Performance investigation of integrated concentrating solar air heater with curved Fresnel lens as the cover

Journal Pre-proof Performance investigation of integrated concentrating solar air heater with curved Fresnel lens as the cover

Rihui Jin, Hongfei Zheng, Xinglong Ma, Yunsheng Zhao PII:

S0360-5442(19)32503-4

DOI:

https://doi.org/10.1016/j.energy.2019.116808

Reference:

EGY 116808

To appear in:

Energy

Received Date:

16 May 2019

Accepted Date:

18 December 2019

Please cite this article as: Rihui Jin, Hongfei Zheng, Xinglong Ma, Yunsheng Zhao, Performance investigation of integrated concentrating solar air heater with curved Fresnel lens as the cover, Energy (2019), https://doi.org/10.1016/j.energy.2019.116808

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Journal Pre-proof

Performance investigation of integrated concentrating solar air heater with curved Fresnel lens as the cover Rihui Jin, Hongfei Zheng, Xinglong Ma*, Yunsheng Zhao School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China

Abstract To obtain a tracking-free, economical medium-high temperature solar air collector, this paper presents an integrated concentrating solar air heater (ICSAH), which is compounded of a curved Fresnel lens, a V-groove secondary reflector, and an absorber placed inside a glass tube flow channel. The optical simulation to the ICSAH was carried out, and the maximum optical efficiency is found 0.77. And its acceptance angles are 9.6° in north-south and 42.5° in east-west. The heat transfer was analyzed in detail and a calculation model was established. Two ICSAHs with different length have been set up and tested to investigate the thermal performance and validate the simulation results. The thermal efficiency is found more sensitive to incident angle α than γ. Besides, an entire daytime test on the fixed full-scale ICSAH shows that the outlet air temperature remains above 100℃ for 4.5h and the maximum temperature differential reached to 108℃ at air flow rate of 8.1 kg/min. With 6.5 working hours per day, its daily efficiency achieves 0.53. The curve of normalized thermal efficiency illustrates that the heat loss rate of the full-scale ICSAH is about 1.758 W∙m-2∙K-1. Finally, a techno-economics comparison was made between the ICSAH and other CSAHs. Keywords: Integrated concentrating solar air heater (ICSAH); Tracking-free; Curved Fresnel lens; Heat transfer calculation model; Optical efficiency.

1

Journal Pre-proof Nomenclature α γ ηop/ ηt L A G T R Q Φ E Χ ε Nu Re Pr ρ u Cp

Symbols projection of relative solar elevation

Subscript/ Superscript

angle in north-south plane () relative solar azimuth () optical/ collection efficiency length of collector (m) unilateral surface area (m2) Direct normal irradiance (W/m2) temperature (℃) thermal resistance (K/W) Heat flux of heat conduction and convection (W) radiant power (W) radiation power (W/m2) angle factor emissivity Nusselt number Reynolds number Prandtl number density of air (kg/m3) air velocity (m/s) specific heat capacity (kJ∙kg-1∙K-1)

u

utilized

v d ab g cav F ref

convection conduction absorber glass tube cavity Fresnel lens aluminum reflector

ins

insulating layer

amb s in o +

ambient sun air inlet air outlet inner surface external surface cross-section of glass tube correctional variable downward heat transfer variable

 c *

'

2

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1. Introduction Solar air collector adopts air as the heat-exchanging medium, which has the advantages of low corrosiveness, low requirement for system sealing and heat supply for users without a second heat exchange, and has received more and more attention. The most commonly used solar air collector is flat plate collector (FPC). It has mature technology and moderate cost, but low outlet temperature and efficiency in winter. To improve the efficiency of the FPC and increase its outlet temperature, different kinds of internal structures and operating modes have been proposed, such as the use of regenerative air circulation [1], multiple air processes and the utilization of heat storage units [2-4]. Although many methods have been tried to improve the performance of the FPC, it is still difficult to meet people's requirements, especially the high outlet temperature in winter. In recent years, concentrating solar air heaters (CSAHs) have been widely used due to their higher output temperature. For example, they can be well integrated with the rooftop, supply domestic hot water or power the solar air conditioner of commercial buildings [5, 6]. When combined with the rockbed storage, it can meet the heating needs of single-family houses in moderately cold regions based on the whole year simulation results [7]. CSAHs can be classified into two types according to their concentrators: reflective and transmissive. Compound parabolic concentrator (CPC) is a commonly used reflective concentrator. Usually, that CPCs have a large acceptance angle and a small concentration ratio to avoid tracking results in low energy density. At the same time, in order to receive both the direct incident light and reflected light, the absorber is typically wholly exposed to the environment, resulting in significant heat loss. Therefore, it is often necessary to combine with a vacuum tube to reduce heat loss and obtain higher temperature. Nkwetta et al. [8] combined part of the evacuated tube heat pipe array collectors with trough CPCs. The new concentrator augmented collector can achieve the higher collection temperature and lower heat loss rate of 1.20 W∙m-2∙K-1 than the unchanged device. The use of heat pipe evacuated tubes results in high collector cost. The all-glass evacuated tube is much cheaper than the heat pipe evacuated tube. Wang et al. [9, 10] designed a set of all-glass evacuated tubular solar air heaters (SAHs) with simplified CPCs to obtain moderate air temperature of 150200°C. By connecting 30 units in series, its outlet air temperature can reach 160°C for 3h continuously on sunny winter or cloudy summer days. However, its heat loss rate is 4.42 W∙m-2∙K1. Shams et al. [11] designed a new SAHs that doesn’t use evacuated tubes. An asymmetric trough CPC with an inverted absorber were utilized to reduce radiation and convection heat loss. Compared with the current commercial glazed collectors, thermal efficiency of the new collector is significantly improved when the normalized temperature is high. However, its heat loss rate of about 6.50 W∙m-2∙K-1 is higher. Multi-surface concentrators (MSCs) are designed based on the trade-off between acceptance angle and concentration ratio. By increasing the concentration ratio, the energy density can be increased and the absorber’s area that is proportional to the heat sink area can be reduced. Moreover, the MSC allows the absorber to be placed under the main reflecting surface for insulation, so that medium-high temperature output can be realized without using a vacuum tube. However, many MSCs need to track the sun due to their small acceptance angle. Tao et al. [12, 13] proposed a design method for a new type MSC and tested the newly designed concentrator. With a collection area of 3.4m2, it obtains a maximum outlet temperature of 140℃ at air mass flow rate of 0.35kg/min. When choosing a reasonable air flow rate, its daily efficiency can reach more than 0.6. However, due to its small acceptance angle, single-axis tracking is required. A numerically solved 3

