balta, Dincer, & Hepbasli, 2011). The integration of solar system and buildings has been extended gradually from the solar photovoltaic and traditional low-temperature (≤80℃) water heating system to the medium-temperature (80℃–250℃) utilization, such as solar absorption refrigeration, solar boiler heating, and desalinated water supply (Wang, Cheng, & Tan, 2017). For example, in northern China, a small parabolic trough solar collecting system is used for steam generation, which replaces industrial coal-fired steam boilers to supply interior heating for buildings. In addition, several small solar concentrators are adopted to raise the water outlet temperature to supply drinking boiled-water in Hebei, China. By increasing the rate of temperature rise, the system can serve with the capacity of several tons to hundreds of tons of boiled-water per day. All active solar buildings are equipped with collectors,

⁎

accumulators, pipelines, pumps and fans to collect, store and distribute solar energy. The performance of solar thermal utilization system affects the energy-conservation performance, as well as design and construction of buildings. For the solar medium-temperature thermal system, concentrators are mostly adopted, which leads to more complexity in system modeling and performance analysis. (Younas, Banat, and Islam (2015) established the transient mathematical model of the multi-stage solar still (MSS) based on Fresnel concentrated solar collector for water desalination. According to the annual direct radiation (DNI) data, seasonal behavior of the system is obtained, and the optimization of system design parameters is finally realized. Al-Othman, Tawalbeh, Assad, Alkayyali, and Eisa (2018) used Aspen HYSYS V8.8 simulation software to simulate a novel trough concentrator and a solar pool-driven multi-effect flash seawater desalination system, and then the optimization design was conducted. Sangi and Müller (2016) adopted three exergy comparative analysis methods to compare the performance of solar energy auxiliary boiler system and conventional boiler system, and the analysis showed that exergetic comparison

Corresponding author. E-mail address: [email protected] (Z. Li).

https://doi.org/10.1016/j.scs.2019.101837 Received 8 June 2019; Received in revised form 13 August 2019; Accepted 10 September 2019 Available online 19 September 2019 2210-6707/ © 2019 Elsevier Ltd. All rights reserved.

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η

Nomenclature A c d D g Gr h Ib l m Nu Pr Q Re R t v

Efficiency

Subscript

Area, m2 Specific heat capacity, kJ/(kg K) Diameter, m Hydraulic diameter, m Gravitational acceleration Grashof number Surface convective heat transfer coefficient Solar radiation, w/m2 Height or length, m Mass velocity, kg/s Nusselt number Prandtl number Heat transfer, J Reynolds number Thermal resistance, K/W Temperature, ℃ Volume flow rate, m3/s

a abs ave b c cd cv f h in inc o oil p r wind

Air Cavity absorb Average Heat oil tank The inner wall of the cavity inclosure Heat conduction Heat convection Working fluid Cavity heat absorb surface Inlet The outer cavity protection inclosure Outlet Heat transfer fluid Pipe; pressure Heat radiation Wind related variables

Greek symbols Abbreviation ρ μ τ λ θ δ

Density, kg/m3 Dynamic viscosity, kg/(m s) Time, minute Thermal conductivity, W/(m K) The incident angle, ° Thickness, m

DNI SIPH HTF PTC LFC

Direct normal irradiation Solar industrial process heating Heat transfer fluid Parabolic trough collector Linear Fresnel collector

efficiency. İbrahim et al. Yılmaz & Söylemez (2014) established a solar energy optics and thermal model based on actual system parameters. By solving the differential and nonlinear algebraic equations and comparing with the experimental data of Sandia National Laboratory, the performance characteristics under different operating conditions are analyzed. In the study of the influence of environmental factors on the performance of solar collectors, Xiao, Zhang, Shao, and Li (2014) established a three-dimensional energy balance model for a V-shaped cavity absorber. Using the constructed MCRT model, it was found that few solar rays could escape from the V-cavity. Using the constructed three-dimensional energy balance model, the fins were found to increase the heat transfer coefficient of the absorber, which in turn enhances the photo-thermal conversion performance of the absorber. The experimental results prove its feasibility and accuracy, and based on this, the effects of mass flow and heat flux distribution of DNI and heat transfer media on heat transfer characteristics are analyzed. Hachicha, Rodríguez, Castro, and Oliva (2013) modeled PTC based on large eddy simulation LES, and the model was validated by the cross-flow condition of the cylinder. The drag forces and heat transfer coefficients were confirmed through experimental measurements. On basis of the model, the different angles of the turbulence Re are simulated to obtain the influence of the wind flow on its performance. It is also found that when the solar trough system is in the horizontal working state, the ambient wind speed around it has minimal impact on its heat collection performance. Jing-jing (2014) analyzed the heat transfer form of a solar collector under non-uniform heat flow boundary conditions and established a heat transfer model for the collector. The heat transfer process of the collector tube was simulated using Fluent software. The results show that the solar radiation intensity, heat transfer medium flow velocity and inlet temperature have a great influence on the circumferential temperature distribution of the heat pipe under the nonuniform heat flow boundary conditions. Silva, Pérez, and FernándezGarciab (2013) modeled the trough collector of a PTC solar power plant. The simulation results show that the root mean square error between the predicted efficiency and the measured data of the model is

