A research on the Ship Hull form optimization using viscous CFD and genetic algorithm

Luận án tiến sĩ mới của TRUNG QUỐC về tính toán sức cản tàu thủy, thông qua luận án này những nhà nghiên cứu trong nước có thể tìm ra được hướng nghiên cứu mới nhất mà quốc gia trung quốc đang phát triển. Hy vọng sẽ giúp ích được các nhà nghiên cứu trong nước. Toàn bộ luận văn bằng tiếng trung quốc tuy nhiên các nhà nghiên cứu có thể dịch ra để hiểu đại ý của luận văn, mục tiêu là tìm ra hướng đi mới!

1

Purpose

The design of a ship with minimum resistance in accordance with the desired conditions of speed and displacement is a major requirement from the ship design point of view The prediction of flow field around hull plays a major role in the development of ship hull form With the rapid developments of computational tools in recent years, computational fluid dynamics has gained a significant importance especially in the early stages of ship design CFD has been used extensively to analyze the flow field around hull, and successful calculations of ship resistance can be found in literatures [1][2][3][4][5]

In recent years optimization of ship has gained great interest in order to minimize the drag of a ship for fuel efficiency which results in minimizing the running cost To obtain a ship with low resistance, its hull form has to be optimized The optimization of hull form for drag reduction requires repetitive analyses of flow field around hull with the variation of different hull design parameters Now conducting all these analyses on towing tank is not economic due to the cost and time involved in performing these tests

Although CFD has great advantage in reducing the time and cost of each analyses, still it is difficult to manually changing the design parameters of the ship hull form and conducting each analysis to obtain optimized shape There is a requirement to solve this problem with a process of optimization which is robust and automatic Ship optimization with respect to optimal shape design can be found in literature which will be briefly described in the later sections

In almost all ship hull form optimization, based on CFD, following are the common major components:

• Determining the objective function to minimize along with design variables and constraints which influence this objective function

• Automatic generation of geometry based on the design criteria/variables and then automatically generating flow domain mesh as the shape evolves

• Calculation of objective function using high performance CFD code

• Requirement of an optimization tool/algorithm to evaluate the objective function.

Research Overviews

Optimization of hull form is a process based on changing a hull form in order to achieve improvement in the performance of the ship The traditional method for improvement in the ship hull form is to produce an initial hull form and test it in towing tank to obtain flow around the hull and then modifying the hull with improvements and test it again With the development of Computational Fluid Dynamics (CFD) based methodologies the initial analysis is carried out more robustly with CFD tools The optimized design of a hull plays a major role in the final operation cost and reduction of carbon dioxide emission of the ship and therefore can be very beneficial

The optimization is based on the minimizing or maximizing the objective function of the problem The objective function for an optimized hull can be composed of any of the single or a combination of objectives such as total resistance reduction, better seakeeping and stability characteristics, propulsion, maneuvering etc Multi objective optimization of hull forms based on two or more above mentioned objectives have been explored and reported in literature[22][29][33][64] mostly based on potential flow theory, however, viscous CFD-based multi-objective optimization is much more complicated and time consuming and has not been widely explored In most of the hull form optimization, minimizing the ship resistance is considered as objective function, and research is still going on by many researchers in this area Optimization of a hull form is generally based on optimizing the offset of the initial hull; another way to improve the resistance of the hull is to change in geometry of the hull which can change the flow around the hull

1.2.1 Automatic Generation of Hull Form

The optimization of hull form starts with the automatic design of hull form The ship hull should be automatically generated in accordance with the given parameters Studies related to computer based automatic geometry generation are found in literatures Calkins et al (2001) [6] , describes the development of a computer-based method for producing chined planing boat hull forms adequate to be applied in concept design The method is based on a principle where the designer specifies a small set of critical parameters he/she wishes to obtain and generates a complete hull form From this set of parameters a detailed and faired drawing with offsets is

3 generated very quickly The method allows, in its execution mode, the flexibility to modify, adjust and enlarge the input set of parameters

Koelman and Aalbers (2001) [7] , proposed a new geometric modeling technique, called hybrid representation (H-rep), for modeling ship hulls The novelty of H-rep is in the integration of wire frame, surface and solid representation in one common data structure, and in providing topological support to surface modeling as well as an enhanced technique for curve fairing

Mahfuzul and Khondoker (2001) [8] , described a methodology for automatic hull form generation of ships with some desired performances using artificial intelligence techniques The whole implementation process is divided into three main components First of all the half-breadth weight matrices are generated that would provide population with pre-fitness Secondly, breadth and draft are adjusted using Neural Network Concepts Breadth, draft, length, displacement and speed of the ship are much related terms and relations among them create some constraints Neural Networks solve these constraints and adjust the parameters Finally, Genetic Algorithm is used for searching the exact solution by examining several generations

Perez-Arribas et al (2006) [9] , presented a thorough procedure for automatic modeling with a fair NURBS surface, having lists of points on the stations of the vessel as initial data Approximation of spline curves fitting the data on the stations is made, the quality of the approximation of the station points determines the quality of the hull NURBS surfaces modeling the hull of the vessel are constructed and then fairing process is adopted to maintain certain ship characteristics

Antonio Mancuso (2006) [10] described the optimization technique for automatically designing a hull The design is based on a few parameters such as waterline length, canoe body draft, stem angle and some adimensional parameters The hull is defined by B-spline curve and then B-spline surface The BFGS (Broyden-Fletcher-Goldfarb-Shanno) quasi-Newton method available in optimization tool box of MATLAB is used for the optimization

Parametric Design for Hull Forms was studied by Zhang Ping et al (2008) [11] and Wang et al (2008) [12] , these studies provides the means for the quick generation of hull form The parametric design is based on the Non-Uniform B-Spline (NURBS)

One of the common techniques to reduce the resistance of hull is the addition of bulbous bow There are many related studies carried out for the reduction of resistance with the integration of bulbous bow An integrated bulbous bow design method for a particular set of requirements consisting of a narrow range of input parameters is presented by Sharma and Sha (2005) [13] The method uses an approximate linear theory with sheltering effect for resistance estimation and pressure distribution, and correlation with statistical analysis from the existing literature and the tank-test results available in the public domain

Peri et al (2001) [14] used total resistance and wave pattern around FP as the objective function In optimization of bulbous bow design of tanker ship hull they used three different algorithms (Sequential Quadratic Programming, nonlinear Conjugate Gradient, and Steepest Descent) coupled with CFD solver Tzabiras GD (2008) [15] presented the combined application of potential and viscous codes to predict the total resistance of hulls with bulbous bow An inverse design algorithm is developed by Chen et al (2006) [16] for determining the optimal shape of the bulbous bow by utilizing the Levenberg-Marquardt method (LMM) and B-Spline surface control technique and basing it on a given target, such as desired wave height or wave resistance

In one of the cases presented in this paper, optimization of a bulbous bow is carried out using CFD tools The design of the bulbous bow is based on different geometric parameters, Series 60 (Cb=0.6) parent hull is integrated with an additive bulbous bow, and low resistance hull is achieved

1.2.3 Optimization of Hull Form Using Genetic Algorithm

This section covers those studies that are carried out with respect to the optimization of ship hull form based on genetic algorithm

Day and Doctors (2001) [17] , presented a method which allows the rapid evaluation of wave-wake field generated by a ship for large number of different hull geometries The method is based on linear thin-ship theory, using the idea of elemental tent functions as building blocks to represent the hull The optimization study was carried out for a mono-hull and catamaran vessel, the optimization technique used in this study is the combination of

5 genetic algorithm with hill climbing algorithm Hybrid genetic algorithm can be used in the situations where simple genetic algorithm is not that efficient