Journal Pre-proof reflector profile was designed by Rabady et al. [14] to reduce the thermal stress and infrared leakage on the receiver tube and improve the collection efficiency by improving the uniformity of light intensity distribution on the surface of the receiver tube. However, since its reflecting surface is designed based on the normal incident ray, it is necessary to accurately track the sun. A CSAH including linear Fresnel reflectors and secondary reflectors was described by Sultana et al. [5], and both its reflectors and receivers are placed in a sealed glazed canopy to reduce the heat loss rate. Still, each of its mirrors needs active-tracking. The use of the tracking system also increases the capital cost and maintenance cost. We also find that an additional glass cover plate is usually added to reflective CSAHs, notably for that with large inlet aperture width, to prevent dust (or rain, snow etc.) from depositing on and corroding the reflective surface during long-term operation, which reduces its optical efficiency. Transmissive CSAHs have the smooth side of the lens facing up, which is more effective against adverse environments than reflective CSAHs. There are fewer studies on transmissive concentrating solar collectors, in which Fresnel lenses are commonly used as concentrators. In order to take advantage of the higher geometric concentration ratio of the Fresnel lenses, tracking systems are often required in their applications. Zhai et al. [15] built a CSAH based on a linear flat Fresnel lens with an acceptance angle of ±2°, so active tracking is necessary. The high concentration ratio and the use of all-glass vacuum tubes reduce its heat loss rate to 0.578 W/m2/K. Perini et al. [16] conducted an experimental study and theoretical analysis of a two-axis tracking linear flat Fresnel lens solar collector system, and found that its thermal efficiency is less than 20%. This is because no vacuum tube is used, its absorber has low solar absorption rate and the flat Fresnel lens has large optical loss. To simplify the tracking process and reduce energy consumption of tracking system, Li et al. [6] proposed a novel semi-passive tracking CSAH consisting of prism arrays for redirecting light with large incidence angle, several flat Fresnel lenses and secondary reflectors, so that the whole device can remain stationary during the tracking process. However, using prism arrays also makes the structure complicated and reduces the light transmittance. All of the foregoing studies used the flat Fresnel lenses, whereas the curved Fresnel lenses have the better optical performance [17]. Cylindrical and cycloidal transmissive Fresnel concentrators are also used in PV/thermal collecting systems [18, 19], whose tolerable tracking errors are found to be no more than 1.5° and 0.5°, respectively. Generally speaking, it’s a major problem that the use of evacuated tubes and tracking systems increases the capital cost and maintenance cost, conversely, there will be a low collection temperature or a high heat loss rate without them. Thus, the authors presented an integrated concentrating solar air heater (ICSAH), using a curved Fresnel lens as both a concentrator and a cover, and a V-groove secondary reflector as the sidewall. By reducing the concentration ratio requirement and using a secondary reflector, there is no need to track. The closed cavity which formed between the absorber and the environment in the integrally enclosed device effectively reduces the convective heat loss even in the absence of vacuum tube. The performance of the ICSAH has been carried out by simulations and experiments.

2. Operation principle and structure Fig. 1(a) illustrates the schematic on a cross-sectional view of the proposed ICSAH. A 3m-long 3D model is shown in Fig. 1(b). The aperture of ICSAH is covered with curved Fresnel lenses. Some 4

Journal Pre-proof of the lights can be directly focused on the absorber by the Fresnel lens, and the others are projected to the secondary reflector, reflected to the absorber. The absorber is placed inside the glass tube which works as an air channel. The absorber captures the concentrated radiant energy and heats the air flowing along the glass tube. The outer surface of the curved Fresnel lens is a part of a cylindrical surface with a diameter of 1m. The curved Fresnel lens has the aperture width of 0.65m and the focal length of 0.95m. The geometrical concentration ratio is 10×. Its prism-profile is designed based on the principle of optimal transmittance [17]. The maximum, minimum and average thickness of the curved Fresnel lens are 7, 2.5 and 5mm, respectively. Both sides of the V-groove secondary reflector are flat mirrors, and the secondary concentrator is not the full length as can be seen in Fig. 1(a). This is because the standard width of reflective aluminum panels on the market is 500mm. It was chosen considering the concentrating requirements and cost of the secondary reflector. The angle between the two faces of the absorber is 60, and the distance from the upper edge of the absorber to the Fresnel lens is 0.765m. This distance was designed to be smaller than the focal length of the Fresnel lens to achieve a higher light reception rate of the device over the entire range of incident angles. Since light incident only from above, the lower part of the glass tube was insulated. Without extra piping, ICSAH can be flexibly assembled to any integer length. The other details of the components are shown in Table 1. Tilt sunlight

Fresnel lens

Secondary reflector Cavity

Glass tube Insulation

Absorber

(a)

(b) Fig. 1. Schematic of the ICSAH: (a) cross-sectional view, (b) 3D axonometric view.

Table 1 Components’ illustration of the ICSAH.

Component Fresnel lens Secondary reflector

Parameters Materials: Polycarbonate (Refractive index:1.59) Materials: Aluminum (Reflectivity: 0.92)

Glass tube

Diameter: 150mm/ Thickness: 3mm

Absorber

Materials: Aluminum with selective coating (TiOxNy/TiN)

Insulation

Materials: Polyurethane foam (Conductive coefficient: 0.02W·m-1·K-1)

5

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3. Optical simulation For this ICSAH, its optical performances were simulated using LightTools in which the structural parameters and optical properties of the components were set according to Table 1. The LightTools Illumination Module uses a Monte Carlo ray trace. In Monte Carlo ray tracing, scattering and diffraction are treated as random processes. The samples are randomly chosen, using the scattering distribution as a probability density. This allows the well-developed techniques of ray tracing to be used to model scattering [20]. Therefore, we do not have to consider the error caused by the software itself, but the error caused by these two factors: the difference between the imported model and the actual structure and the difference between the simulated light source and the actual sunlight. However, professional injection molding manufacturers have been able to effectively control the shape error of Fresnel lenses using mature technologies, so model structural differences are not considered in this paper. By separately setting a monochromatic parallel light source and a source considering the spectrum and sun angle and simulating based on the device, we found that the optical efficiency of the former is only 2-6% higher than that of the latter. Therefore, the effect of the sun angle and spectrum are negligible, too. Zenith

East

South

S2

Zenith



Collectors





S2

North South

 

S1



West

S1: Cross section S2: Lengthwise section

West

Fig. 2. Definition of the incidence angle α, .

As the device is placed along east-west direction facing the ground with a tilt angle δ, the projection of solar elevation angle relative to the lengthwise section (S2) of device in north-south plane is denoted by α, and the projection of solar azimuth in surface S2 is denoted by γ, as shown in Fig. 2. They can be calculated as follow: 𝛼 =𝜃 ―𝛿 (1) tan 𝛾 = cos 𝜃 ∙ tan 𝛾𝑠/cos (𝜃 ― 𝛿 )

{

Where θ is the projection of 𝛼𝑠 in north-south direction, tan 𝜃 = tan 𝛼𝑠 cos 𝛾𝑠, 𝛼𝑠 is the solar elevation angle, 𝛾𝑠 is the solar azimuth. Both α and γ may affect the optical performance. An increase in α will cause a shift in the focal spot, and an increase in γ will shorten the focal length and broaden the focal spot.

