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Wave Impact with a Tall Structure
In two spatial dimensions, it has been quite
convenient to represent the free surface by drawing the markers
as symbols in the form a scatter plot. In three dimensions, however,
surface representation with scattered symbols is confusing at
best since it is not possible to distinguish symbols in the near
and far fields, nor is it easy to connect them in one's mind in
a unique manner. Consequently, a different visualization approach
has been adopted in which the surface markers are post-processed
into shaded, triangular panels. In the post-processing phase,
however, some panels are "lost," and as a result, fictitious
small holes appear on parts of the surface. The post-processing
scheme will be improved to the extent possible. In order to demonstrate
the capabilities of the ELMMC-3D method and provide confidence
in its validity, several examples will be presented below.
In the first example (Figure 1),
the interaction of a single, large wave with a tall structure
is simulated. This problem was chosen in order to validate the
method with the results of experiments conducted by Prof. Harry
Yeh of UW-Seattle as part of the ongoing NSF Cooperative Research
Grant. The tank is 160 cm long, 61 cm wide, and 75 cm tall. The
volume of water initially contained behind an infinitesimally
thin gate is 40 cm x 61 cm x 30 cm. The structure, which is 12
cm x 12 cm x 75 cm, is placed 50 cm downstream of the gate and
24 cm from the near sidewall of the tank. In the physical experiment,
since it is impossible to completely drain the tank downstream
of the gate, a layer of water (approximately 1 cm deep) always
remains on the bottom of the tank. Consequently, a 1-cm layer
of water is also included on the bottom of the computational domain.
The domain is discretized with macro cells of dimensions 2 cm
x 1 cm x 1 cm, resulting in a computational domain composed of
80 x 61 x 75 cells. Surface cells are subdivided into 27 micro
cells, three in each spatial direction.
Figure 1: Simulation of wave impact with
a rectangular structure
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Experimental validation
for wave impact with a tall structure
Toward this aim, corresponding laboratory experiments
were conducted in a tank at UW-Seattle, as mentioned above. Collected
measurements included the time history of the net force on the
structure and the time history of the fluid velocity at different
locations. Forces were measured with a load cell and velocities
were measured with a Laser-Doppler Velocimetery (LDV) system.
The velocity measurement location reported here is 14.6 cm upstream
of the center of the structure and 2.6 cm off the floor of the
tank, i.e., at (75.4 cm, 31 cm, 2.6 cm) in terms of absolute tank
coordinates. The validation results for the net fluid force on
the structure and the horizontal velocity in the main flow direction
upstream of the structure are presented at the bottom of Figure
1. Data from four experiments are included in the graphs as
(blue) circular symbols. The gaps in the experimental data, e.g.,
seen for 0.6 s < t < 0.85 s, are due to the presence of
bubbles in the water, which scatter the laser light and degrade
the signal-to-noise ratio of the LDV measurement system. Additional
comparisons are planned for this proposal. The solid (red) lines
represent the numerical results. Since the ELMMC-3D technique
is a direct numerical technique and does not include a turbulence
model, the turbulent scales resolved are of the same order as
the micro cell, i.e., of the order of 3.3 mm. Higher resolution
simulations would require the use of a large supercomputer; such
numerical experiments are proposed herein. Nevertheless, the present
comparisons between the experimental and numerical results for
the net force and the horizontal velocity provide strong confidence
in the accuracy and consistency of the ELMMC method.
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