FLOW AROUND A CYLINDER - istiarto

Water-surface profile
– 5.27 –
The computed and the measured water surface profiles along the longitudinal section and
along the cylinder circumference are shown in Fig. 5.14. The profiles are made
dimensionless using the approach flow depth, h � , and the cylinder diameter, Dp, as the
scaling factors for the z and x directions, respectively. The following remarks are put
forward on the comparison of the water surface:
� Upstream of the cylinder the computed water surface tends to be slightly above the
measured profile. However, the bow wave in front of the cylinder, due to the
stagnation pressure, is quite well reproduced. The simulation gives a relative increase,
(h � h � ) h � , of 12.2% compared to 12.7% obtained from the measurement.
Fig. 5.14 Computed (line) and measured (symbols) water-surface profiles along the
longitudinal section and the cylinder circumference.
Flow around a cylinder on a flat channel bed.
� Along the upstream circumference of the cylinder, an under-estimation of the water
surface is observed; the maximum depression, (h � h � ) h � , is computed as 23%
while it is measured as 11%. This rather strong is most likely due to the presence of a
strong pressure-gradient along the cylinder circumference. The high (stagnation)
pressure upstream of the cylinder, � = 0°, is accelerating the flow not only towards
the bed (the downward flow), but also towards the downstream along the cylinder
circumference (in the angular direction, �). Consequently, there is a steep water
surface along this circumference. The method of the surface boundary positioning,
which is based on the pressure (see Chapter 4), evidently becomes less accurate when
being confronted with such situation. The inaccuracy can be explained by the fact
that: (1) the surface pressure is not directly obtained from the computation but from
an extrapolation (by assuming a hydrostatic distribution) of the pressure at the cell
center just below the surface, and (2) this surface pressure, defined at the center of the
top face, is linearly distributed to the vertices of the top face with which the vertices