preliminary study on the use of computational fluid dynamics to determine the frictional resistance...

8/14/2019 Preliminary Study on the Use of Computational Fluid Dynamics to Determine the Frictional Resistance of a Trimaran Ship

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Preliminary Study on the Use of Computational Fluid Dynamics toDetermine the Frictional Resistance of a Trimaran Ship

Author: Alexander W. Gray

Thesis Mentor: Dr. Andrei Smirnov

Submitted To:

West Virginia University, The Honors College248 Stalnaker Hall

P.O. Box 6635Morgantown, WV 26506

phone: 304-293-2100

Submitted By:

Alexander W. Gray3909 Autumn Dr.

Huron, OH 44839phone: 419-626-1388

Major: Mechanical and Aerospace EngineeringMinor: Mathematics

Date of Submission:May 4, 2007

Submitted as partial completion of the Requirements

for graduation as a University Honors Scholar


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Preliminary Study on the Use of Computational Fluid Dynamics to

Determine the Frictional Resistance of a Trimaran Ship

Alexander W. Gray

Majors: Mechanical EngineeringAerospace Engineering

Minor: MathematicsSchool Address: West Virginia University

College of Engineering and Mineral ResourcesP.O. Box 6070

Morgantown, WV [email protected]

Thesis Mentor: Dr. Andrei Smirnov

Abstract

The purpose of this study is to assess the use of Computational Fluid Dynamics

(CFD) for the calculation of frictional resistance. To make this assessment, CFD

simulations were implemented on a trimaran hull design; a trimaran is a three hulled ship.

The trimaran ship was modeled from the design waterline down to the keel for the

purposes of eliminating air/water interactions and wave formation that causes wave drag.

The CFD simulations were run at speeds of 2, 5, 7, 10, 14, 17, and 20 m/s and the drag

coefficient was recorded for each simulation and then used to calculate the frictional

resistance of the trimaran. The frictional resistance values from the CFD simulations

were then compared to theoretically correct frictional resistance values calculated by use

of analytical equations.

The study shows that the use of CFD to calculate the frictional resistance proves

to be more complex and requires more time than that required by use of the analytical

method. In addition, the CFD results of this study proved to be inaccurate and produced

a high percent error when compared to the theoretically correct values. The poor results

are believed to be a consequence of either an insufficient finite element mesh for the

trimaran model or an error in the setup of the CFD simulation; i.e. the choice of the

turbulent flow model. Based on the time and knowledge required to properly implement


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and run CFD simulations, it is concluded that CFD is an inefficient method to use for the

calculation of the frictional resistance of a trimaran ship.

Introduction

Computational Fluid Dynamics, abbreviated CFD, is defined as a computational

technology that enables you to study the dynamics of things that flow (FLUENT Inc.,

2007). In broader terms, CFD is a type of computer software that is designed to enable a

user to simulate the flow of fluid matter around or through a computer-generated model.

CFD is utilized in a wide variety of fields, including engineering, biology, physiology,

and meteorology to name just a few. Applications of CFD range from simple 2-D models

of flow over an airfoil shape, to complex 3-D models of dust particles entering a persons

lungs, flow past a boat sail, airflow in a tornado, or more complex models of entire planes

and ships, to name a few examples. In this study, CFD was used to model the flow of

water passed a trimaran ship hull.

When designing any marine vessel it is necessary to determine the ships total

resistance in order to calculate the ships maximum speed, and to determine what size

engine is required to reach a desired cruising speed. The size of the engine will affect the

weight of the ship and the amount of fuel the ship consumes. As the cost of fuel

continues to rise, greater attention must be paid to the fuel economy of a ship. This is

where CFD comes into the picture. CFD allows ship designers to create a computer-

generated model of a ship and then test the ship at various speeds in a simulated

environment. The results from the CFD simulations can be analyzed to determine the

total resistance of the ship at each speed tested. This allows designers to determine if the

total resistance of the ship is at an acceptable level from a financial standpoint as well as

a physical standpoint. The financial perspective relates to the cost of the engine and the

fuel that the engine consumes in order to meet the ships mission requirements. The

physical viewpoint is in reference to the fact that most monohull ships have a maximum

achievable speed of around 30 knots, approximately 15m/s (Zhang 1997). Based on the

results of a CFD simulation, a designer can choose to rethink the ship design or proceed

to a scaled model test.


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Scaled model testing in a water-filled towing tank is still considered the most

accurate method of determining the total resistance of a ship. However, scaled model

testing is a costly and time-consuming process. Therefore, ship designers utilize CFD in

order to save time and money. A designer can change the shape of a computer model

much quicker than a physical model, allowing for a faster and cheaper iterative design

process where a ship design is tested, corrected, and then re-tested using CFD until

achieving the desired results. Via CFD analysis, a manufacturer can lower costs of

building their ships by reducing the amount of time and money spent on towing tank

tests, thereby providing their buyers with optimized designs. This optimized design

process can reduce drag and fuel consumption, saving the buyers on the purchase of

costly fuel; here in lies the importance and many benefits of CFD.

The purpose of this thesis is to discuss the use of Computational Fluid Dynamics

to simulate the fluid flow around a trimaran ship hull. The issues discussed in this thesis

are relevant to any field of study that may apply CFD, but specifically to the areas of

hydrodynamics, fluid dynamics, mechanical and aerospace engineering, and marine

engineering. This thesis discusses some of the numerous methods for use in setting up

and running a CFD simulation. This thesis study will also comment on the steps taken to

create the three-dimensional Computer Aided Design (CAD), finite element mesh, and

boundary conditions of the model. In addition, the study will convey the authors

insights into CFD simulation. These insights may aid in avoiding beginners mistakes

and save precious time.

Background

Computational Fluid Dynamics can be thought of as an approach to studying the

fields of fluid dynamics, aerodynamics, and hydrodynamics. CFD is a relatively new

product of two much older approaches to the study of fluid dynamics and aerodynamics,

namely the experimental and theoretical approaches (Anderson 1995). With time, as

computers became capable of more and more complex calculations, researchers began to

analyze their experimental data and theoretical equations by use of self-written computer

programs. Soon, enough researchers were writing computer programs to solve simple

flow models and CFD was born. Now, with the advances in computer hardware and


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software, CFD is constantly reaching new levels of modeling capabilities and is being

used in hundreds of academic and commercial fields ranging from biology and

engineering to car and swimsuit design.

In the past, relatively simple two-dimensional flow simulations could be coded

and the results would appear as a graph or data output. Todays CFD programs such as

FLUENTand CFXare capable of simulating complex three-dimensional flows and the

results can be obtained in numerous outputs such as graphs, contour plots, flowlines, and

vector plots. Recent advances in CFD have enabled researchers to simulate turbulent

flows and/or mixed flows; mixed flow involves more than one fluid type. Turbulent and

mixed flow types involve numerous complex, non-linear equations to be solved

simultaneously.

The process by which a CFD program works is beyond the scope of this paper.

However, the basic process starts by creating a computer-generated model of an object

and the desired flow domain, i.e. an airplane wing, air duct, pipe, or boat, using a

Computer Aided Design (CAD) software package. The models flow domain is the area

or volume through which the fluid is moving. Using the example of a pipe, the flow

domain is the entire inside of the pipe. For an airfoil (an external flow), the flow domain

consists of the region surrounding the airfoil, and the domain is as large as the user

creates it to be. After creating the model and flow domain, the CAD drawing is then

loaded into another computer program where a grid of points, also called a mesh, is

created across the model and throughout the flow domain. The grid spacing can be of

various shapes and sizes, uniform or non-uniform, structured (Figure1) or unstructured

(Figure 2), in order to properly line up with the geometry of the model.


