Optimisation of pipes with constant diameter using the heuristic optimality criterion

Minimising internal pressure drop in pipes is crucial for energy efficiency of fluid flow applications. Numerous computational optimisation tools that are capable of modifying flow geometries to reduce the pressure drop have been developed. Among these is a comparably simple heuristic optimisation al- gorithm which mimics erosion and sedimentation processes based on the shear stress in the vicinity of the domain boundaries. Although this method succeeds in modifying flow geometries for reduced pressure drop, it allows the fluid domain to widen during the reshaping process. Therefore, a reported reduction of pressure drop is not only caused by an improvement of the flow path, but also by an increase in the domain width. However, pipes with a constant circular diameter are favoured in many applications because they can be easily manufactured.

Here we combine the heuristic optimisation approach with a novel geometrical constraint that maintains constant average diameter throughout the reshaping process. To our knowledge, this is the first application of a diameter-preserving constraint to the heuristic optimality criterion, enabling assessment of pressure drop reduction achieved solely through flow path modification without diameter dilation effects. We determined the applicability of the new algorithm for 2D channel and 3D pipe ge- ometries, conducting numerical simulations using the Lattice Boltzmann method with Reynolds numbers ranging from 40 to 500.

For the novel constant diameter constraint, the method successfully derived improved shapes across most tested Reynolds numbers while maintaining the initial average diameter. Notably, shapes derived at Re = 40 unexpectedly outperformed those derived at higher Reynolds numbers across all tested flow conditions, suggesting that low-Re geometries may capture fundamental flow features beneficial across wider Reynolds number ranges.

This finding suggests applicability to higher Reynolds number flows, potentially even at turbulent industrial flows to be investigated in fu- ture research.

A high pressure drop in pipes limits the energy efficiency of machines, and there are computer tools that can change the pipe design to reduce the pressure drop. One method mimics erosion and sedimentation and is called heuristic optimality criterion. However, this method widens the pipe during the design process. This is problematic, because pipes with varying widths are harder to be produced. In this article, we describe how to restrict the reshaping method to leave the pipe width unchanged. We tested this method using computer simulations for 2D channels and 3D pipes with flows of different behaviours described by their Reynolds number. The Reynolds number describes the flow behaviour—whether it is smooth (laminar) or chaotic (turbulent). We successfully improved pipe shapes while keeping the diameter fixed across all tested conditions. Interestingly, we found that shapes designed for the lowest Reynolds number (Re=40) performed better than shapes specifically designed for higher Reynolds numbers. This unexpected result suggests that simple shapes derived at low flow speeds might work well across a wide range of conditions, potentially even for turbulent flows in industrial applications—an exciting direction for future research.