ArticlePDF Available

Challenges on the numerical prediction of slamming loads on LNG tank insulation panels

Authors:

Abstract and Figures

The load assessment in water impacts problems involving complex geometries is generally a quite challenging task for numerical solvers. Indeed, the occurrence of large free-surface deformation, air cushioning and possible compressibility effects strain the standard Computational Fluid Dynamics (CFD) codes to their limits. In the present work, an enhanced Smoothed Particle Hydrodynamics (SPH) model is adopted to evaluate the pressures acting on the surface of smooth and corrugated panels impacting water and the numerical outcomes are compared to experimental data and analytical solutions. Specifically, the water entry of a flat panel at is firstly studied in order to highlight the main critical aspects underlying the numerical solution of water impacts with small deadrise angles. Then, the water impact of a Mark III type panel (a corrugated insulation panel) adopted in LNG tanks is considered. Experimental data involving wet drop tests of both flat and corrugated panels have been performed and the pressures during the impact have been measured at several points along the panel surface. Complex features of the flow, such as 3D effects and air-cushioning, have been addressed by a developing the numerical study in steps of increasing complexity.
Content may be subject to copyright.
Challenges on the numerical prediction of
slamming loads on LNG tank insulation
panels
S. Marrone a, A. Colagrossi a,, J.S. Park b, E.F. Campana a
aCNR-INSEAN, Natl. Research Council - Marine Tech. Research Inst., Rome,
Italy
bHyundai Heavy Industries Co. Ltd., South Korea
Abstract
The load assessment in water impacts problems involving complex geometries is
generally a quite challenging task for numerical solvers. Indeed, the occurrence of
large free-surface deformation, air cushioning and possible compressibility effects
strain the standard Computational Fluid Dynamics (CFD) codes to their limits. In
the present work, an enhanced Smoothed Particle Hydrodynamics (SPH) model is
adopted to evaluate the pressures acting on the surface of smooth and corrugated
panels impacting water and the numerical outcomes are compared to experimental
data and analytical solutions. Specifically, the water entry of a flat panel at 4
is firstly studied in order to highlight the main critical aspects underlying the
numerical solution of water impacts with small deadrise angles. Then, the water
impact of a Mark III type panel (a corrugated insulation panel) adopted in LNG
tanks is considered. Experimental data involving wet drop tests of both flat and
corrugated panels have been performed and the pressures during the impact have
been measured at several points along the panel surface. Complex features of the
flow, such as 3D effects and air-cushioning, have been addressed by a developing
the numerical study in steps of increasing complexity.
Key words: Smoothed Particle Hydrodynamics; Water impact; Slamming;
air-cushion effects; Trapped gas cavity; LNG tank;
Corresponding author: Tel.: +39 06 50 299 343; Fax: +39 06 50 70 619.
Email address: andrea.colagrossi@cnr.it (A. Colagrossi ).
https://doi.org/10.1016/j.oceaneng.2017.06.041
Fig. 1. Left: A membrane type LNG carrier. Right: Inside view of the Cargo
Containment System (CCS) of a LNG carrier, the surface of the tank is covered
by Mark III corrugation panels.
1 Introduction
In recent years the consumption of the Liquefied Natural Gas (LNG) fuel
has largely increased due to the commitment of nations to reduce noxious
emissions of standard fuels, notably NOx and SOx oxide. In order to reduce
the transportation cost as well as to meet the increased demand of LNG,
designers have considered larger LNG carriers. These vessels are designed and
constructed for safe transportation of natural gas at cryogenic temperatures.
Storage and transportation of LNG are critical issues in the design and safety
aspects of LNG carrier. In particular, the Cargo Containment System (CCS),
which is responsible for keeping the liquid at low temperature (-165C), is
a key component. The CCS is a composite structure of metal membrane,
polyurethane foam and plywood laminated insulator and its strength can be
characterized as the maximum load that the system can sustain before it fails.
The loads acting on the insulation system are due to the sloshing motion of
the liquid in the LNG tank and are typically the result of an impact flow
dynamics, which is generally characterized by an impulsive loading processes.
The design of CCS should adequately take into account such load features to
evaluate the strength and failure mode of the insulation system. This applies
a fortiori in the contemporary shipping context, in which the LNG tank is not
barely filled or empty (as it was the case in the past). Indeed, as remarked in
[19], due to the changed market demand, nowadays any filling level is allowed,
which introduces higher risks related to sloshing fluid motions.
Recently, deformations of primary corrugation membrane (Mark III type,
see right plot of figure 1) adopted in LNG tanks have been reported
(see, e.g.,[4]). As a consequence, the importance of the load assessment
on corrugated insulation panels has become increasingly relevant (see, e.g.,
[6, 5]). The present investigation is dedicated to the numerical simulation of
wet drop tests of a Mark-III insulation panel using the Smoothed Particle
Hydrodynamics (SPH) method and to the validation of the numerical results
against experimental data. The wet drop test consists in the water entry of the
2
panel with a specific configuration and at a fixed velocity. This kind of test
case can be seen as analogous to the problem of a fluid wedge impacting
a vertical wall (see, e.g., [32]) and can give useful insights for the more
complex problem of a wave impacting a wall composed by Mark III panels.
With respect to the latter, in the wet drop test it is simpler to control and
reproduce (also numerically) the impact conditions, allowing for a detailed
comparison between physical model and numerical output. Because of the
small deadrise angle, the numerical simulation of such an impact is quite
demanding and requires suitable models. Among the available solvers, the SPH
method has been selected, being accurate and robust in treating violent free-
surface flows. A brief description of the method is given in section 3. In order
to address the capability of such a solver, a test using a flat plate is used in a
preliminary test. Indeed, for such a simple geometry solutions using potential
theory are available (being aware of the fact that these solutions are referred
to a symmetrical flow, see e.g. [33, 28, 8]) and, furthermore, experimental
data are also available. For the chosen impact angle the air phase can be
neglected, therefore allowing for a simple comparison between experimental
and numerical outcomes. The analytical references and the experimental data
allows the proper establishment of the time-space discretization for the other
test-cases investigated (see section 4). A critical discussion on the comparison
between analytical solution, numerical results and experiments will be given
by focusing the most relevant challenges of the numerical simulation of water
impact.
Regarding the actual focus of the present work, for the Mark-III insulation
panel the entrapping of the gaseous phase by the liquid one can play a
significant role on the time-space distributions of the local loads. Because
of the square geometry, formed by the corrugation stencil, 3D effects can
also be relevant, indeed the water impact jets can be deflected and focused
on specific zones of the panel. The effect of the surface tension can be also
important in the bubble-flow formation as a result of the gas trapped during
the impact stages. Because of the above considerations, numerical simulation
of the water impact against Mark-III insulation panel requires two-phase 3D
simulations with an accurate surface-tension model. To our knowledge this
kind of numerical investigation is not yet available in the literature, even in
the most recent works, mainly because of the high computation costs involved.
In a recent paper by [19] the initial stage of the impact of the Mark-III panel
is studied in 2D with null deadrise angle by means of a Wagner approach. In
that study also the air compressibility and the structure elasticity are taken
into account. Conversely, in the present work a dead-rise angle equal to 4
is considered and, hence, the role of the air can not be a priori assessed.
Therefore, in order to tackle the problem in steps with increasing complexity,
the analysis has been subdivided in three sets of simulations:
3
i) 2D single-phase simulations
ii) 3D single-phase simulations
iii) 2D two-phase simulations
Due to these three steps, it is possible separate the role of 3D effects and the
air cushion phenomena. Future perspectives and conclusions will wrap-up the
paper.
2 Experimental Set-up
Wet drop tests of the Mark-III insulation panel were performed in the
Slamming Research Lab. at Pusan National University. The maximum drop
height tested was 3.8 m. The incident angles were 4, and 6 degrees. In the
present work only the first condition has been considered, it being the most
critical.
The dimensions of the test specimens were 640x520 mm (LxB). The specimens
used in the drop test were: a real Mark III corrugation membrane (steel
SUS304L, of thickness 1.2 mm), a rigid flat plate (steel thickness 20 mm,
hereinafter referred as the flat panel) and a rigid Mark III corrugated panel
(steel, thickness 20 mm).
Fig. 2. Test specimen and setup for the drop test experiment.
4
Fig. 3. Flat (left) and corrugated (right) panels used in the drop tests.The holes
visible in both the pictures indicates the location of the pressure sensors.
The flat plate was tested in order to compare the pressure distribution
measurements with reference data available in the literature. The real
corrugated membrane was tested to find the relation between the drop height
and the deformation of the corrugation, facilitating the analysis of the buckling
strength of the membrane. However, in the present work the hydroelastic
problem is not considered and we focus our investigation only on the rigid
panels in order to study the pressure distributions developed during the water
entry.
The pressure sensors used were ICP type sensors whose maximum capacity is
70 bar. The size of the pressure gauge is 6.3 mm. The sampling rate of the
data acquisition was up to 100 kHz which is expected to be high enough to
capture the time histories of the pressure impacts, even for the small dead-rise
angles considered here (see e.g., [29, 18]).
Figure 2 shows a picture of the drop test facility used in the Slamming
Research Lab of Pusan National University; in figure 3 pictures of the rigid
panels are shown. The total weight of the support, the wedge and the
panels is about 1500 kg, which guarantees that during the impact stages the
deceleration of the wedge is negligible (as confirmed by the time history of the
wedge displacement, which was measured using accelerometers). This allowed
numerical simulations imposing a constant water entry velocity, thus avoiding
the possibility of errors due to changing body velocity during the drop test.
