Topology optimization of Superhydrophobic Surfaces to delay spatially developing modal laminar–turbulent transition

Abstract

Super-Hydrophobic Surfaces (SHSs) have been shown to reduce skin friction of an overlying fluid as a consequence of gas pockets trapped within the surface’s microstructure. More recently, they have also been shown capable of delaying laminar–turbulent transition. This article investigates the applicability of topology optimization in designing the macroscopic layout of SHSs in a channel that are able to further delay K-type transition in a spatial setting. Unsteady direct numerical simulations are performed to simulate the transition scenario. This is coupled with adjoint–based sensitivity analysis and gradient based optimization. The optimized designs found through this procedure are capable of moving the transition location further downstream compared to a homogeneous counterpart by inhibiting the growth of secondary instability modes. This article provides the first application of topology optimization to a spatially developing transition scenario.