Low-friction fluid flow surface design using topology optimization

Several practical applications in fluid mechanics have the interest to reduce energy dissipation by reducing the drag or pressure drop. An example of a solution is to turn the wetted surface into a super-hydrophobic surface (SHS). However, the whole surface coated may adversely affect some regions, depreciating the fluid flow. Furthermore, an SHS may not be cheap, being important to decide which regions to prioritize. Thus, in this work, the topology optimization method is applied to obtain an optimized design of SHS distribution. Derivation of the discrete adjoint problem applied to super-hydrophobic modeling is shown. The numerical implementation is done by using a computational fluid dynamics (CFD) code based on the finite volume method (FVM) as the primal and the adjoint solver, and the internal point optimization algorithm (IPOPT) as the optimizer. The SHS behavior is simplified by adopting the slip length model. Two test cases are presented: internal and external flows. For internal flow case, a stretched-S pipe is used, aiming to reduce the pressure drop; for external flow case, the foil NACA0015 is analyzed, aiming to reduce the drag. Both cases are assumed to be 2D, steady-state flow, using the properties of water, in a fully turbulent flow, and constrained by a maximum material distribution. Optimized topologies for several surface constraints (maximum amount of SH material used) are obtained, showing the regions to be prioritized based on the surface constraint limit. Additionally, the effects of slip length (the level of hydrophobicity), Reynolds number, and angle of attack are analyzed. The obtained results show that regions to be prioritized in order to reduce the dissipated energy are not always intuitive. Furthermore, depending on the operating condition, a fully SHS case may not be the best option.