A new interpolation technique to deal with fluid-porous media interfaces for topology optimization of heat transfer

This paper proposes a new interpolation technique based on density approach to solve topology optimization problems for heat transfer. Natural convection forces are dominated as Richardson number is equal to 2.8. Problems are modeled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation. The governing equations are discretized using finite volume elements and topology optimization is performed using adjoint sensitivity analysis. Material distribution and effective conductivity are interpolated by two sigmoid functions respectively hτ(α) and kτ(α) in order to provide a continuous transition between the solid and the fluid domains. Comparison with standard interpolation function of the literature (RAMP function) shows a smaller transition zone between the fluid and the solid thereby, avoiding some regularization techniques. In order to validate the new method, numerical applications are investigated on some geometric configurations from the literature, namely the single pipe and the bend pipe. Lastly, as two new parameters are introduced thanks to the interpolation functions, we study their impact on results of the optimization problem. The study shows that the proposed technique is a viable approach for designing geometries and fluid-porous media interfaces are well-defined.