Experiments and CFD of a high-speed deep-V planing hull––Part I: Calm water

Applied Ocean Research 96 (2020) 102060

Contents lists available at ScienceDirect

Applied Ocean Research journal homepage: www.elsevier.com/locate/apor

Experiments and CFD of a high-speed deep-V planing hull––Part I: Calm water

T

⁎

Carolyn Judgea, , Maysam Mousaviraadb, Frederick Sternc, Evan Leed, Anne Fullertond, Jayson Geiserd, Christine Schleicherd, Craig Merrilld, Charles Weild, Jason Morind, Minyee Jiangd, Christine Ikedae a

United States Naval Academy, United States Department of Mechanical Engineering, University of Wyoming, United States c IIHR-Hydroscience & Engineering, University of Iowa, United States d Naval Surface Warfare Center Carderock Division, United States e Virginia Tech, United States b

A R T I C LE I N FO

A B S T R A C T

Keywords: Planing hulls URANS CFD Sinkage Trim Resistance Validation Experiment Shallow water

Comparisons of experimental and simulation results for a high-speed deep-V planing hull are presented. The goal of this investigation is to improve the physical understanding of, as well as assess the experimental and CFD capability for, deep-V planing hulls operating in calm water and slamming when running in head waves (both regular and irregular). This paper consists of two parts, which deal with the calm water and slamming in waves, respectively. In Part I, simulations for trim, sinkage, and resistance in calm water are compared with experiments on a deep-V planing hull at the U.S. Naval Academy and at Naval Surface Warfare Center – Carderock. Two model scales of the same geometry were tested in calm water at a range of speeds. Comparisons between the scale models, between the same model tested at both facilities, and comparisons between simulation and experiment are discussed. The results showed the importance of precise geometric (particularly for the transom) and hydrostatic information for simulation predictions. The comparisons also showed the need for greater resolution of the spray root to achieve the best predictions involving trim (and wetted lengths). Overall, there was general agreement between the facilities, even for the calm water trim. The CFDShip-Iowa and STAR-CCM+ calm water validation effort was conducted with the larger model results from NSWCCD. Validation was not achieved for resistance; however, Fn average error was less than 4%DR. In sinkage, both codes were validated at the highest three speeds, but not at the lowest speeds (Fn average error was less than 3%DR). For trim and wetted keel, validation was not achieved, although the validation uncertainty values were small (Fn average error was less than 4%DR). Both codes under-predicted the calm water trim and the wetted keel length was under-predicted for all but the lowest speed (Fn average error less than 1). The overall results provide an assessment of the state of the art for both experiments and CFD for high-speed deep-V planing hull resistance, sinkage, and trim. The experimental and simulation results for hull slamming in waves (both regular and irregular) are presented in Part II of this paper.

1. Introduction As interest in high-speed small craft is growing, there is interest in efforts to experimentally and computationally characterize the behavior of these craft in calm water and waves. Current structural design methods for planing craft rely heavily on empiricism and many decades of historical data from early generation hull designs [1,2]. These methods have been employed reliably for a number of years, however an unknown level of conservatism likely exists that may limit structural ⁎

optimization. A better physical understanding of the dynamic response of high-speed naval craft dynamics in a seaway, and its relationship to hull loading, would allow for improved structural optimization. Previous studies have focused on hydrodynamic forces/moments and motions in calm water and waves [3–8]; impact loads due to slamming in waves (and the associated decelerations of the hull) [9–17]; statistical and probabilistic prevalence of slamming events in seas [18–23]; and structural responses due to slamming loads [24–27]. The current study uses a prismatic planing hull geometry called Generic Prismatic

Corresponding author. E-mail addresses: [email protected] (C. Judge), [email protected] (M. Mousaviraad).

https://doi.org/10.1016/j.apor.2020.102060 Received 10 May 2019; Received in revised form 25 November 2019; Accepted 18 January 2020 0141-1187/ © 2020 Elsevier Ltd. All rights reserved.

Applied Ocean Research 96 (2020) 102060

C. Judge, et al.

Nomenclature

U U UD USN UV z Δ ζ θ λ λp ρ σ σs τ τs ‘z

Variables ∞ A a ak C Cv CL CD Cm D E f fe fn Fn Fnh H h Hs I ky L LWK LWC N P R r2 S T t Te Tp

infinite water depth Acceleration wave amplitude wave steepness CFD setup condition speed coefficient, V/ gB where B is the beam lift coefficient drag coefficient moment coefficient data value error value frequency encounter frequency natural frequency Froude number depth Froude number incoming wave height shallow water depth significant wave height ideal value pitch gyradius ship length wetted keel length wetted chine length number of wave encounters slamming Pressure longitudinal force; resistance correlation simulation value draft; wave period time encounter period peak period

ship velocity uncertainty data uncertainty simulation numerical uncertainty validation uncertainty heave; Standard score displacement wave elevation pitch wavelength peak wavelength water density sinkage hydrostatic sinkage trim hydrostatic trim clearance under the transom when operating in shallow water, nondimensionalized by beam

Acronyms AAM average angle measure CFD computational fluid dynamics DR data range EFD experimental fluid dynamics EV expected value GPPH generic prismatic planing hull IG IGES geometry LCG, VCGlongitudinal, vertical centers of gravity LTP, VTP longitudinal, vertical tow points NSWCCD Naval Surface Warfare Center Carderock Division RMS root mean square SD standard deviation TP tow point URANS Unsteady Reynolds-Averaged Navier-Stokes USNA United States Naval Academy V&V verification and validation

for resistance, 5%D for sinkage, and 8%D for trim. DeMarco et al. [31] performed towing tank experiments and uncertainty analyses in calm water as well as computational validation studies for resistance, sinkage, trim, and wetted surface area using STAR-CCM+ for a stepped planing hull with up to 2M grid points. For resistance and trim, the error values were about 4%D, while larger errors were obtained for sinkage and wetted area, about 42%D and 31%D, respectively. Some preliminary calm water comparisons between experiment and simulation based on the experiments presented in this paper have shown difficulties in predicting planing behaviors at high speeds, specifically with under-prediction of the trim angles. Fu et al. [32] presented comparisons of experiment and simulations for a 4-foot planing model operating in calm water and waves. The calm water comparisons showed the trim being under-predicted. Mousaviraad et al. [33] presented preliminary studies for the current project which investigated hydrodynamic performance on high-speed planing hulls in calm water