As noted in [33], the effects of changes in velocity are not always considered in
many of the works presented in the literature. In [33], the authors also remark
on the importance of the size of the pressure gauges; indeed as discussed in
the following section, this needs to be taken in to account when small deadrise
angles are considered.
5
3 The Riemann-ALE Smoothed Particle Hydrodynamics model
In the present work the Riemann-based solver described in [26] is adopted.
In that work Arbitrary Lagrangian-Eulerian formalism is used allowing for
maintaining a regular particle spatial distribution and smooth pressure fields
while preserving the whole scheme conservation and consistency of the classical
SPH scheme.
Both compressible and incompressible formulations of SPH can be found in
the literature. We focus here in its compressible form, addressing weakly-
compressible fluids. Therefore, the continuity equation is used together with
the Euler equation:
Dt =ρ∇ · u
Du
Dt =p
ρ+g
Dr
Dt =u
(1)
where D/Dt represents the Lagrangian derivative, while r,u,pand ρare,
respectively, the position of a generic material point, its velocity, pressure and
density; and grepresents gravitational acceleration. The system (1) is written
in a Lagrangian form, which represents one of the main attractions of the
SPH method. Since the Reynolds number of the flow is quite high and only
the impact stage is simulated (short time-range regime) viscous effects can
be considered negligible. Moreover, the fluid is assumed to be barotropic and,
therefore, the following functional dependence between ρand pis adopted:
p(ρ) = c2
0ρ0
γ" ρ
ρ0!γ
1#+p0,(2)
where ρ0and p0are constant, c0is the speed of sound, and γis a dimensionless
parameter greater than 1 (in all of the following examples γ= 7 is used).
In the SPH method, the speed of sound c0is chosen much lower than the
real one, but much higher than the reference velocity, Uref , to satisfy the
weakly-compressible assumption. When considering violent free-surface flows,
the proper identification of the reference velocity Uref is crucial, as is discussed
in the following sections. Considering the Mach number Ma = Uref /c0, the
constraint Ma <0.1 is taken into account to make compressibility effects
negligible. Additionally, during violent impact events (i.e., flat impacts) the
acoustic pressure p=ρ u c0can be reached, and in this case the pressure
6
peak intensity becomes proportional to 1/Ma. On the other hand, in such a
condition an incompressible constraint can induce singularities on the pressure
field (see [22] for a discussion on the difference between these two models in
impact situations). This is linked to the fact that for this kind of impacts the
presence of the air phase is generally crucial and the single-phase approach
can lead to incorrect pressure evaluations under the incompressible/weakly-
compressible hypothesis (for a deeper discussion see also [24]). Being aware of
these limits for a single-phase model, the results obtained in this paper have
been produced considering a possible Mach dependency.
The SPH model is based on the interpolation of a generic flow field fthrough
a convolution integral with a kernel function Wover its compact support Ω:
hfi(r) = Zf(r0)W(r0r;h)dV 0(3)
The fluid domain is discretized into a finite number of particles representing
elementary fluid volumes, each with its own local mass miand other physical
properties. At the discrete level a generic field fevaluated at the position ri
of the i-th particle is approximated through a convolution sum. Equation (3)
thus becomes:
hfi(ri) = X
j
f(rj)W(rirj;h)Vj(4)
where Vjis the volume of the j-th particle. Hence any function or its gradient
can be interpolated in total absence of connectivity.
The use of the Riemann-based solver leads to an increased stability and
robustness of the scheme with respect to standard SPH schemes. The
formalism proposed by [30], which is inspired by compressible Finite Volume
techniques, is adopted. For each pair of particle-to-particle interactions (i, j),
a Riemann problem is solved in the direction (i, j) for Tait’s equation of
state, providing a solution for the flux that is then convolved using the
kernel gradient in order to solve for the expected flux divergence. Thanks to
the introduction of Riemann-solvers the fluxes between particles are upwind
oriented and the resulting scheme is characterized by good stability properties.
7
The discrete Euler equations are written as follows:
Dri
Dt =v0i,
D Vi
Dt =ViX
j
(v0jv0i)Wij Vj
D(Viρi)
Dt =ViX
j
2ρE(vEv0(rij ))Wij Vj
D(Viρivi)
Dt =ViX
j
2 [ρEvE(vEv0(rij )] Wij Vj
ViX
j
2PEIWij Vj+ωiρig
(5)
where ρE,PEand vEare the solutions of the Riemann problem at the
interface rij = (ri+rj)/2, between particles iand j. The particle transport
velocity v0is obtained as the summation of the particle velocity plus a small
perturbation which helps preserving a regular particle distribution (details
about the adopted model can be found in [26]).
The two-phase model is based on the work by Leduc et al. [21] where
an approximate Riemann solver without mass fluxes is introduced at the
interface between particles belonging to different phases. Specifically, the
scheme adopted in the present work is an extension of the one described in [16]
where the ALE formulation presented in [26] has been added. In particular,
at the fluid interface the purely Lagrangian form of the ALE equations 5 is
adopted for a strip of particles spanning a kernel radius. Readers can find also
more information on general weakly-compressible SPH multiphase models in
e.g. [15, 14, 12].
4 Preliminary test on a flat panel
In this section the results of the 2D single-phase simulations are described and
compared to the experimental data from a wet drop test performed with a flat
panel (panel length Lequal to 64 cm, see Section 2) impacting with an angle
of 4and a vertical impact velocity Uof 6.0 m/s.
As described in the theoretical work by [33], for this small angle a very thin,
high-speed jet of water is formed, and the time-spatial gradients of the pressure
field are extremely high. This makes the test conditions very demanding for
numerical solvers. From the potential flow theory by [33], the jet thickness
at model scale is about 0.1 mm. It is worth noting that the theory in [33]
is formulated for symmetric wedge impacts whereas in the present case the
8
impact of a inclined single plate is considered. More details about the reference
solution to be adopted are given in section 4.2.
On the base of this theoretical data, the 2D simulation has been conducted
using a very high spatial resolution, corresponding to a particle size ∆x=
15.6µm; by referring the latter to the panel length L, the ratio L/xis equal
to 41,000. The whole tank depth and width are, respectively, 3 m and 6 m.
In order to manage such a small particle size a multi-resolution technique has
been used. Specifically, the particle size gradually changes with a maximum
magnification factor of 3,200 between the most refined region and the lowest
resolution one (see figure 4). The total number of particles is about 3 million.
For small dead-rise angles water compressibility cannot be neglected when
calculating the speed of the water jet Ujet (see e.g. [20, 7, 9]). In the
experimental conditions the speed of sound in water is c?
0= 1481 m/s '247 U,
therefore the Mach number Ma = U/c?
0is about 4 ×103. Under such a
condition an estimate of the jet speed is Ujet 42U250m/s. As noted in
[20], this very thin, high-speed jet disintegrates at some distance from the root
due to interaction with both the surrounding air and the surface of the body.
Note that in such kind of instability surface tension plays an important role
on the jet evolution. This local and complex physics is not taken into account
in the present numerical method but it is not supposed to play a relevant role
on the pressure distribution.
Fig. 4. Flat panel impacting water. Colors are representative of the SPH velocity
intensity. Pressure probe number 12, which is the gauge used for the comparison
with the experimental data, is also depicted.
9
4.1 Selection of the speed of sound for the SPH model
Before starting the SPH simulations the speed of sound needs to be specified.
As mentioned in section 3, the numerical Mach number usually adopted within
the SPH simulations is Ma = U/c0= 0.1, which guarantees the weakly-
compressible regime (i.e., compressibility plays a negligible role). Nonetheless,
for this kind of impact the reference speed for the Mach number can not be the
impact velocity U. Indeed, considering that the intersection point between the
horizontal undisturbed free-surface and the wedge surface has a speed equal
to Uinters =U/sin(α)'14 U. The water jet formed during the impact has a
speed higher than Uinters . Therefore, if one chooses the speed of sound using
the wedge speed U, i.e., c0= 10 U, the jet would not form at all, its speed
being in the supersonic regime. This is a clear example where the weakly-
compressible rule Ma 0.1 needs to be enforced in a proper way, considering
the specific problem at hand.
In the present case the reference speed should be the water jet speed Ujet
which, however, is an unknown of the problem. Using the theory in [20], the
estimate Ujet = 40Ucan be used. Note that, using the latter constraint,
the speed of sound in water would result even higher than the real one,
c0= 400Uversus c?
0= 247U. This means that for the adopted model scale
water compressibility effects are not negligible, at least inside the jet region.
However, considering that in the jet zone the pressure is close to the ambient
pressure, water compressibility effects should not play a relevant role on the
local impact loads.
In order to satisfy the weakly-compressible assumption, at least in the impact
region, the reference velocity used is Uref =qPmax, where Pmax is an
unknown of the problem and needs to be estimated. Then, an ex-post facto
verification of the SPH simulations is required. Using the Wagner theory
(which is valid for small deadrise angles as far as the air presence is negligible)
the maximum pressure predicted is:
Pmax =1
2ρ U2π2/4
[tan(α)]2
α=4
'252 ρ U2(6)
corresponding to about 91 bar in our experiment.
The water-hammer pressure for this impact is ρ c?
0U= 88 bar which is the
maximum pressure level that can be physically reached in the experiments.