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Figure 1: F-16 Airplane with 3-D Structured Grid (Anderson)

Figure 2: Multi-element Airfoil and Flow Domain with

2-D Unstructured Grid (Anderson)

It is desired to have many grid points on and near the surface of the geometry in order to

create a proper representation of the model geometry and flow properties within the CFD

program. Figure 3 shows an airfoil with a uniform rectangular grid; Figure 4 shows an

airfoil with a stretched grid to properly represent the airfoil geometry.


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Figure 3: Uniform Structured Rectangular Grid on Airfoiland Flow Domain (Anderson)

Figure 4: Structured Non-Uniform Grid on Airfoil

and Flow Domain (Anderson)

In the last few steps of the procedure, the model is loaded into the CFD program

where the user enters information about the flow that they are simulating, such as fluid

type, temperature, and speed. The CFD program then takes the information entered by

the user and applies it to each of the models grid points. The final step involves an

iterative process where the governing flow equations are solved at each grid point

repeatedly, until the computer obtains a solution that is constant from one iteration to the

next; when this happens the solution is said to have converged. This is the reason for

having many grid points on or near the surface of the model geometry, the grid points are

where the flow information is being derived during the CFD simulation. Hence, the more

grid points, the more accurate the simulation and the more representative the results are

to the physical flow.

Among its many applications, CFD has been used in the fields of marine and

ocean engineering for quite some time. Because of the demand for fast ships with low

resistance, ship designers have turned to non-conventional designs to try to meet the


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market demands. Conventional designs are thought of as monohull displacement and

planing vessels. A displacement ship is one that constantly displaces an amount of water

equal to its weight while in motion. A planing ship is one that moves atop the water

surface while in motion. Non-conventional designs are typically multi-hull, Small

Waterplane Area Twin Hull (SWATH) vessels, and other unique ship designs.

The vessel being studied in this thesis is a multi-hulled ship called a trimaran.

The typical trimaran design consists of three slender hulls, one long main hull and two

shorter outriggers, also called wing hulls or side hulls, as shown in Figure 5.

Figure 5: Sail Powered Trimaran Showing Location of Main Hull

and Outriggers (Latitude 38 Publishing Co., Inc.)

The trimarans outriggers are attached to the main hull on either side and provide the

trimaran with its excellent sea-keeping and stability characteristics (Kang, et. al. 2001).

Sea-keeping refers to the stability of a ship in a wavy environment, while at rest or in

motion. A trimaran vessel can be driven by wind, as in Figure 5, or mechanically driven

by means of propeller or water-jet.

The unique design of a trimaran ship provides the vessel with many admirable

characteristics that make it attractive for use in high speed marine applications. For

instance, the slender hulls of the trimaran design yield a small beam to length ratio and,

therefore, a decreased amount of wave making resistance (Armstrong 2004). Wave

making resistance is defined as the resistance due to the loss of energy to the formation of

waves (Harvald 1983). It has been shown by (Xu, H. and Zou, Z. 2001) and (Kang, Kuk-


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Jin et. al., 2004) that the wave making resistance can also be decreased by the proper

placement of the outriggers with respect to the main hull. The lower wave making

resistance at high speeds is the biggest advantage to the use of the trimaran design and

has been well documented in numerous studies.

The main drawback of the trimaran design is the increase in wetted surface area,

S, which is the surface area of the ship hull that is in direct contact with the water

(McComas 2007). The increased wetted surface area of the trimaran creates a large body

on which the frictional resistance acts. At lower speeds, the frictional resistance is

greater than the wave making resistance causing the trimaran design to be

disadvantageous at low speeds. It is not until the high speed range, during which the

wave making resistance is greater than the frictional resistance, that the trimaran design

becomes advantageous over the monohull design. For proof of this phenomenon see

Figures 6 and 7, which show the effective power required to overcome the total resistance

on the ship and achieve a given speed.

Figure 6: Predicted Effective Power Requirements for 5000 Tonne Trimaran

and Equivalent Monohull Vessel (Skarda & Walker 2004)


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Figure 7: Predicted Effective Power Requirements for 9500 Tonne Trimaran

and Equivalent Monohull Vessel (Skarda & Walker)

Although the trimaran design produces greater resistance than a monohull vessel

at slower speeds, the increased stability provided by the trimarans outriggers, in addition

to its lower resistance at high speeds, has allowed the trimaran to be utilized for a wide

variety of nautical applications. Trimarans are frequently used for racing, mass transit,

and recreation due to their high speed capability and excellent sea-keeping stability. The

trimaran design is also favorable for military and research applications because of the

wide deck space for placement of armaments and equipment. In addition, trimarans have

a very shallow draft; which is defined as the distance the boat extends below the water

surface. The lower draft would allow a trimaran to navigate waters and ports that are

much too shallow for an equivalent monohull ship. Several studies, (Skarda & Walker)

and (Professional Engineering 1997), have shown that the trimaran design provides added

protection from torpedo attacks and, hence, improved survivability characteristics, in

addition to the fact that the, sleek design would shrink its radar signature (Popular

Mechanics 1996). Due to the trimarans numerous military benefits, a joint study was

conducted by the U.S. Navy and the British Defense Evaluation and Research Agency

(DERA) on a two-thirds scale trimaran ship called the RV Triton (Figure 8); RVstands

for research vehicle.


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Figure 8:RV Triton Test Platform for the Feasibility of the

Trimaran Design (Global Security.org 2007)

The purpose of the study was to demonstrate the feasibility of the trimaran design.

TheRV Triton had a length overall (LOA) of 95 m, weight of 800 tonnes, and draft of

only 3 m. The results from the study on theRV Triton conducted by the hydrodynamics

department of the defense contractor QinetiQ confirmed that the trimaran concept offers

some significant hydrodynamic benefits over a conventional monohull, with no major

drawbacks (Renilson, et. al. 2004).

As seen, the advantages and disadvantages of the trimaran design due to frictional

resistance and wave making resistance are well known. A great deal of research has been

done on the calculation of the wave making resistance using theoretical equations and

numerical analysis. However, the frictional resistance of the trimaran is typically

obtained by theoretical calculations or by performing towing tank tests to determine the

total resistance, and then subtracting the wave making resistance to obtain an estimate of

the frictional resistance. Since, the frictional resistance of a trimaran is of such great

importance at a wide range of speeds, it was desired to devise additional methods of

calculating the frictional resistance of the trimaran. CFD analysis of the trimaran hull

form can be utilized in order to calculate the frictional resistance of the ship.The formal objective of this study is to determine the frictional resistance of a

trimaran hull form using Computational Fluid Dynamics analysis. In doing so, the use of

CFD as a tool for the calculation of the frictional resistance will be evaluated. The

trimaran design, hull form, and dimensions were adopted from a previous study

conducted entitled, A Preliminary Study of Trimarans (Gray 2006).


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Methodology

Resistance of a marine vessel is defined as, the fluid force(s) acting on the ship

in such a way as to oppose its motion (Harvald). The total resistance of a ship,RT, isdivided into two main subcategories of resistance, the residuary resistance, RR, and the

frictional resistance, RF. The residuary resistance is equal to the total resistance minus

the frictional resistance (Munro-Smith 1973),

FTR RRR . (1)

The residuary resistance can be further broken down into numerous individual

components of resistance, with the main component being the wave making resistance,

Rw. The focus of this study however, is on the calculation of the frictional resistance.