analysis method proposed in this paper can more impartially evaluate the performance of renewable and non-renewable building energy system. Solar collector is the key component for a solar thermal system. Kalogirou (2003) compared five types of collectors with TRNSYS simulation software and found that at medium-temperature ranges, the best collector choice is parabolic trough collectors (PTC), since it has the lowest life cycle cost and the highest commercialization. Straightthrough vacuum tubes and straight-through glass and metal tubes are widely-used as the PTCs absorber. However, for the reasons of technical barrier and cost, there are also a variety of alternative absorber forms, such as various types of cavity absorber (Chen, Li, Zhang, & Luo, 2015). As for PTC, extensive researches have been carried out on heat collecting system model establishment and performance analysis. The research on the system characteristics of the PTC mainly includes two aspects, one is the establishment of the theoretical heat transfer model of the collector, and the other is the research on the influence of the environmental factors on the collector heat collecting performance. With regard to the heat transfer model researches, Lu, Ding, Yang, and Yang (2013) studied the heat transfer performance of solar trough collectors, established uniform and non-uniform heat transfer models for absorbers. And the study found that the calculation results of the heterogeneous model are in good agreement with the actual situation. Luo, Yu, Hou, and Yang (2015) constructed a dynamic simulation model of PTC and verified the pump, oil-water heat exchanger, absorber and other component models. This model can simulate system operating conditions under different irradiation conditions in real time. Huang, Xu, and Peng (2016) established the PTC twodimensional heat transfer and three-dimensional optical combined model, which can predict the thermal performance and optical performance of the system, indicating that the simulation results are in good agreement with the experimental results. Liang, You, and Zhang (2016) established mathematical models for three different optical models and geometric dimensions using MCM and FVM methods, respectively, and analyzed the effects of rim angle and aperture width on optical 2

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1.2%, and the optimal working fluid velocity of the system is 0.22 kg/s based on the minimization of thermal energy loss function. Li, Xu, Ji, Zhang, and Yu (2015) studied the compensation of the end loss of the solar collecting system. The results show that the end loss decreases with the increase of the concentrator length. When the length is less than 15 m, the change is obvious, while the loss at the end of the latitude less than 20° does not change significantly. In summary, the heat transfer model and the solar heat collecting characteristics of different collector systems have achieved lots of results that worth for reference. However, most of them are based on independent cycles of the collectors, that is, the small collecting loop, and the heat transfer models are generally not verified under different weather and environment. Therefore, the However, the applicability and accuracy of the theoretical model in different weather conditions are not clear. In this paper, a heat transfer theoretical model is established for the PTC with a novel V-type cavity absorber developed by our research team (Chen et al., 2015; Li, Xu, Ji, Zhang, & Yu, 2015; Xu et al., 2014), which is more close to the actual situation by considering the heat storage, piping, full-year solar operating law and heat load. In addition, to make the theory model more accurate, a correction method was presented, which is suitable for different weather and operation condition. The model could provide a theoretical basis for the system operation optimization. The main work of this paper is as follows: the first section aims to review the background of the utilization of solar energy in the building energy-conservation and development status of the heat transfer characteristics of solar collectors. The second section aims to introduce the structure of the PTC, the operation principle and the modeling of heat transfer theory. The third section focuses on the calculation results of heat transfer under different weather conditions compared with the experimental results. The fourth section aims to analyze the influence of different environmental factors on the collector temperature rise and collecting efficiency. The fifth section aims to discuss the theoretical heat transfer model error. The sixth section aims to summarize the relevant results.