6

Journal Pre-proof 3.1. Design and optimization (1) The selection of the absorber position A change in γ causes the focal spot to move up and down, and an increase in α causes the focal spot to deviate from the center plane. So the selection of the absorber position is a necessary step in the designing process. Five distance (between the Fresnel lens and the receiver) were selected for simulation: 0.95m, 0.85m, 0.765m, 0.70m and 0.65m. A full-length plate was selected as the secondary reflector. A single column of non-sequential (NS) parallel rays was selected as the light source, and the number of rays was set to N=1000 after irrelevance analysis. The ratio of the rays received by the absorber to the rays that go through the Fresnel lens is defined as the light reception rate. The simulation results were shown in Fig. 3. As can be seen from Fig. 3(a), when γ is in the range of 055, the average light reception rate of the device significantly increases as the distance decreases. As can be seen from Fig. 3(b), when α is in the range of 012, the average light reception rate of the device increases first and then decreases with decreasing distance. In view of the low solar irradiance at sunrise and sunset, the device will mainly operate in the range of 0γ45， 0α10, in which, the absorber with the distance of 0.765m has the highest average light reception rate. Therefore, it is suitable to select the distance of the absorber to be 0.765m. 1.0

0.6 0.4 0.2 0

0-55°

H4 H3

0.9

H2

0.8 H1

10

H2

H3

H4

H1

H5

H2

0.8

Average Receiving Rate

0.8

0-45°

1.0

Light Receiving Rate

H5 Average Receiving Rate

Light Receiving Rate

1.0

0.6 0.4

1.0

0-10°

30

40

50

0

 /º

0-12°

H4 0.9

H5

0.8

H1 H1

0.2

20

2

H2

H3

4

H4

6

(b)

(a)

H3

H5

8

10

12

 /º

Fig. 3. Light receiving rate vs. incident angles. (H1H5: 0.95m, 0.85m, 0.765m, 0.70m, 0.65m)

(2) The selection of the secondary reflector Through the optical simulation analysis of several secondary reflectors with different shapes, the design direction of the secondary reflector combined with a curved Fresnel lens is obtained. Fig. 4(a) is the schematic drawing of several shapes of the secondary reflectors. Wherein No.01 are planar; No.24 are externally rotated CPC, paraboloid (y=ax2+b) and inverted paraboloid, respectively, which are outwardly convex; No.57 are tri-fold surfaces that are inwardly convex, and can be determined by three shape parameters (m, n, θ). Fig. 4(b) shows the light reception rate of the device when using the secondary reflectors of the different shapes described above. It can be seen from Fig. 4 that: 1) the light reception rates corresponding to the inwardly convex surfaces are significantly higher than that of the outwardly convex surfaces; 2) by adjusting the shape parameters of the tri-fold surfaces, the light reception rates can be significantly higher than that of the planar type at a large angle, but at a small to medium angle, the receiving rate is lower than that of the planar type. In summary, the planar secondary reflector is a suitable choice because of its high receiving rate and simple fabrication. 7

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Light Receiving Rate

1.0

 n

0.8 0.6

0

1

0.4

2

3

4

5

6

7

0.2

m

0 1

2

3

4

0

5-7

3

6

9

12

 /º

(b) (a) Fig. 4. The light receiving rate when using the secondary reflectors of different shapes.

The standard width of the aluminum sheet on the market is 500mm, which is equivalent to shortening the full-size aluminum sheet by 25%. The shorter aluminum sheet is marked as No.0 in Fig. 4(a). As can be seen from Fig. 4(b), the selection of a shorter planar secondary reflector only results in a slight decreasing in the light reception rate. It is calculated that when α is in the range of 010, the decrement is less than 4.5%, so it is reasonable to save the cost by selecting a standard size reflective aluminum sheet.

3.2. Acceptance angles The maximum values that α and γ can achieve when the light reception rate is kept larger than 90% are defined as the acceptance angles (αmax, γmax). Firstly, a simulation was performed when γ=0 and α was between 015. Then, setting α=0°, a simulation was performed on the case where γ varies between 060. Fig. 5 gives the curves of light reception rate against α and γ. The light reception rate starts to decrease after α9.5° or γ37.5°. When α=9.6°, the light reception rate is 90%, which means that one of the half acceptance angle αmax is 9.6°. It is not large enough so that the seasonal adjustment is necessary. For the same reason, the other acceptance angle γmax can be found to be 42.5 from Fig. 5. Considering that the irradiance intensity at sunrise and sunset is low, the γmax is large enough to ensure that the device has a long enough working hours in a day. Fig. 6 and Fig. 7 are the ray tracing results when α takes 9°, 9.7°, 10.5° and γ takes 15°, 30°, and 42.5°, respectively. In Fig. 7, the components that blocking the rays

Light Receiving Rate

tracing were hidden. 1.0 0.8



0.6



0.4 0.2 0

3

6

9

12

15  /º

12

24

36

48

60  /º

Fig. 5. Light reception rate against α, γ.

8

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Fig. 6. Ray tracing results when γ=0.

1

2

3 1Fresnel lens; 2Secondary reflector; 3Absorber Fig. 7. Ray tracing results when α=0.

3.3. Optical performance The optical efficiency of the ICSAH at different incident angles are needed for the calculation on heat transfer process. The optical efficiency of the in-use device depends primarily on the light incident angle. A single column of NS parallel rays was selected as the light source, and the number of rays was set to N=1000 after irrelevance analysis. The initial energy of each ray is unit 1. Then the optical efficiency of an infinitely long device can be calculated using Eq. (2): 𝑛 ∙ 𝑒1 (2) 𝜂𝑜𝑝 = 𝑁 Where n and e1 are the number and average energy of rays received by the absorber, respectively. According to the acceptance angle analysis in Section 3.2, the optical efficiency was simulated at α=0°12° and γ=0°60°. The optical efficiency contour map of an infinitely long device containing 551 data points is shown in Fig. 8. When the incident angle α=0° and γ (15°, 20°), the device achieves the highest optical efficiency of 0.77. And the optical efficiency remains greater than 0.13 at γ=60°. The optical efficiency is greater than 0.5 in most of the region where α and γ are less than 10° and 45°, respectively. In this region, the optical efficiency is fluctuating rather than simply decreasing with γ, mainly because the distance between the Fresnel lens and the absorber is designed to be less than the original focal length. For any α, there exists a γ equals to γc, which is defined as the critical value, that makes the optical efficiency maximal. As γ increases from 0 to γc, the focal spot gradually shrinks, and more light is directly focused on the absorber instead of being reflected by the secondary reflector first, thereby improving the optical efficiency. When γ continues to increase from γc, the spot begins to expand, and more and more light reaching the absorber needs to be reflected by the secondary reflector first, resulting in a decrease in optical efficiency. In addition, a low optical efficiency area distributes along the dashed line shown in Fig. 8. It has been found that a part of the lights is totally reflected by the inner wall of the glass tube, 9

Journal Pre-proof resulting in a significant reduction in optical efficiency. In all, as for the optical efficiency of larger than 0.5, the incident angles are roughly ranging in (α, γ) = (10°, 45°), which is coincident to the analysis on acceptance angle. 60

0.15

45

0.5

0.55

0.45

0.4

0.3

0.35

0.25

0.2

°

0.65

30

0.1

0.6

15

0.05

op= 0.75

0.7 0.65

0.6

0 0

3

6 °

9

12

Fig. 8. The optical efficiency contour map.

