Comparative Study of a Fixed-Focus Fresnel Lens Solar Concentrator/Conical Cavity Receiver System with and without Glass Cover Installed in a Solar Cooker

Abstract

The glass cover is often situated at the aperture of a cavity receiver in concentrating collectors to reduce heat dissipation. However, the decrease in optical efficiency due to the reflection loss on the surface of the glass cover will directly reduce the thermal efficiency of a collector, especially for a fixed-focus solar concentrator, whose optical axis is generally not coincident with the central axis of the receiver. To fundamentally evaluate the effect of a glass cover on the efficiency of a fixed-focus Fresnel lens solar concentrator/conical cavity receiver system, its performances with and without a glass cover considered under different incidence angles were comparatively investigated. To obtain the optical performance, optical models of the system were first built with TracePro^® 7.0 software. An experimental setup was then constructed to test the thermal performance of the system. The results show that the optical efficiency of a system without a glass cover is much higher than that with a glass cover. The difference between them remains unchanged for incidence angle at a range of 0–20°. The time constant of the system with a glass cover is much less than that without a glass cover, in the ranges of 29–33 s and 48–59 s, respectively. The system with a glass cover for a wide range of higher temperature differences also has better thermal efficiency.

1. Introduction

Cooking is a fundamental need for people worldwide [1]. However, the increasing cost of fossil fuels and the environmental concerns associated with their use, such as pollution, greenhouse gas emissions, and global warming [2], has made the search for alternative energy sources for cooking a pressing issue [3]. Solar cookers have emerged as an attractive solution in this context, especially in developing countries. Solar cookers can be broadly classified into three types: panel, box, and parabolic cookers [4]. While panel and box cookers utilize only thermal energy and achieve lower temperatures than parabolic cookers, they are unsuitable for frying or grilling [5,6]. On the other hand, parabolic cookers can reach high temperatures and are suitable for frying or grilling. However, such parabolic reflectors require frequent tracking along two axes, and the receiver must be fixed at the focal point as an integral part of the reflector.

The limitations of parabolic solar cookers can be overcome by using fixed-focus solar concentrators, such as the fixed-focus Scheffler concentrators [7,8,9] and fixed-focus Fresnel lens solar concentrators [10,11,12]. The latter has many advantages, such as a simple structure, low cost, and ease of manufacturing due to the mass production of Fresnel lenses [13], making it suitable for household solar cookers. Valmiki et al. [10] presented a two-axis fixed focus Fresnel lens solar stove that achieved an efficiency approaching 40% when the stove temperature reached 255 °C. However, this design requires the whole solar stove to be rotated in the horizontal plane to track the azimuth angle, making it less practical for household use. We proposed a fixed-focus Fresnel lens solar cooker [11], as shown in Figure 1. The system achieves sun tracking by concentrating incident sunlight to the fixed conical cavity receiver through the solar concentrator without any other change. However, the concentrated sunlight incidence angle has an important influence on the optical and thermal performance of the fixed-focus Fresnel lens solar concentrator/conical cavity receiver (FSC-C) system, which in turn affects the performance of the solar cooker.

Numerous studies have investigated the performance of fixed-focus solar concentrator/cavity receiver systems. For instance, Nene et al. [14] analyzed two Scheffler solar concentrators with cavity receivers, demonstrating that the conical receiver had the highest efficiency when tilted at 45° and 30° for small and large Scheffler concentrators, respectively. In a subsequent study [15], they investigated two types of receivers with Scheffler concentrators. They found that the conical receiver with tilt was optimal for maximum efficiency compared to the cylindrical receiver. Meanwhile, Senthil et al. [16] experimentally investigated the performance of a flat surface absorption receiver tilted at 13° with a Scheffler concentrator, finding that the thermal efficiency of the receiver with a curved path improved by 3.8% compared to that with the vertical flow. These studies primarily focused on the effects of receiver parameters and tilted angles for fixed-focus solar concentrator/cavity receiver systems.

