Thermal Characteristics of Multilayer Insulation Materials for Flexible Thin-Film Solar Cell Array of Stratospheric Airship

Flexible thin-film solar cell is an efficient energy system on the surface of stratospheric airship for utilizing the solar energy. In order to ensure the normal operation of airship platform, the thermal control problem between the flexible thin-film solar cell and the airship envelope should be properly resolved. In this paper, a multilayer insulation material (MLI) is developed first, and low temperature environment test is carried out to verify the insulation effect of MLI. Then, a thermal heat transfer model of flexible thin-film solar cell and MLI is proposed, and the equivalent thermal conductivity coefficients of flexible thin-film solar cell and Nomex honeycomb are calculated based on the environment test and the temperature profile of flexible thin-film solar cell versus each layer of MLI. Finally, FLUENT is used for modeling and simulation analysis on the flexible thin-film solar cell and MLI, and the simulation results agree well with the experimental data, which validate the correctness of the proposed heat transfer model of MLI. In some way, our study can provide helpful support for further engineering applications of flexible thin-film solar cell.

Solar energy is an ideal choice to provide power for highaltitude and long-endurance airships.This type of power system is actually a photovoltaic (PV) array coupled to an energy storage system [2].The efficiency, mass, surface shape, and position of the PV array significantly influence the airship performance, whereas the PV array performance depends on its operation conditions such as latitude, time, temperature, and geometry.Therefore, the PV array and its operation conditions are critical to the airship design and capabilities.Besides, the PV array also has significant effects on the temperature profile of the airship hull, which can enhance the "superheat" or "supercool" of airship [9].
In the past decade, many investigations have been carried out on the energy system of the stratospheric airship.Harada et al. [5] conducted experiments on the thermal characteristics of a 35-meter-long low-altitude airship equipped with PV array, which was developed as a flying test bed for the development of stratospheric airship.Naito et al. [6] proposed the design and analysis of solar energy power system for stratospheric airship operations.Shi et al. [7] studied the solar energy collected by stratosphere airship's surface.Zheng et al. [8] studied the solar power and power output characteristics of the solar cell array of a stratospheric airship.Li et al. [9] investigated the thermal characteristics of photovoltaic array of a stratospheric airship.In addition, Eskind et al. [10] mentioned a thermal control measure by using 7 mm thick insulation panels between the solar cell array and the envelope.Overall, current investigations mostly focus on the power system but seldom pay attention to the insulation of stratospheric airship solar array.
According to the characteristics of stratospheric airship envelope and flexible thin-film solar cell, this paper develops a multilayer insulation material (MLI) and then proposes a heat transfer model for the MLI.Further, in order to verify the insulation effect of MLI and get the temperature profile of flexible thin-film solar cell and each MLI layer, an experimental test is carried out to calculate the equivalent thermal conductivity coefficient of flexible thin-film solar cell and Nomex honeycomb.Finally, FLUENT is used for modeling and simulation analysis on the flexible thin-film solar cell and MLI.

Physical Model
MLI is a commonly used material in multilayer insulation for space vehicles.It can be composed of multilayer reflector screens, or laminated together with spacer.Since the flexible thin-film solar cell and the hull of stratospheric airship are both of flexible structures, considering the environment of stratosphere, MLI can be applied to insulation of the flexible thin-film solar cell.Yinbing et al. [11] developed an Al/PI/SiO 2 multilayer insulation film with Al film as the heat reflective screen, silicone nano-composite coating as the low thermal conductivity layer, and polyimide (PI) as the flexible substrate.Weidong et al. [12] obtained the patent of a thin flexible insulation composite fabric.Ahluwalia et al. [13] developed a flexible multilayer composite insulation material which was made of metal foil (film) and flexible foam layer.These MLIs have good flexibility, light weight, and good heat insulation performance, but their mechanical strength is very weak.For example, the tensile strength of PI is 200 MP at 20 ∘ C and temperature rise can further decrease its tensile strength.
Based on existing flexible insulation structures and enhancement structures, we develop an MLI by virtue of PET, fiberglass mesh, epoxy resin film, and Nomex honeycomb.The PET film can be used as the substrate to which the fiberglass and Nomex honeycomb are attached.The fiberglass has high mechanical strength and can be used as the enhancement structure.The epoxy resin film can be used as adhesive to combine each layer together.The Nomex honeycomb is a hollow flexible insulation material and has a good capability of thermal insulation.The structure of MLI is shown as Figure 1.