A computational method developed for solving the minimum ship wave resistance problem is presented by Dejhalla et al (2001) (2002) [18][19] The method involves coupling of numerical ship hydrodynamics and genetic algorithms In the optimization procedure, the wave resistance has been selected as an objective function and genetic algorithm as optimization tool Three-dimensional potential flow solver based on Dawson’s method is used to calculate the wave resistance, hull lines of series 60 (Cb=0.6) ship is selected for optimization

Jacquin et al (2002) [20] , presented a numerical performance evaluation tool which integrates four important elements: a hull modeling software, a mesh generator, a free-surface RANSE solver and a VPP (Velocity Prediction Program) VPP is able to calculate the hull speed using RANSE and hydrodynamics input Optimization is performed by commercial optimization software (Frontier), three parameters are used: beam at the water line, longitudinal position of the maximum beam, form of the keel line Multi Objective Genetic Algorithm (MOGA) is used for optimization with objective function is to maximize the speed of ACC (America's Cup Class hull) for upwind and downwind condition

A genetic algorithm is used by Lowe and Steel (2003) [21] , to search the hull design space for a hull form having the required values of various primary and secondary geometric parameters A representative of each distinct cluster of the forms found is identified and presented as a candidate hull design having the required geometric characteristics The geometric parameters considered include the displacement, draft, freeboard, waterline length, waterline beam, and water plane coefficient together with the locations of the centers of flotation and buoyancy The hull surface is represented using the partial differential equation method

Objectives and Scope of Work

The objective of this research work is to achieve an optimized ship hull for total resistance based on computational fluid dynamics and genetic algorithm

In order to facilitate this objective some key issues need to be resolved The issues related to hull form optimization are as follows:

• Change in ship hull geometry in order to reduce total resistance

• Automatic generation of ship hull based on the changes in geometry

• Automatic creation of mesh for each changed geometry

• Automatic CFD solution of new geometry

• Optimizer to track the best solution and give geometry input for new improved hull The scope of the work is to develop a suitable methodology to optimize the hull form for total resistance effectively The geometry of the hull form should be parameterized in such a way that a small number of design variables are required for the generation of new improved geometry The modified region of hull should join the original design in such a way to have smooth hull without discontinuities

For geometry change in ship hull to obtain low resistance hull, addition of bulbous bow to parent hull has been incorporated in the first case study, for second case study change in ship hull lines is incorporated For automatic geometry changes and mesh generation Gambit journal file is created based on the changes in hull form, for automatic CFD calculations FLUENT journal file is created Genetic algorithm is selected for optimization due to its better approach in finding global minima in the solution space.

Organization of Thesis Report

Following is the brief description of the organization of thesis report:

Chapter 1 gives an introduction to the hull form optimization along with research overview of the topics under investigation Studies related to automatic generation of hull form geometry are first examined Secondly bulbous bow optimization studies are reviewed Thirdly studies related to hull form optimization based on various optimization techniques are reviewed; special emphasis is given on the studies that used genetic algorithm Lastly studies related to multihull optimization are examined

Chapter 2 provides theoretical background of the concepts used in the paper The background for genetic algorithm is presented with both binary and real valued genetic algorithm then bulbous bow design is briefly described Basic equations used by FLUENT software for the calculations of fluid flow are presented Various turbulence models are analyzed and compared with experimental results of trimaran FA1 Finally application and background for Gambit and FLUENT journal files, used in optimization, are discussed

Chapter 3 describes the overall methodology used in this paper for hull form optimization The working loop of the optimization process is discussed including the working of genetic algorithm for the research studies

Chapter 4 presents the case study related to Series 60 hull optimization The optimization of the Series 60 (Cb=0.6) hull is carried out with the addition of bulbous bow The results are compared with parent hull results (experimental and calculated)

Chapter 5 presents optimization case studies related to trimaran FA1 A total of eight cases of optimization are presented For the first six cases objective function is selected as total resistance while for the last two cases objective function is selected as total resistance per unit displacement Six optimization cases are based on the optimization of trimaran main hull bulb points, whereas one case is based on the bow station lines optimization For one case (case-6),

11 bulb length of the main hull is evaluated along with the bulbous bow lines The results are compared with the experimental results for validation

Chapter 6 presents the summary of work and conclusions regarding the application of genetic algorithm for hull form optimization.

12

Governing Equations Used in FLUENT

The general equations of fluid flow represent mathematical forms of the conservation laws of physics, such that:

• The rate of change of momentum equals the sum of the forces on a fluid particle

• The rate of change of energy is equal to the sum of the rate of heat addition to and the rate of work done on a particle

FLUENT provides comprehensive modeling capabilities for a wide range of fluid flow problem such as compressible, incompressible, laminar and turbulent flow For all flows, FLUENT solves conservation equations for mass and momentum [49] The equation for conservation of mass or continuity equation can be written as follows:

It is a general form of the three-dimensional unsteady mass conservation equation and is valid for both incompressible and compressible flows Here is the fluid density, the fluid velocity and is the time

For incompressible flow, and assuming that the fluid is Newtonian the continuity equation becomes

(2.4) and the momentum conservation equation is given by

Where is the static pressure, and is the body force

Although the above equations are sufficient for the description of incompressible, laminar flow, and being a description of a continuum, in principle apply to all scales, they are also non-linear and subject to instability Physically, these instabilities propagate to provide a mechanism to describe turbulence Turbulent flows are characterized by fluctuating velocity fields These fluctuations mix transported quantities such as momentum, energy, and species concentration, and cause the transported quantities to fluctuate as well Since these fluctuations can be of small scale and high frequency, they are too computationally expensive to simulate directly in practical engineering calculations Instead, the instantaneous (exact) governing equations can be time-averaged, ensemble-averaged, or otherwise manipulated to remove the small scales, resulting in a modified set of equations that are computationally less expensive to solve However, the modified equations contain additional unknown variables, and turbulence models are needed to determine these variables in terms of known quantities The velocity components are represented by:

(2.6) where is the mean and is the unsteady disturbance quantities in the flow, such that

This gives the most well-known Reynolds-averaged Navier Stokes Equations (RANSE)

On time averaging, the x-component momentum equation becomes:

The equations for the other components take a similar form The Reynolds stresses ( , , etc.) are treated as extra stresses that arise from the turbulent nature of the flow Turbulence models are needed to determine these variables in terms of known quantities In this research following turbulence models are evaluated

The simplest "complete models'' of turbulence are two-equation models in which the solution of two separate transport equations allows the turbulent velocity and length scales to be independently determined The standard k- model [50] is a semi-empirical model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate ( ) The model transport equation for k is derived from the exact equation, while the model transport equation for was obtained using physical reasoning and bears little resemblance to its mathematically exact counterpart

In the derivation of the k- model, the assumption is that the flow is fully turbulent, and the effects of molecular viscosity are negligible The standard k- model is therefore valid only for fully turbulent flows Standard k-ε model was proposed by Launder and Spalding [50] Transport equations of the model are:

(2.8) (2.9) represents the generation of turbulence kinetic energy due to mean velocity gradients represents the generation of turbulence kinetic energy due to buoyancy represents the contribution of the fluctuating dilation in compressible turbulence to the overall dissipation rate , , and are constants and are the turbulent Prandtle numbers of and and are user defined source terms

Turbulent viscosity is computed by combining and as:

The model constants used in the above equations have following default values:

CFD calculations are carried out for trimaran FA1 using Standard k-ε turbulence model and total resistance results are compared with experimental results and presented in Table 2.1 below Trimaran FA1 ship is consisting of a main hull and two identical outriggers The details of the trimaran are presented in the chapter five of this paper

Table 2.1 Resistance Results of standard k-ε Turbulence Model

The RNG-based k- turbulence model is derived from the instantaneous Navier-Stokes equations, using a mathematical technique called "renormalization group'' (RNG) methods The analytical derivation results in a model with constants different from those in the standard k- model, and additional terms and functions in the transport equations for k and [59]

Transport equations of the model RNG k- are similar to standard k- model:

In the high-Reynolds-number limit, turbulent viscosity is computed by combining and as:

Where = 0.0845, derived using RNG theory The main difference between the RNG and standard k- models lies in the additional term in the equation given by:

Where , , The model constants C1 and C2 have values derived analytically by the RNG theory These values, used by default in FLUENT, are:

CFD calculations are carried out for trimaran FA1 using RNG k-ε turbulence model and total resistance results are compared with experimental results and presented in Table below:

Table 2.2 Resistance Results of RNG k-ε Turbulence Model

The realizable k- model [60] differs from the standard k- model in two important ways:

• The realizable k- model contains a new formulation for the turbulent viscosity

• A new transport equation for the dissipation rate, , has been derived from an exact equation for the transport of the mean-square vorticity fluctuation

The term "realizable'' means that the model satisfies certain mathematical constraints on the Reynolds stresses, consistent with the physics of turbulent flows Neither the standard k- model nor the RNG k- model is realizable

An immediate benefit of the realizable k- model is that it more accurately predicts the spreading rate of both planar and round jets It is also likely to provide superior performance for flows involving rotation, boundary layers under strong adverse pressure gradients, separation, and recirculation

The modeled transport equations for k and in the realizable k- model are:

As in other k- models, the eddy viscosity is computed from:

In this model is not constant, it is computed from:

The model constants A0 and AS are given by:

CFD calculations are carried out for trimaran FA1 using Realizable k-ε turbulence model and total resistance results are compared with experimental results and presented in Table below:

Table 2.3 Resistance Results of Realizable k-ε Turbulence Model

The standard k-ω model in FLUENT is based on the Wilcox k-ω model [61] , which incorporates modifications for low-Reynolds-number effects, compressibility, and shear flow spreading The Wilcox model predicts free shear flow spreading rates that are in close agreement with measurements for far wakes, mixing layers, and plane, round, and radial jets, and is thus applicable to wall-bounded flows and free shear flows A variation of the standard k-ω model called the SST k-ω model is also available in FLUENT, and is described in the later section

The standard k-ω model is an empirical model based on model transport equations for the turbulence kinetic energy (k) and the specific dissipation rate (ω), which can also be thought of as the ratio of to k [61]

As the k-ω model has been modified over the years, production terms have been added to both the k and ω equations, which have improved the accuracy of the model for predicting free shear flows

The turbulence kinetic energy, k, and the specific dissipation rate, ω, are obtained from the following transport equations:

CFD calculations are also carried out for trimaran FA1 using Standard k-ω turbulence model and total resistance results are compared with experimental results and presented in Table below:

Table 2.4 Resistance Results of Standard k-ω Turbulence Model

2.1.1.5 Shear-Stress Transport k-ω turbulence model

SST k-ω model is developed by Menter [51] The standard k-ω model and the transformed k- models are multiplied by a blending function and then added together to obtain k-ω SST model

Transport Equations for the SST k-ω Model are given as:

In these equations, represents the generation of turbulence kinetic energy due to mean velocity gradients, represents the generation of , and represent the effective diffusivity of and respectively and represent the dissipation of and due to turbulence represents the cross-diffusion term and are user-defined source terms

All additional model constants ( and ) have the same values as for the standard k-ω model

CFD calculations are carried out for trimaran FA1 using SST k-ω turbulence model and total resistance results are compared with experimental results and presented in Table below:

Table 2.5 Resistance Results of SST k-ω Turbulence Model

The calculations of total resistance with above mentioned different turbulence models are recorded after every 200 iterations and plotted in Figures 2.1 and 2.2

Figure 2.1 Drag Convergent Histories Corresponding to Different Turbulence Models (Fn 0.75)

Figure 2.2 Drag Convergent Histories Corresponding to Different Turbulence Models (Fn 0.55)

The final total resistance results obtained for the higher four Froude numbers for experiment and calculated results with different all turbulence models are plotted in Figure 2.3

Figure 2.3 Comparisons of Turbulence Models

Bulbous Bow Design

Nowadays bulbous bows are integrated part of many ship designs The hydrodynamic effect of the bulbous bow is based on the change of flow distribution around bow, creating waves that interfere with the waves created by hull, and improving the flow around the bow as well A properly designed bulb nearly affects all the hydrodynamic properties of the ship According to Kracht [48] , bulb types can be differentiated by basic three types of bulb sections that extend beyond the forward perpendicular (FP)

Delta (∆) – type: It has drop-shaped sectional area with centroid of the bulb volume concentrated in the lower half part, Taylor and pear-shape bulb falls in this category

O-type: It has oval-shaped sectional area with centroid of the bulb volume concentrated in middle, circular, cylindrical, elliptical, and lens-shaped bulbs fall in this category

Nabla ( ) – type: It also has drop-shaped sectional area but with centroid of the bulb volume concentrated in the upper half part

Figure 2.4 Types of bulb sections

In addition to above mentioned classifications, quantitative parameters are necessary for the design of bulb form As per Kracht [48] , six parameters (three linear and three nonlinear) are sufficient to describe the bulb form These six parameters are described as follows:

(2.23) where is maximum breadth of bulb area, and is breadth of ship at mid-ship section

(2.24) where is protruding length of bulb, and length between perpendiculars

23 where is the height of the foremost bulb point above baseline, and is draft at forward perpendicular

4) CABT (the cross-section parameter)

(2.26) where is cross-sectional area at forward perpendicular, and is midship section area

(2.27) where is area of ram bow in longitudinal direction, and is midship section area

(2.28) where is protruding volume of bulb, and is displacement volume of ship

Figure 2.5 Description of bulb parameters (Kracht, 1978)

Genetic Algorithm

The genetic algorithm (GA) is an optimization and search technique based on the principles of genetics and natural selection A GA allows a population composed of many individuals to evolve under specified selection rules to a state that maximizes the fitness (i.e minimize the cost function) The GA was developed by Holland in 1975 [39] and gained popularity by the work of one of his student, Goldberg [40]

The GA starts with defining a chromosome or a group of variable values to be optimized

If the chromosome has variables ( dimensional optimization problem) given by then the chromosome is written as an element row vector

(2.29) Each chromosome has a cost found by assessing the cost function, at :

(2.30) 2.3.1 Encoding and Decoding of Variables

For binary genetic algorithm, since the variable values are characterized in binary, there must be a method of converting real values in to binary, and vice versa Quantization samples a continuous range of values and classifies the samples into non-overlapping sub-ranges then a unique discrete value is assigned to each sub-range [41] The mathematical formulas for the binary encoding and decoding of the n th variable are given as follows:

The binary GA works with bits; if chromosome has a variable y then the value of y is characterized by a string of bits that is long If = 2 and y has limits defined by 1≤y≤4, then a gene with 2 bits has possible values The quantized value of the gene or variable is found by multiplying the vector containing the bits by a vector containing the quantized levels:

The genetic algorithm can work with the binary encodings, but the cost function usually requires real valued variables Whenever the cost function is evaluated, the chromosome must first be decoded using equation above

When the variables are naturally quantized, the binary GA works well However, when the variables are real valued, it is more reasonable to represent them by floating point numbers The real valued GA also known as continuous GA is naturally faster than the binary GA, since the chromosomes do not have to be decoded before the evaluation of the cost function In this research work, real valued GA is used for the optimization; therefore, the operators of genetic algorithm defined in the later sections are related to real-valued GA

A matrix characterizes the population with each row in the matrix being a 1 array (chromosome) of real values Provided with an initial population of chromosomes, the full matrix of random values is created by

All of the variables are normalized to have values between 0 and 1 (the range of a uniform random number generator) These values of variable are “un-normalized” in the cost function

If the range of values is between and , then the un-normalized values are given by the equation