Planing Hull (GPPH). The GPPH was chosen to facilitate public release of experimental results for validation of computational tools. GPPH was tested at two different facilities and at two different model scales. This testing was conducted in both calm water and waves. This part of our paper presents the comparisons between experiments and simulations for calm water. The comparisons between experiments and simulations for slamming in waves is covered in Part II. There have been some studies comparing simulation predictions with experimental measurements of planing hulls operating in calm water. Pennino et al. [28] performed calm water towing tank experiments and CFD simulations using STAR-CCM+ with about 1.5M grid points for a motor yacht geometry. He observed an under-prediction of resistance, sinkage, and trim with average error values of about 10% of the data value (D), 35%D, and 20%D, respectively. Sukas et al. [29] also performed calm water towing tank experiments and CFD simulations using STAR-CCM+. He used up to 7.5M grid points for the planing hull and provided qualitative comparisons. The trim was underpredicted at high speeds, while the resistance and sinkage were closer to the experimental results. Broglia and Durante [30] performed CFD verification and validation (V&V) studies for resistance, sinkage, and trim of the Grande 95RPH, a 22.5-m luxury yacht using an in-house single-phase level-set URANS solver with about 18M grid points. For sinkage and trim, the error values were as large as about 15%D at speeds close to Fr = 1.0, and were mostly larger than simulation numerical uncertainty (USN) values. The error values for resistance were mostly within USN. Overall, the average error values were about 9%D

Table 1 Characteristics for GPPH geometry. Length overall, m (ft) Max. beam, m (ft) Displacement, metric tons (lbs) LCG (forward of transom), m (ft) KG (above baseline), m (ft) Deadrise Zero speed trim

2

13.0 (42.8) 4.0 (12.84) 15.9 (35,000) 4.6 (15.1) 1.5 (4.8) 18° 0°

Applied Ocean Research 96 (2020) 102060

C. Judge, et al.

system, either fixed to a ship or other frame moving at constant-speed or in the earth system. The rigid body equations are solved in the ship system. STAR-CCM+ is a Reynolds-Averaged Navier Stokes (RANS) solver that is capable of modeling irregular seas, as well as regular sinusoidal waves. It has a robust meshing tool which needs little user interaction, and a volume of fluid (VOF) solver, which is useful for wave impact and fluid structure interactions. The VOF approach assumes that the grid cells near the free surface are filled with both air and water, and within each grid cell the VOF, pressure, velocity, and gravitational force acting on the fluid is calculated. The ocean waves and the free surface are tracked by using the VOF values in the domain. The experiment and simulation comparisons were done for a planing hull operating in calm water, in regular waves, and in irregular waves. The calm water results are presented in this part of the paper. The slamming results from the regular and irregular waves are presented in Part II. All experiments and simulations were done using a representative deep-V planing hull with a realistic bow shape. The geometry was designed at NSWCCD and was designated the GPPH [36]. Table 1 shows the general characteristics of the full-scale GPPH geometry and Fig. 1 shows the body plan and profile views of the geometry. Two scale-models were constructed from this geometry. The “small” model had a length of 1.22 m (4.0 ft) with a scale factor of 10.7. The “large” model had a length of 2.41 m (7.92 ft) with a scale factor of 5.4.

Fig. 1. GPPH body plan and profile view.

and waves for both deep and shallow water conditions. The CFD code in this paper has been used for predictions of the calm water performance of a semi-planing model with good agreement [34–35]. Lee et al. [36] provided preliminary calm water results for this CFD code on the experimental measurements of an 8-foot planing craft model. The objective of the collaborative effort presented here is to improve the physical understanding of, as well as assess the CFD capability for, deep-V planing hulls operating in calm water and slamming when running in head waves (both regular and irregular). The experiments presented were conducted at the United States Naval Academy (USNA) and the Naval Surface Warfare Center – Carderock (NSWCCD) facilities. The simulations using CFDShip-Iowa were conducted at the University of Iowa and the simulations using STAR-CCM+ were conducted at NSWCCD. This work assesses the state of the art of both experimental measurements and CFD by including careful experiments with two model sizes, conducted at two facilities, and comparisons with two CFD codes, one commercial and one developed in-house. Using multiple facilities and codes provides a more robust study of the current capability of experimental measurements and predictions of the performance of high-speed planing hulls. The investigations included careful comparisons on experimental set-up conditions for testing different model sizes as well as differences for the same model tested at different experimental facilities. The comparisons include both the experimental and the simulation uncertainties. The overall results provide an assessment of the state of the art for both experiments and CFD for high-speed deep-V planing hull resistance, sinkage, and trim. Both CFDShip-Iowa and STAR-CCM+ were used to predict the calm water performance on the GPPH models. The single-phase level-set solver CFDShip-Iowa V4.5 is an incompressible Unsteady ReynoldsAveraged Navier-Stokes (URANS) solver designed for ship hydrodynamics [35]. Single-phase level-set approach is used for the freesurface, blended k-ε/k-ω for the turbulence model and curvilinear dynamic overset grids for 6DOF ship motions. Incompressibility is enforced by a strong pressure/velocity coupling, achieved using either Pressure Implicit with Splitting of Operator (PISO) or projection algorithms. The fluid flow equations are solved in an inertial coordinate

2. Calm water experiments Calm water experiments were conducted at both USNA and NSWCCD. The USNA tow tank is a 115.08 m (380 ft) long, 7.9 m (26 ft) wide, and 4.9 m (16 ft) deep tank. There is a beach at one end of the tank for absorbing the wave energy. The ratio of the length of model to USNA tank length is 0.01 for the small model and 0.02 for the large model. The NSWCCD tow tank has a constant width of 6.4 m (21 ft) with an overall length of 870.5 m (2856 ft). The tank has a depth of 3.05 m (10 ft) over 356 m (1169 ft) and a depth of 4.9 m (16 ft) over 514.2 m (1687 ft). The ratio of the length of model to NSWCCD tank length is 0.003 for the large model. The cross sections of the two facility tanks is 38.71 m2 (416 ft2) for the USNA tank and 31.36 m2 (336 ft2) in the deep section and 19.52 m2 (210 ft2) in the shallower section for the NSWCCD tank. The minimum basin blockage coefficient for the NSWCCD was 243, which is greater than the minimum recommended value of 200. Table 2 lists each calm water experiment, along with the variables measured, speed range, and the size model tested. The small model was tested at USNA in August 2013 (D1) and again in December 2016 (D2). The large model was tested at USNA in May 2014 (D3) and again in January 2017 (D4). The large model was also tested at NSWCCD in March (D5) and November of 2015 (D6). The calm water running trim (τ) and sinkage (σ) were measured in all tests. Resistance (R) was measured in all tests except at USNA in August 2013 (D1) and May 2014 (D3), while keel wetted length was only recorded for the November 2015 test run at NSWCCD (D6). All measurements for calm water (sinkage, trim, and resistance) were made at the LCG of the model. The USNA data was sampled at 5 kHz and the NSWCCD was

Table 2 Summary of calm water experimental studies. Test No.

