Heat Transfer Enhancement Analysis of Collector Tube in LFR-CSP

The heat transfer characteristics of the collector tube is one of the cores of a linear Fresnel reflector-solar thermal power generation system (LFR-CSP). In this paper, the heat transfer model of reflective linear Fresnel single-tube compound parabolic collector (CPC) is established. In light of the normal operating conditions during the day, it is found that the direct normal irradiation (DNI) and loop length exert significant effects on the heat collection and thermal loss performance of the linear Fresnel reflector. With the increase of DNI and unit length, the outlet temperature and heat collection capacity of the collector loop increase significantly. Because of the increase of DNI, the increase of collector heat is higher than that of thermal loss. However, the thermal loss per unit length increases correspondingly with the increase in loop length, and the heat collection efficiency decreases. Ambient temperature and wind velocity are not the main factors affecting the heat collection and thermal loss performance of the linear Fresnel reflector under the prerequisite of a good vacuum degree of the collector tube.


Introduction
Good optical performance is the basis of a high-efficiency solar collector system, and excellent thermal performance is the key to the high-temperature collector.The collector is the core component of solar energy heat absorption and transfer.At present, the linear Fresnel reflector system mainly has two forms: single-tube CPC and Compact Linear Fresnel Reflector (CLFR) multi-tube cavity collector.More uniform heat flux distribution can be obtained by multi-tube form, while higher collection temperature can be achieved by single-tube form.
For linear Fresnel power generation technology, China is still in the infant stage, with› only one commercial demonstration project.Du et al. [1,2] calculated the tracking strategy of linear Fresnel system concentrator by geometrical optics method and vector method.They analyzed the optical efficiency and concentrating ratio of the system theoretically and obtained the calculation method of unobstructed mirror spacing through experimental research.Song [3] studied the linear Fresnel system with CPC secondary mirror and analyzed the heat transfer performance of the CPC cavity receiver.He [4][5][6][7] established a three-dimensional real-time optical calculation model based on the MCRT method to analyze the linear Fresnel single-tube and multi-tube collector tube systems.He analyzed the influence of different mirror types, aiming positions, surface errors, and geographical positions on the optical performance of the system.He optimized the geometric mirror parameters and aiming positions.Wang et al. [8][9][10] designed and optimized the single-tube receiver suitable for large-scale linear Fresnel concentrator for molten salt medium; they analyzed the relationship between the distance between primary mirrors and the height of single-tube receiver as well as the influence of the number of primary mirrors on the condensing efficiency.They put forward the optimal arrangement method of condensing mirror field.Zhang et al. [11] and Xiong et al. [12] used the quasi-static equilibrium method to test and analyze the thermal loss of high-temperature vacuum collector tubes.They concluded that the thermal radiation loss of collector tubes accounts for 70%-90% of the total thermal loss of collector tubes.The thermal radiation loss of collector tubes is the main contributor to the overall thermal loss of collector tubes.However, there are few studies on the overall heat transfer characteristics of collector tubes.Therefore, this paper analyzes the heat transfer model of a linear Fresnel reflector tube and the influence mechanism of multiple factors.

Physical model
In the linear Fresnel reflector single-cavity collector, the thermal energy reflected by the collector tube is partly absorbed directly by the metal collector tube with selective coating through the vacuum glass tube, part of which is absorbed by the vacuum tube.The thermal loss of the whole collector tube includes convection heat transfer and radiation heat transfer between the vacuum tube and the environment and radiation heat dissipation between the metal tube and the vacuum tube.The simplifications and assumptions are made for the heat collection system: (1) The influence of convection and heat conduction in a vacuum tube is small and neglected.
(2) The performance of each component of the system and the heat absorption medium is stable, and the physical properties are averaged.
The heat transfer process of a linear Fresnel reflector cavity collector can be simplified as a onedimensional steady heat transfer.A thermophysical model is established as shown in Figure 1, where I b represents solar radiation reflected by Fresnel mirror; subscript R represents radiation heat transfer; C represents convective heat transfer; K represents heat conduction; r, v, cpc, g, s and a represent metal collector tube, vacuum tube, CPC cavity, glass cover, sky and environment respectively.
The DNI is 800 W/m 2 ; the loop length is 400 m; the inlet temperature of the heat absorption medium is 210℃.The width of a single primary mirror is 0.76 m; there are 16 primary mirrors in a single collector unit; the outer diameter of the vacuum glass tube is 125 mm; the outer and inner diameters of the metal tube are 70mm and 66 mm.The ambient temperature is 10℃, and the wind speed is 3 m/s.

