Abstract
A semirigid solar array is an efficient energy system on the surface of stratospheric airships for utilizing the solar energy, which we believe that it has succeeded in providing some impressive results for conceptual design. This paper developed a lightweight photovoltaic composite structure (LPCS) according to the characteristics of the stratospheric airship capsule. In order to improve the flexibility of the solar cell, we studied the mechanical properties in the different thicknesses of the honeycomb core for LPCS by FEM software and three-point bending test, and we also launched experiments to measure the temperature difference between upper and lower surfaces of the LPCS test samples under different solar radiation flux conditions. The experimental data were examined to evaluate the mechanical properties and thermal insulation performances of LPCS. Considering the quality of the whole structure, the paper finally comes up with the conclusion of the optimal thickness of the honeycomb core with further detailed descriptions.
1. Introduction
As a high-altitude platform, stratospheric airships are widely concerned in many important fields, especially in communication, broadcasting, remote sensing, scientific research, and so forth. Currently, United States, Japan, and South Korea are the major countries to develop stratospheric airships [1–10].
Solar energy is an ideal choice to provide power for high-altitude and long-endurance airships. This type of power system is actually a photovoltaic (PV) array coupled to an energy storage system [11]. At present, monocrystalline silicon solar cells and polycrystalline silicon and amorphous silicon thin-film solar cells are mainly used in solar battery applications. Among all the solar cells, monocrystalline silicon solar cell is the most technically matured and widely used. However, still some shortcomings exist such as hard rigidity and poor toughness for mono-Si to be applied in the surface capsule. At the same time, large-scale production of amorphous silicon solar cells and amorphous silicon thin-film solar cells is limited to apply to the stratosphere airship because of the rather low photoelectric conversion efficiency and “optical-induced degradation” [12]. This research aimed at studying a flexible processing of monocrystalline silicon solar cell (mono-Si solar cell) that can be applied to stratospheric airships under low ambient temperature and high solar irradiation flux conditions. On the one hand, the rarefied air and low ambient temperature in the stratosphere would lead to low convective heat conduction and high solar radiation flux, which make the temperature in the stratosphere prone to be overheating or undercooling [11, 13]. In particular, as shown in Figure 1, the solar cell array with high solar absorptivity may serve as the high-temperature heat source at noon and heat the envelope and inner lift gas of the airship [14]. The simulation results indicated that since the solar cells have high solar absorptivity, the maximum temperature on the PV panel would reach about 370 K at noon, which is above the highest temperature of the envelope without the PV panel (320 K) during the summer solstice and even aggravated the overheating problem. In the photovoltaic installed area, the largest temperature difference between PV panel and envelope could also reach 33 K. On the other hand, the solar cell array has a certain amount of flexibility, and they bend but do not break on the airship hull like other brittle materials do. The popularity of stratospheric airships brings increasing demands for several key technologies of these long-duration lighter-than-air vehicles [15, 16]. The solar array is one of the key technologies among these demands because the vehicles require the ability of long-duration fly at high altitudes, especially the flexible processing of the monocrystalline silicon solar cell that is designed in thermal protection systems to keep the temperature of underlying structure within an acceptable range.
(a)
(b)
According to the characteristics of the stratospheric airship capsule and mono-Si solar cell, this paper develops a lightweight photovoltaic composite structure (LPCS), in which the mono-Si solar cell of modified PET packaged as the surface to the asymmetric honeycomb core. A glass-fiber ribbon was used to improve the stiffness characteristic of the structure. The comparison results with experimental data and the theoretical model show that LPCS can not only solve overheating problems on the lower surface of a solar cell for stratospheric airships but also improve the overall flexibility of the mono-Si solar cell and reduce the stress concentration effectively.
Based on the current search, the thermal insulation requirements of solar effects have an effect not only on the solar cell efficiency but also on the thermodynamic characteristics of an airship [17, 18]. LPCS on the stratospheric airship is designed to study the mechanical properties and thermal insulation properties in this paper. The experiments of LPCS with different thicknesses of honeycomb by three-point bending have been conducted, and an experiment to measure temperature difference between upper and lower surfaces of LPCS under different solar radiation flux conditions has been designed. The FE models of LPCS with different thicknesses of honeycomb are built up, and then numerical simulation was implemented by using the software ABAQUS. Considering the quality of the whole structure, the article finally gives the conclusion of the optimal thickness of the honeycomb core with more detailed descriptions.
2. Physical Model
By determining the encapsulation materials, high-strength fiber material and low-density flexible insulation material, and combining with the characteristics of the stratospheric airship envelope, an implement method for engineering application systems for a lightweight photovoltaic composite structure (LPCS) is described.