Furthermore, to reduce heat dissipation caused by external wind conditions, a glass cover is often placed at the aperture of the receiver, enhancing the greenhouse effect to trap more heat in the receiver cavity [17]. Several studies have explored the use of glass covers in cavity receivers. For instance, Liang et al. [18] presented a cavity receiver with a glass plate for the parabolic trough solar collector, demonstrating an efficiency of 64.25%, comparable to that of a metal-glass evacuated tube receiver. Cui et al. [19] numerically studied a cavity receiver with quartz glass at the center of a dish concentrating system and found that the total heat flux of the covered receiver was only about 36% of that for the uncovered receiver. However, the glass cover is also problematic as it increases the optical loss of the system, primarily due to reflection on its surface. In addition, Chen et al. [20] analyzed the optical performance of a porous media receiver, finding that the optical loss caused by the absorption and reflection of solar windows was 7.12%. Nonetheless, there is a lack of reported experimental investigations on the effect of glass covers on the efficiency of FSC-C systems under various concentrated sunlight incidence angles.

This study analyses and compares the optical and thermal performance of the conical cavity receiver and FSC-C system with and without a glass cover. Specifically, the study focuses on evaluating the effect of the glass cover on the system’s optical and thermal efficiency. The optical models of the system with and without the glass cover were constructed using TracePro^® 7.0 software to obtain the optical efficiency of the system and flux distribution of the conical cavity receiver. An experimental setup of the system was built to test and analyze the system’s thermal performance under various concentrated sunlight incidence angles.

2. System Description

2.1. FSC-C System

The system under investigation is a fixed-focus Fresnel lens solar concentrator with a conical cavity receiver, illustrated in Figure 2. The system’s geometric parameters include the diameter (D) and focal length (f) of the Fresnel lens, sun declination angle (δ), solar hour angle (ω), and local latitude angle (Φ). The horizontal angle of the polar axis is set as 23°08′ based on the Φ of Guangzhou, China. The concentrated sunlight incidence angle (θ) on the south-facing tilted conical cavity receiver is calculated as [21,22]:

$$\cos \theta =(\sin \varphi \cos \phi -\cos \varphi \sin \phi )\sin \delta +(\cos \varphi \cos \phi +\sin \varphi \sin \phi )\cos \delta \cos \omega$$

(1)

During the polar axis tracking process, the tilt angle of the conical cavity receiver(φ) needs to be set equal to the local latitude angle, i.e., φ = Φ. Substituting this expression into Equation (1), we obtain:

$$\cos \theta =\cos \delta \cos \omega$$

(2)

In this case, the solar cooker can be used between 08:00 and 16:00, corresponding to the apparent solar time. Throughout the year, the δ varies between −23°27′ south and +23°27′ north [23,24], resulting in a range of θ that is less than 60°.

Figure 3a,b in this work show the cross-section of the conical cavity receiver and a photograph of the absorber, respectively. The conical cavity receiver comprises an absorber, insulation material, shell, and glass cover. The solar energy is concentrated by the Fresnel lens and absorbed by the absorber, as depicted in Figure 4. The absorbed energy is transferred to the working fluid through the copper tube. The helical coil in Figure 3a represents the cavity receiver with an aperture diameter of 0.1 m, a bottom diameter of 0.024 m, and a depth of 0.17 m. The copper tube has a diameter of 0.008 m, and the spacing between the coil turns is around 0.001–0.002 m. The insulation material on the outer side of the tube coils in the conical cavity is 0.05 m thick. The exterior surfaces of the pipes are coated with a black chromium selective coating with a solar absorptance of 0.90. A clear glass cover (2 mm thick) is also provided on the conical cavity receiver to reduce convective heat losses.

2.2. Testing System

An experimental system was constructed to investigate the thermal performance of the FSC-C system. Figure 4 depicts the schematic of the experimental setup, which mainly consists of a fixed-focus Fresnel lens solar concentrator with a geometric concentration ratio of approximately 1181, a conical cavity receiver, a heat exchanger, a thermostat oil tank, and a circulating pump, among other components. The working fluid used was synthetic heat transfer oil. The thermostat oil tank controlled the inlet temperature of the conical cavity receiver, and the mass flow rate was regulated by a flow meter. The circulating pump drove the flow of oil, and temperature sensors were used to measure the oil temperature at the inlet and outlet of the absorber pipe. During the thermal performance test, ambient temperature and wind speed were monitored, and the direct solar irradiance was recorded by a direct radiometer.

Table 1. Uncertainties of the instruments.

No.	Measurements	Type	Uncertainty
1	Temperature	PT-100 sensor	±0.1 °C
2	Mass flow rate	Flow meter	0.5 lpm
3	Wind speed	Hot wire anemometer	±0.01 m/s
4	Direct solar irradiance	TBS-2-2	2%
5	Tracking accuracy	Polar-axis tracking mechanism	±0.1°

provides the overall uncertainties of the instruments used in the experimental setup.

