A University Small Satellite Thermal Control Modeling and Analysis in the Post-Mission Phase

This work includes the thermal control analysis of a small spacecraft in the post-mission phase. The satellite internal component distribution has been modified to fulfill all thermal requirements when using a passive thermal control system. In the post-mission phase, the satellite will be used by the radio Amateur Satellite Corporation (AMSAT) community as a transponder, fully using the AMSAT payload that will maintain active and shall last at least 2 years. Thermal Desktop software is introduced for the mentioned spacecraft. The final analysis predictions show that the passive thermal control system maintains all satellite element's temperatures within their temperature limits. The temperature variation of +X solar panel is 75 °C which is less than experienced by +Z and –Z panels, which are 100 °C. The temperature change on equipment agrees with their panels. Compared with a specialized thermal analysis, software package (ESATAN-TMSs) verified the integrity of the results.


INTRODUCTION
A thermal control system (TCS) is a significant issue in both the designing and manufacturing processes of a spacecraft. It emphasizes the appropriate operation of the satellite in the operating temperature ranges in its orbit [1][2]. Several analytical calculations analyzing spacecraft thermal control have been carried out, for instance, the Fourier analysis [3] and techniques of the linearization method [4][5][6][7]. Anh. et al. [8][9][10] extended the equivalent linearization method to the thermal analysis of satellite using both conventional and dual criteria of linearization. The analytical investigation of satellite thermal control is very difficult due to complicated nonlinear terms existing in the thermal models. Analytical analyses are only beneficial for simple geometric case studies which are not representative of real cases [11]. So, recent complex numerical algorithms were developed and incorporated for satellite thermal problems in commercial software [1,12]. The definition of small satellites is not clear and different organizations define small satellites differently [13]. Table 1 summarizes a number of these definitions. Based on Surrey Space Centre, small-satellite classification [14], the following groups were identified; nanoand pico-satellites (< 10 kg), micro-satellites (10-100 kg), mini-satellites (100-500 kg), interplanetary small missions (< 500 kg).
Certain requirements originating in small-satellite designs due to limited mass and power, limited volume for payload, and housekeeping systems generate major challenges for small satellite thermal control system design and analysis [16].
Most literature showed that the spacecraft TCS is primarily passive; however, uses heaters in critical locations [34]. Assessing the thermal characteristics of a picky contestant design includes the implementation of a complicated and costly numerical simulation. The structure of the proposed system is often represented using a mesh during simulations. Then, numerical solution of the governing equations is carried out by using different schemes namely; finite-difference time-domain (FDTD), finite element (FEM), or moments (MoM) methods boundary conditions related to the studied problem must be set.
The thermal models have been validated with the assistance of actual tests or with results obtained from other software. Corpino et al. [35] proposed finite difference schemes to model the thermal performance of LEO satellites. Their results were validated using ESATAN-TMS modeling software. Diaz-Aguado et al. [36] carried out the thermal design of the FASTRAC Nanosatellite considering vacuum conditions. They used FEM Results to validate their results. Bulut et al. [37] investigated the thermal characteristics of a CubeSat using FEM by investigating different solar panel configurations. To our knowledge, there is no standard method to carry out the design of a Cu-beSat Thermal Control System using highly developed computation, especially for passive thermal systems [11].
The European Student Earth Orbiter (ESEO) spacecraft [25] was selected to carry this work. It was established by candidates of different universities sponsored by the European Space Agency (ESA) education office. ESEO is LEO micro-satellite mission. This satellite has five mission stages: launch and early operations; operational; extended stage; post-mission and finally dispo-sal. This study is concerned with the post-mission stage that begins after the extended stage or the operational stage and shall last at least 2 years. In this stage the spacecraft will be used by the radio Amateur Satellite Corporation (AMSAT) community as a transponder, fully using the AMSAT payload that will remain active. The satellite will be ordered to obtain a safe configuration, permitting it to survive without help from the ground.
The novelty of this paper is to enrich the thin literature on the thermal design of small-sized satellites. Since detailed thermal control modeling and analysis are rare, the work might give an insight to fellow small-size satellite developers. ESEO thermal control system was initially designed as active thermal control and thermal analysis was performed using the ESATAN software package [25]. This paper includes an alternative means for the thermal control system to be passive by using tapes, coatings, radiators, and Multi-Layer Insulation (MLI) applied to the satellite to regulate the interaction between the spacecraft and its surroundings. A detailed thermal model for ESEO satellite has been created using Thermal Desktop software [38]. Results were partially verified using the published data of ESEO for the external radiation absorbed by the satellite.
The work is arranged as follows: first, the selected satellite for study, ESEO is described; then, the thermal analysis model based on a nodal lumped parameter method is elaborated; finally, results, discussions, and conclusions are given. Fig. 1 and 2 show the external and internal views respectively for the satellite under investigation. The satellite is a cuboid shape with six structural panels, two deployable and one fixed solar panel. Its dimensions are 967 × 750 × 680 mm and its mass is less than 100 kg.