For an ICSAH with finite length L, there is a region of length ∆𝐿 = 0.765tan 𝛾 on its end, ∗ where the incident lights with angle of γ cannot reach. So the actual optical efficiency 𝜂𝑜𝑝 is: ∗ 𝜂𝑜𝑝 = 𝜂op ∙ (1 ― ∆𝐿/𝐿)

(3)

4. The steady-state heat transfer model 4.1. Energy balance equation An energy transfer graph of an ICSAH is shown in Fig. 9. The glass tube flow channel is separated by the absorber into channels with two different cross-sectional shapes (Ⅰ, Ⅱ). The absorber is the highest heat source (Tab) by absorbing sunlight, and transmits thermal energy to the air (𝑇𝑎𝑖𝑟, 𝑇'𝑎𝑖𝑟) and the glass tube (𝑇𝑔, 𝑇'𝑔) through convection (𝑄+𝑄') and infrared radiation (𝛷𝑎𝑏+ 𝛷'𝑎𝑏), respectively. A portion (𝑄𝑢) of the thermal energy absorbed by the air is used to raise the air temperature from Tin of the inlet to To of the outlet, and the other is transmitted to the glass tube by convection (𝑄𝑙+𝑄'𝑙). The main heat transfer process in an ICSAH can be described by the heat resistance diagram shown in Fig. 10. The heat transfer process is also divided into two paths, up and down, which are indicated in Fig. 10 by unfilled and gray filled rectangles, respectively. Upward, the glass tube dissipates heat to the in-cavity air (Tcav), secondary reflector (Tref) and Fresnel lens (TF) through both convection and radiation. And a convective heat transfer process also occurs between the in-cavity air and the secondary reflector, Fresnel lens. Downward, the glass tube (𝑇'𝑔) transfers heat to the insulation (𝑇'𝑖𝑛𝑠) through conduction. Finally, the device dissipates heat to the ambient (Tamb) through the secondary reflector, Fresnel lens and the insulation. 10

Journal Pre-proof The use of the heat resistance diagram to describe the heat transfer process is based on these assumptions that each component has a characteristic temperature which can represent its varying temperature in axial direction, that is to say its heat transfer flux is kept unchanged. Considering the small temperature difference between the outer surface of the device and ambient, it is reasonable to neglect the radiation compared to the convection. To simplify the calculation, the contact thermal resistance between the glass tube and the insulation is neglected. s

TF-

F

TF+ Tcav

 ref Tref

 g-

Tg

 g+ Q'

Ql

Tair

Q

Tab

 'ab  ab

Ⅰ

Q'l

T'air

 'g

Ⅰ

T'g T'ins+ T'ins-

Fig. 9. Energy transfer graph of an ICSAH.  g+

Rv1 Tair

Rv0

Qu R'v0 T'air

R'v1

Rd1

Tg+ Tab

 g-

Rv3 Rv2

Tg-

Rv4

Tcav

 ab+'ab

T'g+

R'd1

F

s

TF+ Tref+

Rd2 Rd3

Rv5 TFTref-

Tamb Rv6

 ref

T'g-=T'ins+ R'd2

T'ins-

R'v2

Tamb

'g+

Fig. 10. The heat resistance diagram of heat transfer process.

Under uniform heat flux condition of the receiver surface, the air mainstream temperature can be assumed to be linear. So the characteristic temperature of air is the average of air inlet and outlet temperature: 𝑇𝑎𝑖𝑟 = (𝑇𝑖𝑛 + 𝑇𝑜)/2

(4)

𝑇'𝑎𝑖𝑟 = (𝑇𝑖𝑛 + 𝑇'𝑜)/2

(5)

The energy balance equation for the receiver: ∗ 𝐺 ∙ 𝐴0 ∙ 𝜂𝑜𝑝 ― (𝑄 + 𝑄') ― (𝛷𝑎𝑏 + 𝛷'𝑎𝑏) = 0

𝑄= 𝑄' =

𝑇𝑎𝑏 ― 𝑇𝑎𝑖𝑟 𝑅𝑣0 𝑇𝑎𝑏 ― 𝑇'𝑎𝑖𝑟 𝑅'𝑣0

(6) (7) (8)

Where 𝐺 is the direct normal irradiance (W/m2), 𝐴0 is the aperture area of the heater (m2), 𝑄 and 11

Journal Pre-proof 𝑄' means the convective heat transfer flux from the receiver to the air (W), 𝛷𝑎𝑏 and 𝛷'𝑎𝑏 are the net radiant powers of the receiver surfaces (W), 𝑇𝑎𝑏 is the temperature of receiver (℃), 𝑅𝑣0 and 𝑅'𝑣0 are the convective thermal resistances between the receiver and air (K/W). Eq. (9)  (12) represents the conservation of energy for the air flowing through the absorber. 𝑄 ― 𝑄𝑙 ― 𝜌𝑖𝑛 ∙ 𝑢𝑖𝑛 ∙ 𝜑 ∙ 𝐴𝑐 ∙ (𝐶𝑝,𝑜 ∙ 𝑇𝑜 ― 𝐶𝑝,𝑖𝑛 ∙ 𝑇𝑖𝑛) = 0

(9)

𝑄' ― 𝑄'𝑙 ― 𝜌𝑖𝑛 ∙ 𝑢𝑖𝑛 ∙ (1 ― 𝜑) ∙ 𝐴𝑐 ∙ (𝐶'𝑝,𝑜 ∙ 𝑇'𝑜 ― 𝐶𝑝,𝑖𝑛 ∙ 𝑇𝑖𝑛) = 0

(10)

𝑄𝑙 = 𝑄'𝑙 =

𝑇𝑎𝑖𝑟 ― 𝑇𝑔 +

(11)

𝑅𝑣1 𝑇'𝑎𝑖𝑟 ― 𝑇'𝑔 +

(12)

𝑅'𝑣1

Where 𝑄𝑙 and 𝑄'𝑙 are the convective heat transfer flux between the air and the glass tube inner surface, ρ, u, Cp are the density, velocity and specific heat capacity of the air, respectively, 𝐴𝑐 is the cross-section area of the glass tube, 𝑇𝑔 + is the temperature of the glass tube inner surface. The ratio of the area of the channel I to 𝐴𝑐 is denoted as 𝜑. It’s easy to find out from geometric relationship that 𝜑 = 0.609. Considering the thin wall thickness of the glass tube and the large thermal conductivity of the aluminum reflector, their conductive heat resistance (𝑅𝑑1, 𝑅'𝑑1, 𝑅𝑑3) are negligible compared to the convective heat resistance. Therefore 𝑇𝑔 + = 𝑇𝑔 ― = 𝑇𝑔 , 𝑇'𝑔 + = 𝑇'𝑔 ― = 𝑇'𝑔 , 𝑇𝑟𝑒𝑓 + = 𝑇𝑟𝑒𝑓 ― = 𝑇𝑟𝑒𝑓. According to the thermal circuit diagram shown in Fig. 10, the remaining four independent heat transfer relationships are listed as follow: 𝑄𝑙 + 𝛷𝑔 + + 𝛷𝑠 = 𝑇𝑔 ― 𝑇𝑟𝑒𝑓 𝑅𝑣2 + 𝑅𝑣4 𝑇𝑔 ― 𝑇𝐹 + 𝑅𝑣2 + 𝑅𝑣3