Mathematical model of heat transfer
According to the thermophysical model of the linear Fresnel reflective cavity collector (Figure 1), the energy conservation equations of each part of the collector can be expressed as follows.
v is the vacuum tube.
q DNI -the heat flux density on the surface of the collector tube, W/m 2 .α r -the absorption rate of the metal tube.m  -the mass flow rate of the heat absorption medium, in kilograms per second, kg•s -1 .c p -the specific heat capacity of the heat absorption medium, J•kg -1 •K -1 .
T i -the inlet temperature of the heat absorption medium, ℃.
T o -the outlet temperature of the heat absorption medium, ℃.Q R,r -the radiant heat transfer between the metal tube and the vacuum tube, W. Q R,v -the radiant heat transfer between the vacuum tube and the external environment, W. Q C,v -the convective heat transfer between the vacuum tube and the external environment, W.
Through the above analysis, the thermal loss Q loss , useful work Q u and heat collection efficiency η of the reflective Fresnel cavity collector can be obtained as follows.
According to the basic principle of heat transfer, the main heat transfer experimental correlations used in the linear Fresnel reflector model are as follows.
(1) The experimental correlation of convective heat transfer between the vacuum tube and the environment is as follows:   where λair -the thermal conductivity of air at annular temperature, W•m -1 •K -1 ; Ta -the ambient temperature, K.
(3) Radiation heat transfer between vacuum tube and metal tube: (4) Outer wall temperature of metal tube: , ln 2  (10)   where d o -the outer diameter of the collector tube, m. d i -the inner diameter of the collector tube, m. λ tube -the thermal conductivity of the collector tube, W•m -1 •K -1 , and the default thermal conductivity of 316 stainless steel is 23.9 W/m•K.
T f -the characteristic temperature of the heat transfer oil in the collector tube in K, which can be characterized by the average value of the inlet and outlet temperatures of the collector tube, T f =(T o +T i )/2.

Heat transfer calculation flow of collector tube
According to the above analysis, MATLAB language is used to program and calculate it.At the beginning of the calculation, an initial temperature is given to the outer surface of the vacuum tube, and then Q loss and Q u are calculated.The difference error between the sum of the two and q DNI A v is compared, and T v is accumulated circularly until the error is less than the set standard.At this time, the iteration is considered to have converged, and the T v value is output.The program cycle structure is shown in Figure 2.  From the above calculation results, it is sufficient to say that the change in solar direct radiation intensity will have a significant impact on the heat collection performance of linear Fresnel reflectors.With the increase of DNI, the outlet temperature and heat collection capacity of the collector circuit increased significantly.With the constant temperature of 210℃ at the inlet, the outlet temperature of working condition 5 (DNI is 1000 W/m 2 ) was 50.69℃ higher than that of working condition 1 (DNI is 600 W/m 2 ), and the heat collection capacity was 1.68 times higher than that of working condition 1.At the same time, the thermal loss per unit length also increases with the increase of DNI value, which is due to the higher overall temperature of the collector tube under the higher DNI value, and the resulting convective thermal loss and radiant thermal loss between the collector tube and the external environment are correspondingly higher.Admittedly, it should be noted that the heat collection efficiency also increases slightly with the increase of DNI, which results from the increase of heat collection capacity brought by the increase of DNI being higher than the increase of thermal loss.

Effect of the loop length
In light of the reference working condition during the daytime, the loop length of the concentrating and heat collecting field is analyzed by a single factor.The loop lengths are ranged from 300 to 1000 m.The values of other parameters remain unchanged compared with the reference working condition.The calculation results are shown in Figure 4.
Under the same other calculation conditions, the outlet temperature of heat transfer oil and the heat collection capacity increase almost linearly with the increase of the length of the heat collector loop, and the range of increase is also very significant within the calculation range of this paper.With the increase in the length of the heat collector loop from 300 m to 1000 m, the outlet temperature of heat transfer oil increases from 285.32℃ to 457.50℃, and the heat collection capacity increases from 1.0212 MWt to 3.3282 MWt.According to the distribution law, the outlet temperature and heat collection capacity of heat transfer oil increase significantly with the increase of the length of the heat collector loop, the required loop length can be designed according to the demand of the system for the outlet temperature or heat collection of the heat absorption medium.Then the layout scheme of concentrating and heat collector assembly (SCA) can be designed.
Likewise, as can be seen from the above figure, with the increase of the length of the collector loop, the overall temperature of the collector tube is getting higher and higher, the thermal loss per unit length is correspondingly larger, and the heat collection efficiency decreases with the increase of the loop length.The reason for this is that as the length of the collector circuit increases, the increase in thermal loss is more significant than the increase in the new heat collection capacity of the collector tube, which leads to a decrease in the heat collection efficiency.
(1) Outlet temperature (2) Heat collection capacity (3) Thermal loss per unit length (4) Heat collection efficiency Figure 4. Influence of loop length on various heat collection performance parameters