Analysis of Heat Transfer Process
3.1.Heat Transfer Model.The structure is composed of the thin film solar cell, PET, fiberglass mesh, epoxy resin film, Nomex honeycomb, and airship hull.Thermal property of each layer is different, and solar radiation absorbed on different parts of the thin film solar cell is nonuniform.Thus, the thin film solar cell can be treated as a heat conductor with nonuniform inner heat source.In view of this, a separate heatbalance equation should be written for each layer to obtain a better estimation of the temperature.The heat transfer mechanism of the structure is shown as Figure 2, which can  be expressed by the following five differential time-dependent equations: where where  is the area of flexible thin-film solar cell, m 2 ;  0 = 1367 w/m 2 is the solar constant;  is the reflectivity of flexible thin-film solar cell;  is the conversion efficiency of solar cell;   is the mass of Layer , kg; and   is the specific heat capacity of the material of Layer , J/(kg⋅K).
The radiation heat loss on the surface of thin film solar cell is given by where  is the emissivity of flexible thin-film solar cell;  is the constant of Stefan-Boltzmann,  = 5.67×10 −8 W/(m 2 ⋅K 4 );  1 is the temperature of the upside of flexible thin-film solar cell, K; and  ∞ is the sky equivalent temperature, K.
The conductive heat loss is given by where ℎ is the convection heat transfer coefficient.ℎ can be given by where  is the characteristic length, m;  air is the thermal conductivity of air, = 0.5 × ( 1 +  ∞ ) is the characteristic temperature; and   is the Nusselt number: where   is the Prandtl number,   = 0.804 − 3.25 × 10 −4 ×   ; and   is the Grashof number, in which  is the acceleration of gravity;  is the coefficient of cubic expansion, 1/K; and  is the kinematic viscosity of air, m 2 /s.
To calculate the thermal conductivity of flexible thin-film solar cell and Nomex honeycomb accurately, an experiment is designed to obtain the equivalent thermal conductivity coefficient.

Thermal Conductivity of Flexible Thin-Film Solar Cell.
The surface of flexible thin-film solar cell is exposed to ambient air.The exposed area is  and the temperature of ambient air is  ∞ .When the solar radiation intensity is  0 , the upside and downside temperatures of flexible thin-film solar cell are  up and  down when the solar radiation intensity is, respectively.
The structure of flexible thin-film solar cell is shown in Figure 3.
The flexible thin-film solar cell is composed of PET, EVA, and single-junction amorphous silicon cells, which can be treated as a multilayer model.Parameters of the flexible thinfilm solar cell are listed in Table 1.
To simplify the energy model of flexible thin-film solar cell, it is assumed that a portion of solar flux is absorbed by the solar cell while the other part is reflected back to the atmosphere.The surface has convective heat transfer with the atmosphere.The flexible thin-film solar cell has conductive  heat transfer with the MLI.The mechanism of heat transfer of the flexible thin-film solar cell is shown in Figure 4.
According to the mechanism of heat transfer of the flexible thin-film solar cell, steady-state energy equation of flexible thin-film solar cell can be established.Thus, when the  up ,  down ,  ∞ , and  0 are obtained, we can calculate the thermal conductivity of flexible thin-film solar cell: where  is the equivalent thermal conductivity of flexible thin-film solar cell; and  is the thickness of flexible thin-film solar cell.
Since each layer of the flexible thin-film solar cell is tightly laminated together, the thermal contact resistance can be ignored.Thus, the thermal conductivity can be given by where  1 ,  2 ,  3 ,  4 , and  5 are the thickness and  1 ,  2 ,  3 ,  4 , and  5 are the thermal conductivity of each layer of the flexible thin-film solar cell.Then, the thickness of the flexible thin-film solar cell can be given by The conductive heat can be calculated from the steadystate energy equation, and then we can get the thermal conductivity of the flexible thin-film solar cell according to (5)-(8).