= highest number in the variable range

= lowest number in the variable range

After calculating cost of every chromosome, it is essential to decide which chromosomes are fit enough to survive for the next generation and to reproduce offspring For that purpose, costs and the associated chromosomes are ranked from lowest cost to the highest cost Out of chromosomes in a given generation, only the top chromosomes are retained for mating and the rest are discarded to make room for the new offspring

Two mothers and fathers pair in some random manner Each pair produces two offspring that comprise traits from each parent Furthermore, the parents also survive to be part of the next generation The more alike the two parents, the more likely are the offspring to carry the traits of the parents Different approaches can be applied to find the two mates, for example, pairing from top to bottom, random pairing, weighted random pairing, rank weighting, cost weighting, tournament selection In this research work rank weighting approach is used for selection of parents

Many different approaches have been applied for crossing over in real valued GAs The simplest methods select one or more points in the chromosome to mark as the crossover points Then the variables between these points are only swapped between the two parents For example, consider the two parents

(2.38) (2.39) Crossover points are selected randomly, and then the variables in between are swapped:

The extreme case is selecting points and randomly selecting which of the two parents will contribute its variable at each position Therefore one goes down the line of the chromosomes and, at each variable, randomly chooses whether or not to exchange information between the two parents This method is known as uniform crossover:

The problem with these point crossover methods is that no new information is presented: each real value that was randomly originated in the initial population is promulgated to the next generation, only in different combinations Even though this approach worked fine for binary representations, there is now a range of values, and in this range we are merely interchanging two data points These methodologies totally depend on mutation to introduce new genetic material

The blending methods solve this problem by finding methods to combine variable values from the two parents into new variable values in the offspring A single offspring variable value, , comes from a combination of the two corresponding offspring variable values [42]

= random number on the interval [0, 1]

= nth variable in the mother chromosome

= nth variable in the father chromosome

The same variable of the second offspring is just the complement of the first (i.e., replacing by If = 1, then promulgates in its entirety and expires In contrast, if = 0, then promulgates in its entirety and expires When = 0.5 [43] , the result is an average of the variables of the two parents This method is verified to work well on several problems by Michalewicz [44] Selecting which variables to blend is the next issue Occasionally, this linear combination process is done for all variables to the right or to the left of some crossover point Any number of points can be chosen to blend, up to values where all variables are linear combinations of those of the two parents The variables can be blended by using the same for each variable or by choosing different ’s for each variable These blending methods efficiently combine the information from the two parents and select values of the variables between the values bracketed by the parents, however, they do not allow introduction of values outside the extremes already represented in the population To do this involves an extrapolating method The simplest of these methods is linear crossover [45] In this case three offspring are produced from the two parents by

Any variable outside the bounds is cast-off in favor of the other two Then the best two offspring are chosen to promulgate The factor 0.5 is not the only one that can be used in such method Heuristic crossover [44] is a variation where a random number , is chosen in the interval [0, 1] and the variables of the offspring are defined by

Variations on this subject include choosing any number of variables to modify and generating different for each variable This method also permits generation of offspring outside of the values of the two parent variables Sometimes values are produced outside of the allowed range If this happens, the offspring is cast-off and the algorithm tries another The blend crossover (BLX- ) method [46] begins by selecting parameter that determines the distance outside the bounds of the two parent variables that the offspring variable may fall This method allows new values outside of the range of the parents without allowing the algorithm stray too far Many codes are available that combine the various methods to use the strength of each Methods, for example quadratic crossover [47] , do a numerical fit to the fitness function Three parents are necessary to perform a quadratic fit

Overview of Journaling in Gambit and FLUENT

In all optimization processes based on Computational Fluid Dynamics (CFD) there is a requirement to automate the process This automation requires that geometry, mesh and analyses are carried out without any intervention from a user Journal files available in GAMBIT and FLUENT software allow users to parameterize their problem and therefore the whole process can be automated The major objectives of journal files are:

• Parametric study can be carried out

• Repeat study with changes in the process parameters can be done

• Minor design changes can be employed

• Automate most components of the analysis procedure to maximize analysis efficiency

• Information about a model can be found without the need to run GAMBIT/FLUENT

• Bugs can easily be identified -faster fixing

• Effective for CFD record keeping

• Journals are small files and are easy to transfer by email

Journal files are text files that contain GAMBIT program commands During any GAMBIT session, GAMBIT maintains a temporary journal file that contains all commands executed during the session When a session is saved, GAMBIT copies the temporary journal file to a permanent file The name of the journal permanent file is the same as the session name and its extension is “jou” The syntax of GAMBIT journal file commands is identical to that of commands entered by means of the keyboard GAMBIT journal file can be processed in two ways:

In interactive mode, a text editor appears which can be used for modifications in the GAMBIT commands In the text editor commands lines can be marked to activate for processing, text fields can be edited, and command lines can be processed in auto mode or step mode

In batch mode all commands in the journal file are processed one by one in a sequence without any interruption, beginning at the top of the file During the automatic execution of the journal file, GAMBIT displays a Pause command button at the right side of the Command text box If Pause button is clicked, GAMBIT suspends the command execution (following execution of the current command) and changes the button title from Pause to Resume To resume execution of the journal file commands, click Resume

If execution of a journal file is paused, commands from Command line or GUI or open and run other journal files can be done before resuming its execution GAMBIT maintains a stack of open journal files and executes them on a last-in/first-out basis

In all the optimization cases presented in this paper, GAMBIT journal file is executed as a batch mode using following command:

C:\Fluent.Inc\ntbin\ntx86\gambit.exe -r2.3.16 -inp OptFA1.jou

As in other languages, parameters can be used in GAMBIT journal file for parametric studies Parameters like arrays, control-blocks, do-loops, arithmetic functions, etc can be used Gambit commands are not case sensitive, comments in the journal file can be added with “/” at the start of the comment Parameters can be scalar or array, numeric or string The name of the parameter should be started with $, and it is not case-sensitive ($angle is same as

In this paper, the discussions on hull form and bulbous bow optimizations, two types of parameters are used First type of parameters is those variables which are evolved through genetic algorithm and are stored in a separate variable file, and this file is called within GAMBIT journal file using command: readfile file "FA1.var"

Second type of parameters is those which are defined within journal file to control the geometry and meshing All kind of arithmetic and logical expressions can be applied to these parameters in the journal file

In order to control the geometry change in GAMBIT software for each case in optimization cycle, arrays are used to define vertices, edges, faces and volumes Arrays are defined as: declare $Pt[20] declare $Edge[30] declare $Face[60] declare $Vol[25]

Function can be used in any expression; they return a single numerical, logical, or string value Various string, arithmetic, database and system functions are available in GAMBIT journal Following are few important functions which are applied in the journal files for our optimization cases:

• NTOS(exp): this function converts number to a string and used in journal file to define the names of vertices, edges, faces and volumes For example if $Copt=7 and $Fpt then following command will create a straight edge using “vertex.7” and “vertex.10”: edge create straight ("vertex."+NTOS($Copt)) ("vertex."+NTOS($Fpt))

• LASTID(tag): this function stores ID of last created entity, here tag defines the type of entity (i.e 1 for vertex, 2 for edge, 3 for face, and 4 for volume) This function is very useful in storing the ID number of the previously created entity to a variable For example following command will store the ID of previously created edge into variable

• LOC2ENT(return_type, x, y, z): this function returns the entity name in closest proximity to a specified coordinate location, here return_type is vertex/edge/face/volume and x, y, z are the coordinates of the search point For example following command will store the name of the face present at the coordinates given to variable $F1:

2.4.1.3.3 IF Blocks and DO Loops

GAMBIT allows using IF-blocks and DO-loops as part of a set of journal file commands IF-blocks and DO-loops allow customizing journal files in order to facilitate the creation and/or meshing of GAMBIT models For example, DO-loops can be used to construct, locate, and orient multiple copies of a single entity type

The general syntax of a GAMBIT IF-block is as follows:

Where, X represents a logical expression and the square brackets ([]) indicate that the

