A GiD-based implementation of a panel method for...

II Simposio Internacional de diseño y producción de yates de motor y vela. II International Symposium on yacht design and production.

A GiD-based implementation of a panel method for sailing yachts flow computation.

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A GiD-based implementation of a panel method for sailing yachts flow computation. D. Fernández-Gutiérrez1 M. le Garrec2, J. García-Espinosa3 M. Menec4 A. Souto-Iglesias5. Abstract. This article describes the implementation of a panel method, developed by the Model Basin Research Group (CEHINAV) of the Naval Architecture Department (ETSIN) of the Technical University of Madrid (UPM). The code determines the flow around a vessel considering the lift in the numerical calculations, which is of special importance when the vessel has lifting wing sections as is the case of sailing yachts, where the lift and added resistance due to the keel and the rudder in the yacht behaviour is very important. The code is implemented as a problem-type of the commercial pre and post-processor GiD. The code presented here is itself a new module of the potential flow solver TDYNLIN. The present work is part of a long project, which is to create an easy to use, complete potential code for a wide range of boats (standard, multihull, transom-stern, shallow water), and has been done to validate one of its new options: lift calculations. Finally, experimental results from an America’s Cup boat series are used to analyze the accuracy of the results obtained with this panel method. Results are promising but much work has yet to be done.

1 Introduction. Numerical simulations are of special importance in yacht design, where evaluation of the hydrodynamic characteristics of hulls and appendages, aerodynamic performance of sails, structural optimization of the hull, mast and rigging, sailing performance simulations and statistical racing analysis are essential. Using these codes it is possible to test several geometries, which allows a fast and complete optimisation process prior to fine tuning by basin tests. Computational Fluid Dynamics (CFD) tools have been widely used in the aircraft industry for years. Their importance in yacht design was showed up when Australia II, with its high tech winged/inverted keel took the cup from Dennis Conner on Liberty in 1983 breaking the longest winning streak in the history of sports (132 years). Since then, CFD has played an increasingly important role in the design and analysis of racing sailboats, and in particular America’s Cup yachts. As is clearly indicated by Rosen [9], CFD tools have been widely used in the last America’s Cup Editions by the different teams that have taken part in them. The ETSIN model basin research group CEHINAV has been working on developing a potential flow CFD code, TDYNLIN, which is used as a complement to other commercial codes used in this Towing Tank. This code has been integrated as a problem-type of the commercial code GiD, developed and commercialised by CIMNE (International Centre for Numerical Methods in Engineering), an institute from the Technical University of Catalonia (UPC), in Barcelona, Spain.

1. ETSIN Towing Tank, Naval Architecture Department, TechnicalUniversity of Madrid. Avda Arco de la Victoria s/n. 28040, Madrid,Spain. [email protected].


3. COMPASS Ingeniería y Sistemas S.A. C/Tusset 8, 7º 2º. 08006,Barcelona, Spain. [email protected].

4. ETSIN Towing Tank, Naval Architecture Department, TechnicalUniversity of Madrid. Avda Arco de la Victoria s/n. 28040, Madrid,Spain. [email protected] .


II Simposio Internacional de diseño y producción de yates de motor y vela.

II International Symposium on yacht design and production.


70

Figure 1. GiD logo. Among the potential CFD codes most used in the numerical hydrodynamic optimization of sailing yachts it can be found the SPLASH or RAPID. SPLASH has been developed by South Bay Simulations, Inc. and uses a distribution of constant source and/or doublet singularities over each panel, something in which differs from other free-surface panel codes (Rosen [9]). RAPID has been developed at MARIN and is one of the best-known codes worldwide in this field. It is a non-linear method that uses a distribution of Rankine source panels on the hull and free surface as it is done in TDYNLIN. To solve the non-linear free surface problem, an iterative procedure is used. The details of the implementation of this code are clearly explained in Raven PhD thesis [8]. 2 GiD. GiD (figure 1) is a graphical user interface for geometrical modelling, mesh generation, data input and visualization of results of all types of numerical simulations, including solid & structural mechanics, fluid dynamics, electromagnetism, geomechanics, heat transfer, etc. Finite element, finite volume, boundary element, finite difference or point based numerical procedures can be used to solve the physical problem considered.

Figure 2. Aspect of a hull mesh generated with GiD.

