Full-scale Fluid-structure Interaction Simulation and ...

31st Symposium on Naval Hydrodynamics Monterey, California, 11-16 September 2016

Full-scale Fluid-structure Interaction Simulation and Experimental Validation of High-speed Planing-hull Slamming with Composite Panels S. Volpi1, M. Diez1,2, H. Sadat-Hosseini1, D.-H. Kim1, F. Stern1, R.S. Thodal3, and J.L. Grenestedt3 (1IIHR-Hydroscience & Engineering, The University of Iowa, USA, 2 CNR-INSEAN, Natl. Research Council-Marine Tech. Research Inst., Italy, 3 Dept. of Mechanical Engrg. and Mechanics, Lehigh University, USA) ABSTRACT

INTRODUCTION

The current work presents a partitioned tightly coupled fluid-structure interaction (FSI) simulation of composite panel slamming for a high-speed planing hull including validation with full-scale experiments. The prediction capability of CFD/CSD (computational fluid dynamics/ computational structural dynamics) FSI is shown for composite bottom panels with different layout and resulting stiffness. The CFD is performed using the code CFDShip-Iowa, whereas the CSD implements a modal expansion based on modes and frequencies predicted by the commercial FE code ANSYS. One- and two-way (tightly coupled) CFD/CSD FSI is performed using deterministic captive regular-wave simulations, modeling the sea trial conditions. Simulations provide details of slamming events, including correlation of re-entering and emerging pressure peaks with motions and correlation of pressure and strain peaks. Statistical estimators of experimental pressure and strain are used for the validation. Errors between deterministic CFD/CSD FSI and sea trial expected values are fairly large and equal on average 19%. However, experimental uncertainties from aleatory sea conditions are also large. For all cases and validation variables, errors are always smaller than the standard deviation of experimental data. The main effect of the two-way coupling is the reduction of pressure and strain peak values. Numerical and modeling issues are identified for both CFD (spatial and temporal resolution, environmental and operating conditions) and CSD (damping). The current results are overall promising, laying the groundwork for long term research on development and validation of high-fidelity two-way CFD/CSD FSI, including extensions to multidisciplinary optimization (MDO).

Bottom panels of high speed planing hulls may experience severe slams, especially when operating in rough sea. The effects of slamming loads include local deformation and vibration of bottom panels. In extreme cases, slamming may lead to damage and structural failure of hull, equipment, and payload. Slamming phenomena involve hydrodynamics and structural dynamics and show a complex physics, which is still not well understood. The complexity of experiments and numerical simulations of ship slamming currently places a limitation on the investigation of full-scale fluid-structure interaction (FSI) problems. The FSI equations include fluid, structure, and moving/dynamic mesh. Herein, the solution is based on a partitioned procedure including one- and two-way coupling. The two-way coupling, which involves a mutual exchange of information between fluid and structural solvers, can be loose or tight. In a loose coupling, also referred to as weak, staggered, or explicit, the structural deformation is fed back into the CFD only at the beginning of the time step. In a tight coupling, also referred to as strong or implicit, fluid and structure solvers exchange load and deformation in an iterative manner using non-linear inner iterations (such as predictor/corrector steps or Gauss-Seidel subiterations) until convergence within each time step. The tight coupling can be performed in either a partitioned or a monolithic fashion. Monolithic approaches, which regard fluid and structure as a single system of equations and employ a unique solution strategy, potentially achieve full discipline coupling, since the latter occurs at the governing equations level. For this reason, they are often referred to as full coupling methods. However, the accuracy of the single discipline analysis is limited by

the use of a unique numerical method for both fluid and solid, often implemented by finite elements (FE). Moreover, ill-conditioning of the system of equations and difficulty in integrating state-of-the-art fluid/structure solvers in a single framework remain open issues. In ship hydrodynamics, Reynolds number and free-surface effects limit significantly the use of monolithic FSI. In partitioned methods, the solution of the coupled problem is advanced over the separate fluid, structure, and dynamic mesh partitions, in a sequential or parallel fashion. Although generally this approach conserves momentum and energy only in an asymptotic sense (as grid element and time step tend to zero), it offers several appealing features, including the ability to use available high-fidelity tools specifically designed for complex industrial problems, with well-established discretization and solution methods within each discipline, and preservation of software modularity (Farhat et al., 1998). As a result, a successful partitioned method can solve FSI problems with sophisticated fluid and structural physics models (Hou et al., 2012). Accuracy and robustness of partitioned methods depends on both the conservation properties at the interface and the convergence properties of the nonlinear iterations. The issue of convergence occurs in monolithic methods as well (e.g. Heil, 2004), but within partitioned framework, a formal proof of convergence is often unattainable. It may be noted that ship hydrodynamics involves dealing with convergence of inner iterations even for rigid structures since the CFD is coupled with the rigid body equations for the prediction of the ship motions. Most of available experimental and numerical slamming studies for ship hydrodynamics refer to idealized geometries and conditions, such as rigid and flexible wedge drop tests (see, for instance, Faltinsen 2000, Maki et al. 2011, Khabakhpasheva and Korobkin 2013). More realistic geometries and conditions for slamming of fast ships in regular and irregular waves were addressed by towing tank experiments with segmented-hull backbone models by Dessi and Mariani (2008) and Dessi and Ciappi (2013). Numerical methods often rely on analytical and low-fidelity models such as potential flow, Wagner theory of impact, and beam theory. Nonetheless, CFD has been successfully applied in slamming studies of real geometries. He et al. (2013) presents an uncertainty quantification study for the slamming of the high speed Delft Catamaran. Mousaviraad et al. (2015) show validation of force and motions in waves for the Fridsma planing hull; Fu et al. (2014) report validation of force, motions, and pressure for the USNA planing hull. Volpi et al. (2015) present a preliminary oneway CFD/CSD FSI for full-scale validation of

slamming responses during sea trials of the high-speed planing hull “Numerette,” the slamming load facility designed, built and operated by Lehigh University and shown in Figure 1. The study uses experimental data from Thodal et al. (2015) collected in the Atlantic Ocean near the Barnegat Inlet in Barnegat Light (NJ) for the validation of numerical FSI. Results focus on port and starboard bottom panels of bay 4, which are composite sandwich structures stiffened by a steel longeron. Different fiber orientation in the panels allows assessing the effect of material properties on slamming loads and deformations. The numerical FSI couples CFD (URANS) and CSD (FE) in a one-way fashion without modeling the added mass. The validation includes slamming strains. Experimental data for slamming pressure was not included.

Figure 1: Numerette slamming load facility Building on the research presented in Volpi et al. (2015), the objective of the present work is the extension of the numerical FSI to a high-fidelity tightly coupled two-way approach using URANS and modal expansion based on FE. The full-scale hydrodynamics is validated using captive and free running simulation in calm water. Validation includes a 1D system-based model of free running resistance, pitch, and propeller rounds per seconds (RPS) available through the collaboration with Mercury Marine. The validation of full-scale FSI is performed using captive regular wave simulations. Simulation conditions model speed, wave height, and wave period from the sea trials presented in Thodal et al. (2015). Since the uncertainty on the wave height is large, two wave heights are compared, namely average and most probable from the sea state. Validation includes pressure and strain. It does not include acceleration since, at the current stage, the contribution of the single panel cannot be isolated from the overall structure vibration.