𝑇𝐹 + ― 𝑇𝑎𝑚𝑏 𝑅𝑑2 + 𝑅𝑣5

+

𝑇𝑟𝑒𝑓 ― 𝑇𝑎𝑚𝑏 𝑅𝑣6

𝑇𝑟𝑒𝑓 ― 𝑇𝑎𝑚𝑏

+ 𝛷𝑟𝑒𝑓 =

𝑅𝑣6

+ 𝛷𝐹 + + 𝛷𝑠 =

𝑇𝐹 + ― 𝑇𝑎𝑚𝑏 𝑅𝑑2 + 𝑅𝑣5

𝑇'𝑔 ― 𝑇𝑎𝑚𝑏

𝑄'𝑙 + 𝛷'𝑔 + = 𝑅'

𝑑2

+ 𝑅'𝑣2

(3) (14) (15) (16)

Where 𝛷𝑔 + , 𝛷𝑟𝑒𝑓 and 𝛷𝐹 + are net radiant power on the inner surface of the glass tube, secondary reflector and Fresnel lens (W), respectively, 𝛷𝑠 is the solar radiant power absorbed by the Fresnel lens (W). To simplify the analysis of radiative heat transfer, the following three assumptions were adopted: 1) in the infrared band, all surfaces of the absorber, glass tube, Fresnel lens and reflector are considered to be diffuse-gray surfaces; 2) infrared radiation cannot pass through the glass tube and the Fresnel lens made of Polycarbonate; 3) the effect of air on radiative heat transfer can be neglect. The following two equations present the radiative heat transfer relationships between the absorber and the glass tube inner surface: 𝐸𝑎𝑏 ― 𝐸𝑔 𝛷𝑔 + = 𝛷𝑎𝑏 = 1 ― 𝜀𝑎𝑏 1 ― 𝜀𝑔 1 + + 𝐴𝑎𝑏 ∙ 𝜀𝑎𝑏 𝐴𝑎𝑏 ∙ 𝑋𝑎𝑏 ― 𝑔 (1/3)𝐴𝑔 ∙ 𝜀𝑔

12

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𝛷'𝑔 + = 𝛷'𝑎𝑏 =

𝐸𝑎𝑏 ― 𝐸'𝑔 1 ― 𝜀𝑎𝑏 𝐴𝑎𝑏 ∙ 𝜀𝑎𝑏

+

1 𝐴𝑎𝑏 ∙ 𝑋'𝑎𝑏 ― 𝑔

+

1 ― 𝜀𝑔 (2/3)𝐴𝑔 ∙ 𝜀𝑔

Where 𝐸 and ε are the radiation power (W/m2) and emissivity on the corresponding surface, respectively, 𝑋𝑎𝑏 ― 𝑔 (𝑋'𝑎𝑏 ― 𝑔) is the angle factor between the absorber’s upper (lower) surface and the glass tube. The parameters 𝐸, ε, A and X are determined by the structure and material of the device. After substituting known parameters into the above two equations, simplified forms are obtained as follow: 𝛷𝑔 + = 𝛷𝑎𝑏 = 0.1042 ∙ 10 ―8 ∙ (𝑇4𝑎𝑏 ― 𝑇4𝑔) ∙ 𝐿 4

𝛷'𝑔 + = 𝛷'𝑎𝑏 = 0.1129 ∙ 10 ―8 ∙ (𝑇4𝑎𝑏 ― 𝑇'𝑔

)∙𝐿

(17) (18)

Where L is the length of the collector. According to Radiation thermal circuit diagram shown in Fig. 11, similarly with Eq. (17) 18), simplified Eq. (19) (21) present the radiative heat transfer relationships between the glass tube outer surface, Fresnel lens and the reflector. 1 ― 𝜀𝑔

1 ― 𝜀𝐹

1 𝐴 𝐹 ∙ 𝑋𝐹 ― 𝑔

(1/3)𝐴𝑔 ∙ 𝜀𝑔

𝐴 𝐹 ∙ 𝜀𝐹 EF

Eg-

1 𝐴𝐹 ∙ 𝑋𝐹 ― 𝑟𝑒𝑓

1 𝐴𝑟𝑒𝑓 ∙ 𝑋𝑟𝑒𝑓 ― 𝑔

1 ― 𝜀𝑟𝑒𝑓 𝐴𝑟𝑒𝑓 ∙ 𝜀𝑟𝑒𝑓 E ref

Fig. 11. Radiation thermal circuit diagram between the glass tube, Fresnel lens and reflector.

𝛷𝑔 ― = (0.6739 ∙ 𝑇4𝑔 ― 0.6387 ∙ 𝑇4𝐹 + ― 0.0351 ∙ 𝑇4𝑟𝑒𝑓) ∙ 10 ―8 ∙ 𝐿

(19)

𝛷𝐹 = (0.6385 ∙ 𝑇4𝑔 ― 0.849 ∙ 𝑇4𝐹 + + 0.2104 ∙ 𝑇4𝑟𝑒𝑓) ∙ 10 ―8 ∙ 𝐿

(20)

𝛷𝑟𝑒𝑓 = 𝛷𝑔 ― ― 𝛷𝐹

(21)

4.2. Convective heat transfer coefficients Calculations of convective heat transfer coefficient were done basically according to [21]. Convective heat transfer that occurs in the area between the absorber and glass tube was considered to be internal forced convection. However, both the upper and lower flow channels’ cross-sections are non-circular, with hydraulic diameters of 𝑑ℎ = 1.377𝑟, 𝑑ℎ' = 0.642𝑟, respectively. Here, r is inner radius of the glass tube. When air inlet velocity is in the range of 110m/s, the Reynolds numbers of the upper and lower parts can be roughly estimated that 2800 ≤ 𝑅𝑒𝑑ℎ ≤ 28000 and 6000 ≤ 𝑅𝑒'𝑑ℎ ≤ 60000, involving two kinds of flow regimes: transitional flow and turbulent flow. Eq. (22) that taken from [22] applies to convective heat transfer in smooth tubes including transitional and turbulent zones: 13

Journal Pre-proof

𝑁𝑢 =

(𝑓/8) ∙ (𝑅𝑒 ― 1000) ∙ 𝑃𝑟 1 + 12.7(𝑓/8)0.5 ∙ (𝑃𝑟2/3 ― 1)

2/3

( ( ) )( )

∙ 1+

𝑑ℎ

∙

𝐿

𝑇𝑎𝑖𝑟

0.45

𝑇𝑤

(22)

𝑓 = (1.82 ∙ lg𝑅𝑒 ― 1.64) ―2 , 2300 ≲ 𝑅𝑒 ≲ 106 Where f is the friction factor, 𝑇𝑤 is the wall temperature of flow channel. When calculating the heat transfer coefficient between the air and the absorber, 𝑇𝑤 = 𝑇𝑎𝑏. When calculating the heat transfer coefficient between the air and the glass tube, 𝑇𝑤 = 𝑇𝑔 𝑜𝑟 𝑇'𝑔. Due to the non-circular cross-section of flow channel, friction factor f needs to be modified [23]: ∗

𝑘

(

𝑓 =𝑓∙ 1―

)

∑𝑖 = 1(𝜋 ― 𝜃𝑖)2.5 𝑅𝑒0.62 𝑑ℎ

(23)

Where k is the number of angles in the section of flow channel, 𝜃𝑖 is the radian of the ith angle as can be seen in Fig. 12. Then, modified 𝑓 ∗ is used to replace the f in Eq. (22). Channel type Ⅰ

1

2

Channel type Ⅰ

 '1

Glass tube

 '2  3

Absorber

Fig. 12. Non-circular cross-section air flow channels.