The frictional resistance is defined as, the component of resistance obtained by

integrating the tangential stresses over the wetted surface of the ship in the direction of

motion (Harvald). The wetted surface area of a ship, S, is the area of the ship hull that is

in direct contact with the water. In short, the wetted surface area is the volumetric

displacement of the vessel. The wetted surface area can be calculated directly using

integral techniques, or it can be estimated using analytical approximations, two such

approximations are given in equations 2 and 3,

BLBTCS , (2)

LCS . (3)

In Equation 2,L is the length of the ship at the ships design waterline,B is the breadth of

the ship at the widest location, T is the depth (draft) of the ship, and CB is the block

coefficient. The block coefficient can be calculated using equation 4,

BTLC

pp

B

,

(4)

where The block coefficient is the ratio of the vessels volume of displacement, to the

volume of a rectangular block whose sides are equal to the breadth extreme B, the mean

draught T, and the length between perpendicularsLpp (Figure 9).


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Figure 9: Ship Dimensional Variables (Rawson 1976)

Note, in this paper Lpp is also referred to as L, the total length of the ship at the design

waterline. The design waterline of a marine vessel is the location of the water surface

with respect to the vessels hull. In Equation 3, C is a correction coefficient, generally

about 2.58, is the displacement of the vessel in tonnes, and L is the length in meters

(Munro-Smith). Using either Equation 2 or Equation 3 will give a reasonable

approximation of the wetted surface area of the ship.

One advantage to the use of Computational Fluid Dynamics is that many CFD

programs are capable of calculating several physical properties of the models geometry.These properties include, for example, the integral calculation of the ships entire surface

area or volume. Calculating the surface area of the ship in this manner provides a more

precise answer than can be obtained by the approximations of Equations 2 or 3, since the

area is obtained by direct analysis of surface integrals. After calculating the vessels

wetted surface area, the value for the ships coefficient of friction must be obtained. The

coefficient of friction is a function of the Reynolds number and can be estimated by using

the ITTC 1957 Model-Ship Correlation Line (Harvald), which is produced by means

of,

210 2log075.0

n

FR

C .(5)

Once the value of the ships coefficient of friction is established, the frictional resistance

may be calculated.


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To ascertain the efficiency of using Computational Fluid Dynamics to calculate

the frictional resistance, several properties of the trimaran vessel are determined by

means of CFD simulations. These values include the wetted surface area, S, and the

coefficient of friction, CF. The frictional resistance, RF, is then calculated utilizing the

data resulting from the CFD simulations of the trimaran run at various speeds. The

processes carried out to develop solutions to the frictional resistance of the trimaran hull

form involved the use of several commercial computer software programs. The program

ProE, was utilized for the creation of the Computer Aided Design (CAD) three-

dimensional trimaran model, GAMBITwas then used to create the finite volume mesh of

the model, and lastly the CFD analysis was carried out with the use of FLUENT. The

results of the CFD simulations were examined and compared to analytically calculated

trimaran data and towing tank test data of a scaled trimaran model in order to determine

the efficiency and reliability of the application of CFD to calculate the frictional

resistance for a trimaran ship design.

In order to obtain a CFD calculation of only the frictional resistance of the

trimaran, one must take into consideration that the resistance of a ship consists of several

components of resistance. The total resistance of a ship can be broken down into at least

a dozen different components of resistance other than those already mentioned, i.e.

viscous, pressure, viscous pressure (form), appendage, and air resistances (Harvald).

Care must be taken when deciding how to model the trimaran design in order to maintain

focus on the goal of obtaining only the frictional resistance component of the trimaran.

The two main components of the total resistance are the frictional and wave making

resistances, which are summed to produce the total resistance,

FRT RRR . (6)

In Equation 6,RR is the residuary resistance, of which the greatest component is the wave

making resistance,RW. It is therefore desirable to model the trimaran in such a way as to

eliminate the wave making resistance, thereby isolating the frictional resistance. A novel

approach to the trimaran model was taken to achieve the elimination of the wave making

resistance when running CFD simulations. This approach involved the modeling of the

trimarans hulls from only the design waterline down to the keel. Figure 10 illustrates the

meaning of the design waterline and keel of a trimaran.


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Figure 10: Trimaran Ship Design Waterline and Keel (Clarke 1975)

Modeling the trimaran in this manner eliminates the need to run a multiphase (i.e. more

than one fluid type) CFD simulation. By removing the air/water interface and setting the

design waterline as the top of the control volume domain, the ability to create waves, and

hence wave making resistance, is eliminated.

For this study, the trimaran model was created in the manner as just described,

from the design waterline to the keel. Station coordinates, found in Tables 1 and 2,

describing the trimarans planforms, which may be found in Appendix A, were used to

create a three-dimensional model of the trimaran, using CAD software.

Table 1: Main Hull Trimaran Station Coordinates (mm)

Design

Waterline

Keel


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Table 2: Outrigger Trimaran Station Coordinates (mm)

The station coordinates that are given in units of mm, were converted over to (x, y, z)

coordinates with units of meters for the purpose of creating the trimaran model at full

scale in three-dimensional space. The resulting values may be found in Tables 3 and 4.

Table 3: Station Coordinates for Main Hull Converted to (x,y,z) Coordinates (m)


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Table 4: Station Coordinates for Outriggers Converted to (x,y,z) Coordinates (m)

With the station coordinates for the trimarans main hull and outriggers converted to(x,y,z) coordinates with units of m, the resulting dimensions for the main hull and

outriggers were as tabulated in Table 5.

Table 5: Trimaran Dimensions

Figure 11 shows a schematic representation of the dimensions referred to in Table 5. The

dimensions govern the size of the trimaran hulls, as well as the location of the wing hulls

with respect to the main hull.

Figure 11: Description of Trimaran Main and Wing Hull Dimensions (DUT 2007)


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The remaining dimensions for the trimaran, as obtained from (Gray 2000), result

in the outriggers being placed at a distance b=5 m, in the y-direction from the center, o,

of the main hull and a distance ofa=0 m, in thex-direction from the origin, o. The CAD

package ProEwas utilized for the creation of the three-dimensional trimaran model. A

detailed description ofProEdrawing process may be found in Appendix B.

Once the ProEtrimaran model was complete, the fluid flow domain for the CFD

simulation was then established. The creation of the flow domain can be done using the

any CAD program, such as ProE. For this study, the trimaran drawing was first imported

into the meshing program GAMBIT. After importing the drawing, the flow domain and

finite volume mesh were created using tools within GAMBIT, the details of which may be

found in Appendix D. In an attempt to test for grid independence, which is obtained

when the results from consecutive CFD simulations change a negligible amount after

increasing the number of finite elements in the model and then retesting, the same

trimaran model was meshed two separate times. The resulting meshed trimaran models

are referred to as Trimaran5 and Trimaran7. Again, Appendix D details the meshing

process of both trimarans. Trimaran5 was meshed with a total of 219,923 finite elements

and Trimaran7, as desired, was meshed with a greater number of finite elements,

278,258. Comments will be made later on this studys attempt to test for grid

independence.

