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Multi-objective and multi-load topology optimization and experimental validation of homogenized coupled fluid flow and heat transfer and structural stiffness

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Abstract

This work focuses on designing materials for elasticity and coupled fluid flow and heat transfer. The macroscale equations for homogenized elasticity and coupled fluid flow and heat transfer are presented. The topology optimization problem is formulated, its implementation detailed, and the design sensitivities of the homogenized coupled fluid flow and heat transfer problem deduced. Using the Method of Moving Asymptotes, bidimensional periodic cells are optimized for homogenized coupled fluid flow and heat transfer with a multi-load formulation, in which weights are assigned to the longitudinal and transverse components. The effect of the weighting parameter is discussed. A bidimensional periodic cell is optimized for longitudinal and transverse stiffness by means of a Multi-Objective Sequential Quadratic Programming method. The Pareto curve is presented, and the implementation details are discussed. The MOSQP is then used to perform multi-objective optimization of tridimensional cells for longitudinal homogenized coupled fluid flow and heat transfer and both components of homogenized transverse stiffness. Solutions are presented and compared for two Péclet numbers, for conductive and convective dominated regimes, respectively. Selected optimized geometries were produced and their thermo-hydraulic behavior was characterized in an experimental setup designed for this study. An experimental setup was assembled and tested in order to characterize the thermo-hydraulic behavior of periodic media subjected to forced convective heat transfer. Five samples were selected from the topology optimization results to be produced through additive manufacturing and subjected to thermo-hydraulic characterization. Each sample was tested for four mass flow rates and four heat fluxes.

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Replication of results

For the results in this paper to be reproduced, a detailed description of the numerical implementation was provided in each section. Furthermore, a derivation of design sensitivities considering the drift velocity was provided. The code can be downloaded at https://github.com/franciscopauloricardo/HomogTop

Funding

The support of the MIT Portugal Program and the funding from the Portuguese Foundation of Science and Technology under the doctoral Grant PD/BD/105932/2014 is gratefully acknowledged.

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Authors and Affiliations

  1. LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    Paulo Francisco & Luis Faria

  2. IPCA, Instituto Politécnico do Cávado e do Ave, Barcelos, Portugal

    Ricardo Simões

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  1. Paulo Francisco
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  2. Luis Faria
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Correspondence to Paulo Francisco.

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Francisco, P., Faria, L. & Simões, R. Multi-objective and multi-load topology optimization and experimental validation of homogenized coupled fluid flow and heat transfer and structural stiffness. Struct Multidisc Optim 62, 2571–2598 (2020). https://doi.org/10.1007/s00158-020-02625-0

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  • DOI: https://doi.org/10.1007/s00158-020-02625-0

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