3. Optical Characteristics

3.1. Definition of Optical Efficiency, Incidence Angle Modifier and Uniformity Factor

Optical analysis of the FSC-C system was conducted with several assumptions, including an ideal and error-free Fresnel lens, constant transmittance, reflectance, and absorbance of the receiver. The Monte Carlo ray tracing method was utilized to evaluate the impact of the vertical distance of the receiver from the Fresnel lens (f) and the incidence angle (θ) on the optical efficiency of the system and flux distribution on the conical cavity receiver. To achieve a model closer to reality, commercial software TracePro^® was employed to simulate ray-tracking for designing, analyzing, and optimizing optical and illumination systems. The angular subtense of the sun at any point on earth (ξ = 32′) was considered during ray tracing to improve the model’s accuracy. The variation of θ on the optical efficiency was evaluated, defined as the fraction of direct solar radiation intercepted by the Fresnel lens absorbed by the conical cavity receiver. The mathematical expression for the optical efficiency is given as follows:

$${\eta }_0(\theta )=\frac{Q_{\mathrm{ab}}}{I_{\mathrm{d}}{A}_{\mathrm{c}}}$$

(3)

The absorbed energy of the conical cavity receiver wall is denoted as Q_ab (W), I_d (W/m²) represents the direct solar radiation on the Fresnel lens surface, and A_c (m²) is the area of the Fresnel lens. To analyze the impact of the θ on the system’s optical performance, a global parameter K(θ) [25] is used, which considers the incidence angle modifier and the variation in the intercept factor of the conical cavity receiver. Therefore, the optical efficiency of the proposed system can be expressed as follows:

$${\eta }_0(\theta )=K(\theta ){\eta }_0(\theta =0°)$$

(4)

To assess the degree of uniformity of the flux on the conical cavity receiver surface, a uniformity factor (UF) was employed for comparison purposes. The maximum flux was determined by identifying the areas with the highest flux on the conical cavity receiver surface. In contrast, the average flux was obtained by dividing the incoming energy by the surface area of the conical cavity receiver. The UF can then be calculated using Equation (5) [26].

$$UF=1-\frac{MaximumFlux-AverageFlux}{MaximumFlux}$$

(5)

3.2. The Radiation Flux Profile of the Absorbing Surface and the Optical Efficiency of the System

A series of ray-tracing simulations are conducted investigate the effects of the position of the conical cavity receiver relative to the concentrator focal plane on the radiation flux profile of the absorbing surface and the optical efficiency of the FSC-C system. In this study, the absorptance variation of the black chromium selective coating is assumed to be constant. At the same time, the impact of changes in the θ on the transmittance of the glass cover is taken into account. To evaluate the effect of the glass cover on optical losses, the system is tested with and without the glass cover under the same optical conditions. Figure 5 displays the rays and flux distribution for the conical cavity receiver with five representative incidence angles (f = 1000 mm).

The results indicate that as the θ increases, the loss of reflection and re-reflection rays also increases, especially in the conical cavity receiver with a glass cover. The ratio of rays that are reflected and escape from the cavity is much higher with the glass cover than without it. The flux distribution on the absorber surface is also affected by θ. While the flux distribution is relatively uniform with θ of 0°, some areas on the absorber surface suffer from a lack of flux at θ of 15°, 30°, 45°, and 60°, while some other areas receive higher flux. To better evaluate the optical performance of the conical cavity receiver, Figure 6 presents the optical efficiency for different θ values.

