Design and optimization of a 50 sailing catamaran

Transcription

1 CHALMERS Design and optimization of a 50 sailing catamaran By Clémentine Perret January 2005 Report No. X-05/160 Department of Shipping and Marine Technology Chalmers University of Technology Chalmers Tvärgata 8 SE Göteborg Sweden 1/59

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3 1. Abstract The French firm Yachts Industries builds a series of aluminum sailing catamaran called Yapluka. They have in project a new boat of 50. The existing Yapluka:s which are all based on the same lines creates a large stern wave when sailing at a certain speed. These waves generate a considerable amount of resistance and the catamarans cannot exceed this speed. The aim of the present thesis is to draw the lines of the new 50 catamaran such that the stern wave is reduced while keeping the same silhouette as the existing boats, which is the signature of the yard. The softwares used are Rhinoceros for the design and Shipflow for the CFD calculations. 2. Acknowledgement Thanks to my supervisor Lars Larsson who would always find a moment to follow his students even if he is overbooked. Thanks for his accurate advices and his precious time. Most of this thesis has been done in France, in the firm Yachts Industries. I am very grateful to Sofia Werner, a PhD student who has been also my supervisor. She was really available and helpful even from the other side of Europe! Also Carl-Erik Janson, as the creator of Shipflow had often the right sentence to solve a problem that would have taken hours to everybody else. Un grand merci à Nicolas Bathfield qui m a beaucoup aidé dans l utilisation de Shipflow et dans la résolution de problèmes de télé-transportation. Thanks a lot to Martin Meyer to have been my supervisor in Yachts Industries. Merci à Jean-Louis Hervé pour ses conseils avisés. And last but not least, a warm thanks to Sun Jae-Ouk, my opponent and my friend. 3/59

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5 3. Nomenclature Elongation of hull: Lwl/Bh Relative length: ratio length over displacement Specific capacity: capacity to displacement ratio Transverse clearance: 2b=Bcb/Lwl, c=bcb/bh AM midship section Atr submerge transom area B breadth of the boat b transverse clearance: 2b=Bcb/Lwl Bh breadth for one hull Bcb distance between the centerlines of the hulls c transverse clearance: c=bcb/bh Cb block coefficient CFD Computational Fluid Dynamics Cp coefficient prismatic Ct coefficient of total resistance Ctr coefficient of resistance due to the transom Cw coefficient of wave resistance Di distance between the inner sides of the hulls Disp displacement Fn Froude number; Fn = V/ (g*lwl ) LCB longitudinal center of buoyancy Loa length over all Lwl length of the water line RANS Reynolds Average Navier-Stokes: method for CFD Rf frictional resistance Rt total resistance Rw wave resistance; Rw = Cw*0.5*g*1025*Fn 2 *Sref N.m -3 Shipflow CFD software Sref wetted surface at the first iteration in Shipflow calculation YI Yachts Industries T draft t tones kts knots 5/59

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7 4. Table of Contents 1. ABSTRACT 3 2. ACKNOWLEDGEMENT 3 3. NOMENCLATURE 5 4. TABLE OF CONTENTS 7 5. TABLES 9 6. TABLE OF FIGURES 9 I. INTRODUCTION 11 A. BACKGROUND 11 B. GOAL AND SCOPE THE SUBJECT LIMITATIONS 12 C. WORK PLAN 13 D. DESIGN SPECIFICATION QUALITATIVE SPECIFICATIONS DESIGN SPEED QUANTITATIVE SPECIFICATIONS INITIAL DESIGN 16 II. HYDRODYNAMICS DESIGN 18 A. COMPUTATIONAL METHOD SHIPFLOW CHOICE OF METHODS GRID DEPENDENCE STUDY LIMITATIONS OF THE COMPUTATIONAL METHOD 23 B. INVESTIGATED HULLS CHOICE OF PARAMETERS TO TEST SERIES OF HULLS 27 C. EFFECT OF DESIGN PARAMETERS ON HYDRODYNAMIC PERFORMANCE ON CLEARANCE* EFFECT OF HULL SHAPE ON DISPLACEMENT COMPARISON OF THE DIFFERENT HULLS TRIM 45 D. CONCLUSION 47 III. PRACTICAL DESIGN 48 A. SHIP MOTION STABILITY SEAKEEPING MANEUVERABILITY 52 B. FINAL HULL 53 IV. CONCLUSIONS AND DISCUSSION 55 V. FURTHER WORK AND RECOMMENDATIONS 56 7/59

