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.

通过使用拓扑优化方法设计流体设备，例如通道，阀门，喷嘴和泵，可以提高其性能。为了设计流体装置，可以阐述各种流体流动问题，其中有一种特殊的类型，它包括绕轴旋转的轴对称流动（旋流）。这种特定类型的问题允许将计算上更昂贵的3D流体模型简化为计算上更便宜的2D旋流模型。之前已经分析了应用于二维漩涡流中的牛顿流体的拓扑优化方法，但是，并非所有流体都具有牛顿（线性）特性，并且会表现出非牛顿（非线性）效应，例如剪切变稀，这意味着在较低的剪切应力下，流体应具有较高的粘度。表现出这种行为的某些流体是例如血液，活性污泥和番茄酱。在这项工作中，通过使用拓扑优化方法，在设计二维旋流装置时考虑了非牛顿流体流动的影响。非牛顿流体是通过Carreau-Yasuda模型建模的，该模型已知能够准确预测血流的速度分布。该设计包括考虑粘性，多孔和惯性效应的相对能量耗散的最小化，并通过使用有限元方法解决。采用带有拓扑设计变量的用于拓扑优化的传统伪密度材料模型。针对二维旋流引入了一种惩罚方案，以增强建模固体材料内部非牛顿粘度的低剪切应力行为。使用IPOPT（内部优化算法）进行优化。通过比较非牛顿流体与牛顿流体设计，给出了一些二维旋流问题的数值例子。