Topology optimization of fluid flow problems is still a challenging open problem, especially when considering turbulence, compressibility, or the addition of different physics. In the current implementation of topology optimization for fluids considering density methods, there are essentially three problems. First, the grayscale in the result makes it difficult to identify the precise contour of the fluid region, which may be a problem in some applications and during the optimization process as well. Second, even for low Reynolds flow design problems, a continuation scheme of the material model penalization parameters is necessary to avoid a grayscale and to obtain a clear boundary. Third, in complex fluid flow optimization problems, it is difficult to specify the maximum value of the inverse permeability to avoid the fluid to flow inside the solid. This work proposes a novel methodology that tackles the first two problems, i.e., it avoids the grayscale and obtains clear boundaries. The goal of this work is to implement the Topology Optimization of Binary Structures (TOBS) (Sivapuram and Picelli, Finite Elem Anal Des 139:49–61, 2018) for fluid flow design, which is a novel topology optimization method that has been used in solid mechanics to generate optimized structural solutions considering only binary {0,1} design variables. The main advantage of {0,1} methods is the clear definition of the interface and the absence of grayscale. It is a method easy to implement which preserves the material distribution features. Some classic fluid problems are considered to illustrate the problem, such as the double channel and the bend pipe, and also a more complex example that usually presents grayscale issues, which is the fluid diode design. The optimization results show the feasibility of the TOBS when applied to fluid flow problems. The physical problem is solved by using the finite element method and the optimization problem with CPLEX^Ⓒ, a proprietary optimization package from IBM. The present work successfully eliminates the grayscale problem, bringing clear boundaries in the interface fluid-solid.

流体流动问题的拓扑优化仍然是一个具有挑战性的开放性问题，尤其是在考虑湍流，可压缩性或增加其他物理特性时。在考虑密度方法的当前用于流体的拓扑优化的实现中，本质上存在三个问题。首先，结果中的灰度使得难以识别流体区域的精确轮廓，这在某些应用中以及在优化过程中也可能是一个问题。其次，即使对于低雷诺流动设计问题，也必须采用材料模型罚分参数的连续方案来避免灰度并获得清晰的边界。第三，在复杂的流体流优化问题中，很难指定反渗透率的最大值，以避免流体在固体内部流动。这项工作提出了一种解决前两个问题的新颖方法，即避免了灰度并获得了清晰的边界。这项工作的目标是实施二元结构的拓扑优化（TOBS）（Sivapuram和Picelli，有限Elem肛门Des139：49–61，2018），这是一种新颖的拓扑优化方法，已在固体力学中用于生成仅考虑二进制{0,1}设计变量的优化结构解决方案。{0,1}方法的主要优点是接口的定义清晰，并且没有灰度。这是一种易于实现的方法，可以保留物料分配特征。考虑使用一些经典的流体问题来说明该问题，例如双通道和弯管，以及一个通常表现出灰度问题的更复杂的示例，即流体二极管设计。优化结果表明了将TOBS应用于流体流动问题的可行性。使用有限元方法解决物理问题，并使用CPLEX ^problem优化问题，这是IBM专有的优化软件包。目前的工作成功地消除了灰度问题，在界面流固中带来了清晰的边界。