8 VI. BIBLIOGRAPHY 59 8/59

9 5. Tables Table 1: Design speeds 15 Table 2: Mean main particulars 16 Table 3: Main particulars deducted from the two other catamarans 17 Table 4: Specification of the initial design 17 Table 5: Recommended Atr/Am 24 Table 6: Hulls types 27 Table 7: Effect of design parameters on different assessment variables Table of figures Figure 1: Previous catamaran 14 Figure 2: Shipflow methods of calculation 18 Figure 3: Grid definition in Shipflow 20 Figure 4: Grid zones 20 Figure 5: Choice of the number of points for the grid of the interior free surface 22 Figure 6: Effect of the refinement of the grid on Cw 22 Figure 7: Flow following the hull 25 Figure 8: Flow under a concave hull and pressure due to the flow 25 Figure 9: Hulls shapes 28 Figure 10: Effect of the clearance on Cw for two Fn 29 Figure 11: Effect of the clearance on Cw for two Fn 29 Figure 12: Effect of the clearance on trim for two Fn 30 Figure 13: Effect of the clearance on trim for two Fn 30 Figure 14: Comparison of the wave cuts at the hull axis for the hull H-16 C3 with different clearances 31 Figure 15: Comparison of the waves created by H-16 C3 at Fn= Figure 16: Comparison of the waves created by H-16 C3 at Fn= Figure 17: Comparison of the draft of the aftbodies on Rw for a range of speeds 35 Figure 18: Comparison of the concavity of the hulls on Rw for a range of speeds 36 Figure 19: Comparison of the concavity of the aftbodies on trim for a range of speeds 36 Figure 20: Comparison of the draft of the aftbodies on trim for a range of speeds 37 Figure 21: Flow velocity on convex/concave hulls 37 Figure 22: Influence of displacement on Cw 38 Figure 23: Influence of displacement on Rw 38 Figure 24: Change of displacement for one hull and effect on Rw 40 Figure 25: Change of displacement for one hull and effect on Cw 40 Figure 26: Rw function of displacement for three hulls 41 Figure 27: Comparison of the hulls at Fn= Figure 28: Comparison of the hulls at Fn= Figure 29: Comparison of displacement and wave resistance 43 Figure 30: Grids comparison on the different hulls 44 Figure 31: Cw when trimming 45 Figure 32: Sref when trimming 45 Figure 33: Rw when trimming 46 Figure 34: Effect of an initial trim on the final trim 46 Figure 35: Stability, GMt 48 Figure 36: Zone of motion sickness; ISO 2631 [9] 49 Figure 37: Wave acceleration 50 9/59

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11 I. Introduction A. Background Yachts Industries is the association of two yards: Garcia Aluminum and Yapluka Yacht. The Garcia yard is specialized in luxury mono-hull and Yapluka in luxury sailing catamarans. Both build their yachts in aluminum. They have moved together to Caen-la-Mer two years ago. Wonderful is the first boat built in Caen by Yachts Industries. This 70 catamaran has been launched on the 14 th of September 2004 in Caen-la-Mer. Until now, all the boats were designed by exteriors designers and naval architects. The aim is to develop the engineering and design department and in few years making the boats from the drawing to the light-work at the yard. Their customers are people passionate by the sea who like sailing but who are not always trained. The yachts are usually driven by a crew and most of the time used as a charter. They are very luxurious, good looking, with all the state-of-the-art electronics and equipments. Most of the time will be spent at port so the efficiency of the hull is not so much important, as soon as the boat is still impressive while sailing and as the boat is able to pass through the oceans. The main design goal is to have a maximum of place and volume inside and to carry a maximum of weight without any problem. All the Yapluka:s have a problem of wave resistance: at a certain speed, a very large stern wave is formed and it is difficult to accelerate more. Moreover, this deteriorates the yacht image since the stern wave is so visible and also, to the crew it feels like the boat is breaking apart. Therefore, it could be useful to know why there is such a problem and how to solve it. That is the subject of the thesis. 11/59

12 B. Goal and Scope 1. The subject The subject of the present thesis is design and optimization of a 50 catamaran hull. The aim is to design a new catamaran in the same spirit as the previous ones but the efforts will be put on the aftbody, to avoid the problem of the stern wave. The resistance of the ship gives an idea of the power needed to drive the ship at a certain speed. Thus the lower the resistance, the faster a ship can go with the same amount of energy or the less fuel she will burn at the same speed. Therefore and as the other terms of the total resistance are less important at the speeds studied, hull efficiency will be evaluated with respect to the wave resistance. Different solutions will be purposed and a series of hulls will be drawn. Then they will be tested with Shipflow and compared. The study is oriented mostly on the hydrodynamics of the different hulls. However, a quick review of the effects on the seakeeping and maneuverability will be presented as the consequences of the changes done to improve the wave resistance. The catamaran is aimed to sail on motors or on sails. The speed reached with motors is generally lower than the one reached under sails. This is due to the difference of power provided to the ship and to the place of the forces acting on the ship. So in order to predict the behavior of the ship in all conditions, she has to be designed for two different speeds corresponding to the speed when going with the motors and the speed on sails. Thus the hydrodynamic tests will be done at the two design speeds. 2. Limitations The forebody influences the behavior of the yacht too, but the thesis will not show this aspect, due to the lack of time. Besides as the stern wave is the main problem, the shape of the aftbody should be more influent on the wave resistance. In the Shipflow tests, the sails and the forces acting on it will be neglected. The Yapluka:s are totally customized and so the sails can change from one to another; moreover no precise data concerning the sails were available. The center of gravity will be considered at the vertical of the center of buoyancy for the same kind of reason: The general arrangement is decided during the construction of the hull so that it is impossible to know the place of the weights at the design stage. That means too that the exact weight is unknown. To get an idea of the effects of these three parameters, some tests will be done with a series of initial trims and with different initial drafts. None of the appendages will be designed; only the hull it-self will be studied. It is true that the interaction with keel could be quite important but it will be left apart. 12/59

13 C. Work plan The thesis will go as follow: First the drawings of the new solutions for the hull, Then the description of the tests done with Shipflow Last, the practical choice of the final hull Fourteen hulls have been designed with the 3D CAD software Rhinoceros. They have all the same forebody. The changes are only on the aftbody shape. Among the hulls, there are some with dry transom and some with submerge ones, and different curvatures of the bottom. The changes from on hull to another will be kept as small as possible except for the two parameters above. To find the right clearance, series of calculation with different clearance at different speeds will be done. To evaluate the hulls, Shipflow will be used to calculate the wave resistance. Then some calculations and considerations will be done on the seakeeping and the maneuverability. Last, a final hull will be designed with Rhino and then evaluated with Shipflow. 13/59

