A multitude of the researches focus on the factors of the thermal efficiency of a parabolic trough solar collector, that is, the opticalthermal efficiency. However, it is limited to a single or double factors for available system. The aim of this paper is to investigate the multifactors effect on the system’s efficiency in cold climate region. Taking climatic performance into account, an average outlet temperature of LS2 collector has been simulated successfully by coupling SolTrace software with CFD software. Effects of different factors on instantaneous efficiency have been determined by orthogonal experiment and single factor experiment. After that, the influence degree of different factors on the collector instantaneous efficiency is obtained clearly. The results show that the order of effect extent for average maximal deviation of each factor is inlet temperature, solar radiation intensity, diameter, flow rate, condensation area, pipe length, and ambient temperature. The encouraging results will provide a reference for the exploitation and utilization of parabolic trough solar collector in cold climate region.
Recently, with the increasing attention of the international community about energy problem, solar energy and the other renewable energies rise gradually on largescale application [
Gao et al. [
It is important to study the parabolic trough solar collector according to the above literature summaries. However, it is limited to single or double factors for available system. The aim of this paper is to investigate the multifactors effect on the system’s efficiency in cold climate region. Therefore, effects of different factors on instantaneous efficiency have been determined by orthogonal experiment and simulated for each group of experiments. After that, the influence degree of different factors on the collector instantaneous efficiency is obtained clearly.
In order to analyze the efficiency conveniently, LS2 experiment trough solar collector has been selected for this study designed by Dudley et al. [
The basic parameters of the LS2 collector.
Pipe length (m)  Opening width (m)  Focal length (m)  Metal tube diameter (m)  Glass tube diameter (m) 

7.8  5  1.49  0.067 (inner)/0.075 (outer)  0.115 
The main view and the axial diagram of the collector.
The main principles of the model shown in Figure
The calculation of wall heat flux in collector’s tube is numerically simulated using SolTrace software. Simulation conditions are as follows: the collector of the reflector plate is selected to aluminum with the reflectivity of 0.76, refractive index of 1, shape error of 3 mrad, and specular reflection error of 0.5 mrad; also, the reflectivity of metal collector tube is of 0.1, refractive index of 0, shape error of 0.0001 mrad, and specular reflection error of 0.0001 mrad. It is simulated by the raytracing method after the optical geometric parameters have been set. It is shown that the calculation accuracy is higher and the degree of operation is less when the ray quantities are 10^{6} and the most inputting lights are 10^{8}. According to the simulated heat flux, the optical efficiency is calculated as follows:
The instantaneous efficiency of the collector can be calculated by CFD software. The model of receiver tube and the 2D mesh has been obtained by Gambit tool. The division of grid adopts tetrahedral mesh; the grid size of fluid part is 1 mm, the grid size of the metal part is 2 mm, and grid needs to refine for both inner and outer surface of metal wall. The boundary condition of inlet section is velocity inlet whereas it is pressure outlet for the outlet. According to the simulation results, the instantaneous efficiency is calculated as follows:
Simulation model and heat density distribution with the direct normal irradiance of 968.2 W/m^{2} were shown in Figure
The simulation model and the heat density distribution of the LS2 collector.
To obtain the average outer temperature and the efficiency, the concrete parameter conditions are as follows: wind speed is 3.7 m/s, the ambient temperature is 22.4°C, the inlet flow rate is 0.24 m/s, and the inlet temperature of collector is 151°C. According to the average heat flux of metal tube surface simulated by SolTrace software, the average temperature of the fluid outlet has been simulated with the second boundary condition. Figure
The temperature cloud of the receiver tube.
It can be seen from the above section that the model is correct. In this section, water is used as the heat transfer medium and ambient parameters of the coldest month in Daqing city are regarded as meteorological parameters. The main parameters are the following: fluid inlet temperature is 30°C, flow rate is 0.2 m/s, solar radiation intensity is 800 W/m^{2}, and the ambient temperature is −18.5°C. Firstly, the average heat flux density of receiver is 12884.4 W/m^{2}, which is numerically simulated using SolTrace software and the instantaneous efficiency is 75.86% calculated by (
The heat density distribution of the collector.
The temperature cloud of the receiver tube.
There are many parameters which can affect the collector efficiency, so the analysis of the influence factors can provide theoretical support and technical reserves for promotion and application of solar energy heat utilization technology. The main parameters in this paper are as follows: diameter, pipe length, condensation area, solar radiation intensity, flow rate, inlet temperature, and ambient temperature. Special points from different influencing factors, 7 factors and 3 level orthogonal tables for the orthogonal experiment, choosing L18 (3^{7}) orthogonal tables, the factors, and mathematical method have been used for the test arrangement scheme. Finally, by calculating and analyzing the test results, levels graphs are shown in Table
The factors and levels graph.
Level  Factors  

