A SYSTEMATIC INVESTIGATION OF THE EFFECTS OF VARIOUS BULBOUS BOWS ON RESISTANCE OF FISHING BOATS UDC 629

ITU Fishing Boats Series hull forms of 148/3, 148/4, 148/8 and 148/9 in order to determine the most appropriate bulbous bow for fishing vessels. Initially, in defined Fn values, Computational Fluid Dynamics (CFD) analyses on four main forms are performed by using Realizable k  Model and Volume of Fluid (VOF) method. The total resistance values obtained by the CFD analyses and by the existing test results via Froude and Hughes methods are compared and examined. Thus, the method and reference values of CFD analyses are determined for the hull forms with bulbs which do not have test results. Subsequently, the CFD results of frictional resistance, pressure resistance and total resistance values for actual hulls and hulls with bulbs are compared. Following the examination of results in terms of CB, L/B and bulb types, it is determined that the elliptical bulb type is the most suitable bulb type for the fishing vessels.


Introduction
According to the culture of each country, certain forms of fishing boats have been developed according to needs over time.While improvements have been made in the main forms previously, the application of bulb to fishing boats is carried out because of that efficiency of bulb is observed today.The resistance analyses, which are made in model test basins, can be done on computers with the help of CFD softwares thanks to the development of technology.
The part of head of the ships, that is underwater, is inflated like a prominence or convexity, and it is called bulb [1].The bulb forms are classified according to the form of the crosscut area of the head.As a general definition, there are three basic types of bulb geometry, namely, Delta (Δ), Circular-Elliptic (O) and Nabla (∇) sections [2].The sections of the bulbs are shown in Figure 1.Taylor [3] is the first researcher to experimentally investigate the effects of bulbs on ship form.Later, Bragg [4], Inui et al. [5], Ferguson [6], and Muntjewerf [7] experimentally conducted experiments on the Δ (delta) type, cylindrical and conical bulbs, which are known as Taylor bulbs, by systematically changing the bulb parameters.Weinblum [8], Wigley [9], Inui [10] and Yim [11] studied on the theory of linearized wave resistance theoretically.Inui [10] presented a method to determine the size of the bulb by matching amplitude functions of bulb in regular waves and stem.A connection for a speed has established between the entrance angle of ship head and the size of bulb by Yim [12].A method consisting of three main subjects for designing spherical bulb was presented by Yim [13].Again, Yim [14] discussed the sheltering effect on spherical bulbs.Baba [15] and, Shearer and Steele [16] pointed out that the bulb has benefits like; to reduce the wave breaks on stem, to improve the flow around keel line and bilge turn, as well as preventing flow separation on ship forms.Kracht [2] developed a statistical method from the experience of propulsion tests.The method gives power reduction for the selected bulb or suitable bulb design for a selected power reduction.The Kracht method is more useful for nabla (∇) sectioned bulbs.Sharma and Sha [17] developed a method of designing a bulb by combining Kracht [2] and Yim [13] methods, which are two famous theories accepted in the bulb design.The method can do optimization of bulb parameters for design speed.The method uses a reanalysis of an approximate linear theory with sheltering effect for resistance estimation, and re-correlation with statistical analysis via a non-linear multivariate regression analysis from existing literature and tank test results available in the public domain.
There are different discretization techniques to solve various problems at CFD.The Finite Volume Method (FVM), which is derived from the Finite Difference Method (FDM) formulation, is one of the most widely used methods in CFD.Because it gives good results in non-structural solution mesh as well as in structural solutions.It is developed by Godunov [18].With evolving technology, turbulence models have been developed that can solve the flow around complex and large geometries such as ships.The RANS (Reynolds-Averaged Navier-Stokes) turbulence modeling techniques, which are a simpler approach than other turbulence models, are used to solve the flow around the ship.Generally in CFD, k-ε models (Standard k-ε model, Realizable k-ε model, RNG k-ε model) and k-ω models are used from two-equation models at flow applications of around the ship.The Realizable k-ε Model, which is the most developed version of the k-ε model, was developed by Shih et al. [19].
The CFD study of bulb optimization started in the 1990s.A comparative study of alternative bulb varieties (elliptical, conical, spoon, improved) with the aid of CFD is presented by Stromgren [20].Kim and Jang [21] studied the effect of bulb on wave characteristics with CFD.An optimization of the pressure distribution on the surface and the around Series 60 vessels with bulb is studied with CFD by Huang et al. [22].Lee and Sarath [23] conducted bulb designs in different forms for 12500 TEU containers ships and tried to determine optimum bulb sizes with CFD.A bulb optimization of a 36-meter-long fishing boat