2.1. Typical Selection of Composite Structure
Based on existing flexible insulation structures and enhancement structures, we develop an LPCS by virtue of modified PET (polyethylene terephthalate), 22% efficiency of mono-Si solar cells, fiberglass mesh, epoxy resin film or EVA (ethylene-vinyl acetate copolymer) film, and Nomex honeycomb. The solar cells with membrane surface encapsulation by EVA and modified PET film were used, in order to better stiffness matching with honeycomb core layer. The fiberglass has high mechanical strength and can be used as the enhancement structure. The epoxy resin or EVA film can be used as adhesive to combine each layer together. The Nomex honeycomb can effectively reduce the stress concentration of the overall structure, improve the structure’s load-bearing characteristics, and also has a great capability of thermal insulation. The LPCS connects the stratospheric airship envelope through the mechanical fastening way. The structure is shown in Figure 2.
3. Static Comparative Tests
The static comparative test aims to provide reliable mechanical performance parameters for analysis and optimization of LPCS, and the reliability of the asymmetric honeycomb sandwich structure (AHSS) was validated preliminarily All tests were conducted in the WDS-500 machine at a constant velocity of 5 mm/min as shown in Figure 3. The dimensions of the mono-Si solar cell specimens were 125 mm (length) × 125 mm (width) × 0.29 mm (thickness). The dimensions after EVA encapsulation were 125 mm (length) × 125 mm (width) × 0.49 mm (thickness). The dimensions of 2 mm honeycomb-laminated specimens were 125 mm (length) × 125 mm (width) × 2.74 mm (thickness). The specimens were placed on two supporting rollers with a span of 90 mm.
As the LPCS underwent high deformation during the bending test, simple linear beam theory was not sufficient to calculate the stress on the cells [19]. A model was used to take the large deflections into account.
3.1. A Model for Calculating the Large Deformation under Three-Point Bending Test
As the LPCS underwent high deformation during the bending test, simple linear beam theory was not sufficient to calculate the stress on the cells. A model similar to the one developed by Schoenfelder et al. [20] was used to take the large deflections into account.
With the classic linear beam theory, the maximum moment in the center of the cell iswhere is the load applied and is the span. The maximum stress at the surface of the cell is thenwhere is the moment of inertia of the cell in flexion, is the width, and is the thickness of the cell.
When the deformations are larger, the orientation of the reaction forces, the effective span, and the effective displacement change. Figure 4 illustrates the difference between small displacements approximation and large displacements model.
(a)
(b)
The reaction force becomes
In order to approximate the angle , the deformed shape of the cell is assumed to follow linear beam theory and is expressed aswhere is the span in the Cartesian coordinates and is the deflection at the center so . The angle is then defined by
The moment under the loading point can then be calculated as
With , .
If the friction on the supporting pins is disregarded, the maximum stress can then be calculated with equation (1).
3.2. The Comparison of Test and Analysis
As solar cells are very brittle, brittle fracture occurs when the crack expands to critical size. The LPCS was fabricated with one solar cell as face, so we tested the solar cell in three-point bending. All the solar cells broke at a 45° angle to the loading direction, as observed on the broken sample in Figure 5. This is explained by two reasons. Firstly, this is the maximum shear direction, and secondly, in the mono-Si solar cell as a kind of brittle materials, the angle of transverse bending normal stress and shear stress near the upper roller is about 90° and the resultant force direction is about 45°. Therefore, the mono-Si solar cell is the relatively weaker orthotropic materials, so we take it as orthogonal isotropic material to simplify calculations. But in order to reduce errors of the contrast test, all the main gate line of specimens are placed in parallel with the upper roller.
All materials used in the array fabrication, modified PET, solar cells, and EVA, are isotropic, so the mechanical property of the mono-Si solar cell after encapsulated by modified PET is isotropic as a whole. Previous experimental data and theory have proven that a honeycomb core can be classified as an orthotropic material based on the hexagonal grid of honeycomb cellular [21]. So, the whole mechanical property of LPCS is orthotropic as shown in Figure 6.
The mono-Si solar cell is not brittle after encapsulation by modified PET, and the fracture position is hard to find. Through encapsulating and laminating, pressure can spread by EVA and honeycomb core layer to nonstressed location, preventing local buckling and microcracks from appearing on the edge of the mono-Si solar cell and reducing stress concentration. At the same time, the toughness of EVA also prevents cracks from propagating.
According to the results of the test (Table 1), after encapsulated and laminated by modified PET, the maximum equivalent bending stress of the mono-Si solar cell decreased, while the maximum bending strain increased. The equivalent bending elastic modulus is only 2.41% after encapsulation and the deflection increased by 38.03%. The flexibility of the solar cell is effectively improved, which can enhance the ability to resist damage to a certain extent.