ELSE statement and its associated Commands are optional GAMBIT IF-blocks can contain any number of nested IF-blocks

The general syntax of any GAMBIT DO-loop is as follows:

DO PARA "$parameter" [INIT expression1] COND (condition) [INCR expression2]

Where, the brackets ([]) indicate that the keywords INIT (initial value of the loop parameter) and INCR (increment) and their associated parameters are optional $parameter must be defined before loop and its value is overwritten by the initialization of the DO-loop

Summary

In the present chapter theoretical background of genetic algorithm, bulbous bow, and FLUENT software is given Various turbulence models are defined and CFD analyses based on these turbulence models are carried out for trimaran FA1 It is concluded that SST k-ω turbulence model predicts total resistance of the ship more accurately Gambit and FLUENT journaling is defined in this chapter with working examples used in the optimization cases presented in this paper

37

Optimization Methodology

The complete optimization process should be able to work automatically without any interference from a user The optimization process should be able to solve following major components:

• Geometry and mesh generation based on the design constraints defined for the shape evolution

• Computational Fluid Dynamics software to calculate the required objective function

• An optimization program to communicate among all components

Solutions to above mentioned components are as follows:

• Creation of GAMBIT journal file to automate the process of geometry and mesh creation

• Creation of FLUENT journal file to calculate the objective function

• Creation of genetic algorithm based optimization program written in MATLAB

A methodology defining the complete process of optimization is presented in Figure 3.1 Before starting the optimization process the problem to be solved should be completely defined in terms of objective function and the method to minimize it For the research work presented in this paper, objective function for all study cases is to minimize the total resistance of a ship

Automatic Geometry Modeling and Mesh Generation

In the following sections each process of the methodology is described

For an optimization process it is important to have an optimization tool which evaluates the cost function for hull improvement and provide input parameters for the next improved hull The genetic algorithm program for hull form optimization is written in MATLAB, this program works as a main program which is able to communicate among all the processes of the optimization At the start of the program cost/objective function and the optimization variables along with their constraints as per requirement of the optimization are defined The general working of the genetic algorithm is described below

GA starts with the group of initial population of chromosomes generated randomly based on the pre-defined constraints Each chromosome is evaluated for its fitness The chromosomes with high fitness are selected to continue for the mating based on the selection rate (i.e the number of chromosomes to be kept in each generation) Chromosomes are selected from the mating pool of high fitness chromosomes to produce new offspring to replace the low fitness ones Mutation is carried out in order to prevent the algorithm from converging to local solution After the mutation, cost associated with the chromosomes is calculated At the completion of each generation improvement in the fitness of each chromosome is obtained, this process is continued till the sufficient number of generations for best solution are achieved A flow chart describing the working of GA for this study has been shown in Figure 3.2

Gambit variable file stores all those variables which are required for the geometry changes to optimize the hull form The name of variables in the file are defined with the $ sign Variable values are stored by the input from genetic algorithm program and serves as input to Gambit journal file

As described in the previous chapter, Gambit journal file contains a set of commands that are executed one by one till the end of file Gambit journal file for optimization contains all the required steps starting from generating the required geometry to the final export of mesh

39 for CFD analysis In every journal files created for optimization in all case studies, optimization variables are input from Gambit variable file

Figure 3.2 Flow chart of a Genetic Algorithm

3.1.4 Automatic Geometry Modeling and Mesh Generation

For automatic generation of hull geometry and mesh, the Gambit journal file should be flexible enough to cater for all geometric changes made due to the evolution of design variables input from optimization process Gambit journal file is run in the batch mode from optimization program to execute all the commands in one go Various geometric and mesh generation conditions, as per the changes in the hull in each iteration, are applied in the journal file in order to have desired output mesh file for next step

Define variables and their range

Cost calculation of each chromosome

FLUENT journal file contains all the executable commands to perform the CFD analysis for the required mesh file The journal file contains both TUI and GUI commands At the end of CFD analysis journal file is able to store total resistance results to be evaluated by optimization program

To perform CFD analysis for calculating the objective function (i.e total resistance) of each mesh file generated from Gambit journal file, FLUENT software is used Each time when the analysis is required to be run, optimization program runs the FLUENT software with input file as FLUENT journal file All CFD analyses are run with parallel FLUENT software with four parallel processes The detailed CFD analysis parameters for all case studies are described in the next chapters.

Summary

In the present chapter overall methodology used for the optimization in the research work is defined The flow chart showing the working of the methodology is presented and all the processes of optimization methodology are defined Genetic algorithm based program is developed for the optimization process along with journal files for Gambit and FLUENT

41

Series 60 Parent Hull

The David Taylor Model Basin have carried out a long term methodical research for a single screw ship design and the results are published in literatures [52][53][54][55] Series 60 is the systematic series of large scope which was intended as a benchmark for single screw container ship design For first case study, hull form optimization is carried out for series 60

(Cb=0.6) hull, the hull is selected due to its easily available experimental results

The particulars of model ship, used for both experimental and computational test, are presented below and the isometric-view of three-dimensional model is shown in Figure 4.1

Table 4.1 Particulars of Series 60 Hull Description Parameter Value Units Length between perpendiculars L pp 7.0 m

Figure 4.1 3-D model of the series 60 ship

Before carrying out the optimization process, CFD calculations are carried out for the parent hull and the results are compared with the experimental results presented by ITTC cooperative experiments on a series 60 model at ship research institute – flow measurements and resistance tests [56]

4.1.1 Computational Domain and Mesh Generation

Gambit software is used for the creation of geometry and the generation of grid for the flow domain Due to the symmetry of hull, half of the domain is modeled for flow calculations The flow domain volume is divided in such a way to have hexahedral cells for whole computational domain The Cartesian coordinate system is setup with x-axis, y-axis and z-axis pointing towards bow, upwards and portside respectively The length in front of hull (inlet boundary), behind the hull (outlet boundary), top, bottom, and side boundaries are taken as 1.0Lpp, 3.0Lpp, 0.5Lpp, 1.0Lpp, and 1.0Lpp respectively Care has been taken to generate a mesh to keep turbulence value within desired limit (i.e 30≤ ≤300)

The first node distribution based on value is calculated by [57] :

(4.1) where = distance from ship surface to first node

The total number of hexahedral cells for the flow domain is 0.65M

Figure 4.2 ISO view of domain mesh

Figure 4.3 Symmetry view of domain mesh

Figure 4.4 Top view of free surface mesh

The commercial viscous flow software FLUENT is used for computations in this research work Mesh file generated by Gambit is imported to FLUENT software

Since the motion of the free-surface is governed by gravitational and inertial forces, therefore, gravity effects must be taken into account in boundary conditions Volume of Fluid (VOF) formulation and the open channel boundary conditions available in FLUENT are applied to solve multiphase free-surface flow The VOF model is a surface tracking technique that can model two or more immiscible fluids by solving a set of momentum equations and tracking the volume fraction of each of the fluid in each computational cell throughout the domain Each fluid position in a cell is determined by volume of fraction value of 0 or 1 A value of 0 indicates that the cell is empty of that fluid; the value of 1 determines that the cell is full of that particular fluid, and the value in between 0 and 1 shows that the cell contains interface of two or more fluids The inlet boundary condition upstream is taken as pressure-inlet with open channel; outlet boundary condition downstream is taken as pressure-outlet with open channel No-slip wall boundary condition is taken on top, bottom, side boundaries and the hull surfaces

Figure 4.5 Computational Domain with Boundary Conditions

As discussed earlier in chapter 3, for our case we found that SST k-ω turbulence model gives better results for calculating total resistance of ship as compared to other turbulence models, therefore, the turbulence model of SST k-ω with standard coefficients is employed in all of our later calculations

Discretization is the method of approximating the differential equations by a system of algebraic equations for the variables at some discrete locations (grid/mesh points or cells) in space and time There are number of methods for the solution of the governing partial differential equations on the discretized domain

