=Paper=
{{Paper
|id=Vol-2768/paper11
|storemode=property
|title=Proposal of a Water Shallow Tank for Long and Capillary-Gravity Waves Based on a Numerical Simulation
|pdfUrl=https://ceur-ws.org/Vol-2768/p11.pdf
|volume=Vol-2768
|authors=Damiano Alizzio,Fabio Lo Savio,Giovanni Maria Grasso,Marco Bonfanti
}}
==Proposal of a Water Shallow Tank for Long and Capillary-Gravity Waves Based on a Numerical Simulation==
https://ceur-ws.org/Vol-2768/p11.pdf
Proposal of a Water Shallow Tank for Long and
Capillary-Gravity Waves Based on a Numerical
Simulation
Damiano Alizzioa , Fabio Lo Saviob , Giovanni Maria Grassoc and Marco Bonfantic
a Dip. di Ingegneria, Università degli Studi di Messina, C.da Di Dio, 98166 Sant’Agata, Messina,Italy
b Dip. di Ing. Civile e Architettura, Università di Catania, Catania, CT, Italy
c Department of Electrical, Electronic and Computer Engineering, University of Catania, Catania, CT, Italy
Abstract
In the scientific literature, wave tanks are widely used to reproduce and investigate the behaviour of surface waves and,
particularly, the long waves. Most experiments are aimed to study the performance of wave energy converters. In order
to analyse the basic properties of capillary-gravity waves (reflection, refraction, and diffraction) and related phenomena as
interference, resonance and Doppler effect, ripple tanks are more suitable. In this paper, an instrumented shallow tank was
designed to generate and observe both ripples and long waves. To validate the tank model, some numerical simulations were
performed with an appropriate software, taking into account all the two-dimensional effects, including boundary and edge
effects, relaxation and damping.
Keywords
Wave Tank, Ripples, FEA, Damping
1. Introduction called sloshing phenomenon consisting in high ampli-
tude structural loads on the container [1].
Nowadays, the use of scaled and partially filled wave As damping forces are generated by viscous bound-
tanks and ripple tanks is common in the principal engi- ary layers, their amplitudes have to be evaluated in the
neering applications concerning the study of the fluid end of the tank opposite to the end intended for excita-
motion under fixed conditions and, then, in the coastal tion. As known, the damping effect is affected by kine-
and offshore engineering field. Their design derives matics viscosity of the fluid and tank size. In the litera-
from accurate numerical analysis based on the com- ture regarding numerical simulation, wave absorption
putational fluid dynamics (CFD). Indeed, the dynamic techniques may be classified as active methods [2, 3, 4]
behaviour of a liquid within a container depends on and passive methods [5], whereas active methods are
many factors: the type of excitation and its amplitude aimed to modify the computational results within a
and frequency, properties and depth of the liquid, tank restricted zone or close to the boundary of the tank,
geometry and size. The generation of waves is ob- while passive methods consist in implementing a cer-
tained at one end of the tank through suitable actua- tain slope in the tank to simulate physical beaches [6].
tors, while the other end usually has a wave-absorbing In particular, the relaxation method is a reliable wave
surface. absorption technique [2, 7, 8, 9, 10, 11, 12].
The most common excitation types are periodic (si- In the present work, a prismatic shallow tank was
nusoidal, in particular) or impulsive, but random ex- specially designed to reproduce and study both ripples
citations are sometimes adopted. Another parameter and long waves within a certain frequency range. A fi-
to be considered is the resonance, which occurs when nite element analysis with a specific software was car-
the tank motion frequency fits with one of the nat- ried out to simulate the behaviour of the waves under
ural frequencies of the tank fluid. Under resonance, pre-fixed conditions.