4. Simulation of Multilayer Composite Structure
According to the sealing property of LPCS, stress and strain of mono-Si solar cell cannot be measured. As each layer of LPCS has different material strength and thickness, the test cannot determine if there is a fragile failure under the condition of three-point bending. So in this paper, a last-ply failure (LPF) analysis method for LPCS is incorporated in the finite element code in ABAQUS/CAE with test specification.
4.1. Finite Element Analysis Model
Finite element software package ABAQUS/standard is used for the finite element modeling and simulation of the LPCS in different thicknesses like 2 mm, 5 mm, and 8 mm. The geometrical model, contact property, boundary condition, and load step are modeled and settled in ABAQUS/CAE, and the mechanical properties of modified PET, EVA, and others are given and listed in Table 2 [22–24]. A user-defined material subroutine (UMAT) is developed to introduce the strength analysis method mentioned above into the simulation.
The meshing scheme of the model is shown in Figure 7. An eight-node reduced integration element with hourglass control (C3D8R) and a four-node bilinear rigid quadrilateral element (R3D4) are implemented for mesh discretization of the 3D braided composite specimen and rollers.
4.2. Equivalent Mechanical Performance of Honeycomb Core Layer
Based on the LPCS model, with a view to the discrete heterogeneity of the honeycomb material, to simplify the analysis, the honeycomb core area is simulated to the orthogonal anisotropic body equivalent unit. This places a lot of emphasis on the selection of the equivalent model.
4.3. Equivalent Calculation of Elastic Moduli E1 and E2
For loading in the X and Y directions as shown in Figure 8, the depth of the honeycomb cell is b. By the symmetry of the honeycomb cell, single layer thickness of the hole wall is analyzed, and it has length l. By the condition of equilibrium, , , so
(a)
(b)
(c)
The wall deflects by
Of this, a component is parallel to the X-axis, giving a strain
From which, Young’s modulus parallel to the X-axis is , so
Similarly, Young’s modulus parallel to the Y-axis is , so
4.4. Calculation of Shear Modulus G1
The calculation of the shear modulus is illustrated in Figure 9. The improvement of the model hypotheses is emphasized during the modeling:(1)By symmetry, there is no relative motion of the points A, B, and C(2)Assume that each node is around the same angle(3)The shearing deflection of the structure is entirely due to the bending of beam BD and its rotation about the point B
(a)
(b)
(c)
The forces are shown in Figure 9. By summing moments at B, we find the moment applied to the members AB and BC is .
All the joints rotate through an angle . Then, since there is no deflection of B with respect to A, we have
Assume that shear deformation consists of the rotation of the cell wall BD around point B and bending formation of BD. So , and
The value for is as follows:
The shear strain
The shear stress
So, the shear modulus is given as follows:
Based on the above theory, considering the actual size of the honeycomb core layer after encapsulation by modified PET, the equivalent mechanical properties of the honeycomb model was established as shown in Table 3.
5. Mechanics Performance Optimization of Multilayer Composite Structure
The comparison of the predicted load-deflection curves of the honeycomb core layer in LPCS with different thicknesses under three-point bending with that of experimental data are given in Figure 10.
(a)
(b)
(c)
5.1. Different Thicknesses of Honeycomb Core Layer Effects on Bending Properties
It is observed from Figure 10 that the load-deflection curves show a similar changing tendency of the applied load and can be divided into three stages: the initial linear elastic stage, the nonlinear stage with the minor damage evolution, and the curve descending stage with a sudden drop of the load. The linear stage exhibited the linear elastic relationship between the load and deflection and no damages occurred in the specimens. The initial damages started on the mono-Si solar cell, but multilayer structure disperses pressure and reduces stress concentration, to prevent the crack extension, and meanwhile, the load might still have a corresponding increase. The sharp drop of the load was caused by the damages occurred on the mono-Si solar cell, as shown in Figure 11. Subsequently the multilayer composite structure lost its loading capacity.
Through the comparison between the different thicknesses of the honeycomb core layer, the load-deflection curves of the initial slope and ultimate load increases with the decrease of thickness of honeycomb core layer are shown in Figure 12. But according to the asymmetry of the structure and the local buckling of the honeycomb core layer under large deformation, the nonlinear relation of load-dependent deformation occurs [25, 26].
