“Study of Trim Dependence for Ship performance in the Actual
Sea Conditions by Computational Fluid Dynamics (CFD)
Simulations"Final Report

Submitted by: AYE AYE MON (Dr. Eng)
Lecturer
Naval Architecture and Ocean
Engineering Department
Myanmar Maritime University

Submission Date : June 27, 2016

“Study of Trim Dependence for Ship performance in the Actual
Sea Conditions by Computational Fluid Dynamics (CFD) Simulations"
Abstract
Nowadays, Computational Fluid Dynamics (CFD) simulation techniques are widely usedin ship hydrodynamics applications and resistance analysis based on CFD simulations plays adecisive role in the development of new, eco-friendly ship hull forms. The purpose of thisstudy is to analyze the trim effect on resistance and performance of ship by employing CFD
simulation methodology. In the present study, the free surface flow around the Kriso
Container Ship (KCS) model without rudder is simulated first in even keel condition using
the RANS solver Fluent. The mesh, boundary conditions, and solution techniques arevalidated by comparing the computed resistance value to experimental value in even keel
condition. As a result, a reasonable agreement is found. Afterwards, the validated mesh,boundary conditions, solution techniques are employed to estimate the resistance of KCS hullin different trim conditions at Fn=0.26 and the results are compared with the even condition.
1. Ship ModelIn the present study, Kriso Container Ship (KCS) hull is selected as a model case for CFD
validation because the extensive model test data of this KCS hull are available for resistanceat different Froude numbers (CFD Tokyo Workshop 2005). The profile of the KRISO
Container Ship (KCS) is shown in Figure 1 and the main particulars of the model used in thepresent study are listed in Table 1.

Figure 1 KRISO Container Ship (KCS)
Table 1 Main particulars of ship modelParameters
Length of overall
Length between perpendiculars
Beam
Draft
Wetted surface area w/o rudder
Block coefficient
Displacement
Scale ratio

LWL
LPP
B
TSCb

λ[m]
[m]
[m][m][m2][m3]

Dimensions
7.35707.27861.01900.34189.43790.65101.649031.5992. Numerical method
In the present study, the commercial CFD software FLUENT is used to simulate the freesurface flow of a container ship at a model scale. It solves the RANS equations using a cellcentered finite-volume method. The governing equations are the three-dimensional Reynolds
Averaged Navier-Stokes equations (RANS) for incompressible flow. For the analysis of highReynolds number flows, the Shear Stress Transport k    SST two-equation turbulence1model by Menter is employed with a wall function approach for turbulence closure.
Computational grids are generated using GAMBIT, pre-processor of FLUENT. The
unstructured tetrahedral and structured hexahedral meshes are generated around the modelscale KCS hull geometry without rudder. The Reynolds number based on ship length (LWL)
and ship velocity is 1.26 x 107 and the Froude number is 0.26.
3. Simulation Results
In the present study, the double model flow and free surface flow computations of KCS
model without rudder in even keel condition at Fn= 0.26 is carried out first to validate mesh,boundary conditions, and solution techniques since the model test data is available forresistance of KCS hull in even keel condition(CFD Tokyo Workshop 2005). The validated
mesh, boundary conditions, and solution techniques are later used to calculate resistance indifferent trim conditions.
3.1 Double Model Flow Computations in Even Keel and Different Trim Conditions
As a first step of present study, Double Model flow computations for KCS hull form
without rudder are performed at different Froude numbers in even keel condition to validate
mesh, boundary conditions, and solution techniques. The computed results for Double Model
flow are compared with model test results of case 2.1 proposed in the CFD Workshop 2015
and found reasonable agreement. Same mesh, boundary conditions and solution techniques
are used to calculate the KCS hull resistance at Fn = 0.26 in different trim conditions shownin Table 2. A positive (+) trim value is defined bow up. Comparing with even keel condition,
significant increase in total resistance coefficient is observed when ship was trimmed by stern.
It is noted that trim effect cannot be clearly seen in Double Model computation because
viscous resistance change slightly with change in trim. The fact that there are slight changes
in wetted surface area with change in trim and the effect of trim is dominant on wave making
resistance part.
3.2 Free Surface Flow Computations in Even Keel and Different Trim Conditions
The free surface flow computation around the KCS model without rudder in even keel
condition at Fn= 0.26 is carried out first to validate mesh, boundary conditions, and solution
techniques. Computational domain for free surface flow is defined by  L  x  2.5L ,0  y   L and,  L  z  0.06 L , for all cases. Only the port side is computed due tosymmetry. The computational domain consists of two blocks and 1.7 M cells. The partialviews of computational grid shown in Figure 3 are the magnified views of bow and sternregion for KCS hull model. Transient state computations are performed. The converged
solutions for free surface flow computation with engineering accuracy are obtained with over
10,000 time steps (110 s).
The comparison of the computed resistance coefficient result with corresponding model
test result in even keel condition at Fn=0.26 is shown in Table 2. It is noted that thedifference is not much since the comparison error (%) is about 5.4 % and thus resistanceresult is found as a reasonable agreement. The free surface pattern near the hull is also well
captured since the grid resolution is fine enough.
Afterwards, the same mesh, boundary conditions and solution techniques are employed toestimate the resistance values of KCS hull at design draft in different trim conditions shownin Table 3. Grids for KCS hull in even keel and trim conditions are generated to be the sameas much as possible in order to reduce the effect of grid difference.
2Figure 3 The partial views of computational grid of KCS hull.
Table 2 Comparison of computed and experimental total resistance coefficient results in evenkeel condition at Fn=0.26