The Pmax predicted by potential flow theory is higher than the acoustic
pressure, and this is a further indication that water compressibility cannot
be neglected for this problem. Thus, considering Pmax 80 bar, the reference
velocity is Uref =qPmax15 Uwhich is smaller than Ujet = 40U.
10
Fig. 5. Flat panel impacting water: colors are representative of the SPH pressure
field. Red solid line is the free surface extracted from [33].
Taking this into account, a good compromise for the SPH speed of sound
can be obtained by adopting a reference velocity Uref = 10Uwhich implies
a speed of sound c0= 100 U(i.e., Mach number Ma = U/c0= 0.01). The
resulting time step is equal to ∆t= 1.5 ∆x/c0'0.04 µs which is 250
times smaller than the sampling rate of the pressure probes used in the
experiments (i.e., the SPH sample frequency is 25 MHz versus the 100 kHz
of the experimental pressure probes). This aspect is expected to influence
the observed pressure peak which, for the considered configuration, needs a
high time/space resolution to be captured. Further, in order to verify the
appropriateness of such a choice, also a simulation using c?
0= 247Uhas been
run, the results will be shown at the end of section 4.2.
4.2 Comparison between SPH results, analytical solution and experimental
data
Figure 5 shows the pressure field predicted by the SPH for the flat panel
impact. In the same plot the free surface deformation evaluated by the
potential flow theory by [33] is reported. Left plot of figure 6 shows an enlarged
view of the flow velocity predicted by the SPH in the area of the highest
pressure levels. A thin water jet is formed with a thickness of about 0.1 mm
corresponding to about ten particles, thus justifying the high L/xratio
needed to properly solve such a flow.
In the right plot of the same figure an enlarged view of the pressure field is
shown (in this case the displayed pressure range is enlarged too). From this
plot it is seen that the high-pressure region is limited to an area of 1 mm2with
a pressure peak of about 60 bar. In the same figure the size of the probe used
in the experiments is depicted. Clearly, the pressure sensor has a size much
larger than the pressure bulb formed below the water-jet root. This aspect
will be discussed in the following section.
11
Fig. 6. Flat panel impacting water: enlarged view of the impact zone. Left: contours
of the velocity module. Right: contours of the SPH pressure field. The size of the
pressure gauges used in the experiments is also depicted.
In figure 7 the time histories of the pressure measured at probe P12 are shown.
This probe is positioned 23.6 cm from the left-hand edge of the panel (see
figure 4). The SPH solution is compared with the experiments and with the
pressure peak predicted by Wagner theory. The SPH prediction is between the
two reference data sets, and is characterized by high-frequency components
due to the fragmented jet of water that pass over the numerical pressure
probe. The latter has a dimension of 0.125 mm (which is the size of the SPH
kernel support) and the SPH sampling rate is 25 MHz. Both the SPH and
the analytical predictions overestimate the experimental data for which the
maximum pressure recorded is 34 bar (in the SPH solution the pressure peak
reaches 70 bar whereas the analytical prediction is 91 bar). It has to be noted
that, even though the Wagner theory is referred to the case of a symmetric
wedge entry, the value of the pressure peak should substantially the same of
the case of an oblique flat panel impact (see e.g. [13, 27]). Conversely, regarding
the entire pressure signal, it is not possible to compare to classical analytical
solutions, such as in [33], since they are all formulated for the symmetric wedge
entry case.
As mentioned above, air entrainment is expected to play a minor role for
deadrise angles greater than 3[33, 27]. Notwithstanding that, most of the
experimental measurements available in the literature for angles close to 4
exhibit pressure peaks much smaller than the one predicted by potential theory
(cf., [11, 25, 27, 29]) and the values measured in the present study are in fair
agreement with previous experiments by [27, 11]. As for possible 3D effects,
these have been checked by comparing the pressure values on gauges aligned
at the same distance from the piercing edge. For the probes positioned in
the most central region no relevant differences have been observed. However,
the maximum pressure impact measured in the experiment for small dead-rise
angles can be also affected by:
(1) Changes of the body velocity during the impact stage
(2) Rotations of the body during the impact stage
12
Fig. 7. Flat panel impacting water: SPH pressure time histories at probe P12
compared with experimental data and with analytical solution Wagner theory.
Fig. 8. Flat panel impacting water: SPH pressure time histories versus experimental
data. The SPH signal is filtered with a running average filters (MAF) at 100 kHz
(dashed-dotted line).
(3) Deformations of the wedge surface
(4) Sampling rate of the pressure signals
(5) Size of the pressure gauge
Thanks to the experimental setup adopted (see Section 2) the first three points
can be neglected, while the last two can play an important role. In order to
take into account the experimental sampling rate, the SPH signal has first
been filtered using a moving average filter (MAF) reducing the numerical
sampling rate from 25 MHz to 100 kHz. The result is illustrated in figure 8.
The reduction of the SPH peak due to this filtering procedure is not enough
to get a good agreement with the experimental data.
As a further step the SPH pressure has been measured integrating on a circular
13
Fig. 9. Flat panel impacting water: SPH pressure time histories versus experimental
data . The SPH signal recorded using the size of the experimental pressure gauges
and filtered at 100 kHz is also shown.
Fig. 10. Flat panel impacting water: experimental data for the pressure time histories
on a row of probes (not equispaced). The time history from the first and last probes
on the panel impacting the water are colored in red. The time history in blue is
from probe P12 , used in the previous figures for comparison with the SPH solution.
area equal to the size of the experimental pressure probes and then filtered at
100 kHz. This result is shown in figure 9. In this case the SPH output is much
closer to the pressure recorded in the experiment.
Summarizing, according to the analytical solution very narrow pressure peaks
are expected for this kind of impact. Using pressure gauges with a size of few
millimeters and a sampling rate of 100 kHz it is not possible to record such
a localized event. Having in mind such limits, through SPH it is possible to
get predictions close to the experimental data if the pressures are integrated
over the experimental gauge area, even when using a speed of sound c0smaller
than the real one c?
0.
14
Fig. 11. Flat panel impacting water: SPH pressure time histories on a row of probes.
The original SPH signals have been filtered with a MAF at 100 kHz as in the
experimental signals. The time history from the first probe on the panel impacting
the water is colored in red.
In figure 10 the experimental pressure time histories recorded on a sequence of
pressure probes is reported. Even if the experimental pressure peaks present
some fluctuations, very similar pressure evolutions are recorded with an
almost constant time shift at each probe. The SPH results show quite good
repeatability of the pressure peaks along the wedge surface as well (see figure
11). In this regard, it is worth comparing the propagation velocity of the
pressure peak along the plate, UP. Indeed, in water entry flows the value of
the pressure peak should correlate to U2
P(see e.g. [17, 3]) as:
CP=Pmax
1
/2ρ U2
P
= 1.(7)
In figure 12 the calculated values of UPfor both SPH and experimental results
are reported for several probes. Only the probes far from the panel edges have
been considered to avoid influences of either the initial impact stage or the
final stage, for which the flow self-similarity is not applicable. In the same
figure the values of UPobtained from a simulation adopting the real speed
of sound c?
0= 247U(Ma=0.004) are also reported. The difference between
the simulation with Ma=0.01 and Ma=0.004 is very small (about 2% of the
average value), confirming that within the weakly-compressible regime the
Mach number effect is limited. For the sake of completeness in the same plot
also the analytical value of UP(valid for a wedge entry problem) is reported,
i.e.:
UP=π
2Ucot(α).(8)
In Table 1 The average values of UPare reported. For the simulation at
Ma=0.01 the average value of UPis about 117 m/s corresponding to a pressure
coefficient CP= 1.03 which is close to the expected value (7). On the other
15
Fig. 12. Flat panel impacting water: Peak propagation velocity UPcalculated on
several positions along the panel for the experiment (triangles), SPH simulation
at Ma=0.01 (circles) and Ma=0.004 (squares), and analytical value from potential
flow theory (dashed line). The origin of the x-axis is set at the left-hand edge of the
panel.
UP(m/s) 1/2ρ U 2
P(bar) Pmax (bar) CP
Exp. 104 54 30 0.56
SPH Ma=0.01 117 68 70 1.03
SPH Ma=0.004 119 71 75 1.06
Table 1
Average of the peak propagation velocity UPplotted in fig. 12. The corresponding
pressure peak 1/2ρ U 2
P, the actual average pressure peak measured at the probes
Pmax and the related pressure coefficient CP(7) are also reported.
hand since the value of UPpredicted by the SPH is smaller than the analytical
one this implies that the maximum pressure of the SPH cannot be equal to
the one predicted by the Wagner theory as shown above. This difference is
essentially due to the fact that Wagner theory is referred to a symmetric
wedge entry, while the present case is asymmetric (see section 4.3).
When considering the experimental pressure probes an average value of UP
equal to 104 m/s is obtained (with a standard deviation σ= 3.1). This
propagation velocity of the pressure peak corresponds to a pressure coefficient
CPequal to 0.56. This confirms that the measurement system adopted is not
able to record the real pressure peaks which are therefore underestimated as
shown in this section.
16
4.3 Comparison between symmetric and asymmetric water entry
In the last subsection it has been shown that the pressure peak predicted
by SPH is consistent with the water impact theory. Indeed, the calculated
peak propagation velocity UPand the pressure peak Pmax give a pressure
coefficient CPclose to unity (see eq. 7). Nonetheless, it still remains a
significant discrepancy between SPH results and the analytical solution for
this impact angle. In order to investigate the source of this incongruity a
further simulation has been performed. As already mentioned, most of the
analytical solutions available in the literature refer to a wedge entry problem.