Figure 6 shows that the optical efficiency η₀(θ) mainly decreases with the increase in θ. The η₀(θ) changes slowly before θ = 25°and then falls quickly. For the case with a glass cover, the f is 980 mm, 985 mm, 990 mm, 995 mm, 1000 mm, 1005 mm, 1010 mm, 1015 mm, and 1020 mm. As θ = 0°, the η₀(θ) are 0.6790, 0.6804, 0.6815, 0.6825, 0.6834, 0.6844, 0.6854, 0.6863, and 0.6871, respectively. As θ = 25°, the η₀(θ) are 0.6769, 0.6782, 0.6792, 0.6798, 0.6802, 0.6813, 0.6786, 0.6782, and 0.6752, respectively. As θ = 60°, the η₀(θ) are 0.4418, 0.4840, 0.5104, 0.5246, 0.5264, 0.5131, 0.4870, 0.4429, and 0.3839, respectively. For the case without a glass cover, the f is 980 mm, 985 mm, 990 mm, 995 mm, 1000 mm, 1005 mm, 1010 mm, 1015 mm, and 1020 mm. As θ = 0°, the η₀(θ) are 0.7527, 0.7543, 0.7555, 0.7566, 0.7575, 0.7587, 0.7597, 0.7607, and 0.7614, respectively. As θ = 25°, the η₀(θ) are 0.7571, 0.7583, 0.7506, 0.7598, 0.7601, 0.7530, 0.7554, 0.7564, and 0.7526, respectively. As θ = 60°, the η₀(θ) are 0.5777, 0.6407, 0.6826, 0.7015, 0.6944, 0.6585, 0.5896, 0.5033, and 0.4156, respectively. It means that the η₀(θ) of the FSC-C system is comparable to that of the general Fresnel lens solar collector system (the optical axis of the Fresnel lens coincides with the recenter axis of the cavity receiver) when the θ < 25°. To show the effect of the glass cover on the η₀(θ) of the FSC-C system objectively, the optical efficiency difference between the groups with and without glass cover under various θ is shown in Figure 7. The η₀(θ) of the group without a glass cover is higher than that with a glass cover. The optical efficiency difference changes obviously for the θ of 20–60° but remains unchanged for the θ of 0–20°. The closer the focal length is to 995 mm, the faster the difference increases with the increase in θ. Otherwise, the slower the difference increases and even decreases. For f, it is 980 mm, 985 mm, 990 mm, 995 mm, 1000 mm, 1005 mm, 1010 mm, 1015 mm, and 1020 mm. As θ = 0°, the optical efficiency difference is 0.0738, 0.0739, 0.0740, 0.0741, 0.0741, 0.0743, 0.0744, 0.0744, and 0.0743, respectively. As θ = 25°, the optical efficiency difference is 0.0802, 0.0801, 0.0713, 0.0800, 0.0799, 0.0717, 0.0768, 0.0782, and 0.0774, respectively. As θ = 60°, the optical efficiency difference is 0.1359, 0.1568, 0.1722, 0.1769, 0.1681, 0.1454, 0.1026, 0.0604, and 0.0317, respectively. These observations can be explained by the nature of natural light, which consists of entirely polarized light. When light travels through a transparent medium, the incident and emergent light are coplanar, with the normal plane being the plane of incidence. Additionally, the complete polarization of natural light can be decomposed into p-polarized and s-polarized components. As indicated by Ma et al. [27], the relationships of reflectivities of p-polarized lights R_p and reflectivities of s-polarized lights R_s to the incident angles are shown in Figure 8. The relative index of refraction of glass cover to air (n₂₁) is 1.5. It is noted that the R_p and R_s change slightly before the θ = 20°, but the changing trend subsequently increases with the increasing of θ. Thus, the optical efficiency difference remains unchanged before θ = 20° but changes obviously for the θ of 20°–60°.

Figure 9 shows that the uniformity factor (UF) mainly decreases with the increase in θ. The UF falls rapidly as θ within the range of 0–20° and then decreases slowly with a further rise in θ. The UF of conical cavity receiver generally increases with the focal length increasing within the range of 980–1020 mm. As shown in Figure 5, the flux distribution of the conical cavity receiver with and without the glass cover does not show any significant difference. To show the effect of glass cover on the UF of the conical cavity receiver objectively, the UF difference between the group with and without glass cover under various θ is shown in Figure 10. It shows that the difference fluctuates around 0. Thus, the glass cover has no significant effect on the flux uniformity of the conical cavity receiver absorber surface.

As a result, the fixed-focus Fresnel lens solar concentrator with a focal length of 1000 mm is chosen for all the following cases, as it gives a comparatively higher level of optical efficiency without adjustment. The simulation data can be well-fitted by a polynomial in θ. Given that the optical efficiency is influenced by the incidence angle of sunlight, to demonstrate the impact of the incidence angle on the optical performance of the system, the values of K(θ) for the FSC-C system, both with and without a glass cover, were determined using regression analysis of simulation data. The resulting expressions are as follows:

K(θ) = −0.000004θ³ + 0.0002θ² − 0.0031θ + 1.0055;   R² = 0.9967

(6)

K(θ) = −0.000003θ³ + 0.0002θ² − 0.0031θ + 1.0059;   R² = 0.9782

(7)

