Improvement of lumped thermal models: Calculation of accurate linear conductances and transient correlation to reference data

Resumen

Thermal mathematical models are the main tool an engineer has to optimize the thermal design of a spacecraft. The better the physical system is mathematically approximated, the better the design solution will be. Hence the importance of developing new techniques to improve the modelling process. In this work, two different methods to improve thermal models based on the lumped parameters formulation are presented. The first one, called Conductance Matrix Fitting (CMF) method, is a new method intended to calculate accurate linear conductances. Linear conductances connect different nodes of a thermal model in order to represent conduction heat transfer. The method is based on the generation of a detailed lumped thermal model of the component. After setting-up the detailed model, it is condensed to create a reduced model. The unknown conductances of the reduced model are automatically calculated by correlating the temperature and heat flow of the reduced model with the results of the detailed model. The conductances of the component determined in this way can be used for modelling the complete device. The second one addresses the transient correlation of thermal models to reference data. The correlation is a common problem in the spacecraft thermal control field. The goal is to find the set of parameters of the model that best approach the solution to a given reference data. Here, the problem is formulated as a non-linear least squares minimization and different algorithms are suggested and compared. Because in a typical correlation problem the parameters to be optimized are near the solution, local optimization is expected work well. Thus, iterative minimization algorithms based on quasi-Newton steps are those with the faster convergence. However, these algorithms need the Jacobian matrix at each iteration, which is computationally very expensive. To overcome this limitation, an efficient way to obtain the Jacobian matrix is also presented. Both methods have been tested with thermal models of real hardware, such as the PHI instrument of the ESA Solar Orbiter mission or some cameras of the Sunrise III mission.