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Answer :
In this section, the thermal model is developed from first principles. The variation of the satellite temperature T is governed by the first law of thermodynamics for the case in which no work is performed by (or over) the system.
We present a model for predicting the temperature of three-unit CubeSat on a low Earth orbit, which supposes a single temperature common to all satellite components. Our exposition includes a detailed, to a large extent analytical, computation of the external heat fluxes for a particular orbit and spacecraft assumptions based on the features foreseen for satellite Libertad 2 under development at Universidad Sergio Arboleda. Moreover, supported by specialized thermal analysis software, we compute the heat fluxes and their associated temperature for all possible orbital orientations, and combine these results with a description of the satellite orbital plane rotation (nodal regression) and the solar motion on the ecliptic, to determine the minima and maxima of the orbital temperature oscillation for a mission lifetime of a year. We find that, for feasible model parameters, the temperature extremes are mostly within the operating temperature range of the most sensitive satellite component, 0 ºC ≤ T ≤ 60 ºC, suggesting mission viability. Finally, we discuss possible model improvements which would allow testing of satellite design upgrades. In this regard, it is worth noting that the calculation of the external heat fluxes here described can be carried over, almost unchanged, to a more accurate model describing heat transfer between satellite parts with different temperatures.
KEYWORDS:
CubeSat; Low Earth orbit; Thermal analysis; Nodal regression; Beta angle; Numerical simulation; Linearization
Figure 1
Views of Libertad 2 with the body fixed coordinate system {x,y,z}. The faces are labeled by a numerical index and a word. The front face has dimensions 10 cm × 10 cm and the bottom face is 10 cm × 30 cm.The dark gray hexagons represent solar cells while the light gray circle represents the camera lens opening.
Prediction of a satellite's temperature is justified by the need for all satellite components to function within their operating temperature ranges - defined as "the maximum and minimum temperature limits between which components successfully and reliably meet their specified operating requirements" (Garzon 2012) -, otherwise risking malfunctioning or damage. To forecast the effect of design choices, like the materials on the external surfaces, on the temperature, it is necessary to create a model of the heat transferred between the satellite and its surroundings and between the satellite parts.
The modeling techniques can be found in the available literature on thermal analysis of nano-satellites. Dinh (2012) studied the temperature of internal electronics in a 1U CubeSat using the software packages Thermal Desktop and ANSYS. Jacques (2009) conducted the thermal analysis for the OUFTI-1U CubeSat relying on the software ESATAN-TMS, whereas Garzon (2012) simulated the temperatures of the OSIRIS-3U CubeSat employing the multiphysics software COMSOL. Bulut and Sozbir (2015) investigated the temperature for different solar panel combinations in a 1U CubeSat. Optimization of thermal design parameters through genetic algorithms was pursued by Escobar et al. (2016). Kang and Oh (2016) performed an experimental validation of their model predictions using a thermal vacuum chamber. Active thermal control with phase change materials was investigated by Shinde et al. (2017) and Kang and Oh (2016). A simulation code implemented in MATLAB was developed by Corpino et al. (2015). Mason et al. (2018) compared a thermal model of the Miniature X-Ray Solar Spectrometer 3U CubeSat with actual on-orbit temperature measurements, finding agreement within a few degrees Celsius. Remarkably, their thermal design allowed for the payload to stay at an almost constant on-orbit temperature of -40.91 ºC (standard deviation of 0.19 ºC), isolated from the much wider temperature oscillations of the solar arrays, roughly from -40 ºC to 50 ºC.
DESIGN OF LIBERTAD 2
The satellite will carry several components in addition to the photographic camera. A system of wheels and electromagnets will control the satellite orientation for the purpose of pointing the camera toward a particular target. These actuators together with orientation sensors constitute what is known as the Attitude Determination and Control System (ADCS). Instructions will be sent to the satellite via Very High Frequency (VHF) and Ultra High Frequency (UHF) radio waves.
Therefore, in this section, the thermal model is developed from first principles. The variation of the satellite temperature T is governed by the first law of thermodynamics for the case in which no work is performed by (or over) the system.
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