Facility

Date

Model size

D1 D2 D3 D4 D5 D6

USNA USNA USNA USNA NSWCCD NSWCCD

August 2013 December 2016 May 2014 January 2017 March 2015 November 2015

Small Small Large Large Large Large

3

(1.22 (1.22 (2.41 (2.41 (2.41 (2.41

m) m) m) m) m) m)

Variables measured

Speed range (Fn)

σ, σ, σ, σ, σ, σ,

1.37–1.84 1.37–2.38 1.37–1.84 1.32–1.85 1.14–2.50 1.14–2.51

τ τ, τ τ, τ, τ,

R R R R, LWK

Applied Ocean Research 96 (2020) 102060

C. Judge, et al.

Table 3 Experimental set-up conditions.

Draft, cm (in) Displacement, metric tons (lbs) LCG (forward of transom), cm (in) VCG (above baseline), cm (in) LTP* (forward of transom), cm (in) VTP* (above baseline), cm (in) Trim (τs), deg Pitch gyradius (ky), cm (in) ⁎

USNA – Small (D1 & D2)

USNA – Large (D3 & D4)

NSWCCD – Large (D5)

NSWCCD – Large (D6)

7.21 (2.84) 0.013 (27.9) 42.98 (16.92) 13.72 (5.4) 42.98 (16.92) 13.72 (5.4) 0 27.13 (10.68)

14.63 0.101 85.95 12.80 85.95 12.80 0 54.86

NA 0.101 85.88 13.46 85.95 14.60 NA 44.93

NA 0.102 84.39 13.79 85.96 14.60 NA 45.42

(5.76) (223.2) (33.84) (5.04) (33.84) (5.04) (21.6)

(223.2) (33.81) (5.3) (33.84) (5.75) (17.69)

(223.8) (33.225) (5.43) (33.844) (5.75) (17.88)

TP stands for tow point

Judge et al. [37]. The standard deviation for the USNA mean calm water trim measurements was 0.59% of the mean value for the small model and 0.21% for the large model. The standard deviation for the USNA mean calm water sinkage was 0.50% of the mean value for the small model and 0.47% for the large model. The standard deviation percentage for the USNA mean calm water resistance was smaller than either the trim or sinkage uncertainty. Likewise, the uncertainty measurements for the NSWCCD measurements were smaller than the USNA results. The results from the first set of calm water tests for the small (D1) and large (D3) models (shown in Table 4) show that the trends match well for sinkage and trim. While the sinkage results show reasonably good agreement, the trim shows a definite offset. This can also be seen in Fig. 2. The follow-up experiments were done with extremely careful trim measurements over a wider range of speeds. The results for the comparisons are shown in Table 5 and in Figs. 2 and 3. The sinkage and resistance results show good agreement between the two model scales. However, even under much more carefully conducted conditions, the trim shows a definite offset. In both sets of experiments, the small model is running at a higher trim compared with the large model at the same Froude number. The likely causes for the apparent scale-effect on trim relate to differences in the hull geometry (differences in transom/ hull bottom curvature, for example) and precision of ballast and tow point. Sensitivity studies done using CFDShip-Iowa, and discussed further below, show that small differences in these factors can have significant effects on the running trim. The large model was tested at both USNA and NSWCCD. The calm water comparison of the results are shown in Tables 6 and 7 and shown in Figs. 4 and 5. For the tests that were repeated at each facility (D3/D4 at USNA and D5/D6 at NSWCCD), the correlation, RMSE, and AAM all show very good agreement. The correlation (r2) and AAM are very close to one for all repeated experiments. The RMSE is small for sinkage and trim and less than 2.0 for resistance at NSWCCD (D5 and D6). There is overall very good agreement on the trends between the two facilities. The maximum percent differences of the measurements between the two facilities (i.e., Max %Difftrim = |trimD6 – trimD4|/trimD6*100%) range

Table 4 Nondimensional sinkage and trim comparison between Initial USNA experiments for small (D1) and large (D3) model calm water results. Fn (V/√(gL)

σ/L USNA (D1)

1.37 1.58 1.84 r2 RMSE AAM Max %Diff

0.032 0.036 0.040 1.000 0.002 0.975 7.2%

USNA (D3) 0.032 0.035 0.037

τ (deg) USNA (D1) 6.23 5.76 5.36 0.992 1.022 0.881 33.2%

USNA (D3) 5.49 4.86 4.02

sampled at 25 kHz. Although the same large model was tested at USNA and NSWCCD, differences in the towing set-ups resulted in some differences in the configurations. Table 3 shows the differences in set-up from the experiments. For calm water, the measurements (resistance, sinkage, trim, and wetted keel length) were averaged across all tests runs for each test condition. Total uncertainty values (UD) were derived from the experimental precision uncertainty and the estimated bias uncertainty and the complete description of the method can be found in Lee et al. [36].

2.1. Experimental result comparisons Both the small and large models were tested at USNA to investigate possible scale effects. The calm water comparison results are shown in Tables 4 and 5 and in Figs. 2 and 3. In addition to the experimental results, Figs. 2 and 3 show the initial CFDShip-Iowa predictions for the small model. These results will be discussed in the Simulation Result Comparisons section below. The initial experiments (D1 and D3) indicated a possible scale effect for trim, so the second set of tests (D2 and D4) were conducted to more closely investigate the trim measurement. The complete calm water trim measurement analysis is presented in

Table 5 Nondimensional sinkage, trim, and nondimensional resistance comparison between second set of USNA experiments for small (D2) and large (D4) model calm water results. σ/L

Fn (V/√(gL)

1.33 1.50 1.68 1.84 r2 RMSE AAM Max %Diff

τ (deg)

R/Δ

USNA (D2)

USNA (D4)

USNA (D2)

USNA (D4)

USNA (D2)

USNA (D4)

0.033 0.036 0.037 0.039 0.989 0.002 0.958 9.0%

0.030 0.033 0.035 0.036

6.05 5.40 4.87 4.44 0.999 0.745 0.899 21.0%

5.30 4.69 4.12 3.67

0.168 0.172 0.188 0.204 0.995 0.005 0.982 3.6%

0.166 0.172 0.182 0.198

4

Applied Ocean Research 96 (2020) 102060

C. Judge, et al.

Fig. 2. Nondimensional Sinkage and Trim comparison between USNA Experiments (D1, D2, D3, & D4) and includes CFDShip-Iowa predictions using the 4ft IG1 and 8ft IG2 hydrostatic set ups (see Table 8). Table 7 Nondimensional resistance comparison between USNA and NSWCCD for calm water large model results. Fn (V/√(gL)

Resistance/Displacement USNA (D4)

1.37 0.166 1.58 0.172 1.84 0.198 r2 RMSE AAM Max %Diff USNA (D4) and NSWCCD (D6) r2 0.998 RMSE 0.009 AAM 0.971 Max %Diff 6.7%

Fig. 3. Nondimensional Resistance comparison between USNA Experiments (D2 & D4) and includes CFDShip-Iowa predictions using the 4ft IG1 and 8ft IG2 hydrostatic set ups (see Table 8).