95
was conducted to improve it hydrodynamically with CFD by Sarasquete et al. [24], and the results of CFD analyses were compared with the data of the model resistance tests.A numerical procedure, which based on the genetic algorithm and a potential flow solver, for hydrodynamic optimization of a ship hull form with a bulbous bow has been established by Matulja and Dejhalla [25].Chrismianto and Kim [26] used a cubic Bezier curvature and curve-plane intersection methods to design a bulb for the KRISO container ship model, based on 4 design parameters.The resistance values, which were obtained by the CFD analyses, were compared with the model data, and the accuracy of the analyses was confirmed.
The aim of the study is to determine which type of bulb on the fishing boats will be more effective in reducing total resistance.For this purpose, Delta (Δ), Nabla (∇) and Elliptic (O) sectioned bulbs are added to the forms of 148/3, 148/4, 148/8 and 148/9 coded boats from ITU Fishing Boats Series.The designs of the forms with bulbs have been made.Firstly, Froude [27] and Hughes [28] method are used to calculate the total resistance of the full-scale boat from the model test data.Secondly, the results, which are obtained by CFD analyses, are compared with the test results.Then, CFD analyses of boat forms with bulbs are made.After that, the total resistance values, which are obtained from the CFD analyses, are compared with each other.Finally, the inferences, which are obtained in the study, are assessed according to ship codes, CB, L/B ratio and bulb types.In this way, it has been determined which type of bulb is more beneficial for the fishing boats.

Ship, model and bulb geometry (characteristic features)
In the study conducted, the ship forms were selected from the Fishing Boats Series of ITU.Because of requirement to obtain more suitable boat forms for waters of Turkey, these fishing boat forms were produced by Kafalı et al. [29].Characteristic values of these fishing boat forms are given in Table 1.The characteristic values of the models of these fishing boats are given in Table 2. Fishing Boats Series of ITU has been concluded with the study named "Computer Aided Design of Fishing Boats Suitable for Turkish Waters" which are prepared by Aydin [30].
The effects of bulbs on resistance were examined for 148/1 coded model by Soylemez [31].The bulbs were in the delta profile.They were named A1, A2 and A3.The characteristics of the three bulbs are given in Table 3. Bulb code b/B ratio l/b ratio cross sectional area ratio 0.07 l: length between the endpoint of bulb and the forward perpendicular b: width of the largest width of bulb It was seen that the A1 and A2 bulbs started to become effective after the speed of 9 knots (Fn 0.331) while the A3 bulb started to become effective after the service speed of 10 knots (Fn 0.367), and the A2 was more effective than the A1 [31].
At the bulb application in 148/1 coded model, Soylemez [31] stated that the most effective bulb is A2.The maximum width of the bulb A2 is given by the equation_1a and the maximum length of the bulb A2 from the fore peak by the equation_1b.

3.5
The maximum widths and the maximum lengths of the bulbs of 148/3, 148/4, 148/8 and 148/9 coded boats are calculated by equation (1a) and equation (1b), respectively.The maximum bulb lengths of 148/8 and 148/9 coded boats are multiplied by the length correction coefficient 1.4285 (28.57/20.00).The maximum widths and the maximum lengths of the bulbs are given in Table 4.The non-dimensional offset values of the delta, nabla and elliptical type bulbs are given in Table 5, Table 6 and Table 7, respectively.The displacements of all generated boats for use in CDF analyses are given in Table 8.As an example, the lines plan of 148/3 coded fishing boat is shown in Figure 2. The fore cross sections plan and bulb profile are shown in Figure 3, Figure 4 and Figure 5 for 148/3-D, 148/3-N and 148/3-E coded fishing boat, respectively.The three-dimensional models of all generated fishing boat forms are shown in Figure 6.

