Monte Carlo Methods: Modeling TEG Material Property Uncertainty Propagation and Sensitivity

This study addresses the critical need to quantify the impact of uncertainty in measured thermoelectric material properties on modeled thermoelectric device (TED) performance. Particularly, we focus on segmented Silicon Germanium thermoelectric generator (TEG) unicouples- TEDs that convert heat to electrical power-used in the General-Purpose Heat Source Radioisotope Thermoelectric Generator (RTG) for space power generation applications. Toward this aim, we developed a tool that produces distributions of output system response quantities like electrical power output, open circuit voltage, current output, interfacial temperatures, and other performance metrics based on uncertainties in thermoelectric material properties. Monte Carlo methods estimate output quantity uncertainties as a function of input material property uncertainties and develop robust statistical correlations between input uncertainty and expected performance bounds. A fast unicouple-level mathematical model capable of handling various thermal and electrical phenomena is utilized. Model considerations include varying thermal (Dirichlet and mixed) and electrical boundary conditions, the influence of interconnectors, electrical and thermal contact resistances between constitutive unicouple materials, and temperature-dependent material properties. This mathematical model was validated against a fully-coupled thermal-electric finite-volume model implemented in ANSYS CFX for an exhaustive range of operating parameters. This work can potentially guide manufacturing tolerances and flight-hardware qualification requirements at institutions like the National Aeronautics and Space Administration's Jet Propulsion Lab. Additionally, the tools and framework developed herein can be applied to any arbitrary thermoelectric material set with any arbitrarily varying material properties, assisting with the development of new thermoelectric materials and unicouples for future-generation RTGs. The major findings of this work indicate that mixed thermal boundary condition solvers are better reflections of reality in the modeling of TEGs than Dirichlet thermal boundary conditions. Furthermore, it was established that even small amounts of uncertainty in the Seebeck coefficient, thermal conductivity, or electrical resistivity could propagate into unacceptable levels of uncertainty in power output and interfacial temperatures, potentially resulting in material failure within the TEG.