The Incat1 section tested by Whelan [12, 33] is an extrusion of a true bow section of an INCAT wave- piercing catamaran. The geometry can be seen in Figure 6.7 where the demihulls, centrebow and archways are shown. As this section enters the water, there are three important stages that occur as shown in Figure 6.55 with mass number=0.29 and NDH=0.86.
Figure 6.55: Drop accelerations of Incat1 section with normalised drop height (NDH)=0.86 and mass number=0.29 by Whelan [33]
The first stage is the demihull bottom entry slamming; it is relatively small and can be seen as small fluctuations in the acceleration plot in the first 10 milliseconds of the water entry. The second impact belongs to the centrebow keel water entry and shows itself as a mild deflection in the acceleration graph increasing the section deceleration (see Figure 6.56). The upwash water from the centrebow and demihulls moves upward, deflects around the archway curvature, entraps and forces the air out and creates a severe wetdeck slamming. This is seen as the large sharp acceleration peak (around 150 m/s2). This is a very high acceleration, higher than values seen in any full-scale vessel measurements. The entrapped air finally escapes out and the upwash water of the centrebow and the demihulls meet
-20 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 Dr o p a cc eler a tio n (m /s^ 2 ) time (ms)
Normalised drop height=0.86, mass number=0.29
centrebow keel water entry demihull bottom
slamming
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each other further outboard of the arch top; the high pressures are then alleviated by some water escaping as a planar jet flow from the clearance between the drop geometry and tank walls.
Figure 6.56 shows the pressure contour plot of the Incat1 geometry simulation results for mass number=0.29 and NDH=0.86 compared to the experimental results. At 40ms, the bottoms of the demihull are submerged and the centrebow keel enters the water after 60 ms. The enclosed water surface elevates between the demihulls and the centrebow in the simulations. As seen, at 80 and 90ms, the surface elevation is higher in the simulations compared to the experiments. The reason for this is the slight rise in air pressure underneath the section in the experiments before the water reaches the arch top (similar to the pressure profiles for the 25° wedge with side plates). The consequence of this fast immersion is the early wetdeck slamming at 100 ms in the simulation, 11ms earlier than in the experiments. The large high pressure region underneath the section causes a very high acceleration peak (see Figure 6.57). The enclosed section fills up outboard shortly after this wetdeck slam and creates another peak around 105 ms in the simulations, whereas the first wetdeck slam peak has not occurred yet in the experiments. Again this is predominantly due to the 2-D nature of the simulations thus giving no opportunity for the enclosed water to escape, causing severe containment and high pressures for a large fluid region propagating downward.
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Figure 6.56: Comparison of 2–D SPH simulations of the Incat1 drop section in various time steps (40,60 80, 90,100 and 110 ms) with experiments of Whelan [12, 33] (mass number=0.29 and normalised drop height
(NDH)=0.86)
Figure 6.57 and Figure 6.58 show the comparison of the drop acceleration and velocity of the dropped section for both the SPH and experimental results with mass number=0.29 and NDH=0.86. The results show that prior to wetdeck slamming the section gains a higher velocity, so water reaches the arch top sooner. The magnitude of the slam acceleration is also significantly larger in the simulations; this is due to the increased momentum (higher maximum drop velocity) in the simulations and also
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the creation of air pockets in the experiments working as a cushion alleviating the severity of the slam event.
Figure 6.59 and Figure 6.60 show the drop acceleration and velocity results respectively for mass number=0.29 and NDH=0.77. Similarly the slams occur earlier in the simulations and include two slam acceleration peaks. Comparing this case with NDH=0.86 with a higher initial entry velocity, the first slam peak is lower due to lower momentum available in the drop section prior to the wetdeck slamming.
Figure 6.57: Drop acceleration with SPH of Incat1 section for NDH=0.86 and mass number=0.29
Figure 6.58: Drop velocity with SPH of Incat1 section for NDH=0.86 and mass number=0.29
Figure 6.59: Drop acceleration with SPH of Incat1 section for NDH=0.77 and mass number=0.29
Figure 6.60: Drop velocity with SPH of Incat1 section for NDH=0.77 and mass number=0.29
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Figure 6.61 shows the location of pressure transducers on the Incat1 geometry. P1 and P2 are on the centrebow, P3 is on top of the arch and P4 is located slightly outboard of the top of the archway. Figure 6.62 and Figure 6.63 show the SPH pressure results for P1 and P2 respectively compared to the experimental results. As seen in P1, before the wetdeck slamming, there is a 5 kPa pressure peak that has been captured by SPH but as it gets closer to archway slamming, the discrepancies emerge. In the experiments, the wetdeck slamming peak pressures at P1 and P2 are around 20 kPa whereas in the simulations, they are more than double this amount. In P3 and P4, which are on archtop and closely outboard of the archtop, the pressures are more than 68 kPa and 10 kPa respectively. For both these points, the SPH pressures are more than 100 kPa. The SPH peaks were also occurred earlier in time, for previously mentioned reasons.
Figure 6.61: Incat1 drop section with pressure transducers location
Figure 6.62: Pressure results at location P1 of the 25° wedge with side plates for NDH=0.86 and mass
number=0.29
Figure 6.63: Pressure results at location P2 of the 25° wedge with side plates for NDH=0.86 and mass
number=0.29 -0.3 -0.2 -0.1 0 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 [m] [m] P1 [0.02 -0.151] P3 P4 P2 [0.0536 -0.1116] [0.149 -0.0687] P3 P4 [0.198 -0.0809]
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Figure 6.64: Pressure results at location P3 of the 25° wedge with side plates for NDH=0.86 and mass
number=0.29
Figure 6.65: Pressure results at location P4 of the 25° wedge with side plates for NDH=0.86 and mass
number=0.29
At this stage, from the 2-D SPH slamming simulation of 25° wedge with side plates and Incat1, it can be concluded that it is necessary to model air for the enclosed section drop simulation both for controlling the drop immersion velocity and also creating an air pocket under the archways at the point of wetdeck slamming. Including the effect of the air cushioning at the top of the archway would need a multi-phase solution to be developed. This is a non-trivial task, which would include significant development time since currently this SPH code is only single-phase fluid modelling. Such modelling has been done previously by Oger et. al. [157] for modelling free falling of a wedge to water surface. Modelling the 3-D effects are also important, as these effects were allowed in the experiments as the constrained water could escape from the wall clearance.