Numerical optimisation of segmented thermoelectric elements

Kurzfassung

Graded and segmented thermoelements have been considered for long, aiming at improving the performance of thermogenerators (TEG) which are exposed to a large temperature difference. A numerical algorithm for performance estimation of TEG and Peltier elements has been previously developed using the tool MATHEMATICA. It is capable to calculate the exact temperature profile along a segmented element in a one-dimensional model. The algorithm is based on the constant properties assumption in each of the segments providing the opportunity of treating quasi-continuous gradients. Integral quantities like the internal resistance, thermal resistance, voltage drop, and output voltage as well as performance parameters like cooling power, C.O.P., and temperature difference (for a Peltier device) or output power and efficiency (for a TEG, respectively) are deduced taking into account the real temperature dependence of the materials properties. The process was repeatedly executed in a current loop to select optimum operation parameters. Practical examples illustrate the quantitative improvement of performance which is ideally achievable by segmentation of TEG and Peltier cooler elements. A performance estimation methodology for prepared segmented elements has been established linking this algorithm to an experimental technique of spatial scanning of the Seebeck coefficient on segmented elements by the Seebeck micro-thermoprobe (SMP). The method is regarding temperature dependent thermoelectric (TE) properties which have been measured on homogeneous samples representing properties of individual segments. The performance of a segmented 2-stage TEG element composed of real Czochralski-grown Bi₂Te₃-based alloys has been estimated in dependence on the length ratio of the segments. Optimum segmentation schemes have been selected and maximum efficiency values up to 12–14% have been calculated. The performance was compared to exact calculation results of cascaded elements of identical design. Another practical example is illustrating quantitative improvement of performance achievable by segmentation of a Peltier cooler.