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The study aims at providing a better insight on the physics of planing hull slamming and evaluating the effects of structural properties by comparing the behavior of different composite panels, namely port and starboard sides of bay 4. Specifically, the different fiber orientation results in a larger stiffness of the starboard bottom panel. The panels are long and narrow and more fibers are oriented in the transverse direction in the starboard panel, which leads to higher bending stiffness. Additionally, comparing one- and two-way FSI results addresses the effects of the numerical approach on the prediction of both ship global motions and local load and deformation. The research was conducted in close collaboration between the University of Iowa and Lehigh University. COMPUTATIONAL METHODS The FSI analysis of local panel deformations is based on the coupling between CFD and CSD, as partitioned solvers. CFDShip-Iowa is used for the flow computation whereas a modal expansion based on FE is used for the structure. CFDShip-Iowa V4.5 (Huang et al. 2008) is an overset, block structured URANS solver, designed for ship applications. It employs absolute inertial earth-fixed coordinates and turbulence model kε/k-ω based isotropic and anisotropic RANS. A singlephase level-set method is used for capturing the free surface. Dynamic overset grids use SUGGAR to compute the domain connectivity. The commercial FE code ANSYS Mechanical V14.5 provides the modes and frequencies of the structure, used for the modal expansion. Previously, Paik et al. (2009) used CFDShip-Iowa with modal expansion based on ABAQUS for analysis of global load and deformation. The fluid solver predicts the ship rigid body motions and the forces acting on the hull; it supplies the hydrodynamic load to the structural solver. The structural model, subject to the load exerted by the fluid, provides the corresponding displacement. The structure equation of motion is ρ(𝐱𝐱)𝛅𝛅̈(𝐱𝐱, t) + 𝐶𝐶𝛅𝛅̇(𝐱𝐱, t) + ℒ𝛅𝛅(𝐱𝐱, t) = 𝐟𝐟(𝐱𝐱, t)

(1)

𝐌𝐌𝛅𝛅̈ + 𝐊𝐊𝐊𝐊 = 𝟎𝟎

(2)

where ρ is the density, 𝛅𝛅 is the displacement vector, 𝐱𝐱 is the position vector, t is time, 𝐶𝐶 is the damping operator, ℒ is the structural operator, and 𝐟𝐟 is the source term corresponding to the hydrodynamic load. ANSYS is used to predict modes 𝛗𝛗i and frequencies ωi by solving the discretized homogeneous governing equations (derived from Eq. 1)

where 𝐌𝐌 and 𝐊𝐊 are mass and stiffness matrix, respectively. The solution of Eq. 2 is obtained by the eigenvalue problem (−ω2i 𝐌𝐌 + 𝐊𝐊)𝛗𝛗i = 𝟎𝟎

Under the small deformations displacements are defined as

(3) assumption,

∞

𝛅𝛅(𝐱𝐱, t) = � qi (t) 𝛗𝛗i (𝐱𝐱)

(4)

q̈ i (t) + 2ωi ξi qı̇ (t) + qi (t)ω2i = fi (t)

(5)

fi (t) = � 𝐟𝐟(𝐱𝐱, t) ∙ 𝛗𝛗i (𝐱𝐱) d𝐱𝐱

(6)

where qi are solutions of

i=1

and fi are projections of the load on the modes as per

A general Newmark’s integration method is applied to solve Eq. 5 in time. Herein, ξi is the damping ratio proportional to the system mass and stiffness according to the Rayleigh damping model (Rayleigh 1945). The Rayleigh damping, or classical damping, expresses the damping ratio ξi as ξi = α

1 ωi +β 2ωi 2

(7)

where α and β are mass- and stiffness damping coefficients. The effect of damping on the structural deformation is significant. A parametric analysis on the damping coefficients may be required to optimize the structural model and achieve agreement with experimental data. In order to use the hydrodynamic load predicted by the CFD in the term f of Eq. 6, interpolation is required, since fluid and structure grids are generally non-matching (Maman and Farhat, 1995; Farhat et al. 1998). Here, a mapping between fluid and structural nodes is used along with Gauss integration to compute f on the structural nodes from the fluid pressure. The method conserves momentum and energy asymptotically (when the discretization size tends to zero). Nevertheless, the grid size is deemed sufficiently small to have overall small effects on the results. A systematic study of discretization size effects on the residuals will be performed in future verification studies. Within a one-way FSI approach, shown in the form of a block diagram in Figure 2, structural displacements are not fed back into the fluid solver allowing for independent CFD and CSD simulations. 3

The one-way analysis may or may not account for the effects of added mass due to the fluid by using wet or dry modes in the modal expansion. Wet modes are computed by FE embedding the structure in a fluid domain modeled by acoustic elements. In a tightly coupled two-way approach, represented in Figure 3, fluid and structural solvers exchange hydrodynamic load 𝐟𝐟 and structural displacement 𝛅𝛅 and velocities 𝛅𝛅̇ until convergence, in an inner loop within each time step. Such coupled analysis automatically accounts for the added mass effects. Along with the interpolation of 𝐟𝐟 onto the structure grid, the two-way approach requires also the deformation of the fluid grid according to the structural displacement, within each time step. The grid deforms in a two-step process. The fluid volume grid is structured with indices I, J, and K, where J = 1 corresponds the fluid-solid interface. First, the J = 1 surface is deformed by interpolation from the CSD grid. Then, the volume inner nodes are morphed by linear interpolation between interface (J = 1) and outer (J = JMAX) boundary layer surface as 𝐱𝐱 = 𝐱𝐱 0 +

l∗ − l 𝛅𝛅int l∗

(8)

where 𝐱𝐱 0 is the original coordinate of the node, 𝐱𝐱 is the modified position, 𝛅𝛅int is the displacement at the interface, l is the distance between the volume node and the interface node, and l∗ is the distance between outer and interface node; l and l∗ are computed as girth length along the grid line with constant I and K.

Figure 3: Block diagram of the two-way (tighly coupled) FSI routine using CFDShip-Iowa and modal expansion

EXPERIMENTAL SETUP The slamming load facility is a steel/composite boat designed and manufactured by Grenestedt. The boat is 9-meter long and 1.9-meter wide; it has a maximum speed of 27 m/s and a full load displacement of 2450kg. The engine is a 425 HP Mercury V8. The boat structure consists of a welded AL-6XN stainless steel frame and composite sandwich panels including 10 bottom panels, 10 side panels, 5 deck panels, 16 bulkhead panels, and 4 hatches. Table 1: Bay 4 composite bottom panel layout Bay 4 panel Port

Starboard *

Layout 2 layers DBL700 (0°, ±45°)* Divinycell H250 Foam core 3 layers DBL700 (0°, ±45°)* 1 layer L(X) 440-C10 (0°)* 2 layers DBL700 (0°, ±45°)** Divinycell H250 Foam core 3 layers DBL700 (0°, ±45°)** 1 layer L(X) 440-C10 (0°)*

0° parallel to keel ** 0° transverse to keel

Figure 2: Block diagram of the one-way FSI routine using CFDShip-Iowa and modal expansion 4

