Relevant
results from the numerical solution of the two-dimensional incompressible
unsteady Navier-Stokes equations for streaming flow
past a rotating circular cylinder are presented in this study. The numerical solution of the equations of
motion is conducted with a commercial computational fluid dynamics package
which discretizes the equations applying the control
volume method. The numerical setup is
validated by comparing results for a Reynolds number based on the free stream
of Re = 200 and peripheral speed of 
= 3, 4 and 5 with
results from the literature. After the
validation stage, various pairs of Re
and are specified in order
to carry on the numerical experiments.
These values are Re = 200 with
= 4 and 5; Re = 400 with = 4, 5 and 6, and Re = 1000 with = 3. In all these cases, gentle convergence to
fully developed steady state is reached.
From the numerical vorticity distribution, the
position of the outer edge of the vortical region is
determined as a function of the angular coordinate. This position is found by means of a
reasonable criterion set to define the outmost curve around the cylinder where
the vorticity magnitude reaches a certain cut off
value. By considering the average value
of this profile, a uniform vortical region thickness
is specified for every pair of Re and
.
Next, the
theoretical approach of Wang and Joseph (2004a) and the numerical results are
utilized to determine two different values of the effective vortical
region thickness for every pair of Re
and . One effective
thickness 
is obtained from the
match between the additional drag on the outer edge of the vortical
region according to the viscous correction of viscous potential flow (VCVPF)
and the corresponding numerical profile while the other thickness 
is determined from the
match between the pressure lift on the cylinder obtained from Wang and Joseph
(2004a)'s simple modification of the boundary layer analysis due to Glauert (1957) and the numerical value of the pressure lift
coefficient. Each of these two values of
the effective vortical region thickness is used to
compute various parameters relevant to this type of fluid motion, namely, the
torque on the rotating cylinder; the circulatory velocity at the edge of the vortical region, which links the cylinder’s angular
velocity with the circulation of the irrotational
flow of the viscous fluid outside this region, and the viscous
dissipation. For some of these
parameters, predictions from the theoretical approaches of Glauert
(1957) and Wang and Joseph (2004a) are presented for comparison. The values of both effective thicknesses, and , are found to be fairly close. Then, we show that, with the choice of the
thickness as a unique effective
thickness, the simple modification of Glauert's
boundary layer analysis and the VCVPF applied to balance the shear stress
discrepancy at the outer edge of the vortical region
as proposed by Wang and Joseph (2004a) lead to expressions that exhibit better
general agreement with the numerical results than Glauert's
solution.