Coupled thermo-electro-mechanical topology optimization for cooling applications under electrical constraints

Abstract

This paper addresses the topology optimization of thermocouples for cooling applications, considering stress constraints to enhance reliability under service loads. We provide a first approach to derive sensitivities using SIMP (solid isotropic material with penalization) for thermo-electro-mechanical systems with temperature-dependent material properties. The proposed formulation decouples the thermoelectrical system from the mechanical degrees of freedom reducing computational memory usage from a fully coupled approach. The study focuses on the formulation of thermocouples for cooling applications using the Peltier effect, which considers electrical power limits, electrical working points, and material stress thresholds. Furthermore, while the thermoelectrical problem does not show the need for filtering techniques, including the mechanical degrees of freedom, we show that we recover undesirable porous optimized designs. We provide 2D thermocouple example optimizations with geometries and boundary conditions based on a practical case for the implementation of thermoelectric coolers in the Minimum Ionizing Particle Timing Detector (MTD) at CERN. The optimizations are performed with increased complexity, including the unfiltered thermoelectrical and thermo-electro-mechanical problems and a Helmholtz-filtered examples. The optimizations are compared with constant and nonlinear material properties with temperature and with respect to the consideration of air-conductance losses within the devices. Although more efficient topologies can be achieved without the need for volume constraints, we include an example with a constraint of 60% volume to understand its effect on the design and provide a methodology to reduce semiconductor-associated costs at lower efficiency costs. Finally, we explore the same formulation in 3D. The results provide guidelines for manufacturing compliant thermocouples, increasing their reliability without decreasing efficiency.