Therefore, the comparison between asymmetric (i.e. single flat panel entry)
and symmetric (i.e. wedge entry) problem is useful to clarify the main cause
behind the difference between SPH and analytical solutions.
The symmetric problem has been set by retaining the initial particle
configuration of the asymmetric case and closing the fluid domain at the left
edge of the panel with a vertical wall (see figure 13). The simulation has been
run with Ma=0.01.
In figure 14 the peak propagation velocity for both symmetric and asymmetric
problems are shown. It is clear that in the symmetric configuration the SPH
solution is now much closer to the potential flow prediction, the computed
average value being about 131 m/s (the theoretical value is 135 m/s). Because
of this increase in the value of UP, a larger pressure peak is expected on the
panel surface. The recorded pressure at 0.16 m from the left-hand edge of the
panel is shown in figure 15 for both symmetric and asymmetric SPH solutions.
Consistently with the observed value of UP, the pressure peak of the symmetric
solution is about 88 bar. In the same figures the analytical solutions from [31]
and [33] are also reported. Evidently, the symmetric SPH solution is again
much closer to the analytical prediction and the remaining difference can be
Fig. 13. Flat panel impacting water: fluid domain adopted in the symmetric problem
configuration. Colors refer to the module of the velocity field.
17
mainly attributed to fluid compressibility. It is therefore clear that in the
asymmetric problems the differences are not only limited to the pressure at
stagnation (i.e. far from the pressure peak), which is expected to be lower
due to the uprising jet at the left edge, but also the pressure peak intensity is
affected (at least in the considered test conditions). This is in agreement with
the analytical work in [28]. In that work it is shown that, generally, asymmetric
impacts induce smaller pressure peaks with respect to the symmetric case. This
effect is emphasized when the deadrise angle is smaller (in [28] the smallest
angle considered is 10).
Fig. 14. Flat panel impacting water: Peak propagation velocity UPcalculated
on several positions along the panel for the asymmetric (circles) and symmetric
(triangles) SPH simulations, and analytical value from potential flow theory (dashed
line). The origin of the x-axis is set at the left-hand edge of the panel.
Fig. 15. Flat panel impacting water: pressure time histories of symmetric (solid line)
and asymmetric (dashed) solutions measured at 0.16 m from the left-hand edge of
the panel. Analytical solutions by [31] (dash-dot line) and by [33] (dash dot-dot
line) are also reported.
18
5 Wet drop test of Mark III type insulation panel
In the present section the results of the numerical simulations for the impact
of the Mark III type insulation panel are described. The impact velocity U
and the impact angle are again equal to 6.0 m/s and 4, as for the case studied
in the previous section. The geometry of the Mark-III insulation panel, used
for wet drop test, was initially described by an Initial Graphics Exchange
Specification (iges) file. The latter needed to be manipulated and transformed
into an unstructured surface mesh in order to be a suitable input for the SPH
code.
The geometrical impact configuration is given by the sketch in figure 16. The
angle αhas been set equal to 4, this condition resulting as a critical one in
the experiments. Some numerical pressure probes have been set in order to
record pressure time histories during the simulation. The probe labels adopted
for the experiments have been maintained in order to compare the numerical
data with the reference one without any ambiguity.
Figure 17 shows bottom and lateral views of the numerical reconstruction of
the Mark-III insulation panel along with the pressure probe positions. The
present section is subdivided into three subsections addressing, respectively:
i) 2D Simulation with a single-phase model
ii) 3D Simulations with a single-phase model
iii) 2D Simulation with a two-phase model.
5.1 2D Simulation with a single-phase model
The 2D profile of the corrugated panel has been extracted from central section
of the panel. For this simulation a multi-resolution technique has been used
in order to change the particle size with a magnification factor of 100 from
the most refined region up to the lowest resolution one; the particle size
Fig. 16. Sketch of the impact configuration for the Mark-III insulation panel.
19
Fig. 17. Bottom and lateral views of the Mark-III insulation panel obtained using an
unstructured mesh. On the left-hand plot labels for the pressure probes are shown.
Fig. 18. 2D single-phase model: particle-size distribution.
distribution is shown in figure 18. In the area involved in the impact, the
spatial resolution is ∆x= 0.25mm, the length Lof the panel being 64 cm
and the ratio L/xbeing equal to 2560. Three different simulations with
resolution ratios equal to L/x= 640,1280,2560 have been performed and
figure 19 shows the pressure time histories at probe P40 recorded with the
three different resolutions. The initial time t= 0 is set at the instant when
the left dent touches the free-surface. The same rule has also been adopted for
the following numerical test cases.
The plot depicted in figure 19 shows rather limited discrepancies for the
20
Fig. 19. 2D single-phase model: pressure-time evolution measured at probe P40 .
Fig. 20. 2D single-phase model: time evolution of the pressure field for six different
time instants.
21
Fig. 21. 2D single-phase model: pressure time histories for six different probes.
Comparison between experimental data and 2D single-phase SPH solution.
22
pressure peaks, hence for the present problem it is not necessary to reach
the L/x= 10,000 used with the flat panel (see section 4.2) Thanks to this
first analysis, we decided to use the ratio L/x= 640 for the 3D simulation
(see the next section), and for conformity the results presented in this section
will be compared with 3D ones using this spatial resolution.
Figure 20 depicts the pressure field during the impact stage. For this simulation
the Mach number Ma = U/c has been set equal to Ma = 0.1 since, as shown in
the following, the pressure peaks are less intense relative to the ones recorded
during the impact of the flat panel. At time t= 6.5ms (first plot of figure 20)
the left dent has completely entered in the fluid while the second one is only
partially immersed. At this stage no relevant pressure peaks are observed.
The corresponding recorded pressure time histories are shown in figure 21
where the 2D single-phase SPH solution is compared to the experimental data
for six different probes (the position of the probes is shown in the first plot
of figure 20). At time t= 9ms a pressure shock forms on the left part of the
panel. From these first two pictures it is clear that a cavity is formed between
the two dents and the free surface. Therefore, due to the absence of the air,
this cavity is going to collapse inducing high pressure shocks (see time instants
t= 9ms and t= 12ms). This explains also the two consecutive peaks shown
in figure 19: the first peak at t= 11.5ms is due to the passage of the left jet
propagating towards right; the second peak, at about t= 12.5ms, is due to
the complete collapse of the cavity resulting from the encounter between the
two jets.
As a consequence, in the time range t= 11 14ms the maximum of the
pressure is reached between probes P40 and P47 where peaks of 16 bar are
measured. This pressure is linked to the water-hammer pressure ρ c Ucavity
where Ucavity '27 m/s is the relative velocity of the water fronts during the
cavity collapse (an analogous impact has been described in [23] for the collapse
of a plunging jet). The pressure calculated by the SPH model depends therefore
by the specific speed of sound adopted (i.e. the specific Mach number used).
However even adopting a Mach number of 0.1 the SPH pressure is four times
higher than the pressure recorded in the experiments (4 bar versus 16 bar)
and the experimental time history is much smoother resembling a sinusoidal
function. This is a clear indication that air cushion effects cannot be neglected
in the present problem.
The agreement between the numerics and the experimental data is better for
probe P49 apart from for a slight delay of the SPH data. At time t= 15ms a
third pressure impact is recorded on the right-hand part of the panel reaching a
pressure level of 8.5 bar at probe P53 where the experiments recorded a peak of
10.5 bar. In principle, in this region of the flow field, we do not expect relevant
three-dimensional effects. Further, in this part of the panel air cushion effects
23
are not expected to be dominant and the flow resembles the one discussed for
the flat panel (see Section 4). From figure 21 it is possible to observe that the
duration of the peak registered at probe P53 is about 6 ms which is very close
to the experimental one.
5.2 3D simulation with a single-phase model
After the 2D single-phase simulations a 3D simulation has been performed.
Because of the large number of particles needed to accurately solve the water
impact, a computing cluster has been used.
The computational resources needed to carry out the final 3D simulation were
300 cores running for about 180 hours. A resolution of L/x= 640 is used,
as in the 2D simulations presented in the previous section, and also the Mach
number has been kept equal to Ma = 0.1.
Figure 22 shows the fluid domain used in the simulation. The size of the
domain has been chosen large enough to avoid any possible acoustic wave
reflection within the selected time interval. As in the 2D cases a multi-
resolution technique is used to get high spatial resolution only in the region
of the water impact.
The pressure fields for three instants of time t= 7.7,12.7 and 17.7ms during
the water impact are reported in figures 23 and 24. At time t= 12.7ms the
Fig. 22. 3D single-phase model, wet drop test of Mark III type insulation panel:
fluid domain used for the 3D simulation.
24
Fig. 23. 3D single-phase model, wet drop test of Mark III type insulation panel:
planar and 3D views for two different time instants: 7.7, 12.7. The color contours
are representative of the pressure fields. At time t = 12.7 ms a focusing effect is
quite visible due to the closure of the entrapped cavity which induces a sudden rise
of the pressure.
25
Fig. 24. 3D single-phase model, wet drop test of Mark III type insulation panel:
planar and 3D views at time instant 17.7 ms. The color contours are representative
of the pressure fields.
water jets entrapped in the cavity panel impact each other giving rise to a
focusing effect. At this time the pressures reach values close to those calculated
in the 2D simulations.
