Flow stabilization with active hydrodynamic cloaks

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 (Re's), 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's in the range of 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 eigenperturbations; the second method is a direct numerical integration in the time domain. We show that, by suppressing the von Kármán vortex street in the weakly 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.

A Volumetric Approach to Wake Reduction: Design, Optimization, and Experimental Verification

“…One possible extension to our methodology is the inclusion of elastic elements capable of generating reaction forces that interact nontrivially with the oscillatory vortex motions. Another extension is the introduction of volumetrically distributed thrusters such as micropump arrays [35] as alluded to in the theoretical studies of Urzhumov and Smith [14,15]. sphere independent of changes to boundary conditions and domain size.…”

“…Recently, the effects of these distributions on the turbulent wake of spherically symmetric structures [28] and the transition Reynolds number of cylindrical structures [15] were considered. However, the effect of more spatially complex permeability distributions remains unknown, due to both the computational cost of full three-dimensional solutions and the much larger functional space of permeability maps to be explored.…”

“…Motivated by recent advances in transformation electromagnetics [16] and acoustics [17], they considered both passive and active scenarios for the control of the Stokes flow around a spherical object and found that complete cancellation of both the drag term and the domain-wide wake requires an active system. These studies [14,15] did not address the question as to whether or not any wake reduction can be achieved in hydrodynamics by passive means and also left out any consideration of flow nonlinearity and turbulence. With ever-improving computational hardware and numerical methods, it has recently become possible to perform complete physical modeling of a highly complex fluid-solid composite without the need for local homogenization.…”

“…This is especially true for active scenarios. Urzhumov and Smith [14,15] have investigated the possibilities in volumetric flow control using a simplified, two-scale description based on the local permeability of a porous medium. Motivated by recent advances in transformation electromagnetics [16] and acoustics [17], they considered both passive and active scenarios for the control of the Stokes flow around a spherical object and found that complete cancellation of both the drag term and the domain-wide wake requires an active system.…”

Thermal Illusion of Porous Media with Convection-Diffusion Process: Transparency, Concentrating, and Cloaking

“…Therefore, our theory and parameter settings are reasonable and adopted for creeping flow in porous media. When Reynolds number is large, we should consider the Brinkman- [31][32][33] Stokes flow or turbulent flow. We should also notice that our work may be invalid when Fourier's law breaks down at the nanometer scale.…”