FLUENT uses a control-volume based method to convert a general scalar transport equation to an algebraic equation that can be solved numerically This control volume technique consists of integrating the transport equation about each control volume, yielding a discrete equation that expresses the conservation law on a control-volume basis By default

FLUENT stores discrete values of unknown scalar variable at the cell centers, however, face values of are required for the convection terms and must be interpolated from the cell center values This is accomplished using an upwind scheme Upwinding means that the face value of is derived from quantities in the cell upstream, or "upwind'' relative to the direction of the normal velocity There are several upwind schemes available in FLUENT:

When first-order accuracy is desired, quantities at cell faces are determined by assuming that the cell-center values of any field variable represent a cell-average value and hold throughout the entire cell; the face quantities are identical to the cell quantities Thus when first-order upwinding is selected, the face value of is set equal to the cell-center value of in the upstream cell

When second-order accuracy is desired, quantities at cell faces are calculated using a multidimensional linear reconstruction approach [62] In this approach, higher-order accuracy is achieved at cell faces through a Taylor series expansion of the cell-centered solution about the cell centroid

4.1.3.1.3 QUICK (Quadratic Upwind Interpolation of Convective Kinematics) Scheme

For quadrilateral and hexahedral meshes, where unique upstream and downstream faces and cells can be identified, FLUENT also provides the QUICK scheme for computing a higher-order value of the convected variable at a face QUICK-type schemes are based on a weighted average of second-order-upwind and central interpolations of the variable

For simulations using the VOF multiphase model, upwind schemes are generally unsuitable for interface tracking because of their overly diffusive nature Central differencing schemes, while generally able to retain the sharpness of the interface, are unbounded and often give unphysical results In order to overcome these deficiencies, FLUENT uses a modified version of the High Resolution Interface Capturing (HRIC) scheme The modified HRIC scheme consists of a non-linear blend of upwind and downwind differencing

Two sets of discretization schemes are used for the analysis; First discretization scheme is as follows:

Table 4.2 Discretization Scheme-1 Variable Scheme-1 Pressure PRESTO

Volume Fraction First Order Upwind Turbulent Kinetic Energy First Order Upwind Specific Dissipation Rate First Order Upwind

Second discretization scheme is given below:

Table 4.3 Discretization Scheme-2 Variable Scheme-2 Pressure PRESTO Momentum QUICK Volume Fraction Modified HRIC

Turbulent Kinetic Energy Second Order Upwind Specific Dissipation Rate Second Order Upwind

Analysis are carried out for both set of discretization schemes and results are presented in

Table 4.4 and plotted in Figure 4.6

Table 4.4 CFD Results for Discretization Schemes

Figure 4.6 Comparisons of Two Discretization Schemes

It can be observed that overall second discretization scheme better follows experimental results; especially in the lower Froude number range, resistance prediction is quite accurate For all the further analysis of Series 60 hull, second discretization scheme is applied

For all CFD analysis convergence of the solution is assessed by monitoring the residuals of continuity, velocity, turbulence, volume fraction and drag force The residual convergence criterion for all residuals is taken as 1e-07; the calculated drag on the ship hull is also recorded after every 200 iterations to judge the convergence of the solution

CFD calculations for series 60 parent hull are carried out for Froude number ranging from 0.159 to 0.34 Results obtained from FLUENT software are compared with the ITTC cooperative experiments on series 60 model [56] and presented in Figure 4.7 This can be observed from the results that experiment and CFD results are in good agreement especially in the low Froude number range; however, maximum difference in results is below 10 percent A good comparison between calculated results and experimental results of the wave profile along hull with different Froude number are shown in Figures 4.10-4.13, the global view of the calculated wave pattern are shown in Figure 4.14-4.15

Figure 4.7 Comparison of total resistance (Experiment and Calculation)

Figure 4.8 Dynamic and Static Pressure Contours at Fn 0.34

Figure 4.9 Contours of wall y-plus on hull surface at Fn 0.34

Figure 4.10 Wave profile around hull at Fn 0.34 Figure 4.11 Wave profile around hull at Fn 0.319

Figure 4.12 Wave profile around hull at Fn

Figure 4.13 Wave profile around hull at Fn 0.279

Figure 4.14 Wave Contours at Fn 0.34

Figure 4.15 Wave Contours (Line) at Fn 0.34

Bulbous Bow Optimization For Resistance Reduction

The optimization methodology is applied to Series 60 Cb=0.6 ship hull with additive bulbous bow An additive bulbous bow increases the displacement volume of the ship by the effective total bulb volume; the sectional area curve of the original ship remains unchanged Additive bulb can be manufactured separately For implicit bulb, effective volume of the bulb is part of the displacement volume of main hull; the sectional area curve of the original ship is changed

The hull has been optimized for a single speed corresponding to Fn=0.34 Generation of Hull with additive bulbous bow geometry is defined in Gambit software and FLUENT is used as a calculation tool to solve flow field around hull and obtain total resistance Genetic

51 algorithm is applied for the optimization of bulb design parameters, on which to determine the optimal bulbous form

4.2.1 Design of Bulbous Bow for Optimization

As described in chapter 2, the hydrodynamic effect of bulbous bow depends on the flow change around bow of hull Geometrically, this hydrodynamic effect is a function of bulb size or volume (i.e longitudinal distribution of volume along length of bulb and the form of bulb) [63] The vertical distribution of bulb volume and its distance to the free-surface will affect the amplitude of the wave system along hull The longitudinal distribution of the bulb volume along the length will create the phase lag between bulb and hull waves The appropriate selection of these geometric parameters can create favorable interference of bulb and hull waves, resulting in a decrease in wave resistance

Keeping in view the above, following bulb design parameters are selected:

Table 4.5 Bulbous Bow Design Parameters

Y max m Maximum height of bulb

Y center m Center of the bulb

Y half m Mid-point of the bulb section

Alpha degree Longitudinal profile angle

Figure below presents the profile of bulb sections with design parameters

Figure 4.16 Bulbous Bow Design and Parameters

Where L determines the protruding length of the bulb forward to F.P Ymax determines the maximum height of the bulb, Ycenter determines the shape of the section (Ycenter above Yhalf gives nabla-type bulb section, Ycenter below Yhalf produce delta-type bulb section and Ycenter equal to Yhalf produce O-type bulb section), W presents the maximum width of the bulb, and angle alpha produce longitudinal profile of the bulb forward of F.P The geometry of the bulbous bow is created based on the generation of sectional profile using conic arc creation with three vertex parameters (start, shoulder, and end) and one shape parameter For shape parameter, elliptical shape is used for specifying the general shape of the arc To fit the additive bulb after the FP its basic section remains constant downstream A separate bulb volume is generated and then added into the main hull volume

4.2.2 Constraints for Design Parameters/Variables

In order to search for an optimum solution by optimization algorithm in a design space, range of design variables is required to be given (i.e minimum and maximum values) The design parameters will evolve only within the specified range Constraints applied for this optimization work are presented below:

Table 4.6 Constraints for Bulb Design Optimization

L b [0.007L pp ,0.085L pp ] L b is allowed to evolve 0.007-0.085 times parent hull length between perpendicular value

Y max [0.85T,1.2T] Y max is allowed to evolve 0.85-1.2 times parent hull draft value.

Y center [0.25T,0.8T] Y center is allowed to evolve 0.25-0.8 times parent hull draft value.