4. Thermal Performance

4.1. Time Constant of the FSC-C System

The standard GB/T4271-2007 recommends testing the FSC-C system by measuring the incident solar radiation rate and the energy addition rate to the working fluid under steady-state or quasi-steady-state conditions [28]. Furthermore, it is essential to determine the transient thermal response characteristics of the FSC-C system to assess its transient behavior and choose the correct time intervals for steady-state efficiency tests. The time constant of a solar collector, which is the time required for the fluid leaving the collector to reach 63.2% of its final steady state value after a step change in incident radiation, can be calculated using the following relation [29]:

$$\frac{T_{\mathrm{o}}(\tau )-T_{\mathrm{i}}}{T_{\mathrm{o},\mathrm{ss}}-T_{\mathrm{i}}}=0.632$$

(8)

Here, T_o(τ) represents the collector outlet fluid temperature (°C) at time τ (s), T_o,ss represents the steady-state working fluid outlet temperature (°C), T_i represents the collector inlet fluid temperature (°C).

4.2. Thermal Efficiency of the FSC-C System

The FSC-C system’s thermal efficiency was evaluated per the ASHRAE Standard, using different inlet working fluid temperatures. Due to the flow meter’s maximum operating temperature of 200 °C, the experiments were limited to collector operating temperatures within 170 °C. The proposed FSC-C system’s thermal performance was partly evaluated by its instantaneous efficiency, which was determined by factors such as incident solar radiation, ambient temperature, inlet and outlet temperature, and mass flow rate of working fluid under steady-state or quasi-steady-state conditions. The instantaneous thermal efficiency (η_t) of the FSC-C system can be calculated using the following equation [30,31]:

$${\eta }_{\mathrm{t}}=\frac{\stackrel{·}{m}{c}_{\mathrm{p}}(T_{\mathrm{o}}-T_{\mathrm{i}})}{I_{\mathrm{d}}\cdot A_{\mathrm{c}}}$$

(9)

where $\stackrel{·}{m}$ (kg/s) is the mass flow rate of fluid flow, c_p (kJ/kg/°C) is the heat capacity of the working fluid. The heat capacity of synthetic heat transfer oil can be found in Appendix A to evaluate the thermal efficiency of the FSC-C system under different θ. The instantaneous thermal efficiency equation of the FSC-C system, similar to other energy conversion devices, can be expressed as follows [32,33]:

$${\eta }_{\mathrm{t}}={\eta }_0(\theta )-\frac{U_{\mathrm{a}}}{C}\cdot \left(\frac{T_{\mathrm{r}}-T_{\mathrm{amb}}}{I_{\mathrm{d}}}\right)$$

(10)

$$C=\frac{A_{\mathrm{a}}}{A_{\mathrm{r}}}$$

(11)

In the efficiency equation, T_r (°C) represents the average inner surface temperature of the cavity receiver, while T_amb (°C) is the ambient temperature, U_a (W/m²/°C) is the overall heat loss coefficient based on T_r, and A_r (m²) is the area of the conical cavity receiver. Determining the exact value of T_r can be challenging. However, the inlet and outlet temperatures of the conical cavity receiver can be easily measured. Therefore, the average temperature of the conical cavity receiver T_m = (T_i + T_o)/2 can approximate T_r in the efficiency equation [34]. The equation can be expressed as follows:

$${\eta }_{\mathrm{t}}=F^{’}{\eta }_0(\theta )-\left(\frac{F^{’}{U}_{\mathrm{L}}}{C}\right)\cdot \left(\frac{T_{\mathrm{m}}-T_{\mathrm{amb}}}{I_{\mathrm{d}}}\right)$$

(12)

$$U_{\mathrm{a}}=F^{’}{U}_{\mathrm{L}}$$

(13)

The overall heat loss coefficient U_L (W/m²/°C) is related to T_m, the mean fluid temperature of the collector, and F′, the collector efficiency factor. F′ is the ratio of the actual useful energy gain to the gain if the collector absorbing surface was at the local fluid temperature. The value of F′ depends on the collector heat exchange structure. Using the above equations, the thermal efficiency of the FSC-C system can be calculated and plotted against the temperature difference (T_m − T_amb)/I_d.