The predicted load-deflection curves of the 2 mm, 5 mm, and 8 mm LPCS specimens under three-point bending in comparison with the experimental results are given in Figure 12. The maximum loads of the 2 mm, 5 mm, and 8 mm LPCS specimens in the experimental results are 7.11 N, 10.11 N, and 11.96 N, whereas those of the numerical predictions are 7.03 N, 9.46 N, and 11.04 N. It can be seen that good agreements are obtained in both linear and nonlinear stages between numerical prediction and experimental results. The calculation errors of the predicted maximum loads are within an acceptable range as show in Table 4.
6. Different Thicknesses of Honeycomb Core Layer Effects on Thermal-Barrier Performance
6.1. Experimental Approach
A series of experiments were conducted to optimize the thermal performance and mechanical properties of LPCS and to provide optimized models based on the thermal insulation and mechanical properties. The following is a brief description of the LPCS test sample, experimental apparatus and instrumentation, and the experimental procedure.
6.2. LPCS Test Samples
The insulation layer of the LPCS test samples is mainly composed of honeycomb core. For the present study, three kinds of the LPCS samples with different honeycomb core thicknesses were tested and compared with monocrystalline silicon solar cells. As shown in Figure 11, the thickness of honeycomb core layers for these three different types of the LPCS samples were 2 mm, 5 mm, and 8 mm, respectively. The planar size of the sample is 125 × 125 mm. The density of lightweight Nomex honeycomb is 29 kg/m3 [27]. The solar cells studied in this experiment are monocrystalline silicon solar cells. The basic parameters of the solar cells are shown in Table 2.
6.3. Experimental Apparatus
All experimental tests were conducted in the integrated environmental test cabin, and experimental data can be obtained from related data acquisition equipment. A multiparameter large-scale environment simulation test cabin can simulate multiple parameters of the stratosphere, including items such as solar radiation heat flux, airflow velocity, cold temperature, and lower gas pressure. The test cabin is about 1.5 meters in diameter and 3.2 meters long. A heat shield cooled by liquid nitrogen surrounds the inner wall of the cabin and serves as a radiator for the test sample. The experimental apparatus for measuring the thermal performance consists of an environmental cabin, a vacuum gauge, a wet-type gas meter, a heat flow meter, a data logger, an induced draught fan, a personal computer, and a pressure gauge. As shown in Figure 13, the entire experimental apparatus and LPCS test samples were assembled in a clean room to prevent other factors.
In the course of the experiment, refer experimental design methods of Li et al. [14], the temperature and pressure in the environmental test cabin are set to the stratospheric parameters, such as the environmental temperature is 216 K and the environmental pressure is 3 kPa. The solar radiation simulated by the solar simulator irradiates the upper surfaces of the test sample in the flux range of 300–1260 W/m2. A schematic diagram of temperature measurement points and test circuit of the whole experiment is shown in Figure 14. Figure 14 is reproduced from the study of Li et al., under the Creative Commons Attribution License/public domain. The thermocouples are fixed on both upper and lower surfaces in order to install on the specimen’s heating surface. The thermocouple 1 is located at the middle portion of the upper surface, and the thermocouple 2 is located at the corresponding position of the lower surface. The thermocouples measure the temperatures of the upper and lower surfaces of the test samples. The temperature data are recorded by the data logger when the temperature change per 10 minutes is less than 1°.
7. Results and Discussion
The experimental data of temperature difference between upper and lower surfaces at three types of LPCS and mono-Si solar cell for studying thermal performance are presented in Figure 15. The optimum design of the thermal performance is discussed. From the upper and lower surfaces of experimental date analysis and comparison, the effects of the thickness of the honeycomb core layer on the specific temperature difference are analyzed.
(a)
(b)
(c)
(d)
7.1. Experimental Results of Thermal-Barrier Performance
Based on the experimental approach in Section 6.3, some measurement results are obtained to investigate thermal insulation performance of the LPCSs. The upper and lower surface temperatures were not recorded until the temperature reached the steady state, and the results were not continuous by choosing the value of four typical irradiation. The steady-state temperature of the test samples under different irradiation conditions is shown in Figure 15. The experimental results show that the relationship between the temperature and the solar radiation flux irradiating on the sample exhibited a nonlinear relationship and has a special change trend.
The experimental results of the effects of the honeycomb core thickness on specific temperature differences are shown in Figure 16. It shows the representative results of the measurements, and the ordinate shows the specific temperature difference among three types of LPCSs and mono-Si solar cells. It is observed that there is a positive correlation between the particular temperature differences for three types of LPCSs and mono-Si solar cell, and the solar radiation flux increases. The specific temperature difference also increases with the increase of thickness under the same solar radiation. It is notable that, under the same illumination intensity, the specific temperature difference of the 8 mm test sample is the largest, and the temperature difference of monocrystalline silicon solar cells test sample is the lowest. It is also important to note that this result is different from the conclusion shown in Figure 10. An optimized LPCS can be designed by combing the effect of thickness on specific temperature difference and mechanics performance.
