Case 1.4c

1. Conditions:

· Without rudder

· Towing condition in head waves

· FR_xzθ

· Re = 2.55×10⁶, Fr = 0.142

· Nominal Wave height= 60mm

· Three wave lengths and one calm water conditions

· References:

Not yet available.

2. Test Setup:

a. Spring Stiffness K and F₀:

No.	1	2	3	4
λ/LPP	0.6	1.1	1.6	Calm Water
Measured mean wave height (mm)	57.676	58.484	57.817	0.011
Nominal wave height (mm)	60	60	60	0
F0 (N)	4	6	10	6
K (N/m)	98	98	98	98

b. Mass:

Part	Mass (Kg)	Description
Red	m1=306.2	Mass of hull and pitch free gimbals and a part of heaving rod under the dynamometer(including dynamometer moving part)
Blue	m2=6.4	Mass of dynamometer (0.9Kg) and the rest of heaving rod (5.5Kg)
Green	m3=2.5	Mass of light weight carriage on the rails including all movable parts

Note: I_yy = (0.25L)²(m₁+m₂). This value is adjusted by putting the m₂ at CG.

3. Instructions for Simulation:

Solve the following equations of motion along with flow code:

The comparison should be based on the following table:

Heave	Pitch	Surge	Free Surface Elevation	Resistance Force
+ upward	+ bow up	+ downstream	Measured at x=-5.304m ahead of original CG

* Simulation should be performed for one long period due to spring system (around 22, 12, 10 encounter period of the incoming wave for, respectively).

