Variability in wave impacts

Abstract

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.