Order Top

Bottom Top

Bottom

The hull is divided into five bays, separated by stainless steel bulkheads. In bay 4, which the present study is focused on, the bottom panels have same composite layout but different fiber orientations. All bottom panels are vacuum infused with vinyl ester resin and use Divinycell H250 foam core. Two layers of DB240 reinforcement strips lay along the edges of the foam. Panels are bonded to the steel frame with Proset 176/276 epoxy. The results of the present research focus on the behavior of the port and starboard bottom panels in bay 4. Table 1 summarizes the particular layout. Both panels use Devold AMT DBL700 triaxial carbon and L(X) 440-C10 unidirectional carbon reinforcements but the fiber orientation differs, resulting in a significant difference in bending stiffness. Specifically, the fiber orientation of the starboard panel, transverse to the keel and longeron, provides a larger bending stiffness than the port panel, which has fibers laying parallel to the keel and longeron. The test facility is instrumented with strain gages on both inner and outer skins of the bay 4 panels. Due to the harsh environment of the sea trials and the need for a smooth hull surface, foil strain gages are embedded in the bottom panels by bonding to flat thin fiberglass plates. Vishay CEA-06-250UN-350/P2 and CEA-06-250UT-350/P2 gages were used in quarter bridge configuration to measure strain parallel and perpendicular to the keel in the center of each panel. Figure 4 shows the location of the strain gages (G). National Instruments NI-9237 signal conditioning and ADC modules have been used to acquire 24-bit strain data at 50 kHz per channel. This data was filtered to 5 kHz in post processing. Pressure measurements are available by AC coupled piezoelectric sensors (PCB 113b26) with 25 kHz sampling frequency, filtered to 5 kHz in post processing. The location of pressure taps (T) is shown in Figure 4.

CFD simulations are performed in calm water and regular waves. Captive simulations, in calm water and waves, use a bare hull model. For the free running simulations, performed only in calm water, the hull is appended with the sterndrive and a body force propeller is implemented. The total number of grid points for the simulations with sterndrive is 18.2M (Figure 5). The total number of grid points for the bare hull simulations is 6.94M. Overset grids include body-fitted hull and Cartesian background blocks. Symmetry with respect to the longitudinal plane is imposed; thus, the grid includes only the starboard side of bare hull and halfdomain background.

Figure 4: Sensor location on the slamming load facility

Figure 5: CFD model with sterndrive detail

Modal tests of the dry structure were conducted by exciting the panels at a number of grid points using an instrumented impact hammer and measuring the response with an accelerometer. The least squares complex exponential method was used to extract modal parameters. A National Instruments PXI4472B module signal conditioner was used with the

During the experimental tests, the ship experiences irregular wave, variable heading, and variable speed. A CFD captive regular-wave simulation is used to model the irregular wave pertaining to realsea conditions (He et al. 2013). Available information about test conditions includes wave direction, ship

PCB Piezotronics 086c03 modal analysis impact hammer and 352c04 accelerometer. Sea trials were conducted in the Atlantic Ocean near the Barnegat Inlet in Barnegat Light, New Jersey, USA. The test procedure involved performing 1-2 minute long sustained data logging sessions at speeds of 15-20m/s under constant heading. The strain gages have been zeroed when the craft was at rest before each test sequence. Steering input was used to achieve as close to neutral roll angle as possible. The vessel has since been outfitted with a trim tab to control roll angle. Test segments consisted of nearly straight trajectories. The results focus on head and following wave segments. Wave data during the sea trials were not measured directly. Basic wave conditions, such as significant height and period, were recorded by the closest NOAA buoy, located 130 km from the shore. This limitation will be removed in future studies with the use of unmanned surface vehicles, developed by Lehigh University under DURIP support for local wave measurements in sea trials. COMPUTATIONAL SETUP

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trajectory, and speed. Basic wave conditions are available through buoy data for station 44066 (NOAA). Regular head wave (S1) and regular following wave (S2) simulations model head and following wave segments, respectively, of the sea trial, which are taken as a benchmark for validation. The speed used in S1 and S2 is the average speed V of the trial within the selected segment. The wave frequency fw is derived from the equation for the encounter frequency fe fe = fw − �

2πfw2 V � cos θ g

(10)

Finite element models were developed for the slamming load facility port and starboard bay 4 composite panels extending from the keel to the chine and from the aft vertical bulkhead in bay 4 to the fore vertical bulkhead in bay 4 (Figure 6). SHELL99 elements in ANSYS model the panels. The total number of grid points is 51,648. Figure 7 shows the FE model of the panels embedded in a fluid domain modeled by the acoustic elements FLUID30 and FLUID130; this configuration is used to determine the wet modes of the structure. The validation of the FE models uses full-scale experimental modal tests in air.

where g is the gravity acceleration, and θ is the heading angle. The wavelength is then computed using λ=

g 2πfw2

(11)

The encounter frequency fe is the characteristic frequency in the experimental data record and it is determined by FFT of the experimental pressure and strain time histories (Figure 17). Given the uncertainty of the wave conditions at the time of the trials, two wave heights are used for the numerical simulations. The first is the most probable condition associated to the local buoy data. The second is the average condition corresponding to the same data. They are obtained from the significant wave height reported in the buoy record by assuming a Rayleigh distribution. Table 2 summarizes the regular wave model parameters including ship length L, natural frequency of the pitch motion fθ, wave height H and period T, wave steepness H/λ, Froude number Fr, ship speed u, and period of encounter Te.

Figure 6: FE model of the panel

Table 2: Regular wave parameters Parameter L [m] fθ [Hz] Hp* [m] Ha** [m] T [s] fw [Hz] λ [m] λ/L Hp/λ Ha/λ Fr u [m/s] fe [Hz] Te [s] fs [Hz] * Most probable wave height ** Average wave height

S1

S2 8.8392

0.625 0.60 0.75 3.33 0.30 17.3 1.95 1/29 1/23 0.87 8.10 0.77 1.30 616

0.625 0.60 0.75 2.94 0.34 13.5 1.53 1/22 1/18 1.83 17.0 0.92 1.09 736

Figure 7: FE model of the panel embedded in the fluid domain

Figure 8: Discretization of panel hull surface for the CFD and CSD grids 6

In slamming applications, the impulsive nature of the load requires high spatial resolution of both meshes (current computational grids for the panel hull surface is shown in Figure 8). Additionally, time resolution is essential to the identification of the pressure peak values. The current analysis employs a sampling frequency that is large enough to capture the first seven frequencies in water and the first frequency in air, but it is significantly smaller than the experimental sampling frequency (the ratio equals 13%). The sampling frequency of the numerical simulations included in Table 2 corresponds to a time step equal to 1/800 the wave period. The uncertainty stemming from the choice of the time step will be rigorously assessed by time step studies and application of verification procedures in future research. Preliminary time step studies have been carried out for the hydrodynamic simulations, but convergence was not achieved. The FSI analysis uses Rayleigh coefficients for the structural damping equal to 0.0 and 0.01 for massand stiffness-proportional damping, respectively.

since they are found the most severe and are used for validation of the numerical FSI. The events are considered slams when the peak value is higher than 10% of the global signal RMS. Slams are then aligned in time by their peaks. Peak time and signal dropping below a threshold equal to 1% of the signal peak EV define the event duration. 174 and 43 slams are identified within the head and following wave segments, respectively. Slamming events show a large peak corresponding to the re-entering phase and often a second minor peak corresponding to the emerging phase. Mean pressure and strain are also included in Figure 10 and Figure 11 and appear smooth with a similar trend.