Governing equations
In this study, an Unsteady Reynolds-Averaged Navier-Stokes (URANS) method is used to solve the governing equations.These mass and momentum conservation equations are solved by the commercial CFD software STAR-CCM+.The averaged continuity and momentum equations for incompressible flows are given in tensor notation and Cartesian coordinates by equation_2 and equation_3.
where  is density, i u is the averaged Cartesian components of the velocity vector, i j uu   is the Reynolds stresses and p is the mean pressure.ij  is the mean viscous stres tensor components, as shown in equation_4.
in which  is the dynamic viscosity.

Turbulence model
The "Realizable  k  Model" developed by Shih et al. [19] is the most advanced version of the  k  model.
There are two basic differences from the standard  k  model.The first is that the model contains a new transport equation for the turbulence loss rate  .Second, C  , a critical coefficient of the model, is expressed as a function of the mean flow and turbulence properties rather than being fixed as in the standard model.The understanding of an C  variable is also compatible with the experimental data in boundary layer.
Shih et al. [19] developed transport equations are as follows:

Performing resistance analyses using the CFD method
Star-CCM+ software calculates the total force on the surface; Normal and tangential forces, i.e., pressure and friction (shear) forces [33].
The force on a surface is computed as: where pressure f f and shear f f are the pressure and shear force vectors on the surface face f , and f n is a user-specified direction vector that indicates the direction in which the force should be computed.

Test results
In this study, 148/3, 148/4, 148/8 and 148/9 coded models from ITU Fishing Boats Series hull forms, which carried out model tests by Kafalı et al. [29], are examined.The information of the models and test conditions are given in Table 9.The characteristics of seawater and test basin water are given in Table 10.The results of the resistance tests of the models are given in Table 11.The total resistance values of the full-scale boats are calculated by the methods of Froude [27] and Hughes [28] from the model resistance test data.The total resistance values, which are calculated by the Froude method for 148/3, 148/4, 148/8 and 148/9 coded boats, are given in Table 12.The total resistance values, which are calculated by the Hughes method, are given in Table 13.

Boundary conditions
In this study, the dimensions of the calculation volume were determined with reference to the recommended dimensions for the flow problems around the ship, and the recommended dimensions were taken from the manual of the CFD program [33].
The computational domain is dimensioned according to the LBP (the length between the fore and the aft perpendiculars of the ship) with reference to the intersection of aft perpendicular and loaded water line of the ship as shown in Figure 7.The volume of control was selected to be of rectangular prism.The dimension of the computational domain is 100x50x75 m for 148/3 and 148/4 coded boats.143x72x107 m is the dimension of the computational domain for 148/8 and 148/9 coded boats.
As shown in Figure 7, the surfaces of the rectangular prism, which defines boundaries in the computational domain, are named Inlet, Outlet, Top, Bottom, Symmetry and Side.The surfaces, which are represented the ship form, are named Hull.The boundary conditions of the regions called Inlet, Outlet, Top, Bottom, Symmetry, Side and Boat in Figure 7 are given in Table 14.
The velocity inlet is defined as boundary condition for Inlet, because the flow enters the computational domain on the -x direction.At the Top, Bottom and Side borders, the flow velocity is equal to the potential flow, so the boundary condition is equivalent to the velocity inlet boundary condition.The symmetry plane boundary condition is used to indicate that symmetry of the computational domain is also on the other side of the Symmetry boundary.As a result of the events occurring within the computational domain, the boundary condition  In this study, the rectangular prismatic mesh structure is chosen because it gives better results than other mesh structures at the free water surface flow.
An average of 600 thousand, 1.The mesh structure is produced for 112 computational domains.As an example, the mesh structure of the 148/3 coded boat is shown in Figure 8 and Figure 9.