NSWCCD (D5)

NSWCCD (D6)

0.160 0.172 0.193 0.995 0.007 0.972 5.4%

0.160 0.166 0.185

from 6.7% for the resistance measurement to 11.1% for the trim value. equation is solved with the PETSc toolkit using block Jacobi incomplete factorization (ILU) pre-conditioners and bi-conjugate gradients stabilized (BiCGStab). All equations of motion are solved in a sequential form and iterated to achieve convergence within each time step. The Cartesian background grid extends to −0.5 < x/L < 4; 0.0 < y/L < 2.73 (symmetry); and −1.17 < z/L < 0.44. The boundary layer grid is designed to achieve y+ < 1 for all simulation conditions. A symmetry boundary condition is used at the ship centerline (y = 0.0), far-field at the side, bottom, and top boundaries, and exit at the outflow. At the inflow boundary, constant velocity and pressure are prescribed for calm water simulations.

3. Calm water simulations 3.1. CFDShip-Iowa The single-phase level-set solver CFDShip-Iowa V4.5 is an incompressible URANS/DES solver designed for ship hydrodynamics [38]. The numerical methods include finite difference discretization, with a second-order upwind scheme for the convection terms and second-order centered for the viscous terms. The temporal terms are discretized using a second-order backwards Euler scheme. Since the solver is designed for high-Reynolds number flows, the transport and reinitialization equations are weakly elliptical and thus pentadiagonal line solvers in an alternate-direction implicit (ADI) scheme are used. A MPI-based domain decomposition approach is used, where each decomposed block is mapped to one processor. The resulting algebraic

3.2. STAR-CCM ± STAR-CCM+ v11.06 has a VOF solver and incompressible URANS

Table 6 Nondimensional sinkage and trim comparison between USNA and NSWCCD for calm water large model results. σ/L

Fn (V/√(gL) USNA (D3) 1.37 1.58 1.84 r2 RMSE AAM Max %Diff r2 RMSE AAM Max %Diff

USNA (D4)

0.032 0.030 0.035 0.033 0.037 0.036 0.999 0.002 0.965 6.3% USNA (D4) and NSWCCD (D6) 0.990 0.003 0.956 10.9%

τ (deg)

NSWCCD (D5)

NSWCCD (D6)

USNA (D3)

USNA (D4)

NSWCCD (D5)

NSWCCD (D6)

0.032 0.034 0.037 0.971 0.001 0.972 6.5%

0.034 0.035 0.038

5.50 4.86 4.03 0.998 0.257 0.967 3.8%

5.30 4.69 3.67

5.05 4.35 3.53 1.00 0.037 0.994 0.8%

4.88 4.22 3.42

0.996 0.391 0.945 11.1%

5

Applied Ocean Research 96 (2020) 102060

C. Judge, et al.

Fig. 4. Nondimensional Sinkage and Trim comparison between USNA (D3 & D4) and NSWCCD (D5 & D6) results.

than originally intended and the curvature of the transom radius was found to be important in the trim prediction. The effect of the size difference for the large model was found to be about 9% data range (DR) for the resistance, 15%DR for the sinkage, and 36%DR for the trim results. The difference in the transom curvature was found to effect the resistance by less than 1%DR, the sinkage by about 5%DR, and the trim by about 2%DR. Identifying these differences resulted in several geometry files being created. The small model was built to the intended scale factor and the curvature of the transom radius was very small, so the original IGES file was used for simulation (IG1). However, the large model geometry file was modified to account for the proper sizing (IG2) and then also the curvature where the transom met the hull bottom (IG3). The geometry files used for the different models are shown in Table 8. Investigations into the experimental hydrostatic-setup were carried out using CFDShip-Iowa because the hydrostatic conditions (draft and trim) were not measured for all of the experiments and the computations showed that, with the provided displacement and LCG, the model would have a non-zero static trim angle. When the simulation set-up used displacement and LCG, rather than displacement and assumed zero static trim angle, the running trim angle measurements had better agreement, while little change was noted for resistance and running sinkage. The sensitivity study showed changes in the hydrostatic-setup had errors of about 2%DR for sinkage and resistance, but 6.5%DR for the running trim prediction. It was determined that slight changes in hydrostatic set-up conditions have significant effects at high Froude numbers and accurate static measurements are needed to decrease uncertainty in predicted results. Table 8 shows the simulation conditions used for the validation studies. The IG1 geometry was used for all CFDShip-Iowa comparisons with the Small model (tested at USNA – D1 and D2). The IG2 geometry was used for the CFDShip-Iowa grid verification studies (compared with the Large model results from NSWCCD – D6). The IG3 geometry was used for the calm water validation studies comparing predictions (both CFDShip-Iowa and STAR-CCM+) with the large model results from NSWCCD (D6). The results of the simulation sensitivity studies shows the importance of using precise geometric and hydrostatic information for simulation predictions. Experimental investigations must report model dimensions and hydrostatic set-up conditions as accurately as possible, along with the best uncertainty estimates available. Based on the results of the simulations for the initial USNA calm water results comparing the trim measurements for the large and small