GiD is used initially for the grid generation (figure 2) and TDYNLIN is selected as the problem type to be solved. Boundary conditions are introduced and numerical resolution calculations are done. Finally, the postprocess analysis is done again with GiD, where the results obtained are visualized and studied, as shown in figure 3.

Figure 3. Visualization of flow results obtained with GiD. 3 TDYNLIN. TDYNLIN is a potential CFD code initially developed by the Model Basin Research Group (CEHINAV) of the Naval Architecture Department (ETSIN) of the Technical University of Madrid (UPM) in 1992 (Souto [10]). Since its creation, it has been continuously improved by adding new options and possibilities. TDYINLIN is now commercialised by COMPASS (www.compassis.com). The first code only considered calculation with symmetric hulls. Significant improvements were done since then providing new possibilities with the aim of covering the greatest range of calculation types possible. Following this path, calculation of non symmetric bodies was made available, as well as calculation with multihull geometries (figure 4), shallow water problems and transom-stern flows.

Figure 4. Wave pattern of a multihull vessel calculated with Tdynlin.



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The following step has been the implementation in the code of calculation of lift and induced drag of thin appendages. This is of special importance in yacht design, where the keel and rudder introduce forces which are very important to estimate in order to define the sailing behaviour of the vessel at an specific angle of heel, leeway and rudder (from the centreline). The results given by the program are the velocity field, the pressure coefficients and the wave elevations which in turn allow the possibility of obtaining wave cuts at certain lateral distances. With this new implementation, lift and drag coefficients are also obtained over the lift appendages as well as the numerical results corresponding to their total lift and induced drag. 4 Analysis of forces on a boat. In a displacement keel boat sailing at steady speed in equilibrium windwards, the whole set of forces and moments that act upon the vessel must be balanced. This set of forces and moments is shown in figures 5 and 6.

Figure 5. Front view of the forces and moments on a boat. This equilibrium of forces can be studied by looking at two directions, the longitudinal and the transversal one. On the one hand, the heeling force due to the sails must be equal to the side force developed by the underbody (hull, keel, keel bulb and rudder) and on the other hand the thrust should be equal to the drag of the underbody.

Figure 6. Top view of the forces and moments on a boat. Moments should be also in equilibrium, and here is of special importance the keel bulb, whose main aim is to put the ballast as low as possible in the boat in order to maximize the righting moment and to counteract the heeling moment due to the sails. Estimation of lift forces is very important, as they will determine the leeway angle necessary to obtain enough side force. The aim of the lifting foils then is to reduce the angle as an excessive leeway is not adequate because it reduces the sails driving force and increases the drag. According to Greely [5], drag can be split in five different components:

• Frictional drag. • Viscous pressure drag. • Wave drag (or wave resistance). • Induced drag. • Drag due to leeway.

The first two ones are associated with pure viscous effects, so are not considered in potential flow calculations. Wave drag is due to the generation of free surface waves so it can be estimated with a potential CFD, as well as the induced drag which is the component due to the generation of lift force. Finally, in the drag due to the leeway is considered all the additional frictional, viscous pressure and wave drag caused by the leeway operating angle. 5 Lift&Drag implementation. 5.1 TDYNLIN GENERAL ASPECTS. TDYNLIN is based on a panel method with free surface computation that was initially presented by Dawson [3]. It calculates the




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potential flow around the vessel by a Rankine source method. A generalization of the Dawson method presented by Bruzzone [2] is used. This modification allows a more arbitrary panelization of the free surface, thus eliminating the need to follow the stream lines obtained in the double model calculation. For this type of codes, free surface is not considered at the beginning of the calculations. To maintain the free surface at elevation level of 0, a mirrored image of the hull (called double model) is taken into account. This means that free surface becomes a symmetric plane and the flow around this double model can be calculated. After that, the wave system generated is calculated, where the previous results regarding the velocity field are used as initial conditions on the free surface. Using up-wind operators, radiation condition is introduced by numerical means. Optimization is based upon minimizing wave heights in the wave system. The code is often used in the daily ETSIN basin activities and is also an academic tool used in a Sailing Yacht Design Course given by the Technical University of Madrid. 5.2 LIFT & DRAG APPENDAGES

