Highly Concentrated Solar Flux of Large Fresnel Lens Using CCD Camera-Based Method

Abstract

Fresnel lens is a kind of lens that can concentrate sunlight up to a level of thousands of suns with small space occupation which is widely used in the research of sunlight concentration and transmission systems via optical fiber. Most studies on the concentrated flux of lenses use experimental methods to measure the flux distribution on the receiver of parabolic trough solar concentrators, solar power towers, and parabolic dish concentrators, while for Fresnel lenses, especially large-aperture Fresnel lenses such as the one in this manuscript, the simulation approach was mostly used. In response to this problem, this study has developed an experimental system for measuring the concentrated flux density of Fresnel lenses. A charge-coupled device (CCD) camera was used to capture the image of spot of large-aperture (968 mm) Fresnel lenses in the CCD camera-based method, and a heat flow meter was used to calibrate the spot brightness image obtained by the CCD camera. Experimental data show that the peak flux of concentrated spot can reach 4.06 MW/m². This method confirms the simulation results of previous studies that using the rays tracing method, that is, the flux level of the Fresnel lenses can reach 5000 suns. The experimental results demonstrated the CCD camera-based method combined with a heat flow meter is competent in measuring the intensity of flux with a level of 5000 suns.

1. Introduction

Solar energy, as one of the renewable energy sources, is ubiquitous. However, the density of solar energy is low for applications requiring high power density such as photovoltaic/thermal (PVT) collectors, about 1 kW/m². Concentrated solar systems can produce high flux levels which use parabolic dish solar concentrators [1,2], convex lenses, and Fresnel lenses. Parabolic dish solar concentrators [3,4,5] are often combined with Stirling engines for power generation [6]. The concentrated solar radiation at the receiver is absorbed by the working fluid, liquid, or gas, raising its temperature to 120 to 1500 °C. The working fluid temperature inside a commercial solar power tower absorber can be as high as 565 °C, while experimentally proven values are in the range of 1000 °C [2,7]. Convex lenses and Fresnel lenses are commonly used in concentrating photovoltaic systems and daylighting systems [8]. With the Fresnel lenses reaching multiple thousand suns [9,10,11] and a high concentrator with 5800 suns, geometrical concentration ratio based on multiple primary Fresnel lenses was proposed in 2018 [12]. Benefiting from the advantages of lightweight and small space occupation [13,14], the diameter of Fresnel lenses can reach up to 1 m, which can produce a concentrated flux with the level of 5000 suns, and can reach over 1500 °C when the solar irradiation is a high level. They are also widely used in applications where high flux are required [15,16].

Due to the uneven flux distribution of solar disk and circumsolar and the unique optical structure of the Fresnel lens [14,17], the concentrated flux density distribution of the Fresnel lens is uneven and peaks at the center [18]. The concentrated spot of the Fresnel lens has a high temperature gradient due to local hot spots resulting in severe temperature stresses that have a strong destructive effect on the receiver [19,20]. Therefore, measuring the intensity of flux density of the concentrated spot in high-concentrated systems is significant for optical design and safety research of receivers in concentrated systems [21].

Traditionally, the measurement methods of high flux include the heat flow meter method and CCD camera-based method. There are also novel flux measurement methods, such as the one proposed in 2013, that attached the Dielectric tapers of the circular cross-section to the optical fibers, which were used as secondary optics to ease the coupling of light into the fiber [22]. In the heat flow meter method, the thermopile principle converts concentrated solar flux into a voltage signal. Generally, the water-cooling approach is adopted to protect the heat flow meter. The heat flow meter method has been applied in the measurement of flux density in solar thermal power tower systems [23,24]. Because of the limited heat resistance of the material, the upper limit of the heat flow meter is 3000 suns. The intensity of the concentrated flux produced by the Fresnel lens can exceed 5000 suns, beyond the range of the heat flow meter. Another disadvantage of the heat flow meter is that its capacity of spatial resolution is low and cannot be used for accurate measurement of the flux intensity of the millimeter-scale spot [25]. Typically, CCD cameras are used to observe the distribution of high flux on the receiver [26,27]. Two other methods are used as simulations to simulate the flux distribution at the receiver to aid in the verification of the measurements [28], namely Monte Carlo ray tracing (MCRT) [29,30,31] and the analytical approach. During the process of measurement, the Lambertian target is used as the receiver. The Lambertian target has a characteristic of isotropic uniform diffuse reflectivity; therefore, there is a proportional relationship between the brightness and the intensity of the flux density. The flux density distribution of the concentrated spot can be obtained by calibrating the CCD image of the Lambertian target according to the value of a heat flow meter. The CCD camera-based method and the heat flow meter method have been widely used in parabolic trough collectors [32], solar power tower plants [33], dish-type solar concentrating systems [34], and solar simulators [35,36]. However, studies of flux measurements of the concentrated flux of lenses are rare. The reason is that the size of the focus spot of the general size lens is only millimeter, too small to match the receiver end of the heat flow meter, and its concentration intensity exceeds 5000 suns, greatly exceeding the measurement range of the heat flow meter. Without calibration of a heat flow meter, the CCD camera-based method cannot be used alone.