Fig. 5. Nondimensional Resistance comparison between USNA (D4) and NSWCCD (D5 & D6) results

solver. The numerical methods include a finite volume (FV) discretization, with a second-order upstream scheme for the convection terms and a second-order centered for the viscous terms. The temporal terms are discretized using a second-order backwards Euler scheme. The trimmed mesh background grid extends to −2 < x/L < 6; 0.0 < y/2 < 2.8 (symmetry); and −2.8 < z/L > 0.4. The boundary layer grid is designed to achieve y+ > 30 with the wall function for all simulation conditions. A symmetry boundary condition is used at the ship centerline (y = 0.0). There is no slip condition for the far-field at the side, the bottom boundary to represent the two tank walls and the top boundary is set to be constant speed. A zero gradient condition is applied to the outlet boundary with a hydrostatic pressure distribution. At the inlet flow boundary, constant velocity and hydrostatic pressure are described for calm water simulations. The overset grid topology is used to manage large ship motions and the mesh size is about 12 million cells. 3.3. Simulation comparisons Trim, sinkage and resistance for both models operating in calm water were simulated with CFDShip-Iowa, while STAR-CCM+ predicted these variables only for the large model. Initial simulation investigations considered both simulation (grid size, time step sensitivity) and experimental (LCG, displacement, zero trim) set-up aspects to determine the most critical elements. During this process the large model was discovered to have been built to a slightly different scale factor Table 8 Summary of CFD setup conditions for calm water simulations. Geometry File

Model Size

Hydrostatic Setup Condition

BL Grid Design

Grid Size

No. of Grid Points

IG1 IG2 IG3

Small Large Large (with transom curvature)

Set by Δ and τs=0° Set by Δ and LCG Set by Δ and LCG

Single-block Overset with Local Refinement Overset with Global Refinement

Very Coarse Medium Medium

7.1M 22.9M 21.5M

6

Applied Ocean Research 96 (2020) 102060

C. Judge, et al.

Table 9 Nondimensional sinkage and trim comparisons between USNA and CFDShip-Iowa (IG1) for calm water small model results σ/L

Fn (V/√(gL)

1.37 1.60 1.84 r2 RMSE AAM Max %Diff

τ (deg)

USNA (D1)

CFDShip-Iowa

USNA (D1)

CFDShip-Iowa

USNA (D1)

CFDShip-Iowa

0.033 0.036 0.039 0.961 0.010 0.810 39.3%

0.024 0.027 0.028

6.23 5.76 5.36 0.999 2.620 0.665 106.2%

3.80 3.10 2.60

-

0.147 0.161 0.179

Table 10a Resistance calm water validation studies (comparing with NSWCCD – D6 and using IG3 with 21.5M grid points) for all speeds. Fn

1.14 1.37 1.56 1.84 2.05 2.27 2.50 Average

R/Δ

CFDShip-Iowa

Table 10d Wetted keel length calm water validation studies (comparing with NSWCCD – D6 and using IG3 with 21.5M grid points) for all speeds.

STAR-CCM+

UD %DR

USN %DR

UD/USN

UV %DR

E %DR

E %DR

0.26 0.23 0.22 0.25 0.23 0.30 0.32 0.26

0.17 0.31 0.42 1.10 3.89 5.54 6.10 2.51

1.47 0.72 0.52 0.23 0.06 0.05 0.05 0.44

0.31 0.39 0.47 1.13 3.89 5.55 6.11 2.55

0.61 0.81 1.61 3.22 5.21 7.24 9.72 4.06

3.78 3.53 3.59 2.74 2.42 1.04 1.37 2.64

Fn

1.14 1.37 1.56 1.84 2.05 2.27 2.50 Average

CFDShip-Iowa UD %DR

USN %DR

UD/USN

UV %DR

E %DR

0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21

0.21 0.05 0.08 0.24 0.38 0.38 0.48 0.26

1.00 4.01 2.64 0.87 0.55 0.54 0.43 1.43

0.29 0.21 0.22 0.31 0.43 0.43 0.53 0.35

−0.35 −0.92 −0.86 −1.27 −0.96 −1.04 −0.98 0.91

The bold numbers indicate the test conditions (each Fn speed) and the summary information for each variable for all test conditions.

The bold numbers indicate the test conditions (each Fn speed) and the summary information for each variable for all test conditions.

Table 10b Sinkage calm water validation studies (comparing with NSWCCD – D6 and using IG3 with 21.5M grid points) for all speeds.

models (D1 and D3), CFDShip-Iowa conducted an investigation of scale effect. The results for sinkage, trim, and resistance for both the Small and Large simulations are shown in Figs. 2 and 3. The scale effects for sinkage and resistance were found to be about 3%DR for resistance and 1%DR for sinkage. Trim showed slightly more sensitivity at about 6% DR, but this is still small relative to the differences seen in the USNA experiments (about 17%DR for the experiments). The cause for the differences in trim for the two model sizes has not been definitively identified, but the difficulties of accurate and precise experiments increase as the model size reduces. Having demonstrated the sensitivity of the simulation results to hydrostatic conditions, there may have been differences in set-up between the large and small models that were too small for the instrumentation available to identify, yet had an effect on the running trim. It was also found that there were small geometric differences between the two models (within the accuracy of the manufacturing process), and that could also help explain the trim differences for the two models. The CFDShip-Iowa verification studies follow the detailed procedures explained in Xing and Stern [39]. The grid study used IG2 with 2 refinement ratio and coarse (12.1M), medium (22.9M) and fine (44.4M) grid sizes. The iterative uncertainty (UI) values are much smaller than grid uncertainty (UG) values such that simulation numerical uncertainty (USN = UI2 + UG2 ) values are close to UG. Monotonic convergence is obtained for all variables and at all speeds with P values (ratio of Richard extrapolation and theoretical order accuracies) close to 1.0. CFDShip-Iowa simulated the sinkage, trim, and resistance based on the experimental conditions for the small model at USNA (D1). Table 9 shows the comparison of sinkage and trim between the experimental results (D1) and the simulations predictions from CFDShip-Iowa. The results can also be seen in Figs. 2 and 3. The trends for the predictions match the experimental data for all measurements, including resistance (see Fig. 3). Since the simulation results were done for the initial USNA small model calm water tests (D1) and the only resistance data collected for the small model was from the later small model calm water tests (D2), there is not a direct comparison between the experiment and simulation for resistance. However, Fig. 3 shows the trend matches well

Fn

1.14 1.37 1.56 1.84 2.05 2.27 2.50 Average

CFDShip-Iowa

STAR-CCM+

UD %DR

USN %DR

UD/USN

UV %DR

E %DR

E %DR

1.69 0.96 0.92 0.88 1.17 1.03 0.75 1.06

0.40 0.06 0.11 0.06 0.13 0.51 0.59 0.27

4.23 15.22 8.38 13.85 9.16 2.02 1.27 7.73

1.74 0.96 0.93 0.88 1.18 1.15 0.96 1.11

9.76 4.26 0.88 0.51 −0.23 −0.46 −0.95 2.44

12.65 4.10 0.77 1.35 0.82 0.66 0.37 2.96

The bold numbers indicate the test conditions (each Fn speed) and the summary information for each variable for all test conditions. Table 10c Trim calm water validation studies (comparing with NSWCCD – D6 and using IG3 with 21.5M grid points) for all speeds. Fn

