Circle
flow
S
Basu and A Kulkarni analyse the effect of rotation around the circular
cylinder in terms of suppression of vortex shedding
Flow past a circular cylinder is one of the basic flows of interest
to the fluid dynamicity. A cylinder is often considered as an ideal
bluff body to study the vortex formation and the vortex’s interaction
at the wake of the body. In contrast, flows past a rotating cylinder
has been studied to a much less extent. Although this particular technique
has been used for lift enhancement and boundary layer control over the
airfoils it is characterised by two parameters.
w = rotational velocity
D = diameter of the cylinder
v = kinematic viscosity
It was initially observed by Magnus that rotation causes the occurrence
of a lift force. This force is the result of shift of recirculation
zone at the wake due to rotation. Owing to the non-linearity associated
with the viscous flows around a rotating cylinder very little analytical
treatment has been undertaken. The investigations have mainly been of
the numerical or experimental type. In the lower Reynolds number (Re<
200) range no reliable data exist. Beyond the Reynolds number of 200
the wake becomes three dimensional and turbulent. The Reynolds number
range may be divided into three groups : steady laminar regime (Re <47),
unsteady laminar 2d vortex shedding regime ( 47 <Re <200) and
the unsteady regime (Re > 200). In the last regime wake the complexity
of flow structure increases drastically. This hinders numerical experiments
at this regime beyond an early transient period. For decreasing Reynolds
number the size of the integration domain has to be enlarged significantly
and the formulation of appropriate outer boundary condition gains importance.
Reynolds number can be viewed as a ratio between two length scales:
the cylinder diameter and the length scale of viscous diffusion. Although
the streamline patterns shown by various authors show similar patterns
there is a high inconsistency in the results of drag and lift coefficients
among them. Use of smaller domain and inadequate boundary condition
most probably have attributed to this anomaly. In the present study
the objectives are to detect this newly reported phenomena for a range
of Reynolds number and to try to obtain a relationship between this
and the Reynolds number. The investigation resulted in a consistent
set of data for the limits of this phenomenon and a proposed relation
between Re and aH, aL that demarcates the higher and lower bound of
the occurrence of this periodicity.
Governing equation and numerical method
For a laminar two-dimensional flow of an incompressible
fluid with constant properties, dimensional continuity and momentum
equations are solved. The equations can be written as,
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