Equivalent Thermal Conductivity of Nomex Honeycomb.
Nomex honeycomb is used at the bottom of the MLI.The Nomex honeycomb layer has conductive heat transfer with the adjacent epoxy resin film layer.To establish the calculation model of equivalent thermal conductivity of Nomex honeycomb, it is necessary to study the cell unit of honeycomb, as shown in Figures 5 and 6.
The side length of Nomex honeycomb is  = 1.83×10 −3 m, the height is  = 5.5 × 10 −3 m, and the wall thickness of single layer is  = 0.2 × 10 −3 m.According to the results of Liang et al. [14], convection heat transfer of air inside honeycomb can be ignored.Hence, heat transfer model of the honeycomb mainly consists of solid heat conduction of the sandwich layer of cell wall, air heat conduction inside the honeycomb, and radiation heat transfer between honeycomb    cell wall and the upper and lower panels.The equivalent thermal conductivity can be given by where   is the thermal conductivity of the thin foil parent material of honeycomb;   is the thermal conductivity of air inside the honeycomb;   is the radiation thermal conductivity of honeycomb cell wall and the upper and lower panels; Δ is the cross-sectional area of honeycomb core material, Δ = 16; and  is the cross-sectional area of cell unit,  = 6 √ 3 2 .Thermal conductivity of air inside the honeycomb is given by   = 0.0241 (   273.15 ) where   = ( 1 +  2 )/2 is the characteristic temperature, in which  1 and  2 are the temperatures of the upside and down side of honeycomb.Radiation thermal conductivity of honeycomb is given by Swarm and Pittman [15]: where  = / is the ratio of the height and side length of the honeycomb;  is the emissivity inside the honeycomb;  = 5.67 × 10 −8 W/m 2 ⋅K 4 is Stefan-Boltzmann constant; and  1 and  2 are unknown.In order to determine  1 and  2 , iterative calculations are required.In this paper, according to the experimental test data,  1 =  5 and  2 =  base .

Experimental Test
In this section, an experimental test is carried out to verify the insulation effect of the MLI, as well as to calculate the thermal conductivity of flexible thin-film solar cell and Nomex honeycomb accurately.Besides, the heat transfer model is also validated by the experimental test.The dimensions of environmental cabin are  ×  = 1.8 m × 3.5 m.Two pieces of flexible thin-film solar cell are put in the environmental cabin, and their dimensions are 0.24 m × 0.22 m.The temperature of the environmental cabin is −56 ∘ C, and the pressure is 5 kPa.Radiant intensity of solar simulator is 1260 W/m 2 .Test specimen 1 is just flexible thinfilm solar cell, which is used to test the temperatures of the upside and downside of flexible thin-film solar cell, as shown in Figure 7. Test specimen 2 is composed of flexible thin-film solar cell and MLI, which is used to test the temperatures of the upside and downside of flexible thin-film solar cell as well as the temperature of the downside of MLI, as shown in Figure 8.
Taking test specimen 2 as an example, temperature sensors 1 and 2 are at the upside of the thin film solar cell, temperature sensors 3 and 4 are at the downside of the thin film solar cell, and temperature sensors 5 and 6 are at the downside of the MLI.Here, sensor 1 corresponds to sensors 3 and 5, and sensor 2 corresponds to sensors 4 and 6.

Computational Simulation and Analysis
According to the test data of test specimen 1, the steady temperatures of the upside and downside of the flexible thinfilm solar cell are 65.5 ∘ C and 63 ∘ C, respectively.According to ( 5)-( 8), the thermal conductivity of flexible thin-film solar cell is  = 0.2246 W/(m⋅k). Figure 11 shows that the steady temperature of the downside of the Nomex honeycomb is 25.5 ∘ C. According to the test data of test specimen 2 and ( 1)-( 7) and ( 12)-( 14), through iterative calculation, the final thermal conductivity of Nomex honeycomb is  = 0.021 W/(m⋅k), as shown in Figure 12.
Figure 13 shows the simulation temperature profile of the multilayer insulation. 1 = 61 ∘ C is the average steady temperature of flexible thin-film solar cell, which is measured from test specimen 2.  2 ,  3 ,  4 , and  5 are the simulation temperatures of PET, fiberglass mesh, epoxy resin film, and Nomex honeycomb, respectively, and their final steady temperatures are 59.5 ∘ C, 58 ∘ C, 39.3 ∘ C, and 24.4 ∘ C. It can be seen that the temperatures of flexible thin-film solar cell, PET, and fiberglass mesh are more or less the same, whereas the temperatures of the epoxy resin film and Nomex honeycomb decrease dramatically due to their large thermal resistance caused by the hollow structure.Figure 14 shows the comparison of simulation results with relevant test data of  base .The absolute error of simulation results relative to relevant test data is less than 2 ∘ C; namely, the relative error of the temperature of  base is within 5%.Therefore, the simulation results are accurate and reliable.
Finally, to investigate the applicability of the numerical model of MLI, FLUENT is used for modeling and simulation analysis on the flexible thin-film solar cell and MLI.To simplify the model, a 24 cm × 22 cm × 0.6 cm three-dimensional model of flexible thin-film solar cell and MLI is put in a fixed computational domain.
Solar load model is used to calculate the effect of solar irradiation on temperature distribution of the thin film battery.This model includes direct solar irradiation, diffuse solar irradiation, and ground-reflected solar radiation.Two options, Fair Weather Conditions method and Theoretical Maximum method, are, respectively, put forward for computing the solar load in the software, and Theoretical Maximum method is proved to be more appropriate for stratosphere and outer surface where little atmospheric extinction happens.The equation for this method is where  is the correction factor used to modify the reduction of solar irradiation due to aerosphere.The material of the wall around the computational domain is supposed to be copper (absorptance and emittance are all 0.98).Temperature of the wall is −56 ∘ C. Solar radiation enters the computational domain from the top, and the bottom is set as outflow.Air in the computational domain is set as incompressible-ideal-gas.DO     diffuse solar radiation are calculated by solar calculator.After a 50 min calculation, the accurate temperatures of the upside and downside of the flexible thin-film solar cell and MLI can be obtained, as shown in Figure 15.
Figure 15 shows that the highest temperature of the surface of flexible thin-film solar cell is 336 K (63 ∘ C), and the highest temperature of the downside of MLI is 295 K (22 ∘ C), with the temperature decreasing from center to around.For the upside of flexible thin-film solar cell, the absolute error of simulation result relative to test data is about 2.4 ∘ C, and the relative error is within 10%.For the downside of MLI, the absolute error of simulation result relative to test data is about 2 ∘ C, and the relative error is within 3%.Therefore, the simulation results are accurate and reliable.

