FLOW AROUND A CYLINDER - istiarto

– 2.25 –
�o , and accordingly the friction velocity, u � , from the measured distribution of �u �� w ��.
The measured Reynolds stress shows that it is linearly distributed in the outer region (see
Fig. 2.10). However, within the inner region and towards the bed, the distribution swings
and diminishes. The reason of this phenomenon is not yet been known. It is suspected
that an inherent characteristic of the measuring instrument, due most probably to the
difficulty in obtaining clear acoustic back-scattered signals at regions close to the bed,
might have contributed to this phenomenon (see also Cellino, 1998; Yulistiyanto, 1997).
For that reason, the bed shear stress is obtained by best fitting of Eq. 2.23 to the measured
data at the outer region, z h � 0.2 , and extrapolating the fitted line to the bed, z = 0, to get
�o and u � (see Fig. 2.10). The bed shear stress and the friction velocity obtained at the six
stations are presented in Table 2.3. The average u �-value, being u� � 2.60 [cm s], is
rather close to the one computed previously from the velocity profile.
2.5 Velocity measurements around the cylinder
2.5.1 Measurement strategy
The flow along the channel is assumed to be symmetrical about the line passing through
the center of the cylinder. This assumption was taken for practical reasons since the flow
in the scour hole along the plane of symmetry is not completely two-dimensional as will
be evidenced from the measurements. The measurements were performed at the one-half
area around the cylinder. Vertical distributions of the instantaneous velocities were
obtained at the measuring stations located at P(r,�,z) (see Fig. 2.11), where r [cm] is the
radial distance (r = 0 is the center of the cylinder), � [°] is the angular direction of the
plane (� = � – 180°), and z [cm] is the vertical direction (z = 0 is in the original unerodedbed
level). While the positioning of the measurement stations was expressed according to
the cylindrical coordinate system, (r,�,z), the velocities were decomposed into its
components along the Cartesian coordinate system, (u,v,w). The coordinate
transformation (see Fig. 2.4 and Eq. 2.13) provides the relation between these two
coordinate systems. Five main radial-planes: � = 0°, 45°, 90°, 135° and 180° (see Fig.
2.11a) were selected in which about 15 to 25 verticals were obtained for each plane.
Additional measurements, with fewer verticals (8 to 10 verticals), were performed at 6
planes: � = 15°, 30°, 60°, 75°, 105° and 120°. These measurements provide
supplementary data that may be necessary in the analyses of the flow pattern (this will be
treated in Chapter 5). For technical reasons, each plane was divided into three zones:
A(r � 20,�, z � 5), B(r,�,z � 5) and C(r � 20,�, z � 5) (see Fig. 2.11b). Measurements
were possible in the zones A and B, but technical difficulties hinder the measurement in
zone C, being a ―blank zone‖ where data cannot be obtained. The measurements in zones
A and B were performed such that the data obtained from the two measurements overlap.
The overlap is generally made at 7 ≥ z [cm] ≥ –2, that is, the measurements at zone A
penetrate up to z = –2 [cm] and those in zone B start at z = 7 [cm] (see Fig. 2.11c).