Case 3.5

Conditions:

·         Bare hull

·         Towing condition in head waves

·         FXst;  s = -1.92x10-3, t = -0.136°

·         Incident wave length λ = 1.5 LPP and wave steepness: Ak = 0.025

·         Re= 4.86×106, Fr=0.28

·         Wetted surface area at rest (S/L2) = 0.1476

Reference:

(3-2) Longo, J., Shao, J., Irvine, M., and Stern, F. (2007), “Phase-Averaged PIV for the Nominal Wake of a Surface Ship in Regular Head Waves,” ASME J. Fluids Eng, Vol. 129, pp. 524-540.

Instructions for Simulation: Simulation should be performed for THREE periods of the incoming wave.

 

 

 Table/

 

Figure #

Items

EFD Data

Submission Instructions

 

Data File

Image

Image File/Table

Sample

3.5-T

Comparison of 0th and 1st harmonic amplitudes and 1st harmonic phase of the resistance and moment coefficients.

Refer to sample file for details

Filename:            [Identifier]_T1_3-5.xls
                                        (Excel file)

IIHR-CFDShipV4_T1_3-5.xls

3.5-1

Time histories of CT, CH, and CM

Ct_hist.dat

Ch_hist.dat

Cm_hist.dat

 

[Identifier]_CT_3-5.jpg ( for CT )

[Identifier]_CH_3-5.jpg ( for CH )

[Identifier]_CM_3-5.jpg ( for CM )

X-axis range:  0.0 ≤ t/T ≤ 3.0

Y-axis range:  −0.004 ≤ CT ≤ 0.014

                         −0.08 ≤ CH ≤ 0.01

                         −0.015 ≤ CM ≤ 0.015

Style:    CFD solid line, EFD open circles Δ(t/T) = 0.05

 

 

 

IIHR-CFDShipV4_CT_3-5.jpg

IIHR-CFDShipV4_CH_3-5.jpg

IIHR-CFDShipV4_CM_3-5.jpg

3.5-2

Wave-elevation ζT contours: t/Te = 0, 1/4, 1/2, 3/4

fs_T-Te_EFD.dat

fs_T0_EFD.lpk  (for t/Te=0.0)
fs_T1_EFD.lpk  (for t/Te=1/4)
fs_T2_EFD.lpk  (for t/Te=1/2)
fs_T3_EFD.lpk (for t/Te=3/4)

fs_T0_EFD.jpg (for t/Te=0.0)
fs_T1_EFD.jpg (for t/Te=1/4)
fs_T2_EFD.jpg (for t/Te=1/2)
fs_T3_EFD.jpg (for t/Te=3/4)

Filename:     [Identifier]_fs-T0_3-5.jpg  (for t/Te=0.0)

                      [Identifier]_fs-T1_3-5.jpg (for  t/Te=1/4)                             

                      [Identifier]_fs-T2_3-5.jpg (for t/Te=1/2) 

                      [Identifier]_fs-T3_3-5.jpg (for t/Te=3/4)

Axis:                     -0.2£ x £1.3; 0£ y £0.4

Contours levels:    -0.01 £ zt_0 £ 0.01, Δz=0.001,

                                #levels = 21

Contour style:    Solid and dashed lines for positive and negative values, respectively.

 

3.5-3

Wave-elevation ζT contours: 0th amplitude

zt_0_EFD.dat

zt_0_EFD.lpk

 

 

zt_0_EFD.jpg

Filename:              [Identifier]_zt0_3-5.jpg

Axis:                     -0.2£ x £1.3; 0£ y £0.4

Contours levels:    -0.01 £ zt_0 £ 0.01, Δz=0.002,

                                #levels = 11

Contour style:     Solid and dashed  lines  for positive and negative values, respectively. 

 

3.5-4

Wave-elevation ζT contours:1st amplitude

zt_1_EFD.dat

zt_1_EFD.lpk

 

 

zt_1_EFD.jpg

Filename:              [Identifier]_zt1_3-5.jpg

Axis:                     -0.2£ x £1.3; 0£ y £0.4

Contours levels:    -0.002 £ zt_1 £ 0.01, Δz=0.001,

                                #levels = 11

Contour style:     Solid and dashed lines for positive and negative values, respectively. 

 

3.5-5

Wave-elevation ζT contours: 1st phase

gt_1_EFD.dat

gt_1_EFD.lpk

 

 

gt_1_EFD.jpg

Filename:              [Identifier]_gt1_3-5.jpg

Axis:                     -0.2£ x £1.3; 0£ y £0.4

Contours levels:    -6 £ gt_1 £ 0.5, Δg=0.5

                                #levels = 14

Contour style:      Solid and dashed lines for positive and negative values, respectively.