The CFD program FLUENT, created byANSYS Inc., was used for the simulation

of the fluid flow around the trimaran hull for the purpose of calculating the frictional

resistance of the trimarans hulls. A detailed listing of the steps taken to set up and

perform the FLUENTCFD analyses can be found in Appendix E. Using FLUENT, the

CFD simulations were setup and run for speeds of 2, 5, 7, 10 14, 17, and 20 m/s. The

purpose of running at multiple speeds was to gather frictional resistance data across a

spectrum of the trimarans possible operating speeds. A point of note need be made here;

during the first attempt at performing simulations on Trimaran5, an error was made in the

input of the value for the turbulence kinetic energy, TKE(m2/s

2). The error stems from

assuming the value to be constant during initial simulations of Trimaran5. However, the

TKE is actually a function of the velocity, as noted in Equation 7 (Smirnov 2006), and

therefore not constant from simulation to simulation as the velocity changes,


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2*01.0 VTKE . (7)

The simulations for the CFD model Trimaran5 were consequently run twice to

correct for the error made during the first set of simulations. The two sets of simulations

are referred to as Trimaran5 Old and Trimaran5 Correct, or simply Tri5_Old and

Trimaran5. Later the results are compared to show the effect of the TKEvalue on the

simulations. In addition, the results from Trimaran5 Corrected and Trimaran7 are also

compared in an attempt to prove grid independence.

Several approaches were taken in order to assess the effectiveness of using CFD

for the calculation of the frictional resistance of a trimaran. The CFD data was compared

to analytically determined values of the frictional resistance of the full-scale trimaran, as

well as data obtained from scaled model tests of the trimaran design in a water towing

tank.

Calculation of the trimarans frictional resistance, was used as display in Equation

8,

SVCR FF2

21 . (8)

In order to use Equation 8, one must first determine both the coefficient of friction, CF,

and the wetted surface area, S. For the analytical results, the frictional resistance was

determined using the ITTC 1957 Model-Ship Correlation Line (Harvald), and Equation

5, reproduced here for convenience,

210 2log075.0

n

FR

C ,(5)

to calculate the coefficient of friction, and Equation 8 to then calculate RF. When using

Equation 8, the wetted surface area, S, was found by use of FLUENT. Equation 5 is

dependent on the Reynolds number,Re, calculated using (Young, et. al 2004),

VLRn .

(9)

Since, the coefficient of friction is based on the Reynolds number, which in turn is

based on the length of the ship, the Reynolds number, coefficient of friction, and the

frictional resistance components must be calculated separately for both the main and side

hulls of the trimaran. The separate components are then added to obtain an analytical


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value for the total frictional resistance of the trimaran. The numerical results for the

frictional resistance are calculated using only Equation 8 with the values for CF and S

over the entire trimaran ship being found directly from the CFD simulations using

FLUENT.

Results

The purpose of this preliminary study was to determine the effectiveness of using

Computational Fluid Dynamics for the calculation of the frictional resistance of the

trimaran hull form. In order to assess the effectiveness, the programs ProE, GAMBIT,

and FLUENTwere utilized for the creation of the three-dimensional trimaran drawing,

meshing, and CFD simulations, respectively. The numerical results obtained from

FLUENT, in conjunction with analytical formulas, were used to calculate the frictional

resistance of the trimaran. The results obtained from these calculations were then

compared to results of a towing tank test of a scaled model trimaran. The scaled model

test data was obtained courtesy of the Naval Architecture Department at Dalian

University of Technology in Dalian, China.

The resulting three-dimensional ProE drawings can be seen in Appendix F

followed by pictures of the GAMBIT generated control volume, Trimaran5, and

Trimaran7 meshes in Appendix G. Figure 12 shows the resulting final dimensions of the

GAMBITmodel that was later meshed for use in the CFD simulations.


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Figure 12: Dimensions of Flow Domain for CFD Simulations

After meshing the trimaran and control volume, the CFD simulations were run

using FLUENT and the results for the drag coefficient were compiled. As mentioned

earlier, because of the way in which the trimaran and flow domain were drawn, the

resulting drag coefficient values obtained from the CFD simulations are composed of

only the frictional resistance component and a much smaller pressure drag coefficient

value. Table 6 shows the values obtained for the frictional resistance coefficient at each

speed tested for Trimaran5 Old, Trimaran5, and Trimaran7.Table 6: Coefficient of Friction for all Trimaran CFD Simulations

After obtaining the values for the frictional resistance coefficient, the value of the

frictional resistance was then determined using Equation 8, reproduced here for

convenience,

SVCR FF2

21 . (8)


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In order to determine the frictional resistance, the value for the wetted surface area was

first obtained from FLUENT. The resulting value for the wetted surface area was

determined to be S=233.4694 m2. The frictional resistance values for the three sets of

trimaran simulations were then compiled in Table 7.

Table 7: Calculated Frictional Resistance Values for CFD Trimaran Simulations

In order to verify that the CFD simulations are accurate, the data was compared to

analytically calculated values of the frictional resistance; the analytical values were

assumed to be theoretically correct. Using the ITTC 1957 Model-Ship Correlation Line,

Equation 5, the analytical frictional resistance coefficient values were calculated,

followed by the calculation of the frictional resistance values for the trimaran itself using

Equation 8. The theoretical value of the coefficient of friction for the side and main hull

are as presented in Table 8.

Table 8: Analytical Values for Coefficient of Friction

From the friction coefficient values for the side and main hulls, the frictional resistance of

the side hull, main hull, and total trimaran were calculated and tabulated in Table 9.


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Table 9: Analytical Values for Frictional Resistance of Trimaran

After completing the numerical and analytical calculations for the coefficient of friction,

as well as the frictional resistance for the trimaran design, it is appropriate to compare the

analytical and numerical results to determine the accuracy of the CFD simulations.

Discussion

The purpose of this study was to assess the use of Computational Fluid Dynamics

for the determination of the frictional resistance of the trimaran hull form. In order to

assess the use of CFD for determining the frictional resistance of the trimaran, CFD

simulations were compared to analytical calculations of the frictional resistance and

towing tank test data obtained from a scaled trimaran model. To compare the scaled

model towing tank test data to the CFD data, the results from the towing tank tests were

re-scaled to equivalent full-scale values. The data is referred to as the Converted Model

Data. The resulting comparisons of the numerical CFD data, the analytical values, and

the Converted Model Data can be seen in Table 10 and Figure 13.

Table 10: Frictional Resistance Data for the Trimaran Design


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Figure 13: Results for Trimaran Frictional Resistance Calculations vs. Speed

Table 10 and Figure 13 clearly show that the CFD results for the trimaran

frictional resistance do not agree with the analytical results. Table 10 and Figure 13 also

show that the difference in keeping the turbulence kinetic energy constant versus

changing the value based on the velocity, as in Equation 7, yields a negligible difference

in the results from for the frictional resistance. The differences in the CFD and analytical

results yield large percent errors, as may be observed in Table 11.

Table 11: Percent Error for CFD Frictional Resistance Data Based on Analytical Data

Speed (m/s) Tri5_Old

Corrected

Trimaran5 Trimaran7

2 1.650E+08 1.644E+08 1.511E+08

5 1.171E+09 1.171E+09 1.081E+09

7 2.402E+09 2.403E+09 2.223E+09

10 5.139E+09 5.143E+09 4.759E+09

14 1.052E+10 1.053E+10 9.758E+09

17 1.591E+10 1.593E+10 1.476E+10

20 2.248E+10 2.250E+10 2.087E+10


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A check was made to ensure that the analytical values were correctly calculated. Two

analytical resistance values at speeds of 5 m/s and 6.5 m/s were compared to the

Converted Model Data for the corresponding speeds and shown in Table 12.