Effect of ambient temperature
Based on the daytime reference working condition, the ambient temperature is analyzed by a single factor.The ambient temperature is -10℃, 0℃, 10℃, 20℃ and 30℃ in turn.The values of other parameters remain unchanged compared with the reference working condition.The calculation results are shown in Figure 5.
(1) Outlet temperature (2) Heat collection capacity (3) Thermal loss per unit length (4) Heat collection efficiency Figure 5. Influence of ambient temperature on various heat collection performance parameters On the one hand, from the perspective of parameter change trend, the above calculation results demonstrate that the outlet temperature, heat collection capacity, and heat collection efficiency of heat transfer oil in the heat collection loop increase, and the thermal loss per unit length decreases with the change of ambient temperature of the project site from -10℃ to 30℃.With the increase in ambient temperature, the temperature difference between the outer surface of the collector tube and the environment becomes smaller.Consequently, the thermal radiation loss and convection thermal loss also become smaller.This shows that the heat collection capacity and efficiency of the collector loop in summer are higher than those in winter under the same DNI and wind speed.
On the other hand, from the point of view of specific numerical analysis, it can be noted that the ambient temperature has little effect on the collection performance parameters of linear Fresnel reflector tubes.The ambient temperature increased from -10℃ to 30℃, and the outlet temperature of heat transfer oil only increased from 309.98℃ to 310.15℃, with an increase of only 0.17℃; the heat collection capacity only increased from 1.3570 MWt to 1.3593 MWt, with an increase of only 0.17%; the variation of thermal loss per unit length and heat collection efficiency with ambient temperature is also very small.By and large, it can be considered that the ambient temperature is not the main factor affecting the heat collection performance of linear Fresnel reflectors.

Effect of wind speed
On account of the daytime reference working condition, the wind speed is analyzed by a single factor.The wind speed is 0.1, 1, 3, 10, and 20 m/s.The values of other parameters remain unchanged compared with the reference working condition.The calculation results are shown in Figure 6.
(1) Outlet temperature (2) Heat collection capacity (3) Thermal loss per unit length (4) Heat collection efficiency Figure 6.Influence of wind speed on various heat collection performance parameters Depending on the above calculation results, firstly, from the perspective of parameter change trend, with the wind speed gradually increasing from 0.1 m/s to 20 m/s at the project site, the outlet temperature, heat collection capacity, and heat collection efficiency of heat transfer oil decreased.Accordingly, the thermal loss per unit length increased.This is because the convective heat transfer between the outer surface of the collector tube and the external environment is significantly enhanced with the increase in wind speed when other working conditions are the same.Then, the convective thermal loss increases accordingly, and at this time, the collector performance of the collector tube decreases as a whole.
From the point of view of specific numerical analysis, it can be observed that wind speed has little influence on the collection performance parameters of linear Fresnel reflector tubes.When the wind speed changed in the range of 0.1 -20 m/s increasingly, the outlet temperature of heat transfer oil decreased from 310.29℃ to 309.98℃, with a decrease of only 0.31℃; the heat collection capacity decreased from 1.3612 MWt to 1.3570 MWt, with a decrease of only 0.31%.The change range of heat collection efficiency is also very small, and only the change of thermal loss per unit length is relatively large.Therefore, we can draw a preliminary conclusion that similar to the effect on ambient temperature mentioned above, wind speed affects the heat collection performance of linear Fresnel reflectors weakly.

Conclusions
In this paper, a heat transfer model of a reflective linear Fresnel single-tube CPC is established.The effects of a series of factors on the heat collection performance and thermal loss performance of the collector tube are studied according to normal operating conditions during the day.
The DNI and the length of the loop have a significant effect on the performance of the linear Fresnel reflector tube.With the increase of DNI, the outlet temperature and heat collection capacity increase significantly, and the thermal loss per unit length also increases with the increase of DNI.The increase in the heat collection capacity caused by the increase of DNI is higher than the increase in thermal loss.Under this comprehensive effect, the collector efficiency increases slightly with the increase of DNI.With the increase in the length of the collector loop, both the outlet temperature and the heat collection capacity of the heat transfer oil show a trend of almost linear growth.The growth rate is also very significant.With the increase of loop length, the thermal loss per unit length increases correspondingly while the heat collection efficiency decreases.Based on the good vacuum degree of the collector tube, the main factors affecting the heat collection and thermal loss performance of linear Fresnel reflectors are not included in ambient temperature and wind speed.
In the practical engineering design, consideration should be given to the solar radiation conditions of the project site, the system's demand for temperature rise and heat collection, the pump power consumption required by the system, the heat preservation and anti-condensation of the heat absorption medium, and other factors.The advantages and disadvantages should be weighed from the global point of view, and finally, the reasonable value range of the loop length should be given.

Figure 1 .
Figure 1.Heat transfer model of CPC cavity receiver

Figure 2 .
Figure 2. Heat transfer calculation flow of collector tube3.Analysis of heat transfer characteristics of 3 collector tubes3.1.Impact of DNIA single-factor analysis of the intensity of direct solar radiation is performed with reference working conditions during the daytime.The DNI values ranged from 600 to 1000 W/m 2 .The other parameters remain unchanged compared with the reference working condition.The calculation results are shown in Figure3.

( 1 )
Outlet temperature (2) Heat collection capacity (3) Thermal loss per unit length (4) Heat collection efficiency Figure 3. Influence of DNI on various heat collection performance parameters