14 D. Design specification First of all, the specifications of the new boat must be put down. Most of the specifications will be only qualitative since there is no exact numbers or since the qualities required are uncountable. 1. Qualitative specifications The new yacht is a catamaran. Nowadays, catamarans are used quite often for cruising yachts, as they give the advantage of a wide mess. They enable more living space for the same length. If light, they are faster compare to monohull. The new yacht will be sailed by a crew employed by the owner. In the general arrangement, there will be approximately four cabins of two persons: one for the owners, two for the guest, and one for the crew. Obviously the cabin for the crew is really tiny compared to the others. The boat will cost a fortune and so has to be the pride of the owner: she must look good and impressive, be quite fast at sea, and have a lot of luxury equipments. For example, for the last yacht built (70 catamaran), the owner ask for a Jacuzzi on the center beam. It could be nice, but there is a price to pay: the yacht is very heavy. The 47 has been design for 18.2t and the 53 for 21t, but in fact they were heavier when launching. The class A of the CE and the Bureau Veritas classification are required. Yapluka has become a brand of catamaran. Even if only four catamarans have been built, they dispose of a range of plans from the 47 to the 90. The new one must be in the same kind of silhouette. The next picture (Figure 1) shows the existing 53 catamaran while sailing. Figure 1: Previous catamaran 14/59

15 2. Design speed Two speeds are important for this kind of boat: the speed when running at motors and the one when sailing. Actually, for the existing boats, these speeds are quite different: around 8kts for the motors and around 14kts for the sails. That gives some Froude numbers between 0.35 and 0.6. The aim is to optimize the hull for the speed of 10kts for motors and 14.5kts for sails, i.e. Fn = 0.4 and 0.6. That means that the boat is in the range of semi-displacement or planning. In that range of speed, the main component of the total resistance is the wave resistance [4], so only a quick overview will be given to the frictional resistance and the resistance due to the wake will be neglected. Table 1: Design speeds in knots in m/s Fn motor sail motor sail motor sail 47' ' ' Quantitative specifications The yard wants a new yacht with LOA equal to 50 ; that is the only compulsory value. For the other values, the owner will always be happy with the biggest ones: the more living space the better. A large beam could lead to problem to berth the yacht, but that is the kind of problem let to the owner. Also the beam interferes with the behavior of the yacht on seas and that will be studied further. The hull beam has to be wide enough to contain a bunk for two persons thus it is better to keep it wider than 2m. A man has to stand in the yacht, so the depth has to be around 2m. For the weight, the only limit is what the hull can support. For hydrodynamic efficiency, the beam will influence the interaction between the two hulls wave pattern and so it will be studied. The hull beam has to be as small as possible because the slender the ship will be the better she will sail. For a good sailing yacht naval architects advice a ratio of length over beam hull bigger than 10 to 1 and at least 8 to 1 [10]. But because of the restrictions from the aim of the boat, these values will be impossible to reach. The displacement has to be kept as small as possible, because the resistance increases with it. The class A will be reached easily. It can already be considered as done (See appendices). 15/59

16 4. Initial design The initial design is based on the existing catamarans, some literature and some practical consideration. The initial design taken is a hull with a similar forebody as the one of the 53 Yapluka. Dubrovsky and Lyakhovitsky [3] give some advices for the main particulars depending on Fn; they are reported in Table 2. The data are based on different experiments and from a mean on a large number of existing multi-hulls. Also in Table 2 is shown data for the initial hull design in this study. That shows clearly that the design weight is already too heavy compared with the relative length. The customers of yachts Industries are always adding new equipment into the yacht, so that the catamaran is likely to be even heavier. However these values will be taken as references. Table 2: Mean main particulars Fn on motors Fn on sails First hull designed Fn 0,4 0,6 relative length 8,6 10,3 6,646 Cb mini 0,512 0,461 Cb maxi 0,55 0,5 0,457 Cp mini 0,6 0,642 Cp maxi 0,631 0,681 0,586 Bh/T 2,5 2,5 2,802 transverse clearance, b Depends on the shape of the hulls Di 0,75*B1 0,75*B1 Relative length is the ratio of Lpp/displacement. The advice on the transverse clearance depends on the shape of the hull. For U-shape, as the hulls used for the Yapluka, there is no possibility of good interaction: The interference between the wave patterns coming from the two hulls will add resistance to the yacht whatever the clearance is. Main particulars have been deducted from the ones of the two existing catamaran. With the help of the scale factors from the Principle of Yacht Design [2], kind of mean values has been calculated that are given in Table 3. 16/59

17 Table 3: Main particulars deducted from the two other catamarans L(feet) 50 L(m) 15,25 Lwl (m) 14,25 B(m) 7,80 L/B 1,95 Bcb (m) 5,30 L/Bcb 2,69 Bh (m) 2,50 L/Bh 6,10 Bwl hull (m) 2,10 Toa (m) 1,40 T (m) 0,76 freeboard (m) 1,65 LCB % -5 LCB (m) 7,84 displacement empty (t) 21,00 Cp 0,626 AM (m2) 1,10 Cb 0,388 Bcb is the length between the axis of the hulls To have a better idea of the weight of the yacht, an excel sheet has been compiled summering all the main weights (See appendices). Some of the numbers have been taken from the existing boats and some others are based on the experience of the employees of the yard. Others are simple assumptions. The displacement obtained is then really closed to 21.2t. Keeping a margin because the boats are always too heavy, the design displacement will be 21.7 t. The displacement of the hull will be kept at 21t i.e. 1,04e10 mm 3 adding the displacement of the keel, each around 0.3 m 3 and then the displacement of the rudder, the total displacement will be around 21.7t. The hull beam has been chosen equal to 2.1 m to try to reduce some coefficient used in naval architecture and known as influent on the wave resistance: For example Bh/T is equal at 2.8 in the initial design but it is normally only 2.5 for a catamaran [3]. It is also known that the narrower are the hulls the better the yacht will be. T is 0.77 m, as it is a value in the same range of the existing Yapluka catamaran, but a bit higher to keep Bh/T small. For the initial hull, Cp and Cb have been kept as close as possible to the recommendation of Dubrovsky and Lyakhovitsky [3] keeping the other values constant. The value obtained has been kept constant for the series of hull, as the value of the midship section. The LCB value is of -6.5% for the initial hull, but that couldn t be constant due to the other change in the hull. The length overall is 50 for all hulls tested, but because some have submerge transom and other not, the water length changes. Table 4: Specification of the initial design Volume Displacement (mm3) 1,04E+10 Center of Buoyancy % -6.5 Waterline Length (mm) Maximum Waterline Beam 2026 AM (m2) 1,18 Cp 0,59 Cb 0,44 T (mm) 776 H (height of the transom above the water) 0 17/59