fluid motion within shallow tank can produce the so- The design included also a wave-absorption zone re-
alized with an opportune slope to reproduce the damp-
ICYRIME 2020: International Conference for Young Researchers in ing effect of a natural beach. Tank dimensions were
Informatics, Mathematics, and Engineering, Online, July 09 2020 chosen in order to minimize both boundary effects due
" damiano.alizzio@unime.it (D. Alizzio); flosavio@diim.unict.it to side walls damping and the end wall reflection on
(F.L. Savio); grasso.giovanni.maria@gmail.com (G.M. Grasso);
bonfa.marco@tiscali.it (M. Bonfanti) the waves. Since waves were generated at one end of
the tank and absorbed at the other end, the desired
© 2020 Copyright for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0). waves could be produced within the focus section placed
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
Figure 1: Schematic for the tank model: 1.Upstream wave absorption; 2.Wave-maker; 3.Fan; 4.Slope; 5.Sloped beach with
obstacles.
just after the relaxation zone (equal to approximately 2 ter surface to the quasi-steady state at the given wind
times the wavelength of the maximum wave expected) velocity, then the characteristic of ripples under steady
and in the middle of longitudinal axis of the tank; this wind forcing, and finally the decay of waves when wind
representing the working zone. In the numerical sim- forcing is abruptly shut down.
ulation, the fluid adopted was distilled water that can A double wave-absorption zone was designed: one
be reasonably assumed to be homogenous, isotropic, at the downstream aimed to minimize unwanted re-
viscous and Newtonian. flection effects and the second at the upstream in order
Under these assumptions fluid motions can be con- to avoid multiple bursts while wave generating.
sidered as three-dimensional and the fluid domain can Downstream wave absorption could consist of two
be defined by the well-known governing equations of parts: a) a 30𝑜 slope beach starting at the end of the
Navier–Stokes. working area and ending at the beginning of the sec-
ond beach; b) a 5𝑜 sloped beach, where pyramidal poly-
meric dumping obstacles should be placed in 8 paral-
2. Tank Design lel arrays. Distance and transversal placement of ob-
stacles were designed to achieve a damping effect not
As shown in the schematic drawing of Fig. 1, a pris-
less than 35%. This result was obtained by placing the
matic shallow tank in composites was designed to per-
arrays of obstacles at a distance equal to one sixth of
form 3D-motion tests for long waves and ripples.
the minimal wavelength expected [14]. The wave re-
Regular long waves could be generated upstream
flected from obstacles was projected on opposite verse
using a suitable shaped wave-maker [13], having an
of generated wave and crushed in the backside of the
alternating vertical motion and moved by an actua-
previous array. This caused a significant turbulence
tor operated by a home-made PC-controlled hydraulic
and damping of reflected waves.
system. The wave-maker profile is pseudo-parabolic
Upstream wave absorption could consist of a wave
so to generate sinusoidal-type long waves. The ini-
absorber (made of porous packing material) positioned
tial motion of the fluid particles should appear to be
at a higher level than the front edge of the tank with
circular and this should indicate the low coefficient of
an emerging slope greater than 20%. The most ap-
friction thus obtained between wave-maker and fluid.
propriate tank design dimensions were found to be as
Ripples could be produced by a PC-controlled fan
follows: length of 6500 mm, width of 1000 mm, and
equipped with honeycomb filter in order to align the
height of 700 mm to guarantee a filling up to 500 mm.
air flows right above the free surface of the water and
A rectangular transparent inspection window was
positioned at the same end of the tank but immediately
thought to be located in correspondence with the work-
next at the wave-maker. Frequency working range
ing zone. Its length must be enough to allow real-time
was thought to be between 0 and 5 Hz. Such a de-
visioning and video recording two consecutive wave-
sign will allow studying separately the time-evolution
lengths.
of wind-wave fields rising from the initially calm wa-
67
Figure 2: 2D Simulation, frequency 2 Hz, side border effect, Figure 4: 3D simulation, frequency 2 Hz, side border effect,
no damping. no damping.
Figure 3: 2D Simulation, frequency 2 Hz, side border effect, Figure 5: 3D simulation, frequency 2 Hz, side border effect,
35% damping 35% damping.