1.14 1.37 1.56 1.84 2.05 2.27 2.50 Average

CFDShip-Iowa

STAR-CCM+

UD %DR

USN %DR

UD/USN

UV %DR

E %DR

E %DR

0.14 0.29 0.08 0.16 0.14 0.27 0.16 0.18

0.20 0.83 0.88 0.72 0.71 1.01 0.94 0.76

0.68 0.35 0.09 0.22 0.20 0.27 0.17 0.28

0.24 0.88 0.89 0.74 0.72 1.04 0.96 0.78

2.22 1.95 1.59 1.15 0.68 −0.28 −1.40 1.32

4.43 5.08 5.01 4.06 3.35 3.62 0.75 3.76

The bold numbers indicate the test conditions (each Fn speed) and the summary information for each variable for all test conditions.

7

Applied Ocean Research 96 (2020) 102060

C. Judge, et al.

Fig. 6. CFDShip and STAR-CCM+ (IG3) calm water verification and validation studies.

NSWCCD – D6, was chosen for the calm water validation efforts. Tables 10a-10d summarizes the CFDShip-Iowa calm water validation studies. For resistance, the data uncertainty, UD, values are nearly constant and about 0.3%DR. The USN values range from 0.2 at the low speed to 6% DR at the highest speed. For sinkage, trim, and wetted keel length the UD and USN values are about the same order of magnitude and nearly constant over the speed range. For sinkage, average UD and USN are about 1 and 0.2%DR, respectively, with average UD/USN of about 8. For trim, average UD and USN are about 0.2 and 0.8%DR, respectively, with average UD/USN of about 0.3. For wetted keel length, average UD and USN are about 0.2 and 0.3%DR, respectively, with average UD/USN of

and the simulation values match the experimental measurements for resistance much better than for sinkage and trim. Table 9 shows that the correlation (a comparison of the data trend) is strong for both sinkage (r2 = 0.961) and trim (r2 = 0.999). However, the RMSE and AAM show a difference between the data sets, one that is particularly strong for trim. For the trim measurement at the highest speed, the difference between the experimental and simulation values is on the same order as the measurement itself (106.2%). Going back to the sensitivity analyses discussed above, the likely sources of these differences relate to differences in geometry and hydrostatic set up (see Table 8). Based on the facility results presented above, a single experiment, 8

Applied Ocean Research 96 (2020) 102060

C. Judge, et al.

Table 11 Summary of calm water validation studies. Average (in %DR) NSWCCD D6

R σ τ LWK

CFDShip-Iowa

UD

USN

UD/USN

UV

r2

RMSE

AAM

r2

RMSE

AAM

0.26 1.06 0.18 0.21

2.51 0.27 0.76 0.26

0.44 7.73 0.28 1.43

2.55 1.11 0.78 0.35

0.999 0.988 0.999 -

0.67 0.23 0.11 -

0.96 0.98 0.99 -

0.999 0.967 0.998 -

2.21 0.29 0.28 -

0.98 0.98 0.96 -

about 1.4. Fig. 6 shows resistance, sinkage, trim and keel wetted length results from the NSWCCD experimental results (D6), with UD bars, and CFDShip-Iowa simulation results, with USN bars. Simulation results from STAR-CCM+ are also shown. Fig. 6 also shows the validation uncertainty, UV, compared to the simulation errors (E). For resistance, the maximum UV values are 1, 0.8, and 0.3%DR for sinkage, trim, and wetted keel, respectively. For resistance, validation is not achieved for the CFDShip-Iowa simulations, while for STAR-CCM+ the E values are within the UV bounds for the three highest speeds. The average resistance errors are 4 and 2.6%DR for CFDShip-Iowa and STAR-CCM+, respectively. For sinkage, both codes are not validated at the two lowest

Table 12 Calm shallow water with fixed sinkage and trim simulation conditions for USNA and Fridsma

USNA Fridsma

STAR-CCM+

Fn

Cv2

τ

λ

z′

1 z ′ + sin τ

0.124 + 0.116 λ z ′ + sin τ

h/L

Fnh

1.19 1.12

5.0 5.0

4.0 4.0

2.19 2.80

0.97 0.97

0.96 0.98

0.166 0.159

0.33 0.30

2.06 2.17

Fig. 7. Calm shallow water with fixed sinkage and trim at τ = 4° results and comparison with previous Fridsma simulations and empirical correlations 9

Applied Ocean Research 96 (2020) 102060

C. Judge, et al.

experimental comparisons of model scale, two experimental testing facilities were used to investigate facility effects. Overall, there was general agreement between the facilities, even for the calm water trim measurement. The CFD prediction trends match the experimental data for all measurements, including both models and at both facilities, including the calm water resistance. The small model predictions had better results for the sinkage and resistance than for the trim. The CFDShip-Iowa and STAR-CCM+ calm water validation effort was conducted with the larger model results from NSWCCD. Validation was not achieved for resistance; however, Fn average error was less than 4%DR. In sinkage, both codes were validated at the highest three speeds, but not at the lowest speeds (Fn average error was less than 3%DR). For trim and wetted keel, validation was not achieved, although the validation uncertainty values were small (Fn average error was less than 4%DR). Both codes under-predicted the calm water trim and the wetted keel length was under-predicted for all but the lowest speed (with Fn averaged error less than 1%DR). The under-prediction of both trim and wetted length suggest that increased resolution of the spray root and, possibly, the transom corner is required. High-speed model testing is difficult due in part to small model sizes as well as large forces and moments sometimes related to mount rigidity and motion measurement issues. In addition, small details of geometry, along with mass properties and hydrostatic condition have large effect especially on running trim since the trim is often very small and sensitive to such effects. The overall results provide an assessment of the state of the art for both experiments and CFD for high-speed deep-V planing hull resistance, sinkage, and trim. Future testing should carefully consider these issues and use free to surge mounts or, even more recommended, free running models. The comparison of experimental and simulation results for slamming in both regular and irregular waves is presented in Part II of this paper.

