Meta-hydrodynamics for freely manipulating fluid flows

Abstract

Flow control technologies play a crucial role in modern engineering and scientific research. Hydrodynamic metamaterials, as an emerging branch in the field of flow control, have attracted extensive research due to their remarkable potential in flow control, thus leading to the development of hydrodynamic metadevices. Here, we propose a meta-hydrodynamics theory for the active manipulation of fluid flows, which establishes an equivalence relation between volumetric forces and spaces and, consequently, allows for the design of active hydrodynamic metadevices. This equivalence relation can be utilized to accurately tailor the flow fields as long as the manipulation effects of the hydrodynamic metadevices on the flow fields are predetermined. By constructing a mapping relation of coordinate transformation from virtual space to physical space, we can determine the required volumetric force distributions to realize these hydrodynamic metadevices. We exemplify this theory with three different applications: hydrodynamic cloaks, concentrators, and rotators, for which we calculate the corresponding volumetric force distributions. Subsequent numerical simulations reveal the excellent manipulation performances of these hydrodynamic metadevices in both uniform and non-uniform flow fields. Finally, our research is expected to pioneer new perspectives in the development of hydrodynamic metadevices and methodologies for flow control under nonlinear flows with high Reynolds numbers.