Lagrangian structures and mixing in the wake of a streamwise oscillating cylinder

Abstract

Lagrangian analysis is capable of revealing the underlying structure and complex phenomena in unsteady flows. We present particle-image velocimetry measurements of the wake of a cylinder undergoing streamwise vortex-induced vibrations and calculate the Finite-Time Lyapunov Exponents (FTLE) in backward- and forward-time. The FTLE fields are compared to the phase-averaged vorticity fields for the four different wake modes observed while the cylinder experiences streamwise vortex-induced vibrations. The backward-time FTLE fields characterise the formation of vortices, with the roll up of spiral-shaped ridges coinciding with the roll up of the shear layers to form the vortices. Ridges in the forward-time fields tend to lie perpendicular to the flow direction and separate nearby vortices. The shedding of vortices coincides with a “peel off” process in the forward-time FTLE fields, in which a ridge connected to the cylinder splits into two strips, one of which moves downstream. Particular attention is given to the “wake breathing” process, in which the streamwise motion of the cylinder causes both shear layers to roll up simultaneously and two vortices of opposite sign to be shed into the wake. In this case, the ridges in forward-time FTLE fields are shown to define “vortex cells,” in which the new vortices form, and the FTLE fields allow the wake to be decomposed into three distinct regions. Finally, the mixing associated with each wake mode is examined, and it is shown that cross-wake mixing is significantly enhanced when the vibration amplitude is large and the vortices are shed alternately. However, while the symmetric shedding induces large amplitude vibrations, no increase in mixing is observed relative to the von Kármán vortex street observed behind near-stationary bodies.

Probing vortex-shedding at high frequencies in flows past confined microfluidic cylinders using high-speed microscale particle image velocimetry

“…A commonly used Lagrangian metric of mixing is the Finite-Time Lyapunov Exponent (FTLE), which is a measure of the rate of fluid stretching. 3 In order to calculate the FTLE fields, it is first necessary to find a flow map, φ, which represents the positions of a series of massless "particles." By tracking the rate at which neighboring particles separate with time, the rate of stretching can be measured.…”

“…Vortex-shedding in the wake of these bluff bodies results in periodic changes in the local direction of flow, inducing crossstream flows and reducing the diffusion time. 1 Vortex-shedding from cylindrical structures embedded within microfluidic channels also has the potential to promote heat and mass transfer: the oscillatory motion in the wake can induce stretching and folding of the species streams, 2 resulting in mixing 3 as well as heat transfer enhancement. 4 While vortex-shedding is a well-documented feature of macroscale flows past cylinders, described in detail in many seminal works, [5][6][7] its onset is highly dependent on channel and pin geometry.…”

Mode decomposition and Lagrangian structures of the flow dynamics in orbitally shaken bioreactors

“…30 FTLE has been used extensively to study a wide range of flows and to decompose the flow into distinct regions. 31,32 Despite the power of the FTLE approach for studying mixing, 33 there has been relatively little or no experimental work investigating the Lagrangian dynamics in mixing vessels, or more specifically, in shaken bioreactors.…”

Potential of Lagrangian Analysis Methods in the Study of Chemical Reactors

“…For the determination of the Reynolds number the strut diameter has been selected as a characteristic length. Each strut acts similarly as a cylinder in a transitory regime (starting above Re = 47, based on cylinder diameter) that causes the separation of particle trajectories in its wake , . The strut Reynolds number is defined as …”