speeds, and are validated at the three highest speeds. This issue with the sinkage values at the lowest speeds is consistent with the discrepancies in the experimental data over the same speed range. The average sinkage errors are 2.4 and 3%DR for CFDShip-Iowa and STAR-CCM+, respectively. For trim and wetted keel, validation is not achieved as the validation uncertainty values are small. For trim, the average error values are 1.3 and 3.8%DR for CFDShip-Iowa and STAR-CCM+, respectively. Both solutions under-predict the trim. For wetted keel, the average error value is 0.9%DR for CFDShip-Iowa; although the average error %DR is small, the wetted keel length is under-predicted for all but the lowest speed. The under-prediction of both trim and wetted length suggest that increased resolution of the spray root and, possibly, the transom corner is required. The wetted keel measurement was not evaluated using STAR-CCM+. Table 11 shows the experimental and computational values for resistance, trim, and sinkage. In general, the r2 and AAM values between the experimental and prediction results made by CFDShip-Iowa and STAR-CCM+ are very good (close to 1). The RMSE values are larger than the experimental uncertainty for CFDShip-Iowa and STAR-CCM+. In addition to the calm water simulations for the experiments conducted at USNA and NSWCCD, CFDShip-Iowa also simulated the GPPH under planing conditions in shallow water with fixed sinkage and trim. The effect of water depth on the hydrodynamic lift (CL), the drag (CD), and moment (Cm) were compared with Reyling [40] and Mousaviraad et al. [33]. The simulation and prediction based on Reyling and Fridsma results matched well. 3.4. Shallow water simulations Simulations using CFDShip-Iowa were done with fixed sinkage and trim for calm shallow water performance and the results were compared with both Fridsma [3] and USNA experimental measurements. The calm shallow water with fixed sinkage and trim simulation conditions are summarized Table 12. Fig. 7 compares the ratios of shallow water to deep water results with empirical correlations from Reyling [40]. The results for both the current USNA and the previous Fridsma [3] planing hull geometries collapse into linear correlations with good agreement.

CRediT authorship contribution statement Carolyn Judge: Conceptualization, Methodology, Investigation, Funding acquisition, Visualization, Writing - original draft. Maysam Mousaviraad: Methodology, Software, Validation, Formal analysis, Data curation, Visualization, Writing - review & editing. Frederick Stern: Conceptualization, Methodology, Software, Validation, Supervision, Funding acquisition, Project administration, Writing - review & editing. Evan Lee: Funding acquisition, Project administration, Supervision, Formal analysis, Writing - review & editing, Methodology. Anne Fullerton: Investigation, Project administration. Jayson Geiser: Investigation. Christine Schleicher: Conceptualization. Craig Merrill: Conceptualization. Charles Weil: Investigation, Writing - review & editing. Jason Morin: Investigation. Minyee Jiang: Investigation, Software, Writing - review & editing. Christine Ikeda: Investigation, Validation.

4. Conclusions This paper presents the results of a collaborative effort to improve the physical understanding of deep-V planing hulls operating in calm water when running in head seas as well as assess the current CFD capability for predicting the performance under such conditions. Previous studies showed difficulties with predicting the calm water running trim. This part of the paper presents the results of comparisons between two CFD codes (STAR-CCM+ and CFDShip-Iowa) with planing hull experiments in calm water. Comparisons between the experiment and simulation showed the sensitivity of a performance (particularly trim and wetted length) of a deep-V planing hull to hydrostatic set-up conditions and hull geometry. The experimental results for calm water running trim did not agree for the two scale-model sizes. The experimental measurements did agree for sinkage and resistance between the two models. The CFD results showed a slight scale effect for trim, although not enough to account for the differences found in the experimental data. CFD sensitivity studies showed that small differences in the hull geometry, ballasting conditions, and tow point location can have significant effects on the running trim. These results emphasize the importance of using precise geometric and hydrostatic information for use in simulation predictions. The comparisons documented in this paper emphasize the importance of using precise geometric and hydrostatic information for simulation prediction. Experimental investigations must report model dimensions and hydrostatic set-up conditions as accurately as possible and include the best uncertainty estimates available. In addition to

Declaration of Competing Interest None. Acknowledgments This work was supported by the Office of Naval Research (grant number N000141612747, University of Iowa; grant number N0001414WX00537, Carderock; United States Naval Academy), administered by Dr. Robert Brizzolara. References [1] ABS., Rules for Building and Classing High-Speed Craft, American Bureau of Shipping Houston, Houston, TX, 2016.