EXPERIMENTAL ANALYSIS The experimental data for hydrodynamics (EFD) and structural dynamics (ESD) was collected from operation of the slamming load facility. Figure 9 shows the position track and speed over the duration of the tests for the head and following wave segments.

Figure 10: Port/starboard pressure and strain during the head wave segment

Figure 9: Trajectory and speed of sea trials for head (above) and following (below) wave Figure 10 (head wave) and Figure 11 (following wave) show the port and starboard panel slamming pressure and strains. Strains on the inner skins are primarily in tension (positive strain), while the outer skins are under compression (negative strain). Only the inner skin/transverse strains are presented

Figure 11: Port/starboard pressure and strain during the following wave segment

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The statistical assessment of the experimental record is performed by calculation of the expected value (EV) and the standard deviation (SD) of the reentering peak values, pmax and εmax, and the duration of the slamming events, ∆tp and ∆tε, in terms of pressure and strain, respectively. Statistical estimators also include the uncertainties UEV and USD on the EV and SD, respectively, and the experimental uncertainty UD. UEV is defined using the SD and the number of samples N as UEV =

2 SD √N

(12)

USD is estimated by approximating the confidence interval of the population standard deviation ���� SD using a standard normal distribution ���� ∈ ��SD2 − �Zγ/2 ��2/N SD2 , SD �SD2 − �Zγ/2 ��2/N SD2 �

(13)

By choosing γ=5% (|Z0.025|=1.96), the 95% confidence interval is considered and its semi-amplitude provides the uncertainty USD. The 95% confidence interval of the data is calculated and its semi-amplitude provides UD. Table 3 gives the statistical EV, SD, and uncertainties of pressure peak and duration. Table 4 gives EV, SD, and uncertainties of strain peak and duration. SD and uncertainties are generally large for both peak and duration. SD ranges from 40 to 110% of EV. UEV and USD range from 6 to 27%. UD ranges between 49 to 248%. There is a difference in pressure and strain between port and starboard side, attributed to the fact that the starboard panel is stiffer than the port one. The ratio between port and starboard pressure peak is 0.83 and 0.92 in head and following wave, respectively. According to the stiffness, the deformation of the port panel is larger than the starboard. The ratio between port and starboard strain peak is 1.3 and 1.5 for head and following wave, respectively. Additionally, Figure 12 and Figure 13 show the empirical quantile function of pressure peak and duration with EV, SD, and 95% confidence interval for head and following wave, respectively. Figure 14 and Figure 15 show the empirical quantile function of strain peak and duration with EV, SD, and 95% confidence interval for head and following wave, respectively. The empirical quantile function for the strain duration of the port panel has almost a constant value from 0.4 and 1. This is due to the length of the window used for the duration computation, allowing for a maximum value of 0.7 s.

Table 3: Port and starboard pressure peak value and signal duration (P=port, S=starboard) Parameter pmax (P) [kPa] ∆tp (P) [s] pmax (S) [kPa] ∆tp (S) [s] pmax ratio (P/S) * as %EV

EV

Head wave Following wave UEV* SD* USD* UD* EV UEV* SD* USD* UD*

28.11

15

101

11 233 58.88 22

73

16 117

0.141

11

72

7.6 125 0.121 19

64

14 103

34.04

16

107

11 192 63.68 24

77

17 125

0.121

15

61

6

68

15 119

108 0.144 21

0.83

0.92

Table 4: Port and starboard strain peak value and signal duration (P=port, S=starboard) Parameter

Head wave Following wave EV UEV* SD* USD* UD* EV UEV* SD* USD* UD*

εmax (P) [101.55 17 111 12 248 2.73 4 ] ∆tε (P) [s] 0.167 14 41 4.3 58 0.172 εmax (S) [101.21 15 100 11 198 1.88 4 ] ∆tε (S) [s] 0.176 11 56 6.0 94 0.168 εmax ratio 1.3 (P/S) * as %EV

27

88

19 159

24

43

9.2 49

21

69

15 123

22

74

16 130

1.5

(a)

(b)

Figure 12: Quantile functions of pressure for the head wave segment including (a) peak, (b) duration

8

(a) (a)

(b) (b)

Figure 13: Quantile functions of pressure for the following wave segment including (a) peak, (b) duration

Figure 15: Quantile functions of strain for the following wave segment including (a) peak, (b) duration

(a)

(a)

(b)

Figure 16: Example of slamming pressure and strain for the head wave segment port (a) and starboard (b) panels (b)

Figure 14: Quantile functions of strain for the head wave segment including (a) peak, (b) duration

Figure 16 shows a single slamming event as illustrative example. It is extracted from the head wave experimental record of the port panel. Pressure and strain re-entering peaks show a phase lag ϕ, which is reported in Table 5. The strain peak occurs later in time with respect to the pressure peak. Phase lags are 9

computed by cross-correlation of pressure and strain signals. Additionally, experimental data reveal a phase lag in pressure and strain peaks between port and starboard panels. Table 5 gives the phase lag values including the indication of the preceding panel. Pressure/strain phase lags and port/starboard phase lags are very small with respect to the slamming event duration. The table also gives the characteristic frequencies emerging from the FFT (Figure 17), such as encounter frequency and frequency of vibration fvib after the initial re-entering slam peak, and the first modal frequency fn of the panels in air. fvib is significantly smaller than fn. Specifically, it falls between the first and the second frequency in water, according to the FE prediction (see Section “Structural analysis”). The vibration frequency relates to the transition of the panels from dry to wet condition occurring during the slamming event.

HYDRODYNAMIC ANALYSIS Calm Water

The calm water captive simulations are conducted for a wide range of Fr for the bare hull model free to heave and pitch. The free running simulations are conducted at Fr equal to 1.1, 1.9, and 2.7 for the model appended with sterndrive and body force propeller. The free running model has six degrees of freedom. Figure 18 shows the comparison of steady state values for both captive and free running simulations with the experimental data. Heave and pitch motions are slightly larger for free running simulation, but the trends versus the Fr are similar for both captive and free running simulations. The maximum pitch is found for Fr=1.1 (3.6 and 4.2 degrees for captive and free running simulations, respectively).

