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 difraction) and related phenomena as interference, resonance and Doppler efect, 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 efects, including boundary and edge efects, relaxation and damping.
called sloshing phenomenon consisting in high amplitude structural loads on the container [1].
Nowadays, the use of scaled and partially filled wave As damping forces are generated by viscous boundtanks 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 excitamotion under fixed conditions and, then, in the coastal tion. As known, the damping efect is afected by kineand ofshore engineering field. Their design derives matics viscosity of the fluid and tank size. In the literafrom 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 certained 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 fito be considered is the resonance, which occurs when nite element analysis with a specific software was carthe 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. lfuid motion within shallow tank can produce the so- The design included also a wave-absorption zone realized with an opportune slope to reproduce the dampICYRIME 2020: International Conference for Young Researchers in ing efect of a natural beach. Tank dimensions were Informatics, Mathematics, and Engineering, Online, July 09 2020 chosen in order to minimize both boundary efects due " damiano.alizzio@unime.it (D. Alizzio); flosavio@diim.unict.it to side walls damping and the end wall reflection on (bFo.Ln.faS.amvaiorc);og@ratissscoa.glii.oitv(aMnn.Bi.monafraina@ti)gmail.com (G.M. Grasso); the waves. Since waves were generated at one end of the tank and absorbed at the other end, the desired waves could be produced within the focus section placed © 2020 Copyright for this paper by its authors. Use permitted under Creative CPWrEooUrckReshdoinpgs IhStpN:/c1e6u1r3-w-0s.o7r3g CCoEmUmoRns WLiceonrsekAsthtriobuptioPnr4o.0cIneteerdnaitniognasl ((CCC EBYU4R.0)-.WS.org)
matic shallow tank in composites was designed to perform 3D-motion tests for long waves and ripples.
Regular long waves could be generated upstream using a suitable shaped wave-maker [13], having an alternating vertical motion and moved by an actuator operated by a home-made PC-controlled hydraulic system. The wave-maker profile is pseudo-parabolic so to generate sinusoidal-type long waves. The initial motion of the fluid particles should appear to be circular and this should indicate the low coeficient of friction thus obtained between wave-maker and fluid.
Ripples could be produced by a PC-controlled fan equipped with honeycomb filter in order to align the air flows right above the free surface of the water and positioned at the same end of the tank but immediately next at the wave-maker. Frequency working range was thought to be between 0 and 5 Hz. Such a design will allow studying separately the time-evolution of wind-wave fields rising from the initially calm wajust 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 reviscous and Newtonian. lfection efects 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 30 slope beach starting at the end of the Navier–Stokes. working area and ending at the beginning of the second beach; b) a 5 sloped beach, where pyramidal polymeric dumping obstacles should be placed in 8 paral2. Tank Design lel arrays. Distance and transversal placement of obstacles were designed to achieve a damping efect not less than 35%. This result was obtained by placing the arrays of obstacles at a distance equal to one sixth of the minimal wavelength expected [14]. The wave relfected from obstacles was projected on opposite verse of generated wave and crushed in the backside of the previous array. This caused a significant turbulence and damping of reflected waves.
Upstream wave absorption could consist of a wave absorber (made of porous packing material) positioned at a higher level than the front edge of the tank with an emerging slope greater than 20%. The most appropriate tank design dimensions were found to be as follows: length of 6500 mm, width of 1000 mm, and height of 700 mm to guarantee a filling up to 500 mm.
A rectangular transparent inspection window was thought to be located in correspondence with the working zone. Its length must be enough to allow real-time visioning and video recording two consecutive wavelengths.
Experimental setup for the measurement of long waves could consist of pressure transducers; capacitancetypes wave gauges or ultrasonic probes [15]. These sensors should be placed: a) at the generating region so that incident wave conditions can be detected, measured and calibrated; b) at the working region in order to estimate the long waves; c) at the bottom region in order to evaluate any transmitted waves.
Setup for ripples measurement should include an optical system, equipped with video-recording cameras placed within the working zone, and a suitable image post-processing software.
An anemometer could return the airflow speed, knowledge of which will be essential to appropriately adjust the fan.
Tank Simulation Software of Saint Olaf College.
Thanks to a wave generation simulator, it allowed analysing efects of two-dimension waves, including such wave phenomena as interference, difraction (single slit, double slit, etc.), refraction, resonance, phased arrays and Doppler efect.
The simulator is able to reproduce diferent source types: point-like, plane, multiple etc. The simulator allows then establishing: • Source types (point, multipoint, plane, half plane,
array, etc.) • Wave types (mechanical, radio, micro-waves, etc.) • Simulation speed (works in real time or at accel- In this study, a plane wave source was chosen haverated 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 afected by side edge surface of the tank (0-100%) efects.
A working length ranged between 1000 and 2500 • Obstacle types: Wall, Slit, Box, Point source, Line mm from the wave-maker was identified (approprisource, 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 efect 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 ranging between 1 and 3 Hz. For each of these frequencies damping parameters were identified as functions of the geometry of the applied damping device.
Examples of long wave simulations at frequencies of 2 and 3 Hz respectively as well as the corresponding damping percentages are shown in Figs. 2-9.
In this paper, the model of a water shallow tank for long and capillarity waves was proposed. Numerical simulations, carried out at design values of the most significant parameters, ensured that the central part of the waves was not afected by side edge efects. Also the working zone was demonstrated to be not perturbed by the wave-maker, the blower and dampers.
The future goal is to build such a tank, which seems suitable for various engineering applications on the motion of fluids. In particular, the water tank will be used to experimentally verify and validate a floating spar buoy designed by the authors in a previous study. step method for unsteady free-surface flow with applications to non-linear wave dynamics, 1998. [8] P. A. Madsen, H. Bingham, H. Schäfer,
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