Solution method
After the mesh structure was established, the physical conditions were determined.The solution model is modeled in a 2-phase fluid environment (seawater and air) as in the real environment, and the loaded waterline of fishing boat is free water surface.The physical properties of seawater and air, which is used in calculations, are given in Table 15.The value of gravity acceleration (gravity) is entered as 9.8067 m/s 2 in the direction ofz axis in order to be able to create a gravitational effect on the computational domain as in the world.
The VOF (Volume of Fluid) method is chosen as the surface capture method because of the effects of free surface water.The VOF method is included the effects of free surface water in the analyses.The results of total resistance can be obtained more accurately via this method.It was developed by Hirt and Nichols [35].It gives accurate results in high degree nonlinear free surface problems such as wave breaks.In addition, this method is preferred for calculations of ship wave because it provides flexibility and convenience in mesh production.
The implicit unsteady is chosen as the computation time in order to avoid the timedependent interactions of the phases and increasing the accuracy rates of the results.Realizable k-ε Model is chosen as the turbulent flow model.Segregated Flow is chosen as the solution algorithm because it provides ideal results in incompressible and multiphase flows.
The implicit unsteady is selected as the calculation time.The time step of the solution for each analysis is calculated according to equation_8 [36].In this equation U is the velocity, t  is the time step, and x  is the minimum mesh cell length.As a result of various assays, the value of Courant-Friedrichs-Lewy (CFL) is set at 5. The determined time steps with physical time, number of iteration and computation time, approximately, are given in Table 16.In this study, the maximum number of internal iterations for the each time step is 10.CFD analyses are made at different speeds.Implicit unsteady flow is defined in the CFD program.Therefore, it would be wrong to evaluate for convergence criteria according to the convergence of residues or a fixed physical time.Considering that the CFD analyzes are consistent with the test values, the convergence criteria for the CFD analyses is accepted that the change in values after a certain number of iterations is below 0.01 at low speeds and below 0.1 at high speeds.
The total resistance values vary depending on the physical time due to the fact that timedependent variable flow is defined in the CFD program.Therefore, the total resistance values, at which calculations are terminated, are not used to directly comparison.Depending on the physical time, at high speeds which the resistance value fluctuations are excessive, for more accurate result, ship length is divided by the speed at which the resistance is calculated.In this way, the duration of a flow particle to cross the length of the ship is found.And, the total physical time is divided into pieces according to this duration.The arithmetic mean of the last three total resistance values from the time of convergence of the solution is the final total resistance value for comparisons.Thus, both the accuracy of the convergence is controlled and the physical time-independent resistance values are obtained.

Results and discussions
Firstly, the total resistance values which are obtained by CFD analyses are compared with the total resistance values obtained from the Froude and Hughes methods.Then, the CFD results of boat forms with and without bulb are compared between themselves.Finally, it has been determined that which type of bulb is more beneficial for the fishing boats by taking into account the increase or decrease on the total resistance values of the forms.

