Analytical and numerical approaches of a solar array thermal analysis in a low-earth orbit satellite
Introduction
A solar array of a satellite is a main power source in mission operation in that it converts solar energy into electric power. The performance of a solar array can be estimated from its solar cell efficiency, i.e., the ratio of incident solar energy to converted power.
Although there are many factors influencing solar cell efficiency, an in-orbit temperature of a solar cell is critical and the lower temperature can get better efficiency. Since the temperature variation range of a low-earth orbit satellite solar array is usually very wide, nearly −80 to 80 °C, a severe thermal environment is unavoidable. A thermal surface treatment of the backside of a solar array must reduce the maximum temperature to the greatest extent possible to obtain better solar cell efficiency. Therefore, the maximum temperature of a solar array under the worst hot condition is a baseline for thermal design of the backside of a solar array. And for reliable and conservative thermal design, a thermal surface finish of a passive thermal control method such as surface paint or a coating is applied.
A number of researches have investigated thermal design for satellite thermal control. The purpose of thermal design is to maintain the component temperature of a satellite within the allowable range at any mission phase. Therefore, reliable thermal control with a sufficient margin must be implemented. The selection of a thermal design method is based on the results of a thermal analysis associated with the worst conditions although a satellite cannot experience the worst conditions in orbit as used in analysis. They are predefined conditions only for conservative thermal design. Tsai (2004) proposed simplified governing equations for pure radiation heating and cooling with exact mathematical solutions to eliminate complexity in a general thermal model at the expense of analysis accuracy. Baturkin, 2005, Lee et al., 2006 surveyed current tendencies in thermal control of a micro-satellite and a small-satellite respectively. Thermal control of both satellites is troublesome because mass, power, and volume are all very limited. Narayana and Reddy (2007) successfully executed thermal design of HAMSAT, which is a sort of a micro-satellite. Accordingly, Han and Choi (2004) accomplished thermal design of a low-earth orbit satellite propulsion system by means of a thermal analysis. Their thermal design was successfully verified when compared with the results from a thermal balance test of a structure and thermal model.
On the other hand, some investigators have paid special attention to thermal control of a satellite solar array. Shin et al. (2001) predicted the transient response of thermal distortion of the Korea Multi-Purpose Satellite (KOMPSAT) solar array in orbit. In case of a folded solar array, the combined radiation–conduction heat transfer was analyzed by Yang et al. (2004) who considered a three-dimensional anisotropic conduction. Kim et al. (2005) developed a simple method to predict temperatures of a satellite box during launch stage. This simple method can solve a 1st order ordinary differential equation (ODE), which is simplified from the thermal balance governing equation after applying several assumptions. Moreover, Kim et al. (2009) predicted a solar array temperature both analytically and numerically. The current paper is an extension of their work.
Fig. 1 shows in-orbit thermal environments of a low-earth orbit satellite with a fixed-type solar array during daylight. For more power generation, the solar cell side of a solar array must face the Sun. This requirement determines in-orbit satellite attitudes according to the orientation of a solar array as sun-pointing during daylight. However, satellite attitudes in an eclipse have has no restraint in aspect of generating power. This is defined by a satellite operation concept.
Since a fixed-type solar array is attached to the spacecraft bus through the hinges which are made from a very low conductive material, it can be assumed that the solar array is nearly thermally isolated from the spacecraft bus (Gilmore, 2002). Thus, it can be treated with a thermally isolated one in order to predict the worst temperature. In this paper, an analytical solution of a simplified thermal balance governing equation is used to select an adequate thermal surface finish as a thermal surface treatment. For an actual thermal surface finish, the in-orbit temperature profiles of a solar array based on both the one-node simplified model and the detailed thermal model are evaluated and compared. And the usefulness of an analytical approach is also examined through compared with the detailed thermal analysis.
Section snippets
Solar array design summary
The current solar array has three wings which are fixed to the −Z bottom side in each direction, as shown in Fig. 2. Each solar array wing is a panel structure, which is 2.04 m × 1.00 m in size and is composed of a solar cell package and a honeycomb substrate. One solar cell is a small flat rectangular shape in size of 76.1 mm × 37.16 mm (3″ × 1.5″). Approximately 560 solar cells are mounted with adhesive on the honeycomb substrate. The figures of a solar cell and mounting on the honeycomb substrate are
The concept of a solar array thermal analysis
The thermal balance governing equation is a 2nd order partial differential equation. Although simplified by several assumptions, it is hardly solved analytically except for a few special cases. This is because a numerical analysis of a detailed thermal model is the only mean to a practical solution.
An analytical method is rather simple and can be applied to a lumped-mass thermal model, while a numerical method is a general approach to solve a detailed thermal analysis model for predicting an
An analytical method for predicting the worst hot temperature of a solar array
The worst hot temperature of a solar array is predicted through an analytical approach for a single-lumped mass thermal model in Fig. 5. The assumptions to simplify a solar array thermal model are as follows:
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Solar array is assumed to be a single-lumped mass.
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Because conductive heat transfer is neglected in a solar cell package and a honeycomb substrate, only radiation exists.
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Both sides of a solar array are thermally-coupled with the deep space by radiation.
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For the worst hot condition, a
The development and the analysis of a detailed thermal model of a solar array
The current solar array is attached to the spacecraft bus as an appendage. Hence, the solar array thermal model can be simplified into a single-lumped mass node and the steady temperature under a constant worst hot environment can be predicted independently by an analytical solution of the simplified thermal balance governing equation. Although this analytical approach is sufficient to determine a thermal design method under the worst conditions, it cannot simulate an in-orbit thermal behavior
The results of the detailed solar array thermal analysis
From the detailed solar array thermal analysis, the in-orbit temperature profile and several thermal characteristics of the current solar array are obtained through a thermal analysis. Moreover, the thermal elements affecting the solar cell performance, such as the shadow effect, hot spot, and back current as well as the thermal distortion can be recognized from the temperature distribution and gradient over the surface. In this paper, the in-orbit thermal aspects of the solar array are
Conclusion
First, an analytical steady solution is derived from the simplified one-dimensional thermal balance governing equation for a one-node thermal model under in-orbit thermal environmental conditions.
Generally, if an object is thermally decoupled with the spacecraft bus, its thermal analysis can be performed independently by an analytical approach. Because the current solar array is attached to the outside of the spacecraft bus as an appendage, the influence of the spacecraft bus can be neglected
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