Figure 25 shows the time histories recorded by six different pressure probes:
SPH 3D results are compared with experimental data. Similar to the 2D single-
phase simulation (see previous section), the highest pressure levels are recorded
at probes P40 and P47 . With respect to the 2D cases the highest pressure region
has moved rightward from P40 toward probe P47 .
The impact pressure measured at probe P49 in the 3D simulation remains
similar to the 2D case in terms of intensity while it occurs earlier, producing
better agreement with the experiments.
As in the 2D case, large differences appear for probes P40 to P47 relative to
the experimental measurements, confirming that these discrepancies are more
likely related to air-cushion effects than to 3D effects.
26
Fig. 25. 3D single-phase model: pressure time histories for six different probes.
Comparison between experimental data and 3D single-phase SPH solution.
27
5.3 2D simulation with a two-phase model
The numerical investigation described in this work is concluded by performing
2D simulations with air and water. The air is treated as a compressible gas
using the classical polytropic state equation:
p=P0 ρ
ρ0air !γair
(9)
where ρ0air is the air density at rest, γair the air adiabatic index equal to 1.4,
and P0the ambient pressure.
As opposed to the single-phase model, the speed of sound c0air cannot be
adjusted for computational convenience as is for c0water, since the former is
directly linked with the Euler number used in the experiments (Eu'17):
Eu = P0
ρwater U2,
P0=c2
0air ρ0air
γair
,
w
w
c0air =Uv
u
u
u
tEu γair
ρ0water
ρ0air
(10)
Therefore, maintaining Eu number similitude and correctly simulating the air-
cushion effects can result in quite high CPU costs, even in a 2D framework.
We underline that with an Euler number of order 10 the air compressibility
cannot be neglected, because density variations on the order of 10% are
expected. This can represent a restriction for commercial software where air
is treated as an incompressible medium, like the liquid phase. Moreover, Eu
is of order 10 at model scale, while for full scale, it may reduce to order 1,
thus further increasing the role of air compressibility. This latter aspect can
be very important in the correct design of insulation panels.
The second point that makes the simulations with two phases more critical
and complex with respect to the single phase model concerns the treatment
of the fluid domain (reported in figure 26). The left-hand image shows the
domain at the beginning of the simulation, while the right-hand image shows
the configuration just before water impact. At this latter instant in time the
intensity of the air velocity field is shown. Because of the complexity of the
28
Fig. 26. 2D two-phase model, wet drop test of Mark III type insulation panel: fluid
domain used for the simulation.
air velocity field, we cannot start the simulation of the water impact ignoring
it. On the other hand the domain depicted in the left-hand image of figure 26
is too large and it will incur significant CPU costs even in a 2D framework.
To avoid such a complexity the following strategy has been adopted: a first
simulation from t= 0.0 to t= 1.02s is performed considering the air-water
interface as a solid boundary so only the air phase is simulated; at this stage
the air can be treated as incompressible or weakly-compressible and a fictitious
air speed of sound can be used in order to avoid too small time steps. Once
the time t= 1.02s is reached the air-water simulation is started using as input
the air field from the previous simulation. In this second simulation the real
air speed of sound is used and Eu number similitude is guaranteed. Figure 27
shows three time instants during the water impact stage.
In the left-hand column the air bubble entrapped by the panel is quite visible,
while in the right-hand column the pressure contour levels are depicted. As for
the previous simulations, the initial time for this case is set at the instant when
the left dent touches the free-surface, that occurs 1.07 ms after the beginning
of the air-water simulation. At t= 5.23ms air cushioning effects occur and
the air pressure starts rising. At t= 8.33ms the pressure in the cavity is quite
uniform with values of about 2 bar whereas a violent impact occurs at the
left-hand corner of the panel.
At time t= 11.03ms (see figure 28) an impact event is recorded close to
the right-hand corner of the panel in the region around probe P53, reaching
a pressure level of 8 bar. At the same time the pressure in the panel cavity
29
Fig. 27. Two-phase 2D model, wet drop test of Mark III type insulation panel:
views of liquid surface configuration (left) and pressure field (right) for time instants
t=1.07ms, t= 5.23ms and t= 8.33ms.
remains uniform with levels of about 2.5 bar. At t= 14.33ms the pressure field
starts to decrease consequently to the air escaping under the right dent. This
feature may also be responsible for the inhibition of the air pocket pressure
oscillations, in a manner analogous to the air leakage effect observed in [1].
At the final instant depicted in figure 28, an almost uniform pressure of 1 bar
acts on the panel surface.
In figure 29 the SPH pressure time histories for 6 different probes are compared
with the experimental data. From this figure three relevant observations can
be drawn:
The two-phase SPH pressures inside the cavity panel, probes P37 to P47,
show a similar time behavior of the experimental pressure, thanks to the
30
Fig. 28. Two-phase 2D model, wet drop test of Mark III type insulation panel:
views of liquid surface configuration (left) and pressure field (right) for time instants
t= 11.03ms, t= 14.33ms and t= 19.13ms.
correct simulation of the air-cushion phenomenon. However the two-phase
SPH produces an underestimation of the pressure value (2.5 bar against
4 bar). This is an indication that in the experiments the air bubble is
possibly smaller and more compressed.
The SPH prediction of the pressure at probe P53 (close to the right-hand
corner of the panel) is fair,
All the numerical pressure peaks over-predict the time duration of the
pressure impacts, which could be due to the 2D framework where the impact
energy is more confined relative to the 3D one.
31
Fig. 29. 2D two-phase model: pressure time histories for six different probes:
comparison between experimental data and 2D two-phase SPH solution.
32
Fig. 30. Wet drop test of Mark III type insulation panel: pressure time histories
for probes P40 and P53 . Comparison among the different SPH simulations and the
experimental data.
6 Perspective
From the analysis presented in this paper, the numerical simulations highlight
the relevance of air-cushion effects when considering water impact of the Mark
III type insulation panel with small impact angle. Thanks to the action of the
air phase the pressure loads are drastically reduced with respect to those
measured on a flat panel under the same impact conditions.
However, in our opinion, the present analysis needs to be extended to produce
a more complete panorama of the problem. For example, if different impact
angles are considered we expect that for larger angles air-cushion effects will
not occur and significant loads would be experienced near the corrugation
dents.
An analysis from a structural point of view could also be important. Indeed
in the the work by [6] it is shown that the corrugation dents can be deformed
during a violent wave impact event. Further, in this work we consider a simple
wet-drop test. However, the final application shall be a wave impact against
a wall covered with Mark III panels which represents a more interesting test
from an engineering point of view. In fact, there are already some articles
in the literature where preliminary investigations under these conditions are
presented [see e.g. 5, 4].
In the present paper we stress the relevance of 3D effects together with air-
cushioning. The main difficulties in tackling the problem including both of
these aspects is linked to the high computational costs of the SPH solver. A
further element to be considered in future is the influence of surface tension
on peak duration. Incidentally, considering the ambient conditions inside an
33
LNG tank, the natural gas is close to its boiling temperature (see e.g. [2])
which makes the extension from model to full scale more complex [see e.g. 10].
7 Conclusions
In this work a numerical investigation of wet drop tests of insulation panels
has been conducted. The numerical model adopted is the Riemann Smoothed
Particle Hydrodynamics model. Simulations have been conducted using 2D
and 3D single phase models, whereas the air-water model simulations were
only conducted in a 2D framework, because of the greater complexity and the
high CPU costs needed to take air compressibility phenomena into account.
The water impact case studied is a 4angle of impact, both flat and corrugated
(Mark III type) insulation panel are considered. Because of the small angle of
impact the selected test case is characterized by very high space-time gradients
making the numerical simulations quite challenging.
For the flat panel only a 2D single-phase model has been used, since in the
literature the air entrapment is said to play a minor role at this impact angle.
Comparisons with theoretical and experimental data have been provided.
The validation has regarded several parameters ranging from the free-surface
deformation up to the consistency of the peak propagation velocity. A critical
discussion addressing different key aspects of this simulation, such as the choice
of the speed of sound and influence of the pressure measurement system, has
been given.
For the Mark III type insulation panel, because of its geometrical form at 4
angle of impact both air cushioning and 3D effects can play relevant roles. To
better investigate such aspects different simulations have been conducted. The
comparisons reported in figure 30 summarize the results obtained at INSEAN;
the two most critical probes, P40 (between the two dents) and P53 (close to
the panel edge), are considered.
The most accurate comparisons have been obtained with the two-phase SPH
model for both the probes (even for P53 where the air cushioning is not
expected to be essential).
On the other hand all the 2D simulations present time scales too large with
respect to the experiments. The 3D simulations, even with single phase, show
the complexities of the impact for this geometry, different water jets are formed
by the interaction between the free surface and the four dents of the panel.
Summarizing, a further investigation with a 3D two-phase model would allow
34
further inspection of the phenomenon, providing more accurate results in time-
space pressure distribution. Further, a remarkable improvement of the solution
could be provided by the addition of a surface tension model in order to
simulate the multiple bubble break-up and, consequently, to achieve a more
realistic evolution of the air cushioning.
Acknowledgements
The research activity was supported by the project SinSEOn “Sloshing
SPH Environment for long-time Oscillation simulation, (CNR-INSEAN Prot.
N.17, 8 January 2016) within the Memorandum of Understanding (MOU)
2015-2018 between HTCI-HHI and CNR-INSEAN
The research leading to these results has partially received funding from the
European Union’s Horizon 2020 research and innovation programme under
grant agreement No 724139.