7.2. Discussion of LPCS
This paper describes the concept of deflection weight ratio, which is used to analyze different thicknesses of the honeycomb core layer to improve the deflection of LPCS, considering the structure weight as shown in Table 5. Finally, a factor defined as the ratio of the increase of deflection to discontinuity density is used to estimate the optimal design of LPCS.
On the premise of having the same structural weight, the larger the deflection weight ratio of the LPCS, the more the effect of structure flexibility. We can see from Table 5 that, to improve the deflection of structure, 5 mm honeycomb core layer is the optimal choice compared with 2 mm and 8 mm.
Considering the thermal insulation of LPCS, we also proposed the concept of temperature difference weight ratio. As shown in Table 6, the temperature difference weight ratio actually increases with thickness of honeycomb core layer, so only with that in mind, 8 mm honeycomb core layer was the best choice for LPCS. But considering the capsule volume of stratospheric airships was usually too huge and the surface curvature of the buoyancy capsule was small, so local stress concentration of the airship envelope could easily lead to large transformation and cause the capsule to overpressure damage and blast quickly, and it will be necessary to try avoiding the thermal stress caused by the variation of temperature in the airship envelope. Therefore, the average irradiation of the airship in the stratosphere is considered as 1000 W/m2, and the average temperature of the internal gas in the capsule is considered as −3.15°C (270 K) [28]. As shown in Figure 15, the lower surface temperature of the 5 mm honeycomb core layer of LPCS (−5.86°C or 267 K) is closer to the average temperature of the internal gas (−3.15°C or 270 K) than the 8 mm honeycomb core layer (−11.12°C or 262.03 K). According to Figure 12 and Table 5, the 5 mm honeycomb core layer shows the best flexibility of LPCS. In conclusion, in order to avoid the thermal stress caused by the variation of temperature in the airship envelope, the 5 mm honeycomb core layer is considered the optimal choice compared with 2 mm and 8 mm for LPCS.
8. Conclusion
This paper developed a lightweight photovoltaic composite structure (LPCS) according to the characteristics of the stratospheric airship capsule. In order to improve the flexible of the solar cell, we studied the mechanical properties in the different thicknesses of the honeycomb core for LPCS by FEM software and three-point bending test. The experiments were conducted to measure the temperature difference between upper and lower surfaces of the LPCS test samples under different solar radiation flux conditions. The experimental data were examined to evaluate the mechanical properties and thermal insulation performances of LPCS. Considering the quality of the whole structure, the paper finally gives the conclusion of the optimal thickness of the honeycomb core with more detailed descriptions.(1)The LPCS in 5 mm have the best overall mechanical properties and the most appropriate thermal insulation performance, followed by 2 mm LPCS and 8 mm LPCS. Therefore, the 5 mm LPCS can be used as a suitable lightweight photovoltaic composite structure for application in the solar array on stratospheric airships.(2)As the LPCS underwent high deformation during the bending test, simple linear beam theory was not sufficient to calculate the stress on the cells. A model similar to the one discussed in this paper was used to take into account the large deflections. By comparing with the experimental data, it is also possible to reduce the deviation by modifying specific parameters. The theory of the honeycomb core also requires further study.(3)The different thicknesses of the honeycomb core layer for LPCS considering the structure weight have great influence on the mechanical properties and the thermal insulation performance. Therefore, it can be studied and applied to the optimized design of LPCS.
Nomenclature
| : | Absorptivity of envelope |
| : | Absorptivity of solar cell array |
| : | Temperature of the gas in the airship hull |
| : | Degree of flexing of the airship hull |
| ε: | Strain of the material |
| P: | Load on the solar cell |
| L: | The span of three-point bending test |
| I: | Inertia moment of the cell in flexion |
| B: | Width of the cell |
| t: | Thickness of the cell |
| θ: | Deformed shape of the cell |
| δ: | Deflection at the center |
| b: | Depth of the honeycomb cell |
| l: | Length of hole wall |
| E: | Young’s modulus |
| : | Elastic modulus of Nomex honeycomb paper |
| : | Elastic modulus in the x direction |
| : | Elastic modulus in the y direction |
| G: | Shear modulus |
| : | Shear modulus in the x direction |
| : | Shear modulus of Nomex honeycomb paper. |
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant Nos. 51775021 and 51307004, the Key Laboratory of Aircraft Advanced Design Technology (Beihang University), and the fifth youth top talent support program of Beihang University and Ministry of Industry