Evaluation of the concept of hydrodynamic metamaterial cloak for drag reduction

The goal of this paper is to introduce and evaluate the potential of a hydrodynamic metamaterial cloak for drag reduction of objects in viscous flow. In this paper, the hydrodynamic cloaks for 2D objects of complex shapes such as airfoil are created by coordinate transformation using the Stokes equations for low Reynolds number flows. First, the viscosity tensor for a circular cylinder cloak is derived by coordinate transformation based on the Stokes equations. Then the viscosity tensors for an elliptic-cylinder cloak and an airfoil cloak are obtained by stretching the circular cylinder cloak. The effect of the cloaks is simulated using the commercially available software ANSYS FLUENT 2019R2. By comparing the velocity fields, pressure fields, streamlines and wall skin friction coefficient in flow about various geometries without and with cloak, the potential of a hydrodynamic metamaterial cloak for drag reduction is evaluated. The cloak changes the velocity field and pressure field in the cloak region such that the velocity distribution in the region outside the cloak becomes more uniform, and the pressure difference between the upstream and downstream regions of the object becomes smaller; this produces the hydrodynamic hiding effect and drag reduction. These effects are reduced at higher Reynolds numbers. The results for a cloak around a circular cylinder, an elliptic-cylinder, an airfoil and a flat plate (normal to the flow) show that a hydrodynamic cloak has the effect of hiding the object and reduces the drag, although these effects are reduced at high Reynolds numbers.