CALCULATION. For the lift & drag implementation there are several methodologies that have been published, as for example those from Hess[6] and Katz [7], and it has been the latter the one chosen to evaluate the lift and drag forces due to the presence of lifting appendages. Firstly, the program calculates the flow around the vessel without considering the lifting appendages, and then takes the results as initial conditions in the lift and drag calculation. Finally, the program gives as results lift and drag coefficients on them as well as the velocity field, from which is possible to obtain the pressure coefficients. In this model, a thin wing is considered to represent the foil, and all along the surface of the wing a distribution of constant ring vortices is placed as singularities. On each ring, the intensity of the constant vortices distribution is the same on each of

the 4 segments. The velocity on a point M, due to the presence of a segment 1-2 is expressed by the following expression:

−⋅⋅

∧

∧⋅

πΓ

=2

2

1

102

21

212,1 r

rrrr

rrrr

4)M(q

rrr

rr

rrr

Where the meaning of vectors 0r

r, 1rr

and 2rr

are explained in figure 7.

Figure 7. Graphical explanation of the meaning of 0r

r , 1rr

and 2rr

. Turning to the discretization of the foil, if M panels are put along the chord length and N along the span length, the total number of panels is M x N for the whole foil. To locate each panel, there are two possibilities: either with the index i along the chord and j along the span, or with a unique index k which is expressed by:

( ) Nijk ⋅−+= 1 The indexes i, j and k respectively cover the following intervals: {1,M}, {1,N} and {1,MxN}, as is explained in figure 8.

Figure 8. Graphical example of panel indexation with k counter.



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The calculation of the influence coefficients is a classic calculation where the coefficient ak,s represents the normal component of the velocity on the centre of the panel k due to ring vortex of the panel s.

( ) ksksk nwvua r⋅= ,, So the linear system becomes:

⋅−

⋅−

⋅−

=

Γ

Γ

Γ

⋅

NxMDk

kDk

D

NxM

k

NxMNxMNxM

k

NxMs

nV

nV

nV

aa

a

aaa

rr

rr

rr111

,1,

1,

,1,11,1

...................................................

......

Where Γk represents the intensity of the ring vortex of the panel k and DV

vis the velocity

calculated previously by the Dawson method explained in section 5.1 on the centre of the panel k. It is possible to calculate the induced drag generated by the vortices by calculating another matrix defined by:

( ) ksksk nwvub r⋅= ,*

, Where the vector ( ) skwvu ,

* now represents the velocity on the centre of the panel k, due to the two segments of the ring vortices of the panel s that are situated in the stream flow direction. To ensure that the results have a physical sense it is necessary to fix the circulation by imposing the Kutta condition. This is done adding a wake panel to each one of the panels located on the trailing edge of the foil. This wake panel will have the same intensity of the ring vortices as the trailing edge panel it is connected to. This wake panel will extend itself at the infinite behind the foil to comply with the Helmholtz theorem. Several formulations were tried regarding the shape, number of panels, location and even iterative relocation of the wake. This simplest formulation, with just one wake panel for each ring, placed at the mid plane direction of the foil, was not found worse than any other. Nevertheless, more research has to be done. For the resolution of the linear system, a Jacobi solving method is used. In this case,

resolution is not a problem as the matrix has a large dominant diagonal. Once the constant ring vortices distribution is known, it is possible to calculate a few things concerning the flow around the foil. First of all, it is possible to obtain the pressure difference coefficient (CP) on each panel using the following expression:

∞⋅∆

Γ=∆

VSC

ji

jijiP

,

,,

The lift coefficient (CL) is obtained as follows:

∑∑= = ∞⋅⋅⋅

=M

i

N

j

jiL

VS

LC

1 12

,

21 ρ

Where Li,j is defined as:

jijijiji yL ,,1,, )( ∆⋅Γ−Γ⋅= −ρ Finally, the induced drag coefficient (CD) can be also calculated with the following expression:

∑∑= = ∞⋅⋅⋅

=M

i

N

j

jiD

VS

DC

1 12

,

21 ρ

Where Di,j is defined as:.

( ) jijijijiindji ywD ,,1,,, ∆⋅Γ−Γ⋅⋅= −ρ

Here all the local values are located by the indexes i and j, but it is also possible with the index k as was done previously. As a matter of fact, the vector indwr is defined as follows:

Γ

Γ

Γ

⋅

=

NxM

k

NxMNxMNxM

k

NxMs

NxMind

kind

ind

bb

b

bbb

w

w

w

...