KCS hull

Total Drag coefficientDCT 
1 2 V 2 S

Comparison Error (%)

ComputedExperiment3.910  10 33.711  10 3

5.4%

Table 3 Trim Conditions
Trim Conditions
Trim [m] % LWL
Trim Angle [Degree]
Wetted surface area (S) [m2]

Evenkeel004.785

Trim by bow-0.75%
-0.43
4.756

-1.5%
-0.8594.744

Trim by stern+0.75%
+0.43
4.827

+1.5%
+0.8594.825

The computed resistance coefficients results of KCS in even keel and different trim
conditions at Fn=0.26 are listed in Table 4. The resistance coefficients arenondimensionalized with 0.5V 2 L2 where ρ is a density of water and V and L are speed and alength of a ship model KCS. Table 5 shows the computed resistance results where the total
resistance is decomposed into viscous resistance and wave making resistance in order toanalyze the trim effect on each resistance component.
Table 4 Computed resistance coefficients for the KCS hull in even keel and different trim
conditions
Trimconditions

Trim Angle(deg)Even Keel
Trim by bow
Trim stern
Trim by bow
Trim by stern

0-0.43+0.43-0.859+0.859Cp Rp

1 2 2
L V2
2.235E-04
2.270E-04
2.454E-04
2.444E-04
2.849E-04

CF 

RF

1 2 2
L V2
4.588E-04
4.580E-04
4.578E-04
4.542E-04
4.453E-04

CT 

RT

1 2 2
L V
2
6.824E-04
6.850E-04
7.032E-04
6.987E-04
7.302E-04
3

The wave making resistance Rw (RT - Rv) are calculated by using the corresponding formfactors which are estimated by the double model flow computation. The results show thatviscous resistance changes slightly with change in trim and the effect of trim is dominant on
wave making resistance. The viscous, wave making and total resistance versus trim plots for
the KCS hull are shown in Figure 4, 5 and 6. The computed wave profiles along the hull andthe longitudinal wave cut at y/Lpp=0.15 in even keel condition and different trim conditions
are compared in Figure 7. The difference in bow and stern waves generated by trim by bow
and stern are clearly observed.
Table 5 Computed resistance results in even keel and different trim conditions
Trim Angle(deg)0-0.43+0.43-0.859+0.859

Trim conditions
Even Keel
Trim by bow
Trim stern
Trim by bow
Trim by stern

Rw(N)Rv (N)

RT (N)

19.16421.16022.91622.60826.375

70.91
70.19
69.91
69.81
69.95

90.07490.42492.82392.22696.392Rv (N)Rw (N)

74

2672

2470

2268

2066
−1−0.5

00.5

18−1

1−0.5

00.5

1

Trim Angle (deg)Trim Angle (deg)Figure 4 Viscous resistance as a functionof Trim

Figure 5 Wave making resistance as afunction of TrimRT (N)96949290−1−0.500.5
Trim Angle (deg)1Figure 6 Total resistance as a function of trim (positive (+) trim value is defined bow up)
4Comparing with the even keel condition, the trend of the increased total resistance in trim
conditions is observed. The significant increase in total resistance is about 3 % and 7% when
the ship was trimmed by stern 0.43 deg and 0.859deg. However, on trimming the ship by bow,
total resistance of the hull increases about 0.4% by 0.43 deg and 2 % by 0.859deg.

Figure 7 Computed wave profiles on the hull and longitudinal wave cut at y/Lpp=0.15 in evenkeel and different trim conditions at Fn=0.26
4. Conclusions and Future works
In the present study, CFD simulation techniques have been employed for MOERI
container ship (KCS) hull to analyze the effect of trim on resistance. The method presentedfor free surface flow computation around the KCS model is carried out in even keel and four
different trim conditions in calm water at design speed and draft. The computed resistanceresult in even keel condition is compared with experiment result and found in reasonableagreement since the comparison error is about 5.4%.
Comparing with the even keel condition, the trend of the increased total resistance in trim
conditions is observed. The significant increase in total resistance is observed when the ship
is trimmed by stern. Among four different trim conditions, the resistance of KCS model intrim by bow 0.43 (deg) condition is lower than the rest of three trim conditions. The results
showed that the even keel condition gives minimum drag compared with the different trim
conditions in the design speed and design displacement because a ship is designed to be mostefficient in the design speed and in the design draft.
In future works, CFD simulations in the lower speeds shall be carried for KCS hull sincetrim optimization of container ship is needed in the off-design and conditions such as slowing
steaming or light weight conditions. It is expected that the characteristics of resistancecomponents due to trim can be confirmed by the experiments.
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