double tube differential pressure type, with high temperature resistance up to 400℃. The flow measurement range is 0.1–6.0m3/h, and the accuracy level is 1.0. A set of TBS-2-2 direct normal irradiation (DNI) meter is placed near the solar system. The sensitivity is 7μV/W m−214μV/W m−2, the time constant is 15 s, the internal resistance is 80Ω, the measuring range of wavelength is 300 nm–3000 nm, the working temperature should be not exceed 45℃, the DNI measurement range is 0 W/m2–2000W/m2, the accuracy is ± 2%. 2.2. Theoretical modeling 2.2.1. Heat transfer model of cavity absorber The V-shaped absorption surface of the cavity is internally provided with fins. The semi-circular envelope is surrounded by a glass wool insulation material, and the outermost layer is a protective casing. The specific structure is shown in Fig. 2a. According to this structure, a thermal resistance network as shown in Fig. 2b is used for analyzing the heat transfer process. According to the thermal resistance network, the energy balance equation of the cavity can be obtained (Frank, David, & Theodore, 2006; Yang & Tao, 2006; Zhang & Guo, 2004). Before model establishment, there should be some assumptions: (1) the temperature is uniformly distributed without gradient both on the absorbing surface and on the external insulation surface. (2) The relevant physical parameters of the equipment materials do not change with the temperature in the range of heat collection process. (3) When calculating the convective heat transfer loss from cavity absorbing surface to the environment, the sunlight entering glass of the cavity absorber is placed horizontally with the front surface facing down. It is not considered that the actual condition of the sunlight entering glass is inclined due to the rotation of the shaft of the tracking device. (4) The cavity absorber works in a stable state, without considering the influence of the structure and heat capacity of various components in the system.

2. Operating principle and theoretical model of a solar parabolic trough collector

Q abs = Ib ηopt AF cosθ

(1)

Q abs = Q cv, h − f + Qr , h − f + Q cv, h − a + Qr , h − a

(2)

Qcv,h-f + Qr,h-f − Qcv,f-c = m f c p,f (To,c − Tin,c )

(3)

According to Eqs. (1)–(3), the cavity outlet temperature expression is easily obtained

2.1. Operating and working principle

To,c = (Qabs − Qcv,h-a − Qr,h-a + b2 + (m f cp,f − b1 2) Tin,c )/(m f cp,f + b1 2)

The parabolic trough solar heat collection system with cavity absorber includes a parabolic concentrator, a V-shaped cavity absorber (called ‘cavity’ below), a heat transfer fluid (HTF) pipe, an oil thermal energy storage tank (called ‘oil tank’ below), and its structure is shown in Fig. 1. The PTC works as follows (Chen, Li, Xu, & Wang, 2014; Xu, Li, Ji, & Chen, 2014): PTC is a north-south one-dimensional tracking mechanism, and the parabolic concentrator opening surface is always normal facing the sunlight under the control of the tracking device. The V-type cavity at the focal line with opening down receives the reflected sunlight, HTF is heated when it flows through the interior of the cavity, and then it mixes with the internal HTF when passing through the tank to rise up the temperature, around the route from point 1–3 to 9 and 1. The size parameters of PTC parabolic concentrator are as follows: opening width is 3 m, north-south length is 12 m, and oil tank volume is 0.074m3. This oil tank is used to store the heat energy of the HTF and to compensate for the loss of the working medium during the operation, as well as to reduce the instantaneous fluctuation range of the working medium temperature. SKALN460 heat transfer oil is used as the HTF. The recorder collects meteorological parameters and temperature data, with collecting period of 1 min. There are seven temperature sensors used in the experiment, placed respectively at the inlet and outlet of the cavity absorber, at the inlet and outlet of the heat oil tank, and three sensors in the oil tank at different height. The type of temperature sensor is Pt100 with measurement range of 0℃–350℃ and measurement error no more than 0.1℃. There is one oil orifice flowmeter of

(4)

b1 b2 and are where, b1 = a1 − a12 (a2 + a3) (a1a2 + a1a3 + a2a3) ,

auxiliary parameters, +Q a a (a T − Q ) b2 = 1 2 3 aa a +r ,ainca−+a a a sun − inc , 1 2

1 3

2 3

Fig. 1. The schematic diagram of parabolic trough cavity solar collector system. 3

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Fig. 2. Cross section and the thermal network of the cavity absorber. a. Cavity section b. Heat transfer resistance network. n

a1 = h cv, f − c A c , a2 = h cd, s − inc As , a3 = h cv, inc − a Ainc . where Q abs is solar energy reaching the cavity absorption surface, W; Ib is solar radiation intensity, W/m2 ; ηopt is PTC optical efficiency; AF is concentrated area, m2; Q cv, h − f is convection heat transfer from the absorption surface to the working medium, W; Qr , h − f is radiant heat transfer from the absorption surface to the HTF, W; Q cv, h − a is convection heat transfer from the absorption surface to the environment, W; 1λ 1 1 λ hcv, h − a = 0.664Re 2 Pr 3 D (with wind) and hcv, h − a = 0.27(GrPr ) 4 D 2 (without wind), W/(m K) (Zhang & Guo, 2004); Qr , h − a is radiant heat transfer from the absorption surface to the environment, W; mf is HTF mass flow rate, kg/s; cp, f is HTF constant pressure specific heat capacity, W/(kg K); To, c is cavity outlet HTF temperature, ℃; Tin, c is cavity inlet HTF temperature, ℃; Qr , inc − a is protect the radiation heat transfer from the inclosure to the environment, W; Q cv, f − c is convection heat transfer from the HTF to the inner wall of the inclosure, W; Q sun − inc is heat radiation from sunlight to protective casing, W; Ta is ambient temperature, ℃; h cv, f − c is convective heat transfer coefficient on the inner wall surface of the envelope, W/(m2 K); h cd, s − inc is conduction heat transfer coefficient from the outer wall of the inclosure to the glass wool layer, W/(m2 K); h cv, inc − a is inner surface area of inclosure, W/(m2 K); 1λ

