392
12. Special Topics
0
1
2
3
4
5
8
7
8
0
1
2
3
4
5
6
7
8
T i m e
T i m e
Fig. 12.8. The free surface heights at the side walls as functions of time for inviscid
(left) and viscous (right) sloshing in a 2D tank (from Lilek, 1995)
Fig. 12.9. A block-structured non-matching grid and the predicted free surface
shape for the flow around a NACA 0012 hydrofoil at 5 O angle of attack (F' r =
0.567)
m has a NACA 0012 profile and 5" angle of attack; the undisturbed water
height above the profile is 0.21 m, and the Froude number is 0.567. This flow
was studied experimentally by Duncan (1983). In Fig. 12.10 the steady-state
free surface profiles calculated on four grids using CDS discretization are
shown and compared with experimental data. The improvement with grid
refinement is obvious and although the agreement with the experimental
data is acceptable, it is clear that the converged result is not perfect. Since
discretization errors are small (measured by the difference between solutions
on the two finest grids), the discrepancy between prediction and experiment
is due to modeling errors (different boundary conditions, turbulence effects
etc.).
Finally we present results for 3D flow around the blunt-bow ship model
shown in Fig. 12.11. The upper part is the waterline shape. The semi-circular
bow with radius R = 0.3 m is followed by a parallel middle body 1 m long,
and the 0.7 m long stern is defined by a spline. Thus the total length of
the model is 2.0 m and the beam is 0.6 m. This shape is maintained 0.2 m
above the load waterline to the deck and 0.3 m beneath the load waterline.
There, a half body of revolution, obtained by rotating the waterline around
its longitudinal axis completes the body which has a total draft of 0.6 m.
12. Special Topics
0
1
2
3
4
5
8
7
8
0
1
2
3
4
5
6
7
8
T i m e
T i m e
Fig. 12.8. The free surface heights at the side walls as functions of time for inviscid
(left) and viscous (right) sloshing in a 2D tank (from Lilek, 1995)
Fig. 12.9. A block-structured non-matching grid and the predicted free surface
shape for the flow around a NACA 0012 hydrofoil at 5 O angle of attack (F' r =
0.567)
m has a NACA 0012 profile and 5" angle of attack; the undisturbed water
height above the profile is 0.21 m, and the Froude number is 0.567. This flow
was studied experimentally by Duncan (1983). In Fig. 12.10 the steady-state
free surface profiles calculated on four grids using CDS discretization are
shown and compared with experimental data. The improvement with grid
refinement is obvious and although the agreement with the experimental
data is acceptable, it is clear that the converged result is not perfect. Since
discretization errors are small (measured by the difference between solutions
on the two finest grids), the discrepancy between prediction and experiment
is due to modeling errors (different boundary conditions, turbulence effects
etc.).
Finally we present results for 3D flow around the blunt-bow ship model
shown in Fig. 12.11. The upper part is the waterline shape. The semi-circular
bow with radius R = 0.3 m is followed by a parallel middle body 1 m long,
and the 0.7 m long stern is defined by a spline. Thus the total length of
the model is 2.0 m and the beam is 0.6 m. This shape is maintained 0.2 m
above the load waterline to the deck and 0.3 m beneath the load waterline.
There, a half body of revolution, obtained by rotating the waterline around
its longitudinal axis completes the body which has a total draft of 0.6 m.