Pipe length 
Condensation area 
Diameter 
Solar radiation intensity 
Ambient temperature 
Flow rate 
Inlet temperature  
1  0.1  2  55  200 

0.1  30 
2  2  4.5  70  600  0  0.2  150 
3  7  6.5  100  800  20  0.3  300 
As shown in Table
Experimental program.
Number  Pipe length 
Condensation area 
Diameter 
Solar radiation intensity 
Ambient temperature 
Flow rate 
Inlet temperature 

1  1  1  1  1  1  1  1 
2  1  2  2  2  2  2  2 
3  1  3  3  3  3  3  3 
4  2  1  1  2  2  3  3 
5  2  2  2  3  3  1  1 
6  2  3  3  1  1  2  2 
7  3  1  2  1  3  2  3 
8  3  2  3  2  1  3  1 
9  3  3  1  3  2  1  2 
10  1  1  3  3  2  2  1 
11  1  2  1  1  3  3  2 
12  1  3  2  2  1  1  3 
13  2  1  2  3  1  3  2 
14  2  2  3  1  2  1  3 
15  2  3  1  2  3  2  1 
16  3  1  3  2  3  1  2 
17  3  2  1  3  1  2  3 
18  3  3  2  1  2  3  1 
The experimental results of instantaneous efficiency.
Serial number  Instantaneous efficiency (%)  Serial number  Instantaneous efficiency (%)  Serial number  Instantaneous efficiency (%) 

1  53.15  7  51.09  13  63.77 
2  63.65  8  60.93  14  45.26 
3  54.83  9  58.79  15  62.09 
4  54.04  10  64.20  16  53.15 
5  64.10  11  50.29  17  63.65 
6  59.02  12  52.18  18  54.83 
According to the results of Table
Instantaneous efficiency factors analysis of parabolic trough collector (%).
Pipe length  Condensation area  Diameter  Solar radiation intensity  Ambient temperature  Flow rate  Inlet temperature  


56.38  58.38  55.38  52.51  57.17  56.25  60.12 

58.05  56.36  58.50  59.49  57.03  59.00  59.93 

57.50  57.19  58.05  59.94  57.74  56.68  51.89 

1.664  2.020  3.120  7.431  0.712  2.745  8.227 
The influence of inlet temperature on the instantaneous efficiency.
The influence of solar radiation intensity on the instantaneous efficiency.
The influence of metal tube diameter on the instantaneous efficiency.
It can be seen from Figure
Figure
Taking climatic performance into account, effects of different factors on instantaneous efficiency have been determined by orthogonal experiment and single factor experiment. The main conclusions are as follows:
The results show that the order of effect extent for average maximal deviation of each factor is inlet temperature, solar radiation intensity, diameter, flow rate, condensation area, pipe length, and ambient temperature.
The inlet temperature is the uppermost factor. The efficiency of collector is lower and lower, and the decrease extent is gradually strong with the increasing inlet temperature.
The ambient temperature has a minimum effect on the efficiency. The instantaneous efficiency of collector has a slight increasing of about 1% when the ambient temperature increases.
In this model, there is an optimal outer diameter of 75 mm for the collector. Also, the instantaneous efficiency of collector has a maximum in this case.
The results can provide a reference for the exploitation and utilization of this collector in cold climate region.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the National Natural Science Foundation of China (nos. 51176024 and 51406033) and University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province (no. UNPYSCT2015075). Besides, a very special acknowledgement is made to the editors and referees who made important comments to improve this paper.