5. Results and Discussion

5.1. Time Constant of Different Incidence Angle

The experiments to evaluate the FSC-C system were conducted over several days under clear sky conditions and moderate wind speed. The tests were conducted around solar noon between 9:00 and 15:00 solar time. Figure 11 displays typical recorded data for the day when the system time constant was tested with one-minute intervals. It shows the variation of direct solar irradiation I_d, wind speed V_w, and ambient temperature T_amb, with a heat transfer fluid discharge rate of 0.008 kg/s. The direct solar radiation exhibited an increase from 708 W/m² at solar time 9:00 to 781 W/m² at solar time 11:46. The wind speed varied between 0–3.2 m/s, while the ambient temperature fluctuated within the range of 20.84–22.24 °C throughout the day. The air quality was also assessed as “good”, considering a relative humidity of 72%, a PM2.5 concentration of 35, and a PM10 concentration of 55.

The heating tests were conducted to determine the time constants of the FSC-C system with and without a glass cover for different incidence angles. As presented in Figure 12a,b, the time constants of the FSC-C system with and without a glass cover for incidence angles of 25°, 30°, 35°, and 40° were evaluated to be 31 s, 29 s, 31 s, 33 s, and 49 s, 59 s, 57 s, 48 s, respectively. The time constant of the FSC-C system with a glass cover was lower than that without a glass cover. The time constant of the FSC-C system was estimated to be 29–33 s with a glass cover and 48–59 s without a glass cover. The time constants with a glass cover remained relatively stable under different incidence angles, while those without a glass cover exhibited significant variations.

During the outdoor tests of the FSC-C system, a pre-data period of 15 min and a data period length of 5 min were used. As the time constants for FSC-C system with and without glass cover were less than 1 min, the length of the data period was set at 5 min. The incident angle variations with solar time at different time intervals were analyzed and are shown in Figure 13a. It was observed that the incident angle variations decreased with the increase in solar time, and the absolute values of the incident angle variations increased with the rise in time intervals. The maximum value of incident angle variations with a time interval of 5 min was 1.064°. Additionally, the changes in incident angle variations with solar time at different solar declination angles and a time interval of 5 min are shown in Figure 13b. It was found that the absolute values of incident angle variations decreased with increasing solar declination angle, and the maximum value of incident angle variations with a solar declination angle of 0° was 1.062°. Thus, the incident angle variations were small during the experiments and had little effect on the results. Based on the analysis of time constants, it can be concluded that the FSC-C system stabilizes quickly and has no significant effect on the steady-state performance analysis.

5.2. Thermal Efficiencies of Different Incidence Angles

To investigate the impact of the glass cover on the thermal performance of the FSC-C system, experiments were conducted at four different incidence angles: 16°, 24°, 32°, and 40°. The FSC-C system was also tested without the glass cover to assess the contribution of the glass cover. To ensure the accuracy of the measured values at different incidence angles, the data collected within 2.5 min before and after the measured incidence angle were selected, and the average value of each minute was calculated to determine the thermal efficiency. The thermal efficiency of the FSC-C system with and without glass cover under different incidence angles, plotted against the temperature difference, (T_m − T_amb)/I_d, is shown in Figure 14a–d. Linear equations were used to fit the experimental data and provide the characteristic parameters of the FSC-C system. The values of F′η₀(θ) and F′U_L/C for the FSC-C system with and without a glass cover at each incidence angle are presented in

Table 2. F′η₀(θ) and F′U_L/C values of the FCS-C system for each incident angle.

System Type	Incident Angle	16°	24°	32°	40°
With glass cover	F′η0(θ)	0.5471	0.5377	0.529	0.5081
Without glass cover	F′UL/C	1.5503	1.6321	1.7514	1.8869

.