The heat transfer between in-cavity air and its surroundings is considered as natural convective heat transfer in a large space. As working in the region of 40 north latitude, the device is facing the ground with a small tilt angle. So the experimental correlation of natural convection on the vertical wall is adopted to approximate the heat transfer process between in-cavity air and the outer surface of glass tube, in which the wall height is characteristic size, 𝐻𝑔 = 0.13 m. It’s the same when describing the heat transfer process between in-cavity air and Fresnel lens inner surface, whose characteristic size is 𝐻𝐹 = 0.65 m. As for the two sides of the secondary reflector, they are treated as flat plates with their cold faces inclined downward and horizontally upward, respectively. The convective heat transfers between the outer surfaces of the device and the surroundings is highly dependent on specific weather conditions. Fortunately, considering its slight influence on the entire heat transfer process, an average ambient wind speed (e.g. 1.5m/s) can be taken to calculate the Nu numbers in two extreme cases of the wind lateral flowing around or longitudinal sweeping the outer surfaces of the device, and then their average value is used.

5. Experiments and error analysis The preliminary experiment was conducted in August 2017, Beijing (116.3° E, 39.9° N), and a 3m-long ICSAH was tested to analyze the effects of different α, γ angles and air flow rate on the thermal performance. Air flows through the glass tube in an open loop. The absorber with a length of 1.9m was placed in the middle of the glass tube. The schematic diagram of testing system and the main information of the measuring instruments used therein are shown in Fig. 13 and listed in 14

Journal Pre-proof Table 2, respectively. The temperature probes were placed in the center of the glass tube at both ends of the absorber to measure the inlet and outlet air temperatures, and to basically avoid the influence of radiation from the absorber. The air velocity probe was placed at the outlet of the collector and in the center of the flow channel. The pyranometer was placed parallel to the lightincident surface of the concentrator. The incidence angle of the light was manually adjusted by a simple mechanical device. The blower with a rated power of 330W and a rated flow of 11m3/min was controlled by the frequency modulator to achieve different air flow rates. All the experimental data were recorded after the device reached a stable state. In the further experiment, we tested the thermal performance of the ICSAH throughout the day. An experimental system combined with greenhouse soil heat storage was built, and two rows of 41m-long ICSAH were used in parallel as collectors. The greenhouse area is 660m2. The air is heated by the ICSAH, then sent to the greenhouse soil through a pipe submerged under the soil. Finally the cooled air returns to the ICSAH, forming a closed loop. The 41m-long ICSAH was fixed on the ground in the east-west orientation and facing the ground with a tilt angle of 30. The air flow rate is not changed during the experiment. Two blowers were used in series but no frequency modulator was used, and the measuring instruments were identical to that shown in Fig. 13. The image of this experimental set-up is shown in Fig. 14. The experiment was conducted in Beijing on November 14, 2017 from 9:00 to 15:45. The thermal collection efficiency ηt for the ICSAH is 𝜂𝑡 =

𝜌𝑜𝑢𝑜𝐴𝑐 ∙ 𝐶𝑝(𝑇𝑜 ― 𝑇𝑖𝑛)

(24)

𝐺𝐴0

During the experiment, repeated measurements of experimental data were achieved by simultaneous measurement of multiple probes at the same measuring point and continuous measurement over a short period of time. According to the theory of experimental error, the error of the indirectly measured data is ∆𝑦 = ∑

∂𝑦 2 2 𝑥𝑖 ∂𝑥𝑖

( )∆

(25)

Where 𝑥𝑖 is the directly measured data, y is a function of 𝑥𝑖 and ∆𝑥𝑖 is the error of direct measurement. The relative error is 𝛿𝑦 =± ∆𝑦/𝑦. So the thermal efficiency uncertainty propagation terms are presented by Eq. (26), 𝛿𝜂𝑡 𝜂𝑡

2

∂𝜂𝑡 2

∂𝜂𝑡 2

( ) ∆ +( ) ∆ +2∙( ) ∆ ∂𝜂𝑡 ∂𝑢𝑜

2 𝑢𝑜

∂𝐺

=±

𝜂𝑡

2 𝐺

∂𝑇

2 𝑇

(26)

In the preliminary experiment， the minimum air flow rate was 1.0m/s, and the corresponding average solar radiation, inlet and outlet air temperature were 878 W/m2, 34.3 and 57.6 ℃, respectively. Substituting above measured data and error of measuring instruments into Eq. (26), the maximum relative error is 31.0%. When 𝑢𝑜 ≥ 3m/s, the relative error will not exceed 16%. In the further experiment, the maximum relative error of the instantaneous thermal efficiency is 15.4%.

15

Journal Pre-proof Direct solar radiation meter with tracker Sun light

Data logger

Pyranometer

Air

L=3m

Frequency modulator

Blower T 1, T 2

Flow channel

T 3, T 4 uo

Absorber

Temperature data recorder

Temperature and velocity probe layout

Hot-wire Anemometer

Fig. 13. The schematic diagram of testing system.

Fig. 14. The system combined with soil heat storage. Table 2 Measuring instruments and uncertainly errors. Instrument

Range

Accuracy

Uncertainty

Pyranometer/TBQ-2

02000W/m2

1 W/m2

±3%

Direct Solar Radiation Meter/TBS-2-2

02000W/m2

1 W/m2

±3%

K type Thermocouple/WRNT-01

0300℃

0.1℃

±0.5℃

Hot-wire Anemometer/AR866A

030m/s

0.1m/s

±1%

16

Journal Pre-proof

6. Results and discussion 6.1. The effects of the major factors on thermal performance (1) The effects of incident angles Fig. 15 shows the test results at different angle α when γ=0 and 30. The outlet air velocity was adjusted around 6.0 m/s. Each point on these curves is the average of test data during 16min. As can be seen from Fig. 15(a), solar irradiance G was basically stable and located in 940-990 W/m2. The outlet and inlet air temperature differentials at α=0 and α=11 were 6.7℃ and 3.2℃, respectively. In Fig. 15(b), G varies between 908 W/m2 and 989 W/m2, and the outlet and inlet air temperature differentials at α=0 and α=11 were 6.6℃ and 2.9℃, respectively. Fig. 15 indicates that the effect of angle α on the temperature differential is not significant when α 5 and the temperature differential decreases gradually when α 5.

42

700 550 400

36 30 3

6

9

48 42

700 550

36

400

30

250 0

850 G To Tin

250 0

12

2

54

1000 Irradiance/ W/m

48

850

Temperature/ ºC

G To Tin

60 2

54

1000 Irradiance/ W/m

Temperature/ ºC

60

3

6

9

12

/ º

/ °

(b) γ=30

(a) γ=0

Fig. 15. The outlet and inlet air temperature against α under a basically stable solar irradiance.