Fig. 2 Internal view of ESEO satellite adapted from [25]
The mission was based on sun-synchronous orbit with an altitude of 520 km and an inclination of 97.48° with Local Time of Ascending Node (LTAN) 10:30. Satellite systems/components are given in Table 3.

Thermal Control Design
ESEO thermal control system was initially designed as active thermal control and thermal analysis was per-formed using ESATAN software package [25]. The satellite has been partially modified by changing the placement of the internal components and controlling external radiation exchange by managing the exterior thermo-optical properties. All spacecraft equipment is redistributed on the six structural panels to meet all thermal requirements when a passive TCS instead of an active TCS was used. The distribution of the internal components on different structure panels is shown in Table A.1 in Appendix A.

Thermal Energy Balance
The thermal modeling is based on a nodal or lumped parameter method. In this method, the satellite is divi-ded into several regions, assumed isothermal, which are called nodes. These nodes exchange heat among each other by conduction and radiation. The external nodes exchange heat with the surroundings via radiation. The temperature of each node is the result of these interactions. The energy balance on node i is expressed by Equation (1) [39] , , , , , The conductive heat rate, Q conductive,ij, and radiative heat rate, Q radiative,ij exchange between nodes is given by equations (4), (5) respectively [40].
The conductive and radiative heat exchange factors are defined as: where K ij is conductive heat rate exchange factor between nodes i and j [W/K]; R ij is radiative heat rate exchange factor between nodes i and j [W/K 4 ]; A i is the nodal area [m 2 ]; dx is the distance between two adjacent nodes [m]; ε ij is the emissivity between nodes i and j; T i and T j are the temperatures of nodes i and j, respectively [K]. F ij is the view factor between nodes i and j which is defined as the fraction of radiation leaving surface i that is intercepted by surface j Then, Equation (1) becomes:

Geometry Creation and Methodology
The first step in model creation is defining the external geometry. The spacecraft geometry consists of a cuboid structure (six structure panels) and three solar panels (one fixed and two deployable panels). Each external solar or structural panel was created in the thermal desktop software by a rectangle. From structure designers, the external panels are designed of two different materials-honeycomb and aluminum 2024. Aluminum was used for panels number one, four, and five (in the directions +X, -X, and -Y respectively). For design reasons, the aluminum panels have a thickness of 20.6 mm. Honeycomb panels were used for panels number two, three, and six (in the directions +Y, +Z, and -Z respectively) and the three solar panels. The body or equipment panels have a shell thickness of 0.3 mm and a core thickness of 20 mm with a total thickness of 20.6 mm. The solar panels have a shell thickness of 0.3 mm and a core thickness of 13 mm with a total thickness of 13.6 mm. The second step is defining the internal geometry that represents the equipment. To create a thermal model of the internal equipment in the Thermal Desktop, all equipment was represented as cylindrical or box shapes. Each piece of equipment has a thickness of 5 mm, heat capacity of C p =921 J/kgK, and thermal conductivity of k = 155 W/mK which approximates all equipment to aluminum [25]. Fig. 3 shows the final view of the ESEO spacecraft geometry in the Thermal Desktop.
Nine nodes were defined for each panel, coming to a total of 81 nodes for the external structural and solar panels. Six nodes were defined for each internal equipment to create a total of 126 nodes and the Multi-Layer Insulation (MLI) was modeled with 36 nodes. The numerical model has a whole of 243 nodes. Three types of nodes can be identified in the model: diffusion, arithmetic, and boundary nodes. The satellite is represented by 207 diffusion nodes and 36 arithmetic ones. Some experience is needed to determine the suitable number of nodes for each element (grid sensitivity analysis). In general, more nodes lead to higher resolution in the results. At the same time, increasing the number of nodes will increase the complication of the model and the time needed to build and run the model. Once a well-defined model is settled and initial conditions are specified, steady-state and transient computations can be obtained for all nodes over the chosen time interval.
This analysis is carried on Thermal Desktop (TD) software, which is capable of either finite difference or finite element investigations [37] with/without graphical interfaces. These graphical interfaces include a nongeometric sketchpad-style Sinaps and the geometry-based Thermal Desktop with its companion modules RadCAD and FloCAD [38].
The analysis starts with gathering enough infor-mation about satellite equipment nominal operation temperature ranges and predicted heat dissipation. Thermal boundary conditions for the post-mission phase must be identified, including spacecraft altitude, orbital parameters, and orientation relative to the Sun and Earth.

Boundary and Operating Conditions
The orbital parameters define the location of the satellite relative to the Earth and Sun as presented in Table A.2. The external fluxes that encounter a satellite are solar, albedo, and planet Infra-Red (IR). Solar flux varies throughout the year because of the varying distance between the earth and sun because of the eccentricity of Earth's orbit. It is assumed that the solar flux is 1371 W/m 2 as a mean value in our study. Albedo fraction (AF) is defined as a fraction of the incoming solar radi-ation reflected by the Earth's surface. It can vary between 0.18 and 0.55 depending on satellite orientation and orbital parameters. For this analysis, a constant va-lue of 0.3 for AF is chosen [41]. The absorbed solar radiation by the earth is reemitted as a long-wave, called IR radiation [42]. The IR energy radiated by the Earth varies with season, latitude, the local, and the covering clouds. For most practical purposes, it is assumed that the Earth radiates IR with a constant intensity of 237 W/m 2 [2].
The internal components consume electrical power which is converted to heat. The entire internal heat dissipation in this stage for spacecraft equipment is 155.28 W. Table A2 shows dissipated heat for each piece of equipment in Watts.
The operating temperature limits of satellite components are usually determined by the manufacturer as given in Table 4. The thermo-physical properties for structural panels, solar panels, and internal equipment are defined in Table A3, Table A4, and Table A5 respectively. The optical properties of the internal satellite components and inner faces of structural panels were chosen to have the surface finish of polished aluminum with an emissivity of 0.05 and absorptivity of 0.15 [31]. The external optical properties were selected as presented in Table 5.

First Analysis -Single Mode
The single-mode analysis consists of having distinctive dissipated heat with time in both sun tracking and nadir pointing scenarios. The boundary conditions were constant and non-chained radiative cases were studied.
The external heat flux (solar, albedo, and planetary IR) along one orbit impinging the external faces (6 structure and 3 solar panels) for 81 nodes at sun pointing and nadir pointing modes of operation are calculated by Thermal Desktop. The results are compared with the corresponding results obtained by ESATAN-TMSs analyses [25]. The behavior of the external fluxes on the spacecraft is mainly affected by the orientation changing during the orbit.
Node 10 is located on the solar panel which is presented here as a sample of the results obtained. Fig. 4 demonstrates the time evolution of the heat fluxes on the external faces of the solar panel +X along one orbit at sun pointing (left) and nadir pointing ( right ) modes of operation respectively. when solar panel +X is facing the Sun (Fig. 5A (left)) the solar flux is maximum, while it tends to be zero when pointing to nadir as shown in Fig 5A (right).
The albedo is dependent on solar flux. IR depends on the view factor F ij between the spacecraft and the Earth. Node 50 located on the structural panel +Y is presented as a sample of the structural panel. Fig. 5 shows the external fluxes on structural panel +Y.
By examination of all results, it is found that no major deviations in heat fluxes have been recorded between all nodes of the same surface calculated with both softwares.