Comparison of CFD results with test results
The CFD analyses are performed on Froude numbers which are determined for 148/3, 148/4, 148/8 and 148/9 coded boats.The compatibility of the CFD results and the test results is examined by comparing the ship total resistance values obtained from the CFD analyses with the ship total resistance values obtained from Froude and Hughes methods.The percentage difference between the CFD value and the Froude method value is found by the equation_9.The percentage difference between the CFD value and the Hughes method value is found by the equation_10.As can be seen from Table 17, 18, 19 and 20, according to Froude method, the arithmetic mean value of the difference percentages is around 13% while according to Hughes method the average is about 4%.When each analysis is evaluated in its own group, CFD results are more compatible with the total resistance values, which are obtained from the test data, at low speeds.It is also seen that the results on ships with low CB are more consistent than the results on ships with high CB.When the velocity increases, it is observed that the percentage of difference between CFD results and test data rises while calculating the total resistance of the ship with CFD because of the difficulty in accurately modeling the turbulence phenomenon.
Turbulence density, turbulence velocity scale and turbulence viscosity ratio values are taken constant for each ship form and speed in the ship resistance calculation problems with CFD.In this study, the constants, which are suggested by the instruction manual of CFD program [33], are adopted for the values of turbulence intensity, turbulence velocity scale and turbulence viscosity ratio.(11) The comparison between total resistance of the forms with bulb and total resistance of the forms without bulb are done via Equation (11).Thus, it is determined that, how much increase (+) or decrease (-) are on the total resistance according to the bulb shapes.
The values of friction resistance and pressure resistance, which constitute the total resistance of the ship, are shown in Figure 10, 11, 12 and 13 for 148/3, 148/4, 148/8 and 148/9 coded boats, respectively.
As can be seen from Figure 10, Figure 11, Figure 12 and Figure 13 frictional resistance is higher than pressure resistance at low Fn values while pressure resistance is higher than frictional resistance at high Fn values.While the frictional resistance is higher at boat forms with bulb according to forms without bulb, the pressure resistance is less at forms with bulb than at forms without bulb.In general, the most significant decrease in pressure resistance is seen by elliptical type bulb and this is followed by nabla and delta type bulbs.As can be seen in the Figure 14 for 148/3 coded fishing boat, delta, nabla and elliptical bulbs start to become effective after value of Fn 0.158, Fn 0.261 and Fn 0.246 value, respectively.In other words; the delta, nabla and elliptical bulb are beginning to provide benefit after 4.3, 7.1 and 6.7 knot speeds, respectively.The three bulb types also provide the maximum benefit at value of Fn 0.339, namely, at the speed of 9.2 knots.At value of Fn 0.384, i.e., at a speed of 10.50 knots, the efficiency of the bulbs is somewhat lower than that of Fn 0.339.At 10 knot service speed and higher speeds, the elliptical type bulb provides the most benefit.While delta and nabla bulb have same benefit at the service speed, the delta bulb more useful than the nabla bulb at low speeds.It is the type of elliptical bulb that provides the most benefit at service speed.
At the specified Fn numbers, increase (+) or decrease (-) percentages of the total resistance values of the 148/4-D, 148/4-N and 148/4-E coded boats with respect to 148/4 coded boat are shown in Figure 15.As can be seen in the Figure 15 for 148/4 coded fishing boat, delta, nabla and elliptical bulbs start to become effective after value of Fn 0.189, Fn 0.213 and Fn 0.200, respectively.In other words; the delta, nabla and elliptical bulb are beginning to provide benefit after 5.1, 5.8 and 5.4 knot speeds, respectively.The nabla and elliptical type bulb provide the maximum benefit at value of Fn 0.282, namely, at the speed of 7.6 knots.The delta bulb type also provides the maximum benefit at value of Fn 0.339, namely, at the speed of 9.2 knots.It is also seen that the nabla bulb form is more useful than the elliptical type bulb at the speed range of 6.7-9.2 knots.At the service speed of 10 knots and and higer speeds, the elliptical type of bulb is the most beneficial, while the nabla type bulb is more beneficial than the elliptical type bulb at speed of between 6.7 and 9.2 knots.
At the specified Fn numbers, increase (+) or decrease (-) percentages of the total resistance values of the 148/8-D, 148/8-N and 148/8-E coded boats with respect to 148/8 coded boat are shown in Figure 16.As can be seen in the Figure 16 for 148/8 coded fishing boat, delta, nabla and elliptical bulbs start to become effective after value of Fn 0.204, Fn 0.257 and Fn 0.246, respectively.In other words; the delta, nabla and elliptical bulb are beginning to provide benefit after 6.6, 8.4 and 8.0 knot speeds, respectively.The three bulb types also provide the maximum benefit at value of Fn 0.378, namely, at the speed of 12.3 knots.In addition, the delta bulb form performs better than the elliptical type bulb at low Fn numbers.While at the 10 knot service speed and higer speeds the elliptical type bulb provides more benefits, the delta type bulb provides more benefits at lower speeds.The three types of bulbs are the same benefit at service speed, but at lower speeds it appears that the delta type bulb is more useful than the other types of bulbs.
At the specified Fn numbers, increase (+) or decrease (-) percentages of the total resistance values of the 148/9-D, 148/9-N and 148/9-E coded boats with respect to 148/9 coded boat are shown in Figure 17.
As can be seen in the Figure 17 for 148/9 coded fishing boat, delta, nabla and elliptical bulbs start to become effective after value of Fn 0.177, Fn 0.213 and Fn 0.205, respectively.In other words; the delta, nabla and elliptical bulb are beginning to provide benefit after 5.8, 6.9 and 6.7 knot speeds, respectively.The three bulb types also provide the maximum benefit at value of Fn 0.302, namely, at the speed of 9.8 knots.It is also seen that the nabla bulb form is more useful than the elliptical type bulb at the speed range of 7.6-11.5 knots.While the elliptical type bulb is more useful than the nabla type bulb at the speed range of 0.0-7.6 knots, the nabla type bulb is more useful than the elliptical type bulb at the speed range of 7.6-11.5 knots.After the speed of 11.5 knots, the elliptical type bulb is more useful.When all of the percentages of increase and decrease in total resistance are evaluated together, it turns out that the most suitable bulb form for 148/3, 148/4, 148/8 and 148/9 coded fishing boats is the elliptical bulb type at service speed of 10 knots and at higher speeds.
According to CB, when the efficiency of the bulb is evaluated at the service speed of 10 knots; • At the CB 0.405, value of the benefit of the bulbs is 10% on average.
• At the CB 0.495, value of the benefit of the bulbs is 13% on average.
The higher the CB value, the greater the benefit that the bulbs have at the service speed.Also, as the CB value increases, the speed range at which the bulbs maximum benefit is also increasing.
When the effectiveness of bulbs is evaluated according to L / B ratio; • It has been found that the bulbs have started to benefit at lower speeds in boats with the L/B ratio of 3.5 compared to boats with the L/B ratio of 5.0.• At 10 knots service speed, it has been determined that the bulbs benefit at average rate of 11% at boats with the L / B ratio of 3.5, and at average of 10% at boats with the L / B ratio of 5.0.It has been found that the bulbs have started to benefit at lower speeds in boats with the L/B ratio of 3.5 compared to boats with the L/B ratio of 5.0.At the L/B ratio of 3.5, bulbs have been found to be more beneficial in service speed.
When the efficiencies are evaluated according to types of bulbs; • It has been found that the delta type bulb is beginning to provide benefit after the speed of 5.4 knots.It has an average benefit of 8.9% at the service speed.• It has been found that the nabla type bulb is beginning to provide benefit after the speed of 7.0 knots.It has an average benefit of 11.0% in service speed.
• It has been found that the elliptical type bulb is beginning to provide benefit after the speed of 6.7 knots.It has an average benefit of 11.2% in service speed.At different low speeds, the delta, nabla and elliptical type bulbs cause 4%,14% and 8% increase in total resistance, recpectively.
As an example, the wave deformations in the boat symmetry plane and the wave deformations on the free water surface at Fn 0.339 of the 148/3, 148/3-D, 148/3-N and 148/3-E coded fishing boats are shown in Figure 18 and 19, respectively.