To, p =

∑ ⎛⎜Tin,p − i= 1

⎝

qp,1 − 4 ⎞ cp, f A1ρf ⎟ ⎠

(6)

where, qp,1 − 4 ——heat flow from the pipe inner wall to the outer shell for unit length, W/m; Tin, p ——HTF temperature at pipe inlet, ℃； To, p ——HTF temperature at pipe outlet, ℃; hp,1 ——the surface heat transfer coefficient of convection heat transfer over the inner wall of the pipe, W/(m2·K); hp,4 ——the surface heat transfer coefficient of convection heat transfer over the pipe shell, W/(m2·K); dp,1 ——inner diameter of pipe, m; dp,2 ——outside diameter of pipe, m; dp,3 ——outside diameter of glass cotton layer, m; dp,4 ——outer diameter of shell, m; λp,3 —— thermal conductivity of glass cotton layer, W/ (m·K); λp,4 ——thermal conductivity of pipe shell, W/(m·K); A1 ——area of pipe internal cross section, m2; ρf ——HTF density, kg/m3; n——total pipeline length, m. 2.2.3. Oil tank heat transfer model In the experiment, an energy storage tank was used as a storage unit of thermal energy. The tank was composed of a stainless steel inner liner and an outer bladder, and the inner and outer bladders were filled with glass wool. This structure increases the upper temperature limit of the energy storage and is beneficial to balance the thermal stability of the heat collection process. The horizontal cross-section thermal resistance network is shown in Fig. 4. The tank energy balance equation and the tank outlet temperature equation are shown in Eqs. (7) and (8).

1 λ

h cv, inc − a = 0.193Re 0.618Pr 3 D with wind and hcv, inc − a = 0.48(GrPr ) 4 D without wind, W/(m2 K) (Frank et al., 2006); A c is inner surface area of inclosure, m2; As is outer surface area of inclosure, m2; Ainc is protective casing surface area, m2.

2.2.2. Heat transfer model of the HTF pipeline The HTF pipeline adopts a three-layer design method, that is, the interior is a stainless steel straight pipe or bellows, the middle layer is glass wool, and the outer layer is a thin aluminum shell. The three-layer structure facilitates the reduction of the heat transfer coefficient in the longitudinal section of the pipe. Fig. 3a shows the thermal resistance network of the longitudinal section of the working pipe. Combining thermal resistance network of longitudinal cross-section of HTF pipeline, the heat flow expression of unit tube length can be obtained by

q b,1 − 4 =

To, b =

To, b − Ta 1 hb,1 +

δb,2 + δb,3 + δb,4 λb,2 A'b,1

//(

δb,2 + δb,4 λb,2 Ab,1

+

δb,3 λb,3 Ab,1

cp, in, f , b ρin, f , b vf (Tin, b − T'o, b)⋅60 − Qb,1 − 4 c'p, o, f , b ρo' , f , b Voil,b

) + 1 hb,4

(7)

+ T'o, b (8)

where, q b,1 − 4 ——heat flux of oil tank through cross section, W; Tin, b ——HTF temperature at the tank inlet, ℃; To, b ——HTF temperature at the tank outlet, ℃; T'o, b ——HTF temperature at the tank outlet at the last moment, ℃; hb,1 ——the surface heat transfer coefficient of

qp,1 − 4 =

π (Tin, p − Ta) 1 (hp,1dp,1) + ln(dp,3 dp,2) (2λp,3) + ln(dp,4 dp,3) (2λp,4 ) + 1 (hp,4 dp,4) (5) The temperature of the pipeline outlet HTF can be expressed as:

Fig. 3. Heat transfer resistance network in the longitudinal cross-section of HTF pipeline. 4