Table 5: Slamming pressure and strain characteristics Parameter ϕ (pmax/εmax) [s] ϕ%∆tp (pmax/εmax) ϕ (pmax, P/S) [s] ϕ (εmax, P/S) [s] fe [Hz] fvib [Hz] 1st fn [Hz] in air

Head wave Following wave Port Starboard Port Starboard 0.0024 0.0012 0.0058 0.0032 1.7 1.0 4.8 2.2 0.0030 (port) 0.0012 (starboard) 0.0012 (starboard) 0.0046 (starboard) 0.77 0.77 0.92 0.92 ~70 ~68 ~70 ~85 238 246 238 246

(a)

(b)

Figure 17: FFT of pressure and strain for head (a) and following (b) wave (P=port, S=starboard)

Figure 18: Comparison of CFD and EFD results in calm water

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Validation is performed by comparison of experimental and numerical results and uncertainties. The percentage error between CFD and EFD is E= D−S

(14)

|E| ≤ UV

(15)

resistance, and total resistance show good agreement with CFD free running simulations. However, the 1D simulation predicts larger trim angle as no model has been used for the stepped bottom of the boat. CFD free surface and pressure distribution on the hull are shown as example in Figure 19 for Fr = 2.1 and 2.7.

where D and S are the experimental and simulation values, respectively. Validation is achieved if

where UV is the validation uncertainty, approximated here by UD. The error is reported in the following as percentage of the experimental value (%D). Compared to the available experimental data, the errors on the pitch are 6.4 and -8.9% for captive and free running simulations, respectively. Roll motion is only predicted for the free running model. The roll angle increases with Fr and it is about 2.5 degrees for the highest speed, very close to the available experimental value at Fr equal to 2.7 (E=0.8%). The propeller RPS shows the same trend as EFD, however, it is over predicted for high Fr (E=12%). Since the experimental resistance could not be measured for the full-scale Numerette, it is estimated from the propeller input power computed using both the engine curve and propeller open water torque curve. The estimated experimental resistance based on engine curve shows similar resistance for low and high Fr, while open water curve estimates very small resistance at high speeds. The captive CFD simulations show E=58, 49, and 13% for Fr=1.1, 1.9, and 2.7, respectively. Corresponding errors for free running simulation are 49, 36, and -9%. The study of the free running results show that the pressure resistance of the sterndrive is comparable with the resistance of the bare hull. Therefore, captive simulations for the bare hull geometry with no sterndrive under-predicted the resistance significantly.

Figure 20: Comparison of motions and resistance including USNA (CFD), USCG (EFD), and Fridsma (EFD) Figure 20 shows the comparison of the captive simulations with the results for other ship hulls including USNA, USCG, and Fridsma models. All geometries show similar non-dimensional resistance at high speed. The non-dimensional heave motion is smaller for Numerette, but it follows the same trend as for other geometries. The largest heave motion is for Fridsma, which has the shortest length among all geometries (4.5ft). For pitch motion, Numerette and USNA show similar values for high speed and both show smaller values compared to those for USCG and Fridsma. The trends for pitch motion are the same for all geometries, i.e. there is a peak for pitch motion around Fv=2.5-3.0, where Fv is the volume-based Fr 1

Fv = V��∆3 g

Figure 19: Free surface and pressure distribution for calm water simulation at Fr = 2.1 and 2.7 Figure 18 also shows the comparison of CFD results with 1D-simulation results, provided by Mercury Marine. The propeller RPS, sterndrive

(16)

Sensitivity studies on VCG are conducted since VCG is not available from EFD and is assumed equal to 0.02L for all simulations. The VCG studies are only conducted for captive model. The studies show 11

that the steady state resistance and motions vary less than 3% if VCG changes from 0.02L to 0.06L suggesting that the errors of the simulations are not due to the assumed VCG value (Figure 21).

The regular wave simulations S1 and S2 described in Section 4 take the inputs in Table 2. Simulations are performed over ten wave periods of encounter; force coefficients and motions indicate satisfactory convergence and a highly nonlinear response. Preliminary hydrodynamic results for S1 and S2 using the wave height Ha are shown in Figure 23 to Figure 26. Figure 23 depicts slamming pressures probed at P, heave and pitch motions, wave elevation at P, and wave elevation at the ship center of gravity (CG). The ship impacts the wave face close to the crest in both head and following conditions. Pressure waveforms show the re-entering slam, associated to the first and largest pressure peak, and the emerging slam, associated to the second peak. Figure 24 and Figure 25 display the pressure distribution over the hull (bottom view) corresponding to the re-entering and emerging phases.

Figure 21: Sensitivity study for the VCG in calm water

Regular Wave

Two preliminary regular wave simulations are conducted close to the resonance conditions for heave and pitch (fz=0.5Hz and fθ=0.65Hz). The nondimensional wavelength λ/L used is 3.12 and 2.42 whereas the wave steepness H/λ is 1/47 and 1/36. RAO for motions show z/A and θ/Ak equal to ~1.5 and ~0.7, respectively. The RAO are compared with other planing hulls such as Fridsma and USNA models in Figure 22. Motion trends appear comparable for all geometries.

Figure 24: Hull pressure distribution for S1

Figure 25: Hull pressure distribution for S2

Figure 22: RAO of motions of several planing hulls

Figure 23: Panel pressure, motions, and wave elevation for S1 (left) and S2 (right)

Time resolution plays a critical role in describing accurately slamming pressure, especially the re-entering peak, since the characteristic time scale of the impact is small. Therefore, preliminary time-step studies are conducted for S1 and S2 using the average wave height Ha. Figure 26 shows the slamming pressure using a time step equal to 1/400, 1/566, 1/800 of the wave encounter period, i.e. √2 ratio increments. The pressure is probed at the locations P, K, and C (Figure 4). For S1, discrepancy is found in predicting the peak pressure, while the trend is well captured even with the largest time step. For S2, pressure peak, waveform, and duration time differ significantly. Overall, in order to identify the slamming pressure peak, a time step as small as 1/800 of the encounter period is needed. Such 12

time step corresponds to a sampling frequency of 616 and 736 Hz for S1 and S2, respectively. In order to define accurately the pressure peak, a smaller time step may be required. Additional validation and time step verification is desirable for improving the accuracy of the computational setup.

(a)

(b)

(a) (c)

Figure 27: Port panel first three modes in (a) vacuum, (b) air, and (c) water

(b)

(a)

(b)

(c)

Figure 26: Time step study of the pressure time history in S1 (left) and S2 (right) from the center probe (a), the keel probe (b), and the corner probe (c) (c)

STRUCTURAL ANALYSIS The modal analysis of the panels is performed in order to assess modes and associated frequencies. The modal analysis is carried out with no structural damping. CSD results for modes are available in vacuum, air, and water. ESD results are available for air. Figure 27 and Figure 28 show the first three modes of port and starboard panel, respectively, as computed by FE method (Eq. 3). Table 6 summarizes the modal frequencies. Table 7 provides the validation of CSD results using ESD. The analysis proves that the starboard panel is stiffer than the port one, presenting higher frequencies. Specifically, the frequencies in vacuum of the starboard panel are 7, 12 and 13% larger than port.

Figure 28: Starboard panel first three modes in (a) vacuum, (b) air, and (c) water The effects of the added mass are evaluated by comparing dry conditions (vacuum) with wet conditions (air and water). Coupling with air has a negligible effect, whereas coupling with water has a significant effect on both modal shape and frequency, the latter being strongly reduced. During the sea trials, the panels experience a transition from dry to wet conditions, therefore fully dry and fully wet approximations underand over-estimate, respectively, the added mass effects. Validation of frequencies in air shows average 4.6% and 5.3% error on the first three frequencies for port and starboard panels, respectively.

