Analytical and Experimental Study to Predict Radiated Heat Power Between a Satellite and Thermal Shroud

Abstract

Nanosatellites, a class of small satellites, are becoming increasingly popular because of their small form factor and many other attractive features. In the process of qualifying nanosatellites for space readiness, their thermal behavior can be investigated in a laboratory setup using a thermal vacuum system to mimic orbital conditions. For these reasons, a thermal vacuum system suited specifically for nanosatellites was desired for performing thermal vacuum testing. Analytical calculations and laboratory testing were performed as part of the design of this thermal vacuum system. A set of simultaneous equations was solved using the LU Decomposition method to find the radiosities of several surfaces in an enclosure. The radiosities along with their respective view factors were then used to solve for the heat power required to heat and cool the thermal shroud under steady state conditions at the most extreme operating conditions expected. The analysis was performed on a system of three concentric cylinders of varying heights: the outer being the vacuum chamber wall, the middle the thermal shroud inside the chamber, and the inner the satellite. Under the most extreme operating conditions expected, the thermal shroud was cooled to −40°C and the satellite heated to 80°C during satellite cooling and the reverse during satellite heating. All surfaces in the enclosure were assumed to be diffuse, grey, opaque and isothermal. The thermal shroud was separated into two surfaces: the cylindrical shroud body and the shroud top disc. From the analytical results, the expected heating power for the shroud body was found to be 704.0 Watts, and 229.8 Watts for the shroud top. During cooling, where the temperatures were reversed, the expected heat power for the shroud body was calculated as −685.5 Watts, and −220.9 Watts for the shroud top. An experimental setup was tested under similar conditions as a comparison and as a method to validate the thermal shroud design and the analytical calculations. The shroud body and top heaters were selected to output 750 Watts and 230 Watts, respectively, and were driven at their maximum output, with the satellite held at −40°C. The shroud reached 80°C with no difficulty, indicating that the analytical calculations had correctly predicted the required heat power and that the design of the thermal shroud was capable of supporting testing under the most extreme conditions expected.