Post-Mission Phase
Transient thermal analysis of the Thermal Desktop model was run and tested for different time intervals (No. of orbital periods). It was found that a time of 4 orbital periods is an adequate amount of time for the satellite temperature to reach steady-state conditions. The temperatures of solar panels, structural panels, and all internal satellite components were examined. Fig. 6 through Fig. 13 show the temperature variation of the central node of each panel for the postmission stage as analyzed by TD. The central nodes have been chosen as the representative of the average condition of the whole surface [35]. Results show that the temperature variations are periodic for each orbit.
The upper limit temperature occurs when the spacecraft faces all three external fluxes-solar, albedo, and IR. Then, the spacecraft goes into the shadow and all spacecraft temperatures start to drop off as a result of the absence of the solar and albedo fluxes. As the spacecraft leaves the shadow, the temperature begins to rise.  Fig. 6 illustrates the temperature variation for the solar panels in four cycles. The temperature change (between the extreme high and low levels) of the +X solar panel is 75 °C (-10 to 65) which is less than the change in temperature (100 °C (-50 to 50)) faced by +Z and -Z solar panels. The maximum heat input is received by the solar panel +X because this panel is fixed on the structural panel +X and receives heat flux dissipated from the internal components of 68.04 W from AMST and Gyro in addition to external heat flux.
The difference in heat input received by the panel -Z and +X is caused by the change in surface area and view factors. All solar panels function inside their required limits (-100 to +100 °C).
The temperature experienced for all structural panels is shown in Fig. 7. The maximum and minimum temperatures for all panels are 25 °C and 16 °C respectively. All panels work within their required limits (-40 to +85 °C). Panels 1 (+X) and 5(-Y) have the maximum temperature due to high external heat fluxes and high internal heat dissipation of internal components (68.04 W and 26.06 W for panels 1 and 5 respectively). Panel 2 (+Y) has the lowest maximum temperature due to low internal heat dissipation of internal component (2.16 W) and low external heat flux calculated in section 4.1.
Analyzed results show that external heat flux is more effective than internal component heat dissipation. Fig. 8 to Fig. 13 illustrate the temperature variation for all spacecraft equipment fixed on all structural panels. The temperature variations on equipment match their attached panel's temperature. The battery has the smallest temperature range that is used to be the design limits of all internal components (-20 to +40 °C). The results confirm that all equipment normally works within required limits. Finally, the TCS accomplishes the temperature requirements for all spacecraft elements.

CONCLUSION
A detailed thermal model for ESEO satellite in the postmission phase has been created using Thermal Desktop software. Some results were compared with published data for the external radiation absorbed by the satellite. The results showed that the passive thermal control system was able to meet requirements and maintain component temperatures and panels within their design limits. From this study we come to the following conclusion: • Satellite thermal design is an iterative process and the model is subsequently modified to improve the thermal performance of the spacecraft.
• Equipment distribution, emissivity, absorptivity, and MLI placement are the main parameters that can be varied to change the temperature distribution.
• The spacecraft internal equipment location, physical and optical properties were taken into consi-deration to accomplish the required component's thermal requirements.
• The results gathered from the simulation present that all spacecraft elements were kept within their margins.
• Comparison with a specialized thermal analysis software package (ESATAN-TMSs) verified the integrity of the results.
Finally, concerning future work, Thermal Vacuum Tests should be conducted in a vacuum chamber where the satellite (or equipment) is under vacuum and subjected to the worst hot and cold conditions including adequate margins. It is hoped that, this study aid future researchers in understanding the thermal design process and serves as a basis to perform a similar type of design and analysis using Thermal Desktop software.