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environmental wind speed is low, about 0.3 m/s. The HTF flow rate is consistent with the sunny days in the first test. 3.2. Theoretical calculation results and experimental results of heat transfer model The theoretical calculation results and experimental results under different weather conditions are shown in Fig. 9∼12. From the Figs. 9(a)–12 (a), it can be seen the changes of the inlet and outlet temperature, of which the simulated and experimental values under different weather conditions, have the similar tendency to increase, with the most error of 42.5%. Meanwhile, compared with the experimental temperature, the theoretical values vary visibly when DNI suddenly changes. As is revealed in the Figs. 9(b)–12 (b), the temperature change curve can describe the change trend better, which is the inlet and outlet temperature of the HTF in the PTC change slowly due to the experimental device and heat of the working medium under the experimental condition, while the theoretical values emerge sudden change apparently because of the theoretical heat transfer calculation. In addition, in the Fig. 9(b)–12 (b), the theoretical and experimental values of heat collector efficiency emerge singular point duo to the individual experimental values, and the overall variation trend is in line with the rule, with the theoretical values equaling to the experimental one in the Figs. 11(b) and 12 (b). In the Figs. 9(b) and 10 (b), the theoretical values differ from the experimental values a lot, as is influenced by DNI fluctuation and wind speed. Notably, the inlet and outlet temperature of HTF in the PTC is inconsistent with the ones in different conditions: In the Fig. 9(a), the theoretical values of the inlet and outlet temperature are equal to the experimental one, and beginning to arise change tendency at 30 min for the first time, with change arising again 20 min later. That’s because DNI in the Fig. 5 decline lightly at the 30 min, while wind speed appears greater decline, resulting in the theoretical values of the inlet and outlet temperature vary distinctly when compared with the experimental values and leading to the theoretical values are identical with the experimental ones. In the Fig. 10(a), the theoretical values of the inlet and outlet temperature are equal to the experimental values at the beginning, but 37 min later, they tend to change visibly and the theoretical values are far greater than the experimental ones. The reason is that, compared with the conditions in the Fig. 5, DNI in the Fig. 6 fluctuates for some time and maintain low wind speed for some time after wind speed plunges at 37 min, thus making the theoretical temperature of the inlet and outlet change more obviously than the experimental values. In the Fig. 11(a), the theoretical values of the inlet and outlet temperature are equal to the experimental values at the beginning, but 13 min later, they tend to change visibly and the theoretical values are start to be less than the experimental values. Later, the inlet and outlet temperature have been rising until the 22 min. Then they rise again at 28 min, bringing about the theoretical values are less than the experimental values generally. That’s because when compared with the conditions in the Fig. 6, the DNI in the Fig. 7 tend to decline entirely, and keep about 100 W/m2 for a long time, making the theoretical values of the inlet and outlet temperature less than the experimental values obviously. In

Fig. 4. Tank cross-section heat transfer resistance network.

convection heat transfer on the tank inner wall, W/(m2 K); hb,4 ——the surface heat transfer coefficient of convection heat transfer on the tank outer wall, W/(m2 K); δb,2 ——thickness of inner lining, m; δb,3 ——thickness of glass cotton layer, m; δb,4 ——the thickness of the outer wall, m; λb,2 ——thermal conductivity of inner lining, W/(m K); λb,3 ——thermal conductivity of glass cotton layer, W/(m K); A 'b,1 ——the cross-section area of the pipe between internal and external wall, m2; Ab,1 ——the surface area of the inner wall, m2; cp, in, f , b ——HTF specific heat capacity at constant pressure at oil tank inlet, W/ (kg K); c'p, o, f , b ——HTF specific heat capacity at constant pressure at oil tank outlet at the last moment, W/(kg K); ρin, f , b ——HTF density at the tank inlet, kg/s; ρo' , f , b ——HTF density at tank outlet at the last moment, kg/s; vf ——HTF volume flow velocity, m3/s; Voil,b ——HTF volume inside the tank, m3. The parameters of HTF (mineral oil), dry air, and PTC used for theoretical calculations in this paper are shown in Tables 1–3.

3. Theoretical calculation results and experimental results of the PTC 3.1. Environmental parameters under different weather conditions Fig. 5 shows the results of environmental parameters under typical sunny weather conditions. From Fig. 5(a), it can be seen that direct radiation was maintained at around 800 W/m2 within one hour before and after 12:00, there was only slight fluctuation in 10 min, almost no clouds were blocked, and the ambient temperature remained stable at 22.5 °C or so. From Fig. 5(b), it can be seen that the ambient wind speed is maintained at around 3 m/s, but as the temperature of the heat transfer working medium increases, the density decreases and the kinematic viscosity decreases, which affects the flow characteristics and leads to heat transfer fluid volume flow decreases with the change of the physical properties of the thermal oil, and finally stabilizes at 3.5 m3/h. Figs. 6 and 7 show the results of environmental parameters under sunny and cloudy conditions. From Figs. 6 and 7, it can be seen that the maximum value of the solar radiation is mainly sunny weather conditions, and the two results are equivalent. Affected by clouds, the test process is accompanied by a small amount of fluctuations, and the results of the direct radiation test of the second test are significantly higher than the results of the first test. The ambient temperature at the first test was stable at about 20 °C, and the environment at the second test was stable at 22 °C. The wind speed in the two tests was basically the same, which was about 1.5 m/s. The operating flow rate of the HTF is kept in line with the law of sunny days in the first test, while the second test has the law of increasing first in the beginning stage, because of the sudden change of the solar radiation and its ambient temperature and the corresponding time. Fig. 8 shows the test results of environmental parameters under a weather conditions of cloudy mainly and sunny day. It can be seen from Fig. 8 that the maximum value of solar radiation is dominated by sunny weather conditions. Affected by clouds, there are more fluctuations in the test process, and it lasts for a long time under low direct radiation conditions. The ambient temperature is stable at about 27 °C; the

Table 1 HTF (mineral oil) parameters.