Table 12: Percent Error for Analytical Frictional Resistance Data

Based on Converted Scale-Model Test Data

Speed (m/s) Analytical

5 1.53

6.5 50.84

The percent error for the speed of 5 m/s proved to be a reasonably small value.

However, the percent error for the speed at 7 m/s was higher than desired. One reason for

the high percent error may be due to the difference in calculated wetted surface area

between the converted model data and the CFD data. The wetted surface area of the

scaled model was S=2.302 m2, which converts to S=230.2 m

2, whereas the wetted

surface area calculated for the CFD trimaran model was S=233.4696 m2. The differences

in wetted surface area could be due to small differences in the trimaran hull shape for the

scaled model versus the CFD model. Taking into consideration the differences in the hull

wetted surface areas between the scaled and CFD models, it is still reasonable to assume

that the analytical results were correctly calculated. Since the analytical values are based

off of the International Towing Tank Conference 1957 Model-Ship Correlation line,

which is a proven method of calculation, these analytical values are used as the

theoretically correct values for the comparison of the frictional resistance of the trimaran

ship.

Knowing that the analytical results were correctly calculated, using Equations 5

and 8, the CFD results are revisited. The percent error between the analytical results and

the CFD results is extremely high. This extreme difference indicates that the CFD results

inappropriately represent the frictional resistance on the trimaran ship. Due to the

complexity of setting up a CFD analysis, there are many opportunities for error. One

possible source of error is an inappropriate finite volume mesh of the model. To test this

theory, an initial effort was made to check for grid independence of the CFD model. If

grid independence is obtained then the finite volume mesh is appropriate, if it is not


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obtained this would indicate a need to refine the mesh by increasing the number of

elements in the mesh. The efforts to check for grid independence resulted in the

simulations Trimaran5 Corrected and Trimaran7 with respective mesh sizes of 219,923

and 278,258 finite elements. The CFD simulations were run at several speeds between 2

m/s up to 20 m/s, and the results are shown in Figure 14.

Figure 14: Frictional Resistance Plot for Trimaran5 Correct and Trimaran7

Figure 14 indicates that as the speed increases the values for the frictional

resistance for Trimaran5 Corrected and Trimaran7 diverge. This leads to the conclusion

that grid independence was never reached for the CFD simulations. If there are not

enough grid points in the finite element mesh of the model, then the CFD program will

not see the appropriate geometry when running simulations. Figure 15 shows an

explanation of the correlation between the finite grid representation and the CFD

interpretation of the grid.


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Figure 15: Interpretation of Finite Grid in CFD Program

In Figure 15, the black dots represent finite elements. The shape with the greater amount

of finite elements retains a better representation of its true geometric shape when

interpreted by the CFD program. The lack of grid independence leads to the conclusion

that the true shape of the trimaran ship is not being accurately depicted within FLUENT.

It is recommended that the finite element mesh of the three-dimensional trimaran

model continue to be refined until achieving grid independence. Once grid independence

has been achieved, the new CFD results could then be compared to the analytical results

in order to re-assess the accuracy of using CFD to determine the frictional resistance of

the trimaran ship.Another source of error could come from the interpretation of the FLUENTdrag

coefficient value itself. For the numerical calculations, it was assumed that the drag

coefficient value from FLUENT was a result of only the frictional resistance, having

eliminated the wave making resistance, and ignoring the contribution of the pressure or

form drag component. It is possible that the form drag component is not of a negligible

amount and, therefore, the assumption to ignore its contribution would be inappropriate.

However, this is an unlikely source of error since the form drag of a ship is typically less

then the frictional resistance, and it would certainly not be as large as the numerically

calculated resistance values.

As it stands, the results for the frictional resistance of the trimaran ship as

determined by use of CFD are inaccurate. The inaccuracy of the results means that the

CFD values cannot be used to calculate any additional information about the ships


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hydrodynamic properties, such as the power requirements. Although the CFD results are

inaccurate, the analytically calculated results are correct and could be utilized to calculate

additional hydrodynamic properties of the ship. This leads to the assessment that CFD is

not the most efficient method of calculating the frictional resistance of the trimaran ship.

There are several reasons for this conclusion. The main reason is the significant increase

in time needed to setup and perform the CFD calculations. The time necessary to draw

and mesh the trimaran model, and run the simulations, is much greater than the time

required to perform the analytical calculations. Increasing the number of finite elements

until achieving grid independence will only increase the time required for computations

and convergence of the governing flow equations.

In addition to the increased time, the solutions for the CFD results were

inaccurate. However, it should be noted that the poor results could be due to an incorrect

user input, when the simulation reaches a boundary condition value, for example.

Because of the numerous opportunities to make an input error when setting up a CFD

simulation, it can be asserted that CFD is a difficult tool for beginners to properly use.

This is not to say that CFD should not be used or cannot be used to properly simulate the

flow around the trimaran hull for the purposes of calculating the frictional resistance of a

trimaran ship. However, if one takes into consideration the difficulty of properly setting

up the CFD simulations and the time required to design and mesh the trimaran model, to

obtain an approximate value of the frictional resistance, it is simpler and quicker to use

the analytical formulas instead of Computational Fluid Dynamics.

In order to properly implement Computational Fluid Dynamics it is important that

one have a good understanding of the governing flow physics. If CFD is implemented

without a proper understanding of the flow physics, the results are often incorrect or

misinterpreted. The analytical formulas for calculating the frictional resistance are much

simpler and do not require an understanding of the flow physics. Even with a

knowledgeable understanding of the flow physics, there is a vast array of settings within

the program FLUENTfor which the user can define flow properties, boundary conditions,

flow models, etc. that it is difficult for a novice to use the CFD program to properly

model anything other than simple flows. For this reason, it is recommended that

analytical equations be used for the calculation of the frictional resistance of the trimaran.


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Appendix A

Trimaran Planform


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Appendix B

Detailed Description ofProE

Trimaran Drawing Process


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The (x,y,z) coordinates that form the trimarans XY and YZ planforms (Appendix

A) were typed up in Microsoft Notepadto form separate *.ibl files describing the

contours of the trimarans hulls in the horizontal and vertical directions. An example

*.ibl file for the main hulls vertical contours is included in Appendix C. Note, in order

to save theMicrosoft Notepadfile as an *.ibl file, it is important to change the file type

to All files when saving the file. After changing the file type, be sure to enter the

desired file name along with the .ibl ending.

The *.ibl files for the vertical and horizontal directions are easily loaded into

ProE to create datum curves. The combination of the horizontal and vertical datum

curves yield the three-dimensional wire frame trimaran model. The final steps then

involve connecting the vertical and horizontal datum curves and creating surface areas

from the wireframe model. These steps are rather basic and are not described here.

Note, for this study the main hull and outriggers were created as separate parts

in ProEand then added together to form a complete assembly drawing. The outriggers

were placed at a distance b=5 m, in the y-direction from the center, o, of the main hull

and a distance ofa=0 m, in thex-direction from the origin, o.


