### Behavior of Particle Tracers in the Steady and Periodic Wakes of a Circular Cylinder

#### Abstract

Tracer particles introduced into the flow domain

for experimental flow visualization often tend to exhibit chaotic

behavior even for the simplest of configurations. These passive

tracers do not exactly follow the regime in general. The spatial

distributions formed by such particles within the flow field and

the probable trajectories followed by them are governed by the

phenomenon of Lagrangian chaos. Since the problem at hand

has it's foundations in the theories of Hamiltonian dynamics and

deterministic chaos, drawing a relation between the Eulerian

flow field and the Lagrangian tracer field is a difficult task.

However, analyzing this behavior would provide useful insight

in interpreting the results of flow visualization experiments

which involve particle tracking. Based on this background,

the phenomenon of chaotic advection for a laminar cross-flow

over a circular cylinder has been investigated numerically. Two

configurations are considered, one involving a steady flow at

Re=20 while the other characterizing a periodic shedding regime

at Re=100. Computational visualization of the flow is carried out

by locally injecting neutrally buoyant particles at zero momentum

and tracking the same by FLUENT's discrete phase model. The

tracks made by the tracers, being equivalent to streaklines, are

generated for different injection locations and the trajectories

have been compared with the streamline patterns. It has been

observed that the steady regime at Re=20 does not exhibit chaotic

advection and the streaklines coincide with the streamtraces. On

the other hand, the shedding regime, being temporally dependent,

depicts a high degree of tracer mixing. The particles tend to

form complex spatial distributions in this case. Further, the

formation of a particular tracer distribution has been observed

to be strongly dependent on the location of the injector within the

domain. Since the tracer particles exhibit stochastic behavior for

an otherwise simple and periodic underlying flow, it is expected

that such patterns can be misleading. A careful study of all

possible tracer distributions is hence advisable for visualization

of such time dependent flows.

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