18 II. Hydrodynamics design To optimize the hull, tests are done with a CFD software, Shipflow, in order to compare different solutions from a hydrodynamic point of view. These tests are done in order to compare the effects of different parameters on the hull efficiency. These parameters are the clearance between the hulls of the catamaran, the transom of the yacht and the convexity of the aftbody. The efficiency of the hulls will be evaluated on the total resistance, the trim and the wave height. A. Computational method 1. Shipflow The CFD (Computational Fluid Dynamics) software Shipflow is developed by Flowtech International AB and Chalmers University of Technology. This software makes use of three different methods to compute the resistance of a ship: A potential method, a boundary layer method and the Reynolds Average Navier-Stokes equations (RANS). Each of these methods is applied to a certain area of the flow domain as shown in Figure 2. Figure 2: Shipflow methods of calculation The computation could be done resolving the RANS equations on the whole domain, but that needs too much memory and time to obtain accurate results and the actual computers can not handle it. That is why Shipflow use a decomposition of the flow domain. The assumption is that the wave resistance depends on an inviscid process far from the hull and that the viscous resistance is unaffected by wavemaking and is occurring close to the hull, in the boundary layer. The wave generation can therefore be modeled by the potential method, as well as the far field flow. Close to the hull and aft of the transom, other methods have to be used. The boundary layer method in zone 2 considers the pressure across the boundary layer as constant. The domain of the boundary layer is very fin so that assumption is close to the reality. This method simplifies the calculations comparing to the RANS method and that enables to compute the viscous resistance in the second zone. The flow in the zone 3 is turbulent and difficult to model. That is why if the resistance coming from this zone is needed, the RANS method has to be used to compute it. This method is not a free surface code. The shape of the free surface will be computed with the panel code, and then the flow under the surface will be computed with RANS, so that all parts of the hull under the free surface are taken into account after the wave pattern calculation and not only under the still water surface 18/59

19 In Shipflow all the data are without dimensions: The length used to take off the dimension is Lwl. So the length of the model boat will be around 1, the displacement of the model yacht will be the one of the real yacht divided by Lwl 3, etc. 2. Choice of methods To compute the wave resistance, the potential method will be used. Then the viscous resistance will be calculated with the boundary layer method in order to make a comparison on total resistance. The viscous resistance in the wake is not so important in the range of speed studied here; even if to calculate it would have enabled to give more accurate results. The potential method can not compute breaking waves. So if one wants to calculate accurately the resistance, another method (Volume of Fluid or Level Set Techniques) has to be used, but these methods are still on studies. Another solution to obtain some results is to use a very coarse grid. A coarse grid enables to compile the hull because it smoothes the wave system; but that reduces the wave amplitude and could affect the wave lengths and directions. This phenomenon is known as numerical dispersion and leads to non-accurate results. The best hulls will create a smaller and probably non-breaking wave and so the computations of these hulls will support a refine grid. The results will be more accurate and also the obtained values will be higher than with a coarse grid (see Figure 6 and [5]). Shipflow can either compute wave resistance with linear or non-linear calculations. The linear method is faster (a computation takes around 5 seconds) and can calculate most of the problems, whereas the non-linear method will use many iterations (until 30 iterations and sometimes 20 min) and maybe find a divergent solution. The linear method is quite accurate for slow ships or very fast and slender ones. This catamaran is fast (Fn > 0.4) and slender (B/L > 7), so this method could be good enough. But in linear method the domain is bounded to the undisturbed free surface and anything above is disregarded [4]. However the hulls to be tested differ only by small changes in the stern, some will have dry transom, others submerge transom, and that is the kind of differences that will be badly computed. Therefore the nonlinear method will be used. When the ships are going forward, the flow will follow the hull and so at a certain speed, the submerge transom will become dry. Unfortunately, Shipflow can not calculate if the transom is still wet. It will be assumed that at the computed speed, the transom is dry. This is a reasonable assumption because Fn > 0.4, and that speed should be sufficient to have a dry transom. 19/59

20 3. Grid dependence study Before doing any test on the hull, to know how to model the grid is very important. That is the aim of the grid dependence study. The grid in Shipflow is done as describe in Figure 3. Figure 3: Grid definition in Shipflow The points longitudinally are called stations, and along the beam, points. On Figure 3, the ship is placed between XBOW and XSTE. XUPS is the furthest point above the ship and XDOW the lowest one. STAU is the number of station between XUPS and the bow, STAM is the number of station along the ship and STAD is the number of station between the transom and XDOW. No heeling angle will be studied; therefore the model is totally symmetrical from the center axis. Then, only half of the domain will be modeled with a mirror. There are different grids: one for the body, 3 or 4 for the water. The water is decomposed in three main parts; one ahead of the ship, one along the ship and one aft of the ship. For the ships with transom stern, a grid can be added below the stern. In the case of this catamaran, the stern shape is so that a transom grid is required to obtain correct results. Figure 4: Grid zones /59