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Appendix C

Sample *.ibl File for the Vertical (YZ)

Trimaran Datum Curves


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openarclength

Begin section!Begin curve!1

-20 1.7000 0.8

-20 1.7410 1.2Begin curve!2-20 1.7410 1.2

-20 1.7820 1.6Begin curve!3

-20 1.7820 1.6-20 1.7920 1.7

Begin curve!4-18 0.0500 0.7

-18 1.7000 0.8Begin curve!5

-18 1.7000 0.8-18 1.7410 1.2

Begin curve!6-18 1.7410 1.2

-18 1.7820 1.6Begin curve!7

-18 1.7820 1.6-18 1.7920 1.7

Begin curve!8-16 0.0500 0.6

-16 1.7000 0.8Begin curve!9

-16 1.7000 0.8-16 1.7410 1.2

Begin curve!10-16 1.7410 1.2

-16 1.7820 1.6Begin curve!11

-16 1.7820 1.6-16 1.7920 1.7

Begin curve!12-14 0.0500 0.5

-14 1.7000 0.8Begin curve!13

-14 1.7000 0.8-14 1.7410 1.2

Begin curve!14-14 1.7410 1.2

-14 1.7820 1.6Begin curve!15

-14 1.7820 1.6

-14 1.7920 1.7Begin curve!16-12 0.2430 0.4

-12 1.7000 0.8Begin curve!17

-12 1.7000 0.8-12 1.7410 1.2

Begin curve!18-12 1.7410 1.2

-12 1.7820 1.6Begin curve!19

-12 1.7820 1.6-12 1.7920 1.7

Begin curve!20

-10 0.0500 0.36-10 0.4960 0.4

Begin curve!21-10 0.4960 0.4

-10 1.7000 0.8Begin curve!22

-10 1.7000 0.8-10 1.7410 1.2

Begin curve!23-10 1.7410 1.2

-10 1.7820 1.6Begin curve!24

-10 1.7820 1.6-10 1.7920 1.7

Begin curve!25-8 0.0500 0.32

-8 0.6550 0.4Begin curve!26

-8 0.6550 0.4-8 1.7000 0.8

Begin curve!27

-8 1.7000 0.8-8 1.7410 1.2

Begin curve!28

-8 1.7410 1.2-8 1.7820 1.6Begin curve!29

-8 1.7820 1.6-8 1.7920 1.7

Begin curve!30-6 0.0500 0.28

-6 0.7640 0.4Begin curve!31

-6 0.7640 0.4-6 1.6940 0.8

Begin curve!32-6 1.6940 0.8

-6 1.7380 1.2Begin curve!33

-6 1.7380 1.2-6 1.7790 1.6

Begin curve!34-6 1.7790 1.6

-6 1.7890 1.7Begin curve!35

-4 0.0500 0.24-4 0.8290 0.4

Begin curve!36-4 0.8290 0.4

-4 1.6620 0.8Begin curve!37

-4 1.6620 0.8-4 1.7250 1.2

Begin curve!38-4 1.7250 1.2

-4 1.7660 1.6Begin curve!39

-4 1.7660 1.6-4 1.7770 1.7


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Begin curve!40

-2 0.0500 0.20

-2 0.8470 0.4Begin curve!41-2 0.8470 0.4

-2 1.5940 0.8Begin curve!42

-2 1.5940 0.8-2 1.6970 1.2

Begin curve!43-2 1.6970 1.2

-2 1.7410 1.6Begin curve!44

-2 1.7410 1.6-2 1.7520 1.7

Begin curve!450 0.0500 0.16

0 0.8230 0.4Begin curve!46

0 0.8230 0.40 1.4960 0.8

Begin curve!470 1.4960 0.8

0 1.6500 1.2Begin curve!48

0 1.6500 1.20 1.6990 1.6

Begin curve!490 1.6990 1.6

0 1.7110 1.7Begin curve!50

2 0.0500 0.122 0.7710 0.4

Begin curve!512 0.7710 0.4

2 1.3710 0.8Begin curve!52

2 1.3710 0.82 1.5930 1.2

Begin curve!532 1.5930 1.2

2 1.6560 1.6Begin curve!82

Begin curve!54

2 1.6560 1.6

2 1.6700 1.7Begin curve!554 0.0500 0.08

4 0.6990 0.4Begin curve!56

4 0.6990 0.44 1.2280 0.8

Begin curve!674 1.2280 0.8

4 1.5120 1.2Begin curve!58

4 1.5120 1.24 1.6000 1.6

Begin curve!594 1.6000 1.6

4 1.6200 1.7Begin curve!60

6 0.0500 0.046 0.6130 0.4

Begin curve!616 0.6130 0.4

6 1.0750 0.8Begin curve!62

6 1.0750 0.86 1.4000 1.2

Begin curve!636 1.4000 1.2

6 1.5150 1.6Begin curve!64

6 1.5150 1.66 1.5410 1.7

Begin curve!658 0.0500 0.0

8 0.4990 0.4Begin curve!66

8 0.4990 0.48 0.8990 0.8

Begin curve!678 0.8990 0.8

8 1.2190 1.2

Begin curve!68

8 1.2190 1.2

8 1.3840 1.6Begin curve!698 1.3840 1.6

8 1.4190 1.7Begin curve!70

10 0.0490 0.010 0.3930 0.4

Begin curve!7110 0.3930 0.4

10 0.7280 0.8Begin curve!72

10 0.7280 0.810 0.9990 1.2

Begin curve!7310 0.9990 1.2

10 1.2050 1.6Begin curve!74

10 1.2050 1.610 1.2470 1.7

Begin curve!7512 0.0440 0.0

12 0.3010 0.4Begin curve!76

12 0.3010 0.412 0.5680 0.8

Begin curve!7712 0.5680 0.8

12 0.7910 1.2Begin curve!78

12 0.7910 1.212 0.9830 1.6

Begin curve!7912 0.9830 1.6

12 1.0250 1.7Begin curve!80

14 0.0320 0.014 0.2100 0.4

Begin curve!8114 0.2100 0.4

14 0.4130 0.8


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14 0.4130 0.8

14 0.5870 1.2Begin curve!8314 0.5870 1.2

14 0.7380 1.6Begin curve!84

14 0.7380 1.614 0.7740 1.7

Begin curve!8516 0.0160 0.0

16 0.1230 0.4Begin curve!86

16 0.1230 0.416 0.2570 0.8

Begin curve!8716 0.2570 0.8

16 0.3800 1.2Begin curve!88

16 0.3800 1.216 0.4960 1.6

Begin curve!8916 0.4960 1.6

16 0.5250 1.7Begin curve!90

18 0.0000 0.018 0.0470 0.4

Begin curve!9118 0.0470 0.4

18 0.1090 0.8Begin curve!92

18 0.1090 0.818 0.1750 1.2

Begin curve!9318 0.1750 1.2

18 0.2530 1.6Begin curve!94

18 0.2530 1.618 0.2710 1.7


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Appendix D

Detailed Description of Modeling Processes

Using GAMBITfor Trimaran5 and Trimaran


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In order to import the ProEtrimaran model into GAMBIT, the drawing was saved

as a *.igs file. An *.igs file is a type of CAD drawing file that is compatible with

GAMBIT. The program GAMBITcan be used to draw the CFD model, however, its main

function is to generate the mesh on a two or three-dimensional model. After importingthe *.igs trimaran model, there are several quick procedures that can be done to ensure

that the model is not dirty, meaning free of holes, gaps, and excess geometry such as

lines and areas. Some of these steps include: a) the Make Tolerant option, which

improves geometric connectivity of lines, b) Heal Geometry option, which is an

alternate method to improve geometric connectivity of lines and areas, c) Cleanup

Duplicate Faces, used to eliminate any instance of a repeated geometric area, and d) the

Cleanup Holes function, used to locate holes in the geometry of the model (FLUENT

Inc. 2006).

