FLOW AROUND A CYLINDER - istiarto

– 5.29 –
using a Joukowski transformation to construct the xy-grid, and by stretching this grid in
the z direction to form the xyz control-volume grid. The grid sizes in the x and y
directions vary between 0.11 to 12 [cm] and 0.5 to 8 [cm]; in the z direction, the grid
sizes are 4% to 8% of the local flow-depth. To generate the bed level of the
computational domain, the elevations of the bottom cell vertices were interpolated from a
5 � 5-[mm 2 ] uniform bed-level grid. This grid was constructed based on the measured
bed-level data obtained by point gauge measurements. Fig. 5.15 illustrates the xy and xz
grids at an intermediate solution of the simulation.
5.6.2 Boundary and initial conditions
There are five boundary conditions in this run, i.e. inflow, outflow, symmetry, wall, and
surface boundaries. These are all boundary-condition types that can be handled by the
present model.
� Upstream inflow, x = –2.5 [m]: Q 2 � 0.1[m 3 s] and u, v, w, k, � are available from
the measurement in the approach flow region (see Chapter 2). The values of � are
obtained by � � c � k 2 � t (see Eq. 5.1), where the eddy viscosity, � t , and the kinetic
energy, k, are obtainable from the measured velocities (see also Eq. 5.2) such as
�t � �u ��w
�� �u �z and k � 1 2�u
�� u ���
v �� v ���
w ��w
���.
� Downstream outflow, x = 2.5 [m]: constant surface elevation, which corresponds to
the depth of the uniform approach flow, h � = 17.8 [cm].
� Left (north) boundary, y = 0: wall boundary along the cylinder (persplex glass),
BCC ��B
��,
(–0.75 ≤ x [m] ≤ 0.75) with ks = 0.22 [mm] and symmetry plane along the
rest, ABB ��A
��and
CDD �� C ��.
� Right (south) boundary, y = –1.225 [m]: wall boundary along the channel glass sidewall
with k s = 0 [mm].
� Bottom boundary: wall boundary along the channel uniform-sand bed with
k s = 2d 50 = 4.2 [mm] (see Sect. 5.3.3).
� Top boundary: water surface.
The initial conditions of the simulation are horizontal flow depth corresponding to the
known uniform flow depth (h∞ = 17.8 [cm]), hydrostatic pressure distribution,
p � ��gz �zsurface � z�
[Pa], velocity and k-� according to the known distributions at the
inlet boundary. Within the initial stage, as in the simulation of the flat-bed case, the water
surface was kept constant until the flow field was more or less constant. The simulation
was then restarted and the water surface was let to move following the surface boundary
treatment, except at the downstream boundary.