Accurate measurement of the true flux density distribution of the Fresnel lens is important [37]. For example, in order to study the thermal load distribution of optical fiber and filters in sunlight concentration and transmission systems via optical fiber [38], it is necessary to obtain the flux density distribution of the concentrated spot of the Fresnel lens.

The purpose of this study is to achieve the flux density distribution of the Fresnel lens spot. This study adopted a large-aperture (968 mm in diameter) Fresnel lens that the concentrated spot diameter can reach about 15 mm. In this study, the concentrated spot is furtherly expanded and homogenized using a homogenizer to match the heat flow meter. The flux density distribution and total flux after the beam expansion are measured to calibrate the CCD image, and then the true flux density distribution of the Fresnel lens concentrated spot is obtained.

2. System Configuration

2.1. Instruments

The experimental system consisted of a two-axis rotating platform, a concentrated system, and a measurement system. The two-axis rotating platform can be manually adjusted to track the solar in azimuth and altitude angles, as shown in Figure 1. The concentrated system consisted of a Fresnel lens with a diameter of 968 mm, 32 pieces of scalloped shelters, and a quartz-glass homogenizer. The measurement system consisted of a heat flow meter, a Lambertian target as a receiver, and a CCD camera for capturing the brightness images of the spot. The Fresnel lens was equipped with 32 shelters. By changing the number and location of the shelters, the effective lighting area ratios of 1/32, 1/16, 1/8, 1/4, 1/2, and 1 can be achieved to provide energy flow of different intensity levels for the heat flow meter and CCD image detection.

In the CCD images capture experiment, a quartz-fiber board of 100 mm × 100 mm in area was used as the Lambertian target. The color of the quartz-fiber board was white and it had an excellent isotropic of diffuse reflection. Quartz-fiber board can also work under high temperatures, as shown in Figure 2. In this study, the quartz board was used as a receiver, placed at the focal plane of the lens, and its surface is vertical to the optical axis. A CCD camera facing the receiver was installed at the center of the lens for taking images of the concentrated spot on the receiver, as shown in Figure 3a. Figure 3b shows the CCD camera. To avoid overexposure, a neutral filter was added in front of the CCD camera lens.

In the measurement process of the heat flow meter, the HT-50-20 heat flow meter, the water-cooling system, and a quartz-glass rod with a diameter of 20 mm and a length of 200 mm were adopted. The heat flow meter converts the heat signal into a voltage signal. Inside the quartz-glass rod, the incident light was transmitted to the receiving surface of the heat flow meter in the form of total reflection with a transmission efficiency of 90%. The role of quartz-glass rod was to expand the focused beam from about 15 mm to 20 mm, so that it was consistent with the heat flow meter, while reducing the density to meet the range requirements of the heat flow meter. Figure 3c–e show the instrument diagram of the experimental equipment.

Table 1. Parameters of large Fresnel-focused spot flux density measurement system.

Parameters	Units	Values
Lens aperture	mm	968
Focal length	mm	1300
Lens ring distance	mm	0.5
Lens thickness	mm	5
Lens transmittance	%	89
Size of homogenizer	mm	Φ20 × 200
Transmittance of homogenizer	%	90
Diameter of heat flow meter	mm	20
Range of heat flow meter	MW/m2	0–3.14
Maximum operating temperature of heat flow meter	°C	1600
Size of Lambertian target	mm	100 × 100 × 3

describes the parameters of each component of the system.

