Two dimensional topology optimization of heat exchangers with the density and level-set methods

Miguel A. SALAZAR DE TROYA, Daniel A. Tortorelli, Victor A. Beck

Research output: Contribution to journalConference articlepeer-review


We design heat exchangers using two topology optimization approaches: the density, i.e. volume fraction and level set methods. Our goal is to maximize the heat exchange between two fluids in separate channels while constraining the pressure drop across each channel. The heat exchanger is modeled with a coupled thermal-flow formulation. The flow is governed by an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation with high Peclet number. We solve one set of Stokes-Brinkman equations per fluid. Each Brinkman term in the flow equation serves to model the other phase as a solid, thereby preventing mixing. We first represent the solid and fluid phases using a volume fraction variable and apply a SIMP-like penalization in the Brinkman term to drive the optimization to a discrete design. The cost and constraint function derivatives are automatically calculated with the library pyadjoint and the optimization is performed by the Method of Moving Asymptotes. In a second optimization formulation, we use the level set approach to define the interface that separates the two fluids. Pyadjoint calculates the shape derivatives of the cost and constraint functions and the Hamilton-Jacobi advects the interface, allowing for topological changes. We present results in two dimensions and discuss the advantages and disadvantages of each approach.

Original languageEnglish (US)
Pages (from-to)1-25
Number of pages25
JournalWorld Congress in Computational Mechanics and ECCOMAS Congress
StatePublished - 2021
Externally publishedYes
Event14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020 - Virtual, Online
Duration: Jan 11 2021Jan 15 2021


  • Heat Exchanger
  • Stokes flow
  • Topology Optimization

ASJC Scopus subject areas

  • Mechanical Engineering


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