13

Table 6: CSD modal frequencies [Hz] Mode 1st 2nd 3rd

Vacuum 233 337 417

Port Air 232 333 413

Starboard Water Vacuum Air Water 50 237 235 57 97 403 401 114 120 484 479 142

Table 7: Validation of structural variables (modal frequencies [Hz] in air) Mode 1st 2nd 3rd

ESD 238 373 411

Port CSD 232 333 413

E%D 2.5 11 -0.5

ESD 246 394 437

Starboard CSD E%D 235 4.5 401 -1.8 479 -9.6

FSI ANALYSIS: ONE-WAY COUPLING Figure 29 shows pressure, heave, and pitch motions time histories including experimental EV and SD of pressure peak value and duration for S1. EFD data includes port and starboard pressure at the location T. CFD data include results obtained with both Hp and Ha. The pressures are probed at the same location of the experimental pressure taps (T). The bow re-entering slam appears in correspondence to minimum pitch. The pressure peak value obtained with Hp is underestimated on average by 21%EV. When using Ha, the pressure peak is over-estimated for the port panel and it is under-estimated for the starboard one, with a 9%EV average error. The duration of the event is overestimated by 28 and 34%EV using Hp and Ha. Overall, the numerical results agree qualitatively well with the experimental EV for both wave heights. Average errors are 24 and 22%EV for Hp and Ha whereas experimental uncertainties are UEV=13%EV, SD=85%EV and UD =165%EV (Figure 12).

Figure 30: One-way pressure and motions for S2 Figure 30 shows pressure, heave, and pitch motions time histories for S2. The bow re-entering slam appears in correspondence to minimum pitch. The pressure peak value is under-estimated on average by 42%EV for both Hp and Ha. The duration of the event is over-estimated by 9.2%EV using Hp and underestimated by 5.7%EV using Ha. Average errors are 26 and 24%EV for Hp and Ha whereas experimental uncertainties are UEV=21%EV, SD=71%EV, and UD=116%EV (Figure 13).

Figure 31: One-way FSI displacement and strain for S1

Figure 29: One-way pressure and motions for S1

Figure 31 shows the deformation of the panels as displacement at the location T and transverse inner strain at the location G for S1. Using Hp, the strain of the port panel is over-estimated by 8%, whereas it is under-estimated by 38% on the starboard side. Using Ha, it is over-estimated by 38% and under-estimated by 21% for port for starboard panels, respectively. The port peak strain is larger than starboard according to the difference in stiffness between panels. However, the port/starboard strain ratio is over-estimated for both Hp and Ha. The duration of the event for the port panel is under-estimated by 10%EV using both Hp and Ha and over-estimated by 39%EV for the starboard panel. Average errors are 24 and 27%EV for Hp and Ha whereas experimental uncertainties are UEV=12%EV, 14

SD=77%EV, and UD=150%EV (Figure 14). A phase lag is found between the pressure and strain peaks. When expressed as percentage of pressure event duration, the difference with the experiments is 0.8 and 0.7%EV for Hp and Ha, respectively. Displacement peak values are approximately 11 and 13% of thickness for Hp and Ha. The ratio between port and starboard peak displacements is 1.6.

UEV=13%EV, SD=85%EV SD and UD=165%EV (Figure 12). Experimental starboard panel pressure is higher than port one. No significant difference appears between port and starboard numerical pressures. Figure 34 shows pressure, heave, and pitch motions time histories for S2. The bow re-entering slam appears in correspondence to minimum pitch. The duration of the event is over-estimated on average by 16%EV using Hp and it is under-estimated by 7.8% using Ha. Average errors are 31 and 27%EV for Hp and whereas experimental uncertainties are Ha UEV=21%EV, SD=71%EV, and UD=116%EV (Figure 13). No significant difference is found between port and starboard pressures.

Figure 32: One-way FSI displacement and strain for S2 Figure 32 shows the deformation of the panels as displacement and strain for S2. Using Hp, the strain of the port panel is over-estimated by 14%, whereas it is under-estimated by 23% on the starboard side. Using Ha, it is over-estimated by 17% and under-estimated by 21% for port for starboard panels, respectively. The port peak strain is larger than starboard but the port/starboard strain ratio is over-estimated. The duration of the event for the port panel is underestimated by 28 and 24%EV using Hp and Ha and overestimated by 50 and 59%EV for the starboard panel. Average errors are 29 and 30%EV for Hp and Ha whereas experimental uncertainties are UEV=21%EV, SD=69%EV, and UD=115%EV (Figure 15). Pressure/strain phase lag difference with the experiments is 2.0 and 1.5%EV (normalized with pressure event duration) for Hp and Ha, respectively. Displacement peak values are approximately 20 and 21% of thickness for Hp and Ha. The ratio between port and starboard peak displacements is 1.6. Overall, the behavior of port versus starboard is qualitatively captured.

Figure 33: Two-way FSI pressure and motions for S1

Figure 34: Two-way FSI pressure and motions for S2

FSI ANALYSIS: TWO-WAY COUPLING Figure 33 shows pressure, heave, and pitch motions time histories for S1. The bow re-entering slam appears in correspondence to minimum pitch. The pressure peak value is under-estimated on average by 40 and 30% using Hp and Ha, respectively. The duration of the event is over-estimated on average by 20%EV using both Hp and Ha. Average errors are 30 and 25%EV for Hp and whereas experimental uncertainties are Ha

Figure 35: Two-way FSI displacement and strain for S1 15

Figure 35 shows the deformation of the panels including displacement and transverse inner for S1. Using Hp, the strain of the port panel is under-estimated on average by 32%. Using Ha, it is over-estimated by 32% on the port side and under-estimated by 30% on the starboard side. The port peak strain is larger than starboard but, the port/starboard strain ratio is overestimated for both Hp and Ha. The duration of the event is under-estimated by 12%EV on the port panel using both Hp and Ha; it is over-estimated on the starboard panel by 23%. Average errors are 25 and 24%EV for Hp and Ha whereas experimental uncertainties are UEV=12%EV, SD=77%EV, and UD=150%EV (Figure 14). Pressure/strain phase lag is difference with the experiments is 2.8 and 0.8%EV (normalized with pressure event duration) for Hp and Ha, respectively. Displacement peak values are approximately 10 and 14% of thickness for Hp and Ha. The ratio between port and starboard peak displacements is 1.6.

Figure 36: Two-way FSI displacement and strain for S2

Figure 36 shows the deformation of the panels as displacement transverse inner strain for S2. Using Hp, the strain of the port panel is over-estimated by 13%, whereas it is under-estimated by 35% on the starboard side. Using Ha, it is over-estimated by 10% and under-estimated by 30% for port for starboard panels, respectively. The port peak strain is larger than starboard but the port/starboard strain ratio is overestimated. The duration of the event is under-estimated by 10 and 39%EV on the port panel using Hp and Ha; it is over-estimated on the starboard panel by 68 and 48%EV. Average errors are 31 and 32%EV for Hp and whereas experimental uncertainties are Ha UEV=21%EV, SD=69%EV, and UD=115%EV (Figure 15). Pressure/strain phase lag difference with the experiments is 2.7 and 0.8%EV (normalized with pressure event duration)for Hp and Ha, respectively. Displacement peak values are approximately 21% of thickness. The ratio between port and starboard peak displacements is 1.5. Overall, errors for pressure and strain peak values are reasonable and always within both 95% confidence interval and EV +/- SD. The trend of port versus starboard panel appears well represented by the current simulations. Nevertheless, there are several sources of modeling and numerical uncertainty that needs to be addressed. For instance, numerical simulations are conducted in captive conditions; the ship speed is constant throughout the analysis. Experimental ship speed shows significant fluctuations especially occurring during the slamming. Free-running simulation with controller may be required to fully address the asymmetric pressure distribution effects.

