Variability in wave impacts: An experimental investigation

The prospect of stricter national and international emission standards for the shipping industry are a driving force in the search for alternative shipping fuels, such as liquefied natural gas (LNG). However, new challenges arise with the widespread use of LNG. For example, there is a desire to use LNG cargo containment systems at lower filling levels. These filling levels are strictly limited to prevent the movement of liquid inside the containment system, which is known as sloshing. Sloshing inside a cargo containment system can result in extreme wave impact events with the potential to cause structural damage. Therefore, a fundamental understanding of these extreme wave impact events is required before studying increasingly complex phenomena.   The study of wave impacts on a wall has been an active area of research for decades. Moreover, the impact of waves upon structures is relevant for many fields such as ocean, coastal, and maritime engineering. The generation of repeatable waves in a laboratory environment is not trivial (Bagnold, 1939). Small changes in the experimental conditions, such as the water depth and the wave generation method, result in significant impact pressure variability. The impact pressure variability is even observed in carefully repeated wave impact experiments with minimal variability of the input parameters. For these measurements, the source of the impact pressure variability is thought to be the instability development on the wave crest. However, the mechanism that is responsible for the formation of these instabilities is still largely unknown.   The aim of this work is to gain insight in the sources of wave impact pressure variability. This is accomplished using direct measurements of the liquid free surface and particle image velocimetry of the surrounding air. The measurements are limited to a single wave (i.e., with a fixed steering signal and water depth) at atmospheric conditions, because of the complexity of the experimental measurements. A plunging breaking wave with a large gas pocket is generated that impacts on a vertical wall. The compression of the large gas pocket induces a significant gas flow between the wave crest and the vertical impact wall, which results in the formation of instabilities on the wave crest.   Quantitative measurements of the liquid free surface are obtained with an extension of the planar laser induced fluorescence (PLIF) method. The newly developed scanning stereo-PLIF measurement technique uses a stereo-camera set-up with a self-calibration procedure adapted for free surface flows. Thereby, the stereo-PLIF technique enables measurements of a free surface over a two-dimensional domain (e.g., y=f(x,z,t)). The system is versatile with a minimal influence on the fluid properties and the measurement domain can be scaled as needed.  A repeatable plunging breaking wave is created in the wave flume of the Hydraulic Engineering Laboratory at the Delft University of Technology. The wave encloses a gas pocket as it approaches the vertical impact wall. Initially, the plunging breaking wave is globally comparable to waves that do not impact on a vertical wall. The aspect ratio of the cross-sectional area of the gas pocket remains relatively constant at Rx/Ry = 1.6 ( ∼√3). Furthermore, the wave velocity (√gh0) and wave tip velocity (1.2√gh0) are initially similar to that of a plunging breaking wave. On the other hand, the trajectory of the wave tip is altered compared to that of a typical plunging breaking wave.   The trajectory of the wave tip is globally similar over repeated wave impact measurements. However, moments before impact the wave tip is deflected by the gas expelled from the gas pocket. The deflection of the wave tip introduces significant variation between the repeated measurements. On close inspection, the wave tip resembles a liquid sheet, that is destabilized by an initial Kelvin-Helmholtz instability (Villermaux et al., 2002). The flapping liquid sheet accelerates the wave tip, which triggers the development of a Rayleigh-Taylor instability. This results in approximately equally spaced liquid filaments (i.e., liquid fingers) over the spanwise direction of the wave. The spanwise wavelength depends on the density ratio (ρa/ρl) and surface tension, which was previously shown to be a source of wave impact pressure variability.  Additionally, particle image velocimetry measurements are performed to determine the interaction between the liquid and gas during a wave impact event. The global gas flow is similar to that of a plunging breaking wave, where a vortex develops on the leeward side of the wave. The vortex consistently separates from the breaking wave and lingers at the back of the breaking wave in the stagnant air. The development of circulation is typical for a vortex that eventually separates at a universal time scale denoted by the formation number (Gharib et al., 1998). However, a typical formation number can not be defined in this particular case, due to the simultaneous change of both the length and velocity scales.  The velocity profile between the wave tip and the vertical impact wall resembles that of a flow past a bluff body. A fit of the measured velocity profile agrees well with the velocity derived from mass conservation. Interestingly, the velocity close to the wave tip is approximately 2 times higher than the bulk velocity estimate. The high velocity close to the wave tip can thus result in an earlier onset of instability development compared to estimates based on the bulk velocity. Furthermore, the flow tends to separate close to the tip just before impact on the vertical wall. The effect of this flow separation on the impact pressure variability depends on the global wave shape prior to impact. For the case with a disturbance on the wave crest, the secondary vortex that forms close to the wave tip tends to break up. On the other hand, if the wave crest is smooth the secondary vortex remains attached. The attached secondary vortex increases the lift on the wave tip, which results in a significant deflection of the wave tip. Consequently, the development of secondary vortices close to the wave tip results in wave impact pressure variability, as the typical deflection is larger than the membrane diameter of a contemporary pressure transducer.   Local phenomena such as flow separation and the development of instabilities define the variability of the peak pressure during wave impacts. On the other hand, the global characteristics of an air-water wave impact on a vertical wall can be retrieved with pressure impulse models (Cooker et al., 1995). The maximum wave impact pressure is relevant for LNG containments systems and wave energy converters. Consequently, numerical models that aim to quantify wave impact pressure variability require accurate models of both the gas phase and the development of free surface instabilities.