Fig. 16 shows a comparison of the calculated thermal efficiency and the experimental thermal efficiency at different α when γ is taken as 0° and 30°, respectively. As can be seen from Fig. 16, the change of γ from 0° to 30° has no obvious effect on the thermal efficiency. For example, when α=

Thermal Efficiency

0, thermal efficiency at γ= 30 is 0.60 and only 4.6% lower than the thermal efficiency at γ= 0. The ICSAH maintains high thermal efficiency until α reaches 5, and then its thermal efficiency decreases dramatically. When α= 11, the thermal efficiency drops below 0.30. As a consequence, α should be kept smaller than the acceptance angle αmax to get a good operation performance. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

calculation ( calculation ( experiment ( experiment ( 0

3

6

9

12

  Fig. 16. Thermal efficiency at different incident angles.

By comparison, it turns out that both calculated and experimental values are in a high level when α 5, and the former are about 519% higher. The calculated results at γ=30 and γ=0 show 17

Journal Pre-proof a significant decrease after α reaches 5° and 9°, respectively, and decrease faster than the experimental values. As a result, the calculated values at γ= 30 and γ= 0 are smaller than the experimental values when α 6 and α 10.5°, respectively. This is because when the incident angle is small, the absorber has a high reception rate of direct radiation, and neglecting the scattered radiation in the calculation has little influence on the thermal collection efficiency. As the incident angle increases, the reception rate of absorber to the direct radiation decreases, and the effect of scattered radiation is gradually enhanced. Therefore, at large incident angles, if the scattered radiation is ignored in the calculation, the calculated thermal efficiency is significantly lower than the experimental value. (2) The effect of air flow rate The test was performed at different air flow rates when α= γ= 0. The outlet and inlet air temperatures at different air flow rates are illustrated in Fig. 17, each point on these curves is the average of test data during 10min. Fig. 17 shows that the outlet and inlet temperature differential

1000

54

850

48

700

G To Tin

42

550

36

400

30

2

60

Irradiance/ W/m

Temperature/ ºC

decreases with the increase of air flow rate when G was 875960 W/m2. The temperature differential reaches 23.0℃ at air flow rate of 1.0 kg/min, indicating that the ICSAH has the potential to deliver high temperature thermal energy.

250 1

2

3

4

5

6

Air Flow Rate/ kg/min

Fig. 17. The outlet and inlet air temperatures against air flow rate under a basically stable solar irradiance.

Fig. 18 shows a comparison between the calculated thermal efficiency and the experimental thermal efficiency at different air flow rates. It indicates that the low air flow rate will lead to the low thermal efficiency. For instance, the thermal efficiency is less than 40% at the air flow rate of 1.0 kg/min. When the air flow rate increases, the operation temperature of the device will decrease, reducing heat loss, and accordingly improving the thermal efficiency. This comparison indicates that the calculated and experimental values have the same tendency and their deviation gradually decrease with the increase of the air flow rate. For example, when the air flow rate is 1.0 kg/min, the calculated value is 50% higher than the experimental value, and when the air flow rate is 6.5kg/min, the deviation falls to 12%. The large deviation at low air flow rate is mainly ascribed that the air velocity is low and the radiative heat transfer accounts for a large proportion of the total heat transfer. Besides, low air velocity increases the relative error of the air velocity measurement. The higher the proportion is, the more the deviation is affected by the assumptions about radiation. The deviation is mainly due to our assumption that the emissivity of selective coating is constant. Wang et al. [10] found that the emissivity of their selective coating increased significantly with the increasing temperature, and the emissivity at 120 °C was 62% higher than that at 20 °C.

18

Thermal Efficiency

Journal Pre-proof 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

calculation experiment

1

2

3

4

5

6

Air Flow Rate/ kg/min

Fig. 18. The thermal efficiency at different air flow rate.

6.2. Test results of the full-scale ICSAH with a fixed angle For the ICSAH with a tilt angle of 30, the variation in sunlight incident angle (α and γ) curves during the test period in the day is shown in Fig. 19. Before 10 o’clock (or after 14 o'clock), α rapidly decreases with time to less than 2 (or rapidly increases to more than 12); γ decreases first and then increases once after 12 o’clock, and basically changes linearly. From 10 to 14 o’clock, α and γ are less than 2 and 30, respectively. According to Fig. 8, the optical efficiency at this time is greater than 0.7. The ambient temperature is between 7℃ and 9℃ during the experiment. The global solar radiation on the aperture surface, air velocity and inlet/outlet air temperature profiles over time are shown in Fig. 20. It shows that the global solar radiation increases considerably in the morning, then remains above 950 W/m2 from 10:30 to 13:30, and drops rapidly after 14:00. The total solar radiation incidents on a single row of the ICASH throughout the day (9:00-15:45) is 553.1MJ. The air velocity decreases (or increases) slightly as the temperature increases (or decreases) and varies between 8.8 and 9.2 m/s. The inlet air temperature (Tin) is basically stable and ranges from 11℃ to 17℃, indicating that the heat transfer between air and soil is adequate. Under the assumption of constant heating power and adequate heat transfer, higher collection temperature means lower air flow rate and fan power requirement, therefore greatly reduces energy consumption during longterm operation. As shown in Fig. 20, the outlet air temperature (To) is much higher than that at the inlet. From 9:45 to 14:15, To stays above 100°C for 4.5h and reaches the maximum value of 125°C, and the maximum temperature differential (To- Tin) reaches 108°C, indicating the considerably good heating performance of ICSAH in winter. With 6.5 working hours per day, a single row of ICSAH supplies a total of 292.2MJ of heat to the soil, and the electric power consumed by the blowers is 15.4MJ. The daily efficiency is calculated to be 0.53 by Eq. (27). ∑𝜂𝑡 ∙ ∆𝑡

𝜂𝑡,𝑑𝑎𝑦 = working hours per day

Where ηt is the thermal collection efficiency, Δt is the interval of data logging (hr.).

19

(27)

Journal Pre-proof

9

 

60

 

45

6

30

3

15

0 8:00 2017-11-14

10:00

12:00

14:00

 

12

0 16:00

Beijing time/ hh:mm

9

130

900

8

110

800

90

700

Solar irradiation Air velocity To Tin

70 50

600 500

7 6 5 4

30

400

3

10

300

2

9:00 10:00 2017-11-14

11:00

12:00

13:00

14:00

Air velocity/ m/s

1000

2

150

Irradiance/ W/m

Temperature/ ºC

Fig. 19. The variation in α and γ curves during the test period.

15:00

Beijing time/ hh:mm

Fig. 20. Global solar radiation, air velocity and inlet/outlet air temperature curves over time.

The curves of simulated optical efficiency, calculated thermal efficiency, and experimental thermal efficiency over time are shown in Fig. 21. The optical efficiency is obtained by interpolation using the data from Fig. 8 and Fig. 19. It can be found that the variation of the optical efficiency in Fig. 21 during the noon time period is consistent with the change of the collection temperature in Fig. 20. The experimental thermal efficiency is higher than the optical efficiency before 9:30 or after 14:45.This is because when the fan was started at 9 o’clock, the device had absorbed amount of solar energy. Then, the stored solar energy gradually released, resulting in a higher measured thermal efficiency. Furthermore, the reception rate of absorber to direct solar radiation is lower and the scattered radiation plays an important role before 9:30 or after 14:45, however, the contribution of the scattered radiation is ignored in the optical simulation. Since the calculation model was built for steady-state study, the experimental thermal efficiency and calculated thermal efficiency from 10:15 to 14:00 when the product of solar irradiance and optical efficiency varied less than 10% were compared in Fig. 21. The deviation between them is less than 10%.