10

Applied Ocean Research 96 (2020) 102060

C. Judge, et al.

from slamming of small craft, J. Ship Prod. Design 28 (3) (August 2012) 112–127. [24] R. Allen, R. Jones, A simplified method for determining structural design-limit pressures on high performance marine vehicles, Proceedings of the Advanced Marine Vehicles Conference, San Diego, California, April 1978. [25] M. Hoggard, M. Jones, Examining pitch, heave, and accelerations of planing craft operating in a seaway, Proceedings of the High-Speed Surface Craft Exhibition and Conference, Brighton, U.K., June 1980. [26] J. Koelbel, Comments on the structural design of high speed craft, Mar. Technol. 32 (2) (April 1995) 77–100. [27] D. Allen, D. Taunton, R. Allen, A study of shock impacts and vibration dose values onboard high speed marine craft, Int. J. Maritime Eng. 118 (2008) 1–14 150, paper. [28] S. Pennino, H. Klymenko, A. Scamardella, S. Mancini, and E. Begovic, ThreeDimensional Pressure Distribution on Planing Hulls: Proceedings of the 3rd International Conference on Maritime Technology and Engineering (MARTECH 2016, Lisbon, Portugal, 4-6 July 2016), p. 353-360. [29] O.F. Sukas, O.K. Kinaci, F. Cakici, M.K. Gokce, Hydrodynamic assessment of planing hulls using overset grids, Appl. Ocean Res. 65 (April 2017) 35–46 https://doi.org/ 10.1016/j.apor.2017.03.015. [30] R. Broglia, D. Durante, Accurate prediction of complex free surface flow around a high-speed craft using a single-phase level set method, Comput. Mech. 62 (September (3)) (2018) 421–437 https://doi.org/10.1007/s00466-017-1505-1. [31] A. De Marco, A. Mancini, A. Miranda, R. Scognamiglio, L. Vitiello, Experimental and numerical hydrodynamic analysis of a stepped planing hull, Appl. Ocean Res. 64 (March) (2017) 135–154 https://doi.org/10.1016/j.apor.2017.02.004. [32] T.C. Fu, K.A. Brucker, M. Mousaviraad, C.M. Ikeda, E.J. Lee, T.T. O'Shea, Z. Wang, F. Stern, C.Q. Judge, An assessment of computational fluid dynamics predictions of the hydrodynamics of high-speed planing craft in calm water and waves, Proceedings of 30th Symposium on Naval Hydrodynamics, Hobart, Tasmania, Australia, November 2014 2-7. [33] M. Mousaviraad, Z. Wang, F. Stern, URANS studies of hydrodynamic performance and slamming loads on high-speed planing hulls in calm water and waves for deep and shallow conditions, Appl. Ocean Res. 51 (June 2015) 222–240. [34] E. Lee, A. Fullerton, L. Geiser, C. Schleicher, C. Merrill, C. Weil, M. Jiang, V. Lien, J. Morin, F. Stern, M. Mousaviraad, Experimental and computational comparisons of the R/V athena in calm water, Proceedings of 31st Symposium on Naval Hydrodynamics, Monterey, CA, USA, September 2016 11-16. [35] A.M. Fullerton, C.R. Weil, E.J. Lee, M.J. Jiang, F. Stern, M. Mousaviraad, Assessment of hydrodynamic Tools for R/V Athena Model 5365 in Calm Water, Proceedings of the The 30th American Towing Tank Conference (ATTC), Bethesda, Maryland, October 2017. [36] E.J. Lee, C.C. Schleicher, C.F. Merrill, A.M. Fullerton, J.S. Geiser, C.R. Weil, J.R. Morin, M.J. Jiang, F. Stern, M. Mousaviraad, C.Q. Judge, Benchmark Testing of generic prismatic planing hull (GPPH) for validation of CFD Tools, Proceedings of the 30th American Towing Tank Conference (ATTC), Bethesda, Maryland, October 2017. [37] C. Judge, B. Beaver, J. Zselecsky, An evaluation of planing boat trim measurements, Proceedings of the The 30th American Towing Tank Conference (ATTC), Bethesda, Maryland, October 2017. [38] J. Huang, P. Carrica, F. Stern, Semi-coupled air/water immersed boundary approach for curvilinear dynamic overset grids with application to ship hydrodynamics, Int. J. Numer. Methods Fluids 58 (October (6)) (2008) 591–624. [39] T. Xing, F. Stern, Factors of safety for Richardson extrapolation, J. Fluids Eng. 132 (6) (June 2010) 1–13. [40] C. Reyling, An experimental study of planing surfaces operating in shallow water, Davidson Laboratory Report SIT-DL-76-1835, Hoboken, Stevens Institute of Technology, New Jersey, September 1976.

[2] DNV., Rules for Classification of High-Speed, Light Craft and Naval Surface Craft, Det Norske Veritas, 2013. [3] G. Fridsma, A Systematic Study of The Rough Water Performance of Planing Boats, Davidson Laboratory, Stevens Institute of Technology, November 1969 Technical Report 1275. [4] G. Fridsma, A Systematic Study of the Rough Water Performance of Planing Boats – Irregular Waves – Part Ii, Davidson Laboratory, Stevens Institute of Technology, March 1971 Technical Report 1495. [5] D. Taunton, D. Hudson, R. Shenio, Characteristics of a series of high-speed hard chine planing hulls – Part I: Performance in Calm Water, Trans. R. Instit. Naval Arch. Part B 152 (2010) 55–75. [6] D. Taunton, D. Hudson, R. Shenio, Characteristics of a series of high-speed hard chine planing hulls – Part II: Performance in waves, Trans. R. Instit. Naval Arch. Part B. 153 (2011) 1–22. [7] E. Begovic, C. Bertorello, S. Pennino, V. Piscopo, andA. Scamarfello, Statistical analysis of planing hull motions and accelerations in irregular head sea, Ocean Eng. 112 (January) (2016) 253–264. [8] D. Blount, D. Schleicher, P. Buescher, Seakeeping: An experimental study of accelerations and motions of a high-speed, double-chine craft, Proceedings of the International Symposium on Marine Design, RINA, 2004. [9] M. Riley, T. Coats, A simplified approach for analyzing accelerations induced by wave impacts in high-speed planing craft, Proceedings of the 3rd Chesapeake Power Boat Symposium, June 2012. [10] M. Riley, T. Coats, K. Haupt, D. Jacobson, The characterization of individual wave slam acceleration responses for high speed craft, Proceedings of the 29th American Towing Tank Conference, Annapolis, MD, August 2010. [11] D. Blount, J. Funkhouser, Planing in extreme conditions, Proceedings of the ASNE High Performance Marine Vehicles, November 2009. [12] L. Soletic, Seakeeping of a systematic series of planing hulls, Proceedings of the 2nd Chesapeake Power Boat Symposium, Annapolis, MD, August 2010. [13] P. Brown, W. Klosinski, An Experimental and Theoretical Study of High LengthBeam Ratio Planing Boats in Rough Water, Davidson Laboratory, Stevens Institute of Technology, June 1980 Technical Report SIR-DL-80-9-2133. [14] E. Zarnick, C. Turner, Rough water performance of high length to beam ratio planing boats, David W. Taylor Naval Ship Research and Development Center, December 1981 Technical Report 1495. [15] D. Savitsky, P. Brown, Procedures for hydrodynamic evaluation of planing hulls in smooth and rough water, Mar. Technol. 13 (4) (October 1976) 381–400. [16] D. Savitsky, Direct measure of rigid body accelerations for wave impact of a planing hull, J. Ship Prod. Design 32 (November (4)) (2016) 235–244. [17] A. Rosen, K. Garme, Slamming studies on high-speed planing craft through fullscale trials and simulations, Proceedings of the Fast Sea Transportation Conference, Seattle, Washington, September 1999, pp. 683–698. [18] D. Schleicher, Regarding statistical relationships for vertical accelerations of planing monohulls in head seas, Proceedings of the 1st Chesapeake Power Boat Symposium, Annapolis, Maryland, March 2008. [19] J. Grimsley, Methodology to Quantify Vertical Accelerations of Planing Craft In Irregular Waves, Old Dominion University, Norfolk, Virginia, 2010 Ph.D. thesis. [20] M. Razola, K. Oausson, K. Garme, A. Rosen, On high-speed craft acceleration statistics, Ocean Eng. 114 (March 2016) 115-113. [21] D. VanDerwerken, C. Judge, Statistical analysis of vertical accelerations of planing craft: common pitfalls and how to avoid them, Ocean Eng. 139 (July 2017) 265–274. [22] A. Somahajula, J. Falzarano, Non-gaussian analysis methods for planing craft motion data, Ocean Syst. Eng. 4 (4) (2014) 293–308. [23] L. McCue, Statistics and design implications of extreme peak vertical accelerations

11