CFD SIMULATION OF RESISTANCE OF HIGHSPEED TRIMARAN HULLFORMS. Changhwan Son (SM), Prasanta K Sahoo (M), Vaibhav Aribenchi (SM) and Srikanth Asapana(SM) This paper attempts to carry out a CFD analysis on total resistance for trimaran hull forms based on established NPL systematic series which are high-speed round bilge hull forms. The resistance of high-speed trimaran hull forms have been determined using ANSYS FLUENT, a CFD software package. A systematic series of round bilge demi-hulls were generated, and their resistance in calm water were determined by using ANSYS FLUENT to briefly examine nature and degree of reliability of ANSYS FLUENT. The primary aim of this investigation is to determine resistance characteristics of slender round bilge trimaran hull forms in the high-speed range corresponding to Froude numbers up to 1.0. Model test results obtained from the paper Molland et al (1994) have been used to verify the efficacy of the CFD analysis. The results obtained from CFD have shown considerable promise and further analysis need to be carried out for accurate determination of resistance in trimaran configuration.

KEY WORDS Trimaran; resistance; wave resistance; total resistance; computational fluid dynamics.

NOMENCLATURE AMCSHC Australian Maritime College Ship Hydrodynamic Centre CFD Computational Fluid Dynamics DINMA Department of Naval Architecture, Ocean and Environmental Engineering VOF Volume of Fluid CA Incremental resistance coefficient CAA air resistance coefficient. CF Frictional resistance coefficient CFS Frictional resistance coefficient of outrigger CFT Total frictional resistance coefficient of a trimaran CP Pressure resistance coefficient CRNI non-interference component of the residuary resistance Ctr ∗ (θ) and Str ∗ (θ) An amplitude function for the trimaran CW Wave resistance coefficient CV Viscous resistance coefficient RT Total resistance force RF Frictional resistance RR Residual resistance RA Appendage resistance SC wetted surfaces of main hull S/L Separation ratio between the center hull and side hull SS wetted surface area of outrigger ST Total trimaran wetted surface area (1+k) Form factor according to Hughes-Prohaska τ wave resistance interference factor

INTRODUCTION The demand for faster transportation by sea have continued to increase in the field of commercial and military applications.

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Although catamarans have adequately fulfilled such demands in the last decades, the high-speed ferry industry and navies around the world still require novel hull forms which provide much more deck space and high-speed operation than the conventional hull forms. One of the multi-hull forms to meet these strict requirements is a trimaran which has two outriggers placed in both sides of the center hull since it is able to significantly reduce the wave making resistance in high-speed operation, also having the advantages of economy of fuel consumption and time. A trimaran has a large wetted surface compared to the conventional hull forms so thus resulting in an increase in viscous resistance at low speed operation. However, by using the slender hull form based on the slender body theory the fine hull configuration provides less wave-making resistance at a higher speed. This paper attempts to quantify the total resistances for slender round bilge configurations of trimaran hull forms in high-speed operation. The resistance of mono-hull and catamaran hull forms are briefly examined using ANSYS FLUENT, and then compared with experimental data and theoretical analysis. There appears to be good agreements between predicted values and experimental data thus by proving the possibility over the efficacy of CFD analysis. The systematic series of trimaran hull forms are developed based on the NPL systematic series of round bilge hulls, where the side hulls are scaled to one third size of the main hull. Finally, CFD analysis implements predictions of wave making resistances corresponding to Froude number up to 1.0.

BACKGROUND Narita (1976) carried out research to verify the theoretical prediction compared with towing test and wave observation. This study investigated wave resistance characteristics of a trimaran hull form at Froude number, Fn = 0.3162 and different hull arrangements such as a single hull, twin-hull and three-hull. The wave resistance coefficient is defined as:

𝐶𝑤 = 1

𝑅𝑤

𝜌𝑣 2 𝐿2

(1)

2

CFD SIMULATION OF RESISTANCE OF HIGHSPEED TRIMARAN HULLFORMS

1

Then the equation (1) is transformed to π/2

Cw = ∫0

[{Str ∗ (θ)}2 + {Ctr ∗ (θ)}2 ]dθ

(2)

Where, Ctr ∗ (θ) = √

2π L

2π

Str ∗ (θ) = √

L

3

(3)

. Cos 2 θ . C(θ) 3

(4)

. Cos 2 θ . S(θ)

