Non-newtonian laminar 2D swirl flow design by the topology optimization method

The performance of fluid devices, such as channels, valves, nozzles, and pumps, may be improved by designing them through the topology optimization method. There are various fluid flow problems that can be elaborated in order to design fluid devices and among them there is a specific type which comprises axisymmetric flow with a rotation (swirl flow) around an axis. This specific type of problem allows the simplification of the computationally more expensive 3D fluid flow model to a computationally less expensive 2D swirl flow model. The topology optimization method applied to a Newtonian fluid in 2D swirl flow has already been analyzed before, however not all fluids feature Newtonian (linear) properties, and can exhibit non-Newtonian (nonlinear) effects, such as shear-thinning, which means that the fluid should feature a higher viscosity when under lower shear stresses. Some fluids that exhibit such behavior are, for example, blood, activated sludge, and ketchup. In this work, the effect of a non-Newtonian fluid flow is considered for the design of 2D swirl flow devices by using the topology optimization method. The non-Newtonian fluid is modeled by the Carreau-Yasuda model, which is known to be able to accurately predict velocity distributions for blood flow. The design comprises the minimization of the relative energy dissipation considering the viscous, porous, and inertial effects, and is solved by using the finite element method. The traditional pseudo-density material model for topology optimization is adopted with a nodal design variable. A penalization scheme is introduced for 2D swirl flow in order to enforce the low shear stress behavior of the non-Newtonian viscosity inside the modeled solid material. The optimization is performed with IPOPT (Interior Point Optimization algorithm). Numerical examples are presented for some 2D swirl flow problems, comparing the non-Newtonian with the Newtonian fluid designs.