Conclusions
This paper developed a multilayer insulation material (MLI) according to the characteristics of stratospheric airship hull and flexible thin-film solar cell.The insulation effect of MLI was verified by environmental test, and its heat transfer model and thermal characteristics were analyzed.The main conclusions are as follows.
(1) The equivalent thermal conductivity coefficients of flexible thin-film solar cell and Nomex honeycomb are calculated as 0.2246 W/(m⋅k) and 0.021 W/(m⋅k), respectively.
(2) MLI has a good heat insulation performance of 36.5 ∘ C. The temperature difference between the layers of flexible thin-film solar cell, PET, and fiberglass mesh is small due to the small thickness and heat resistance, whereas the temperatures of the epoxy resin film and Nomex honeycomb decrease dramatically due to their large thermal resistance caused by the hollow structure.
(3) The heat transfer model established in the paper and simulation results of MLI agree well with the environmental data.It can be concluded that the simulation results are accurate and that the heat transfer model is reliable.
(4) FLUENT is used for modeling and simulation analysis on the flexible thin-film solar cell and MLI, and the results agree well with the environmental test data.
In some way, our study can provide support for further engineering application of flexible thin-film solar cell.Our future research will focus on the effects of MLI on the thermal characteristics and output efficiency of the photovoltaic array, and the effects of MLI on thermal characteristics of the airship.

Figure 3 :
Figure 3: Structure of flexible thin-film solar cell.

Figure 4 :
Figure 4: Mechanism of heat transfer of the flexible thin-film solar cell.
Figure 9 illustrates the test circuit diagram.Temperature data are recorded by temperature inspection instrument until temperature change <3 ∘ C/10 min.The test data of test specimen 1 and test specimen 2 are shown in Figures 10 and 11, respectively. 1up1 and  1up2 are the temperatures of the upside of test piece 1.  1down1 and  1down2 are the temperatures of the downside of test piece 1.  1up ( 1up = ( 1up1 +  1up2 )/2) and  1down ( 1down = ( 1down1 +  1down2 )/2) are the average temperatures of the upside and downside of thin film solar cell, respectively. 2up1 and  2up2 are the temperatures of the upside of test piece 2.  2middle1 and  2middle2 are the temperatures of the downside of thin film solar cell of test piece 2.  2down1 and  2down2 are the temperatures of the downside of the MLI of test piece 2.  2up ( 2up = ( 2up1 +  2up2 )/2) and  2middle ( 2middle = ( 2middle1 +  2middle2 )/2) are the average temperatures of the upside and downside of thin film solar cell, respectively. 2down ( 2down = ( 2down1 +  2down2 )/2) is the average temperature of the downside of the MLI.

Figure 15 :
Figure 15: Temperature distribution on upside of the thin film cell and downside of the MLI.

Table 1 :
Parameters of each layer of the thin-film solar cell.