Conclusions
The delta, nabla and elliptic type bulbs are applied to 148/3, 148/4, 148/8 and 148/9 coded boats from ITU Fishing Boats Series in order to find out which type of bulb is more effective on the fishing boats.In order to inspect the accuracy of the CFD analyses, the total resistance values, which are obtained by the Froude and Hughes methods from the test results of the 148/3, 148/4, 148/8 and 148/9 coded boats, are compared with the total resistance values which are obtained by CFD.The CFD analyses of 148/3, 148/4, 148/8 and 148/9 coded boats forms with delta, nabla and elliptic type bulb are performed.The total resistance values of the forms with bulbs and without bulbs are compared.The results are evaluated according to boat forms, CB, L/B ratio and the efficiencies of the bulbs.
When the results are evaluated according to boat forms, it is seen that elliptic type bulb is found to be more useful than other type bulbs at range of 0-12 knots.

Fig. 1
Fig.1The sections of the bulbs

Fig. 3 Fig. 5 Fig. 6 3 .
Fig. 3 Fore cross sections plan and bulb profile of Fig. 4 Fore cross sections plan and bulb profile the 148/3-D code fishing boat of the 148/3-N code fishing boat

A
Systematic Investigation of the Effects of Various Dursun Saral, Muhsin Aydin Bulbous Bows on Resistance of Fishing Boats Ercan Kose 101 In this equation k G is the turbulent kinetic energy production due to the average velocity gradients, b G is the production of turbulence kinetic energy depending on the density changes due to temperature differences, M Y constrictive turbulence shows the effect of the expansion in the turbulence to the whole spread.The terms K S and S  are user-defined source terms.