The SPH simulations performed under the present research have been
obtained using the SPH-Flow solver, software developed within a collaborative
consortium composed of Ecole Centrale de Nantes, NextFlow Software
company and CNR-INSEAN.
The research activity has been developed within the Project Area “Applied
Mathematics” of the Department of Engineering, ICT and Technology for
Energy and Transport (DIITET) of the Italian National Research Council
(CNR).
References
[1] Bjørn C Abrahamsen and Odd M Faltinsen. The effect of air leakage and
heat exchange on the decay of entrapped air pocket slamming oscillations.
Physics of fluids, 23(10):102107, 2011.
[2] Matthieu Ancellin, Jean-Michel Ghidaglia, Laurent Brosset, et al.
Influence of Phase Transition On Sloshing Impact Pressures Described
By a Generalized Bagnold’s Model. In The Twenty-second International
Offshore and Polar Engineering Conference. International Society of
Offshore and Polar Engineers, 17-23 June 2012.
[3] JL Armand and R Cointe. Hydrodynamic impact analysis of a cylinder.
Journal of offshore mechanics and Arctic engineering, 109(3):237–243,
1987.
[4] H. Bogaert, L. Brosset, and L.M. Kaminski. Interaction Between Wave
Impacts And Corrugations of MarkIII Containment System For LNG
35
Carriers: Findings From the Sloshel Project. In International Offshore
and Polar Engineering Conference (ISOPE). The International Society
of Offshore and Polar Engineers (ISOPE), 20-25 June 2010.
[5] H. Bogaert, S. Lacuteeonard, L. Brosset, and M. L. Kaminksi. Sloshing
and Scaling: Results from the Sloshel Project. In International Offshore
and Polar Engineering Conference (ISOPE), 495 North Whisman Road,
Suite 300 Mountain View, CA 94043-5711, USA, June 2010. The
International Society of Offshore and Polar Engineers (ISOPE), ISOPE.
[6] L Brosset, M Marhem, W Lafeber, H Bogaert, P Carden, J Maguire,
et al. A Mark III panel subjected to a flip-through wave impact: results
from the Sloshel project. In The Twenty-first International Offshore
and Polar Engineering Conference. International Society of Offshore and
Polar Engineers, June 19-24 2011.
[7] EF Campana, Antonio Carcaterra, E Ciappi, and A Iafrati. Some
insights into slamming forces: compressible and incompressible phases.
Proceedings of the Institution of Mechanical Engineers, Part C: Journal
of Mechanical Engineering Science, 214(6):881–888, 2000.
[8] Antonio Carcaterra, E Ciappi, A Iafrati, and EF Campana. Shock
spectral analysis of elastic systems impacting on the water surface.
Journal of Sound and Vibration, 229(3):579–605, 2000.
[9] Antonio Carcaterra and Elena Ciappi. Prediction of the compressible
stage slamming force on rigid and elastic systems impacting on the water
surface. Nonlinear Dynamics, 21(2):193–220, 2000.
[10] EP Carden, C Zegos, NJ Durley-Boot, JR Maguire, D Radosavljevic,
S Whitworth, et al. Modelling of full scale wave impacts on the Sloshel
Mk III test panel. In The Twenty-first International Offshore and Polar
Engineering Conference. International Society of Offshore and Polar
Engineers, 2011.
[11] Sheung-Lun Chuang. Experiments on slamming of wedge-shaped bodies.
Journal of Ship Research, 11(3):190–198, 1967.
[12] A. Colagrossi and M. Landrini. Numerical Simulation of Interfacial Flows
by Smoothed Particle Hydrodynamics. J. Comp. Phys., 191:448–475,
2003.
[13] Odd M Faltinsen and Yuriy A Semenov. Nonlinear problem of flat-plate
entry into an incompressible liquid. Journal of fluid mechanics, 611:151,
2008.
[14] N. Grenier, M. Antuono, A. Colagrossi, D. Le Touz´e, and B. Alessandrini.
An Hamiltonian interface SPH formulation for multi-fluid and free surface
flows. Journal of Computational Physics, 228(22):8380–8393, 2009.
[15] N. Grenier, D. Le Touz´e, A. Colagrossi, M. Antuono, and G. Colicchio.
Viscous bubbly flows simulation with an interface SPH model. Ocean
Engineering, 69(0):88–102, 2013.
[16] Pierre-Michel Guilcher, Nicolas Couty, Laurent Brosset, and David Le
Touz´e. Simulations of breaking wave impacts on a rigid wall at
two different scales with a two-phase fluid compressible SPH model.
36
International Journal of Offshore and Polar Engineering, 23(04):241–253,
2013.
[17] A Iafrati. Experimental investigation of the water entry of a rectangular
plate at high horizontal velocity. Journal of Fluid Mechanics, 799:637–
672, 2016.
[18] A Iafrati, S Grizzi, MH Siemann, and L Ben´ıtez Monta˜es. High-speed
ditching of a flat plate: Experimental data and uncertainty assessment.
Journal of Fluids and Structures, 55:501–525, 2015.
[19] TI Khabakhpasheva, AA Korobkin, and S Malenica. Fluid impact onto
a corrugated panel with trapped gas cavity. Applied Ocean Research,
39:97–112, 2013.
[20] Alexander A Korobkin and Alessandro Iafrati. Numerical study of jet flow
generated by impact on weakly compressible liquid. Physics of Fluids,
18(3):032108, 2006.
[21] J Leduc, JC Marongiu, F Leboeuf, M Lance, and E Parkinson. Multiphase
SPH: a new model based on acoustic Riemann solver. In Proc of 4th Int
SPHERIC Workshop, pages 8–13, May 2009.
[22] S. Marrone, A. Colagrossi, A. Di Mascio, and D. Le Touz´e. Prediction
of energy losses in water impacts using incompressible and weakly
compressible models. Journal of Fluids and Structures, 54:802–822, 2015.
[23] Salvatore Marrone, Andrea Colagrossi, Andrea Di Mascio, and
David Le Touz´e. Analysis of free-surface flows through energy
considerations: Single-phase versus two-phase modeling. Physical Review
E, 93(5):053113, 2016.
[24] D. Meringolo, A. Colagrossi, S. Marrone, and F. Aristodem. On the
filtering of acoustic components in weakly-compressible SPH simulations.
Journal of Fluids and Structures, to appear, 2017.
[25] Sumitoshi Mizoguchi and Katsuji Tanizawa. Impact wave loads due to
slamming–a review. Ship Technology Research, 43(4):139–154, 1996.
[26] G. Oger, S. Marrone, D. Le Touz´e, and M. De Leffe. SPH
accuracy improvement through the combination of a quasi-Lagrangian
shifting transport velocity and consistent ALE formalisms. Journal of
Computational Physics, 313:76–98, 2016.
[27] Shinzo Okada and Yoichi Sumi. On the water impact and elastic response
of a flat plate at small impact angles. Journal of marine science and
technology, 5(1):31–39, 2000.
[28] Yu A Semenov and A Iafrati. On the nonlinear water entry problem of
asymmetric wedges. Journal of Fluid Mechanics, 547:231–256, 2006.
[29] Matthias Tenzer, Ould el Moctar, and Thomas E Schellin. Experimental
investigation of impact loads during water entry. Ship Technology
Research, 62(1):47–59, 2015.
[30] J.P. Vila. On particle weighted methods and Smooth Particle
Hydrodynamics. Mathematical Models & Methods in Applied Sciences,
9(2):161–209, 1999.
[31] T. Watanabe. Analytical expression of hydrodynamic impact pressure by
37
matched asymptotic expansion technique. Trans. West-Japan Soc. Naval
Arch., (71):77–85, 1986.
[32] GX Wu. Fluid impact on a solid boundary. Journal of fluids and
structures, 23(5):755–765, 2007.
[33] R. Zhao and O. M. Faltinsen. Water entry of two-dimensional bodies.
Journal of Fluid Mechanics, 246:593–612, 1993.
38
... in which for this problem of water entry, instead of the impact velocity, the estimated maximum velocity in the flow field |u max | is used in the calculation of the sound speed for liquid phase . Thanks for the discussion in Marrone et al. (2017), for such impact problems with small dead-rise angles, the velocity of the water jet formed by the impact cannot be neglected and can be viewed as the estimated maximum velocity to determine the sound speed. Considering a reasonable proposal for the estimated jet velocity mentioned in Marrone et al. (2017), the velocity of water jet is taken as 10 times of the impact velocity, that is, c water = 100U impact (Ma = U impact /c water = 0.01), which is considered as a good compromise for the WCSPH. ...
... In this subsection, focusing on the air-cushion effect in the water entry, a complex practical problem studied in Marrone et al. (2017), i.e., the slamming of the LNG tank insulation panel, is simulated, and the related accuracy test is provided in Appendix A. For the simulation of the slamming of LNG tank insulation panel in the present work, the computational model including the water region and the insulation panel is sketched in Fig. 10, which is similar to that in Marrone et al. (2017). In the present simulation, the mass of the insulation panel is 69.7 kg, and the insulation panel impacts on the water with a vertical velocity of 5.5 m/s. ...
