Level set topology optimization of cooling channels using the Darcy flow model

The level set topology optimization method for 2D and 3D cooling channels, considering convective heat transfer for high Reynolds number flows, is presented in this paper. The Darcy potential flow, which is a low-fidelity linear flow model, is used to simulate the flow using the finite element method. The resulting velocity field is used in a convection-diffusion model to simulate the heat transfer using the finite element method. A linear combination of the pressure drop and the average temperature is considered as the objective function, which is minimized subject to a volume constraint and a maximum length scale constraint. The results show that the pressure drop and the average temperature are conflicting criteria, and the trade-off between the two criteria is investigated. We perform a verification study by comparing the Darcy flow field of the obtained optimum designs with that of a high fidelity turbulence model. The verification study shows that there exists a reasonable agreement between the Darcy and the turbulent flow field for narrow channels. Therefore, by restricting the design space to narrow channels, we optimize the cooling performance and sufficiently capture the turbulent flow physics using the low-fidelity Darcy flow model. Finally, we show an example in 3D where we optimize the cooling channel topology that conforms to the surface of a sphere.