Fig. 7
Fig.7The dimensions of the computational domain and the names of the surfaces 2 million, 2.8 million, 3.7 million, 4.7 million and 7.4 million cells were created in the computational domains.It has been found that the resistance values, which are obtained in mesh structures with over 2.8 million cells, have not changed or that the change has not had much effect on the solution.For this reason, the CFD calculations are made with an average of 2.8 million cells and 8.6 million surfaces for 148/3, 148/3-D, 148/3-N, 148/3-E, 148/4, 148/4-D, 148/4-N and 148/4-E coded fishing boats.The CFD calculations are made with an average of 3.8 million cells and 11.4 million surfaces for 148/8, 148/8-D, 148/8-N, 148/8-E, 148/9, 148/9-D, 148/9-N and 148/9-E coded fishing boats.

Table 1
[32] characteristics values of the developed fishing boat forms[32]

Table 2
[32] characteristics values of the models used in the tests[32]

Table 4
Maximum widths and lengths of the bulbs

Table 6
Non-dimensional offset values of the nabla type bulbs 0.0 T 0.1 T 0.2 T 0.3 T 0.4 T 0.5 T 0.6 T 0.7 T 0.8 T 0.9 T 1.

Table 11
Model resistance test data

Table 12
Total resistance values obtained by Froude method

Table 13
The total resistance values obtained by the Hughes method selected the pressure outlet, because the values such as speed, pressure are not known at the boundary.The wall is assigned to the Hull as boundary condition, and it is assumed that the flow velocity components on the ship surface are zero (no-slip boundary condition).

Table 15
Physical properties of seawater and air

Table 16
Time steps of the solver, physical time, number of iteration and computation time According to Froude numbers, total resistance values, which are obtained from Froude and Hughes methods, and the difference percentages of CFD values than Froude method values, and the difference percentages of CFD values than Hughes method values are given in Table 17, 18, 19, 20 for 148/3, 148/4, 148/8, 148/9 coded boats, respectively.

Table 17
The comparison between the total resistance values, which are obtained from Froude and Hughes methods, and the total resistance values, which are obtained CFD analyses, for 148/3 coded boat

Table 18
The comparison between the total resistance values, which are obtained from Froude and Hughes methods, and the total resistance values, which are obtained CFD analyses, for 148/4 coded boat

Table 19
The comparison between the total resistance values, which are obtained from Froude and Hughes methods, and the total resistance values, which are obtained CFD analyses, for 148/8 coded boat

Table 20
The comparison between the total resistance values, which are obtained from Froude and Hughes methods, and the total resistance values, which are obtained CFD analyses, for 148/9 coded boat Block coefficient of 148/3 and 148/8 coded boats are averages 0.405 while block coefficient of 148/4 and 148/9 coded boats are averages 0.495.The total resistance values of 148/4 and 148/9 coded boats, i.e., at the boats with high CB value, are calculated with a greater percentage of difference than the total resistance values of 148/3 and 148/8 coded boats because the flow around the underwater forms of 148/4 and 148/9 coded boats is more turbulent.CFD analyses of forms with delta, nabla and elliptical bulb are carried out with the program settings and constants, which are used in CFD analyses for 148/3, 148/4, 148/8 and 148/9 coded boats.Comparison of CFD results for the boats without bulb and with bulb The total resistance values are calculated by performing CFD analyses for 148/3, 148/3-D, 148/3-N, 148/3-E, 148/4, 148/4-D, 148/4-N, 148/4-E, 148/8, 148/8-D, 148/8-N, 148/8-E, 148/9, 148/9-D, 148/9-N and 148/9-E coded fishing boats at the determined Fn values.The difference percentages of the total resistance values of forms with bulb according to forms without bulb are calculated according to equation_11.