5

T ℃

cp KJ/kg ℃

λ W/m ℃

ρ kg/m3

100 150 200 250 300 Fitting formula R2

2.15 2.33 2.51 2.69 2.88 1.7884 + 0.00363t 0.99989

0.128 0.124 0.120 0.116 0.112 0.1359-0.00008t 0.99996

820 790 760 725 690 885.8-0.65t 0.99799

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Table 2 Dry air parameter at the pressure of 100kPa. t ℃

ρ kg/m3

cp kJ/(kg K)

λ 10−2W/(m K)

DT 10−6 m2s-1

μ 10−6Pa s

ν 10−6 m2s-1

Pr dimension-less

0 5 10 15 20 25 30 35 40

1.252 1.229 1.206 1.185 1.164 1.146 1.127 1.110 1.092

1.009 1.009 1.009 1.011 1.013 1.013 1.013 1.013 1.013

2.373 2.413 2.454 2.489 2.524 2.552 2.582 2.617 2.652

3.478 3.414 3.350 3.292 3.233 3.183 3.131 3.083 3.033

17.160 17.456 17.750 17.995 18.240 18.486 18.731 18.976 19.221

13.706 14.203 14.718 15.186 15.670 16.131 16.620 17.095 17.602

0.730 0.730 0.730 0.731 0.732 0.734 0.735 0.735 0.734

4. Influence of environmental factors on the collecting characteristics of PTC

Table 3 Collector structure parameters. Parameter

Value

Parameter

Value

Cavity length /m Total length of HTF pipeline /m Solar collecting area /m2

12 25

HTF quality /kg HTF flow rate /m3 h−1

65 3∼6

36

0.1

oil tank capacity /m3

0.074

Temperature measurement accuracy /℃ HTF heating limit temperature /℃

4.1. Orthogonal experimental design These experiments were conducted under the similar HTF volume flow and environmental temperature condition, and these two factors have significant effect on the inlet and outlet temperature of HTF, as well as the heat collection efficiency. Therefore, in order to explore the influence of solar direct normal irradiation (DNI), ambient temperature, ambient wind speed and heat transfer fluid flow on heat collecting and transfer characteristics, orthogonal experiments were carried out at three levels for four factors respectively, and 9 groups of experiments were carried out, and the experimental scheme was shown in Table 4.

250

the end, the theoretical values slow down the increase, because wind speed is over than that in the condition of the Fig. 6. In the Fig. 12(a), the theoretical values are bigger than experimental’ s at the beginning, and the difference is getting bigger and bigger. This’s because the wind speed is basically zero in the Fig. 8, despite that DNI of it fluctuates more apparently than the other working condition, with the maximum value lower visibly. In summary, DNI values and wind speed can make a clear difference to the theoretical values of the inlet and outlet temperature, while the experimental values are influenced slightly duo to the heat collector structure and heat carried by working fluid. Besides, heat transfer mathematical model of the PTC is accurate better under the bigger wind speed condition (Fig. 5). In the case of Figs. 5 and 6 condition, that is, DNI values are similar, it can be drawn that increasing of wind speed can make the theoretical values reduce. When wind speed is similar, as condition show in the Figs. 6 and 7, the theoretical values change at a low rate because of reduce of the DNI values. Under the circumstance of no wind, as the condition in Fig. 8, the theoretical value is bigger than experimental value remarkably.

4.2. Orthogonal experimental theory calculation results and analysis In this paper, the maximum difference analysis of the orthogonal experimental results is carried out by using the two indexes of thermal efficiency and temperature rise rate. The results are shown in Table 5. Where kij represents the value for column j (i.e. factors) and row i (i.e. levels), which equal to the average of index x1 for three levels, while kij' is for the index x2. R and R' represent the indexes fluctuation intensity when the level of the factor changes, and through which the main and secondary order of factors can be determined. As can be seen from Table 5, with the heating rate as the evaluation index, the change of solar DNI has the greatest influence on the heating rate, followed by the wind speed, the environmental temperature and the HTF flow. To obtain a faster temperature rise, the optimal conditions are maximum DNI, maximum environmental temperature, minimum HTF velocity and minimum wind speed. While regarding the

Fig. 5. Environmental parameters of a sunny day test condition. (a) Solar radiation and ambient temperature (b) Workflow and ambient wind speed. 6