2.2. Method

The formation of a Fresnel-focused spot is shown in Figure 4. The diameter of the focal spot of the lens is determined by the receiving angle $\theta$, the half angle of sun viewing $\delta$, the radius of lens R, and the ring spacing L. The diameter of the focal spot diameter is d

$$d=\frac{2R\sin \delta }{\sin \theta \cos \theta }+L=13.8 \mathrm{mm}+0.5 \mathrm{mm}=14.3 \mathrm{mm}$$

Fresnel lens has strong concentration performance. The concentrated spot produced by the large Fresnel lens (diameter 968 mm) is slightly less than 15 mm in diameter, which means that the average concentration ratio of the Fresnel lens is higher than 4000 suns. The concentrated spot has poor uniformity, and its peak flux is higher than that of average concentrated level [39]. For precise analysis of the flux density distribution of concentrated spot input and output of the homogenizer, Monte Carlo ray tracing is a suitable tool and was adopted [40]. The simulation results reveal that the peak flux of the concentrated spot can reach 5756 suns. Under the condition that the direct normal irradiation (DNI) of the sun is 800 W/m², the peak flux value of the concentrated spot can reach 4.61 MW/m², as shown in Figure 5d, exceeding the range of heat flow meter. The quartz-glass rod here as a homogenizer, can reduce the peak flux to 3.15 MW/m², within the measurement range of the heat flow meter, as shown in Figure 5e.

In practice, due to chromatic dispersion, diffraction, and slope deformation, the diameter of the concentrated spot is slightly larger than the theoretical value. For the large Fresnel lens used in this study, the focus spot diameter observed in the experiment is 15 mm, as shown in Figure 5b, which is smaller than the diameter of the heat flow meter (20 mm). The homogenizer expands the concentrated spot to 20 mm, same as the diameter of the heat flow meter. This allows the concentrated flux to be coupled to the heat flow meter for accurate measurement, which facilitates the next step of measurement.

Spot images taken by CCD cameras reflect the flux density distribution [41]. In 2002, an indirect method was proposed for indirectly measuring flux based on the assumption that the gray value has a linear relationship to the flux [42]. Since the relationship between flux density and image gray value is affected by many factors, such as dark current [43], the linear relationship between them is a rough assumption. In practical application, it is necessary to introduce correction methods to improve the measurement accuracy [44]. This study adopts the mapping method based on the real camera response function Z = F(E), which describes the relationship between the incident flux E and the gray value Z [41].

In this study, the response function of the CCD camera used in this experiment was calibrated. The CCD camera was fixed to a camera tripod and a set of images was taken with static scene. The shooting process was completed in a short period of time (within 1 min), ensuring that the ambient brightness was the same throughout the process.

Figure 6a–f shows the images under different exposure times. The shorter the exposure time, the lower the brightness. There is a linear relationship between the brightness and the irradiation intensity for Lambertian target. Therefore, the calibration of CCD camera response function is to establish the relationship between brightness and irradiance. The radiation intensity is expressed by logarithm and the brightness is expressed by gray value. When the gray scale value is less than 40 and more than 240, the logarithm of irradiation intensity changes too quickly, and most of the images taken are not in this range, so the gray scale value of these two parts is not considered. When the gray value is between 40 and 240, the relationship between the gray value and the logarithm of irradiation intensity is approximately linear, which is suitable for measurement.

The gray value of CCD image was calibrated by using theoretical result and the value of the heat flow meter, and then compared with the result of the Monte Carlo rays tracing method. The diagram of measurement is shown in Figure 7. Firstly, the circumsolar ratio was figured out based on the two pyrheliometers with different acceptance angles, and then the direct irradiation from the solar disk surface was obtained. The theoretical value of the power of the concentrated spot of the lens was then achieved. The power of the flux output of the homogenizer was also measured by the heat flow meter. The theoretical value and the value of the heat flow meter were used to verify the gray value of CCD images. Finally, the flux density distribution calculated from the gray value of the CCD images was further compared with the results of the Monte Carlo ray tracing method. In practice, minor deformation of the Fresnel lens caused by gravity will result in a larger size of the focus spot than the theoretical value, but still smaller than the diameter of the homogenizer and heat flow meter. The whole focus spot can be completely transmitted by the homogenizer to the heat flow meter. The slight deformation of the lens has an impact on the actual distribution of the spot flux intensity. As a result, the flux density distribution of the actual spot measured by the CCD camera-based method is slightly lower than the results of Monte Carlo ray tracing method. The peak value of experimental spot is lower than the result of computer simulation, which conforms to reality.