20

Journal Pre-proof 0.9

 op *

0.8

Efficiency

0.7

t_cal

0.6 0.5

t_exp

0.4 0.3 0.2 9:00 2017-11-14

10:00

11:00

12:00

13:00

14:00

15:00

Beijing time/ hh:mm

Fig. 21. Optical and thermal efficiency profiles for the 41m-long ICSAH.

In Fig. 20, the weather conditions at noon are basically stable and the device is considered to be in a steady state. Under the same condition (DNI=944W/m2, air flow rate=8.1kg/min, Tin=15℃, Tamb=8℃), the outlet temperature of the ICSAH at different lengths was calculated and displayed in Fig. 22. As can be seen, the calculated outlet air temperature at a length of 41m is 127℃. The deviation between it and the experimental result is less than 8%, which further verifies that the heat transfer calculation model can be accepted at high air flow rate. In brief, the comparative analysis of the experimental and calculated results reveal that when the air flow rate is small or α and γ are large, the calculated results differ greatly from the experimental results, however, when air flow rate is large (e.g. 6.5kg/min) and α and γ are less than 5 and 35, respectively, the heat transfer calculation model is acceptable. Based on the calculation model, the performance rating of the 41m-long ICSAH at α=γ=0 is represented using a best fit linear efficiency curve against (TairTamb)/G as displayed in Fig. 23. It shows that the 41m-long ICSAH attains an optical efficiency of 0.76, and its heat loss rate is 1.758 W∙m-2∙K-1. 0.8

Tin=15 ºC

140

Thermal Efficiency

Outlet Temperature/ ºC

160 120 100 80 60 40 20 8

16

24

32

40

48

calculated value

0.6 0.5 0.4 0.00

56

y= -1.7578x+0.7581 2

R = 0.9981 0.04

0.08

0.12

0.16

0.20

(Tair-Tamb)/G

Length of ICSAH/ m

Fig. 22. The outlet air temperature at different

0.7

Fig. 23. Thermal efficiency for a 41m-long ICSAH.

length.

6.3. Techno-economics comparison with other CSAHs This part compares the ICSAH with other CSAHs in terms of thermal performance and capital cost per collection surface area (CCPA). Table 3 shows the component cost of the ICSAH, which is estimated based on the bulk purchases price. The tracking requirements, capital cost and thermal performance of different CSAHs are listed in Table 4, and a conventional flat plate collector (FPC, ref. [24]) is added as a baseline. The listed capital cost includes only the cost of the solar collectors, 21

Journal Pre-proof excluding the fan cost and labor cost for installation. The use of heat pipe evacuated tubes (ref. [8]) and complex tracking structures (ref. [6]) results in a significant increase in CCPA, which is 6 and 10 times that of the FPC, respectively. CCPA in ref. [9] that uses all-glass vacuum tubes is only 2.8 times that of the FPC, but its heat loss rate is much higher than that in ref. [8]. The heat loss rate in ref. [15] that combines an all-glass vacuum tube with a high concentration ratio flat Fresnel lens is small, but the use of tracking system makes the CCPA 3.5 times that of the FPC, and its optical efficiency is low. In this paper, curved Fresnel lenses with better optical properties are used, which are combined with secondary concentrators to avoid tracking demands. In this paper, curved Fresnel lenses with better optical properties are used, which are combined with secondary concentrators to avoid tracking. Furthermore, the ICSAH is integrally enclosed and the lower half of the receiver is well insulated. Therefore, a lower heat loss rate, which is less than 1/6 that of the FPC is obtained in this paper at a CCPA less than twice that of the FPC. Table 3 Details of the cost (material and fabrication cost) of the ICSAH. Item

Quantity

Approx. cost (CNY/m2)

Curved Fresnel lenses

41 × 0.65 × 1 m2

284.62

41 m

407.13

Glass tube

41 m

153.85

Absorber with selective coating

41 m

76.92

Steel framework, insulation and reflective aluminum plate

Total cost

922.52

Table 4 The comparison between the ICSAH and other CSAHs in terms of thermal performance and capital cost. Capital cost

Heat loss rate

Optical

(CNY/m2)

(W∙m-2∙K-1)

efficiency

No

3096.37a

1.197

0.6618

No

1398.75a

4.420b

0.7616b

Active single-axis

1763.31a

0.578

0.5690

5012.92

0.550c

0.78c

502.32

10.5-12.6

0.84-0.88

922.52

1.758c

0.7581c

Refs.

Tracking demand

Nkwetta et al. [8] Wang et al. [9] Zhai et al. [15] Li et al. [6] Gill et al. [24] This paper

Semi-passive single-axis No No

*Conversion rate USD to CNY, Oct 2019 (1 USD=7.081 CNY). a

It was estimated based on the characteristics of the solar collectors given in these refs. and the real-time market

prices of different materials (the heat pipe evacuated tube in ref. 8, 400 CNY each; tracking and control system in ref. 15, 800 CNY). b

We obtained this fitting result based on the experimental data given in the reference.

c

It is a calculated value based on a theoretical model.

7. Conclusions In this paper, we designed and investigated a novel ICSAH. An optical simulative analysis 22

Journal Pre-proof based on LightTools was processed and the heat transfer calculation model was established. In addition, an experiment was carried out to investigate its thermal performance and validate the simulation and calculation. The main conclusions are listed below: 1) The ICSAH has the acceptance angles of 9.6° in north-south and 42.5° in east-west, which can work about 6.5 hours a day with a seasonal adjustment. Its maximum optical efficiency was simulated to be 0.77. 2) The maximum temperature differential of the full-scale ICSAH reached 108°C at air flow rate of 8.1 kg/min. A total of 292.2MJ of heat is supplied to the soil by the ICSAH, whose daily thermal efficiency is found 0.53. 3)

4)

The calculation model is found acceptable at large air flow rates (e.g. 6.5 kg/min) and low incident angles (α5, γ35), which covers most of the operating conditions. The calculation results illustrate that the heat loss rate of the ICSAH is 1.758 W∙m-2∙K-1. The ICSAH has higher optical efficiency and lower heat loss rate at a lower CCPA of ￥922.52.

Acknowledgement This work is supported by the National High-tech Research and Development Program “863” of China (No. 2013AA102407-2).

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Conflict of Interest Statement of Interest This paper is submitted to the international journal, Energy. We declare that we have no actual or potential conflict of interest including any financial, personal or other relationships with other people or organizations within three years of beginning the submitted work that could inappropriately influence, or be perceived to influence their work.

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Highlights An integrated concentrating solar air heater (ICSAH) was designed and investigated; An optical efficiency contour map was given to reflect the performance of the ICSAH; The ICSAH can provide higher than 100℃ heated air in winter without tracking; The ICSAH has lower heat loss rate of 1.758 W/m2/K at a low cost of 922.52 CNY/m2.