FLOW AROUND A CYLINDER - istiarto

3.2.5 Vorticity fields
– 3.20 –
The data of the velocity fields (see Fig. 3.1 and Fig. 3.2) can readily be used to generate
the vorticity contours; this is shown in Fig. 3.8, where only the region of significant
vorticity, z ≤ 2 [cm], is displayed. The vorticity in a vertical plane, � � , is computed by:
� � � �u �
�z
� �w
��
(3.2)
where � is the x-axis rotated by � and u � the corresponding velocity component. The
transformation of the Cartesian coordinate axes and velocities is obtained by:
� � x cos� � ysin� and u � � ucos� � vsin� . The central finite-difference technique
was applied to the velocity data from all measuring stations in each plane. The following
is to be observed:
� In the plane � = 0°, a strong positive vorticity is seen at the upstream edge of the
scour hole, which is due to a change in the bed slope; this is possibly related to the
start of a separating flow (Fig. 3.8a). Similarly, a countour line of � � = 5 [m -1 ], which
extends towards the cylinder bottom corner, is most likely related to the separation
line. A weak negative vorticity is observed at � = –35 [cm]. Another strong positive
vorticity is created in the downstream edge of the scour hole, � = –10 [cm], caused by
the adverse pressure gradient due to the flow obstruction of the cylinder. This positive
vorticity is accompanied by another strong (negative) vorticity underneath. In the
remaining part of the scour-hole, the vorticity is rather weak, being of the same order
as the vorticity in the approach flow. Behind the cylinder, the positive vorticity seen
at the vicinity of the bed is probably due to the boundary-layer flow. The negative
vorticity in the upper layer is related to the rotating flow as seen in the velocity fields;
this disappears when the flow moves away from the cylinder and out of the scour
hole.
� In the plane � = 45°, a rather similar picture as in the plane � = 0° is observed; a
strong positive vorticity is created on entering the scour hole, subsequently a weak
negative one is seen at � = –35 [cm]. Another strong positive one is found at the
bottom corner close to the cylinder; unlike in the previous plane, however, the
accompanying negative vorticity underneath is weak. Immediately behind the
cylinder, a rather weak negative vorticity is displayed at the bed and upper layer. A
boundary-flow positive vorticity is seen at the vicinity of the bed. In the remaining
part of the scour hole, none of important activity can be observed.
� In the plane � = 90°, a positive vorticity, but weak, is also observed on the brink of
the cylinder. A positive and negative vorticities at the bottom corner of the cylinder is
also detected, but with a much weaker strength than that in the other planes. In the
remaining part, a weak negative vorticity is observed.