The results had a fairly good agreement with the theoretical prediction, towing test, and wave observation in every different arrangement. Zhang (1997) investigated the effects of trimaran configuration with regard to the characteristics of trimaran wave making resistance on two different trimaran hull forms. The total resistance of a trimaran thus can be written: RT = RF + RR + RA

(5)

Suzuki et al. (1997) carried out the wave resistance prediction using the CFD at Yokohama National University in Japan. This study investigated the numerical analysis of wave making resistance of trimaran hull forms based on the ordinary and modified Rankine source methods with the vortex effects in order to take into account the lifting effect. They used the numerical examples for trimaran hull forms, and optimizing positioning of small outriggers from the viewpoint of wave making resistance. Its main hull is based on the Wigley hull, having waterlines of cosine curve and frame lines of forth order parabolic curve, expressed as: y= ±

B 2

Cos

πx L

Z 4

{1 − ( ) }

Figure 1: Model Testing Configuration, Suzuki & Ikehata (1993) The result indicated that the total wave making resistance coefficient of the trimaran was acceptable compared to the experimental wave analysis. Ackers et al. (1997) carried out the investigation on the interference effect between the main hull and the outriggers. They studied four different side hull displacement conditions corresponding to 5.8%, 8.4%, 10.9% and 13.6% of the total trimaran displacement and four different angles of attack, ranging from -2o to 4o of the side hull on each condition. The trimarans were tested in different side hull positions and configurations corresponding to Froude numbers 0.3 to 0.6

(6)

T

Where L, B, and T are ship length, breadth, and draught, respectively, and y is the half breadth, x is the position of section, and z is positive upwards. The outriggers have a scale factor of 1:3 with respect to the main hull. Table 1 shows the model names and positions of the outriggers that are represented in Figure 1. Table 1: Model testing conditions [Suzuki et al. (1997)]

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Stagger 2X0/L (%) Without outriggers

Clearance 2Y0/L (%) Without outriggers

-

0

± 0.900

TR-1F

0.4

-0.667

± 0.322

TR-1A

0.4

0.667

± 0.322

TR-2F

0.5

-0.667

± 0.195

TR-2A

0.5

0.667

± 0.195

Model

Design Fn

MH-0

-

TR-0

Figure 2: Model side hull configurations (Ackers et al (1997)) The results reported that side hull symmetry and position are most important for the trimaran resistance, while a side-hull angle of attack or increasing side-hull displacement is not effective for resistance reduction. When the side hulls are symmetrical, the lowest interference position of the side hulls is approximately 75% of the main hull length aft and with a transverse clearance of about 87% of the main hull beam throughout the entire speed range. As regards the symmetric hull form of the side hulls, asymmetric outboard side hull interference tends to be of the smallest variation. Symmetric and asymmetric inboard side hull interferences have more resistance than asymmetric outboard types.

CFD SIMULATION OF RESISTANCE OF HIGHSPEED TRIMARAN HULLFORMS

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Battistin (2000) studied the wave resistance interference effect by using analytical, numerical, and experimental methods. The model tested was a Wigley trimaran with the main hull two times longer than the outriggers. Experimental method: Sixteen different trimaran configurations have been tested, the tests were carried out in the model basin at the Department of Naval Architecture, Ocean and Environmental Engineering (DINMA), University of Trieste. The resistance data had been analyzed by means of the ITTC’78 procedure and the form factor had been calculated using the Prohaska (1966) method.

Figure 3: Wave resistance coefficients, X/L -0.2 [Mynard et al. (2008)]

Analytical method: It was based on the classical thin ship theory (Michell’s theory). To extend the Michell’s theory to the multi-hulls case, it is necessary to sum up the contributions coming from the different hulls, considered as isolated, so for a trimaran with three hulls the general wave resistance equation can be expressed as: π

2

R𝑤 = 8πρK 0 ∫ 2π sec 3 θ|∑3j=1 Hj (θ, K 0 sec 2 θ)| dθ −

(7)