Figure 14 and Table 2 indicate that the highest F′η₀(θ) value of the FSC-C system is obtained at an incident angle of 16°, while the lowest F′U_L/C value is obtained at this angle. Hence, according to Equation (12), the thermal efficiency of the FSC-C system is the highest at this incident angle. Comparing the thermal efficiencies of the FSC-C system with and without glass cover under different incident angles, it is observed that the thermal efficiency with glass cover is higher than that without glass cover for a wide range of temperature differences. Based on the fitting curves, it can be observed that at θ = 16° and (T_m − T_amb)/I_d = 0.03, the η_t for the cases with and without a glass cover are 0.5006 and 0.5304, respectively. At (T_m − T_amb)/I_d = 0.21, the η_t for the cases with and without a glass cover are 0.2215 and 0.1688, respectively. At θ = 24° and (T_m − T_amb)/I_d = 0.03, the η_t for the cases with and without a glass cover are 0.4887 and 0.5212, respectively. At (T_m − T_amb)/I_d = 0.21, the η_t for the cases with and without a glass cover are 0.194959 and 0.139112, respectively. Similarly, at θ = 32° and (T_m − T_amb)/I_d = 0.03, the η_t for the cases with and without a glass cover are 0.4765 and 0.5143, respectively. At (T_m − T_amb)/I_d = 0.21, the η_t for the cases with and without a glass cover are 0.1612 and 0.0978, respectively. Lastly, at θ = 40° and (T_m − T_amb)/I_d = 0.03, the η_t for the cases with and without a glass cover are 0.4515 and 0.4890, respectively. At (T_m − T_amb)/I_d = 0.21, the η_t for the cases with and without a glass cover are 0.1119 and 0.0584, respectively. The value of F′η₀(θ) is the dominant parameter for small temperature differences, i.e., (T_m − T_amb)/I_d < 0.0951, (T_m − T_amb)/I_d < 0.0962, (T_m − T_amb)/I_d < 0.0973 and (T_m − T_amb)/I_d < 0.1043 for θ of 16°, 24°, 32° and 40°, respectively, whereas F′U_L/C is the dominant parameter for higher temperature differences. The value of F′η₀(θ) without a glass cover is greater than that with a glass cover in the lower temperature differences range. Therefore, according to Equation (12), the thermal efficiency without a glass cover is greater than that with a glass cover in this range. However, in higher temperature differences range, i.e., (T_m − T_amb)/I_d > 0.0951, (T_m − T_amb)/I_d > 0.0962, (T_m − T_amb)/I_d > 0.0973 and (T_m − T_amb)/I_d > 0.1043 for θ of 16°, 24°, 32° and 40°, respectively, the value of F′U_L/C with glass cover is smaller than that without glass cover. Thus, the thermal efficiency with a glass cover in this range is higher than that without a glass cover.

Based on previous studies of the optical performance of the FCS-C system with and without a glass cover at a focal length of f = 1000 mm, it was found that the optical efficiency without a glass cover is higher than with a glass cover for incident angles between 20° and 60°. The difference in optical efficiency between them increases with the increase in θ. Therefore, for small temperature differences, the thermal efficiency without a glass cover is higher than with a glass cover. However, at high temperature differences, the heat losses from the FCS-C system to the environment increase, which depend on fluid temperature. The amount of heat-loss enhancement with temperature is quite explainable in the current case. Thus, it can be concluded that the effect of heat losses becomes more important as the fluid temperature increases. Based on the results and Table 2, it can be concluded that the effect of heat loss on the reduction in thermal efficiency is smaller than that of optical loss in the small temperature differences range. Moreover, increasing the fluid temperature in the FCS-C system causes an increase in heat loss. However, in higher temperature differences, the heat loss for the FCS-C system without a glass cover increases in comparison with the optical loss of the FCS-C system with a glass cover.

6. Conclusions

To explore the impact of the glass cover on the performance of a fixed-focus concentrating solar collector, this study proposes a fixed-focus Fresnel lens solar concentrator/conical cavity receiver (FSC-C) system in a solar cooker. The study uses numerical simulation and experimental methods to evaluate the system’s performance with and without glass cover. The following key findings were obtained:

(1)

The optical efficiency of the FSC-C system without a glass cover is higher than that with a glass cover. The difference between them is more significant at incidence angles of 20–60°. The increase in differences is faster with the decrease in the focal length, while it is slower or even decreasing when increasing the focal length;

(2)

The incidence angle has a significant influence on optical efficiency. Two models were proposed to predict the effect of incidence angle on the optical performance of conical cavity receiver coupled fixed-focus Fresnel lens solar concentrator;

(3)

The time constant of the FSC-C system with a glass cover is less than that without a glass cover. The time constant for incidence angles 25°, 30°, 35°, and 40° with and without glass cover was determined as 31 s, 29 s, 31 s, 33 s and 49 s, 59 s, 57 s, 48 s, respectively. The incident angle variations during the experiment were small, with a maximum of 1.064° over a 5-min interval;

(4)

Comparing the thermal efficiencies of the FSC-C system with and without glass cover under different incidence angles, it is found that the thermal efficiency with glass cover is higher for a wide range of higher temperature differences. The parameters F′η₀(θ) and F′U_L/C dominate at lower and higher temperature differences, respectively.