Table 8: Summary of numerical results S1

S2

Hp

Port

Star.

Port/ Star.

pmax [kPa] ∆tp [s] εmax [10-4] ∆tε [s] ϕ (pmax,εmax) [s] ϕ%∆tp pmax [kPa] ∆tp [s] εmax [10-4] ∆tε [s] ϕ (pmax,εmax) [s] ϕ%∆tp pmax ratio εmax ratio

Ha

Hp

Ha

Oneway

Twoway

Oneway vs two-way

Oneway

Twoway

Oneway vs two-way

Oneway

Twoway

Oneway vs two-way

Oneway

Twoway

Oneway vs two-way

24.29 0.381 1.67 0.495 0.0056 1.5 24.29 0.381 0.75 0.495 0.0056 1.5 1.0 2.2

18.43 0.359 1.37 0.485 0.0139 3.9 18.43 0.359 0.58 0.438 0.0109 3.0 1.0 2.4

32 5.7 18 2.0 -151 -2.4 32 5.7 23 12 -97 -1.6 0.0 -6.1

29.29 0.400 2.14 0.495 0.0051 1.3 29.29 0.400 0.96 0.495 0.0051 1.3 1.0 2.2

21.57 0.358 2.04 0.485 0.0135 3.8 21.57 0.358 0.85 0.438 0.0105 2.9 1.0 2.4

36 12 4.9 2.1 -62 -66 36 12 13 13 -51 -56.4 0.0 -7.1

35.32 0.291 3.12 0.390 0.0108 3.7 35.32 0.291 1.45 0.390 0.0108 3.7 1.0 2.2

32.71 0.309 3.08 0.485 0.0135 4.4 32.71 0.309 1.23 0.435 0.0135 4.4 1.0 2.5

8.0 -5.7 1.3 -20 -20 -15 8.0 -5.7 18 -10 -20 -15.4 0.0 -14

35.45 0.251 3.19 0.413 0.0082 3.3 35.45 0.251 1.49 0.413 0.0082 3.3 1.0 2.1

33.48 0.246 3.01 0.332 0.0185 7.5 33.48 0.246 1.31 0.385 0.0155 6.3 1.0 2.3

5.9 2.3 6.0 24 -56 -57 5.9 2.3 14 7.3 -47 -48.4 0.0 -6.8

16

Table 9: Validation of FSI variables for S1 EFD/ESD

Port

Star.

Port/ Star.

Ave.

CFD/CSD (Hp)

One-way UEV SD UD %E E E %EV %EV V %EV %UD pmax [kPa] 15 101 233 14 5.8 ∆tp [s] 11 72 125 -37 -30 εmax [10-4] 17 111 248 -7.7 -3.1 ∆tε [s] 6.2 41 58 10 18 ϕ (pmax, εmax) [s] -131 ϕ%∆tp -0.6 pmax [kPa] 16 107 192 29 15 ∆tp [s] 9.3 61 108 -18 -17 εmax [10-4] 15 100 198 38 19 ∆tε [s] 8.5 56 94 -39 -41 ϕ (pmax, εmax) [s] -363 ϕ%∆tp -1.1 pmax ratio -20 εmax ratio -74 Peak 16 105 218 22 11 Duration 8.7 58 96 26 26 Phase lag 124 Ratios 47 Overall peak 12 81 157 24 18 and duration

CFD/CSD (Ha)

Two-way

One-way

Ep-Ea

Two-way

E %EV 34 -29 12 12 -481 -3.0 46 -12 52 -23 -811 -3 -20 -84 36 19 324 52

E %UD 15 -23 4.7 21 24 -11 26 -24 17 20 -

E %EV -4.2 -44 -38 10 -112 -0.4 14 -24 21 -39 -324 -0.9 -20 -74 19 29 109 47

E %UD -1.8 -35 -15 18 7.3 -23 10 -41 8.7 29 -

E %EV 23 -29 -32 12 -461 -2.9 37 -11 30 -23 -773 -2.5 -20 -87 30 19 310 54

27

19

24

19

25

One-way

E E %UD %EV 10 18 -23 7.0 -13 30 21 0.0 -19 -0.2 19 15 -11 6.1 15 17 -24 0.0 -38 -0.2 0.0 0.2 14 20 20 3.3 14 0.1 17

12

Two-way

E %UD 7.6 5.6 12 0.0 7.6 5.6 8.7 0.0 9.1 2.8 -

E %EV 11 -0.2 43 0.0 -19 -0.1 9.2 -0.1 22 0.0 -39 -0.1 0.0 3.0 21 0.1 15 1.5

E %UD 4.8 -0.1 17 0.0 4.8 -0.1 11 0.0 10 0.1 -

5.9

11

4.8

Table 10: Validation of FSI variables for S2 EFD/ESD

Port

Star.

Port/ Star.

Ave.

CFD/CSD (Hp)

One-way UEV SD UD %E E E %EV %EV V %EV %UD pmax [kPa] 22 73 117 40 34 ∆tp [s] 19 64 103 -15 -15 εmax [10-4] 27 88 159 -14 -9.0 ∆tε [s] 13 43 49 28 57 ϕ (pmax, εmax) [s] -86 ϕ%∆tp -1.4 pmax [kPa] 24 77 125 45 36 ∆tp [s] 21 68 119 -3.3 -2.7 εmax [10-4] 21 69 123 23 19 ∆tε [s] 23 74 130 -50 -39 ϕ (pmax, εmax) [s] -237 ϕ%∆tp -2.6 pmax ratio -8.7 εmax ratio -48 Peak 23 77 131 30 24 Duration 19 62 100 24 28 Phase lag 82 Ratios 28 Overall peak 21 70 116 27 26 and duration

CFD/CSD (Ha)

Two-way

One-way

Ep-Ea

Two-way

One-way

Two-way

E %EV 44 -22 -13 10 -133 -2.1 49 -10 35 -68 -322 -3.2 -8.7 -72 35 27 115 41

E %UD 38 -21 -8.0 21 39 -8 28 -52 28 26 -

E %EV 40 0.5 -17 24 -41 -1.0 44 11 21 -59 -156 -2.1 -8.7 -47 30 24 50 28

E %UD 34 0.5 -11 48 35 9.1 17 -46 24 26 -

E %EV 43 2.8 -10 39 -219 -5.2 47 13 30 -48 -384 -5.2 -8.7 -58 33 26 153 33

E %UD 37 2.7 -6.4 78 38 11 25 -37 26 32 -

E %EV 0.2 -16 2.6 4.2 -45 -0.4 0.2 -14 2.1 8.9 -81 -0.4 0.0 -0.7 1.3 11 32 0.4

E %UD 0.2 -15 1.6 8.6 0.2 -12 1.7 6.8 0.9 11 -

E %EV 1.3 -25 -2.6 -28 86 3.2 1.2 -22 4.3 -19 63 1.9 0.0 -14 2.3 24 38 7.1

E %UD 1.1 -24 -1.6 -57 1.0 -19 3.4 -15 1.8 29 -

31

27

27

25

29

29

6.0

5.8

13

15

FSI ANALYSIS: EFFECTS OF ONE- VERSUS TWO-WAY COUPLING AND WAVE HEIGHT Table 8 summarizes the results including comparison between one- and two-way approaches. Table 9 and Table 10 provide the error between CFD and EFD EV as percentage of experimental EV and UD; it also includes SD and UD. One-way versus two-way values

