Optimal design for non-Newtonian flows using a topology optimization approach

We study non-Newtonian effects on the layout and geometry of flow channels using a material distribution based topology optimization approach. The flow is modeled with the single-relaxation hydrodynamic lattice Boltzmann method, and the shear dependence of viscosity is included through the Carreau Yasuda model for non-Newtonian fluids. To represent the viscosity of blood in this model, we use non-Newtonian similarity. Further, we introduce a scaling to decrease the effects of the non-Newtonian model in porous regions in order to stabilize the coupling of the LBM porosity and non-Newtonian flow models. For the resulting flow model, we derive the non-Newtonian sensitivity analysis for steady-state conditions and illustrate the non-Newtonian effect on channel layouts for a 2D dual-pipe design problem at different Reynolds numbers.