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Fig. 6. Environmental parameters of a sunny mainly and cloudy day test condition. (a) Solar radiation and ambient temperature (b) Workflow and ambient wind speed.

used for increasing the temperature of mechanical equipment itself. This latter part of heat keeps the temperature gradually change under the DNI mutation, and the heat loss of each sub-unit is different due to the actual equipment. In addition, the theoretical model adopts the wind formula to calculate its heat loss, and there are doubts about whether it is reasonable to use the formula under the condition of no wind (e.g. the situation in Fig. 8). Therefore, it is assumed that the heat absorbed by collector is accurate and each heat loss item would be corrected without considering the heat stored by the equipment itself. The heat loss items include the that of the cavity absorber itself, as well as the heat loss of the pipeline and oil tank. Firstly, HTF temperature values at inlet and outlet of the collector were calculated by the natural convection heat transfer coefficient with wind and with no wind, respectively, as red and blue curves shown in Fig. 13. It is found that both results still exist obvious difference with the actually measured value, and the calculation of heat loss value is still undervalued. The calculated results by natural convection heat transfer coefficient with wind is closer to the experiment value, so the follow-up calculation is still conducted by the formula with the wind. The calculation distortion of heat loss caused by the instability of DNI still needs to introduce correction factor, so that the simulated value is close to the experimental value. The heat loss correction factors of the cavity absorber, pipeline and heat storage tank are defined as K1,

heat collecting efficiency as evaluation index, the impact of wind speed is the largest, followed by the impact of DNI, the HTF flow rate and the environmental temperature. It is worth mentioning that under the condition of high DNI, the influence of the wind velocity on the inlet and outlet temperature is relatively small; and under the condition of low DNI, the influence of the wind velocity is significantly greater than that of the DNI. This is why in Fig. 10(a) the theoretical values of inlet and outlet temperature are larger than the experimental value from 37 min, while in Fig. 11(a) the theoretical values are less than experimental value from 11 min.

5. Discussion The calculated results based on the theoretical calculation model are in good agreement with the experimental results under higher wind velocity, while there is deviation between the two types of result under the lower wind velocity. This means that there exist some problems on the theoretical model of heat transfer calculation. As for the theoretical model, HTF heat absorption capacity in each time step directly associated with the transient value of the DNI, then heat transfer to the working medium, and each step include the heat loss calculation, finally the theoretical inlet and outlet temperature are obtained. However, the actual operation is that part of the heat absorbed by the collector is transferred to the working medium, and part of the heat is

Fig. 7. Environmental parameters of another sunny mainly and cloudy day test condition. (a) Solar radiation and ambient temperature (b) Workflow and ambient wind speed. 7

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Fig. 8. Environmental parameters of a cloudy mainly and sunny day test condition. (a) Collector inlet and outlet temperature (b) Real-time temperature rise and heat collecting efficiency of the collector.

Fig. 9. Theoretical calculations and experimental results under sunny conditions. (a) Collector inlet and outlet temperature (b) Real-time temperature rise and heat collecting efficiency of the collector.

storing the heat which causes the slow rebound. Therefore, it is reasonable and necessary for the theoretical calculation model to consider the heat sink of the mechanical equipment itself. When the DNI goes back up, subtract from the absorbed heat to make the temperature slows down from the high slope increase. Therefore, the theoretical model can be added with a correction term to the heat balance equations. The correction term consists of two parts, one is the heat sink dissipative term which has a linear relationship with the HTF temperature, and the other is the heat loss correction term which is expressed as a power function form of the wind velocity. Thus, the calculated results based on theoretical model will reach a higher agreement with the actual situation.

K2 and K3, respectively. When only correcting the heat loss of cavity absorber, the simulated value of outlet temperature under K1 = 2.10 (see purple curve in the Fig. 13) is the closest to the measured value. However, the simulation value of the first half is still relatively large, while the simulation value of the second half is gradually smaller. When only correcting the heat loss of the heat storage oil tank, the simulated value under K3 = 1.56 (see green curve in the Fig. 13) is more consistent with the experimental value, which is better than the correction by K1. The average relative error compared with the measured value is 6.54%, which is a quite accurate correction method. The heat loss of the pipeline is relatively small and the influence is not obvious. The calculated results by K2 = 2 (see orange curve in the Fig. 13) and K2 = 1 (see green curve in the Fig. 13) are almost identical. Both the correction K1 and the correction K3 can be regarded as adding a wind velocity correction which is expressed as a power function of wind velocity in the heat loss term. It is important to note that the experimental curves and the closest correction calculation curve are still has a maximum error of 19.64% at some point, and also shows the experimental temperature rise or fall more smoothly all the time. This is related to the system equipment, which itself is as a heat sink in the foregoing analysis. The heat sink reserves heat and releases, equipment temperature rises slowly for

6. Conclusion In this paper, the heat transfer model is established based on the consideration of radiation heat dissipation, convection heat dissipation, and heat loss in the flow process of the PTCs in the middle-high temperature solar heat utilization system. And verified under different weather conditions to obtain the accuracy of its heat transfer law. Then based on theoretical models, the effects of different environmental factors such as solar radiation, fluid flow, ambient temperature, and 8

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Fig. 10. Theoretical calculations and experimental results under sunny mainly and cloudy conditions. (a) Collector inlet and outlet temperature (b) Real-time temperature rise and heat collecting efficiency of the collector.