 

3.5-6

U contours at x / LPP = 0.935, and t / Te = 0, 1/4, 1/2, 3/4

U_t-Te_EFD.dat

U_T0_EFD.lpk  (for t/Te=0.0)
U_T1_EFD.lpk  (for t/Te=1/4)
U_T2_EFD.lpk  (for t/Te=1/2)
U_T3_EFD.lpk  (for t/Te=3/4)

U_T0_EFD.jpg (for t/Te=0.0)
U_T1_EFD.jpg (for t/Te=1/4)
U_T2_EFD.jpg (for t/Te=1/2)
U_T3_EFD.jpg (for t/Te=3/4)

Filename:        [Identifier]_U-T0_3-5.jpg (for t/Te=0)

                          [Identifier]_U-T1_3-5.jpg (for t/Te=1/4)

                          [Identifier]_U-T2_3-5.jpg (for t/Te=1/2)

                          [Identifier]_U-T3_3-5.jpg (for t/Te=3/4)

Axis:                     -0.0475£ x £0; -0.045£ y £0

Contours levels:  0. £ U£ 1.0, ΔU=0.05, #levels = 21

Contour style:     Solid lines     

 

3.5-7

V contours at x / LPP = 0.935, and t / Te = 0, 1/4, 1/2, 3/4

V_t-Te_EFD.dat

V_T0_EFD.lpk  (for t/Te=0.0)
V_T1_EFD.lpk  (for t/Te=1/4)
V_T2_EFD.lpk  (for t/Te=1/2)
V_T3_EFD.lpk (for t/Te=3/4)

V_T0_EFD.jpg (for t/Te=0.0)
V_T1_EFD.jpg (for t/Te=1/4)
V_T2_EFD.jpg (for t/Te=1/2)
V_T3_EFD.jpg (for t/Te=3/4)

Filename:        [Identifier]_V-T0_3-5.jpg (for t/Te=0)

                          [Identifier]_V-T1_3-5.jpg (for t/Te=1/4)

                         [Identifier]_V-T2_3-5.jpg (for t/Te=1/2)

                          [Identifier]_V-T3_3-5.jpg (for t/Te=3/4)

Axis:                     -0.0475£ x £0; -0.045£ y £0

Contours levels:  0 £ V£ 0.08, ΔV=0.01

Contour style:     Solid lines     

 

3.5-8

W contours at x / LPP = 0.935, and t / Te = 0, 1/4, 1/2, 3/4

W_t-Te_EFD.dat

W_T0_EFD.lpk (for t/Te=0.0)
W_T1_EFD.lpk (for t/Te=1/4)
W_T2_EFD.lpk (for t/Te=1/2)
W_T3_EFD.lpk (for t/Te=3/4)

W_T0_EFD.jpg (for t/Te=0.0)
W_T1_EFD.jpg (for t/Te=1/4)
W_T2_EFD.jpg (for t/Te=1/2)
W_T3_EFD.jpg (for t/Te=3/4)

Filename:     [Identifier]_W-T0_3-5.jpg (for t/Te=0)

                       [Identifier]_W-T1_3-5.jpg (for t/Te=1/4)             

                      [Identifier]_W-T2_3-5.jpg (for t/Te=1/2)             

                      [Identifier]_W-T3_3-5.jpg (for t/Te=3/4)

Axis:                     -0.0475£ x £0; -0.045£ y £0

Contours levels:  -0.01 £ W£ 0.13, ΔW=0.01

Contour style:     Solid and dashed lines for positive and negative values, respectively. 

 

3.5-9

U contours of 0th and 1st amplitudes and 1st phase at x/LPP=0.935

U_0_EFD.dat

U_1_EFD.dat

GU_1_EFD.dat

U_0_EFD.lpk

U_1_EFD.lpk

GU_1_EFD.lpk

 

 

 

U_0_EFD.jpg

U_1_EFD.jpg

GU_1_EFD.jpg

Filename:        [Identifier]_U0_3-5.jpg (for U_0)

                          [Identifier]_U1_3-5.jpg (for U_1)

                          [Identifier]_GU1_3-5.jpg (for GU_1)

Axis:                     -0.0475£ x £0; -0.045£ y £0

Contours levels:  0.4 £ U_0 £ 0.95, ΔU=0.05

                              0 £ U_1 £ 0.1, ΔU=0.005

                              -2.1 £ GU_1 £ 1.1, ΔGU=0.2

Contour style:    Solid and dashed lines for positive and negative values, respectively.