... In this subsection, focusing on the air-cushion effect in the water entry, a complex practical problem studied in Marrone et al. (2017), i.e., the slamming of the LNG tank insulation panel, is simulated, and the related accuracy test is provided in Appendix A. For the simulation of the slamming of LNG tank insulation panel in the present work, the computational model including the water region and the insulation panel is sketched in Fig. 10, which is similar to that in Marrone et al. (2017). In the present simulation, the mass of the insulation panel is 69.7 kg, and the insulation panel impacts on the water with a vertical velocity of 5.5 m/s. ...
Article
The impact of structure on water is an important and practical issue in ocean engineering. For some cases, the influence of air on the impact characteristics is non-negligible. In particular, when the flat-bottomed structure impacts on water such as the emergency landing on the water of an aircraft and helicopter, the air cushion will be formed which buffers the impact of the structure, thereby reducing its slamming load. In this paper, considering the advantages of the Riemann solver in dealing with discontinuities, a multiphase Riemann-SPH method using the PVRS Riemann solver is applied to analyze the air-cushion effect and slamming load in water entry problems. To reduce the numerical dissipation led by the Riemann solver, a dissipation limiter for the PVRS Riemann solver is given. Through the test of the water slamming of the plate, the accuracy and convergence of the adopted method are firstly validated. Then, the influences of the air cushion and the plate length on the slamming load are discussed. Finally, a complex engineering problem, i.e., the slamming of the LNG tank insulation panel is simulated, and the influences of the impact velocity and deadrise angle on slamming load characteristics are analyzed.
... The adopted SPH method relies on a weakly-compressible approach and a Riemann Solver for the calculation of the particle interactions. The latter increases the stability of the scheme and allows for accurate predictions of the pressure during water impact stages (see also [26]). The intrinsic properties of mass and momenta conservation makes it well adapted for the simulation of such kind of violent freesurface flows for long-time evolution. ...
... • the high accuracy in the prediction of pressure liquid impacts (see e.g. [25], [26] ); • the high robustness of the scheme which helps handling long-time simulations; • the good volume conservation properties when simulating long-time violent free-surface flows, while for other SPH schemes, like the popular δ + -SPH schemes, special treatments are needed as discussed recently in [21]; ...
Conference Paper
Full-text available
The present work is dedicated to the numerical investigation of three-dimensional sloshing flows inside a ship LNG fuel tank. Long time simulations, involving 3-hours real-time duration with realistic severe sea-state forcing, have been performed using a parallel SPH solver running for several weeks on a dedicated cluster. The adopted SPH method relies on a weakly-compressible approach and a Riemann Solver for the calculation of the particle interactions. The latter increases the stability of the scheme and allows for accurate predictions of the pressure during water impact stages (see also [26]). The intrinsic properties of mass and momenta conservation makes it well adapted for the simulation of such kind of violent free-surface flows for long-time evolution. Single phase model has been adopted with a considerable reduction of the CPU costs (for an in-depth discussion see also [27]). The high values of Reynolds numbers involved requires the implementation of a sub-scale model which was embedded in the SPH scheme following the recent literature (see e.g. [9]). Three different filling height conditions are considered. For all of them energetic sloshing flows are induced with the occurrence of several water impact events. The latter are focused on specific zones of the tank depending on the considered filling height (see also [15]). For some conditions the SPH pressure predictions are compared with the experimental ones provided by Hyundai Heavy Industries (HHI). A critical discussion of these predictions is performed in order to highlight in which cases the numerical solver is able to provide good local loads estimations. Conversely, when the SPH results appear to be not realistic, comments on the causes linked to the disagreements with experiments are given.
... • the high accuracy in the prediction of pressure liquid impacts (see e.g. Marrone et al. (2015Marrone et al. ( , 2017 ); ...
... The latter, benefiting from the air cushioning effect, is expected to be much less intense (see e.g. Marrone et al. (2017)). Figure 24 shows for the four considered probes the plots of the pressure peaks versus their rise time at model scale. ...
Article
Full-text available
The present work is dedicated to the numerical investigation of sloshing flows inside a ship LNG fuel tank. Long time simulations, involving 3-hours real-time duration with realistic severe sea-state forcing, have been performed using a parallel CFD solver running for several weeks on a dedicated cluster. The numerical model adopted is the Smoothed Particle Hydrodynamics model (SPH). This model has been chosen for its Lagrangian approach and for the intrinsic properties of mass and momenta conservation which makes it well adapted for the simulation of violent free-surface flows. The adopted SPH method relies on a Riemann Solver for the calculation of the particle interactions which increases the stability of the scheme and allows for accurate predictions of the pressure during water impact stages. Three different filling height conditions are considered. For all of them energetic sloshing flows are induced with the occurrence of several water impact events. The latter are focused on specific zones of the tank depending on the considered filling height. For some conditions the SPH pressure predictions are compared with experimental ones. A critical discussion of these predictions is performed, highlighting the cases in which the numerical solver is able to provide good local pressure estimations.
... The applications include marine hydrodynamics (see e.g. Marrone et al., 2017;Verbrugghe et al., 2018;Domínguez et al., 2019;Cao et al., 2019;He et al., 2020), hydroelastic Fluid-Structure Interaction (FSI) problems (see e.g. Khayyer et al., 2018aKhayyer et al., , 2021aO'Connor and Rogers, 2021;Zhang et al., 2021b), multi-phase flows (see e.g. ...
Article
This paper is dedicated to (1) emphasizing the importance of removing the Tensile Instability (TI) induced by negative pressures in Smoothed Particle Hydrodynamics (SPH) simulations, and (2) proposing new modifications for the Tensile Instability Control (TIC) and Particle Shifting Technique (PST) to simulate Fluid-Structure Interaction (FSI) phenomena with violent free-surface evolutions. Four numerical benchmarks associated with classical FSI problems characterized by negative pressures are simulated to show how the tensile instability destroys an SPH simulation without any TI prevention strategies. Therefore, PST and TIC are adopted into the SPH simulations for the sake of suppressing the tensile instability. However, different combinations of TI prevention strategies, i.e. different combinations of PST and TIC, lead to different results, and hence detailed investigations and discussions are provided. It is demonstrated that when negative pressures are moderate, solely using either PST or TIC works well. Nonetheless, it is in favor of using both PST and TIC if an SPH simulation is characterized by extremely strong negative pressures. Furthermore, for the problems with a convex-shaped structure penetrating a free-surface, special modifications are necessary for both PST and TIC in order to obtain accurate SPH results.
... The wedge cavity and the air flow inside obtained by the SPH method show good agreements with the experimental results. Marrone et al. [18] conducted a comprehensive numerical study on predicting slamming loads of a LNG tank insulation panel with a deadrise angle of 4 • using the Riemann-ALE-SPH method. For this case, 3D effects and air-cushioning play relevant roles because of its small deadrise angle. ...
Article
Full-text available
The water entry is a classic fluid-structure interaction problem in ocean engineering. The prediction of impact loads on structure during the water entry is critical to some engineering applications. In this paper, a multiphase Riemann-SPH model is developed to investigate water entry problems. In this model, a special treatment, a cut-off value for the particle density, is arranged to avoid the occurrence of negative pressure. A remarkable advantage of the present multiphase SPH model is that the real speed of sound in air can be allowed when simulating water-air flows. In the present work, considering the air effect, several typical water entry problems are studied, and the evolution of multiphase interface, the motion characteristic of structure and complex fluid-structure interactions during the water entry are analyzed. Compared with the experimental data, the present multiphase SPH model can obtain satisfactory results, and it can be considered as a reliable tool in reproducing some fluid-structure interaction problems.
Article
The cross-sectional shape of a trimaran is more complex than that of a monohull and consists of a main hull, side hull, and cross deck. When a trimaran moves downward in a severe sea state, air trapped between the main and side hulls forms a cushion under the cross deck, and this has a significant effect on the slamming pressure on the structure. In this work, laboratory experiments are performed on a scale-model trimaran section to gain deeper insight into the dynamic interactions between hull structure, water, and air and to investigate the effects of the air cushion on slamming loads. The air–water–structure interactions are investigated through particle image velocimetry, the accelerations of the ship section are measured by inertial motion units, and the slamming loads are obtained from pressure sensors. To enhance the influence of the air cushion, two plates are installed, one on each side of the ship section, to restrain the escape of air during the experiments. In addition, to eliminate the influence of the air cushion, numerical simulations of water entry are conducted with air replaced by hydrogen, whose density is much lower. The experimental and numerical results confirm that the air cushion under the cross deck can significantly reduce the slamming pressure.
Article
In this paper, we propose a targeted essentially non-oscillatory (TENO) SPH scheme. In this scheme, a 5-point stencil consisting of 3 candidate sub-stencils is adopted to implement the TENO reconstruction as originally proposed in the mesh-based methods. In the original TENO reconstruction, these five points are fixed and equidistant. However, it is difficult for SPH to determine these five points due to the random particle distribution. To remedy this issue, for two interacting particles, we first consider them as two existing stencil points. Then, for the other three points, we search for the closest particles to their exact positions. Subsequently, considering the gradient of these particles, we can finally obtain the values of these target points. Afterwards, the primitive values of points are reconstructed by TENO reconstruction where the polynomial interpolations are modified. Numerical results show that the proposed TENO-SPH scheme can be applied to reproduce some compressible flows involving shocks and small-scale structures, some incompressible vortex flows and free surface flows with superior accuracy.
