Abstract
We consider a model for density-based topology optimization (TO) of stationary heat transfer problems with design-dependent internal convection in 3D structures with periodic design obtained by extruding a 2D design in 3D. The internal convection takes place at the interface between a solid material and a cooling fluid in internal channels through the design domain. The objective of the TO is to minimize the maximum temperature, which is approximated by means of an Lp norm. The finite element method is used to discretize the state problem and the resulting optimization problem is solved using gradient-based methods. The internal convection is modeled to be dependent on the design density gradient in the continuous problem. In discrete form, it is approximated as proportional to the difference in design densities of adjacent elements in the finite element mesh. The theory is illustrated by numerical examples based on a simplified guide vane geometry.
Highlights
Topology optimization (TO) enables design of intricate structures, which cannot be done as effectively by a classical trial and error approach
The 2D design approach limits the number of design variables in the optimization problem, but keeps the complexity of a full 3D state problem, enabling, e.g., temperature gradients in 3D
In contrast to the present work, the periodic boundary conditions are still only implemented in a 2D model
Summary
Topology optimization (TO) enables design of intricate structures, which cannot be done as effectively by a classical trial and error approach. Pure heat conduction problems can be solved by easy-to-implement TO codes in Matlab, and some codes are presented as open source for educational purposes (Bendsøe and Sigmund 2003; Liu and Tovar 2014) These codes are in standard versions restricted to minimizing thermal compliance, whereas in many applications, maximum temperature is probably more relevant as an objective. Thellner and Torstenfelt (2005) investigated design-dependent loads by means of a changing design domain, Zhou et al (2016) considered an industrial application for heat transfer problems with design-dependent boundary conditions for external convection, and Ahn and Cho (2010) discussed design-dependent convection boundaries with a level set approach.
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