Flow stabilization with active hydrodynamic cloaks

TL;DR

This paper demonstrates the existence and stability of active hydrodynamic cloaks for fluid flow around cylinders, significantly increasing the critical Reynolds number and suppressing vortex shedding.

Contribution

It introduces active hydrodynamic cloaking solutions for 2D flows around cylinders, extending stability up to Re ~120, which is a substantial improvement over uncloaked cases.

Findings

Cloaking solutions are stable for Re 5-119.

Flow cloaks suppress vortex shedding and increase critical Re.

Flow cloaks can raise the critical Reynolds number up to about 120.

Abstract

We demonstrate that fluid flow cloaking solutions based on active hydrodynamic metamaterials exist for two-dimensional flows past a cylinder in a wide range of Reynolds numbers, up to approximately 200. Within the framework of the classical Brinkman equation for homogenized porous flow, we demonstrate using two different methods that such cloaked flows can be dynamically stable for $Re$ in the range 5-119. The first, highly efficient, method is based on a linearization of the Brinkman-Navier-Stokes equation and finding the eigenfrequencies of the least stable eigen-perturbations; the second method is a direct, numerical integration in the time domain. We show that, by suppressing the Karman vortex street in the weekly turbulent wake, porous flow cloaks can raise the critical Reynolds number up to about 120, or five times greater than for a bare, uncloaked cylinder.