Homogenization design and drag reduction characteristics of hydrodynamic cloaks

Abstract

Hydrodynamic cloaks have attracted extensive attention because of their ability to significantly reduce the surface resistance of designated target. However, most of parameters of traditional hydrodynamic cloaks present inhomogeneous and anisotropy, which increases the challenge of manufacturing hydrodynamic cloaks for us. To overcome this limitation, equivalent medium theory and integral median theorem are used to homogenize the parameters of hydrodynamic cloaks. Numerical simulations verify that the simplified homogeneous hydrodynamic cloaks exhibit the equivalent cloaking effect as inhomogeneous hydrodynamic cloaks, which can be applied to different flow fields as well. This simplified method not only can simplify inhomogeneous hydrodynamic cloaks to homogeneous hydrodynamic cloaks, but also can be applied to other physical fields, such as optics, acoustics, electromagnetics, and thermodynamics among other areas for the homogenization of metamaterial design, providing a new method to relax the difficulty of metamaterial design. In addition, based on the applicability of homogeneous hydrodynamic cloaks to different flow fields, hydrodynamic camouflage devices are designed that can camouflage the flow fields generated by the original objects into fields caused by arbitrary objects, offering a scheme for achieving hydrodynamic camouflage. Finally, as Reynolds numbers increase, the cloaking and drag reduction performance of hydrodynamic cloaks are quantitatively compared and analyzed. The results show that hydrodynamic cloaks still exhibit high performance in cloaking and drag reduction in non-creeping flows.

Hydrodynamic metamaterials for flow manipulation: Functions and prospects

“…1(b)), hydrodynamic rotators can be designed by varying the coordinate transformation of the rotation angle [34] (Fig. 1(c)), and hydrodynamic camouflage devices can be designed by adding the corresponding camouflage based on hydrodynamic cloaks [35] (Figs. 1(d) and 1(e)).…”

“…To homogenize the hydrodynamic cloak, [29] the authors in Ref. [35] then simplified the anisotropic inhomogeneous cloak to an anisotropic homogeneous cloak by using the integral median theorem and coordinate transformation theory. It is concluded that the drag force on the cloak in creeping flows becomes zero, and the cloak continues to exhibit remarkably strong drag reduction characteristics in laminar flows.…”

“…Aiming to enable the cloak to be constant and extendable to non-creeping flows, the authors in Ref. [35] utilized the convection-diffusion-balance method, to solve Eqs. ( 9) and ( 10) analytically, and designed a microscale cylindrical cloak effective in a certain Reynolds number range (Re ≤ 42), the parameters of which are only related to the radius of the object and the cloak (…”

Convective thermal cloaks with homogeneous and isotropic parameters and drag-free characteristics for viscous potential flows

“…To overcome this challenge, numerous research studies have been carried out in hydrodynamic metamaterials through transformation theory and Darcy’s law in porous media. 40 , 41 On the basis of these studies, a surge in hydrodynamic metamaterials investigations 42 , 43 , 44 , 45 , 46 , 47 , 48 has emerged by virtue of transformation hydrodynamics, 42 , 43 , 47 , 48 scattering cancellation method, 44 convection-diffusion-balance method, 45 coupling electro-osmosis method, 46 and so forth. More comprehensive investigations of hydrodynamic metamaterials can be found in the review.…”