重访原点，弥合流体流动问题的拓扑和地形优化之间的差距
Revisiting the origin to bridge a gap between topology and topography optimisation of fluid flow problems
摘要：
本文回顾了流体流动问题的拓扑优化的起源，即基于Poiquille的摩擦阻力项用于参数化固体和流体区域。传统模型仅适用于真正的拓扑优化，其中它用于将固体区域近似为具有非常小的通道高度的区域，因此具有非常高的摩擦阻力。它将表明，如果通道高度被允许连续变化和/或最小通道高度是相对较大的和/或意义是归因于中间设计字段值，那么传统模型的预测是错误的。为了解决这个问题，这项工作引入了一个增广的质量守恒方程，允许连续变化的通道高度。所提出的平面模型准确地描述了充分发展的流动之间的两个不同的通道高度的板。它允许在自由度的数量显着减少，同时通常确保在层流状态下的低到中等雷诺数的高精度。传统和建议的模型的准确性和局限性进行了探讨，使用深入的参数研究。所提出的模型是用来优化两个平行板之间的流体通道的高度，因此，地形的板的流量分配问题。最后，据观察，该模型实际上产生更好的拓扑设计比传统的模型时，应用到拓扑优化的流量歧管。
英文摘要：
This paper revisits the origin of topology optimisation for fluid flow problems, namely the Poiseuille-based frictional resistance term used to parametrise regions of solid and fluid. The traditional model only works for true topology optimisation, where it is used to approximate solid regions as areas with very small channel height and, thus, very high frictional resistance. It will be shown that if the channel height is allowed to vary continuously and/or the minimum channel height is relatively large and/or meaning is attributed to intermediate design field values, then the predictions of the traditional model are wrong. To remedy this problem, this work introduces an augmentation of the mass conservation equation to allow for continuously varying channel heights. The proposed planar model accurately describes fully-developed flow between two plates of varying channel height. It allows for a significant reduction in the number of degrees-of-freedom, while generally ensuring a high accuracy for low-to-moderate Reynolds numbers in the laminar regime. The accuracy and limitations of both the traditional and proposed models are explored using in-depth parametric studies. The proposed model is used to optimise the height of the fluid channel between two parallel plates and, thus, the topography of the plates for a flow distribution problem. Lastly, it is observed that the proposed model actually produces better topological designs than the traditional model when applied to the topology optimisation of a flow manifold.
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