– Structural vibrations of the rig, since the pressure transducers
are mounted in the aluminium base (lower cap or transducer
holder).
– Presence of unconfined waves. At the instant of impact, water
away from the wall does not have any information about the
wall deformation and waves travel at the unconfined speed of
1500 m/s, producing high-frequency radial and axial
reflections.
A clearer picture can be obtained if the trace is smoothed. The
red line in Fig. 5-right represents the history smoothed (by averaging
over 100 points), thus cancelling out all signals with a period
smaller than 0.1 ms. According to this smoothed trace, immediately
after impact pressure rises to approximately 5 bar and then
suddenly drops to 2.5 bar. This is due to natural oscillations of the
bottlewall, which expands radially due to the internal pressure that
starts to build up at the base. This increase in diameter then causes
a pressure drop next to the bottle wall. Consequently, information
about wall movement travels from the bottle wall towards the
central axis in a form of pressure drop. The bottle wall continues to
oscillate (‘breathe’) and causes a disturbance of the fluid pressure to
travel in the radial direction.
The radial ‘breathing’ due to natural oscillation is relatively
quickly damped. Pressure continues to drop until the vapour
pressure is reached (w0.1 bar absolute pressure). At this stage, even
a very small amount of gas (air) present in the water causes the
pressure wave to travel at a speed lower than the one expected in
a flexible system. This can be easily observed as a longer period of
the low pressure part of the trace (from 2 to 5.5 ms). After this
event, a new period starts, the pressure rises again, but this time
the magnitude of the high-frequency oscillations is significantly
reduced. The whole event dies out after 15 ms.
Fig. 6 presents the pressure histories from two strain gauges:
SG1 positioned at 80 mmfrom the base and SG2 at 25 mmfrom the
base. The SG2 history shows that the impact is followed by a sudden
pressure (strain) rise, reaching its maximum of 4.8 bar. The slope of
the trace represents the pressure rise rate. The strain rate can be
obtained using thin-wall assumption (derivative of Eq. (10)). Here,
the value of 12,500 bar/s is obtained, which corresponds to strain
rate of 14 s1. The positive pressure part of the trace (first 1.65 ms),
which corresponds to a half of the waterhammer period, is superimposed
with small higher frequency oscillations with a period
approximately equal to 0.9 ms. Similarly to PT history, these oscillations
are attributed to natural oscillations (see Table 1, TNO, Eq.
(7)). The duration of this part corresponds to the time in which the
pressure wave travels two water levels. According to values
measured, the wave speed in the system is 155 m/s, and corresponds
well to the theoretical value given in Table 1 (Eq. (2)). Fig. 6
also indicates that there is a time delay between the signals
recorded by the two strain gauges, thus proving the existence of
awave travelling through the bottle. The time delay at a pressure of
2 bar is around 0.35 ms, which corresponds well to a wave speed of
155 m/s predicted by waterhammer theory.
Fig. 7-left presents the pressure histories from the strain gauge
SG2 for four different drop heights. All traces follow the same
pattern, having almost the same period. This is expected according
to both waterhammer and mass-spring model theories, since in
both cases the period of the main oscillation does not depend on
the drop height. On the other hand, the maximum pressure
magnitude increases with drop height, and it agrees well with
waterhammer predictions as shown in Fig. 7-right.
4.1.2. Results for bottles with an originally manufactured base
Fig. 8-left shows pressure histories from all sensors when the
bottle with an originally manufactured base is tested. Again, the
pattern of all traces is very similar to each other, but noticeably
different than that observed in the tests on bottles with a flat base.
The pressure rise after the impact is not as fast as in the previous
tests, and a long low pressure part of the trace (pressure magnitude
around minus 1 bar of relative pressure) has practically disappeared.
In addition, many oscillations with significantly reduced