2

Numerical method: The code used for the numerical simulations is a Rankine source panel code developed at DINMA based on the inviscid and irrotational fluid assumptions. By comparing the three methods, it appeared clear that the numerical panel method predicts the interference effect better than the analytical one. In particular, it shows quite well the position of maxima and minima of the interference, while the analytical method cannot do it. However, there is an important gap between numerical simulations and experiments to find the absolute value of the interference. Mynard et al. (2008) investigated a systematic series of highspeed trimaran hull forms to determine the wave resistance for each model corresponding to Froude number up to 1.0 in conjunction with varying longitudinal side hull locations. This study used the tank testing data on the TRI-9 model having a clearance of 0.2 and was conducted at AMCSHC. The experimental result of wave resistance coefficients are shown in Figure 3 compared with original testing data. Mahmood (2011) investigated the prediction of wave resistance on the trimaran hull forms using ANSYS FLUENT. Three different mesh sizes are used to investigate the mesh effects, and two different turbulence models of standard κ- ε and SST κ-ω are used to calculate free surface of the ship. The total resistances were computed corresponding to Froude Number ranges 0.14 to 0.75. The results obtained were compared with the experiment data so that they were acceptable, as shown in Figure 4.

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Figure 4: Comparison of CFD and experimental results [Mahmood (2011)]

THEORY The wave resistance is the most important component of the ship resistance as the speed increases, so it is essential to reduce it in order to improve the performance of any hull form including trimarans. Generally, to do this, high values of L/1/3, or increasing the dynamic lift of the hull, are required. Also, in order to limit the main hull wave resistance, L/B of the main hull has to be higher than 10. Wave making resistance is also affected by the interference between the separate hull wakes. Indeed the favorable wave interference can compensate for the increase in wetted surface, ensuring the advantages of very slender hulls over a significant range of Froude numbers together with good stability characteristics. However, it can either increase or decrease the total wave resistance, depending on the dimensions and mutual positions of the three hulls. In 1978, ITTC suggested using a tentative standard called “1978 ITTC Performance Prediction for Single Screw Ship” proposed by Hughes-Prohaska, as a new method to evaluate the resistance where CT and CF are always the same form as show by:

CFD SIMULATION OF RESISTANCE OF HIGHSPEED TRIMARAN HULLFORMS

3

CT = CW + (1+k) CF+CA+CAA

(8)

Where CA is incremental resistance coefficient for model ship correlation taking into account the effect of roughness of the surface of the ship and CAA is the air resistance coefficient. In the case of a trimaran, it consists of one long slender main hull and two smaller hulls. Combining the main hull and the side hulls, the total frictional resistance coefficient of a trimaran (subscript T) is given by: CFT = CFC (SC/ST) + CFS (2SS/ST)

(10)

Where CRNI is “non-interference” component of the residuary resistance defined as: CRNI = CRC (SC/ST) + CRS (2SS/ST)

TRIMARAN

Table 2: Models of trimaran particulars Model

4a

4b

4c

L(m)

1.6

1.6

1.6

L/B

10.4

9

8

1.5

2

2.5

7.4

7.41

7.39

CB

0.397

0.397

0.397

CP

0.693

0.693

0.693

CM

0.565

0.565

0.565

WSA (m2)

0.348

0.348

0.348

-6.4

-6.4

-6.4

B/T

L/∇

1 3

(11)

Here, a negative interference factor is a favorable situation.

OF

The models are initially created as the trimaran, which has a main hull with two outriggers, and the separation ratio (S/L) between the centre hull and side hull is 0.2. Based on NPL systematic Series, trimaran models were generated by using Maxsurf Modeler, which is standard modelling software. The outrigger was scaled to 1:3 with respect to the mainhull, as shown in Table 2. The main hull body plans are shown in Figure 5.

(9)

Where the CFC and CFS are the frictional resistance coefficient of the main center hull and outrigger, respectively; SC and SS are wetted surfaces of main hull and outrigger, respectively; and ST is the total trimaran-wetted surface. The residuary resistance coefficient is then calculated by subtracting CFT from CT. To evaluate the interference effects of each configuration, depending on the side hulls position, the following interference factor has been defined as: IF = (CR-CRNI)/CRNI

THE CONFIGURATION MODEL

LCB(%) from midship

VALIDATION OF CFD To determine the degree to which a model is an accurate representation of the real world from the perspective of the intended use of the model it is important to validate the data from CFD.

Comparison of Total Resistance The ITTC-57 ship-model correlation line (1978) suggested the total resistance components of mono-hull should be expressed by equation (12): CT = (1+k) CF + CW

(12)

Where, (1+k) is the form factor according to Hughes-Prohaska CF is always calculated according to the ITTC’57 correlation line and is given by:

CF = (log

0.075

2 10 Rn −2)

(13)

Molland (2011) proposed the total resistance of catamaran was Figure 5: S-NPL Lines Planes [Molland et al. (1994)]

practically expressed by equation (14): CTcat = (1 + βk)CF + τCW

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CFD SIMULATION OF RESISTANCE OF HIGHSPEED TRIMARAN HULLFORMS

(14)

4

Where τ is the wave resistance interference factor.

