FLOW AROUND A CYLINDER - istiarto

– 5.4 –
d 50 � 2.1[mm]. The cylinder, with a diameter of Dp = 15 [cm] (B D p �16.3), was
vertically installed at x L = 11 [m] downstream of the entrance. A nearly uniform
approach flow (Q � 0.2 [m 3 s], U � � 0.45 [m s], and h � � 18[cm]) was established and
can be considered to be two-dimensional (B h � � 13.6), turbulent (Re = 81,000), and
subcritical (Fr = 0.34). The velocity measurements were performed at the equilibrium
scour hole (d s � 25 [cm], d s D p �1.67 ) under a clear-water scour condition. The scour
hole had been previously established by performing a continuous run of 5 days. The
scour geometry was mapped by point gauge measurements. The new version of the
ADVP instrument (see Hurther et al., 1996), which has a finer spatial resolution than the
one previously used in the flat-bed case, was utilized to get the vertical distribution of the
instantaneous velocity vector. In all measurements the ADVP was placed at the water
surface, attached on a moveable carriage.
5.3 Model calibration of k s and h ∞
The model has various constants, such as the ones of the k-� transport equations (c � , c 1 ,
c 2 , � k , and � � ) and of the logarithmic law of the wall (� and k s ). Except k s , all model
constants are kept the same as the standard model values for any flow conditions. The
equivalent roughness, k s , characterizes the roughness of the solid boundary (wall,
cylinder, bed). Its value depends on the roughness size of this solid boundary. A series of
preliminary runs using uniform flow conditions, based on the data of measurements
without the cylinder in place, indicated that the measured values of the equivalent bed
roughness (k s = 0.54 [mm] for Yulistiyanto data and k s = d 50 = 2.1 [mm] for the present
measurement) did not result in a satisfactory agreement between the computed and
measured flow fields. For this reason, calibration runs were performed by varying the
values of k s in the model. The calibrated k s value was selected by matching the vertical
distributions of the velocity, u(z), eddy viscosity, � t (z), and the shear stress per unit mass,
� zx z
� � �, obtained from the computation and the measurements.
It was found during the runs that the flow depth (h ∞ [cm] = 18.5 and 18.0 for Yulistiyanto
and the present data, respectively) should also be adjusted accordingly.
5.3.1 Computational domain
The flow, being essentially 2D, is simulated by a computational domain that represents
only a slice of the channel (see Fig. 5.1). The quasi 2D computational domain is created
by taking a 1-cell grid in the y (cross flow) direction representing a 4-[cm] portion (2%)
of the channel width. The discharge entering the domain is accordingly adjusted to
maintain the discharge per unit width (Q B [m 2 /s] = 0.125 and 0.0816 for Yulistiyanto
and the present data, respectively). The computational domain in the x (streamwise)
direction is uniformly divided into 500 cells with a step size of �x = 4 [cm]. This
represents a 20-[m] long channel reach, which is about one half of the channel length. In
the z direction, the flow depth is divided into 22 cells whose heights vary from 4% to 8%
of the local depth. This discretisation results in 36,144 nodes, of which 1,000 are