Abstract
Steady-case thermal analysis plays an important role in dimensioning thermal control systems for spacecrafts and aircrafts. Usually a trial and error approach is used based on engineering judgement and experience. When thermal models become complex or there are conflicting thermal requirements, however, it becomes harder for an engineer to gain insight as to which design decisions will lead to better results. Numerical optimization, on the other hand, could provide a more robust approach for the thermal design of complex spacecraft or aircraft models. In this paper, we suggest a gradient-based multidisciplinary optimization of thermal models where the coupled derivatives of the multidisciplinary system are obtained with the adjoint method. We show that in the case of steady-state thermal analysis, there is an analytic solution of a partial derivatives of implicit heat-transfer equation that can be used to derive total derivatives of the system. We present a practical application of this method by solving a small interplanetary spacecraft thermal optimization problem consisting of one objective, 15 design variables, and 10 constraints. We found that by using gradient-based optimization with exact derivatives, the best results can be achieved by exploring the design space at multiple initial starting points without major computational overhead.
Highlights
The spacecraft and aircraft thermal-control system is responsible for maintaining and controlling components’ temperature within the required operating conditions
Formulation of the multidisciplinary thermal optimization problem Instead of looking into thermal design as a single-discipline problem, we suggest formulating it within a multidisciplinary context
The multidisciplinary thermal model was implemented in an open-source multidisciplinary analysis framework called OpenMDAO (Gray et al, 2019), which focuses on supporting gradientbased optimization with analytic derivatives
Summary
The spacecraft and aircraft thermal-control system is responsible for maintaining and controlling components’ temperature within the required operating conditions. By looking into equation (1), we can see that it contains inputs from external heat fluxes and heat dissipation from equipment, meaning that the thermal problem is inherently coupled with the spacecraft attitude and power disciplines This formulation would make it easy to integrate the thermal discipline into a multidisciplinary optimization framework of the whole satellite as a system. The power discipline takes the absorbed fluxes and component power outputs as inputs and calculates internally dissipated heat flux Qdis and generated electrical power from solar arrays Pel. the temperature discipline assembles matrices GL (eq 3) and GR (eq 4) and solves the direct problem (eq 2) as a system of nonlinear equations.
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