W b [0.02B,0.75B] W b is allowed to evolve 0.02-0.75 times parent hull breadth value Alpha [-20 o ,20 o ] Alpha angle is allowed to evolve -20 to 20 degrees

GA starts with defining the chromosomes as an array of variable values to be optimized Chromosomes= [v1, v2… vn]

Where n is the number of variables

Here the cost function is the calculation of total resistance of ship subject to the above mentioned constraints Since the calculation of cost function in this optimization case is time

53 consuming, therefore, population size and mutation rate are selected as per to optimize the problem quickly The genetic algorithm optimize quickly with small population and high mutation rate The mutation rate is selected based on the number of variables Here the mutation rate is calculated as ‘1/n’, where n is the number of variables Following genetic algorithm parameters are applied for this optimization:

4.2.4 Generation of Hull Geometry and Meshing

Gambit journal file has been used to automatically generate the hull form and design of bulbous bow in accordance with the design parameters The original hull form of Series 60 ship is imported in Gambit as IGES file The design parameters/variables for the bulb are imported from variable file in a vertex format From these bulb design variables, bulb sections and then volume is created and then it is integrated in to parent hull

For flow calculations half of the model is modeled due to symmetry The domain volume is taken as a box shape with flow domain around hull is divided into several volumes Due to the complexity of shape with the addition of new bulb, mesh for small volume around hull has been created with tetrahedral cells and the rest with hexahedral mesh However, care has been taken to generate a mesh to keep turbulence y + value within desired limit Mesh file for the CFD analysis created after applying boundary conditions to the flow domain, same boundary conditions previously adopted for the parent hull calculations are applied for this case

FLUENT journal file is created to automatically run every solution with new design Same FLUENT solution parameters that are adopted for parent hull calculations are applied for this case The residual convergence criterion of continuity for optimization is taken as 1e-03 The results for the total resistance are stored in a text file (Figure 4.18) which is read by optimization program

Figure 4.17 Domain mesh for optimization

Optimization is carried out on Intel Core2 Quad CPU @ 2.66GHz Figure 4.19 shows the evolution history of total resistance, each point in this figure represents the absolute value of total resistance obtained through optimization Figure 4.20 represents the minimum, average and maximum cost obtained over generations It can be observed that the solution for minimum cost has converged along the generations Evolution of bulbous bow design parameters along number of generations and number of evaluations are presented in Figure 4.21 and Figure 4.22 respectively

It is pertinent to mention that since evaluation of the cost function (calculation of total resistance) is time consuming, therefore, in each generation only costs of offspring of mutated chromosomes are evaluated Non-mutated parents have already associated cost evaluated earlier, so they are not evaluated again In every new generation there consist non-mutated

55 parents, mutated parents, offspring and mutated offspring, if any identical chromosome which has already evaluated and has associated cost then this cost is assigned to the new chromosome

Figure 4.19 Evolution history of optimization

Figure 4.20 Cost trend against number of generations

Figure 4.21 Evolution of bulb parameters per generation

57 Figure 4.22 Evolution of bulb parameters per evaluation

After the completion of optimization process, bulbous bow parameters are obtained for the top two optimized forms and are presented in Table 4.7 The bulbous bow sections for both optimized hulls are shown in Figures 4.23-4.25

Table 4.7 Bulbous Bow Parameters for the Best Two Hulls

Figure 4.23 Bulbous bow sections of optimized hulls

Figure 4.24 Longitudinal bulbous bow sections of optimized hull-1

CFD calculations for the two optimized hulls with additive bulbous bow are carried out with the same FLUENT solution parameters that are used for parent hull Since the effect of bulbous bow in reducing the resistance of ship hull is better seen in high speed range, therefore, further calculations are carried out for four high speeds and comparison has been made against parent hull (without bulbous bow) The results are tabulated in Table 4.8 and presented in Figure 4.26

Table 4.8 Resistance Results of Parent and Optimized Hulls

Parent Hull Calculation Optimized Hull-1 Optimized Hull-2

Figure 4.26 Comparison of total resistance for parent 1 and optimized hulls

1 Parent hull test results are obtained from ITTC cooperative experiments on series 60 model [56] The test results mentioned here and also in the following sections of this chapter are referred to the above mentioned experimental results

Goose-Neck Bulbous Bow (GNBB) Optimization

Typical bulbous bow nowadays is called “goose-neck” bulb with an upside down drop form, the upper contour profile of the bulb is rising forward In this part of the present wok on bulb optimization series 60 hull is fitted with various goose-neck bulbous bows The design of the bulb is produced based on the various parameters defining the shape, and these parameters are optimized to achieve a low resistance hull

4.3.1 Constraints for Design Parameters/Variables

The design parameters for optimization are defined with a range of minimum and maximum values, and these parameters are allowed to evolve in that specified range Following constraints are applied for this optimization work:

Table 4.10 Constraints for Bulb Design Optimization

L b [0.04L pp ,0.07L pp ] L b is allowed to evolve 0.04 to 0.07 times parent hull length between perpendicular value

Y 1 is allowed to evolve -0.01 to -0.02 value in y-coordinates

Y 2 [0.01, 0.02] Y 2 is allowed to evolve 0.01 to 0.02 value in y-coordinates

W b [0.17B,0.43B] W b is allowed to evolve 0.17 to 0.43 times parent hull breadth value Alpha [0 o ,10 o ] Alpha angle is allowed to evolve 0 to 10 degrees

Figure 4.37 presents the geometry of bulb profile with the design parameters The geometry of the bulbous bow sections is created based on the generation of sectional profile using conic arc creation with three vertex parameters (start, shoulder, and end) and one shape parameter For shape parameter, elliptical shape is used for specifying the general shape of the arc The longitudinal profile of the bulb is created using NURBS using interpolate method To fit the additive bulb after the FP its basic section remains constant downstream A separate bulb volume is generated and then added into the main hull volume For this optimization case the value of ymin, ymax and ycenter are fixed as follows:

Figure 4.37 Bulb Geometry with design parameters

The cost function for this optimization is selected as minimization of total resistance subject to the variation of above mentioned constraints Following genetic algorithm parameters are applied for optimization:

Gambit and FLUENT journal files are created for the optimization process The optimization is carried out for Froude number 0.34 with the use of genetic algorithm program written in MATLAB The results of the optimization are stored in a text file, each generation almost took one day to complete The evolution history and cost trends of the optimization are presented in Figure 4.38 and 4.39 respectively After the completion of optimization, bulbous bow design parameters for low resistance hull are obtained The final results are presented in table 4.11

Figure 4.38 Evolution history of optimization

Figure 4.39 Cost trend against number of generations

Table 4.11 Bulbous Bow Parameters for the Optimized Hull

The bulbous bow sections for optimized hulls are shown in Figures 4.40-4.43

Figure 4.40 Bow profile of optimized hull Figure 4.41 Bulbous bow sections of optimized hull

Figure 4.42 Longitudinal sections of optimized hull-1

A new hull form is generated based on the optimized bulbous bow parameters and CFD analyses are carried out for higher four Froude numbers The mesh generation and solution parameters for CFD analyses are kept same as for parent hull The final CFD results of optimized hull (with bulbous bow) are compared with the parent hull (without bulbous bow) CFD results The results are presented in Table 4.12 and comparison is shown in Figure 4.44.