Table/ Figure #	Items	EFD Data		Submission Instructions
		Data File	Image	Table/Image File	Sample
1.4c-1	Comparison of 0th and 1st harmonic amplitudes and 1st harmonic phase of the X force (FX) in model scale, surge motion (x), heave motion (z) and pitch angle (θ)	Refer to sample file for details		Filename: [Identifier]_3waves & clam water_1-4c.xls  (Excel file)	[Identifier]_3waves & clam water_1-4c.xls
1.4c-2-C1	Time histories of X force (FX) in model scale, surge motion (x), heave motion (z) and pitch angle (θ) (λ/LPP=0.6)	time_history_EFD_C1.dat	Refer to sample file for details	Filename: [Identifier]_FX_T-his_C1_1-4c.jpg ( for FX ) [Identifier]_surge_T-his_C1_1-4c.jpg ( for x ) [Identifier]_heave_T-his_C1_1.4c.jpg ( for z ) [Identifier]_pitch_T-his_C1_1-4c.jpg ( for θ ) X-axis range:  100.0 ≤ t(s) ≤ 115.0 Y-axis range: 3.0 ≤ FX ≤ 10.0; 0.80 ≤ x ≤ 5.0; -0.65 ≤ z ≤ 0.0; -0.25 ≤ θ ≤ 0.10 Style:    CFD solid line EFD open circles	[Identifier]_FX_T-his_C1_1-4c.jpg [Identifier]_surge_T-his_C1_1-4c.jpg [Identifier]_heave_T-his_C1_1.4c.jpg [Identifier]_pitch_T-his_C1_1-4c.jpg
1.4c-2-C2	Time histories of X force (FX) in model scale, surge motion (x), heave motion (z) and pitch angle (θ) (λ/LPP=1.1)	time_history_EFD_C2.dat	Refer to sample file for details	Filename: [Identifier]_FX_T-his_C2_1-4c.jpg ( for FX ) [Identifier]_surge_T-his_C2_1-4c.jpg ( for x ) [Identifier]_heave_T-his_C2_1.4c.jpg ( for z ) [Identifier]_pitch_T-his_C2_1-4c.jpg ( for θ ) X-axis range:  90.0 ≤ t(s) ≤ 105.0 Y-axis range: 6.0 ≤ FX ≤ 17.0; 5.0 ≤ x ≤ 9.0; -3.0 ≤ z ≤ 3.0; -2.0 ≤ θ ≤ 2.0 Style:    CFD solid line EFD open circles	[Identifier]_FX_T-his_C2_1-4c.jpg [Identifier]_surge_T-his_C2_1-4c.jpg [Identifier]_heave_T-his_C2_1.4c.jpg [Identifier]_pitch_T-his_C2_1-4c.jpg
1.4c-2-C3	Time histories of X force (FX) in model scale, surge motion (x), heave motion (z) and pitch angle (θ) (λ/LPP=1.6)	time_history_EFD_C3.dat	Refer to sample file for details	Filename: [Identifier]_FX_T-his_C3_1-4c.jpg ( for FX ) [Identifier]_surge_T-his_C3_1-4c.jpg ( for x ) [Identifier]_heave_T-his_C3_1.4c.jpg ( for z ) [Identifier]_pitch_T-his_C3_1-4c.jpg ( for θ ) X-axis range:  85.0 ≤ t(s) ≤ 100.0 Y-axis range: 2.0 ≤ FX ≤ 15.50; -1.0 ≤ x ≤ 4.0; -3.20 ≤ z ≤ 3.0; -3.0 ≤ θ ≤ 3.0 Style:    CFD solid line EFD open circles	[Identifier]_FX_T-his_C3_1-4c.jpg [Identifier]_surge_T-his_C3_1-4c.jpg [Identifier]_heave_T-his_C3_1.4c.jpg [Identifier]_pitch_T-his_C3_1-4c.jpg
1.4c-2-C4	Time histories of X force (FX) in model scale, surge motion (x), heave motion (z) and pitch angle (θ) (Calm water)	time_history_EFD_C4.dat	Refer to sample file for details	Filename: [Identifier]_FX_T-his_C4_1-4c.jpg ( for FX ) [Identifier]_surge_T-his_C4_1-4c.jpg ( for x ) [Identifier]_heave_T-his_C4_1.4c.jpg ( for z ) [Identifier]_pitch_T-his_C4_1-4c.jpg ( for θ ) X-axis range:  45.0 ≤ t(s) ≤ 55.0 Y-axis range: -0.50 ≤ FX ≤ 8.0; -1.0 ≤ x ≤ 4.0; -0.530 ≤ z ≤ -0.160; -0.380 ≤ θ ≤ 0.10 Style:    CFD solid line EFD open circles	[Identifier]_FX_T-his_C4_1-4c.jpg [Identifier]_surge_T-his_C4_1-4c.jpg [Identifier]_heave_T-his_C4_1.4c.jpg [Identifier]_pitch_T-his_C4_1-4c.jpg

Data files show

t(sec) ζ(cm) Fx(N) z(cm) pitch(cm) x(cm) ζ(tank fixed)　 ζ(servo)　 V(m/s)

Submission Instructions: 

· Filename: [Identifier]_3waves_1-4c.xls  (Excel file)

· [Identifier] should be [Institute Name]-[Solver Name]. For example, if your institute is Chalmers and solver is SHIPFLOW4.2, identifier should be Chalmers-SHIPFLOW4.2

Identifier in the Figure should be [Institute Name]/[Solver Name]. For example, if your institute is Chalmers and solver is SHIPFLOW4.2, identifier should be Chalmers/SHIPFLOW4.2

· Sample files:         Chalmers-SHIPFLOW4.2_3waves_1-4c.xls

· All figures should have aspect ratio of 1:1

Remarks:

· Coordinate system for comparisons is fixed to x=0.0 (original CG on the carriage).

x: positive downstream, y:starboard direction, z:upward

· Symbols:

a- Incident wave amplitude

- Frequency of the incident wave,

- Encounter frequency,

- Encounter period,

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

- Carriage speed

- Incident wave length

- Free surface elevation,

· Instructions:

As a time reference, incident wave height at mean x of CG is defined as

where is the initial phase and is equal to be zero from the present definition of above.
Fourier Series for time history are determined as follows:

is n-th harmonic amplitude and is the corresponding phase.