21 (1) Grid on the ship body This grid corresponds to the zones 1 and 2 of the Figure 4. The zone 2 is done by mirroring the zone 1. When the linear methods are used, a good way to find the error due to the model of the ship is to do the calculations without any free surface. The resulted resistance should then be zero. Shipflow calculates the coefficient Cxpi by the integration of the pressure around the ship. Instead of zero, Shipflow gives a positive value which can be considered as the error. For the non-linear computation, the grid on the ship will change at each iteration, following the wave height, so that the previous approach is not anymore valid. However that gives an approximation of the error and the smaller the error due to the ship grid for the linear calculation will be, the smaller will be the error for non-linear calculation. The error is calculated by the percentage that Cxpi represents compare to Cw calculated with the linear method. The computations show that there are almost no differences if the ship grid is composed of 30 stations and 7 points or if it is composed of 30 stations and 15 points. On the other hand, the computing time needed is almost divided by two. So the chosen grid is 30 by 7. The minimal error found is 1.3%. (2) Grid on free surface In Shipflow manual [5], it is recommended to have around 25 stations in the grid of the free surface per wave. In the present case Fn = 0. 4, there will be one wave along the hull and at least one wave is required after the ship to calculate the wave resistance. Ahead of the ship the recommendations ask for half the number of stations that are along the ship. Different grids have been tested by a non-linear method and the error is based on the comparison of the wave resistance of the finest grid tested: Error = (Cw(finest grid)-cw)/cw(finest grid) First a series of computation are done to find the right length of the grid aft the ship and the right beam of the grid, i.e. respectively XDOW and Y4SIDE. These computations are done with a fine grid: free point STAU STAM STAD transom point The best grid seems to be around XDOW=2.5 and Y4SIDE=2; finer grid do not give a significant decrease in the error but coarser one increases the error. Then this study is improved in changing the number of station at the same time as XDOW and Y4SIDE change slightly. free point STAU STAM STAD transom point XDOW Y4SIDE , correspond exactly to 25 panels per waves: Fn = 0.4 so wave length = 1, XDOW = 2.4 so there are 1.4 waves aft; and 25*1.4 = 35! So the recommendations of the Shipflow manual are suitable. For Fn = 0.6, the same study has been done and that gives XDOW = 2.5 and STAD=35. With these values, the computation is quite quick and the error is still less than 1%. 21/59

22 Then the number of points for the interior free surface group (i.e. zone 4 on Figure 4) has been studied. This grid is quite problematic: in the study, the clearance will be changed and for facilities reasons, it could be good to have the same number of points for all the computations. That is why different clearance have to be taken into account. The study advices 9 points for a clearance of 0.35; but when the clearance will become higher, this study may become out of date. So another study has been done with a clearance of 0.5. Figure 5: Choice of the number of points for the grid of the interior free surface error Interior Free surface 7,00E+00 6,00E+00 5,00E+00 4,00E+00 3,00E+00 2,00E+00 1,00E+00 0,00E ,02 0,04 0,06 0,08 0,1 clearance/points clearance 0.35 clearance 0.5 The Figure 5 shows that the error is really dependant on the number of points comparing to the surface to grid. Looking at the figure, if the points taken are so that the clearance divided by the points is 0.4, the error is less than 1%. For b=0.35 that corresponds to almost 9 points but for b=0.5, 12 points are needed. So 12 points will be taken. In reality, when it came to do the computation, almost none of the hulls have been compute with a transom free surface grid of 12 points because these calculations did not converge. The most problematic grid is the one in transom group (zone 5 in Figure 4), because that is the place where breaking waves appear. Thus, for some hulls the grid has to be coarse to get a convergent result. Figure 6 shows the wave resistance coefficient changes due to the grid in the transom group. Figure 6: Effect of the refinement of the grid on Cw Cw 4,50E-03 4,40E-03 4,30E-03 4,20E-03 4,10E-03 4,00E-03 3,90E-03 3,80E-03 3,70E-03 Grid on transom free surface number of points Cw b=0.35 Cw b=0.5 The value of Cw is stabilized when the number of points is 10 for b=0.35 and 12 for b=0.5. Moreover, it underlines the affirmation of the Shipflow manual [5], that Cw is increasing with the refinement of the grid. 22/59

23 4. Limitations of the computational method There are some restrictions to put on the final results of the computations [5]: The amplitude of the stern wave could be overestimated, so the prediction of wave resistance can be inaccurate quantitatively. However, the comparison of wave resistance between alternative designs will be correctly predicted, i.e. the ranking will be accurate. The region of dead water and the breaking waves are due to an unstable process dependent on factors not included in the potential method. If the phenomenon of wave breaking is really important, the solution can even be divergent, but if the solution converges, there will be no indication on whether or not waves will break. That will cause some problems later on. Still, if the solution converges the wave pattern is mostly a good prediction even if the breaking waves are not taken into account. As said before, with transom stern, it is assumed that the ship is on planning and that the transom get dry. That means that low speeds can not be handled. 23/59