Article
Full-text available
This paper aims at providing a state-of-the-art review on the applications of particle methods in hydrodynamics-related problems in ocean and coastal engineering. The problems are placed into three categories according to their physical characteristics, namely, wave hydrodynamics and corresponding mass (air, oil, etc.) transport, wave-structure interaction, and wave-current-sediment interaction. For the first category, particle-based simulations of wave generation, propagation, breaking, as well as the associated turbulence production and dissipation, air entrainment, and mass transport, are reviewed. For wave-structure interaction, extensive structural types are considered that include fixed and moving (floating) structures, rigid and deformable structures, impermeable and porous structures, etc. For the third category, the latest advances of particle methods in wave/current interaction with sediments, i.e., sediment transport and coastal morphological changes, are outlined. This article also reviews the latest developments of particle methods with respect to enhancement of numerical stability, accuracy, efficiency and consistency in order to handle the multi-physics and multi-scale problems emerging from coastal and ocean engineering practices. Finally, the future perspectives of extending particle methods to a wider range of ocean and coastal engineering applications are highlighted.
Article
The air usually has a major influence on the water entry of a typical cavity body (cavity body is a hollow, cylindrical, semi-closed structure), which not only lowers the slamming load but also affects the dynamic characteristics of water entry. In this paper, a two-phase smoothed particle hydrodynamics (SPH) model for simulating the water entry of cavity body is presented. The SPH model combined with Riemann solver is improved to deal with the two-phase flows with the discontinuous quantities across the interface. One-sided Riemann problem is used to impose the fluid–structure interaction and a switch-function-based Riemann solver dissipation is formulated to improve the interfacial instability owing to the strong impact. The motion equations of rigid body are incorporated into two-phase SPH model to describe the motion of cavity body. The proposed model is validated by research on the test cases in the published literature. Finally, this work presents a study of water entry of cavity body by experiment and this two-phase SPH method. The dynamics phenomena in the coupling process between cavity body and two-phase flow are investigated. And the effects of air, mass, the sizes and incline angles of cavity body on the dynamic characteristics of cavity body and two-phase flows are shown.Graphic abstract An improved two-phase SPH model was used to simulate the water entry of cavity body. The cavity body impacts the water surface and the cavity body is closed by the flooding water. It comes into being open air cavity and water jets. The jet walls protrude and the air cavity is closed. With the increase of the water entry depth, the complex hydrodynamic phenomena can be seen again. The sinking depth shows the law of fluctuation up and down with time.
Article
At present, the dynamic stress of a cylinder during water entry is generally investigated by the explicit dynamics method involving multiphases, which has a long calculation period. In this paper, a fast forecast method for dynamic stress of cylinders entering water is proposed. The water impact is replaced by an equivalent classical impact load, and the explicit dynamic analysis of multiphases is transformed into the implicit dynamic analysis of a single phase. Therefore, the dynamic stresses of cylinders can be solved rapidly and the relative errors with the results in existing literature are less than 10%. This study can be used to evaluate the dynamic stress and strength of cylindrical structures in a relatively short time.
Article
Full-text available
The present paper is dedicated to the post-processing analysis of the time pressure signals when a weakly-compressible Smoothed Particle Hydrodynamics (SPH) model is used to simulate free-surface flows. Indeed, it is well known in literature that this particle model is characterized by the occurrence of high-frequency acoustic noise making the pressure signals unusable for engineering applications. This non-physical pressure noise is both linked to the weakly-compressible approach and to numerical inaccuracies. To reduce the latter, different enhanced SPH models have been developed in recent years. Nonetheless, even using accurate and stable SPH schemes when simulating water impacts, acoustic signals can be generated and, since the speed of sound used in the model is not the real one, these acoustic components need to be filtered in a suitable way. Indeed, for low Mach number regime the solution of the compressible Navier-Stokes equation can be decomposed in an incompressible solution plus an acoustic perturbation. In this work, a filtering technique based on Wavelet Transform is presented. In the proposed procedure the acoustic frequencies are individuated through a preliminary analysis which takes into account: the adopted speed of sound, the spatial resolutions and the fluid domain configuration. The filtering technique to remove the acoustic components is finally applied to several test-cases ranging from prototype problems to more practical applications such as a violent sloshing flow.
Article
Full-text available
The study of energetic free-surface flows is challenging because of the large range of interface scales involved due to multiple fragmentations and reconnections of the air-water interface with the formation of drops and bubbles. Because of their complexity the investigation of such phenomena through numerical simulation largely increased during recent years. Actually, in the last decades different numerical models have been developed to study these flows, especially in the context of particle methods. In the latter a single-phase approximation is usually adopted to reduce the computational costs and the model complexity. While it is well known that the role of air largely affects the local flow evolution, it is still not clear whether this single-phase approximation is able to predict global flow features like the evolution of the global mechanical energy dissipation. The present work is dedicated to this topic through the study of a selected problem simulated with both single-phase and two-phase models. It is shown that, interestingly, even though flow evolutions are different, energy evolutions can be similar when including or not the presence of air. This is remarkable since, in the problem considered, with the two-phase model about half of the energy is lost in the air phase while in the one-phase model the energy is mainly dissipated by cavity collapses.
Article
Full-text available
The multi-fluid SPH formulation by Grenier et al. (2009) is extended to study practical problems where bubbly flows play an important role for production processes of the offshore industry. Since these flows are dominated by viscous and surface tension effects, the proposed formulation includes specific models of these physical effects and validations on specific benchmark test cases are carefully performed. The numerical outputs are validated against analytical and numerical reference solutions, and accuracy and convergence of the proposed numerical model are assessed. This model is then used to simulate viscous incompressible bubbly flows of increasing complexity. These flows include the evolution of isolated bubbles, the merging of two bubbles, and the separation process in a bubbly flow. In each case, results are compared to reference solutions and the influence of the Bond number on these interfacial flow evolutions is investigated in detail.
Article
Full-text available
The objective of the present investigation was to provide reliable experimental data suitable to validate numerical tools aimed at predicting impact loads on and elastic deformations of wedge-shaped structures. To investigate impact-induced hydroelastic effects on slamming pressure peaks, four test bodies were examined. Two bodies were fitted with stiffened, rigid bottom plating and two bodies with thin elastic bottom plating, each case with 5° and 10° deadrise angles. Results comprised impact-induced pressures, accelerations, forces, and structural strains. Measurement repeatability, sampling rate effects, and hydroelastic effects were emphasised. Measured pressures and forces were compared with published experimental data. Additionally, this paper documents body geometries, test rig set-ups including instrumentation, and experimental procedures.
Article
The water entry of a rectangular plate with a high horizontal velocity component is investigated experimentally. The test conditions are representative of those encountered by aircraft during emergency landing on water and are given in terms of three main parameters: horizontal velocity, approach angle, i.e. vertical to horizontal velocity ratio, and pitch angle. Experimental data are presented in terms of pressure, spray root shape, pressure peak propagation velocity and total loads acting on the plate. A theoretical solution of the plate entry problem based on two-dimensional and potential flow assumptions is derived and is used to support the interpretation of the experimental measurements. The results indicate that, as the plate penetrates and the ratio between the plate breadth and the wetted length measured on the longitudinal plane diminishes, the role of the third dimension becomes dominant. The increased possibility for the liquid to escape from the lateral sides yields a reduction of the pressure peak propagation velocity and, consequently, of the corresponding pressure peak intensity. In particular, it is shown that, at the beginning of the entry process, the pressure peak moves much faster than the geometric intersection between the body and the free surface, but at a later stage the two points move along the body at the same speed. Furthermore, it is shown that the spray root develops a curved shape which is almost independent of the specific test conditions, even though the initial growth rate of the curvature is higher for larger pitch angles. The loads follow a linear increase versus time, as predicted by the theoretical model, only in a short initial stage. Next, for all test conditions examined here, they approach a square-root dependence on time. It is seen that, if the loads are scaled by the square of the velocity component normal to the plate, the data are almost independent of the test conditions.
Article
This paper addresses the accuracy of the weakly-compressible SPH method. Interpolation defects due to the presence of anisotropic particle structures inherent to the Lagrangian character of the SPH method are highlighted. To avoid the appearance of these structures which are detrimental to the quality of the simulations, a specific transport velocity is introduced and its inclusion within an Arbitrary Lagrangian Eulerian (ALE) formalism is described. Unlike most of existing particle disordering/shifting methods, this formalism avoids the formation of these anisotropic structures while a full consistency with the original Euler or Navier-Stokes equations is maintained. The gain in accuracy, convergence and numerical diffusion of this formalism is shown and discussed through its application to various challenging test cases.
Article
A series of experimental investigations of rigid-body slamming was performed at the Naval Ship Research and Development Center by dropping one flat-bottom steel model and five wedge-shaped steel models with small deadrise angles (up to 15 deg) from various elevated positions above a calm water surface. The test results were used to provide a set of charts for estimating the maximum impact pressure due to rigid-body slamming of wedges.
Article
The water entry of a flat plate with a high horizontal velocity component is investigated experimentally. The objective is to achieve a better understanding of the physical phenomena occurring during aircraft ditching. The study is a part of the SMAES-FP7 project, which was aimed at developing simulation tools for aircraft design and certification. The experimental data are used to support their validation. In order to perform the tests, which are done at realistic ditching speeds, a new facility has been designed and built at CNR-INSEAN. The use of quasi-full scale velocity allows to overcome the troubles of scaling the structural behavior in such a complicated fluid–structure interaction problem. In this paper two test conditions are considered for which several repeats were performed allowing to assess the uncertainty of the data. Results are presented in terms of pressures, strains and loads and an interpretation of the measured data on the basis of theoretical solutions of the problem is provided.