The impact of a deep-water plunging breaker on a finite height two-dimensional structure with a vertical front face is studied experimentally. The structure is located at a fixed horizontal position relative to a wave maker and the structure’s bottom surface is located at a range of vertical positions close to the undisturbed water surface. Measurements of the water surface profile history and the pressure distribution on the front surface of the structure are performed. As the vertical position, $z_{b}$ (the $z$ axis is positive up and $z=0$ is the mean water level), of the structure’s bottom surface is varied from one experimental run to another, the water surface evolution during impact can be categorized into three classes of behaviour. In class I, with $z_{b}$ in a range of values near $-0.1\unicode[STIX]{x1D706}_{0}$, where $\unicode[STIX]{x1D706}_{0}$ is the nominal wavelength of the breaker, the behaviour of the water surface is similar to the flip-through phenomena first described in studies with shallow water and a structure mounted on the sea bed. In the present work, it is found that the water surface between the front face of the structure and the wave crest is well fitted by arcs of circles with a decreasing radius and downward moving centre as the impact proceeds. A spatially and temporally localized high-pressure region was found on the impact surface of the structure and existing theory is used to explore the physics of this phenomenon. In class II, with $z_{b}$ in a range of values near the mean water level, the bottom of the structure exits and re-enters the water phase at least once during the impact process. These air–water transitions generate large-amplitude ripple packets that propagate to the wave crest and modify its behaviour significantly. At $z_{b}=0$, all sensors submerged during the impact record a nearly in-phase high-frequency pressure oscillation indicating possible air entrainment. In class III, with $z_{b}$ in a range of values near $0.03\unicode[STIX]{x1D706}_{0}$, the bottom of the structure remains in air before the main crest hits the bottom corner of the structure. The subsequent free surface behaviour is strongly influenced by the instantaneous momentum of the local flow just before impact and the highest wall pressures of all experimental conditions are found.
The generation of spray during the vertical impact of a flat plate (length $L=1.22~\text{m}$, width $B=0.38~\text{m}$) on a quiescent water surface is studied experimentally. The plate is held in an orientation tilted up from horizontal by angles $\unicode[STIX]{x1D6FD}$ ranging from $10^{\circ }$ to $25^{\circ }$ about one of its long edges, which is positioned close to a vertical wall. The plate motion, which is driven by a servo motor system, is set to maintain a constant speed, $W_{0}$, until the trailing (upper) long edge of the plate passes the still water level (SWL) and then to decelerate to a stop. The impact Froude numbers $\mathit{Fr}$ ($=W_{0}/\sqrt{gB}$, where $g$ is the gravitational acceleration) range from 0.21 to 0.63. The evolution of the water surface underneath the plate and outboard of its trailing edge is measured with a cinematic laser induced fluorescence technique. As the plate’s leading (low) edge passes the SWL, the local water surface rises and develops into a thin spray sheet that travels along the plate’s lower surface toward the trailing edge. The horizontal speed of the under-plate spray tip is approximately $2.25W_{0}/\tan \unicode[STIX]{x1D6FD}$, as high as $15~\text{m}~\text{s}^{-1}$. In agreement with published similarity theory for the flow during the vertical water entry of a wedge, the under-plate surface profiles scaled by $W_{0}t$ nearly collapse on a single curve for each $\unicode[STIX]{x1D6FD}$. As the under-plate spray passes the plate’s trailing edge, it develops into the leading portion (called herein the Type I spray) of the outboard spray system. As the trailing edge of the plate passes through the local water surface, a crater develops and a large nearly vertical spray sheet (called the Type II spray) is generated from the outer edge (called the outboard spray root) of the crater. The characteristic horizontal length scale of the crater is found to expand in time following a power law with an exponent of approximately 0.77 for all conditions. A short time after its formation, the outboard spray root becomes the crest of a gravity wave whose propagation speed is of the order of $1~\text{m}~\text{s}^{-1}$ for all $\unicode[STIX]{x1D6FD}$ and $\mathit{Fr}$. The dimensionless envelope of the Type II spray profiles collapse to a single curve at high $\mathit{Fr}$ for each $\unicode[STIX]{x1D6FD}$. The connecting spray sheet between the Type I and Type II sprays tends to break up at small $\unicode[STIX]{x1D6FD}$ and large $\mathit{Fr}$.