Experimental setup for the measurement of long wa- 3. Numeric Simulation
ves could consist of pressure transducers; capacitance-
types wave gauges or ultrasonic probes [15]. These Numerical simulation was carried out through Ripple
sensors should be placed: a) at the generating region Tank Simulation Software of Saint Olaf College.
so that incident wave conditions can be detected, mea- Thanks to a wave generation simulator, it allowed
sured and calibrated; b) at the working region in order analysing effects of two-dimension waves, including
to estimate the long waves; c) at the bottom region in such wave phenomena as interference, diffraction (sin-
order to evaluate any transmitted waves. gle slit, double slit, etc.), refraction, resonance, phased
Setup for ripples measurement should include an arrays and Doppler effect.
optical system, equipped with video-recording cam- The simulator is able to reproduce different source
eras placed within the working zone, and a suitable types: point-like, plane, multiple etc. The simulator
image post-processing software. allows then establishing:
An anemometer could return the airflow speed, knowl- • Source types (point, multipoint, plane, half plane,
edge of which will be essential to appropriately adjust array, etc.)
the fan.
• Wave types (mechanical, radio, micro-waves, etc.)
68
Figure 6: 2D Simulation, frequency 3 Hz, side border effect, Figure 8: 3D simulation, frequency 3 Hz, side border effect,
no damping. no damping.
Figure 7: 2D Simulation, frequency 3 Hz, side border effect, Figure 9: 3D simulation, frequency 3 Hz, side border effect,
35% damping 35% damping.
• Simulation speed (works in real time or at accel- In this study, a plane wave source was chosen hav-
erated speed) ing the same width of the entire tank so to generate
waves in the direction of propagation along the ma-
• Target frequency (0-5 Hz) jor axis. This allowed designing such a width that the
• Percentage of energy damping on the bottom central part of the waves was not affected by side edge
surface of the tank (0-100%) effects.
A working length ranged between 1000 and 2500
• Obstacle types: Wall, Slit, Box, Point source, Line mm from the wave-maker was identified (appropri-
source, Multipole source, Phased array Source, ately far from both the source and the target), within
Solid box, Moving Wall, Moving Source, Cavity, which the waves were not significantly perturbed by
Medium, Mode box, Gradient, Ellipse, Prism, El- the effect of the generator and dampers.
lipse Medium, Parabola, Lens, Probe. It was therefore possible to identify the amount of
energy dissipated during the impact with the back wall
The simulator also took into account side edge ef- constituted by the dynamic dampers.
fects of the tank. Simulations were carried out with frequencies rang-
69
ing between 1 and 3 Hz. For each of these frequen- step method for unsteady free-surface flow with
cies damping parameters were identified as functions applications to non-linear wave dynamics, 1998.
of the geometry of the applied damping device. [8] P. A. Madsen, H. Bingham, H. Schäffer,
Examples of long wave simulations at frequencies of Boussinesq-type formulations for fully non-
2 and 3 Hz respectively as well as the corresponding linear and extremely dispersive water waves:
damping percentages are shown in Figs. 2-9. derivation and analysis, Proceedings of the
Royal Society of London. Series A: Mathemat-
ical, Physical and Engineering Sciences 459
4. Conclusion (2003) 1075–1104.
[9] A. P. Engsig-Karup, J. S. Hesthaven, H. B. Bing-
In this paper, the model of a water shallow tank for
ham, P. A. Madsen, Nodal dg-fem solution of
long and capillarity waves was proposed. Numerical
high-order boussinesq-type equations, Journal
simulations, carried out at design values of the most
of engineering mathematics 56 (2006) 351–370.
significant parameters, ensured that the central part of
[10] D. R. Fuhrman, P. A. Madsen, H. B. Bingham, Nu-
the waves was not affected by side edge effects. Also
merical simulation of lowest-order short-crested
the working zone was demonstrated to be not per-
wave instabilities, Journal of Fluid Mechanics 563
turbed by the wave-maker, the blower and dampers.
(2006) 415.
The future goal is to build such a tank, which seems
[11] A. Kamath, H. Bihs, Ø. A. Arntsen, Numerical
suitable for various engineering applications on the
modeling of power take-off damping in an oscil-
motion of fluids. In particular, the water tank will be
lating water column device, International Journal
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of Marine Energy 10 (2015) 1–16.
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