Level set topology optimization of cooling channels using the Darcy flow model
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RESEARCH PAPER
Level set topology optimization of cooling channels using the Darcy flow model Sandilya Kambampati1
· H. Alicia Kim1
Received: 21 August 2019 / Revised: 9 December 2019 / Accepted: 13 December 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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. Keywords Convective heat transfer · Reynolds Averaged Navier Stokes RANS · Conformal cooling channels · Maximum length scale control
1 Introduction Heat dissipating devices, such as cooling channels and heat sinks, are typically used in engineering and automotive structures to dissipate heat emanating from batteries, engines, or other heat-generating sources. A common way to dissipate heat is to pass a cooling liquid through the structure. The performance of such cooling systems, in terms of the amount of heat exchanged and the pressure Responsible Editor: Ole Sigmund Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-019-02482-6) contains supplementary material, which is available to authorized users. Sandilya Kambampati
[email protected] H. Alicia Kim [email protected] 1
Structural Engineering, University of California San Diego, San Diego, CA, 92093, USA
gradient required to pump the fluid, depends on the topology of the cooling channel. Therefore, an efficient cooling channel design is crucial for such heat-dissipating devices. There has been a lot of research on parametric optimization of cooling channels. In such parametric optimization methods, the channel path is defined by a set of parameters in a predefined layout. In Qiao (2006), a 2D pipe section optimization design is presented, where the channel is descr
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