3. Experiment and Discussions

3.1. Verification

In order to verify the method used in this study, the power of the concentrated spot was measured by the heat flow meter and compared with the CCD camera-based method. Three kinds of data were used for the calibration operation, which are namely the theoretical value of the power of the concentrated spot, the value of the heat flow meter, and the gray value of the CCD image. The theoretical value is the product of the transmittance of the lens and the homogenizer, the DNI and Fresnel lens area.

The transmittances of the lens and the homogenizer were obtained by using an illuminometer, which are both 90%. The parameters of the illuminator are shown in

Table 2. Parameters of the illuminator.

Parameters	Unit	Value
Model		Z-10
manufacturer		Ever fine
Test range	lx	0.01–300,000
Spectral range	nm	380–760

. However, the illuminometer only responds to the visible spectrum and does not react to infrared light, so there was error in the measurement. In the solar spectrum on the sea level (AM = 1.5), the red curve in Figure 8, the wavelength distribution of visible light is 380–780 nm, while the energy ratio of infrared light (>780 nm) accounts for about 50%. The material of the Fresnel lens in this study is polymethyl methacrylate (PMMA), which has a high attenuation rate in the infrared band, up to 10⁶ dB/km. The relationship between attenuation rate and transmittance is shown below.

$$10\times {\log }_{10}(T(=A$$

where T represents the transmittance per kilometer (%), and A represents its attenuation rate (dB/km).

According to the attenuation curve, the transmittance of the 5-millimeter thick Fresnel lens used in this study is shown in the blue curve of Figure 8, and the theoretical transmittance in the visible light is 92%, which is consistent with the illuminometer measured value. As the wavelength increases, the transmittance of the lens gradually decreases. The average transmittance of the full solar spectrum is 88%. The transmittance of this lens is measured with a broadband irradiation meter, and the results show that the total transmittance is 88% ± 1%, which coincides with the theoretical value.

The measurement of the direct normal irradiation from the solar disk is complex and it needs to remove the circumsolar irradiation from the value of the pyrheliometer with a view field of 5°. The dual pyrheliometers were adopted in this study to achieve the CSR (circumsolar ratio), which is shown in Figure 9, according to the sun shape mode proposed by Buie et al. [45]. The theoretical sun shape and CSR are the actual sun shape and CSR at that moment in time when the ratio of the measured circumsolar irradiation at different reception angles is equal to the ratio of the theoretical relative radiation.

In this study, the heat flow meter measured value and the CCD camera measured value are compared under the same incidence conditions (DNI = 800 W/m²). In the case of an incident area ratio accounting for 1/4 and 1/2, which is shown in Figure 10b,c, the total measured energy of the spot obtained by the heat flow meter is 114 W and 229 W, respectively. The total measured energy of the concentrated spot obtained by the CCD camera is 112 W and 233 W, respectively. The relative error is −1.8% and 1.7%, respectively. The relevant data are shown in

Table 3. Comparison of heat flow meter measured value and CCD camera measured value under DNI = 800 W/m².

Area Ratio	Energy of the Focus Flux (W)
	Theoretical	Heat Flow Meter	CCD Image
1/4	117	114	112
1/2	233	229	233

.The measurement results are consistent, indicating that the measurement method used in this study is reliable.

3.2. Experiment

In the experiment, by adjusting the two-axis rotating platform in real time, the direct normal irradiation is always perpendicular to the Fresnel lens to achieve the best focus. The exposure time of the camera was set to 1/2000 s, and the exposure time remained constant throughout the shooting process. During the experiment, the incident area was changed by changing the number of sector shields, and the concentrated spot images with incident area ratios of 1, 1/2 and 1/4 were captured, respectively. The CCD images of the Lambertian target are shown in Figure 10d–f.

In the experiment, the symmetrical occlusion method was used to achieve different levels of incident flux. As the number of sector shields decreased by two pieces in axially symmetrical order, the incident flux changed regularly. In the case of an incident area ratio of 1, 1/2 and 1/4, when the DNI = 800 W/m², the flux density distributions of the concentrated spot obtained by rays tracing simulation are shown in Figure 11a–c. When the incident area ratio is 1, 1/2 and 1/4, the peak flux density of the spot reaches 4.60 MW/m², 2.26 MW/m², and 1.13 MW/m², respectively. The actual flux density distribution of the CCD images measured by the CCD camera-based method is shown in Figure 11d–f, and the peak values are 4.06 MW/m², 2.12 MW/m², and 1.12 MW/m², respectively.