In naval hydrodynamics most the reseach on the impact of the hull of a vesel to the water surface has focused primarily on mapping the forces on the hull and much less to the formation of the spray. The latter is the topic of the present work, where the spray generated by the impact of a flat plate on a quiescent water surface is studied by experiments and simulations at different impact Froude numbers. Overall two types of sprays are formed: Type I, which is a cloud of droplets and ligaments generated at the impact of the plate's leading edge with the water surface, and Type II, which is formed after the trailing edge of the plate enters the local water surface. Detailed analysis of the experimental data for the Type II spray revealed that the spray envelopes and root point trajectories are independent of Froude number close to the trailing edge, while further away reach higher vertical positions for larger Froude numbers. The numerical simulation captures the general behavior of the Type II spray and agrees favorably with the experimental results. A series of computations with a flexible plate is also reported, where it is shown that increased flexibility reduces the height of the spray and suppresses the formation of droplets.
The investigation of fluid-structure interaction during the impact of a flexible plate on a water surface has received much attention. Measurement of highly transient, distributed strain of the plate during the slamming event is of great interest. Multiplexed fiber Bragg grating (FBG) strain sensors provide a promising solution for such measurement since these sensors are inherently waterproof and are immune to electromagnetic interference. However, in order to monitor the highly transient, distributed strain responses (up to 20 kHz), high-speed simultaneous interrogation of multiplexed FBG sensors is required, which is challenging by using commercial optical interrogators. We present a tunable-wavelength-filter-based optical interrogation system for high-speed simultaneous interrogation of multiplexed FBG strain sensors and demonstrate its application for structural monitoring of a flexible plate during the slamming event. The interrogation system employs a piezoelectric-transducer-controlled Fabry–Perot tunable filter. By operating the tunable filter at its resonant frequency and demodulating the sensor signal based on a peak tracing method, we demonstrated an interrogation speed of 100 kHz, an interrogation range of 98 nm, and an interrogation resolution of 5 pm. For proof-of-performance, the interrogation system was used to monitor the vibrational responses of a cantilever plate under impact loading and the measurement of vibration modes up to 6.785 kHz was demonstrated. Finally, the slamming experiments were carried out with six multiplexed FBG strain sensors mounted on a flexible plate. The dynamic strain measurement of the plate during the slamming event was successfully demonstrated by using the high-speed FBG interrogation system.
The impact of flexible rectangular aluminum plates on a quiescent water surface is studied experimentally. The plates are mounted via pinned supports at the leading and trailing edges to an instrument carriage that drives the plates at constant velocity and various angles relative to horizontal into the water surface. Time-resolved measurements of the hydrodynamic normal force ( $F_n$ ) and transverse moment ( $M_{to}$ ), the spray root position ( $\xi _r$ ) and the plate deflection ( $\delta$ ) are collected during plate impacts at 25 experimental conditions for each plate. These conditions comprise a matrix of impact Froude numbers ${Fr} = V_n(gL)^{-0.5}$ , plate stiffness ratios $R_D= \rho _w V_n^2 L^3D^{-1}$ and submergence time ratios $R_T= T_sT_{1w}^{-1}$ . It is found that $R_D$ is the primary dimensionless ratio controlling the role of flexibility during the impact. At conditions with low $R_D$ , maximum plate deflections on the order of $1$ mm occur and the records of the dimensionless form of $F_n$ , $M_{to}$ , $\xi _r$ and $\delta _c$ are nearly identical when plotted vs $tT_s^{-1}$ . In these cases, the impact occurs over time scales substantially greater than the plate's natural period, and a quasi-static response ensues with the maximum deflection occurring approximately midway through the impact. For conditions with higher $R_D$ ( $\gtrsim 1.0$ ), the above-mentioned dimensionless quantities depend strongly on $R_D$ . These response features indicate a dynamic plate response and a two-way fluid–structure interaction in which the deformation of the plate causes significant changes in the hydrodynamic force and moment.
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