...

................................................

......

...

...1

,1,

1,

,1,11,11

5.3 REST OF UNDERBODY SIDE

FORCE CALCULATION. For the hull calculations, the velocity field distribution is used and using the Bernouilli




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equation the pressure distribution along the hull is obtained.

( ) iii zgVVP ⋅⋅−−⋅= ∞ ρρ 22

21

Where Vi and zi are the velocity and elevation of the point where the pressure is being evaluated. Since the normal to each panel is obtained during the calculation, it is possible to obtain the force vector on each panel by multiplying the pressure times the area of the panel and the normal vector:

ii nAPF rr⋅⋅= .

Integrating then the forces along the hull, the total longitudinal (wave drag), transversal (side force) and vertical (displacement) forces are obtained. This code does not consider circulation on the hull panels, so the lift forces due to the hull and keel bulb are not calculated although its implementation in the code is now being studied to improve the accuracy of the total lateral force estimation. Therefore, only pressure forces are calculated over the hull and keel bulb, which can be added to the lift and induced drag from the lifting appendages in order to obtain the total forces estimated for the case that is being calculated. 6 Comparison with Experimental Data. 6.1 DESCRIPTION OF THE CASES

STUDIED. As in every new CFD code, it is necessary to evaluate the accuracy of the results obtained. Therefore, numerical results are compared with experimental ones obtained from a previous study where different America’s Cup boat geometries were tested. The geometry analyzed has been selected from the series used to obtain the final geometry of the boat used by the Spanish Team of the America’s Cup 30th Edition (2000). This geometry is represented in figure 17, and will be referred to as CB3B. Its main dimensions and characteristics are described in table 1:

Table 1. CB3B main dimensions and characteristics.

CB3B Length 18.761 mBeam 3.730 mDraught 4.031 m.Displacement 26352 kgWetted Surface Area 71.83 m2

In this vessel, the lift appendages considered have been two, the keel and the rudder. The keel bulb, although it has a certain lift influence, is not considered in the calculations as it does not fulfil the condition of having a thin wing section. The first action was adapting the geometries to the computation method, and both lift appendages were substituted by their middle plan. Once the vessel geometry was adapted, different sailing conditions corresponding to the experimental tests have been calculated so as to compare results and evaluate TDYNLIN with lift calculation. The conditions studied, from which there are available experimental results, are indicated in table 2. Table 2. Sailing conditions in which calculations have been made. Heel Angle Leeway Angle Rudder Angle

0º 0º 3º 0º 0º 5º

15º 2º 0º 15º 4º 0º 15º 6º 0º 25º 2º 0º 25º 4º 0º 25º 6º 0º

The codification that will be used in the rest of the paper to refer to a sailing condition will be XH;YL;ZR, where X, Y and Z are the heel, leeway and rudder angles respectively. In the experiments, total drag and lateral forces are the only available results. This means that appendages effects cannot be isolated from the hull effect. 6.2 MESH GENERATION It is very important to use an adequate mesh so as to avoid the introduction of numerical errors. The hull mesh should present a smoothed aspect, concentrating the



75

elements in those places that are more significant, such as the keel bulb or the bow areas. GiD allows different mesh types, distinguishing between structured and non-structured, and is the structured one that TDYNLIN requires. The panels in which the hull and free surface are discretized are quadrilateral, so the NURBS surface patches that define the hull and free surface are four sided. In a structured mesh, the parameters that GiD needs to mesh the surfaces are the number of cells to assign to each side of them. Once this information is given to the program, GiD generates automatically the mesh. The final hull mesh of CB3B can be observed in figure 22. The final number of panels of the whole vessel is 2640, and has been kept in all the calculations with the different sailing conditions. However, the free surface mesh is not fixed as the significant parameter that determines the number of panels to be used is the wave length which varies with the boat speed and is given by the following expression:

LFn ⋅⋅= 22πλ Where L is the length of the vessel and Fn is the Froude Number. According to Souto [10], for each wave length between 15 and 20 panels are necessary. As the evaluation of the free surface deformation is not crucial in this particular case, 15 panels per length to be meshed have been chosen, so the optimum number of panels in a chosen distance (D) is given by the formula:

LFDNn22

15π

∗=

This formula shows that as the speed is lower the wave length is shorter and hence more panels are necessary. Taking into account that there is a computational limitation in the total number of panels used due to memory requirements, the lowest speed considered is determined by the maximum number of panels considered. The free surface mesh covers half a ship length ahead, 1.5 ship lengths aft, and one ship length asides. The maximum number of panels considered has been 10.830 with a

vessel speed of 7.972 knots. The aspect of the final mesh of the hull and free surface in this situation can be observed in figure 21. To give an idea of the demands of this type of calculations, the computing time taken with a computer of 3 GB of RAM memory and a processor of 3.19 GHz has been approximately 10 hours. With each geometry and sailing condition mentioned before, different velocities have been calculated. In the next subsections, the results obtained will be analysed, beginning with the lift forces. 6.3 LIFT AND SIDE FORCE ANALYSIS. Regarding the lift and side force values, different issues have been observed. First of all, it is very interesting to distinguish between the lift from the lifting appendages (the keel and the rudder as indicated in section 6.1) and the side force from the rest of the underbody because the calculation procedures are different as was explained in the sections 5.2 and 5.3. According to Greely [5], the hull contributes significantly to the generation of lateral force, being on 12-meter yachts, for example, approximately half of the total value.

CB3B Appendages Total Lift

0

200

400

600

800

1000

1200

1400

1600

1800

2000

7.5 8.0 8.5 9.0 9.5 10.0 10.5Speed (Knots)

15H;2L;0R 15H;4L;0R 15H;6L;0R 25H;2L;0R25H;4L;0R 25H;6L;0R 0H;0L;3R 0H;0L;5R

Figure 9. CB3B appendages total lift (kg). If both sources of lateral force are analysed independently, as can be seen in figures 9 and 10, it is clearly noticed that the hull side force component does not follow a trend as uniform as the keel and rudder lift component. Their values are also clearly lower than those from the appendages. In the hull and keel bulb side force calculation, the cases corresponding to 0º of heel and 0º




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of leeway have not been calculated because there is only lift due to the rudder that is the only one that presents an angle of inclination with respect to the flow direction.

CB3B Hull & Bulbous Side Force

0

50

100

150

200

250

7.5 8.0 8.5 9.0 9.5 10.0 10.5Speed (Knots)

15H;2L;0R 15H;4L;0R 15H;6L;0R25H;2L;0R 25H;4L;0R 25H;6L;0R

Figure 10. CB10 hull and keel bulb side force (kg). This implies that the main source of error is placed in the hull side force calculation. Viscous effects, which are much higher on the hull than on the foils, as well as the lack of considering the lifting forces due to the hull are reasons that explain the previous result. As there are experimental results for the whole set of situations, it has been possible to evaluate the error made in the total lateral force prediction, which is showed in figure 11.

CB3B Total Lateral Force Errors

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

7.5 8.0 8.5 9.0 9.5 10.0 10.5Speed (knots)

0H;0L;3R 0H;0L;5R 15H;2L;0R 15H;4L;0R15;H;6L;0R 25H;2L;0R 25H;4L;0R 25H;6L;0R

Figure 11. Lift and side force error (%) for CB3B. First of all, it is important to notice that the error obtained in the lift results in the three geometries varies mainly between 20% and

35%. It is also noticed that the error is lower as the angle of heel is higher. Turning to the leeway angle, the general tendency is obtain higher errors as its value increases. The rudder angle follows an opposite pattern, as the error decreases when the angle is higher. These tendencies are explained taking into account the effect of the hull interaction in the flow in which is placed each appendage, which is not really well achieved in a potential CFD as viscous effects are not considered. This provokes that the higher the leeway angle, the higher influence in the flow. But in the cases where the influence of the rudder angle is analysed, the hull is kept in the same position, so this source of error is not introduced changing the previous tendency. The errors obtained can then be explained in part due to the viscous influence as well as the evaluation of the interaction between the hull and the appendages. The code used is potential, so these influences are not considered and therefore the viscous lift component is not calculated. This introduces an error in the numerical results that affects to the overall accuracy of the results. Nevertheless, we think that the main source of error is the one due to ignoring the hull contribution to lift and drag, for which we lack yet experimental results of isolated hull under the same leeway and heel angle conditions. It must not be forgotten also that this type of solution for the numerical prediction of lift forces is based on a simplification made on the foil, which is substituted by its middle plan and obviously this introduce a certain error as the specific characteristics of the foil are not considered. 6.4 LIFT COEFFICIENT ANALYSIS. If the attention is focused on the lift coefficients, and more specifically in those corresponding to the lifting foils, their values can be theoretically estimated as:

απ ⋅= 2LC . Where α is the angle of attack of the foil. This coefficient comes from the extrapolation of the lift coefficient of a 2D foil, so it corresponds to an infinite span



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rectangular 3D foil in a uniform flow, which is not the case of the rudder neither the keel. The first one differs clearly from a rectangular plane as can be seen in figure 18, having an area inferior to this one but the second one is more similar to a rectangular plane as shown in figure 19. This provokes the lift coefficients to be smaller than the predicted by the previous formula. The previous expression is independent of the speed, and the numerical lift coefficients of the keel and rudder, which are shown in figures 12 and 13 can be observed that are also quite constant with each attack angle, which agrees with the previous statement. However, this is not absolutely fulfilled as the velocity field in which the foil is working varies with the speed. As a matter of fact, it is very clear the differences from the CL values when there is a leeway angle in which the influence of the hull is higher from those when there is only a rudder angle that are indicated in figure 13.

CB3B Keel CL

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0.450

7.5 8.0 8.5 9.0 9.5 10.0 10.5Speed (knots)

15H;2L;0R 15H;4L;0R 15;H;6L;0R25H;2L;0R 25H;4L;0R 25H;6L;0R

Figure 12. CB3B Keel CL values.

CB3B Rudder CL

0.000

0.050

0.100

0.150

0.200

0.250

7.5 8.0 8.5 9.0 9.5 10.0 10.5Speed (knots)

0H;0L;3R 0H;0L;5R 15H;2L;0R 15H;4L;0R15;H;6L;0R 25H;2L;0R 25H;4L;0R 25H;6L;0R

Figure 13. CB3B Rudder CL values.

It is possible to compare the average values of the lift coefficient for each angle of attack with the values obtained with the theoretical values of an infinite span 3D rectangular foil, whose values are indicated in table 3. In this table it is also shown the CL standard deviation so as to indicate the dispersion of the CL values with different velocities which is quite lower, as can be concluded from figures 12 and 13. In the situations where the rudder angle is not zero, there is no leeway. This means that the attack angle of the rudder fits in with the rudder angle while the keel attack angle is zero. In the same way, when there is a leeway angle but no rudder one, the attack angle, now of the rudder and the keel, fits in with the leeway angle. The heel angle affects only to the direction of the lift force. This is the reason why it is distinguished in table 3 between this two different situations and why Keel CL values are empty when there is a rudder angle. Table 3. CB3B keel and rudder average CL coefficient calculated, theoretically predicted value and CL standard deviation.

CB3B Average

CL calculated CL standard

deviation Angle

of Attack Keel Rudder

2·π·α Keel Rudder

With Leeway Angle 2º 0.137 0.041 0.219 0.008 0.012 6º 0.401 0.175 0.658 0.013 0.011 4º 0.270 0.110 0.439 0.010 0.011

With Rudder Angle 5º -- 0.197 0.548 -- 0.001 3º -- 0.118 0.329 -- 0.001

Another thing which is observed is that the lift coefficients of the keel, in the situations with a leeway angle, are always higher than the ones of the rudder. This can be explained in part by the difference in the velocity field in which each appendage is working as can be seen in figure 27. But the main reason for this difference is the presence of the keel bulb on the bottom of the keel, which represents a bottom closure for this appendage, while the rudder does not have any. 6.5 DRAG ANALYSIS Turning to the drag results, the code calculates the induced drag, which is one of the five drag components in which the total drag was split as explained in section 4 of this paper. This component can be




78

estimated with the lifting surfaces theory, so potential CFD codes are very suitable tools to calculate it. The induced drag values are indicated in figure 14. No estimated value for foil sections drag coefficient (CD) has been used so far, but they can be obtained from the literature (Abbot [1]) or from XFOIL program as indicated by Drela [4] (http://raphael.mit.edu/xfoil/).