24 B. Investigated hulls The existing catamarans are designed with displacement U-shape hulls: very thin at the forebody, the maximum sectional area a bit aft of midship, and a dry transom. The transom is designed so that the owner can have a step to go swimming. It is a sensitive area in the visual design. The LCB is placed at -5.5 and -6.5 % Lwl from midship. 1. Choice of parameters to test The hulls have been drawn from the one of the 53. Then keeping the forebody unchanged, the aftbody has been changed in function of different parameters. As soon as the first computations has been done, the problem of breaking stern waves appears. A breaking wave takes more energy than a normal one, which means that a hull that is followed by breaking waves is not good. The first idea to solve that was to change the place of the LCB to see if the trim at speed which is quite severe on the existing yacht can be reduced. But after a while changing the stern part seems to be a better strategy. (1) Transom 0.4<Fn< 0.6, is the range of semi-displacement or semi-planning hulls [4]. Typical hulls at these speed are with a submerge transom at zero-speed. An advice on the wet area of the transom at zero speed is given [4], depending on the design speed (table 5). A submerge transom get the following advantage: As soon as the ship reaches a critical speed (generally around Fn = 0.4), the transom get dry; the water is following the curvature of the central plane until the stern wave (see Figure 7). The curve described by the water can be considered from a hydrodynamic point of view as the ship itself. That means that the Lwl is becoming fictively larger and that will decrease the wave resistance which will allow the ship to go faster On the other hand, there is a resistance component created by the lack of water pressure on the transom. The corresponding coefficient of resistance is Ctr = -Atr*z tr *2/(S*L*Fn²). (z tr is negative) This resistance coefficient is getting lower and lower with the speed! Table 5: Recommended Atr/Am Fn Cp LCB Atr/AM ; ; ; /59

25 The transom beam will be adjusted so that the recommendation for transom area are followed as much as possible. Figure 7 shows how the flow should look like when the transom get dry: thus the deeper the transom draft the longer the efficient Lwl may be. Then, while changing the transom draft, the transom beam has been adjusted so that the transom area was constant. Figure 7: Flow following the hull Still water (2) Longitudinal curvature of aft hull As explain above, the water will follow the curvature of the ship to create the aft wave. That means also: the more convex the aft, the steeper the stern wave will be. That is why a straight aft or even a concave aft coul d be considered. Moreover, the water passing along the hull is creating a pressure in function of the curvature of the bottom of the hull. This pressure is depending of the water speed along the hull. Along a concave hull, the flow will create a lift that will equilibrate the sinkage due to the reduction of the draft and which can not be avoided. Figure 8: Flow under a concave hull and pressure due to the flow 25/59

26 (3) Clearance Catamaran could take an advantage on monohull by creating a good interaction between the two bow waves. This interaction will obviously depend on the shape of the hulls and on the clearance between them. It seems that the previous studies [3] did not find any optimum for the clearance between two U-shape hulls around Fn = 0.5. Unfortunately, that is the kind of hulls on study. Anyway, tests on clearance will be run to see how these catamarans react. The parameters that will be studied are the draft at the backward perpendicular, the concavity of the hulls, the clearance. Then, a closer look will be put on the effect of changing of initial trim and of displacement. Finally, more than 200 calculations have been run and some others for the grid dependence study. 26/59

27 2. Series of hulls A set of 14 hulls have been designed with Rhino. Three hulls have a non-submerge transom, 6 are with a submerge transom at -16cm and 5 with the submerge transom at -30cm. In addition, the hull of the 53 has been compiled. You can find the general characteristics of these hulls in the table 6. For more complete information, see appendices. The hulls are called as followed: H for hull The number following the H is representing the draft at the aft perpendicular in cm: o so H0, is a hull with aft touching the water o H16 is a hull with a dry transom 16cm above o H-16 is a hull with submerge transom 16cm under water o H-30 have a submerge transom 30cm under water 53 is the hull of the existing 53' catamaran. The hulls with a star *, are the drafts from other hulls with displacement more closed the design one. H-16 C3 LCB is based on H-16 C3, but the LCB is more aft. Table 6: Hulls types name transom convex/concave others panel in transom H0 non-submerge, 0cm convex 3 H16* non-submerge, 16cm convex draft H16 non-submerge, 16cm convex 3 H-16* submerge, -16cm convex draft H-16 submerge, -16cm convex 3 H-30* submerge, -30cm convex draft H-30 submerge, -30cm convex 4 H-16 C1 submerge, -16cm concave 5 H-16 C2 submerge, -16cm concave flat aft 7 H-16 C3 submerge, -16cm concave aft going backwards 7 H-16 C3 LCB submerge, -16cm concave LCB going more aft 7 H-30 C1 submerge, -30cm concave flat aft H-30 C3 submerge, -30cm concave aft going backwards 7 53 non-submerge, 16cm convex Existing catamaran 3 27/59

28 What is called first convexity is the fact that this hull has a horizontal part at the aft perpendicular; second convexity is with an aft horizontal and third convexity corresponds to an aft with a negative angle. Figure 9: Hulls shapes 3 rd convexity H-16 C3 1 st convexity H-16C1 H-16 C1 H16 H-16 C3 H-16 H-30 C3 28/59

29 C. Effect of design parameters on hydrodynamic performance The complete results can be found in the appendices. 1. On clearance* On the opposite of the monohull, the multihull can play on the interaction between the waves create by the different hull. That is why the clearance is a very important parameter in the wave resistance of the catamarans. With the following tests, an optimum clearance could be found or at least the influence of the clearance on the wave resistance will be drawn. Wave resistance is a function of clearance as shown in Figures 10 and 11. For each hull, the same phenomenon in the results appears. The bigger the clearance, the smaller the Rw: it decreases until 2*Rw(monohull). The effect of clearance is not really depending on the Froude number. The two curves are decreasing exponentially with the clearance. For Fn = 0.4, the changes in Cw are less important when the clearance is higher than 0.35 and for Fn = 0.6, the clearance is less influent if it is higher than Obviously, a catamaran with a clearance of 1 cannot be sailed because of the seakeeping and ma neuverability consideration. Thus the solution is to take the smallest clearance which gives a not too high Cw. So the clearance should stay higher than Figure 10: Effect of the clearance on Cw for two Fn Cw, hull H-16 C3 6,00E-03 5,00E-03 Cw 4,00E-03 3,00E-03 2,00E-03 Fn 0.4 mono, Fn 0.4 Fn 0.6 1,00E-03 0,00E ,2 0,4 0,6 0,8 1 1,2 clearance Figure 11: Effect of the clearance on Cw for two Fn Cw, Hull H-16 7,00E-03 6,00E-03 5,00E-03 Fn 0.4 Cw 4,00E-03 3,00E-03 2,00E-03 1,00E-03 mono fn 0.4 Fn 0.6 mono fn 0.6 * In that whole chapter, clearance means b, as explain in the nomenclature. 0,00E ,2 0,4 0,6 0,8 1 1,2 clearance 29/59

