Unsteady topology optimisation for suppression of vortex-dominated compressible flows

The current literature on topology optimisation is lacking in investigating unstable flows, where the transient nature is self-excited; as well as compressible transient flows in general. In a novel approach, we optimise a vortex-dominated compressible flow, where the unsteady von Kármán street inherently forms downstream of a cylinder. For this purpose, the distribution of solid and fluid in a fixed grid is carried out by topology optimisation to minimise the energy dissipation under a volume constraint in two separate instances: One limits the amount of fluid from above; while the other, from below. Two design domain sizes are considered, placed downstream of the body in each case, with an initial uniform distribution of fluid. The long-standing computational issues represented by memory requirement and storage are circumvented and discussed. Simulations are carried out with reasonable cost and accuracy, corroborated by our sensitivity analysis, contrasting primary sensitivities, obtained through automatic differentiation with those by finite differences. Optimised topologies demonstrate able to harness the flow and mitigate the vortex wake in the smaller design domain. Some of these structures closely resemble classical near-wake stabilisers, including fairings, oblique plates and splitter plates. Their now optimised configurations (assessed in entirely body-fitted grids, free from porous medium effects) exhibit improved behaviour previously unseen, as corroborated by vorticity contours, time histories of force coefficients, mean and root mean square lift values, and wake formation length. Results with the larger design domain show that the optimised different topologies are successful in fully suppressing vortex interaction.