The dimensions of the control volume for this study are a length ofx=125 m, a

width ofy=50 m, and a height ofz=10 m. The top of the control volume is matched up to

the top of the trimaran model, which is the design waterline of the trimaran, and the

trimaran is set back 22.5 m from the front of the flow domain (Figure D-1).

Figure D-1: Dimensions of Flow Domain and Placement of Trimaran in Domain


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The dimensions were set to these particular values in order to ensure that the size of the

control volume would not have an effect on the flow development during CFD

simulations. To complete the model, it is necessary to join the trimaran volume to the

control volume so that there is a connection between the two components. The

connection is necessary for the CFD program to properly understand the boundaries of

the model. GAMBIT was chosen for the creation of the control volume, because it

provides simple steps for creating and connecting the trimaran and flow domain volumes.

Several steps are taken in GAMBITin order to join the two volumes together. The

following description of the GAMBITprocesses assumes a general familiarity with the

program. In general, these steps involve (FLUENT Inc. 2006):

o

Creating a brick with the desired dimensions of the control volumeo Properly aligning the trimaran within the control volume

o Deleting the High Level Brick Geometry and retaining its Lower Geometry

o Connect Faces (Note: areas are referred to as faces in GAMBIT)

-Pick top faces of trimaran hulls and top face of control volume

-Select Real and Virtual (tolerance) option

-Select T-Junctions option and apply

o Create the flow domain by Stitching Faces

- Select any one of the faces of the brick

- Retain the Number: Single Volume option

- Select Type: Virtual option and apply

With the trimaran and flow domain volumes joined together, the entire geometry

of the model was completed. GAMBITwas then utilized to generate the finite element

mesh on the trimaran areas, and the finite volume mesh throughout the control volume.

To create the finite element mesh of the trimaran, a size function was used in

GAMBIT. The size function was attached to the faces of the trimaran and the variables

used were as follows: angle=10, growth rate=1.2, size limit=10. After creating the size

function, the faces of the trimaran were meshed using triangular paved elements. Finally,

the entire model volume was meshed with tetrahedral/hybrid elements of the TGrid

type. The resulting mesh generated for the CFD model was of the unstructured type.


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Before proceeding to the CFD program, the surfaces of the completed model must

be labeled according to the boundary types and conditions that they will represent in the

CFD simulation. The front of the control volume was labeled INLET, and set to be a

velocity inlet, meaning that the velocity is specified at this location when running theCFD simulation. The back surface of the control volume was labeled OUTLET and set

as a pressure outlet, meaning that the pressure is a known input for the CFD simulation.

The trimaran was labeled as HULL and set to a wall, which tells the CFD simulation

that these surfaces should be treated as a solid wall. The remaining surfaces were set as

walls by default. Specification of the boundary types and conditions was the first step in

the process of setting up the actual CFD simulation and the last step performed in

GAMBIT. This model resulted in a total of 219,923 finite elements and is referred to as

Trimaran5, since it was the fifth attempt at properly creating and meshing the trimaran

CFD model.

The Trimaran7 CFD model was created following all the same steps as were used

to create the Trimaran5 model except for the meshing process. Trimaran7 was meshed

with an increased number of finite elements, 278,256 total elements, consequently

increasing the detail of the models geometry. As mentioned in the methodology section

of this document, the intended function of the two models was to show grid independence

for the results of the CFD simulations.

The increase in finite elements for Trimaran7 was achieved by ensuring that the

bow edge and keel edges of the trimarans hulls would have a greater number of finite

elements representing their geometry. To do so, first the edges that form the bow edge of

the trimarans main hull (Figure D-2 shows the edges) were meshed while specifying a

meshing ratio equal to 1.16 and Type: successive ratio with an interval size of

0.216945.

Figure D-2: Bow Edge of Trimaran Model


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The main hull keel edges (Figure D-3) were then meshed using all default values and

changing Type: successive ratio to a ratio of 1.0 and an interval size of 0.5. The

wing hulls were then meshed in a similar manner as the main hull.

Figure D-3: Bottom View of Trimaran Model Showing Keel Edges

The edges of the wing hulls were meshed using the same settings as the main hull

bow edge, but with different values. When meshing the wing hull bow edges, a ratio of

1.0 and interval size of 0.504 was used. When meshing the keel edges, the interval

size was changed to 0.25. All the faces of the trimaran were then meshed using the

Tri elements of type: paved, the default spacing value, and an interval size of

0.25. The default spacing value follows the mesh already in place on the keel and bow

edges of the trimaran model. Lastly, the control volume of the model was meshed using

the tetrahedral/hybrid elements again, but with an interval size of 4.0. The finished,ready-for-CFD-analysis, model was saved as Trimaran7.


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Appendix E

Steps Followed for Setup of CFD Simulations for Tri5_Old,

Trimaran5, and Trimaran7 Using FLUENT


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The main steps in running a CFD simulation involve preprocessing, running the

simulation, and post-processing. During preprocessing, the user inputs all relevant

physical properties that pertain to the simulation. The running of the simulation involves

solving iterations of the governing flow equations until the simulation converges on a

solution. Lastly, post-processing involves using CFD tools, in conjunction with ones

knowledge of aerodynamics or hydrodynamics, to analyze the data from the convergence

of the simulation.

The first step in launching the program FLUENTwas to chose the 3ddp solver

control. 3ddp stands for three-dimensional double precision solver, and the results

from the double precision solver are generally more accurate then the single precision

solver. The drawback of the double precision solver is that it does require longer running

times. After selecting the solver precision, click the browse button and search for the

trimaran file. Trimaran5 was chosen first since it posses a smaller mesh size. Once the

mesh is loaded into FLUENT, it is common practice to perform a grid check and a grid

smooth/swap. The main purpose of performing a grid check is to ensure that the

minimum volume is a non-negative value. Using the grid smooth/swap FLUENTvisits

all the nodes in the mesh and checks instances where the skewed nodes can be made

smoother or swapped out and replaced by a virtual node. Skewness is defined as the

difference between the shape of the cell and the shape of an equilateral cell of equivalentvolume (FLUENT Inc. 2006). The grid swap function is repeatedly utilized until zero

nodes are swapped. This is an important step in preprocessing since, Highly skewed

cells can decrease accuracy and destabilize the (CFD) solution (FLUENT Inc.). The

next step would be to set the scale of the geometric units, however the scaled units of

FLUENTare SI units of length equal to meters (m), mass in kilograms (kg), etc., which

are the same units used to create the full-scale trimaran model. Thus, the scale was left at

the default values.

The next step in preprocessing is to define the Model properties for the

simulation. The steps taken are as follows:

1) Define Models Solver, default values were used

2) Define Models Viscous, the k-epsilon model was chosen since it is

considered to be robust and an industry standard (FLUENT Inc.)


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initial simulations a critical error was made in neglecting to account for the changes in

TKEvalue for each change in velocity, as noted in Equation E-1,

2*01.0 VTKE . (E-1)

This is equivalent to assuming a constant value for TKE during each simulation, even

though the simulations were run for speeds of 2, 5, 7, 10, 14, 17, and 20 m/s and TKEis

dependent upon the velocity. This gave the results that are referred to as Trimaran5 Old

or simply Tri5_Old. After the realization of this error, the Trimaran5 model was retested

for each speed while taking into account the change in TKEfor each change in velocity,

the results are referred to as Trimaran5 Corrected or simply Trimaran5.