CB3B Induced Drag

0

20

40

60

80

100

120

140

160

7.5 8.0 8.5 9.0 9.5 10.0 10.5Speed (Knots)


Figure 14. CB3B Induced Drag values (kg). Integrating the pressures over the hull it is also possible to obtain the wave drag, but the results are not satisfactory presenting very lower values as can be seen in figure 15. This confirms the fact that the evaluation of the forces on the hull, both longitudinal (wave drag) and transversal (hull lateral force) should be improved in order to get more accurate results. Actually it is more sensible to compare wave cuts in order to estimate which hull is more efficient as was stressed by Souto [10] and indicated in section 5.1.

CB3B Wave Drag

0

20

40

60

80

100

120

140

160

7.5 8.0 8.5 9.0 9.5 10.0 10.5Speed (Knots)


Figure 15. CB3B Wave Drag values (kg). Dividing the induced drag by the total drag measured in the experiments, it is possible to evaluate its influence in the total drag.

Results obtained, which can be seen in figure 16, are quite high at low velocities. But as the speed increases, the influence of this induced drag decreases. This is logical, as the wave drag turns to be the most important component and the rest of them are less important.

CB3B % Induced Drag

0%

5%

10%

15%

20%

25%

30%

7.5 8.0 8.5 9.0 9.5 10.0 10.5Speed (Knots)


Figure 16. CB3B percentage of induced drag of the total experimental drag (%). In these types of codes, the usual way of studying the wave drag is, as mentioned before, by taking wave cuts at certain lateral distances and analysing the wave elevations. This information can be then used to validate the code by comparing with experimental wave cuts measured in a Towing Tank. Unfortunately, there is a lack of experimental wave cuts regarding this boat so it is impossible to analyse them. However, it is possible to compare between the wave cuts obtained with TDYNLIN at different sailing conditions and speeds so as to observe the changes introduced in the wave system generated by the boat. In figure 23 there are two wave cuts obtained at a lateral distance of 1.05·B, where B is the beam of the boat, at two different speeds. In that figure it is clearly seen that as the speed increases, the wave height is higher as well. In this type of graphs the longitudinal position and the wave height are made dimensionless with the length of the vessel. 6.6 VISUALIZATION OF RESULTS. As was explained in section 3, the results that are obtained with TDYNLIN are the wave elevations, the pressure coefficients, the velocity field and with this new implementation, the lift and induced drag coefficients on the lifting appendages. From



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all this distribution of values it is possible to obtain the total lift and induced drag due to the appendages and the side force and wave resistance due to the rest of the underbody. However, it is very interesting to analyse not only the total values but the distribution of them on the free surface and underbody and here is where GiD is very useful as a complete post-processor which enables to visualize al the results. It is possible to choose between different visualization modes, such as the contour fill, contour lines, isocurves, etc. The program also demands in the preprocess to assign a condition (hull, flotation, appendage) to each surface that allows in the postprocess to select between the different conditions so as to concentrate in those where the magnitudes calculated are representative. Finally, with the zoom, rotate and pan tools it can be easily observe those places which are of special importance or whose results are especially significant. Figures 24 to 33 in the annex show different results obtained for the different sailing conditions and speeds calculated which has been analysed before. From figures 24 and 25 it is clearly seen the influence of the leeway on the wave pattern. Figures 24 and 26 show also the influence of speed on the wave height because although both figures are similar, the scales used are different, confirming that the wave height increases with speed as shown in figure. Finally, figures 27, 28, 29, 30, 31, 32 and 33 represent the pressure, lift and drag coefficient distributions. 7 Conclusions. To sum up, there are several final conclusions obtained from this study which must be indicated. Firstly, it must be said that this implementation represents the first potential CFD code that runs on GiD and allows the calculation with lifting appendages. Focusing on the results, the implementation of the lift and drag calculations of thin foils approximating them by their middle plan gives quite satisfactory results, especially in what respects to the induced drag results but foil drag coefficients have to be included.

However, calculation of hull lift component should be improved, following a new approach in a different way as proposed by other authors to get more accurate results. Finally, it would be very interesting to go deeper in this study experimentally, carrying out tests from which could be possible to measure the different lift and drag components, especially distinguishing those coming from the hull and those which come from the lifting surfaces and rest of appendages. These data have not been found on the literature, but would give a clear idea of the influence of each element in the whole forces equilibrium in which the vessel must be. A new experimental device (see figure 34) has been set up in the ETSIN model basin facilities that will allow these tests in the near future. Bibliography. [1] Abbot, I.H. & Von Doenhoff, A.E. (1959).