Fig. 11. Theoretical calculations and experimental results under another sunny mainly and cloudy conditions. (a) Collector inlet and outlet temperature (b) Real-time temperature rise and heat collecting efficiency of the collector.

This work provides a theoretical basis for theoretical modeling of collectors in solar thermal systems. At the same time, it is also indicated that determination of the effective coefficient of the heat loss term of the collector requires more experiments and a more detailed division of the heat transfer network. Of course, filtering and other algorithms such as Kalman filter method for linear equations, particle filter method for nonlinear equations, can further make the results of theoretical calculation converged to that of the experiments, accordingly establishing the prediction and correction of exit temperature data combined with historical data and theoretical models. This is one of the future work for the next researches, and these are the foundations of theoretical modeling of solar thermal utilization systems.

wind speed on the collector outlet temperature and collector efficiency were compared and the following conclusions were obtained: 1) 1)As for the solar energy utilization system, the theoretical calculation model of heat collecting unit was established, and the result trend is consistent with the experimental process. The calculation has high accuracy especially under the bigger wind velocity. 2) 2)The heat transfer based on the theoretical calculation process is very sensitive to the change of the solar DNI, which makes the outlet temperature of the collector significantly change when the solar DNI value changes abruptly. Especially when the solar DNI decreases significantly, even the heat release phenomenon occurs. The heat loss term should be corrected to obtain the theoretical calculation model which is more consistent with the experimental equipment. 3) The effect of DNI on the temperature of the HTF at inlet and outlet of the collector is the largest, followed by wind velocity. However, the two factors are both have the equivalent influence on the collecting efficiency.

Acknowledgements This work is supported by the Collaborative Innovation Center of Research and Development of Renewable Energy in the southwest area in China (No.: 05300205020516009), NSFC China (No.: 51979261), Taishan Scholar in China (tsqn201812025), the Project on Co9

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Fig. 12. Theoretical calculations and experimental results under cloudy mainly and sunny conditions. (a) Collector inlet and outlet temperature (b) Real-time temperature rise and heat collecting efficiency of the collector. Table 4 Parameter Sensitivity Analysis Orthogonal Experimental Scheme. TestsNo.

1 2 3 4 5 6 7 8 9

Factors A DNI (W/ m2) Levels

B Environmental temperature(℃)

C HTF volume flow(m3/h)

D Wind velocity (m/s)

300 300 300 600 600 600 900 900 900

10 20 30 10 20 30 10 20 30

2.00 4.00 8.00 4.00 8.00 2.00 8.00 2.00 4.00

0.50 2.00 4.00 4.00 0.50 2.00 2.00 4.00 0.50

Fig. 13. Influence of the heat loss items on collector outlet temperature.

Table 5 Orthogonal experiment range analysis. Tests No.

1 2 3 4 5 6 7 8 9 k1j K2j K3j R k1j ' k1j ' k1j ' R'

Factors

Evaluation indicators

A DNI(W/m2) Levels

B Environmental temperature (℃)

C HTF volume flow(m3/h)

D Wind velocity (m/s)

x1 Temp. rising rate (℃/min)

x2 Efficiency (%)

300 300 300 600 600 600 900 900 900 0.064 1.666 3.348 3.285 18.123 25.999 30.252 12.130

10 20 30 10 20 30 10 20 30 1.243 1.733 2.102 0.859 24.250 24.175 25.948 1.773

2.00 4.00 8.00 4.00 8.00 2.00 8.00 2.00 4.00 1.495 1.754 1.829 0.333 25.546 22.631 26.196 3.565

0.50 2.00 4.00 4.00 0.50 2.00 2.00 4.00 0.50 2.350 1.646 1.081 1.270 31.724 23.069 19.580 12.144

0.075 0.118 −0.002 0.666 2.500 1.832 2.989 2.579 4.477

25.269 13.625 15.474 18.086 33.720 26.189 29.394 25.181 36.182

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establishing China-Laos Joint Lab for Renewable Energy (No.: 2015DFA60120), the Science and Technology Planning Project in Yunnan Province, China (Grant No.: 2017FB092) and Australia ARC DECRA (No.: DE190100931).

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