Geometrical design of thermoelectric generators based on topology optimization

• Published in: International journal for numerical methods in engineering Vol. 90; no. 11; pp. 1363 - 1392
• Main Authors: Takezawa, A., Kitamura, M.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 15.06.2012; Wiley
• Subjects: Exact sciences and technology; finite element method; Fundamental areas of phenomenology (including applications); multiphysics; Physics; sensitivity analysis; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; thermoelectricity; topology optimization; Geometrical shape; Temperature; Sensitivity analysis; Adjoint method; Topology; Conversion; Modeling; Physical properties; Moving asymptote; Optimization; Thermoelectric properties; Thermoelectric effect; Finite element method; Equations of state; thermoelectricity; Density function; Geometrical method; Objective function; topology optimization; Resistor; multiphysics; Multidisciplinary
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.3375

SUMMARY This paper discusses an application of the topology optimization method for the design of thermoelectric generators. The proposed methodology provides the optimized geometry in accordance with various arbitrary conditions such as the types of materials, the volume of materials, and the temperature and shape of the installation position. By considering the coupled equations of state for the thermoelectric problem, we introduce an analytical model subject to these equations, which mimics the closed circuit composed of thermoelectric materials, electrodes, and a resistor. The total electric power applied to the resistor and the conversion efficiency are formulated as objective functions to be optimized. The proposed optimization method for thermoelectric generators is implemented as a geometrical optimization method using the solid isotropic material with penalization method used in topology optimizations. Simple relationships are formulated between the density function of the solid isotropic material with penalization method and the physical properties of the thermoelectric material. A sensitivity analysis for the objective functions is formulated with respect to the density function and the adjoint equations required for calculating it. Depending on the sensitivity, the density function is updated using the method of moving asymptotes. Finally, numerical examples are provided to demonstrate the validity of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.