Table 4.12 Resistance Results of Parent and Optimized Hull

Parent Hull Calculation Optimized Hull

Figure 4.44 Comparison of total resistance for parent and optimized hull

After the addition of bulbous bow to the parent hull, its displacement volume increased by 2.47%, therefore, comparison is also made for total resistance per unit volume and presented in Table 4.13

Table 4.13 Resistance Comparison per unit Displacement of Parent and Optimized Hull

Parent Hull Calculation Optimized Hull

R t /Vol R t /Vol Reduction in Resistance per unit volume (%) 0.279 61.93 63.48 -2.5 (Increase in R t /V)

It can be seen from the results presented in the above tables that optimized hull has achieved reduction in resistance as compared to parent hull for top three Froude numbers, while for Froude number 0.279 the optimized hull achieved increase in total resistance

Pressure contours of the optimized hull are presented in Figure 4.45, and free surface wave contours and volume of fraction (water) contours are presented in Figure 4.46 and 4.47 respectively

Figure 4.45 Static and dynamic pressure contours of optimized hull at Fn 0.34

Figure 4.46 Free surface wave contours of optimized hull at Fn 0.34

Figure 4.47 Contours of volume of fraction (water) of optimized hull at Fn 0.34

Wave profiles of the optimized hull and parent series 60 hull are compared with each other for all Froude numbers and presented in Figures 4.48 to 4.51 It can be observed that the amplitude of optimized hull wave at the forward portion is lower as compared to parent hull, generating small bow wave

Figure 4.48 Comparison of wave profile at Fn 0.34

Series 60 Hull Turbulence Intensity Comparisons

For the optimization cases of series 60 mono hull, turbulence intensity calculated along the length of the hull is compared with the parent hull results Seven sections are taken along the length of the hull and turbulence intensity (max and surface integral) results are calculated for these seven section The results are presented and compared in figures below

Figure 4.52 Comparison of maximum turbulence intensity for parent and optimized hulls at Fn 0.34

Figure 4.53 Comparison of turbulence intensity surface integral for parent and optimized hulls at Fn 0.34

It can be observed from the comparisons that the optimized series 60 hulls not only have low resistance as compared to parent hull but also have low turbulence intensity throughout the length of the hull Therefore it can be deduced that the decrease in total resistance of hull due to the addition of bulbous bow also decreases the turbulence intensity around the hull.

Summary

In the present chapter two different cases related to the optimization of bulbous bow for series 60 hull are presented Initially CFD analyses of parent hull are carried out to predict the total resistance of the ship and the results are compared with the experimental data It is concluded that VOF scheme with open channel boundary condition and discretization scheme-2 are appropriate for calculating ship free surface analysis and the results are in good agreement with experimental data

Optimization of series 60 hull is carried out using genetic algorithm to obtain low resistance hull For two optimization cases, bulbous bow parameters are defined for the design of bulb added to the hull For first optimization case, all three bulb sections (nabla, delta, circular) are investigated Total resistance calculated by CFD for the optimized hulls are compared with the parent hull CFD results and it is observed that the reduction in resistance achieved for optimized hulls For second optimization case, goose neck type bulbous bow design parameters are defined for the optimization The CFD results of optimized hull shows a better reduction in resistance as compared to the first optimization case It is also observed that reduction of resistance per unit displacement is higher for both optimization cases as compared to reduction of resistance

APPLICATION CASE-2: TRIMARAN FA1 HULL

Recently ship building authorities have shown great interest in the development of multihull ships due to their better seagoing performance A trimaran ship consisting of a main hull and two outriggers has advantages of low resistance due to its slender hulls, large available deck area, large internal volume, and better stability and sea keeping characteristics Trimaran is designed with slender hull shapes in order to decrease the wave making resistance of the ship The favorable wave interference among hulls compensates the increase of wetted surface [58]

One of the major requirements from ship owners and ship building industry is the development of low resistance ship The optimal arrangement of Trimaran hulls is one of the solutions to lower the overall resistance Yang et al (2000)(2001) [37][38] determined the optimal position of the outer hulls of Trimaran for minimizing wave drag using a nonlinear method based on Euler’s equations and three linear potential flow methods.

Trimaran FA1 – Parent Hull

Before carrying out trimaran optimization, total resistance of parent trimaran ship is calculated by CFD and results are compared with the experimental data

A complete CFD solution requires three major steps: preprocessing, analysis of the problem using a solver, and post processing the results Preprocessing of the solution involves geometry creation of the model, and an appropriate mesh generation In this study, preprocessing of the solution is carried out in GAMBIT software The geometry of the hulls is obtained by the use of offset table This offset data is imported into Gambit in the form of vertices and then 3-D model is generated

The parent hull trimaran used in this paper is FA1, which was a trimaran already optimized by Prof Huang De Bo in Harbin Engineering University, with a nonlinear programming technique combined with a potential theory of wave resistance It is thus itself a low resistance form

The trimaran FA1 consists of a main hull and two identical outriggers The major dimensions of the trimaran are given in Table 5.1 The distance between the centers of main hull and outrigger is 0.4 meters

Table 5.1 Major Dimensions of Trimaran

Due to symmetry of geometry, only half of the model is created The computational domain around trimaran is created as rectangle and the main volume is divided into several small volumes in order to generate hexahedral cells The Cartesian coordinate system is setup with x-axis pointing towards the bow, y-axis upwards, and z-axis to portside The computational domain stretches out for 1.0 times length of main hull (Lmh) in front of the ship,

3.0 times Lmh behind the hull, 1.0 time Lmh under the still water, and 0.4 times Lmh above the still water surface The overall dimension of the computational domain is 5Lx1.4Lx1L

Figure 5.2 Mesh of Computational Domain

The computational domain is mostly discretized using H-type grid The overall grid size of domain is 0.74M hexahedral cells

Figure 5.3 Mesh on Symmetry Plane

Figure 5.4 Mesh on Free Surface

The commercial viscous flow software FLUENT is used for computations in this research work Mesh file generated by Gambit is imported to FLUENT software For calculations, three-dimensional steady, incompressible, two-phase (air and water), and viscous turbulent flow is considered

The inlet boundary condition upstream is taken as pressure-inlet with open channel; outlet boundary condition downstream is taken as pressure-outlet with open channel No-slip wall boundary condition is taken on top, bottom, side boundaries and the hull surfaces

For turbulence modeling SST k-ω developed by Menter (1994) [51] is selected due to its better results for free surface computations [4] Volume of Fluid (VOF) formulation along with open channel boundary conditions is applied to solve the multiphase free surface flow

Table 5.2 Discretization Scheme-1 Variable Scheme Pressure PRESTO

Table 5.3 Discretization Scheme-2 Variable Scheme Pressure PRESTO Momentum QUICK Volume Fraction Modified HRIC

It can be observed that first discretization scheme better follows experimental results; and the resistance prediction is quite accurate with maximum error around 7% For further analyses of trimaran hull, first discretization scheme is applied For all CFD analysis convergence of the solution is assessed by monitoring the residuals of continuity, velocity, turbulence, volume fraction and drag force The residual convergence criterion for all residuals is taken as 1e-07

Figure 5.6 Comparisons of Calculation Results with Two Different Discretization Schemes

The total resistance of the trimaran is calculated The calculations are carried out for Froude number (Fn) ranging from 0.14 to 0.75 The calculated drag on the trimaran is recorded, after every 200 iterations, and plotted as shown in Figure 5.7 in order to judge the convergence of the solution

Figure 5.7 Drag History of Trimaran Analysis

The calculated results of total resistance for trimaran FA1 are compared with the experimental results and presented in Figure 5.8

Figure 5.8 Comparison of Calculated and Test Results of Total Resistance

It can be observed that CFD calculations of trimaran are in good agreement with experimental results The free surface wave contours and water volume of fraction are shown in Figures 5.9-5.12

Figure 5.9 Free Surface Wave Contours at Fn 0.75

Figure 5.11 Contours of volume fraction (water) at Fn 0.61

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APPLICATION CASE-2: TRIMARAN FA1 HULL

Recently ship building authorities have shown great interest in the development of multihull ships due to their better seagoing performance A trimaran ship consisting of a main hull and two outriggers has advantages of low resistance due to its slender hulls, large available deck area, large internal volume, and better stability and sea keeping characteristics Trimaran is designed with slender hull shapes in order to decrease the wave making resistance of the ship The favorable wave interference among hulls compensates the increase of wetted surface [58]

One of the major requirements from ship owners and ship building industry is the development of low resistance ship The optimal arrangement of Trimaran hulls is one of the solutions to lower the overall resistance Yang et al (2000)(2001) [37][38] determined the optimal position of the outer hulls of Trimaran for minimizing wave drag using a nonlinear method based on Euler’s equations and three linear potential flow methods