A “poor man's approach” to topology optimization of cooling channels based on a Darcy flow model

- A topology optimization method for cooling-channel design using a low-cost model is developed.
- The convection heat-transfer simulation is based on linear Darcy flow.
- The governing equations are cast in a monolithic form for topology optimizaiton.
- Manufacturable cooling-channel designs are obtained with geometric constraints.
- The proposed approach is an efficient alternative to turbulent flow based topology optimization.

A topology optimization methodology for optimizing cooling channels using an approximate but low-cost flow and heat transfer model is presented. The fluid flow is modeled using the Darcy model, which is a linear problem that can be solved very efficiently compared to the Navier-Stokes equations. The obtained fluid velocity is subsequently used in a stabilized convection-diffusion heat transfer model to calculate the temperature distribution. The governing equations are cast in a monolithic form such that both the solid and fluid can be modeled using a single equation set. The material properties: permeability, conductivity, density and specific heat capacity are interpolated using the Solid Isotropic Material with Penalization (SIMP) scheme. Manufacturable cooling-channel designs with clear topologies are obtained with the help of a pressure drop constraint and a geometric length-scale constraint. Several numerical examples demonstrate the applicability of this approach. Verification studies with a full turbulence model show that, although the equivalent model has limitations in yielding a perfect realistic velocity field, it generally provides well-performing cooling channel designs.