 

3.5-10

V contours of 0th and 1st amplitudes and 1st phase at x/LPP=0.935

V_0_EFD.dat

V_1_EFD.dat

GV_1_EFD.dat

V_0_EFD.lpk

V_1_EFD.lpk

GV_1_EFD.lpk

 

 

 

V_0_EFD.jpg

V_1_EFD.jpg

GV_1_EFD.jpg

Filename:        [Identifier]_V0_3-5.jpg (for V_0)

                          [Identifier]_V1_3-5.jpg (for V_1)

                          [Identifier]_GV1_3-5.jpg (for GV_1)

Axis:                     -0.0475£ x £0; -0.045£ y £0

Contours levels: 0 £ V_0 £ 0.07, ΔV=0.005

                              0 £ V_1 £ 0.04, ΔV=0.002

                              -2.0 £ GV_1 £ 3.0, ΔGV=0.5

Contour style:     Solid and dashed lines for positive and negative values, respectively.

 

3.5-11

W contours of 0th and 1st amplitudes and 1st phase at x/LPP=0.935

W_0_EFD.dat

W_1_EFD.dat

GW_1_EFD.dat

W_0_EFD.lpk

W_1_EFD.lpk

GW_1_EFD.lpk

 

 

 

W_0_EFD.jpg

W_1_EFD.jpg

GW_1_EFD.jpg

Filename:        [Identifier]_W0_3-5.jpg (for W_0)

                          [Identifier]_W1_3-5.jpg (for W_1)

                          [Identifier]_GW1_3-5.jpg (for GW_1)

Axis:                    -0.0475£ x £0 ; -0.045£ y £0

Contours levels:    0 £ W_0 £ 0.13, ΔW=0.01

                              0 £ W_1 £ 0.03, ΔW=0.03

                              -2.5 £ GW_1 £ 2.5, ΔGW=0.5

Contour style:     Solid and dashed lines for positive and negative values, respectively.

 

 

*[Identifier] should be [Institute Name]-[Solver Name]. For example, if your institute is IIHR and solver is CFDShip-Iowa V.4, identifier should be IIHR-CFDShipV4.

 

All figures have aspect ratio of 1:1.

 

Nomenclature

·         zt_0; 0th harmonic amplitude of total free surface elevation

·         zt_1; 1st harmonic amplitude of total free surface elevation

·         gt_1; 1st harmonic phase of total free surface elevation

·         U_0, V_0, W_0; 0th harmonic amplitude of U, V, W, respectively.

·         U_1, V_1, W_1; 1st harmonic amplitude of U, V, W, respectively.

·         GU_1, GV_1, GW_1; 1st harmonic phase of U, V, W, respectively

Remarks:

$\displaystyle C_{T}(t)$

$\displaystyle = \dfrac{F_{x}(t)}{\frac{1}{2} \rho U^2 S}, \quad

   

$ A $

Incident wave amplitude

$ A_k $

Wave steepness $ A_k = \dfrac{2 \pi A}{\lambda} $

$ f_w $

Frequency of the incident wave, $ \sqrt{\dfrac{g}{2 \pi \lambda}} $

$ f_e $

Encounter frequency, $ f_w+\dfrac{U}{\lambda} $

$ T_e $

Encounter period $ \dfrac{1}{f_e} $

$ t $

Time, at t=0 a crest of the incident wave is coincident with the FP of the ship

$ U $

Ship speed

$ u,v,w $

Velocity components in $ x,y,z $directions, respectively

$ \lambda $

Incident wave length

$ \zeta_T(x,y,t) $

Free surface elevation $ \dfrac{z(x, y, t)}{L_{PP}} $


As a time reference, incident wave height at FP of the ship is defined as

$\displaystyle \zeta_I (t)$

$\displaystyle = \dfrac{A}{L_{PP}} \cos \left( 2 \pi f_e t + \gamma_I \right)$

   

where $ \gamma_I $is the initial phase and is equal to be zero from the present definition of $ t = 0 $above.
Fourier Series for time history $ X ( X = C_T, C_H, C_M, $and $ \zeta_T ) $are determined as follows:

$\displaystyle X_F (t)$

$\displaystyle = \dfrac{X_0}{2} + \sum_{n=1}^N X_n \cos \left( 2 \pi n f_e t + \Delta \gamma_n \right)$

   

$\displaystyle \Delta \gamma_n$

$\displaystyle = \gamma_n - \gamma_I$

   

$\displaystyle a_n$

$\displaystyle = \dfrac{2}{T} \int_0^T X(t) \cos \left( 2 \pi n f_e t \right) dt \quad ( n = 0, 1, 2, \cdots )$

   

$\displaystyle b_n$

$\displaystyle = \dfrac{2}{T} \int_0^T X(t) \sin \left( 2 \pi n f_e t \right) dt \quad ( n = 1, 2, \cdots )$

   

$\displaystyle X_n$

$\displaystyle = \sqrt{a_n{}^2 + b_n{}^2}$

   

$\displaystyle \gamma_n$

$\displaystyle = \tan{}^{-1} \left( - \dfrac{b_n}{a_n} \right)$

   

$ X_n $is $ n $-th harmonic amplitude and $ \gamma_n$is the corresponding phase.