  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.
