Topology optimization of the shear thinning non-Newtonian fluidic systems for minimizing wall shear stress

This paper suggests the topology optimization process to minimize wall shear stress by considering shear thinning non-Newtonian fluid effects in the systematic design of fluidic systems dealing with blood. Topology optimization was originally developed for mechanical design problems, and within the last decade the method has been extended to a range of fluidic applications. In this paper, the Carreau–Yasuda constitutive equation model is used for shear thinning non-Newtonian fluid modeling. The fundamental idea is that the material density of each element or grid point is a design variable, thus, the geometry is parameterized in a pixel-like pattern. Then, material interpolation functions for inverse permeability and dynamic viscosity are used to ensure convergence of the solution and resolve non-linearity. In order to define wall shear stress on implicit boundary between solid and fluid (i.e., blood) occurring in fluidic topology optimization, the relaxation method of wall shear stress is first proposed in this study. We then apply the proposed fluidic topology optimization to actual fluidic systems dealing with blood (e.g., a femoral bypass graft). These design examples validate the efficiency of the proposed approach and show that topology optimization can be used for the initial conceptual design of various fluidic systems.