High-Fidelity Spacecraft Thermal Modeling: Synthesis of STK, SPENVIS, MATLAB, Simulink, and Thermal Desktop using Model-Based Systems Engineering

High-Fidelity Spacecraft Thermal Modeling: Synthesis of STK, SPENVIS, MATLAB, Simulink, and Thermal Desktop using Model-Based Systems Engineering

Utah State University, Logan, UT

Verification and Validation (V&V) by analysis for required spacecraft Heater Wattage (HW) and Radiator Area (RA) is a rigorous, iterative procedure highly dependent on spacecraft areas, surface absorptivity, surface emissivity, orbital position, orbital attitude, and operational heat generation. The Alabama Burst Energetics eXplorer (ABEX) mission adopts a Model-Based Systems Engineering (MBSE) approach to analysis wherein model strengths and weaknesses are considered synergistically and integrated using SysML parametric and structural diagrams to create a System of Models (SoM). In this work, a procedure for comprehensive spacecraft thermal modeling is detailed using MBSE-centric Modeling and Simulation (M&S) practices. The SysML model is used as a foundational data source for all other models, and non-SysML model exports are provided back to the SysML model in useful format. Because the analytical models in Systems Tool Kit (STK), MATLAB, Simulink, Thermal Desktop, and the Space Environment Information System (SPENVIS) are sourcing input data only from the SysML model, V&V for input data pedigree is only required in SysML for the purposes of National Aeronautics and Space Administration (NASA)-STD-7009: Standard for Models & Simulations, saving valuable program schedule time. Common of many thermal analysis approaches, a low-fidelity, isothermal model is first developed in MATLAB to provide environmental calculations and preliminary HW and RA values to a higher-fidelity model, here developed in Simulink. The non-isothermal Simulink model results inform a Thermal Desktop model, which is used as the basis for qualification-level hardware development. In the analytical models, STK simulates spacecraft modes of operation and communication profiles to export transient spacecraft position and velocity state vectors, solar position state vectors, Earth position state vectors, and unit vectors orthogonal to each spacecraft face, among non-thermal data. An orbital model in SPENVIS produces corpuscular radiation integral flux data for the determination of Charged Particle Heating (CPH), and the MATLAB model imports the STK and SPENVIS data. In MATLAB, heat fluxes from direct solar emission, Earth emission, Earth albedo, CPH, and Free Molecular Heating (FMH) are calculated and converted to absorbed heat values; radiation surface reflectivity is calculated using specular, spectral Fresnel relationships accounting for complex, spectral refractive indices of both the spacecraft surface coating material and base layer material, surface coating material thickness, and radiation Angle of Incidence (AOI). The MATLAB model utilizes an isothermal energy balance to output a low-fidelity HW and RA value required to stay above and below component operational temperatures, respectively. In Simulink, component thermal capacitances are distributed in a thermal resistance network with each discrete spacecraft component considered isothermal; absorbed heat and advanced reflectivity calculations are also recalculated per component. An array of values is generated for both HW and RA between zero and twice the value provided by the MATLAB isothermal model to create a matrix of potential HW and RA combinations. The Simulink model determines an operational envelope of viable HW and RA combinations for user-defined heater and radiator locations; acceptable HW and RA combinations are those that result in component temperatures within operational boundaries. The HW and RA combinations at the edges of the Simulink-derived operational envelope are provided to a three-dimensional, geometry-specific Thermal Desktop model wherein high-fidelity HW and RA values can be analyzed specific to mounting considerations. In this SoM progression from MATLAB to Simulink to Thermal Desktop driven by data inputs from STK and SPENVIS with a central source of truth for all models based in SysML, uncertainty and risk regarding thermal control analysis results are systematically mitigated.