12.0

CT-Cal

A satisfactory fit to the mono-hull form factors is

(1 + k) = 2.72 (

L 1

CT-CFD

10.0 (16)

) − 0.40

∇3

103CT

8.0

A satisfactory fit to the catamaran form factors is

6.0

L

(1 + βk) = 3.03 ( 1 ) − 0.40

(17)

∇3

4.0

In CFD the total viscous drag is measured from a wake traverse so that the direct physical measurement of resistance components is given by equation.

Where CV is viscous resistance coefficient and CP is pressure resistance coefficient. To calculate the total resistance, the wave resistance coefficient is obtained by experimental data (Molland, 1994), and the frictional resistance coefficient is calculated by using the form factor and ITTC’57 correlation line so that the total resistance coefficient can be expressed as:

CTcal = (1 + k) CFITTC + CWexp

CT-Cal CT-CFD

103CT

6.0 5.0 4.0 3.0 0.2

0.4

0.6 Fn

0.8

Figure 6: Comparison of total resistance [Mono-hull form - 4a]

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0.4

0.6 Fn

0.8

1.0

Figure 7: Comparison of total resistance [catamaran - 4a]

CFD ANALYSIS OF TRIMARAN

(19)

Comparisons of total resistance between CFD and calculation data for mono-hull and catamaran are plotted as shown in Figure 6 and 7.

7.0

0.2

(18)

CT = CV + CP

8.0

2.0

1.0

Figure 6: Wave profile around the hull [Fn=0.8] With good agreements between experimental results and CFD data, the total resistance of the trimaran hulls are computed by ANSYS FLUENT. It carries out to calculate the total resistance of the trimaran hull forms in the high-speed range corresponding to Froude number from 0.4 to 1.0. Multiphase boundary condition defined as air and water flows involves the simultaneous flow of two interacting phases. The VOF applied in CFD are the separated multiphase flows that are only interested in the liquid phase and free surface flows of open channel. The turbulence model is set up for realizable k-ε method, and the pressure boundary is chosen for the coupling of inlet and outlet, which involves the turbulence intensity and length scales setup. Particularly in this model, the turbulence intensity is set below 1% for external flow, which is a condition for low turbulence. In this study the solver are set in the pressure-velocity coupling scheme so that SIMPLE scheme applies to the VOF models. When the residuals scale is converged, the wave resistance coefficients of a trimaran hull configuration are computed and solved. The results of the wave resistance coefficients on the systematic trimaran model are given by Table 3 and figure 8. It indicates the wave resistances slightly decline when the Length to Beam ratios (L/B) increase over Froude number 0.6. The volume fraction on the free surface computed by CFD is shown in Figure 9.

CFD SIMULATION OF RESISTANCE OF HIGHSPEED TRIMARAN HULLFORMS

5

3.5

TRI-4a [L/B=10.4] TRI-4b [L/B=9.0] TRI-4c [L/B=8.0]

2.5 2.0

Model

B/T

L/B

Form factors

4a

1.5

10.4

1.21

4b

2

9

1.32

4c

2.5

8

1.44

103CW

3.0

Table 4: Form factors of trimaran

1.5 1.0 0.3

0.5

Fn 0.7

0.9

Figure 8: Wave resistance coefficients of trimaran hull [S/L=0.2] Table 3: Total and wave resistance coefficients of trimaran 4a 4b 4c Fn 3 3 3 3 3 10 CT 10 CW 10 CT 10 CW 10 CT 103CW 0.4

5.483

2.125

5.773

2.433

5.996

2.664

0.5

5.97

2.93

5.994

2.983

5.952

2.944

0.6

5.97

2.81

6.034

2.879

6.088

2.927

0.7

5.739

2.435

5.765

2.475

5.812

2.515

0.8

5.518

2.115

5.559

2.177

5.659

2.272

0.9

5.199

1.758

5.234

1.821

5.326

1.918

1.0

4.9

1.417

4.933

1.495

5.038

1.624

TOTAL RESISTANCE OF TRIMARAN The total resistance of a trimaran hull form consists of the fictional resistance and wave resistance as expressed by equation: As per CFD