Compared with the simulation result, the actual flux density is a little lower and there is a slight deformation in the symmetry of the spot. The Fresnel lens used in the experiment is a large-sized thin shell structure, with a diameter of nearly 1 m and a thickness of only 5 mm. There is gravity deformation on this structure. The deformation leads to the damage to the asymmetry of the flux.

3.3. Discussion

The strong gradient of the concentrated flux distribution is an issue that must be carefully considered in applications. In the experiment, the flux density distribution of the concentrated spot shows a trend of high at the center and low in the surrounding area, which is like the Gaussian distribution. The peak flux could reach 5000 suns, three times the average concentration ratio. This means that the receiver will be subjected to severe uneven irradiation, which may lead to local overheating. Differences in the concentrated ratio of thousands of times over distances in the millimeter-level can cause severe thermal stress. Using a homogenizer for uniform flux output is a viable option. The homogenizer can be a prism or a cylindrical glass rod, and the prismatic glass rod is better than the cylindrical glass rod.

The homogenizer is the key to achieve the measurement of flux intensity at the 4 MW/m² level in this study. The spot is matched with the size of the heat flow meter through the homogenizer so that the verification of CCD image was carried out. The combination of a homogenizer, heat flow meter, and CCD camera provides a virtually unlimited flux measurement range. The homogenizer made of quartz glass can withstand millions of times of suns, and the CCD camera can be combined with multiple layers of neutral density filters to prevent overexposure when shooting a concentrated spot. The upper limit of the measurement method is determined by the intensity and gradient of flux that the incident end of the homogenizer can withstand. The damage threshold of the quartz material used in the homogenizer exceeds 10⁶ suns, which means that the method can measure the flux density in any solar concentrated system. The theoretical upper limit of the geometric spot ratio of solar concentrators is 46,000 suns, which is below the damage threshold of the homogenizer. Therefore, this method can be used for the measurement of focused energy flows in solar concentrated systems with high flux levels.

By comparing the flux distribution with that in the literature, the flux distribution in this paper is like that in the literature, which shows a distribution with high center and low surroundings.

Table 4. Optical specification comparisons among Fresnel in references and our manuscripts.

	Reference [12]	This Manuscript
Concentration ratio	5831	4164.5
Half acceptance angle (deg)	0.4	0.33
f−number		0.74
Maximum concentrated level	14k suns	6k suns
Flux distribution map

is describing the optical specification of the two types of Fresnel lenses.

We have performed experiments on concentrating on a receiver with a large-aperture Fresnel lens; the experimental system is shown in Figure 12. We found that the temperature gradient within the concentrated spot was particularly large causing a huge thermal stress effect, as shown in Figure 13, resulting in local overheating, localized high-temperature boiling of the water in the receiver, and a breakage of the receiver, which is shown in Figure 14.

In this experiment, we found that the temperature gradient of the focused spot was significantly reduced due to the use of filters, water cooling, and air cooling to dissipate the heat of the focused spot, and a cylindrical homogenizer was used to homogenize the spot. However, the temperature gradient on the filter is not as large as the gradient at the focal point, but cracks caused by the temperature gradient still appeared on the filter, as shown in Figure 15. Therefore, based on the experiment, our proposed solution for receiver overheating protection is to add a prismatic homogenizer in front of the filter in addition to the filtered, water-cooled, air-cooled, and cylindrical homogenizer to resolve the overheating problem of the receiver.

4. Conclusions

The aim of this study is to obtain the flux density distribution of a Fresnel lens with a high concentration level to provide a solution to the problem of receiver overheating protection. The key to this study is the use of the homogenizer for flux intensity measurements, which allows the spot to be sized to the contact surface of the heat flux meter, the flux intensity to be within the range that can be measured by the heat flux meter, and the CCD images to be calibrated. In this study, a measuring system consists of a CCD camera, a heat flow meter, and a homogenizer. In the experiment, the flux density distribution of the Fresnel lens is successfully obtained. Experiments reveal that the peak of the concentrated spot (diameter 968 mm) of large Fresnel lens can reach 4.06 MW/m² under DNI 800 W/m², the equivalent of 5000 suns. Experiments demonstrated the simulation result of the literature, where there is a serious gradient distribution inside the spot of the lens and the central flux reaches three times the average flux density. The measured peak value of the concentrated spot is about 10% lower than the theoretical value, and the reason for this phenomenon is that there is a gravity deformation of the large-aperture plastic Fresnel lens, which means the flux density distribution of a concentrated system with a high flux level can be obtained by using this method.