30 Looking at the Figure 12 and 13 leads to the same conclusion: The clearance should be mainta ined as high as possible. The influence of the clearance reduces when it is higher than 0.25 for Fn = 0.6 and 0.35 for Fn = 0.4. Figure 12: Effect of the clearance on trim for two Fn trim, Hull H-16b4 1,60E+00 1,40E+00 1,20E+00 trim (degree) 1,00E+00 8,00E-01 6,00E-01 4,00E-01 2,00E-01 Fn 0.4 mono, Fn 0.4 Fn 0.6 0,00E ,2 0,4 0,6 0,8 1 1,2 clearance Figure 13: Effect of the clearance on trim for two Fn Trim, Hull H-16 3,00E+00 2,50E+00 (degree) trim 2,00E+00 1,50E+00 1,00E+00 5,00E-01 Fn 0.4 mono, Fn 0.4 Fn 06 mono Fn 0.6 0,00E ,2 0,4 0,6 0,8 1 1,2 clearance 30/59

31 To show the influence of the clearance on the wave pattern, the wave cut tool of Shipflow could have been used. The results are shown in Figure 14. Figure 14: Comparison of the wave cuts at the hull axis for the hull H-16 C3 with different clearances The clearance compared are respectively 0,25 ; 0,3 ; 0,35 ; 0,4. The higher the clearance the more smooth the stern wave. The interaction between the wave patterns of the two hulls is going further aft with the clearance. The Bernoulli waves are going aft with an angle of 19, so that the previous remark is confirmed by theory. There is no optimum clearance for the wave pattern. The maximum wave height on that wave cut is decreasing with the clearance. But the maximum wave height might be in another place. 31/59

32 It seems that the best catamarans with this kind of hulls are really the wider ones. For ultimate performance, multihull designer Peter Wormwood once remarked, "When you've made the boat wide enough that you're not sure whether it will first capsize to the side or pitchpole, then you have the dimensions about right," but for maneuvering in tight quarters and finding docking space, narrower beams still make more sense and will result in a boat unlikely to pitchpole. That corresponds to a clearance equal to 2b= Effect of hull shape Different aft shapes have been tested. Looking separately to the tests done on the hulls, there is no noticeable change in the curvature of the graphs: The effect of the clearance and the displacement are comparable for all the hulls. But the efficiency of the different hull shapes will be compared in that section. A good method to compare them is to look at the wave patterns and some wave cuts. Normally, the smaller waves are created, the lower the wave resistance will be. 32/59

33 Figure 15: Comparison of the waves created by H-16 C3 at Fn= 0.4 H-16 C3 is the hull to the port side and the curves in red. H-16 C3 is compared with respectively H16 (Graph 1), H-16 (Graph 2) and H-30 C3 (Graph 3). Graph 1 Graph 2 Graph 3 Graphs 1 and 3 should show the effect of the aftbody draft. Graph 2 shows the effect of the concavity. The four results are really close. However, the grids are different from one case to another: the transom grid in free surface is refined only for the hull H-16 C3. The grids used are always the closest to the one given by the grid dependency study as soon as the computations converge. Thus for all the case but H-16 C3, the real waves should be higher and steeper. The stern wave behind H16 is wider than behind the other hulls. Also the hull with the wave pattern the closest to H-16 C3 is H-30 C3. Both are with submerge transom and concave shape. The difference lies on the first stern wave which is steeper for H-30 C3. 33/59

34 Figure 16: Comparison of the waves created by H-16 C3 at Fn= 0.6 Comparison Fn = 0.4/0.6 (Graph 1); comparison at Fn=0.6 of H-16 C3 with respectively H16 (graph 2), H-16 (graph 3), H-30 C3 (graph 4). H-16 C3 is the hull starboard and in green. Sailing faster pushes the stern waves aft the ship and reduces the wave height (Graph 1). Graph 1 Graph 2 Graph 3 Graph 4 The wave pattern of H16 (Graph 2) shows clearly the big stern wave that Yachts Industries wants to avoid. H-16 C3 is creating the smaller stern wave, although further aft, the three solutions with submerge transom leads to the same result. Graphs 2 and 4 should show the effect of the aftbody draft. Graph 3 shows the effect of the concavity. 34/59

35 But, in real life, sailing yachts can not go at a constant speed. So looking at the evolution of Rw with the speed can have a great interest. This study has been done for a hull with dry transom, one convex hull with submerge transom at -16 cm (H-16), two concave hulls with a submerge transom of -16 cm (H-16 C3 and H-16 C2) and one concave with a submerge transom of -30 cm (H-30 C3). Figure 17: Comparison of the draft of the aftbodies on Rw for a range of speeds Comparison of Rw for a range of speed 3,50E+00 3,00E+00 2,50E+00 Rw 2,00E+00 1,50E+00 1,00E+00 5,00E-01 0,00E+00 0,35 0,4 0,45 0,5 0,55 0,6 0,65 0,7 0,75 Fn H16 H-16 C3 H-30 C3 That is quite obvious that the ships with transom are better at high speed (Figure 17). The curvature of the curves is the same for all ships with a submerge transom (Figure 17 and 18). That does not depend on the curvature of the aft body. In conclusion, only the fact to length the virtual Lwl is acting on the curve shape. The effect of the submerge transom is to move the resistance hump towards lower Fn; or in other words, to increase the effective Lwl compared to dry transom. This effect seems to be independent on hull curvature and transom shape. However, the amount of Rw will change with the hull curvature or transom shape, as shows the Figure 17 and 18. The hull with 30 cm submerge transom has a larger Rw than the hull with 16 cm submerge transom. Figure 18 shows that for the speed higher than Fn=0.45, the more concave the hull, the better efficiency. 35/59