CT (CFD) =CV+CP

Figure 9: Free surface wave contours at Fn 0.8 – 4a Table 5: Calculated resistance coefficients of trimaran-4a 103CT

103CT

(Cal)

(CFD)

2.125

7.025

5.483

4.686

2.93

7.616

5.97

1.21

4.521

2.81

7.331

5.97

0.7

1.21

4.389

2.435

6.824

5.739

0.8

1.21

4.279

2.115

6.394

5.518

0.9

1.21

4.185

1.758

5.943

5.199

1

1.21

4.104

1.417

5.521

4.9

Fn

1+k

103(1+γk) CF

103CP

0.4

1.21

4.9

0.5

1.21

0.6

(20) Table 6: Calculated resistance coefficients of trimaran-4b

As per calculation `

CT cal = (1 + γk) CF + τCW

103(1+γk)CF

103CP

(21)

To calculate the total resistance, the form factor is used for calculation of the fictional resistance coefficient with ITTC’57 correlation line. Calculated total resistances and CFD results are given by Table 5 to 7, and the comparisons are shown in Figure 10 to 12.

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1+k

103CT

103CT

(Cal)

(CFD)

0.4

1.32

5.345

2.433

7.778

5.773

0.5

1.32

5.112

2.983

8.095

5.994

0.6

1.32

4.932

2.879

7.811

6.034

0.7

1.32

4.787

2.475

7.262

5.765

0.8

1.32

4.667

2.177

6.844

5.559

0.9

1.32

4.565

1.821

6.386

5.234

1

1.32

4.476

1.495

5.971

4.933

CFD SIMULATION OF RESISTANCE OF HIGHSPEED TRIMARAN HULLFORMS

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Table 7: Calculated resistance coefficients of trimaran-4c Fn

1+k

3

3

103(1+γk)CF

103CP

10 CT

10 CT

(Cal)

(CFD)

10.0

CT-Cal

9.0

CT-CFD

8.0

1.44

5.841

2.664

8.505

5.996

7.0

0.5

1.44

5.586

2.944

8.53

5.952

6.0

0.6

1.44

5.389

2.927

8.316

6.088

5.0

0.7

1.44

5.231

2.515

7.746

5.812

0.8

1.44

5.1

2.272

7.372

5.659

0.9

1.44

4.988

1.918

6.906

5.326

1

1.44

4.891

1.624

6.515

5.038

103CT

0.4

4.0 3.0 0.3

0.5

Fn 0.7

0.9

Figure 12: Comparison of total resistance [trimaran – 4c]

CONCLUSION 10.0 CT-Cal 9.0

CT-CFD

8.0

103CT

7.0 6.0 5.0 4.0 3.0

0.3

0.5

Fn

0.7

0.9

Figure 10: Comparison of total resistance [trimaran – 4a] 10.0

CT-Cal

9.0

CT-CFD

With good agreements between calculated results and CFD investigation data, the wave resistance coefficients of trimaran hull forms were computed as having shown considerable promise and economical advantage when compared to model testing. The results show that the wave resistances decreases with respect to increases in the Length to Beam ratio (L/B) of trimaran hull forms. Indeed, those results are very achievable works, since few published articles are in existence regarding to the resistance characteristics of trimarans. In addition, with the obtained total resistance, the form factors of NPL systematic series of 4a, 4b and 4c models were found by using the Prohaska (1966) method. The results showed the form factor increased corresponding to the Beam-Draft ratio (B/T), as given by Table 4. With the obtained form factor, the total resistances were calculated, and CFD results were compared with calculated results. In conclusion, this thesis shows that the characteristics of wave resistance obtained by CFD reveal a significant consistency with another prominent research paper including the experimental and numerical analysis. Therefore, the process of this study provides the advantages of economy of time and cost consumption in the relevant fields.

ACKNOWLEDGEMENTS

8.0 The authors would like to express their sincere gratitude to Florida institute of technology for its support, encouragement throughout the course of this research work. The authors also extend their sincere thanks to numerous people without whose valuable contributions this paper would not have seen the light of the day.

103CT

7.0 6.0 5.0 4.0

REFERENCES

3.0 0.3

0.5

Fn

0.7

0.9

Figure 11: Comparison of total resistance [trimaran – 4b]

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