are given as the difference between one- and two-way results, as percentage of the two-way one. In general, the effect of the two-way coupling is that of reducing pressure and strain peak values. The average reduction is 23 and 8% for S1 and S2, respectively. For pressure and strain duration a unique trend cannot be identified; average difference between one- and two-way results is 8 and 10% for S1 and S2. Pressure/strain phase lag 17

normalized with slam duration increases using the twoway coupling with respect to the one-way by 2.0 and 2.2% for S1 and S2. Port/starboard pressure ratio is equal to 1 using both approaches. Port/starboard strain ratio instead increases by 6.0 and 10%. The effects of two-way versus one-way coupling are due to the physics of the problem and may be indirectly observed in the experiments, comparing port and starboard panel pressure peaks. The port panel has the largest deformation and experiences smaller pressure peaks than the starboard panel. Specifically, the average pressure peak is 20% and 10% smaller in head and following waves respectively. This shows that deformations have significant effects on the hydrodynamics, confirming indirectly the significant effects of two-way versus one-way couplings. Table 9 and Table 10 include a comparison of Hp versus Ha. From Hp to Ha, pressure and strain peaks increase for all cases, by an average of 11%. Duration increases for head wave one-way port and starboard panel pressure, following wave one-way port and starboard panel strain. CONCLUSIONS AND FUTURE RESEARCH Code development and prediction capability for complex real world FSI problems have been demonstrated through numerical investigation of highspeed planning hull slamming in ocean environment, with comparison to experimental data. Composite bottom panels with different panel layout and resulting stiffness were investigated. Most trends were correctly predicted, including the effects of different structural properties. Hydrodynamic analysis by CFD provided details of slamming events such as re-entering and emerging slamming dynamics for head and following waves, including correlation of pressure peaks with motions. CFD/CSD FSI provided correlation of pressure and strain peaks. Errors between deterministic CFD/CSD FSI and sea trials data are fairly large and equal on average 30% for peaks, 24% for duration, 2% for phase lag between pressure and strain peaks (normalized with duration), and 41% port versus starboard peak ratio of pressure and strain. However, experimental uncertainties from aleatory sea conditions are very large. On average, UEV equals 17%EV, SD is 75%EV and UD based on 95% confidence interval equals 136%EV. For all cases and variables, errors are always smaller than SD and significantly smaller than UD. Additionally, the sensitivity of peaks versus wave height is significant. Peaks increase on average by 11% comparing Hp to Ha, confirming significant effects of the environmental conditions. Overall, the sea trail conditions used in the current work are affected by two

types of uncertainty. The first is an epistemic uncertainty related to the knowledge of the actual wave spectrum and heading experienced during the tests. This uncertainty could be reduced, provided that wave measurements are performed in situ. The second is an intrinsic aleatory uncertainty associated to random waves, which cannot be reduced. The latter could be modeled and propagated through the simulations using uncertainty quantification methods. The main effect of starboard versus port panel is a decrease of strain peak (56%) and duration (2.5%), due to larger stiffness. The average ratio between strain peaks is 2.3. Pressure peak and duration are similar. Errors are 6% larger for starboard. The main difference between head (S1) and following (S2) wave segments is an increase of S2 pressure and strain peaks (48%) and decrease of duration (20%), mainly due to increased speed. Errors are 4% larger for S2. The main effect of the two-way coupling is the reduction of pressure and strain peak values, with an average reduction of 16%. Pressure/strain phase lag increases on average by 2.1% (normalized by the duration). Additionally, port/starboard strain ratio increases by 8%. Differences between two-way and one-way are within the experimental uncertainty. Numerical and modeling issues were identified for both CFD (spatial and temporal resolution, environmental and operating conditions) and CSD (damping). The slamming pressure was found very sensitive to computational time step. Simulations were performed with a sampling frequency less than one fifth of the one used for the experiments. A smaller numerical time step is appropriate for an accurate pressure peak identification and comparison of port versus starboard panels. To address the issue of spatial and temporal resolution, grid size and time step verification is needed. Moreover, a full-domain simulation is required including simultaneously port and starboard side. This would allow modeling the asymmetric hydrodynamics experienced by the craft. The effects of the ride control for real sea operations versus current captive simulations needs to be evaluated. Results for strain were significantly affected by the structural damping. A parametric analysis is required to quantify the effects of damping and choose the appropriate values for CSD. Finally, in order to achieve the statistical validation of all variables, irregular wave simulations, and/or uncertainty quantification models need to be applied considering the actual wave spectrum. The results are overall promising. The way forward is continuing improving FSI capabilities with focus on momentum and energy conservation on the fluid and structure interface and its effect on the pressure and strain prediction, along with convergence properties and criteria for the non-linear FSI iterations. 18

Moreover, validation of FSI requires both the reduction of the epistemic uncertainty associated to sea trial conditions and the modeling and propagation of the aleatory uncertainty of irregular waves through UQ. Modelling of the wave conditions will be carried out using a system of unmanned surface vehicles developed by Lehigh University under DURIP support for local wave measurements. The current results have shown the significant effects of composite material design on the structural response of slamming. Composite materials offer multiple design choices (number of layers, fiber orientation, etc.) that can be optimized in order to achieve desired properties, for instance load and acceleration reduction. Due to the inherent coupling of disciplines involved (fluid and structure) MDO is required to achieve the design goals while optimizing simultaneously structural parameters and shape. Extensions of FSI to MDO will profit from the authors’ research in design optimization (Diez et al., 2015; 2016). ACKNOWLEDGEMENTS The research is sponsored by the Office of Naval Research (ONR), grants No. N00014-13-1-0616 and N00014-13-1-0617, administered by Dr. Roshdy Barsoum. Matteo Diez is also grateful to the National Research Council of Italy, for its support through the Short-Term Mobility Program 2015.

Farhat, C., Michael, L., and Le Tallec, P., “Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity,” Computer methods in applied mechanics and engineering, Vol. 157, No. 1, 1998, pp. 95-114. Fu, T.C., Brucker, K.A., Mousaviraad, S.M., Ikeda, C.M., Lee, E.J., O’Shea T.T., Wang, Z., Stern, F., and Judge C.Q., “An Assessment of Computational Fluid Dynamics Predictions of the Hydrodynamics of HighSpeed Planing Craft in Calm Water and Waves,” Proceedings of the 30th Symposium on Naval Hydrodynamics, Hobart, Tasmania, Australia, 2014. He, W., Diez, M., Zou, Z., Campana, E. F., and Stern, F., “URANS study of Delft catamaran total/added resistance, motions and slamming loads in head sea including irregular wave and uncertainty quantification for variable regular wave and geometry,” Ocean Engineering Vol. 74, 2013, pp. 189-217. Heil, M., “An efficient solver for the fully coupled solution of large-displacement fluid–structure interaction problems,” Computer Methods in Applied Mechanics and Engineering, Vol. 193, No. 1, 2004, pp. 1-23.

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