36 Figure 18: Comparison of the concavity of the hulls on Rw for a range of speeds Comparison of Rw for a range of speed 3,00E+00 2,50E+00 2,00E+00 Rw 1,50E+00 1,00E+00 5,00E-01 0,00E+00 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 Fn H-16 C2 H-16 C3 H-16 Trim angle are to avoid: Besides the trim angle give more draft to the aft and so more drag, for a luxurious yacht it is quite embarrassing to have a ship which is trimming when sailing. Thus, the smaller the trim angle, the happier the sailors. The next Figures 19 and 20 are showing the trim plot against Fn with different hull shapes. Figure 19: Comparison of the concavity of the aftbodies on trim for a range of speeds Comparison on trim in function of Fn 2,50 2,00 1,50 trim 1,00 0,50 0,00 0,30 0,40 0,50 0,60 0,70 0,80 Fn H-16 C2 H-16 C3 H-16 Here the effect of the suction due to the curvature of the aft is underline: at higher speed, the ship with a convex aft is trimming more and more while the ships with concave aft are going back to their lines. The most concave hull is the one with the smallest trim angle. 36/59

37 Figure 20: Comparison of the draft of the aftbodies on trim for a range of speeds Comparison on trim in function of Fn 4,00E+00 3,50E+00 3,00E+00 2,50E+00 trim 2,00E+00 1,50E+00 1,00E+00 5,00E-01 0,00E+00 0,30 0,40 0,50 0,60 0,70 0,80 Fn H16 H-16 C3 H-30 C3 The figure 20 is showing that hulls with submerge transom trim the less. At the same time, that shows that even if the aft hull shape is concave, if it is too deep, the good effect from this shape is lost: The hull H-30 C3 has a larger trim than the hulls with only 16cm transom stern. Figure 21: Flow velocity on convex/concave hulls Here are the hulls H-16 C3, a concave hull (up) and H-16, a convex hull (down). The pressure and the flow velocity are link by Bernoulli equation: The higher the velocity the smaller the pressure. The green parts are for low velocity and red ones are for high velocity. Therefore there is a low pressure on the aft of the convex hull while there is a high pressure on the aft of the concave one. Moreover the pressure on H-16 C3 seems more symmetrical fore/aft. Thus that verify the assumption as the concave hull will create a lift at the aftbody and that can explain why concave hulls are trimming less. 37/59

38 3. On displacement The displacement is an influent parameter on the wave resistance. However, the hulls tested do not have the same displacement and comparing Cw as a function of displacement could lead to find a correction to adjust Cw as a function of displacement and obtain a series of resistance for a constant displacement. The set of hulls has been drawn quite quickly because of the lack of time and even if the hulls were as closed as possible to each others, keeping the displacement constant was really difficult when changing the other parameters. If some draft hulls are taking into account, the range of displacements given by Shipflow is from 5.86e-3 to 7.27e-3. Shipflow gives the displacement as a volume non-dimensionalized by Lpp 3. Looking at Figures 22 and 23, the influence of the displacement on the wave resistance could be imagined. Figure 22: Influence of displacement on Cw Cw function of disp CW 8,00E-03 7,50E-03 7,00E-03 6,50E-03 6,00E-03 5,50E-03 5,00E-03 4,50E-03 4,00E-03 5,50E-03 5,70E-03 5,90E-03 6,10E-03 6,30E-03 6,50E-03 6,70E-03 6,90E-03 7,10E-03 7,30E-03 7,50E-03 disp equation of the linear correlation y = x Figure 23: Influence of displacement on Rw Rw function of displacement 2,00E+00 y = 496,24x - 1,8688 1,50E+00 Rw 1,00E+00 5,00E-01 0,00E+00 5,50E-03 5,70E-03 5,90E-03 6,10E-03 6,30E-03 6,50E-03 6,70E-03 6,90E-03 7,10E-03 7,30E-03 7,50E-03 Displacem ent 38/59

39 It could be interesting if a correction could be found to adjust the hulls to the same displacement. The gradient from the previous scheme can not be used because the hulls do not have the same efficiency. But, if the gradient of Rw(disp) is the same for each hull, it could be used as a correction. From another point of view, these figures show the importance to have a well designed hull. The displacement increases strongly the resistance of the ship, and at the same time, it is the parameter the more likely to increase. A well designed hull could carry more weight for the same resistance as a less efficient hull. Some tests have been done to see the influence of the displacement on one hull. The results are shown in Figure 24 and 25. In order to change the displacement, the initial draft has been modified. The study could also have been done with different hulls similar in all the main particulars but the displacement. This method could give the effect on displacement independently of other parameters. The problem is that, drawing hulls with all parameters constant but displacement is very difficult and time consuming. And finally, for a boat already built changing displacement causes a change of draft; so this model is closer to reality. Problems are that changing the initial draft leads also to a change of the aft draft and of Atr, two values that are of great importance as shown before. Then there are no distinction between the resistance changes due to the displacement, the aft draft or the transom area. Anyway, the results give almost a perfect line: The heavier the ship, the larger the resistance. 39/59