Theory of wing sections: including a summary of airfoil data. Dover Publications.

[2] Bruzzone, D. (1994). Numerical

evaluation of steady free surface waves. Proceedings of CFD Workshop, Tokyo, Vol. 1, pp. 126-134.

[3] Dawson, C. W. (1977). A practical

computer method for solving ship wave problems. Proceedings of 2nd Int. Conf. on numerical ship hydrodynamics, Berkley.

[4] Drela, M. (1989). XFOIL: An Analysis

and Design System for Low Reynolds Number Airfoils. Proceedings of the Conference on Low Reynolds Number Airfoil Aerodynamics, University of Notre Dame.

[5] Greely, D. S. & Cross-Whither, J. H.

(1989). Design and hydrodynamic performance of sailboat keels. Marine Technology, Vol. 26, nº 4, pp. 260-281.

[6] Hess, J. L. (1975). Review of integral-

equation techniques for solving potential-flow problems with emphasis on the surface-source method. Computer methods in applied mechanics and engineering, nº5, 1975. pp. 145-196.




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[7] Katz, J. & Plotkin, A. (2001). Low speed aerodynamics (2nd Edition). Cambridge University Press.

[8] Raven, H. C. (1996). A solution method

for the non linear ship wave resistance problem. (PhD Thesis). Delft University of Technology.

[9] Rosen, B. S., Laiosa, J.P. & Davis, W.

(2000). H. CFD design studies for America’s Cup 2000. Proceedings of 18th Applied Aerodynamics Conference, Denver. AIAA-2000-4339.

[10] Souto Iglesias, A. (2000). Nuevas

herramientas de diseño de formas de buques basadas en códigos de flujo potencial. (PhD Thesis). Technical University of Madrid.



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APPENDIX.

. Figure 1. CB3B body plan, lateral view and waterlines.

Figure 2. Rudder Figure 3. Keel Figure 4. Keel bulb .

Figure 5. Hull Mesh with a boat speed of 7.972 knots and a total number of panels of 10.830.




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Figure 6. CB3B Hull mesh (2.640 panels)

Analysis of Speed Influence

-0.01

5-0.

010

-0.00

50.0

000.0

050.0

100.0

15

-1 -0.5 0 0.5 1 1.5 2 2.5 3X position

Wav

e El

evat

ion

25H;6L;0R (7.972kn) 25H;6L;0R (9.988kn)

Figure 7. Comparison between the wave cuts obtained at 1.05·B (where B is the beam of the boat) at two different speeds and in the same sailing conditions.



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Figure 8. Wave pattern obtained with 0º of heel, 0º of leeway and 5º of rudder at a speed of 7.972 knots.

Figure 9. Wave pattern obtained with 25º of heel, 6º of leeway and 0º of rudder at a speed of 7.972

knots.




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Figure 10. Wave pattern obtained with 15º of heel, 6º of leeway and 0º of rudder at a speed of 9.520

knots.

Figure 11. Velocity field distribution on the free surface and over the underbody obtained with 25º of

heel, 6º of leeway and 0º of rudder at a speed of 7.972 knots.



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Figure 12. Pressure coefficient distribution on the hull and keel bulb obtained with 25º of heel, 6º of leeway and 0º of rudder at a speed of 7.972

knots.

Figure 13. Detail of the pressure coefficient distribution on the keel bulb obtained with 25º of heel, 6º of leeway

and 0º of rudder at a speed of 7.972 knots.

Figure 14. Detail of the lift coefficient

distribution on the rudder obtained with 25º of heel, 6º of leeway and 0º of rudder at a speed of

7.972 knots.

Figure 15. Detail of the lift coefficient distribution on the keel obtained with 25º of heel, 6º of leeway and 0º of

rudder at a speed of 7.972 knots.




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Figure 16. Detail of the drag coefficient

distribution on the rudder obtained with 25º of heel, 6º of leeway and 0º of rudder at a speed of

7.972 knots.

Figure 17. Detail of the drag coefficient distribution on the keel obtained with 25º of heel, 6º of leeway and 0º of

rudder at a speed of 7.972 knots.

Figure 18. New experimental device set up in the ETSIN basin facilities to measure lateral forces and moments of sailing yachts.

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