With the model controls, boundary conditions, and operating conditions set, the

last few steps before iterating involve setting up the monitoring of residuals and forces

during the iterations. Residuals are defined as the small imbalance that is created during

the course of the iterative solution algorithm. A small non-zero value that typically

decreases as the solution converges (FLUENT Inc.). The residuals can be thought of as

the truncation error of the Taylor Series developed, finite difference representations, of

the governing flow equations. In order to enable plotting of the residuals for the purpose

of monitoring convergence of the simulation, a short procedure was followed:

o Solve Monitors Residual

- select Plot and Print under options

- set the convergence value to 10-6 for each residual

The residuals monitored and plotted for this study include continuity, x-velocity, y-

velocity, z-velocity, energy, kvalue, and epsilon ().

The Plot option produces an XY plot of the monitored values at every iteration.

The Print option produces a list of each residual monitored at every iteration. In a

similar fashion the drag force, static pressure, total pressure, and velocity of the trimaran

hull were monitored during the iterations. To monitor the force on the hull the following

procedure was performed:

o Solve Monitors Force

o select Plot and Print

o under Wall Zones select hull

o under Coeff: select drag then click apply


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Three surface properties of the hull were monitored during the iterations, namely

the total pressure, static pressure, and velocity magnitude. The velocity magnitude was

monitored for the sole purpose of ensuring that the boundary conditions were correctly

applied to the hull and that it had no relative velocity. In order to set up the surface

monitors the following procedure was followed:

o Solve Monitors Surface

o Under Surface Monitors enter a value of 3

o The Names used for this study for each of the monitors were stat-press,

total-press, and vel-mag

o Click the Plot and Print options

o

For each monitor click Define- On the next screen under the dropdown menus, chose:

1) Pressure then static pressure

2) Pressure then total pressure

3) Velocity then magnitude

The reader is encouraged to keep in mind that the residuals, forces, and monitors

can be altered, and the user is free to monitor whatever values they desire, within the

capabilities of FLUENT. Here, the author is strictly detailing the monitors used for

current study. Also, note that the author has learned that if you wish to have access to the

exact value of each residual, force, or surface monitors anytime after running the

simulations, be certain to also select write to file, which creates a file of each exact

value throughout the iterations. With the monitors for the simulation set, the next step is

to begin the iterations.

To start the iteration process, the simulation must first be initialized. Initializing

the simulation tells the CFD program what the starting, known or guessed, values are.

The starting values are used by the CFD program to begin the iteration process of solving

the governing flow equations for the model. To initialize the simulation, the following

procedure was performed:

o Solve Initialize

o From the dropdown menu choose Inlet under compute from


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o Click Init (short for initialize)

o Close the panel

The final step before beginning the iterations is saving the case file. FLUENTsaves the

preprocessing settings as a *.cas file. This is a very important step and will save a lot of

time. Otherwise, it is quite possible that a CFD simulation will crash the first few times it

is run, due to some minor discrepancies in the preprocessing setup, such as boundary or

operating conditions or due to a computer hardware problem, such as not enough free

computer memory. After saving the case file, the next step is to start the actual CFD

iterations, using the following procedure:

o Solve Iterate

o Enter the number of desired iterations. Choose a large number to ensure

that the CFD program will iterate until all the residuals have converged.

o Click iterate

At this point, FLUENTwill begin solving the governing flow equations by iterating until

reaching convergence of all residuals, or until the input number of iterations is reached.


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Appendix F

ProETrimaran Drawings


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Figure F-1: Front View of Trimaran

Figure F-2: Skew View of Trimaran

Figure F-3: Skew View of Trimaran


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Figure F-4: Side and Bottom Views of Trimaran Model


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Appendix G

GAMBITModel and Mesh Pictures


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Figure G-1: Four Isometric Views of Trimaran Model and Control Volume

Figure G-2: Trimaran5 Meshed Hulls


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Figure G-3: Mesh of Trimaran5 Control Volume

Figure G-4: Close-up View of Mesh Surrounding the Trimaran5 Model


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Figure G-5: Finite Volume Mesh Surrounding Trimaran5 Model

Figure G-6: Trimaran7 Meshed Hulls


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Figure G-7: Mesh of Trimaran7 Control Volume

Figure G-8: Close-up View of Mesh Surrounding Trimaran7


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Figure G-9: Finite Volume Mesh Surrounding Trimaran7

Notice the increase in the number of finite elements in the Trimaran7 mesh versus the

Trimaran5 mesh. Additionally, notice the increased clustering of the elements in the

immediate vicinity of the Trimaran7 model. This increase provides better detail of the

flow properties near the trimaran.


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Bibliography

Armstrong, NA. Coming Soon to a Port Near You The 126 Metre Austal Trimaran,International Conference: Design and Operation of Trimaran Ships, April 2004,

London, U.K. 2004.

Anderson, John D. Jr., Computational Fluid Dynamics: The Basics With Applications,McGraw-Hill, Inc., New York, NY. 1995.

Clarke, D. H., Trimarans: An Introduction, Fletcher and Son Ltd., Norwich, Great

Britain. 1975.

FLUENT, Fluent Inc., date visited: 02/22/07, FLUENT Inc., Subsidiary of ANSYS Inc.,.

Gray, Alexander, A Preliminary Study of Trimarans, Research Experience for

Undergraduates: Marine Science and Engineering China 2006, Report No. 06-13,Department of Civil and Environmental Engineering, Clarkson University

Potsdam, NY, 2006

Harvald, SV. AA., Resistance and Propulsion of Ships, John Wiley & Sons, Inc., NewYork, NY. 1983.

Kang, Kun-Jin, Lee, Chun-Ju, et. al., Design and Hydrodynamic Performance of a

Frigate Class Trimaran, International Conference: Design and Operation ofTrimaran Ships, April 2004, London, U.K. 2004 pgs 184-194

Munro-Smith, R. Ships and Naval Architecture. Institute of Marine Engineers, St.Stephens Bristol Press Ltd., Filton, Bristol. 1973.

Rawson, K.J. Basic Ship Theory, Vol. 1. Logman Inc., New York, 1976

Renilson, Martin, Scrace, Bob, et. al., Trials To Measure The Hydrodynamic

Performance of the RV Triton, International Conference: Design and Operationof Trimaran Ships, April 2004, London, U.K. 2004 pg 5 & 17.

SeaKayak, Hank McComas, date visited: 03/01/07,.

Skarda, RK, & Walker, M., Merrits of the Monohull and Trimaran Against the

Requirement for Future Surface Combatant, International Conference: Designand Operation of Trimaran Ships, April 2004, London, U.K. 2004 pg 132.

Smirnov, Andrei. Re: Dr. Smirnov, Email to Alexander Gray 13 November 2006

Three hulls are better than one, Professional Engineering, June 1997, Vol. 10,Issue 12, 1997 pg 18


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Three hulls for one warship, Popular Mechanics, February 1996, Vol. 173, Issue 2,1996 pg 26.

Young, Donald F., Bruce R. Munson, & Theodore H. Okiishi, Fluid Mechanics, John

Wiley & Sons, Inc., U.S.A. 2004.

Zhang, Junwu, Design and Hydrodynamic Performance of Trimaran Displacement Ships,PhD Thesis, Department of Mechanical Engineering, University College London,

1997.

preliminary study on the use of computational fluid dynamics to determine the frictional resistance...

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