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Topology optimization of a coupled thermal-fluid system under a tangential thermal gradient constraint

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Abstract

This paper presents a continuous adjoint approach for topology optimization of a coupled heat transfer and laminar fluid flow system under tangential thermal gradient (TTG) constraints. In this system, the thermal gradient along the boundary of multiple heat sources needs to be controlled. The design goals are to minimize the temperature of the domain, the fluid power dissipation and the TTG along the boundary of the heat sources. The first two goals are combined into a single cost function with weight variables. The TTG is constrained in one of two forms, an integral form where the integral of TTG squares along the boundaries of heat sources is constrained, or a point-wise form where TTG is constrained point-wise. A gradient-based approach is developed to obtain the optimized designs. A salient feature of our approach is the use of the continuous adjoint approach to derive gradients of both the cost function and two forms of TTG constraints. Numerical examples demonstrate that the continuous adjoint approach leads to successful topological optimization of the constrained thermal-fluid system. The use of TTG constraint is effective in lowering the TTG along the heat source boundaries. The resulting designs exhibit clear black/white contrast.

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Acknowledgments

The first author wants to acknowledge the support from the National Science Foundation grant #1404665 #1435072. The authors are thankful for reviewers’ thorough and constructive feedback.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI, 53706 - 1572, USA

    Xiaoping Qian

  2. Electronics Research Department, Toyota Research Institute of North America, 1555 Woodridge Avenue, Ann Arbor, MI, 48105, USA

    Ercan M. Dede

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  1. Xiaoping Qian
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  2. Ercan M. Dede
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Correspondence to Xiaoping Qian.

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Qian, X., Dede, E.M. Topology optimization of a coupled thermal-fluid system under a tangential thermal gradient constraint. Struct Multidisc Optim 54, 531–551 (2016). https://doi.org/10.1007/s00158-016-1421-6

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  • DOI: https://doi.org/10.1007/s00158-016-1421-6

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